SMART DISTRIBUTION SYSTEM AUTOMATION: NETWORK RECONFIGURATION AND ENERGY MANAGEMENT

Transcription

1 SMART DISTRIBUTION SYSTEM AUTOMATION: NETWORK RECONFIGURATION AND ENERGY MANAGEMENT by FEI DING Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy Dissertation Advisor: Dr. Kenneth A. Loparo Department of Electrical Engineering and Computer Science CASE WESTERN RESERVE UNIVERSITY January, 2015

2 CASE WESTERN RESERVE UNIVERSITY SCHOOL OF GRADUATE STUDIES We hereby approve the thesis/dissertation of Fei Ding candidate for the degree of Doctor of Philosophy Committee Chair Kenneth A. Loparo Committee Member Marija Prica Committee Member Mingguo Hong Committee Member Vira Chankong Date of Defense Nov.11, 2014 * We also certify that written approval has been obtained for any proprietary material contained therein.

3 Table of Contents SMART DISTRIBUTION SYSTEM AUTOMATION: NETWORK RECONFIGURATION AND ENERGY MANAGEMENT... 1 Table of Contents... iii List of Figures... vi List of Tables... ix Chapter 1 Introduction... 1 Chapter 2 A Review on Existing Approaches for Reconfiguring Distribution Systems... 8 Chapter 3 Three Methods Proposed for Reconfiguring Distribution Systems Problem Formulation Heuristic Method Hybrid Method Hybrid Method Sensitivity Analysis Based on OPF Solutions Genetic Algorithm Case Studies Case I : Three-Feeder Test System Case II : 33-Bus Test System Comparison of Three Methods Chapter 4 Hierarchical Decentralized Network Reconfiguration Study Decentralized Structure Operational Rules Multi-Agent Technique Dynamic Network Reconfiguration Case Study Case I : 118-Bus Test System Case II : 69-Bus Test System Case III : 216-Bus Test System Result Discussion and Remark Dynamic Network Reconfiguration Chapter 5 Modeling and Primary Control for Distributed Generation Systems iii

4 5.1 Wind Power Generation Unit Mathematical Model Control System Micro-Gas-Turbine Generation Unit Mathematical Model Control System Photovoltaic Generation Unit Mathematical Model Control System Fuel Cell Generation Unit Mathematical Model Control System Super-Capacitor Energy Storage System Mathematical Model Control System Operation of Grid-Connected / Islanded Distributed Generation Systems Control System for Grid-Tie Inverter Control System for Islanded Inverter Small-Signal Stability Analysis Case Study Grid-Connected Operation Islanded Operation Chapter 6 Distribution Network Reconfiguration and Energy Management of Distributed Generation Systems Three-Phase Power Flow and Power Loss Minimization Three-Phase Unbalanced System Modeling Power Flow Equations Power Loss Minimization Optimal Planning of DG Units Optimal Locations of DG Units Optimal Capacity of DG Units Network Reconfiguration and Optimal Operation of DG Units iv

5 6.4 Case Study Gaussian-Mixture Load Modeling Case I: 25-Bus Unbalanced Distribution System Case II: Revised IEEE 123-Bus Unbalanced Distribution System Chapter 7 Conclusions and Future Work Reference v

6 List of Figures Figure 3.1 Structure of the switches Figure 3.2 Flowchart of the heuristic algorithm based on branch-exchange and single-loop optimization Figure 3.3 Flowchart of the proposed hybrid method Figure 3.4 Flowchart of the proposed genetic algorithm Figure 3.5 The genes included in each chromosome Figure 3.6 Three-feeder test system Figure 3.7 Results of sensitivity of power loss with respect to S9, S10, S16 and S17 respectively Figure 3.8 Results of power loss changes for shifting S9, S10, S16 and S17 from their OPF solutions to 0/1 respectively Figure 3.9 Iterative results of the revised GA for the 3-feeder test system Figure 3.10 Single-line diagram of 33-bus test system Figure 3.11 Voltage magnitudes of all nodes before and after the reconfiguration Figure 3.12 Sensitivity of the power loss with respect to different switch states Figure 3.13 Iterative results of the revised GA for the 33-bus test system Figure bus radial distribution system Figure 4.2 The graph for zone Figure 4.3 Components of G 1 -U Figure 4.4 Decomposition with fictitious loads and fictitious generators representing power flows through the interconnecting lines Figure 4.5 Operation procedures for the 118-bus distribution system Figure 4.6 The framework of two intelligent agents Figure 4.7 Coordination between two agents Figure 4.8 Framework of dynamic network reconfiguration Figure 4.9 Dynamic network reconfiguration with time-ahead planning Figure 4.10 The demonstration system built using MATLAB Figure 4.11 Node voltages of the 118-bus system before and after reconfiguration Figure 4.12 Power losses in the 118-bus system before and after reconfiguration Figure 4.13 Single-line diagram of the 69-bus test system Figure 4.14 Decomposed systems and hierarchical agents for the 69-bus system Figure 4.15 Single-line diagram of the 216-bus test system Figure 4.16 Decomposed systems for the 216-bus system Figure 4.17 Voltage results of the 216-bus system before and after the reconfiguration Figure 4.18 Ten load shapes Figure 4.19 Hourly solar radiation and temperature profiles Figure 4.20 Two faults happened in the 118-bus system Figure 5.1 Three types of wind energy conversion system Figure 5.2 Two-mass model for the shaft system of WTG vi

7 Figure 5.3 Electrical circuit for the induction machine in d-q frame Figure 5.4 Conventional pitch angle control system Figure 5.5 Control for rotor-side converter Figure 5.6 Single-shaft MT model Figure 5.7 Electrical circuit of PMSG in d-q frame Figure 5.8 Configuration of a micro-turbine generation system Figure 5.9 The physics of a PV cell Figure 5.10 Single-diode equivalent circuit for a PV cell Figure 5.11 Characteristics curves for the PV array model Figure 5.12 Flow-chart for variable-step P&O method Figure 5.13 Block diagram of the MPPT controller Figure 5.14 Equivalent electric model for the fuel cell Figure 5.15 Medium-term dynamic fuel cell model Figure 5.16 Configuration and control for fuel cell generation system Figure 5.17 Typical charge/discharge characteristic curves of the super-capacitor and battery Figure 5.18 Classic equivalent circuit for ultra-capacitor Figure 5.19 Control for the bi-directional DC/DC converter Figure 5.20 A sketch of multiple distributed generation systems Figure 5.21 The configuration of a distributed generation unit for grid-connected and islanded operations Figure 5.22 Three-level controller block diagram in d-axis for the grid-tie inverter Figure 5.23 The complete controller for the grid-tie inverter Figure 5.24 Three-level controller block diagram in d-axis for the autonomous inverter. 108 Figure 5.25 Block diagram of the state-space model for the grid-connected DG system Figure 5.26 Configuration of the distribution system with multiple distributed energy resources Figure 5.27 Two faults occurred at the system Figure 5.28 Simulation results for the system at steady-state Figure 5.29 Changes in wind speed and solar irradiance Figure 5.30 Simulation results for wind power unit and DC generation unit Figure 5.31 Simulation results of the microgrid Figure 5.32 Designed scheme of the synchronization Figure 5.33 Simulation results of the synchronization process Figure 6.1 Components between two buses in an unbalanced distribution system Figure 6.2 The framework of the strategy Figure 6.3 The flowchart of the proposed methodology Figure 6.4 The genes included in each chromosome Figure 6.5 GMM approximations of load pdfs Figure 6.6 Single-line diagram of the 25-bus unbalanced distribution system Figure 6.7 Power loss in the system with DG units installed at different locations vii

8 Figure 6.8 Decomposed systems and hierarchical reconfiguration agents for the 25-bus system Figure 6.9 Four groups of load shapes Figure 6.10 Optimal outputs of two DG units in the 25-bus system for 24 hours Figure 6.11 System power losses for different scenarios during 24 hours Figure 6.12 The configuration of the revised IEEE 123-bus test system Figure 6.13 The graph of 123-bus system Figure 6.14 Decomposed systems and hierarchical reconfiguration agents for the 123-bus system Figure 6.15 The optimal outputs of three DG units in the revised 123-bus system for 24 hours Figure 6.16 System power losses for different scenarios during 24 hours Figure 6.17 Maximum voltage unbalance and line loading level in the revised 123-bus system during 24 hours Figure 7.1 The conceived framework viii

9 List of Tables Table 3.1 Simulation Results of Centralized Method For Three-Feeder Test System Table 3.2 Solutions of OPF for Three-Feeder Test System Table 3.3 Power Losses for Different 0-State Switch in Loop Table 3.4 Power Losses for Different 0-State Switch in Loop Table 3.5 Simulation Results Of Centralized Method For 33-Bus System Table 3.6 Solutions of OPF for 33-Bus Test System Table 3.7 Results of 0-State Switches for 33-Bus Test System Table 3.8 Comparison of Three Methods Table 4.1 Fifteen Loops and Associated Buses in the 118-bus System Table 4.2 Decentralized Structure for the 118-bus System Table 4.3 Simulation Results of 118-Bus System Table 4.4 Simulation Results of 69-Bus System Table 4.5 Simulation Results of 216-Bus System Table 4.6 Capacity of Each PV Unit During 24 Hour Period Table 4.7 Simulation Results of The Dynamic Reconfiguration Table 4.8 Simulation Results When Fault Occurs Table 5.1 Comparisons of Two Types of Microturbines Table 5.2 Parameters of A PV Array Table 5.3 Comparisons of Different Types of MPPT Algorithm Table 6.1 Optimal Capacity of DG Units for Three Scenarios Table 6.2 Simulation Results of The Optimal Switching Plan Table 6.3 Optimal Capacity of DG Units for Three Scenarios Table 6.4 Simulation Results of The Optimal Switching Plan ix

10 ACKNOWLEDGEMENTS First of all, I am profoundly grateful to my research advisor, Professor Kenneth A. Loparo. He has persuasively provided the guidance for my research topic, critical thinking and problem solving. His invaluable help is indispensable for my accomplished research work during the past four years. Besides, professor Loparo is a successfully researcher and has made great contributions to different research areas, and he is really my role model of academic career. Then, I would like to thank Professors Marija Prica, Vira Chankong and Mingguo Hong for serving as my advisory committee and reviewing my dissertation. Their comments are of great importance for me to improve my dissertation. Besides, I would like to extend my thanks to all colleagues in the lab. I believe that the support and encouragement received from each other are important for us, and I will treasure the time that we shared together. Also, many thanks are due to my friends who had given numerous help while I studied at CWRU. Finally and importantly, I would like to express my gratitude to my beloved parents for their unconditionally spiritual supports and understandings. They always provide their love to me without any reservation. I hope that they will be proud of their loving daughter who has already grown up and become a real Ph.D.. Besides, I would like to use this dissertation in memory of my passed grandfather whom I didn t have a chance to accompany at the last moment due to the long distance from the United States to China. In sum, the past more than four years have recorded an important and treasured experience in my life journey. I will keep on doing my best in the following career life. x

11 Smart Distribution System Automation: Network Reconfiguration and Energy Management Abstract by FEI DING Smart distribution system automation is the key to realizing a highly reconfigurable, reliable, flexible and active distribution system. Automated network reconfiguration including restoration is the most studied area in distribution automation, and it contributes to power loss minimization, voltage improvement and also can enable the distribution network to respond to contingencies and changes happened in the grid. Distributed energy resources at the customer premises, energy storage systems and plugin electric vehicles are indispensable parts of future smart distribution systems. Their participations have brought more dynamics and uncertainties into the grid, and hence new technologies at both planning and operation levels must be developed to manage the energy dispatched from distributed energy resources and energy storage units, the charging and discharging behaviors of electric vehicles so that the entire power distribution system could operate stably and efficiently. Meantime, due to the intermittent, imperfectly predicted renewable energy and more complicated, uncertain load patterns, two challenges have arisen on network reconfiguration study, including more frequent reconfiguration actions and more complicated optimization problems for determining the xi

12 optimal network topology. Thus, new approaches for reconfiguring distribution networks must be developed to overcome these challenges. In order to address the above challenges which distribution systems are facing to and develop new technologies for realizing smart distribution automation, a comprehensive study on network reconfiguration and energy management of distributed generation systems was studied. The contributions of this dissertation include: (1) proposed a novel problem formulation for network reconfiguration problem based on switch states ; (2) developed three new methods to solve the optimization problem including heuristic algorithm, hybrid algorithm and revised genetic algorithm; (3) proposed a hierarchical, decentralized network reconfiguration approach that has been proved to have significant computational advantage compared with other existing methods; (4) proposed the concept of dynamic network reconfiguration in which the impact of time-varying load demands, renewable energy generation and other contingencies on the optimal distribution network topology were fully addressed and analyzed. (5) Since DG has become one of the most important parts in distribution systems. The mechanism of distributed generation itself and the impact of distributed generation on distribution system analysis must be studied. This dissertation has studied the modeling and reactive control of multiple DG systems, and also studied the unbalanced distribution feeder reconfiguration and proposed energy management strategy for controlling all gridconnected DGs in order to optimize distribution system operation. xii

13 Chapter 1 Introduction The traditional electric power system is designed for unidirectional power flow with very limited observability, intelligence and autonomous response. Electricity users are simply waiting for the electric power transferred from power plants through transmission lines and distribution feeders, without any active interaction or demand response. The limited one-way interaction makes it difficult for the grid to respond to the ever changing and rising energy demands of the 21st century. Besides, concerns about global climate change have increased the penetration of renewable energy resources worldwide. As a result, in order to build a more secure, reliable, efficient and greener power grid, the concept of smart grid has been proposed. Generally speaking, there is no specific or unique definition of smart grid. Smart grid technology includes the application of automation and intelligent controls to power systems, and it includes several significant characteristics [1], including: 1) increased use of digital control and information technology with real-time availability; 2) dynamic optimization relating to grid operability; 3) inclusion of demand side response; 4) demand side management strategies; 5) integration of distributed resources including renewables and energy storage; 6) deployment of smart metering; 7) distribution system automation; 8) smart appliances and customer devices at the point of end use. With the emphasis on the distribution level, distribution systems are facing the challenge of evolving from passive networks with unidirectional flow supplied by the transmission grid to active distribution networks highly involved with distributed generation (DG) requiring bidirectional power flows. Such a transition requires a paradigm shift in both system design and operations. It is noted that both planning and 1

14 operation depends on two basic parameters: technical constraints (equipment capacity, voltage drop, radial network structure, reliability indices, etc.) and economical targets such as minimizing investment and operating costs, minimizing energy imported from transmission, energy loss and reliability costs, etc. Distributed generation at customer premises, self-healing protection mechanisms, and distribution automation are three crucial aspects for future (smart) distribution systems. According to the statistics released by US Department of Energy in 2011 [2], transmission and distribution losses associated with the delivery of electricity for residential, commercial, and industrial consumption accounts for 7% of gross generation, or 246 B kilowatt hours. Besides, with the transition to electric vehicles, their fueling will become part of the electricity generation infrastructure, thereby adding significantly to the transmission and distribution costs of centralized generation. By contrast with conventional coal fuel power stations that are centralized and often require electricity to be transmitted over long distances, distributed energy resources (DER) are decentralized, modular and more flexible technologies, and are usually located close to the loads they serve. Due to these significant advantages, DG has emerged as an alternative to supply electric power and DG technologies have been widely developed [3]. DG systems typically use renewable energy resources, including, but not limited to, wind, solar, hydro, biomass and geothermal power. Based on REN21 s 2014 report [4], worldwide renewable energy contributed 19% to energy consumption and 22% to electricity generation in 2012 and 2013, respectively. In the United States, President Obama has called to secure 25% of electricity from clean, renewable resources by According to [5], renewable energy in the United States accounted for 12.9% of the 2

15 domestically produced electricity in 2013, and 11.2% of total energy generation. Among all renewable energy, wind and solar are two important types. Until now U.S. wind power installed capacity has exceeded 60,000 MW and the installed photovoltaic capacity has passed 10.5 GW. Fuel cells also show great potential to work as distributed energy resources because of they are highly efficienct and environmentally friendly. The efficiency of low temperature proton exchange membrane fuel cells is around 35~45% [6], and the efficiency of high temperature solid oxide fuel cells can be as high as 65% [7]. Fuel cells are considered as clean energy resources because there is zero or very low pollutant emission. Microturbines are touted to become widespread in distributed generation and combined heat and power applications [8]. They are one of the most promising technologies for powering hybrid electric vehicles. The capacity of a commercial size microturbine usually ranges from tens to hundreds of kilowatts [9]. The outputs of renewable energy based DG systems are intermittent and unpredictable. In addition, electrical energy demand is set to rise with the electrification of transportation and heat, putting additional strains on distribution networks [10], [11], [12]. A plug-in hybrid electric vehicle is a hybrid vehicle that utilizes rechargeable batteries that can be fully charged by connecting to an external electric power source. Compared to conventional vehicles, plug-in hybrid electric vehicles (PHEVs) reduce air pollution and the reliance on petroleum [13]. The penetration of PHEVs in the power grid is increasing, as of September 2014 about 248,000 highway-capable plug-in hybrid electric cars have been sold worldwide since December 2008 [14], about 41.3% of the total 600,000 plug-in electric cars sold worldwide until Oct However, all these changes will result in 3

16 more stochastic and dynamic behaviors that the distribution system has not experienced nor been designed for. It is indispensable to develop flexible and intelligent planning methodologies in order to properly exploit the integration of DG and manage changing load patterns caused by PHEVs, while still satisfying both power quality and reliability constraints. Besides, the stochastic representation of generation and load is a must for these methodologies in order to plan a safe and reliable system. In order to realize all these objectives, the first step is to understand the mechanisms of distributed generation by building appropriate simulation models and developing stable control methods. From the perspective of the distribution network, a reliable distribution automation system is the key to enable autonomous smart distribution system operation to any changes, such as time-varying load demands, unexpected faults and planned actions, and to ensure the efficiency, reliability and optimality during distribution network operations. Distribution automation refers simply to greater automation of processes within the distribution system. A relatively short-term vision for distribution automation is a distribution system that, through automation, has a more flexible electrical system architecture that is supported by open-architecture communication networks [15]. Distribution automation should result in a system that is multifunctional and takes advantage of new capabilities in power electronics, cyber technology and system simulation. Real-time state-estimation tools should be used to perform predictive simulations and to continuously optimize performance, including real-time demand-side management, efficiency, reliability, and power quality to help bridge the communicationpower architectures. 4

17 Automated network reconfiguration including restoration is the most studied area in distribution automation, which is a promising option because it uses existing assets to achieve important and timely goals. Importantly, network reconfiguration is generally referred to, but not limited to, distribution feeder reconfiguration. In transmission systems, network topology optimization or reconfiguration has also been studied widely [16], [17], [18], [19]. However, the objectives and methods of reconfiguration problems in transmission and distribution systems are totally different. Switching actions in transmission systems are mainly used to avoid overloads, reduce operation costs and improve system security, while switching actions in distribution systems are used to reduce power losses, improve voltage profiles and improve system reliability. Besides, transmission networks are meshed and balanced, while distribution networks are radial and unbalanced, so the constraints and methodologies for reconfiguring transmission and distribution systems are totally different. This dissertation is focused on smart distribution automation and thus the terminology of network reconfiguration always indicates distribution feeder reconfiguration. A distribution network can change its topology by opening or closing switches to optimize system operation, isolate faults, and to restore the supply during outages due to contingencies. In addition, the change of topology can improve load balancing between feeders by transferring loads from heavily loaded feeders to other feeders, thus improving voltage levels, reducing losses and increasing levels of reliability. It is also possible to reduce average customer outage times, annual unavailability and expected unserved energy by distribution system automation. In recent years, new methodologies of distribution network reconfiguration have been presented, exploring the greater capacity 5

18 and speed of computer systems, the increased availability of system-wide data, and the advancement of automation, in particular supervisory control and data acquisition (SCADA). With the increased use of SCADA and distribution automation using switches and remote controlled equipment, distribution network reconfiguration becomes more viable as a tool for real-time planning and control. As the operating conditions vary, network reconfiguration can be used to minimize power losses provided that technical operational limits are not violated and protective devices remain properly coordinated. This distribution automation functionality is highly desirable given the deployment of remotely controlled switches in smart distribution networks that are expected to facilitate the integration of power from distributed energy sources and to serve varying load patterns, for instance, from electric vehicle charging. It must be noted that network reconfiguration is a short-term problem that tries to find the optimal network configuration for a specific operating period, and the switching plan obtained for the reconfigured system will achieve the desired operations within the current operating period. Due to the high level of uncertainty regarding future network conditions, it is extremely unlikely that a single network topology is optimal for all periods over a long time horizon. Thus, it is necessary to reconfigure the distribution network from time to time. Although many approaches have been proposed to solve the reconfiguration problem, one of the main remaining challenges with network topology optimization is the required computational time and resources. Network reconfiguration is a complicated non-convex optimization problem with binary decision variables and operational constraints. Heuristic approaches have been shown to perform most quickly with satisfying 6

19 approximations, but they are still not efficient enough when dealing with large-scale networks with thousands of buses. The occurrence of intermittent renewable energy, uncertain load demands for charging electric vehicles and more complicated demand responses have changed the traditional static network into a highly dynamic one. It is necessary to more frequently reconfigure the network in response to changes that occur in the grid. Thus, a highly efficient and effective approach to reconfigure distribution feeders to improve system operation is highly desired. This dissertation is organized as follows. Chapter II gives a review of existing approaches for distribution system reconfiguration. Chapter III gives the optimization problem formulation for the network reconfiguration problem and also presents three new methods to solve the reconfiguration problem. Each method is tested on different distribution systems, and the performance of each of these methods is discussed and compared. As mentioned earlier, a highly efficient and effective approach to solve the reconfiguration problem is significant and necessary for future smart distribution systems. A hierarchical, decentralized reconfiguration approach is given in Chapter IV, and this approach has been shown to be very efficient and have good accuracy. In order to study the impact of DG network reconfiguration and develop appropriate energy management strategies, dynamic modeling and primary control of multiple DG units are studied in Chapter V. Then, a comprehensive study of reconfiguring unbalanced distribution systems with distributed generation is presented in Chapter VI. Finally, Chapter VII concludes the dissertation and discusses possible future work. 7

20 Chapter 2 A Review on Existing Approaches for Reconfiguring Distribution Systems Network reconfiguration in distribution systems is realized by changing the status of sectionalizing switches (normally closed) and tie-switches (normally open). It can be used to reduce power losses by transferring loads from heavily loaded feeders to lightly loaded feeders without violating system security and stability constraints, and it can also be used to restore loads in response to the problems that have occurred in the system. Distribution feeder reconfiguration can be used for system planning as well as real-time control and operation. From an optimization perspective, network reconfiguration is a mixed-binary nonlinear optimization problem where binary variables represent the switch states and continuous variables model the electric network. However, even for a distribution system of moderate size the number of switching options is so large that conducting load-flow studies for all the possible options is computationally inefficient and impractical as a real-time feeder reconfiguration strategy. As a result, during the past decades, numerous approaches have been proposed to solve reconfiguration problems. The first publication about network reconfiguration problem by Merlin and Back [20] determined the network configuration with minimum or near-minimum line losses using a branch-and-bound type heuristic technique. According to their proposed method, all network switches are initially closed to obtain a meshed network. Then, network switches are opened one at a time until a new radial structure is reached, and the switch selected to open at each time minimized the losses of the resulting network. Merlin and Back s work has been the foundation for all other network reconfiguration studies that have followed. However, there are several major drawbacks of the methodology including the 8

21 assumption of purely active loads represented by current sources, neglecting voltage angles and network constraints. As a result, Shirmohammadi and Hong [21] modified Merlin s methodology to avoid these drawbacks and their approach also starts by closing all network switches which are then opened one-by-one another by determining the optimum flow pattern in the network. They also developed an efficient power flow method suitable for both radial and weekly meshed distribution networks. Accordingly, Gaswami and Basu [22] used the concept of optimum flow pattern assuming that only one switch was closed each time to form one loop, and improved configurations were obtained by successively conducting single-loop switch exchange until no further improvements are obtained. [20] - [22] start by switches to obtain a meshed network, and then switches are opened successively to obtain the radial structure. This implementation pattern can be considered as a sequential switch opening method, and most reconfiguration approaches follow this pattern. On the contrary, McDermott et al. [23] developed a reconfiguration algorithm starting with all network switches open, and a list of candidate switches is built at each step and the candidate with minimum loss increment is closed at that step. This proposed reconstruction procedure is repeated until a connected, radial network is achieved. Because the number of normally closed switches is much larger than the number of normally opened switches, more load flow calculations are needed in this approach than other sequential opening methods. A branch-exchange type heuristic algorithm has been suggested by Civanlar and Grainger [24], and a formula to estimate loss reduction caused by transferring load between two feeders was also derived. According to their work, loss reduction can be attained only if there is a significant voltage difference across the normally open tie- 9

22 switch and if the loads on the higher voltage side of the tie-switch are transferred to the other side. This conclusion is quite significant because the number of switches that need to be studied can be greatly reduced. Based on their work, Baran and Wu [25] introduced two different methods to approximate power flow in the system after a load transfer, and these approximate power flow methods are then used to estimate both loss reduction and load balance in the system. Since there are generally multiple tie-switches existing in a system, it is important to determine the implementation scheme of multiple loops. Fan et al. [26] provided an analytical description and a systematic understanding about the single-loop optimization approach. Each time a loop is selected, and the best switch to be opened is determined by finding the minimum loss increment associated with a particular switch in the loop. The evaluation procedure starts from the original open switch and then goes up in one direction toward the source node by one switch at a time until the minimum loss increment is reached. Recently, more new heuristic approaches are proposed on the basis of the above classic algorithms. Gomes et al. [27] proposed a two-stage reconfiguration algorithm. The computation also starts from a meshed network with all switches closed. The first-stage requires finding all maneuverable switches and computing the power loss if a maneuverable switch is opened; the open switch the minimum power loss is identified. The selected maneuverable switches are revised and this procedure is repeated until a radial network is achieved. The second-stage is used to improve the solution obtained at the first stage. For each opened switch selected from the first stage, two exchange operations are performed involving pairs of switch neighbors. If a reduction in power loss can be achieved, replace the opened switch with its neighbor switch. This algorithm is 10

23 quite simple and effective, but many load flow computations are needed so it can be computationally expensive. As a result, Raju and Bijwe [28] developed a reconfiguration approach that included sensitivity analysis to supplement the two-stage heuristic approach. The sensitivity of power loss with respect to the impedance magnitude of each branch is computed and only the top ranked switches are investigated to determine the one that provides the minimum power loss when opened. The loss sensitivity of the new system with the selected switch opened is computed and the procedure is repeated until the radial network structure is obtained. Finally, the power loss reduction for exchanging opened switches with their neighbors is also checked to determine if the solution can be improved. Besides, optimum power flows were considered in many reconfiguration studies before conducting the heuristic algorithms. Gomes et al. [29] developed a refined heuristic algorithm by including optimum power flow (OPF) where the status of all maneuverable switches are represented as continuous values. The OPF is solved for the meshed network to obtain the switch status results for all maneuverable switches. Instead of studying the power loss reduction by opening each of the maneuverable switches, only six switches with the smallest values are studied to reduce the computational time. The switch with minimum power loss is selected as the opened switch and the list of maneuverable switches is updated. The OPF and heuristic checking are repeated for the remaining maneuverable switches until the radial structure is achieved. Schmidt et al. [30]formulated the reconfiguration problem as a mixed integer nonlinear optimization problem with integer variables representing the status of switches and continuous variables representing the current flowing through all branches. The Newton method was used to compute the branch currents within the integer best-first search. 11

24 Heuristic algorithms are generally simple and fast, but optimality of the global solution can not be guaranteed. Another type of reconfiguration approaches uses meta-heuristics or artificial intelligent techniques. In a two-part paper presented by Chiang and Jean- Jumeau [31], [32], a two-stage solution methodology based on a modified simulated annealing technique and the ε-constraint method was proposed for solving network reconfiguration problems with the objective of reducing losses and balancing the load. Simulated annealing is a generic probabilistic meta-heuristic for locating a good approximation to the global optimum of a given objective function in a large search space. The name and inspiration come from annealing in metallurgy, a technique involving heating and controlled cooling of a material to increase the size of its crystals and reduce their defects. Chang and Kuo [33] also applied simulated annealing to the network reconfiguration problem for loss minimization. They presented a set of simplified line flow equations to compute the line loss and developed an efficient perturbation scheme and initialization procedure for dynamically determining a better starting temperature for the simulated annealing so that the entire computation could be sped up. Ant algorithms are another class of artificial intelligence techniques inspired by the foraging behavior of real ant colonies using a population-based approach with exploration for positive feedback. Through a collection of cooperative agents called ants, the near-optimal solution to the optimization problem can be effectively achieved. Su et al. [34] proposed a method employing an ant colony search algorithm to solve network reconfiguration problems using artificial ants. State transition rules along with global and local updating techniques were introduced to ensure near optimal solutions. Recently, Chang [35] used the ant colony search algorithm to solve the combinatorial optimization problem of 12

25 network reconfiguration and capacitor placement. Particle swarm optimization (PSO) algorithm was first proposed by Kennedy and Eberhart [36] to solve optimization problems by simulating the migration and aggregation of bird flocks when seeking food to determine a search path according to the velocity and current position of particle without more complicated evolutionary operations. PSO algorithms have also been used by many literatures to solve network reconfiguration problems [37]-[38]. In [39] a discrete PSO algorithm was applied to two test systems but it was found to be inefficient because large numbers of infeasible non-radial solutions that appeared at each generation significantly increased the computation time before reaching a desired solution. Then Abdelaziz et al. [40] revised this discrete PSO algorithm to overcome the drawbacks of the proposed algorithm in [39]. The Tabu search is another popular approach in network reconfiguration studies [41], [42]. Besides the above-mentioned approaches, genetic algorithms (GAs) that mimic the process of natural selection and genetics are popular artificial intelligence techniques. GA was first applied to the loss minimum reconfiguration problem by Nara et al. [43]. In the proposed GA, the genetic strings are defined to represent the arc (branch) numbers and the switch position on each arc, and an approximated fitness function was used to represent the system power loss. The principle disadvantage of this basic GA is that such binary codification problems can require very long string lengths that grow in proportion to the number of the switches. To improve the performance of the GA, Zhu [44] modified the string structure and fitness function to reduce the string depending on the number of open switches. The fitness function also considered system constraints and an adaptive mutation process that was used to change the mutation probability. Similarly, a refined 13

26 GA was proposed by Lin et al. [45] to take advantage of the optimum flow pattern, genetic algorithm and tabu search method Real number codifications were used instead of binary codification, and the genes in each chromosome represented the open switches in the network. A competition mechanism based on the fitness value was implemented in the search process to decide whether crossover or mutation was needed for the next step. A tabu list was introduced to define forbidden moves in the searching process. Recently, a large number of literatures have been published to present their contributions on improving genetic algorithm for solving network reconfiguration problems [46], [47], [48], [49], [50]. The improvements include new codification methods, adaptive operators, and changes in fitness functions. In addition to these classic meta-heuristics or artificial intelligence techniques, some new approaches have also been introduced in network reconfiguration studies. The harmony search algorithm (HSA) is a new meta-heuristic population search algorithm proposed by Geem et al. [51], which is developed by mimicking the process of searching for better harmony in musical performance. The significant terms used in HSA include harmony memory (HM), harmony memory size (HMS), harmony memory considering rate (HMCR), pitch adjusting rate (PAR) and the number of improvisations (NI). HSA was introduced to solve network reconfiguration problem by Rao et al. [52], and its performance was well compared with GA and tabu search approaches. Compared to heuristic methods, meta-heuristics or artificial intelligence techniques are well suited for solving mixed-binary optimization problems and are more likely to achieve solutions that are near the global optimal. However, these methods are generally not repeatable and may require several executions to obtain the best solution. 14

27 Different from heuristics and artificial intelligence techniques, mixed-integer programming methods can also be used to solve network reconfiguration problems. This type of approach can acquire global optimal solutions but is much more complicated than the other two approaches, and often requires commercial numerical solvers to obtain a solution. However, with the aid of advanced high-performance computers, mixed-integer programming methods are becoming more and more popular for solving network reconfiguration problems. Ramos et al. [53] linearized the problem and then solved the linearized optimization problem using mixed-integer linear programming, however the solution does not represent losses exactly. In order to overcome such a drawback, Romero-Ramos et al. [54] presented a nonlinear formulation using a nonconventional group of variables to be solved using a mixed-integer nonlinear optimizer. Khodr et al. [55] also employed an exact model of losses in a Benders decomposition solution apporach. However, the optimization problem models in [54] and [55] are both nonconvex so there is no assurance of convergence to the global optimal solution. Thus, Jabr et al. [56] presented an exact mixed-integer conic programming model using convex continuous relaxation, so the solution obtained was guaranteed to be globally optimal. The study of network reconfiguration traces back to 1970 s, with thousands of related papers published in the past 40 years, and many of the solution approaches are quite mature. However, the distribution system infrastructure is faced with many new changes including more remotely controlled maneuverable switches, the integration of distributed energy resources and highly uncertain, time-varying load patterns, for instance, from electric vehicle charging, requiring new approaches to the reconfiguration problem. In [1], [57] and [58], the opportunities and new challenges for the design and implementation of 15

28 reconfiguration algorithms are discussed within the context of smart grid development efforts. With the development of the smart grid comes increased numbers of smart meters, advanced monitoring technology, intelligent control agents with better communication capabilities, and well-developed demand response strategies and selfresponse capabilities. All these new developments will enable faster and more accurate reconfiguration of distribution feeders. However, stricter power quality constraints, new topologies including meshed structures and islanding, and the increase in operating data present challenges to the development of efficient reconfiguration strategies. The authors in [58] conceived a system for automatic reconfiguration of distribution networks based on a heuristic method to determine the best network topology, and some preliminary results were also given. In [59], studies of time-domain three-phase transient behaviors of large-scale distribution networks were conducted, which have been proven to be of great importance for implementation of smart grid reconfiguration principles. With the increased penetration of distributed energy resources, the effects of distributed generation are included in most recent network reconfiguration studies. Wu et al. [60] proposed a reconfiguration methodology based on an ant colony algorithm that is aimed at achieving the minimum power loss and incremental load balance factor for radial distribution networks with distributed generators, and it was shown that lower system losses and better load balancing results would be achieved with the help of distributed generation. Rao et al. [61] presented their study based on harmony search to determine the optimal network reconfiguration and optimal outputs of grid-connected distributed energy resources at the same time in order to minimize power losses in distribution systems. Song et al. [62] proposed both operation and integration schemes of distributed energy 16

29 resources in network reconfiguration for loss reduction and service restoration, for both radial and meshed network structures. Network reconfiguration is indeed an important feature of active distribution network management at both planning and operation levels, and thus comprehensive studies including network reconfiguration as only one part have been presented. Martins and Borges [63] gave a model for active distribution system expansion planning based on a genetic algorithm, and distributed generation was considered together with conventional alternatives for expansion including rewiring, network reconfiguration, and the installation of new protection devices. Two different methods for uncertainties incorporation through the use of multiple scenario analysis were also proposed and compared. In [64], a multi-objective optimization model for the operation of distribution systems with large numbers of single-phase solar generators was proposed, which was used to minimize phase imbalances and energy losses in threephase unbalanced distribution systems by controlling switched capacitors, voltage regulators and reconfiguration switches. The genetic algorithm with a decision-making process was used for solving this multi-objective optimization problem and stochastic data of solar generators was also included. 17

30 Chapter 3 Three Methods Proposed for Reconfiguring Distribution Systems Network reconfiguration involves determining the optimal open or close switch states in the distribution network. In this Chapter, the network reconfiguration problem is formulated as a nonlinear optimization problem with an objective that is a function of the switch states. Three new solution methods are proposed, including a revised heuristic algorithm based on branch-exchange and single-loop optimization, a hybrid method based on optimal power flow and heuristics and a revised genetic algorithm. 3.1 Problem Formulation Network reconfiguration is mostly used to reduce power losses in distribution systems, and thus the objective function is defined as min M 2 f min Ploss Ii ri (3.1) i1 where, M is the total number of branches in the system. I i is the i th branch current. r i is the i th branch resistance. Line reactance is constant regardless of the structure, so the power loss only depends on line currents that can be calculated using nodal voltages. Suppose A is the node branch incidence matrix for the system, then T A V Z I bus branch branch (3.2) where V bus is the nodal voltage vector, I branch is the branch current vector, and Z branch is the branch reactance (diagonal) matrix. Total power losses in the system are computed as 18

31 P I R I V AZ R Z A V (3.3) loss T * T -T -* T * branch branch branch bus branch branch branch bus -T -* T branch branch branch Let T AZ R Z A, and M 2 M M a1i ri a1i a2i ri a1i ani r i i1 Zi i1 Zi i1 Zi M M 2 M a2i a1i ri a2i ri a2i ani ri T i 1 Zi i 1 Zi i 1 Z (3.4) i M M M 2 ani a1i ri ani a2i ri ani ri i1 Zi i1 Zi i1 Zi where, N is the total number of buses, a ij is the ij-th element of matrix A, Z i = r i + j x i is the reactance for the i th branch. Except the substation node, all nodes are considered as PQ nodes, and the nodal voltages can be obtained from N N Pi ei Gij e j Bij f j fi Gij f j Bij e j j1 j1 N N Qi fi Gij e j Bij f j ei Gij f j Bij e j j1 j1 (3.5) where V i = e i +j f i is the i th node voltage. Y ij = G ij +jb ij is the ij-th element of the node admittance matrix, which is defined by Y = AY branch A T (3.6) and, Y branch =Z -1 is the (diagonal) branch admittance matrix. The nodal branch incidence matrix (A) is constant for a fixed topology, but changes when the network is reconfigured. Network reconfiguration is essentially an optimal decision to open or close switches, so the states of switches are the primary parameters in the reconfiguration study. It is assumed that each branch is equipped with a remotely controlled switch, and the state of 19

32 each switch is defined as S j 1, switch j is closed and directionis same astheinitial 0, switch jisopen 1, switch j is closed and directionis opposite (3.7) where, the direction refers to the direction of current flow. The calculation starts from the assumption that all switches are initially closed, and the node branch incidence matrix for this network is A 0, which is constant for a specific system. Then the node branch incidence matrix (A) for any other topology of the system can be determined by the initial node branch incidence matrix and the switch states, as A(i, j) = A 0 (i, j) S j (3.8) 0 where a ij =A(i, j) is the matrix element and a ij =A 0 (i, j), and S j is the state of switch j. Substituting (3.4) and (3.8) into (3.3), the power loss becomes N N M a * ika jkrk S k Ploss V j Vi 2 j1 i1 k1 Z k (3.9) Substituting (3.8) into (3.6), G ij and B ij can be represented as G ij a a r S a a x S M M ik jk k k ik jk k k B 2 2 ij 2 2 k1 rk xk k1 rk xk (3.10) Besides, several constraints must be considered when solving the optimization problem: (1) System Structure Constraint The distribution network is radial without meshes before and after reconfigurations, so M k1 S N d k (3.11) where, d is the total number of slack buses. 20

33 All loads are served without disconnections, so In addition, at least one branch is open in each loop, so rank(a) = N d (3.12) M k i1 S i M k 1 (3.13) where, M k is the amount of branches in the k th loop. (2) Voltage Limit ANSI C84.1 [65] recommends voltage magnitudes be within 5% of the norminal value. No overvoltage (>1.1 pu) or undervoltage (<0.9 pu ) is allowed [66]. In the following study, the ±5% limit is considered as strict and excellent, and ±10% limit is considered as loose and fair. 0.9 V norm V i 1.1 V norm (3.14) (3) Current Limit Each line is loaded within its capacity. And, branch currents are limited by max I branch,i I branch,i (3.15) In summary, according to the above analysis the network reconfiguration problem can be finally formulated as N N M * a ik a jk r k S k min f min V j Vi 2 j1 i1 k1 Z k st.. (3.5),(3.7),(3.11) ~ (3.15). (3.16) All the parameters except the switch states are constant for a specific system. Thus the above formula is a function of switch states and because the switch states are discrete variables, network reconfiguration is a constrained, interger, nonlinear optimization 21

34 problem. 3.2 Heuristic Method The heuristic algorithm is developed based on branch-exchange and single-loop optimization. Generally multiple tie-switches exist in a distribution network, and the closures of these switches will lead to a meshed network with multiple loops. Single-loop optimization indicates that each time only a loop is studied, and this loop is the one with the largest voltage difference between two sides of the initially opened tie-switch. In order to regain radial system structure, a switch must be selected from the studied loop to open, and this switch is determined using branch-exchange method. Suppose the sectionalizing switches 1 ~ k-1 are at one side of the initially opened tieswitch n, and sectionalizing switches k ~ n-1 are at the other side, shown in Fig All other switches are represented as the set C. b k b k+1 b n-2 b n-1... k k+1 n-1 n k-1 b 0 b 1 b 2 b k-2 b k-1 Figure 3.1 Structure of the switches. Then, the total power losses can be calculated as k1 n1 (0) loss i i i i j j i1 ik jc P I R I R I R (3.17) where, I i and R i are respectively the magnitude of the current and the resistance at branch i. If the tie-switch is closed and its adjacent sectionalizing switch n-1 is opened, the load at bus b n-1 is transferred to the other side. Because all the network loads can be modeled 22

35 as constant current injections, the switching operation in a loop only changes the flow pattern of the loop itself. Thus, the new branch currents can be defined as Ii I, i 1,2,..., k 1, n Ii Ii I, i k, k 1,..., n 1 Ii, i C (3.18) The new power loss can be evaluated using new currents, and the changes in power loss are n 1 1 (1) (0) 2 k n Ploss Ploss Ploss I Ri 2I Ii Ri Ii Ri i1 i1 ik (3.19) Bus voltages V k-1 and V n-1 for the initial network can be respectively calculated as k1 n1 (3.20) V V I R V V I R k1 0 i i n1 0 i i i1 i1 If V k-1 V n-1, k1 n1 I R I R and P loss is always greater than zero. For opening of i i i i i1 ik the next switch n-2, the new power loss is compared with P (1) loss using the same method, and it is easily proved that the power losses increase. Besides, opening all of the other switches in the same direction will produce more power losses. Thus, the power loss reduction cannot be achieved by opening the sectionalizing switches in the higher-voltage side. Instead, power loss reduction could only be achieved if V k-1 >V n-1, i.e. opening the switch at the lower-voltage side of the initially opened tie-switch. Besides, according to (3.9), power loss is a function of switch states, and it can be easily calculated if the switch states are known. Thus, the power losses in the system after reconfiguration are calculated using the exact power flow results instead of approximate formulas that are used in [22] and [24] so that the algorithm is able to get closer to the 23

36 true optimal solution. In summary, the flowchart of the proposed heuristic algorithm is given as Fig First, number all buses and branches, and identify all tie-switches in the subsystem being studied. Divide all other sectionalizing switches into two groups according to their locations at the left or right side of the tie-switch. Solve the power flow for the initial system. Then, determine the optimal switch-pair to minimize power losses according to the following steps. (1) Each time, the tie-switch with the biggest voltage difference across it is chosen. Then the initially closed switch will be selected from the sectionalizing switches in the loop that is formed if the studied tie-switch is closed. The location of candidate switches at two directions makes it necessary to determine the opening of switches at the side that can lead to power loss reduction. It is proved that power loss reduction can only be achieved by opening the switch at the lower voltage side of the initially opened tie-switch and closing the tie-switch. (2) Start the search from the adjacent switch of the tie-switch. Let the states of the adjacent switch and tie-switch be zero and 1/-1 (dependent on the current direction) respectively. (3) Calculate power losses using the new switch states. If the power losses are not reduced, exchanging the switch states in this loop cannot attain power loss reduction, so keep the switch states at their initial values. Otherwise, keep checking the power loss reduction by letting the state of the next switch in the same side be zero instead. Repeat until no further power loss reductions occur. (4) Check whether the system with the new switch states satisfies all constraints. If so, 24

37 record the results and refine the switch states for the system. Otherwise, choose the switch states with the minimal power loss that satisfies all constraints. (5) Repeat procedures (1)~(4) until finishing all loops and no more reduction occurs. The final switch states are taken as the optimal solution for the reconfiguration problem. Number all buses and branches. Identify all tie-switches and divide left / right side sectionalizing switches. Conduct a load flow. Choose the tie-switch with the biggest voltage difference V(left-side)-V(right-side)<0? Left-side YES Decide search direction Revise switch states Calculate power losses using (3.9) NO Power Loss Reduced? YES Continue with the next switch in the same side YES Power Loss Reduced? NO Back to the result obtained at last iteration Choose the NO feasible, secondary All constraints satisfied? optimal switch YES states instead. Record the new switch states, and prepare for next iteration. NO Finish all possible branch-exchanges? YES Get the optimal solution STOP NO Right-side Figure 3.2 Flowchart of the heuristic algorithm based on branch-exchange and single-loop optimization. 3.3 Hybrid Method Hybrid Method The second method is called hybrid because it is a combination of optimal power flow (OPF) and heuristic method. From (3.16), it is known that network reconfiguration can be 25

38 considered as an OPF problem. If we relax the discrete switch states into continuous values between -1 and 1, the new and continuous OPF problem can be solved using conventional nonlinear programming techniques. After solving OPF, the solutions are continuous values between -1 and 1. In order to obtain the finally feasible results, it is necessary to determine the integer values based on OPF solutions. Thus, the proposed hybrid method is composed of two stages: the first stage is to solve OPF using interior-point method; and the second stage is to revise OPF solutions into integer switch states using heuristic corrections. The flowchart of the entire algorithm is given as Fig (1) Number all the buses and branches at first. (2) Determine the infeasible switches. Those switches that must be always closed are defined as infeasible switches because their openings will lead to disconnected network, and the states of these switches are deleted from the decision variables in the objective function so that the order of the matrix formed during computation is reduced. (3) Determine the loops possibly formed by the closures of tie-switches. A loop is defined by the closing of an initially opened tie-switch and other initially closed sectionalizing switches. (4) Form the OPF problem as (3.16) and use the interior-point algorithm to solve the optimization problem. 26

39 1. Number the buses and branches 2. Determine the infeasible switches, and delete the states of them from the decision variables in the objective function 3. Determine the loops formed by the closures of tie-switches 4. Form the OPF problem and then solve the optimization problem Recover integer values from the OPF solutions. 5.1 Obtain the final results for those switches if their OPF solutions are already integers 5.2 Acquire candidate switches waiting for recovery and divide them into groups according to the loops which they belong to. Choose the unsolved group with the least number of candidate switches to study. Open a switch k and close all other switches in the studied group, then compute the new power loss dp k. All switches in the studied group tested? YES Decide the 0-state switch that leads to the smallest dp k and revise the switch states in the studied group into integer values. Update the candidate switches in the remaining groups. NO All groups solved? YES STOP NO Figure 3.3 Flowchart of the proposed hybrid method. (5) Decide the opened switch for each loop based on OPF solutions. After the first four steps, the relaxed OPF problem is solved and the solutions of continuous switch states are obtained. In order to determine the integer states (0, 1 or -1) of all switches, the following procedures are conducted: (5.1) Obtain the results for parts of switches based on the OPF solutions: the OPF solutions of all decision variables can be divided into integers and decimal numbers. The 27

40 switches with the integer solutions (0, -1 and 1) are marked as finally solved and their states are exactly the OPF solutions. Then, on the basis of these solved switches, new infeasible switches could be induced. Thus find the infeasible switches from the remaining ones, and revise the states of these switches into 1/-1 (the positive/negative sign is decided according to the current direction). (5.2) After (5.1), the remaining switches are considered as candidate switches, and their states need to be revised into integers using the following heuristic method. (5.2.1) Divide the candidate switches into groups according to the loops which they belong to. (5.2.2) Study the unsolved group with the least number of candidate switches and decide the 0-state switch. The 0-state switch is selected provided the power loss increment is least if its state is changed from OPF solution to 0 and the states of all other candidate switches in the same group are changed from OPF solutions to 1/-1. (5.2.3) Update the candidate switches in all unsolved groups and repeat (5.2.2) until finishing all groups. Before moving to the next group, the candidate switches in all other groups are checked again to find the infeasible switches on the basis of the new switch states solved in (5.2.2). The infeasible switches are deleted from the candidated switches and their states are revised into 1/ Sensitivity Analysis Based on OPF Solutions As illustrated in the above study, power loss is the function of switch states. The optimal solution (S*) of the relaxed OPF problem minimizes the power losses (P loss *) by neglecting the constraint that switch states can only be three integer values. Any 28

41 deviations of switch states from S* will cause changes in power losses. Thus, the sensitivity of power loss with respect to switch states is evaluated. From (3.9), the power loss can be represented as N N M * a ik a jk r k S k Ploss V j Vi f ( V ( S), S) 2 j1 i1 k1 Z k (3.21) If a small change S is added into the switch state vector S, then the new power loss is f V f Ploss Ploss f V,S S S V S S (3.22) where P loss is the power loss change due to the change of switch states. Thus, the sensitivity value around the operating point S 0 can be calculated as P f V f loss S S V S S 0 V( S ) V( S 0),S 0,S0 0 (3.23) The representations of the three matrices in (3.23) could be acquired from (3.5)~(3.10) and the results are given in (3.24)~(3.26). f Ploss Ploss P loss,,, S S1 S2 SM (3.24) where, N N Ploss 2 P loss * 0 0 r h Vj a jh Vi aih, h 1,2,..., M. 2 Sh S h j1 i1 zh where, f Ploss Ploss Ploss P loss,,,, V e1 f1 en f N P 2e t 2e t 2e t P loss 1 i1 2 i2 N in e M i aika jkrk Sk, tij 2 loss k 1 2 f1 t zk i f ti fn tin fi. (3.25) 29

42 y y y y y y e f e f S S y y y y y y e f e f S S V S yph yph yph yph yph y e2 f2 en f N S1 S yqh yqh yqh yqh yqh y e2 f2 en f N S1 S P1 P1 P1 P1 P1 P1 2 2 N N 1 M Q1 Q1 Q1 Q1 Q1 Q1 2 2 N N 1 M 1 Ph M Qh M (3.26) N N ei Gij e j Bij f j fi Gij f j Bij e j Pi y Pi j1 j1 where, y, N N Qi fi Gij e j Bij f j ei Gij f j Bij e j Qi j1 j1 n n yph (0) (0) (0) eh k fh k ei aik eh k fh k fi aik 2ah, k Sk S k i1 i1 rk xk, k, n n k y r x r x (0) (0) (0) eh k fh k ei aik eh k fh k fi aik 2ah, k Sk S k i1 i1 n (0) (0) fi aik 2ah, k Sk i1 rk xk, k, n 2 2 k 2 2 (0) r (0) k xk rk xk fi aik 2ah, k Sk i Qh k k k k h eh hh, j fh lh, j, j h yph and n, iei hh, i fi, j h f j eh hh, j fh lh, j lh, i fi hh, iei, j h i1 j h eh lhj fh hhj, j h yqh and n hi fi hhiei, j h f j eh lhj fh hhj lhiei hhi fi, j h i1 a a x S a a r S a a x S and l, h. ij m m ik jk k k ik jk k k 2 2 ij 2 2 k1 rk xk k1 rk xk, e l f h, j h e yph y n Ph and ej e l f h l e h f, j h f e eh hhj fh lhj, j h e yqh yqh n and e j eh hhj fh lhj lhi fi hhiei, j h f j e i1 h h, j h hj h h h, j h hj h, i i h, i i j h i1 h h As a result, the sensitivity is solved and it is a 1 m row vector. Thus the power loss change for shifting switch states from OPF solutions to the extreme integer values is evaluated by solving (3.27) iteratively with a small step. 30

43 f V f Ploss S S * * * * V S S V( S ),S V( S ),S * (3.27) 3.4 Genetic Algorithm Compared with the existing GAs used in network reconfiguration studies, both encodings and operators in the algorithm are improved in order to better solve the reconfiguration problem for distribution systems with the consideration of distributed generation. Fig. 3.4 shows the flowchart of the revised genetic algorithm. (1) Encoding and Initialization The size of the population and the maximal allowed generations are defined first. In the first generation, all chromosomes in the population are required to be feasible, i.e. satisfying all defined constraints. The great majority of the existing GA applications to the reconfiguration problem are done using binary codifications to represent the locations and status of switches, and thus the string is quite long even without the inclusion of DG parameters. In this thesis, the real-valued string is used instead of the binary codification to reduce the number of bits. Each chromosome in a population is defined as Fig. 3.5 and it has T+2K genes in total: (a) Suppose there are totally T initially opened tie-switches in the system. The first T genes represent the opened switches. (b) The following 2K genes are the active power and reactive power generated from K grid-connected DG units. 31

44 Initialization: pop_ size, max_ gen k=1. Define 1 st generation and each chromosome must be feasible. NO NO i=1 rand<0.5? YES i=i+1 i>pop_size? YES j=1 rand<0.5? j=j+1 YES j>after_co? YES Select an offspring Cross-Over after_co=pop_ size+1 NO Mutation after_mu=after_co+1 NO NO System Structure Constraints Satisfy all constraints Voltage and Current Constraints Satisfy all constraints Keep this offspring in the population and compute its operating costs All offsprings are evaluated? YES Elitism selection from the remained feasible population Violate any constraint Violate any constraint Delete this offspring from the population NO k=k+1 k>max generation YES STOP Figure 3.4 Flowchart of the proposed genetic algorithm. OS 1 ~OS T P DG1 Q DG1... P DG,K Q DG,K Figure 3.5 The genes included in each chromosome. 32

45 (2) Cross-Over Based on the above encodings, each string is mixed of integers and continuous values. It is assumed that there are both half chance to apply the cross-over and mutation operators. The cross-over operator randomly selects two chromosomes (A, B) and then exchanges their information to create two new chromosomes (C, D) following the rule based on one-point technique and arithmetical operator: (a) Select a gene i from T+2K genes randomly. (b) If i T, C (1: i ) = A (1: i ), C(i+1: T) = B (i+1: T), and C(T+1 : T+2K ) = 0.2 A(T+1: T+2K ) B( T+1: T+2K ). (c) If i >T, C (1: T) = A (1:T), C(T+1: i ) = 0.8 A(T+1: i ) B( T+1: i ), and C(i+1: T+2K ) = 0.2 A(i+1: T+2K ) B( i+1: T+2K). The other chromosome D is obtained in the opposite way to C by reversing A and B in the above equations. (3) Mutation The mutation operator randomly changes one bit in the string to introduce new information into the offspring, and suppose the j th gene is selected. If (a) j T, this gene is replaced by another value in its domain, i.e. another switch in the corresponding loop. (b) j > T, this gene is replaced by another feasible value within the capacity of DG units. (4) Elitism Selection Before evaluating the fitness values of the new population, all repeated chromosomes are deleted and the feasibility of each offspring is evaluated by checking the system 33

46 structure constraints and voltage/current constraints in turn. Then, the operating costs of all feasible offsprings are computed and the elitism is used to select the best population. 3.5 Case Studies In order to test the performance of the proposed three methods, they are applied to reconfigure two test systems, respectively. The first test system is a three-feeder distribution system [24] and the second test system is a 33-bus distribution system [25] Case I : Three-Feeder Test System Fig. 3.6 shows the topology of the three-feeder test system, which includes three feeders, three tie-switches and sixteen buses. The numbers with circles denote the numbers of switches and branches. The nominal voltage is 13.8 kv and system frequency is 60 Hz. Total power losses are kw and the minimal nodal voltage is p.u. at bus Figure 3.6 Three-feeder test system. First, all branches and buses are numbered in the figure. There are three loops formed after closing all tie-switches 16, 17, 18, which are respectively: 1)

47 8-7 (loop-1); 2) (loop-2); 3) (loop-3). (1) Heuristic Algorithm The voltage differences across three tie-switches are V, V and V, respectively. Thus, loop-2 is first studied and switches 7 and 9 are the candidate open switches. In summary, the finally optimal results of the centralized approach are obtained after five iterations. Table 3.1 gives the simulation results and only the iterations with power loss reductions are shown. The final opened switches are 9, 10 and 18. The power loss is reduced to kw by 9.08%, and the minimum voltage is 0.96 p.u. at bus 12. CPU computing time is only seconds. Table 3.1 Simulation Results of Centralized Method For Three-Feeder Test System Iterations Switch Pair Power loss after Close Open reconfiguration kw kw kw (2) Hybrid Method In the system, the infeasible switches are 1, 2, 3, 7, 11, 12, and the values of their states are: S1 = S2 = 0, and S3 = S7 = S11 = S12 = 1.The OPF problem is formed as (3.16), and then solved using interior-point algorithm. Table 3.2 shows the OPF solutions. Table 3.2 Solutions of OPF for Three-Feeder Test System Objective Function f min (minimal power loss) kw Solutions of Switch States S18=0, S9= , S16=0.4773, S10=0.5227, S17=0.6768, All others = 1. 35

48 After solving the relaxed OPF problem, the solutions of most switch states are integers and these values are exactly the final results. Because S18=0, switch 18 will be opened for removing loop-3. Thus, the switch states that need revise are S9, S16, S10 and S17, only 4/18 of total switches. These four candidate switches are divided into two groups: 1) S10 and S16 (at loop-1); 2) S9 and S17 (at loop-2). Because the states of all other switches in loop-1 and loop-2 are 1, the state of one candidate switches in each group has to be revised to 0 and the other one is revised to 1/-1. Since each of two groups have two candidate switches, the selection of 0-state switch can start from any group and group-1 is chosen randomly. S16 and S10 are selected to be 0 in turn, and the power losses for two scenarios are compared in Table 3.3. Finally, the states of switches 10 and 16 are respectively revised to 0 and 1. Table 3.3 Power Losses for Different 0-State Switch in Loop-1 0-state Switch States of the Switches in the Same Group Power Losses 16 S10=1, S16= kw 10 S10=0, S16= kw Selected Opened Switch 10 Because the opening of 10 doesn t affect the connection of loop-2, no infeasible switch is deleted from group-2. S9 and S17 are respectively chosen to be 0, and the power losses for two scenarios are compared in Table 3.4. Similarly, the states of switches 9 and 17 are respectively revised to 0 and -1 based on the comparison. Table 3.4 Power Losses for Different 0-State Switch in Loop-2 0-state Switch States of the Switches in the Same Group Power Losses 9 S9=0, S17= kw 17 S17=1, S9= kw Selected Opened Switch 9 36

49 Sensitivity Finally the states of all candidate switches are revised and the optimal opened switches for the system are 9, 10 and 18. The power loss for the new structure is kw, 9.08% reduction from the initial power loss. The entire computation costs 1.9 s. The results of sensitivity around different switch states changing from the OPF solution to 0 and 1 are solved using (3.23). Fig. 3.7 shows the sensitivity of power loss to S9, S10, S16 and S17 respectively, and the difference of switch state between two points is chosen as Then the results of power loss changes for shifting S9, S10, S16 and S17 from their OPF solutions to 0 and 1 are obtained, shown as Fig Because the values of sensitivity are all negative, reducing switch states will lead to power loss increment and increasing switch states will lead to power loss reduction on the contrary. The results have shown that system power loss is more sensitive if switch states are reducing to 0 than increasing to 1. And the power loss is more sensitive to S17 than S9, and more sensitive to S16 than S10 when the switch states are close to 0. Consequently, the best choice would be opening S9, S10 and closing S16, S17, which is same as the result obtained using the hybrid method Switch States S9 S17 S10 S Figure 3.7 Results of sensitivity of power loss with respect to S9, S10, S16 and S17 respectively. 37

50 Power Loss Changes / W Switch States Figure 3.8 Results of power loss changes for shifting S9, S10, S16 and S17 from their OPF solutions to 0/1 respectively. S9 S17 S10 S16 (3) Revised Genetic Algorithm Fig. 3.9 gives the iterative results of the revised GA, and it finally converges to the optimal result kw after 1.64 s. The optimal opened switches are 9, 10 and 18. Figure 3.9 Iterative results of the revised GA for the 3-feeder test system Case II : 33-Bus Test System Fig shows the topology of the 33-bus test system, which includes 33 buses and 5 tie-switches ( ). Total loads are 3715 kw and 2300 kvar. For the initial structure, system power losses are kw and the minimal voltage is p.u. at bus Figure 3.10 Single-line diagram of 33-bus test system. 38

51 (1) Heuristic Algorithm The algorithm stops after 23 iterations. Table 3.5 gives the simulation results and only the iterations with power loss reductions are shown. The final opened switches are 7, 9, 14, 32 and 37. System power loss is reduced to kw by 31.15%, and the minimum voltage is 0.94 p.u. at bus 32. CPU computing time is only 1.65 seconds. Fig shows the voltage magnitudes of all nodes before and after the reconfiguration. It shows that voltages at most buses have increased a lot after the reconfiguration. Figure 3.11 Voltage magnitudes of all nodes before and after the reconfiguration. Table 3.5 Simulation Results Of Centralized Method For 33-Bus System Iterations with Power Loss Switch Pair Power loss after Reduction Close Open reconfiguration kw kw kw kw kw kw kw kw kw kw (2) Hybrid Method 39

52 Solutions of the relaxed OPF are given in Table 3.6 and the results of opened switches obtained after heuristic revision are given in Table 3.7. Finally, the optimal configuration of the system is the one with switches 7, 14, 9, 32, 37 opened and all other switches closed. Sensitivity of the power loss with respect to each candidate switch is studied and the result is shown as Fig The first three sensitive switches are S25, S26 and S37. The entire computation time is 15.1 seconds. Table 3.6 Solutions of OPF for 33-Bus Test System Objective Function f min (minimal power loss) kw Solutions of Switch States S9=0, S10=0.391, S7=0.469, S32= , S14=0.53, S6=0.531, S25=0.6582, S26=0.688, S11=0.7275, S28=0.8218, S37=0.8552, S36=0.8577, S27= All others=1. Table 3.7 Results of 0-State Switches for 33-Bus Test System Studied Group Candidate 0-State Switch Power Losses kw kw kw kw kw kw kw kw kw Selected Opened Switch Figure 3.12 Sensitivity of the power loss with respect to different switch states. 40

53 (3) Revised Genetic Algorithm Fig gives the iterative results of the revised GA, and it finally converges to the optimal result kw after 8.1 s. The optimal opened switches are 7, 14, 9, 32, 37. Figure 3.13 Iterative results of the revised GA for the 33-bus test system. 3.6 Comparison of Three Methods According to the above simulation results, the performances of three proposed methods are compared as Table 3.8. All three methods can help reduce power losses in distribution systems, but their performances are quite different. The heuristic algorithm based on branch-exchange and single-loop optimization always converges very quickly. Because the OPF is first solved in the hybrid method, its solution and convergence speed depends on the initial value chosen to solve OPF and also depends on the size of the studied system. The number of loops determines the size of each gene in the GA in the system, so the computational speed of GA could be slow for reconfiguring large systems, with computation times most probably in tens of seconds. Further, because of the mechanism of heuristics, both heuristic method and hybrid method are not guaranteed the reach the global optimal, instead, the revised GA is able to reach the global optimal solution after a sufficient number of evolutions. Because the three methods perform differently, the method that is preferred depends on 41

54 the characteristics of the system being studied. For small-scale systems, the revised GA is chosen to get the optimal topology with fast computational speed. For large-scale distribution systems, the heuristic method is chosen to reduce power loss with high computational efficiency. Heuristic Algorithm Hybrid Method Solve Problem? Table 3.8 Comparison of Three Methods Global Optimal? Speed Implementation Yes No Fast Very Easy Yes No Revised GA Yes Close to Depends on the initial value and could be slow for large system. Might be slow for large system. Medium Easy 42

55 Chapter 4 Hierarchical Decentralized Network Reconfiguration Study Traditional distribution systems are designed for unidirectional power flow with very limited dynamics. Distributed generation, energy storage and plug-in electric vehicles are being integrated into the grid and all these will bring more dynamics, uncertainties and stochastic behaviors into distribution systems. Reconfiguring such new, dynamic distribution networks with high efficiency and reliability will be very challenging. Three methods are proposed in Chapter III, and they can solve the reconfiguration problem successfully. However, all these methods are implemented in a centralized manner and the burden of excessive computational complexity is inevitable. Past research on power systems has considered a variety of decentralized approaches [67], [68], [69], [70]. Further, multi-agent systems have been used in power system studies in order to deal with the problems of complexity and large-scale distribution systems [71], [72], [73]. A proximal message passing method was presented to solve security constrained optimum power flow by Chakrabarti et al. [74], and it can minimize the cost of operation of all devices, over a given time horizon, across all scenarios subject to all constraints. Inspired by past work, a hierarchical decentralized methodology for network reconfiguration is proposed in this chapter, which decomposes the network into subnetworks within a multi-agent architecture where agents are responsible for the reconfigurations of sub-networks based on the two-stage operating principle. It can help reduce operational and computational difficulties because local control agents are responsible for collecting local information and for controlling local switches. 43

56 Simultaneous computations of various agents are used for reconfiguring the decomposed systems, and thus the total computation time is greatly reduced compared with centralized methods. Because real-time information exchange is necessary, this scheme will require the deployment of appropriate sensor and communication networks. In order to explain the proposed hierarchical decentralized approach, a standard 118- bus distribution system [42] is used as the example, and its initial topology is shown as Fig TS TS TS TS-11 1-substation TS TS TS TS-8 38 TS Figure bus radial distribution system. 3 TS TS TS-1 TS-4 TS TS Decentralized Structure A loop is defined by the closing of an initially opened tie-switch and other initially closed sectionalizing switches. The loops defined in the manner are easily recognized and are unique regardless of switching operations. Fifteen loops (loop 1 ~loop 15 ) exist in the 118-bus system and Table 4.1 shows the buses included in each loop. These fifteen loops cannot be solved totally independently because they share common branches and the status of the same switch states solved in different loops can be different. A feasible approach is to decompose the entire system into several 44

57 relatively independent clusters in which highly dependent loops are studied together. Table 4.1 Fifteen Loops and Associated Buses in the 118-bus System Loop No. Buses included in the loop 1 2,4,5,6,7,8,24,23,22,21,20,19,18,11, ,12,13,14,15,16,17,27,26,25,24,23,22,21,20,19,18 3 2,10,11,18,19,20,21,22,23,24,25,26,27,52,51,50,49,48,47,46, 45,44,29,28,4 4 2,10,11,18,19,20,21,22,23,24,25,35,34,33,32,31,30,29,28,4 5 4,5,6,7,8,9,46,45,44,29, ,30,31,32,33,34,35,36,37,38,39,40,41,42,43,49,48,47,46,45, ,30,53,54,62,61,60,59,58,57,56, ,30,31,32,33,34,35,36,37,38,62,61,60,59,58,57,56,55 9 1,2,4,28,29,55,56,57,58,96,91,90,89,65,64, ,66,67,68,69,70,71,72,73,74,75,76,77,99,98,97,96,91,90, ,66,67,68,69,70,71,72,91,90, ,65,66,67,68,69,70,71,72,73,74,75,88,87,86,79, ,63,64,78,79,86,105,104,103,102,101, ,63,64,78,79,80,81,82,83,108,107,106,105,104, 103,102,101, ,101,102,103,104,105,106,107,108,109,110,118,117,116,115,114 In order to facilitate differentiating the tightly connected and loosely connected areas, the notion of connectivity degree of two areas is defined: Total number of the common buses D(A,B) = min total number of buses in A,total number of buses in B ( ) (4.1) If D(A,B) = 0, areas A and B are relatively independent. For a given threshold δ, if D(A,B) δ, A and B are loosely connected and if D(A,B) > δ, A and B are tightly connected. If δ is small, very few loosely connected areas will be identified, and if δ is large the number of loosely connected areas can be over-estimated. For the sake of illustration, 0.2 is chosen as the threshold value. A systematic procedure for decomposing the system using the cut vertex set concept, similar to the cut set in graph theory, is described next. A cut vertex set of the connected graph G=(V, E) is a vertex set U ÍV such that (a) G-U (remove all the vertices in U and delete all related edges connecting the vertices in U) is not connected, and 45

58 (b) G-K is connected whenever K U, and (c) Each vertex u in U is connected with at least one vertex in each component of G- U in graph G. Specially, a cut vertex set is a cut vertex if only one vertex exists in the cut vertex set. Then, the procedure consists of (1) Obtain the modified adjacency matrix C. Let m be the amount of loops. The modified adjacency matrix is a m-by-m matrix where the ij-th element is D(loop i, loop j ). (2) If there are separate areas that have no common buses except for the source node of the system, these areas are named as fundamental decomposed zones. The tie-switches between two fundamental decomposed zones are their connections. The steps that follow are conducted for all fundamental decomposed zones, respectively. (3) Draw the graph. In the graph G=(V,E), the vertices V ={v 1,,v n } represent loops 1~n, and the edges E connecting the vertices indicate the loops are coupled. Draw vertices to represent all the loops in the studied zone. Add an edge connecting v i and v j if C(i, j) is not zero. If loop i and loop j are loosely connected, write L on the edge. Otherwise, write T on the edge. (4) Check whether the graph G is connected. If not, find the isolated vertices, denoted by S. The corresponding loops for the isolated vertices consist of the first members of decomposed systems. (5) Determine the cut vertex sets of G-S. Start the search from the first vertex (parent) and look for the cut vertex set from all the vertices (child) that are incident to the parent node. If the cut vertex set is empty, turn to the vertices incident to the child nodes to search. If a cut vertex set is found, delete the cut vertex set and related edges defines two 46

59 separate components. Continue to find the cut vertex sets for each component until no more cut vertex sets exist. The separate components represent the decomposed systems, and the tie-switches corresponding to the cut vertex sets represent the connections among the decomposed systems. (6) Obtain additional decomposed systems based on the components obtained in (5). If two vertices are connected with an edge labeled by L, their corresponding loops are decomposed into two subsystems. If two loosely connected vertices are tightly connecting with another vertex, the corresponding tie-switch of this vertex is the interconnection between two subsystems. If all vertices in a component are tightly connected, no extra decomposition is needed. (7) Arrange all decomposed systems layer by layer such that the upper layers include the lower layers. Consider the 118-bus system, three fundamental decomposed zones are divided: zone- 1 including tie-switches 1~8, zone-2 including tie-switches 10~12, and zone-3 including tie-switch 15. The former two zones are connected by tie-switch 9, and the latter two are connected by tie-switches 13 and 14. Each zone is further decomposed according to the above steps (3)~(6). Zone-1, studied as the example, includes loops 1~8 and its graph G 1 is connected, as shown in Fig The cut vertex set U 1 is {3,4,5} and the two induced components of G 1 -U 1 are given in Fig Then, cluster-i comprising loop 1 ~loop 2 and cluster-ii comprising loop 6 ~loop 8 are thus decomposed. Tie-switches 3~5 are the connections between two clusters and if they are initially open, these two clusters are independent of each other. According to step (6), the first component in Fig. 4.3 cannot be separated. In the second component, vertices 6 and 7 are loosely connected so cluster- 47

60 II can be decomposed further into two subsystems - loop 6 and loop 7, which are related by tie-switch 8. Similarly, the graphs of zone-2 and zone-3 can be obtained and both are not separable, so zone-2 and zone-3 cannot be decomposed further. Finally, after arranging the decomposed systems layer by layer, the 118-bus system is decomposed into hierarchical layers with multiple systems as shown in Table T T T T 2 T 3 T 4 L 5 T T T T L T 6 L 7 T 8 Figure 4.2 The graph for zone-1. 1 T L T T T 2 T Figure 4.3 Components of G 1 -U 1. Table 4.2 Decentralized Structure for the 118-bus System Layer bus distribution system (Buses 1~62) *2 (Buses 1,63~99) (Buses 1,100~118) Zone-1 9 Zone-2 Layer-1 Zone-3 *1 tie-switches tie-switches 13,14 1~8 10~12 tie-switch 15 (Buses 1~28) Layer-2 System-1 3,4,5 (Buses 29~62) System-2 tie-switches tie-switches 1,2 6~8 (Buses (Buses 29,30, 29~52) 53~62) Layer-3 Sub-1 8 Sub-2 tie-switch 6 tie-switch 7 *1- The tie-switches included in its zone/system *2- The tie-switches shared by two zones/system When decomposing the system, interconnecting lines are disconnected and fictitious loads and fictitious generators representing power flows through the interconnecting lines, as depicted in Fig. 4.4, are used for the analysis. The fictitious load is the accumulation of all the loads supplied by the interconnecting line. The bus connecting to the fictitious 48

61 generator is a slack bus with voltage = 1.0 p.u.. This paper aims at finding the optimal configuration with the minimal power losses, and although bus voltages can affect the value of the power losses they cannot change the optimality of the configuration, so using a slack bus is appropriate. Fictitious Generator P, Q P, Q Fictitious Load Figure 4.4 Decomposition with fictitious loads and fictitious generators representing power flows through the interconnecting lines. 4.2 Operational Rules The principle for solving the optimization problem is from small to large: first solve the optimization problem for the lowest layer and then proceed to higher layers. This is because the switch states solved in the lower layer are used as fixed values in higher layers. At each layer, two stages are defined and each stage is essentially a reconfiguration problem, so any of three proposed method including heuristic method, hybrid method and GA could be used to solve each optimization problem. Because the heuristic method has best computational efficiency, it is used in the decentralized approach so that more computation time could be saved. Stage-1: Begin from the lowest layer. Keep the switch states of all the tie-switches shared by two of the subsystems at their initial values (=0). Solve the following optimization problems individually to acquire the states of switches (S i ) that are exclusive to each subsystem. 49

62 min min f 1 iswitch set only in subsystem1 f T g S g S iswitch set only in subsystemt (4.2) where, f 1, f 2,, f T are respectively the problem formulations in (3.16) for subsystem 1, 2,, T. Stage-2: Let the solutions of (4.2) be S , S 1 k, solve for the states of the shared tieswitches using (4.3). Record the results of all switch states, and use these as fixed (constant) values for the upper layer. min f =g(s jshared tie-switch set, S i =1,2,...,k = S 1 i ) (4.3) where f is the formulation given in (3.16) and two subsystems with interconnections in the same layer are treated together, and S j is the state of tie-switch j shared by two subsystems. Considering the 118-bus distribution system, the entire operation consists of ten procedures to finish all layers, as shown in Fig The exact load flow result is obtained at procedure 10. Procedures 1 ~ 5 can be solved simultaneously by different computational agents, and 8 can be solved simultaneously with Hence the entire computing time is t decentralized = max(t 1,T 2,T 3,T 4,T 5 ) + max(t 8, T 6 +T 7 +T 9 ) + T 10 provided that the communication among agents is negligible. If the system is reconfigured in a centralized manner, the necessary computing time depends on the iteration times which will certainly be larger than the sum of T 1 ~T 10. Thus, t decentralized is always smaller than the computational time of the centralized method. In summary, the entire network reconfiguration is realized by combining parallel computations 50

63 implemented simultaneously and hierarchical computations taken sequentially. Due to the simultaneous operations of multiple agents, the overall operation time can be greatly reduced. 10 Optimal Configuration for 118-bus distribution system 8 Reconfigure Loop 13,14 9 Reconfigure Loop 9 7 Reconfigure Loops 3, 4, 5 6 Reconfigure Loop-8 Reconfigure Reconfigure Reconfigure Reconfigure Reconfigure Loop -15 Loops 10,11,12 Loops 1, 2 Loop-6 Loop Figure 4.5 Operation procedures for the 118-bus distribution system. 4.3 Multi-Agent Technique Network reconfiguration problem is solved in a decentralized manner with the decomposed sub-problems given in (4.2) and (4.3). Separate agents, organized in a hierarchical structure, are assigned to the sub-problems and parallel computations are implemented. Fig. 4.6 shows the framework of two intelligent agents. Each agent is composed of three units: data unit that collects its local information and communicates with other agents, computation unit that implements the heuristic algorithm given in Chapter III to solve the local reconfiguration problem, and the decision unit for control/coordination. The computational results of the lower-layer agents are sent to the data units of the agents in the upper-layer. The final optimal configuration is decided based on collaboration/coordination among the multiple agents. 51

64 Figure 4.6 The framework of two intelligent agents. Communication and coordination among agents are of great importance. For the decomposed systems at different layers in the same fundamental decomposed zone, the communication between agents involves sending switch states from the lower-layer system and no coordination is needed. However, agents within the same layer affect each other in the form of fictitious loads. Denoting these two systems as I and II, there are two different scenarios: (1) I and II are relatively uncoupled. Thus the structure of II has no effect on the fictitious load in I, and vice versa. The constant fictitious load is the sum of loads that are supplied by the initial interconnecting line. Any two of zone-1, zone-2 and zone-3 in Table II are examples of such systems, and system-1 and system-2 are as well. Thus, each agent of these two systems obtains the value of the constant fictitious load from another agent in the beginning, but no coordination is needed. (2) I and II share branches/buses in common, i.e. the connectivity degree is nonzero. In this scenario, various structures of II alter the values of fictitious loads in I and vice versa. 52

65 Sub-1(loop 6 ) and sub-2(loop 7 ) in Table II are examples of such systems. Coordination between agents is indispensable and the coordination strategy is presented in Fig Local Information The relation between fictitious loads and switch states in agent II. Local Information The relation between fictitious loads and switch states in agent I. flag1 Agent-II Data Unit flag2 Agent-I Data Unit S(I)k S(II)k flag1 flag2 S(I)k S(II)k S(I)k Computation Unit S(I)k S(II)k Computation Unit flag2 Stop2 flag1 S(I)0 S(II)init S(II)0 S(I)init S(I)k+1 S(II)k S(min)=S(max)? NO k=k+1 S(I)k+1 S(II)k = S(I)k? NO Stop2=1 S(I)k+1 S(II)k=S(I)1~k-1? S(min)=S(max)? YES YES NO Stop2=1? Stop2=2? flag2=1 flag2=0 YES NO flag1=1 flag1=0 YES Done. YES flag1 flag2 =1? NO NO Done. S(II)final = S(II)k-1 Stop2=2 YES Done. flag1 flag2=1? YES S(II)final=S(II)k S(I)final = S(I)k+1 Done. S(II)final = S(II)0 Done. S(I)final = S(I)k YES Done. S(I)final = S(I)0 Decision Unit Decision Unit k = 0, S(I)k = 0, S(II)K = S(II)init, S(I)k+1 S(II)K = S(I)0 Figure 4.7 Coordination between two agents. 53

66 (2.a) In the beginning, the maximal, minimal and initial values of the fictitious loads in I and II are computed based on the relationship between fictitious loads and switch states. Then, the optimal switch states of each system are solved independently, given that the fictitious load is maximal, minimal and at the initial value respectively, and the results are denoted as S(max), S(min) and S 0. If S(max) = S(min), it means that the optimal result is independent of values of the fictitious load. This condition is checked in the decision unit in each agent, and if true, no further coordination is needed and the optimal solution of each agent is the value of S(max), S(min) or S 0 (S(max)=S(min)=S 0 ). The grey lines with arrows represent the inputs and outputs used in the above procedure. (2.b) If any of the two conditions is false, coordination is activated. During coordination, the agent for the system with more loads is the master agent (agent-i) and the other is the slave agent (agent-ii). S(X) k denotes the solution of switch states for agent-x at the k th iteration. S(X) i S(Y) j denotes the solution of switch states for agent-x computed at the i th iteration given that the switch states in agent-y is S(Y) j. The first iteration starts with the master agent. Let k=0, S(I) 0 =0, S(II) 0 =initial switch states of II, and thus S(I) k+1 S(II) k is the value of S 0 solved by agent-i in (2.a). Then, let k=k+1 and send new S(I) k to the data unit that will communicate with the data unit in agent-ii. Thus iteration in the master agent is finished, and the inputs/outputs are denoted by dash dot lines. (2.c) With the new value of S(I) k, the fictitious load in agent-ii is updated, and the optimal switch states for area II are determined by the computation unit. The result is denoted by S(II) k S(I) k, which is sent to agent-i via the communication channel between 54

67 two data units. Dashed lines with arrows represent the inputs and outputs in the slave agent. (2.d) The iteration repeats by computing S(I) k+1 based on the new fictitious load calculated using S(II) k. The stopping criterion that S(I) k+1 is same as the results of S(I) obtained in the former iterations is checked in the master agent, and if it is true, a stopping signal stop 2 is sent to agent-2 via the communications channel between data units. There are two different scenarios: 1) if S(I) k+1 =S(I) k, the final solutions for agent-i and agent-ii are respectively S(I) k+1 and S(II) k, and both agents achieve optimality. 2) if S(I) k+1 is the same as former results, additional iteration will cause endless loops. Thus we choose the final solutions as S(I) k and S(II) k-1 in order to make sure the master agent is optimal. Note, coordination occurs between the agents of the two decomposed systems, corresponding to stage-1, and a third agent is responsible for solving the stage-2 problem after receiving the coordinated results from agents I and II. 4.4 Dynamic Network Reconfiguration Renewable energy resources, energy storage and plug-in electric vehicles are being integrated into the power grid, and they will play important roles at both transmission and distribution levels. Many renewable energy resources, such as wind and solar, depend on environmental conditions, and their power generations are intermittent. The increasing penetration level of plug-in electric vehicles will add more uncertainties on the system operation. All these changes lead to more stochastic behaviors and dynamics happened in distribution systems, and it is necessary to alter system topology from time to time so that the grid could respond to changes and the system operation could be improved. Thus, in response to time-varying loads, fluctuating generation of renewable energy resources and 55

68 unexpected situations (such as faults), the application of dynamic network reconfiguration is proposed, and its framework is shown as Fig Read the Realtime System Data T0+ T Use the proposed decentralized approach to solve the reconfiguration problem. T0 Plan-0 Read the Real-time System Data Check whether there are changes: if so, activate the lowest-layer agent and resolve the optimization problem. If the result is different from the last time window, activate the upper-layer agent. Figure 4.8 Framework of dynamic network reconfiguration. Let the starting time be T 0 and the operating period be ΔT, and the decentralized network reconfiguration algorithm is conducted based on the operating data at the beginning of each operating window. At T 0, the optimal switching plan is solved using the proposed hierarchical decentralized approach, and the studied distribution network is thus reconfigured and this new topology is kept same for the remaining time in the current operation period. At T 0 + ΔT, the new operation period starts, and the real-time system data is collected again and also compared with former data to check whether changes occur. If there are no changes, the reconfiguration is not needed so the system topology is kept same until next time window arrives. Instead, if there are changes, the lowest-layer agent corresponding to the subsystem where the change happens is activated, and its computation unit resolves the local optimization problem. If the solution is same as the former operation period, the happened changes do not alter the optimal system topology, so there is no need to reconfigure the network. Otherwise, the new solution is transmitted to the corresponding upper-layer agents where the reconfiguration problems are resolved. Finally, the new switching plan is obtained, and the distribution network 56

69 will be reconfigured again and the new topology is kept consistent until the next period arrives. Further, in order to avoid neglecting important changes in the system, a time-ahead planning approach is implemented in the agents of the lowest-layer systems. At the midpoint of each operating period, the data units of the lowest-layer agents get data from their local systems. If there have been no changes, all agents wait for the next operation period to begin. Otherwise, any agent that detects important changes in its local load power or DER generation levels activates its computation agent to resolve the reconfiguration problem based on the new data, and if the result is different, it will send the new result to its upper-layer agents to inform them to re-compute. After all agents complete their work, the distribution network is reconfigured based on new switch states and the current time becomes the new starting point for the following period T. Fig. 4.9 shows the implementation of the dynamic network reconfiguration with time-ahead planning. At T 1, the dynamic network reconfiguration for the system with new optimal topology is rescheduled. There is a small time lag of t between T 1 and the time when changes are detected, which is the time required for executing the hierarchical decentralized reconfiguration. Initially Planned Operation 0 0.5T Important T changes detected 1.5T and the problem 2T solution is 2.5T 3T differnt... nt Enable upperlayer agents to re-compute the optimal switch states New Planned Operation t T 1 T 1 +T T 1 +2T Figure 4.9 Dynamic network reconfiguration with time-ahead planning. 57

70 If a fault occurs in the system, the agent of the subsystem where the fault is located removes the affected buses/ branches/ loads from its system information before reevaluating the optimal system topology. After the fault is cleared, the agent will detect the change at the beginning of the next planning period, and then resolve the problem by revising the system information. 4.5 Case Study The proposed hierarchical decentralized network reconfiguration approach is applied to three test systems: 69-bus distribution system, 118-bus distribution system and 216-bus distribution system. The simulations are conducted on a computer with the Intel 2.53 GHz processor and 3 GB RAM. Despite of the application of decentralized method, simulation results obtained by using two centralized approaches are also given to compare the performance of different methods. These two centralized approaches are the heuristic algorithm based on branch-exchange and single-loop optimization proposed in Chapter III and the harmony search algorithm (HSA). HSA is recently introduced to solve distribution network reconfiguration problems and its performance is proved to be better that GA and Tabu search in [51], so it is chosen to compare with the proposed hierarchical decentralized approach. At first, a simulation system, shown in Fig. 4.10, is implemented using Matlab/Simulink in order to demonstrate the hierarchical, decentralized reconfiguration approach. The demonstration system consists of the distribution system being studied and includes distributed control agents. The distribution system is modeled using Simulink elements, and each branch includes a R-L line and an initially closed switch. Distributed agents control the switches in their own subsystems remotely, based on the switch state 58

71 results obtained by computational units. Each block with the dashed-line rectangular frame represents an agent modeled using S-Functions [75], which includes a data unit (orange block), computational unit (blue block) and decision unit (grey block). Figure 4.10 The demonstration system built using MATLAB. 59

72 The operation of multiple agents is guided by the operational rules for the decentralized approach. All the computational agents are initially disabled and enabled when reconfiguration is required. The first input to the data unit of each agent is the enable (1) or disable (0) signal. Each computational unit or decision unit has two outputs: the first output is the switch to be opened obtained from the heuristic algorithm that is written to a data file for access by upper-layer agents, and the second output is the signal used to enable/disable upper-layer agents. The demo system is a general computational utility that can be used to reconfigure the network structure of any distribution system by changing the model and updating the system information. The 118-bus system has control agents 1~10 that implement the procedures 2, 3, 1, 6, 7, 4, 5, 9, 8, 10 given in Fig. 4.5, respectively. Coordination is only required for agents 1 and 2, so decision units are only modeled for these two agents. Agents 1, 2, 3, 6, 7 are associated with lowest-layer systems in the three fundamental decomposed zones, and are enabled immediately by setting their first inputs to 1 when reconfiguration is needed. The enable signals in agents 1 and 2 are both transmitted to agent 4 to initiate procedure- 6 based on the switch states determined by the lower-layer agents. The outputs from agents 3 and 4 are transmitted to agent 5 to activate the higher-level computation. Outputs from agents 6, 7 and 5 are then transmitted to agents 8 and 9 to compute the final switch states. Agent 10 then calculates the load flow results for the entire system, and the two outputs are displayed. The first output is all the opened switches, which are sent to the distribution system so that the network structure is changed appropriately, and the second output is the minimal power loss. 60

73 To simulate the dynamic network reconfiguration, periodic pulse signals are used as the inputs to the data units of the lowest-layer agents and the second input to the data unit of each upper-layer agent. For the upper-layer agents, the period of the pulse signals is the operating period scheduled for the dynamic network reconfiguration. For the lowestlayer agents, the period of the pulse signals is half the operating period because timeahead planning is done in the lowest-layer agents at the mid-point of each operating window Case I : 118-Bus Test System Fig. 4.1 has given the topology of 118-bus test system, and Total loads are kw and kvar. For the initial network, the minimum voltage is pu at bus 77, which is well beyond the recommended range (5% deviation from the nominal value). Total power losses are kw, 5.7% of the total load power. The parameters used in HSA include harmony memory (HM), harmony memory size (HMS), harmony memory considering rate (HMCR), pitch adjusting rate (PAR) and the number of improvisations (NI). In the following case studies, these parameters are given as: HMS = 10, NI = 250, HMCR=0.85 and PAR=0.3. The results of the hierarchical decentralized approach, centralized approach and HSA are shown in Table 4.3. The power loss reduction of the decentralized approach is 1.3% less than the centralized approach and 2.7% more than HSA. The computing time of the decentralized approach is 28.5% of the computing time needed for the centralized approach and only 1.33% of the computing time needed for HSA. Table 4.3 Simulation Results of 118-Bus System Proposed Decentralized Centralized HSA Approach Approach Open Switches 21, 25, 48, 32, 45, 40, 60, 23, 26, 48, 34, 45, 40, 23, 25, 50, TS-4, 44, 61

74 37, TS-9, 76, 71, 73, TS- 13, 82, , TS-8, 95, 97, 71, 74, TS-13, TS-14, , 61, 37, TS-9, 97, 70, 73, TS-13, 82, 109 Power Loss Reduction 31.4 % 32.7 % 28.7 % Minimum Voltage pu pu 0.93 pu Voltages 0.95 pu 88 buses 104 buses 84 buses CPU Time 3.2 s 7.82 s s When reconfiguring the network using the decentralized approach, the coordination between agents 1 and 2 results in both agents obtaining the true optimal results. The demonstration system is used to simulate the decentralized reconfiguration process, and the results for different switch states are observable from green blocks in Fig The solver is discrete with fixed step size s and the simulation time is set to be s. The total computation time required is 5.3 seconds. If only one agent is used to reconfigure the distribution system, i.e. using the centralized approach, the total computation time is 29.5 s, or about 5.6 times that of the decentralized approach. The results of nodal voltages for the initial network, the centralized method, HSA and the hierarchical decentralized method are compared in Fig Most voltages are increased after reconfiguration, especially for buses 29~43, 65~77 and 101~113. Fig compares the power losses distributed at 132 branches before and after reconfiguration. It is observed that the power losses at branches 29~38, 64~69 and 100~109 are reduced greatly after reconfiguration. Power losses at branches 113~132 are increased instead, which is due to the closure of TS-15 and the loads at buses 110~113 being transferred to the feeder However, even though the power losses for some branches are increased, the total power losses are significantly reduced after reconfiguration. 62

75 p.u Initial System Centralized Approach HSA Approach Bus Number Figure 4.11 Node voltages of the 118-bus system before and after reconfiguration. Figure 4.12 Power losses in the 118-bus system before and after reconfiguration. 63

76 4.5.2 Case II : 69-Bus Test System Figure 4.13 Single-line diagram of the 69-bus test system. Fig shows the single-line diagram of a 69-bus test system, and system data can refer to [76]. There are five tie-switches in total, and total load powers are kw and kvar. For the initial topology, system power losses are kw and the minimum voltage is 0.91 pu. Fig gives the structure of the decomposed subsystems and the hierarchical arrangement of the computational agents. The results of decentralized approach, centralized approach and HSA are given in Table 4.4. The centralized and HSA approaches both reduce the power losses to kw, but HSA needs 5.8 s more time 64

77 than the centralized approach. For the decentralized approach proposed, final power losses are 108 kw and the computation time is the least. 69- Bus Distribution System Layer-0 Layer-1 Buses 1~46, 51, Buses 4~9, 52, 66~69 47~50, 53~65 TS-5 System-1 System-2 (Tie-switches 1~3) (Tie-switch 4) Layer-2 Decomposed Subsystems Buses 1~11, 28~46, 51, 52, 66, 67 System-1.1 (Tie-switch 1) TS-3 Buses 12~27, 68, 69 System-1.2 (Tie-switch 2) Hierarchical Computation Agents 5 Agent-5 Whether close TS-5? 4 Agent-4 Whether close TS-3? 1 Agent-1 2 Agent-2 3 Agent-3 Reconfigure 1.1 Reconfigure 1.2 Reconfigure 2 Negotiate to Coordinate the Results Figure 4.14 Decomposed systems and hierarchical agents for the 69-bus system. Table 4.4 Simulation Results of 69-Bus System Decentralized Approach Centralized Approach HSA Opened Switches 10, 17, 12, 58, 63 69, 70, 14, 58, 61 69, 70, 14, 58, 61 Power Loss Reduction 52 % 56.2 % 56.2 % Minimum Voltage pu 0.95 pu 0.95 pu Voltages 0.95 pu 67 buses 69 buses 69 buses CPU Time 0.39 s 0.5 s 6.3 s 65

78 4.5.3 Case III : 216-Bus Test System Figure 4.15 Single-line diagram of the 216-bus test system Fig shows the single-line diagram of a 216-bus system with 25 tie-switches. This system is constructed by enlarging the system given in [77]. Nominal voltage is 20 kv and total load is MW and MVar. For the initial network structure, total power losses are kw and the minimum node voltage is p.u. at bus 143. Based on the cut-vertex set concept, the 216-bus test system is decomposed into multiple subsystems, illustrated as Fig Table 4.5 gives the results obtained using the three methods. It shows that the power loss reduction of the decentralized approach is 4.2% less than the centralized approach and 8.8% more than HSA. The computation time of the decentralized approach is only 6.14% of the computational time of the centralized 66

79 approach and 0.45% that of HSA. Besides, the voltage results for the initial network, the centralized method, HSA and the hierarchical decentralized method are given in Fig It shows that system voltage magnitudes have increased a lot after the reconfiguration for all three methods. Layer bus distribution system Layer-1 (Buses 1~65) Zone-1 TS 1~7 TS 22~23 (Buses 1, 66~148) Zone-2 TS 24~25 TS 8~16 (Buses 1, 149~216) Zone-3 TS 17~21 Layer-2 (Buses 1~36) System-1 TS 1~3 TS-4 (Buses 37~65) System-2 TS 5~7 (Buses 1,66~97) System-3 TS 8~10 (Buses 98~148) System-4 TS 11~16 Layer-3 (Buses 1~10, 19,33~36) System-1.1 TS-1 TS-2 (Buses 11~18, 20~32) System-1.2 TS-3 (Buses 37~44, 54~57) System-2.1 TS-5 (Buses 45~53, 58~65) System-2.2 TS 6~7 (Buses 98~126) System-4.1 TS 11~14 (Buses 127~148) System-4.2 TS 15~16 Layer-4 (Buses 98~104,110~112) System TS-11 (Buses 105~109, 113~126) System TS 12~14 (Buses 127~135, 145~148) System TS-15 (Buses 136~144) System TS-16 Layer-5 (Buses 105~109, 113~118) System TS-13 TS-12 (Buses 119~126) System TS 14 Figure 4.16 Decomposed systems for the 216-bus system. Open Switches Power Loss Reduction Minimum Voltage Voltages 0.95 pu Table 4.5 Simulation Results of 216-Bus System Decentralized Approach Centralized Approach HSA 43, 49, 51, 9, TS-3, 22, TS-4, 87, 83, TS-14, 116, 122, 111, 134, 141, TS-9, 207, 210, 161, TS-21, TS-19, 118, 81, 144, 130 9, 22, 23, TS-4, 43, 51, 49, 83, TS-9, 87, 111, 121, 117, TS-14, 134, 141, 207, 171, 167, 160, TS-21, TS- 22, TS-23, 144, 129 8, 26, 25, 52, 42, 50, TS-7, TS-8, TS-9, 86, 109, TS-12, 116, 122, 134, 140, 207, TS- 18, 165, 159, TS-21, 118, 81,147, % 39.6% 26.6% 0.92 pu pu 0.90 pu 165 buses 173 buses 148 buses CPU Time s 33.7 s 477 s 67

80 Figure 4.17 Voltage results of the 216-bus system before and after the reconfiguration Result Discussion and Remark (1) System Improvement and Optimal Result According to the simulation results of 69-bus system, 118-bus system and 216-bus system, both the proposed decentralized approach and two other approaches can reduce power losses. The power loss reductions and voltage improvements made by the hierarchical decentralized approach are always very close to those made by the centralized approach with less than 5% difference. The performance of HSA is quite different for the different test systems, and the solution of HSA can deviate considerably from the solutions of the decentralized and centralized approaches depending on the choices of initial HM parameters and the number of allowed improvisations. It is remarkable that preference to the hierarchical decentralized approach increases with the size of the system, indicating that our proposed approach have significant potential for applications. The heuristic approach cannot guarantee global optimality of a solution even in a centralized implementation, and can only ensure that a solution is optimal during the operation of a given loop. For the decentralized method, each decomposed system is reconfigured using the heuristic approach based on a two-stage methodology, and the 68

81 solution obtained for each system is locally optimal, not necessarily globally optimal. Also, the agents for the decomposed systems only have local information, so it is not possible to achieve the same solution as the centralized method without information about the rest of the system. However, each decomposed system reduces the local power losses, and these solutions are optimal for each decomposed sub-network. Further, the hierarchical decentralized approach has the best numerical stability compared with two other methods. Because the buses involved in the computation for each subsystem are quite few, the occurrence of infeasible solutions is reduced and also the convergence speed is greatly increased. (2) Computation Time The hierarchical decentralized approach can have significant computational time advantages, particularly as the size of the system increases. The proposed decentralized approach uses system decomposition to reduce the total number of iterations and the order of the matrices formed at each iteration, which results in reductions in the computational time. In the 118-bus system, the orders of the matrices for the centralized and HSA approaches are 132, and the load flow is solved 143 times in the centralized approach. However, for the decentralized approach, the order of the matrix for each subproblem is only around 10~20, and the most the load flow needs to be computed is only 15 iterations. For the 216-bus system, the reduction is even greater. Although multiple iterations might occur because of the coordination between agents, the computation time of each agent is quite short. The largest computing time of all agents in the 118-bus system is 2.76s, with the smallest only 0.343s. The longest and shortest computing time for the 216-bus system is respectively 4.715s and 0.095s. Further, 69

82 because multiple agents are processing in parallel, the final computational time of the decentralized approach is not the sum of the computational times of all agents, but instead depends on the maximal computing time of all the agents in the same layer. As a result, the computational time for the decentralized approach is much shorter than the other approaches. Besides, although multiple agents are cooperating to solve the problem, the data that need to be exchanged among agents are restricted to the switch states. Thus with limited data being exchanged, the time needed for transferring data is small compared to the computational time. (3) Simulation Environment All algorithms and the demo system are developed using Matlab and Simulink. The implementation of the proposed decentralized network reconfiguration on real distribution systems will need much more effort other than developing new approaches. At present, a demo system built using Matlab is mainly used to illustrate how the decentralized approach is developed and conducted. The hierarchical decentralized reconfiguration approach will be definitely demonstrated using an agent-based software platform. Besides, in the future, this approach will be test using hardware in the loop simulation (HILS) and then finally implemented in hardware using a laboratory demonstration system [78] available at Case Western Reserve University. (4) Remark Based on the simulation results provided, it can be concluded that the computational time of HSA and centralized approach for reconfiguring larger systems will increase significantly, and hence these centralized algorithms might become infeasible for real applications if the system scale is large enough. Instead, the proposed decentralized 70

83 0:00 1 h 2 h 3 h 4 h 5 h 6 h 7 h 8 h 9 h 10 h 11 h 12 h 13 h 14 h 15 h 16 h 17 h 18 h 19 h 20 h 21 h 22 h 23 h p.u. approach has no such drawback. Although currently there is no explicit time limitation for network reconfiguration, as we move to modernization of the distributions system with more complex network topologies that include DER, demand response, etc. with a focus on increasing the reliability, resiliency, and efficiency of the system, reconfiguration approaches with fast computing capability will be necessary to achieve the desired levels of real-time operation and automation Dynamic Network Reconfiguration Taking the 118-bus distribution system as the example, dynamic network reconfiguration is implemented using the demonstration system to study the impacts of time-varying loads, fluctuating generation from distributed energy resources and permanent faults on the optimal topology. As shown in Fig. 4.18, ten groups of load profiles are extracted from load measurements of different areas on the same day. Each load shape covers 24 hours and the time interval between two points is 15-min. The per unit values are obtained by dividing the instantaneous power by the maximal value in each load group. In order to simulate time-varying loads, each load in the 118-bus system is selected from ten shapes randomly, with actual instantaneous power computed as the product of the initial value and the per unit value at the current time Time Figure 4.18 Ten load shapes. 71

84 The effects of distributed energy resources are studied by integrating six photovoltaic (PV) generation units into the grid. Each PV unit is of same type and its simulation model will be explained in the next chapter. The maximal PV output power is kw at the reference condition when the temperature is 298 K and solar irradiance is 1000 W/m 2. Fig shows the profiles of hourly solar radiation and temperature for a 24 hour period based on ten years of measured data [79]. The corresponding PV output power for each hour is obtained as shown in Table 4.6. For the network reconfiguration study, distributed energy resources can be considered as time-varying negative loads. The placement and sizing of a DG unit affect the value of power losses, and Chapter VI will give detailed analysis about optimal placement and sizing plan. Here, we arbitrarily suppose six PV units are locating at buses 27, 43, 62, 76, 77, 113 respectively. Figure 4.19 Hourly solar radiation and temperature profiles. Table 4.6 Capacity of Each PV Unit During 24 Hour Period Time (h) 0~1 1~2 2~3 3~4 4~5 5~6 Capacity (kw) Time (h) 6~7 7~8 8~9 9~10 10~11 11~12 Capacity (kw) Time (h) 12~13 13~14 14~15 15~16 16~17 17~18 Capacity (kw)

85 Time (h) 18~19 19~20 20~21 21~22 22~23 23~24 Capacity (kw) Because only hourly PV power data is available, the operating period for the dynamic network reconfiguration is set to be 1 h and the starting point is at 0 h. The entire study time is 24 hours. Table 4.7 shows the simulation results of the final time windows adjusted after the time-ahead planning, the opened switches scheduled for each operating window and the minimal power losses calculated at the beginning of each operating window. The fifth column shows the power losses of the system without any reconfiguration operation. In order to verify the positive effects of the selected PV buses on reducing power losses, the power losses of the system without any reconfigurations are also computed for the case when PV units are connected to six randomly selected buses (25, 48, 61, 84, 95, 110), and the results are given in the sixth column. The comparison between the fifth and the six columns has proved that the power losses are reduced when the PV units are connected to the buses with the largest positive sensitivities. It has been shown previously that the computational time of the hierarchical decentralized network reconfiguration is relatively short, so the time lag between two operating windows isn't shown. It is seen that the operating window is first adjusted at t=0.5 h when the switch states solved by one lower-layer agent (agent-1) changes. The network is then reconfigured and 0.5 h becomes the starting time for the next operating window. Similarly, the operating windows are also adjusted at 1 h, 16.5 h and 17 h. During the entire 24-hour period, the system topology is changed at 0, 0.5 h, 1 h, 8 h, 9 h, 10 h, 12 h, 15 h, 16 h, 16.5 h, 17 h and 18 h. 73

86 Suppose the power losses for each hour are constant, the total energy losses for 24- hour period are kwh if no reconfiguration is implemented. If the dynamic network reconfiguration is implemented without time-ahead planning, the total energy losses are computed to be kwh for a 32.2% reduction, and total energy losses for dynamic reconfiguration with the time-ahead planning are only kwh for a 37.7% reduction. The simulation is implemented in Simulink, and 0.02 s is used to mimic an operating period, and the entire simulation time is 0.46 s for an entire day. It took 41 seconds to complete the simulation using decentralized reconfiguration, and more than 100 s using centralized reconfiguration. Table 4.7 Simulation Results of The Dynamic Reconfiguration Time Power Initial Power Opened Switches Window Losses (kw) Losses (kw) (kw) 0 Initial TS-1~TS ~0.5 h 21, TS-2, 48, TS-4, 45, 39, TS-7, TS-8, TS-9, 75, 71, , TS-13, TS-14, , TS-2, 49, 34, 45, 40, 2 0.5~1 h TS-7, TS-8, TS-9, 75, 71, , TS-13, TS-14, ~ 2 h 21, TS-2, 49, 34, 45, 40, TS-7, TS-8, TS-9, 76, 71, , TS-13, 82, ~3 h 21, TS-2, 49, 34, 45, 40, TS-7, TS-8, TS-9, 76, 71, , TS-13, 82, ~4 h 21, TS-2, 49, 34, 45, 40, TS-7, TS-8, TS-9, 76, 71, , TS-13, 82, ~5 h 21, TS-2, 49, 34, 45, 40, TS-7, TS-8, TS-9, 76, 71, , TS-13, 82, ~6 h 21, TS-2, 49, 34, 45, 40, TS-7, TS-8, TS-9, 76, 71, , TS-13, 82, ~7 h 21, TS-2, 49, 34, 45, 40, TS-7, TS-8, TS-9, 76, 71,

87 9 7~8 h 10 8~9 h 11 9~10 h 12 10~11 h 13 11~12 h 14 12~13 h 15 13~14 h 16 14~15 h 17 15~16 h 18 16~16.5 h ~17 h 20 17~18 h 21 18~19 h 22 19~20 h 23 20~21 h 24 21~22 h 73, TS-13, 82, , TS-2, 49, 34, 45, 40, TS-7, TS-8, TS-9, 76, 71, 73, TS-13, 82, , TS-2, 49, 34, 45, 40, TS-7, TS-8, 95, TS-10, 70, 72, TS-13, 82, , 15, 49, 34, 45, 40, TS- 7, TS-8, 95, TS-10, 70, 72, TS-13, 82, , 15, 49, 34, 45, 40, TS- 7, TS-8, 95, TS-10, 70, 73, TS-13, 82, , 15, 49, 34, 45, 40, TS- 7, TS-8, 95, TS-10, 70, 73, TS-13, 82, , 15, 49, 34, 45, 40, TS-7, TS-8, 95, TS-10, 70, 73, TS-13, 82, , 15, 49, 34, 45, 40, TS- 7, TS-8, 95, TS-10, 70, 73, TS-13, 82, , 15, 49, 34, 45, 40, TS- 7, TS-8, 95, TS-10, 70, 73, TS-13, 82, , 15, 49, 34, 45, 40, TS- 7, TS-8, 95, TS-10, 70, 72, TS-13, 82, , TS-2, 49, 34, 45, 40, TS-7, TS-8, 95, TS-10, 70, 72, TS-13, 82, , TS-2, 49, 34, 45, 41, TS-7, TS-8, 95, TS-10, 70, 73, TS-13, 82, , 26, 49, 34, 45, 41, TS- 7, TS-8, TS-9, TS-10, 71, 73, TS-13, 82, , 26, 49, 33, 45, 41, 59, 37, TS-9, TS-10, 71, 73, TS-13, 82, , 26, 49, 33, 45, 41, 59, 37, TS-9, TS-10, 71, 73, TS-13, 82, , 26, 49, 33, 45, 41, 59, 37, TS-9, TS-10, 71, 73, TS-13, 82, , 26, 49, 33, 45, 41, 59, 37, TS-9, TS-10, 71, 73,

88 25 22~23 h 26 23~24 h TS-13, 82, , 26, 49, 33, 45, 41, 59, 37, TS-9, TS-10, 71, 73, TS-13, 82, , 26, 49, 33, 45, 41, 59, 37, TS-9, TS-10, 71, 73, TS-13, 82, If a fault occurs in the system and is not cleared before the operating window arrives, the agent of the subsystem where the fault is located will detect the fault and the optimal system topology is re-computed. The procedure is as follows: 1) The computational unit starts to resolve the reconfiguration problem by first revising the system data to delete the infeasible buses/branches/loads affected by the fault. 2) Check whether DG units exist in the isolated areas. If not, go to step-3. Otherwise, the DG unit will work as a back-up energy resource for restoring the loads isolated during the outage. The principle for the load restoration is to maximize the restored loads as well as keep the power losses in the induced microgrid to be minimal using a the formulation as an optimization problem: min M N2 2 fmg w1 PL, i w2 Ii ri i1 i1 M N2 2 L, i i i DG,max i1 i1 s.. t P I r P (4.4) where N 2 is the amount of connected branches in the microgrid after restoration, M is the amount of restored loads in the microgrid, P L,i is the active power of the restored load i, w 1 and w 2 are weighting coefficients, and P DG,max is the maximum output power of the DG. Both P L,i and P DG,max are for the current time window. All voltages and currents after the restoration should be within acceptable operating limits. 76

89 3) This agent then reports to its upper-layer agents about the new switch states together with the infeasible branches so that re-computations in the upper-layer agents are activated to obtain the new switches that are to be opened. 4) Wait for next operating time or planning time, if the lowest-layer agent detects the fault has been cleared, it will add the deleted system information before resolving the optimization problem. All other agents are working normally to resolve their optimization problems. Fig shows the case where two faults occurred in the 118-bus system at times 6:15 and 14:30 respectively, and each fault is cleared after 1 hour. All other system information is the same as the former case, so the results of switch states for the periods 0~6.5 h and 16~24 h are the same as given in Table 4.7, and the results for other periods are given in Table 4.8. The optimal opened switches for the distribution system are solved for the two faults respectively. During the second fault, two time windows are split because the results of the optimal opened switches calculated at the planning time are different. 1-substation 2 Zone-3 64 Zone Fault Fault Figure 4.20 Two faults happened in the 118-bus system. 77

90 Before fault-1 occurs, the configuration is that tie-switch 6 is closed and branch is open, so buses 37~40 are isolated and no DG exists in the outage area when fault-1 occurs. On the contrary, buses 56~62 form a microgrid that includes a PV unit connected at bus-62 when fault-2 occurs. Thus the optimization problem (4.4) is solved for two windows with different load power and PV output power data, and the loads at buses 59~62 are restored. Time Window Table 4.8 Simulation Results When Fault Occurs Opened Switches Power Losses (kw) 6.5 ~ 7.5 h 21, TS-2, 48, 34, 45, 59, 95, 76, 71, 73, TS-13, 82, ~ 8 h 21, TS-2, 49, 34, 45, 40, TS-7, TS-8, TS-9, 76, 71, 73, TS-13, 82, ~ 14.5 h Same as table VI 14.5~15 h 20, 15, 49, 34, 45, 39, TS-10, 70, 73, TS-13, 82, Restore loads connecting at buses 59~62. 15~15.5 h 21,15, 48, 34, 45, 39, TS-10, 70, 72, TS-13, 82, Restore loads connecting at buses 59~ ~16 21, 15, 49, 34, 45, 40, TS-7, TS-8, 95, TS-10, 70, 72, TS-13, 82,

91 Chapter 5 Modeling and Primary Control for Distributed Generation Systems Wind power and solar power are two most important types of renewable energy. By the end of year 2013, wind power capacity has been over 60,000 MW and the installation PV capacity has been over 10 GW. Fuel cells also show great potential to be green power sources of the future because of many merits they have, such as high efficiency, zero or low pollution, and flexible modular structure. Micro-gas-turbine (MT) has been widely used in distributed generation and combined heat and power applications. Besides, energy storage device is extremely useful to cooperate with intermittent renewable energy. Super-capacitor, also known as ultra-capacitor, is widely used in many applications because of its high power density and ability to store and release power within short time periods. In order to study the performance of distributed energy resources and optimize their interactions with power grids, it is primarily necessary to develop appropriate mathematical models, controllers and conduct multiple scenario simulation tests. Considerable effort has gone into modeling energy generation sources and storage systems, but very often these models are simplified to reduce computational complexity for long-term simulation. However, for short-term dynamic simulation, detailed dynamic modeling of the energy resources, storage systems, power electronic devices, and controllers are required. 5.1 Wind Power Generation Unit Generally there are two types of wind energy conversion system including constant 79

92 speed system and variable speed system. Fig. 5.1(a) shows the configuration of a constant speed wind energy conversion system, in which the generator is a squirrel cage induction generator that is connected to the utility grid or load directly. Since the generator is directly coupled with the grid or load, the wind turbine rotates at a constant speed governed by the utility frequency and the number of poles of the generator. Fig. 5.1(b) and Fig. 5.1(c) show two different types of variable wind energy conversion system. In the former type, the permanent magnet synchronous machine is usually used as the generator, and it is directly connected with the power converter that is then connecting with load or grid. The latter one is a double-fed induction generator, and the rotor of the generator is fed by a back-to-back voltage source converter. The stator of the generator is directly connected load or grid. While the generator in the latter system is usually a permanent magnet synchronous machine, and it is directly connected with the power converter that is then connecting with load or grid. The variable-speed and pitchcontrolled double-fed wind energy system widely exist because it can convert wind energy with high efficiency, control both active and reactive power, reduce power fluctuations and generate high quality power [80], [81], [82]. Gear Box G Grid/ Load (a) Gear Box G (b) 80 Converter Grid/ Load

93 Gear Box DFIG Grid (c) Figure 5.1 Three types of wind energy conversion system. Twt Tgen H Jwt D Jgen Wind Turbine Induction Generator Figure 5.2 Two-mass model for the shaft system of WTG Mathematical Model (1) Wind Turbine Model The mechanical power that wind turbine extracts from wind can be computed as P 0.5 AC (, ) v (5.1) 3 m p w where ρ is air density in kg/m 3, A = π R 2 is the turbine swept area in m 2, v w is wind speed in m/s, C p is the power coefficient which is a function of tip-speed-ratio λ and blade pitch angle β. The specific representation of power coefficient curve depends on the blade design and will be given by wind turbine manufacturers. In this thesis, it is modeled using equation (5.2), as Cp, e (2) Model for Shaft System (5.2) 81

94 Fig 5.2 shows a two-mass model for the shaft system. It consists of a low-speed wind turbine mass and a high-speed generator mass, neglecting the gearbox mass because of its relatively small inertia. The electromechanical dynamic equations are dwt Twt Jwt Dwt wt gen Hwt wt gen dt dwt wt dt d T J D H dt d gen gen dt gen gen gen gen gen wt gen gen wt (5.3) where, wt and gen are turbine rotational speed and generator rotational speed in rad/s, T wt and T gen are turbine torque and generator torque, J wt and J gen are moments of inertia of the turbine and generator respectively, D wt and D gen are linear damping coefficients of the turbine and the generator, H wt and H gen are stiffness coefficients of the turbine and the generator. (3) Induction Generator Model Generally, all stator and rotor parameters are transformed into a two-axis reference frame (d-q frame). Its electric system is depicted as Fig ωλ R sq sd L + - lsd L (ω-ω r )λ rq lrd R ωλ rd R sd sq L R lsq L (ω-ω r )λ rd lrq - rq + + v sd i sd L md i rd v rd - - d-axis v sq i sq L mq i rq v rq - - q-axis Figure 5.3 Electrical circuit for the induction machine in d-q frame. The voltage equations are 82

95 vsd ( t) Rsd isd ( t) d sd ( t) ( t) sd ( t) vsd ( t) Rv sdsq ( t) isd ( t) R sq d isq ( t ) sd ( t) dt sq ( t () t ) sd ( t( ) t) sq ( t) vsq ( t) R v ( ) sq isq ( t) dt ( sq ) ( t) ( ) sq ( t) rd t Rrd ird t d rd t ( t) r ( t) rd ( t) vrd ( t) Rrd ird ( t) d rd ( t) ( t) r ( t) rd ( t) vrq ( t) R rq irq ( t) dt rq ( t) ( t) r( t) rq () t (5.4) The flux equations are sd t Ls isd t Lm ird t Llsd isd t md t sq t L s isq t L m irq t L lsq isq t mq t (5.5) rd t Lr ird t Lm isd t Llrd ird t md t rq t L r irq t L m isq t L lrq irq t mq t Control System Control of the wind generation system consists of control for the wind turbine, control for the rotor-side converter and control for grid-side converter [83], [84], [85], [86]. Wind turbine control is aimed at extracting mechanical power from wind. Rotor-side converter control manages active and reactive power at the stator terminal. Grid-side converter control maintains the dc-link voltage constant regardless of the magnitude and direction of rotor power. The grid-side converter is actually a grid-tie inverter, and its control strategy will be given later. P elec + - P ref k s p 0 s max k i Pitch angle Figure 5.4 Conventional pitch angle control system. At a specified wind speed, there exists a unique rotational speed to achieve the maximum power coefficient C p,max and thus obtain the maximum mechanical power from 83

96 the available wind power. If wind speed is below the rated value the rotational speed is adjusted so that power coefficient remains max when the pitch angle is zero. Meanwhile, if wind speed increases above the rated value pitch angle control is activated to increase the pitch angle to limit the mechanical power. Fig 5.4 shows the pitch angle control system. The stator-voltage oriented reference frame, in which q-axis is aligned with stator voltage vector v s is used in rotor-side converter control. For constant stator flux the voltage at the stator resistance is small compared to the grid, thus d dt d 0, 0, R 0, v 0, v v (5.6) dt sd sq s sd sq s Substituting (6) into stator voltage and flux equations yields, i Lm i sq L s rq vs L i m i sd Ls Ls rd (5.7) are Then, active power and reactive power injected into the grid from the stator terminal 3 3 Lm Ps vsdisd vsqisq vsirq 2 2 Ls 3 3 vs Lm Q v i v i v i 2 2 Ls Ls s sq sd sd sq s rd (5.8) Consequently, from equation (5.8) P s and Q s are proportional to i rq and i rd respectively. Substituting (5.5) and (5.7) into rotor voltage equations, yields 84

97 v R i L L d i L L i 2 2 m m rd r rd r rd r r rq Ls dt Ls 2 2 L m d L m Lmvs vrq Rrirq Lr irq r Lr ird r Ls dt Ls Ls (5.9) Using a proportional-integral (PI) control algorithm and combining (5.8) and (5.9) the block diagram of the rotor-side converter is given in Fig. 5.5, which includes an external power loop and an internal current loop. P s, ref + - P s P k rq, p I rq,max k s I rq,min rq, i I rq, ref + - I rq k rq, p max k V rq1 + rq, i s + min + Lm s r v s L s s L 2 m r Lr Ird Ls V rd, ref Q s, ref + Q s Q - k rd, p I rd,max k s I rd,min rd, i I rd, ref + I rd - - Figure 5.5 Control for rotor-side converter. + dq-> abc V rq, ref V abc, ref Rotor-side converter control signal k min rd, p max k s rd, i V rd1 L 2 m r Lr Irq Ls PWM 5.2 Micro-Gas-Turbine Generation Unit Microturbines are small and simple-cycle gas turbines with outputs ranging from around 25 to 300 kw. There are essentially two types of microturbines: one is the highspeed single-shaft unit and the other one is the low-speed split-shaft unit. The comparisons of two types are listed as Table 5.1. Table 5.1 Comparisons of Two Types of Microturbines Single-Shaft Configuration Compressor and Turbine are mounted on the same shaft as the electrical alternator. Features High-speed turbine: ~50000 to ~ rpm Permanent magnet machine Power converter is needed to convert high frequency signals into 60 Hz. 85

98 LVG Split-Shaft Power turbine and the conventional generator are connected via a gearbox Low speed: 3600 rpm Induction or synchronous machine Power converter is not needed Mathematical Model Single-shaft microturbine is studied as the example. Its model is composed of four parts including speed and acceleration control, fuel control, temperature control and gas turbine. Fig. 5.6 shows the block diagram for the mathematical model. P ref F min F max W(Xs+1) Ys+Z T5s 1 T s FD t F max F DT T C Vce 1 K5 T K4 4s 1 T 3 s 1 Temperature Control K 3 K e st T f 1 a 1 W f bs c s 1 T f T R W f1 e se TD e se CR F min speed control Acceleration Control Speed Control g Fuel Control P m K f W f2 f 2 1 T CD s 1 n g Turbine Figure 5.6 Single-shaft MT model. (1) Speed and acceleration control Speed control is to control the rotational speed almost constant within a range of loads changing. It is realized by regulating fuel demands of the micro-gas-turbine. In Fig. 5.6, P ref is the load reference; ω g is the speed deviation of the generator; F D is fuel demand; Z represents the governor mode (droop or isochronous); W is the controller gain; X and Y are lead and lag constants of the controller respectively (s). Acceleration control is used primarily to limit the turbine acceleration rate during the process of startup. If the rotate speed of the turbine is closed to its rated speed, acceleration control will be automatically closed. 86

99 (2) Fuel control Fuel control part includes fuel limiter, valve and actuator. The fuel flow dynamics is dominated by the inertia of the fuel system actuator and the valve positioner. In the figure, V ce represents the least amount of fuel needed for the particular operating point; ω n is the rated rotated speed of the generator; ω g is the real rotated speed; speed deviation is ω g =ω g -ω n ;K 3 is the gain of the delay; T is fuel limiter constant (s); a, c are known valve parameters; b is the time constant of the valve(s);t f is time constant of the actuator (s);k f is the feedback efficient of the valve and actuator;w f is the fuel demand signal in per unit (p.u); K 6 is the fuel flow coefficient when the turbine operates at rated speed without loads. At steady state, the signal V ce generated from low-value gate and the fuel flow signal W f have the following relationship: (3) Gas Turbine V ce 1 c Wf K fwf K6 K a 3 (5.10) The compressor-turbine is the heart of the system, and it is composed of combustion system, compressor and turbine. The compressor is a dynamic device with a time lag associated with the compressor discharge volume. There is also a small time delay (E CR ) associated with the combustion reaction and a transport delay (E TD ) associated with transport or gas from the combustion system through the turbine. In the figure, W f1 is the output signal of fuel control system; W f2 is the output signal of the compressor. T CD is the compressor discharge time constant (s). The torque and the exhaust temperature characteristic of the single-shaft gas turbine are linear with regard to fuel flow, turbine speed and turbine rotor speed. 87

100 Exhaust temperature function f1 TR a f (1 Wf ) bf g (5.11) Torque function f a b W c (5.12) 2 f 2 f 2 f 2 f 2 g where, T R is the actual temperature of the turbine (K); a f1 b f1 a f2 b f2 c f2 are constants. So the output mechanical power is P T f a b W c m m g 2 g f 2 f 2 f 2 f 2 g g (5.13) At steady state, ω g =0, ω g =1.0,so Since s = 0, so Then, W f 2 P m a b f 2 f 2 Wf W f 2 (5.14) (5.15) V ce 1 c 1 c P m a f 2 Wf K fwf K6 K f K6 K3 a K3 a bf 2 (5.16) Thus, load power reference P ref in speed control system has the following relationship with the output mechanical power P m : Z Z c P a m f 2 Pref Vce K f K6 W WK3 a bf 2 (5.17) (4) Temperature control Temperature control is in command whenever the exhaust temperature exceeds the exhaust temperature reference, or when the unit is picking up load faster than the turbine dynamics can handle, which is due to the fact that the exhaust temperature responds faster because of the increases in fuel flow before the moderating action of air flow with 88

101 increase in engine speed. Rs r q Ldls Rs r d Lqls v d id L m i m vq i q L m Figure 5.7 Electrical circuit of PMSG in d-q frame. The generator is a two-pole PMSG with a non-salient rotor. Fig. 5.7 shows the equivalent electrical circuit of the PMSG in synchronous rotational (d-q) frame. R s is the stator armature resistance, L ls is the leakage inductance, L m is the mutual inductance, total inductance L=L ls +L m. PMSG generates a constant d-axis flux m, which is represented by an inductance in parallel with a constant current source i m, as (5.18) L i m m m Voltage equations for the electrical part in d-q frame are d vd Rsid d rq dt d vq Rsiq q rd dt (5.19) The mechanical part of PMSG is a single-mass model, as d dt r J Te Fr Tm (5.20) Control System Micro- Turbine PMSG G Grid/Load Figure 5.8 Configuration of a micro-turbine generation system. 89

102 Fig. 5.8 shows the configuration of a micro-turbine generation system. PMSG is connecting with the single-shaft micro-turbine. Because the rotational speed of singleshaft micro-turbines are usually at to rpm, power converter is necessary to convert high frequency outputs from PMSG into utility frequency. To simplify the control system, uncontrolled diode rectifier is used. The universal bridge inverter is used to manage the outputs at its terminal, and its control strategy is different for grid-connected and island operations, which will be explained in the following. 5.3 Photovoltaic Generation Unit Photovoltaic effect is a basic physical process through which solar energy is converted into electrical energy directly. The physics of a PV cell is similar to the classical p-n junction diode, shown in Fig At night, a PV cell can basically be considered as a diode. When the cell is illuminated, the energy of photons is transferred to the semiconductor material, resulting in the creation of electron-hole pairs. Figure 5.9 The physics of a PV cell Mathematical Model There are several equivalent circuits widely used for modeling a PV cell, including the ideal model, single-diode model and double-diode model. Single-diode equivalent model 90

103 has been proved to have great performance on mimicking the characteristics of the PV cell, and it is used in the thesis. Fig shows the single-diode equivalent circuit, which is composed of a photocurrent I ph, a nonlinear diode D, a series resistance R s and a parallel resistance R sh. I + I ph D R sh R s V _ Figure 5.10 Single-diode equivalent circuit for a PV cell. The output current and voltage are related by q( V IR s ) V IR AkT I I ph Is( e 1) R sh s (5.21) where, I ph is photocurrent; I s is diode saturation current; q is coulomb constant; k is Boltzman s constant; T is cell absolute temperature (K); A is P-N junction ideality factor. Photocurrent is the function of solar radiation and cell temperature, described as S I ph I ph, ref CT ( T Tref ) S ref (5.22) where, S is the real solar radiation (W/m 2 ); S ref, T ref, I ph,ref is the solar radiation, cell absolute temperature, photocurrent in standard test conditions respectively; C T is the temperature coefficient (A/K). Diode saturation current varies with the cell temperature T Is Is, ref e T ref 3 qeg 1 1 Ak T ref T (5.23) where, I s,ref is the diode saturation current in standard test conditions;e g is the band-gap energy of the cell semiconductor (ev),depending on the cell material. 91

104 The output power of a PV cell is less than 2 W at ~0.5 volts DC output voltage, so a group of PV cells are usually connected in series and parallels to form a PV array for practical application. The output voltage and current of a PV array can be formulated as q V IRs ( ) AkT N N NP V IRs S P I NPI ph NPIS ( e 1) ( ) R N N sh S P where, N s and N p are cell numbers of the series and parallel cells respectively. (5.24) Fig shows current versus voltage and power versus voltage curves for a PV array model at the reference condition ( T = 298 K and S = 1000 W/m 2 ) based on the parameters given in Table 5.2. The maximum output power is kw when the voltage is 2400 V and current is A. Table 5.2 Parameters of A PV Array A Tref Sref Is,ref Rs Ns Np Figure 5.11 Characteristics curves for the PV array model Control System As indicated in Fig. 5.11, there exists a maximum value for the output power of a PV array under the given temperature and solar irradiance. Besides, the maximum output power will be different for variant environmental conditions. Maximum Power Point Tracking (MPPT) is a way to help a PV array extract maximum power under different 92

105 operating conditions. A large number of MPPT methods have been proposed in literatures, and Esram and Chapman [87] gave a detailed comparison of these methods, summarized as Table 5.3. Perturbation and Observation (P&O) method is one of the most used MPPT methods because of its simplicity and requirements for fewer measured variables. P&O algorithm operates by constantly measuring the terminal voltage and current of the PV array, constantly perturbing the voltage by adding a small disturbance, and then observing changes in the output power to determine next control signal. If the output power increases the perturbation will continue in the same direction in the following step, otherwise the perturbation direction will be reversed. To improve tracking speed and algorithm accuracy, the perturbation needs be continuously adjusted. Table 5.3 Comparisons of Different Types of MPPT Algorithm. By observing the characteristic curves of PV cells, the power increment dp and voltage 93

106 increment dv satisfy: At the left of MPP: dp / dv > 0 At the right of MPP: dp / dv < 0 At the MPP: dp / dv =0 As the operating point gets closer to the MPP the value of dp/dv is smaller, and the perturbation can be chosen small and tracking is slow but accurate. When the operating point is far from MPP the perturbation is large and tracking is fast. In sum, the variablestep P&O algorithm is given as Fig Measure Vk, Ik P k V I k k Yes P k Pk 1 0 No PkPk 1 0 Yes Vref Vref Yes Pk Pk 1 Vk Vk 1 No Vk Vk 1 0 No Vref Vref Pk Pk 1 Vk Vk 1 VkVk 1 0 No Vref Vref Pk Pk 1 Vk Vk 1 Yes Vref Vref Pk Pk 1 Vk Vk 1 V V, I I k1 k k1 k Figure 5.12 Flow-chart for variable-step P&O method. MPPT can be realized by regulating the duty cycle of IGBTs in the boost converter connected to the PV array, and the control block diagram is shown as Fig By detecting the present voltage and current, the MPPT algorithm can determine the optimal output voltage that leads to the maximum output power, and PI controllers are used for tracking the voltage reference signal. 94

107 + I pv Vpv MPPT Vref + - Voltage Control + - Current Control PWM IGBT Figure 5.13 Block diagram of the MPPT controller. 5.4 Fuel Cell Generation Unit Fuel cells (FCs) are static energy conversion devices that convert the chemical energy of fuel directly into DC electrical energy. Fuel cells have a wide variety of potential applications including micro-power, auxiliary power, transportation power, stationary power for buildings and other distributed generation applications, and central power. At present, mostly used fuel cells mainly include five kinds, which are alkaline fuel cells (AFC), proton exchange membrane fuel cells (PEMFC), phosphoric acid fuel cells (PAFC), molten carbonate fuel cells (MCFC) and solid oxide fuel cells (SOFC). Amongst these types, polymer electrolyte membrane fuel cells (PEMFC) and solid oxide fuel cells (SOFC) both show great potentials in transportation and DG applications Mathematical Model stack E nernst stack R ohm stack R act stack R con - stack V FC C Figure 5.14 Equivalent electric model for the fuel cell. Fig shows the equivalent electric model of a fuel cell [88]. It is noted that this equivalent model could be used for both SOFC and PEMFC, but the representations for the elements are different. The capacitor simulates the double-layer effect of the cell, and it can be considered as a first-order delay existing in the activation and concentration 95

108 voltages, as and Ra is given as R a CR a (5.25) V V act con (5.26) IFC where, I FC is the operating current; V act is the activation over-voltage, V con is the concentration over-voltage. There are three nonlinear resistances and an internal Nernst voltage. These four parts all depend on the cell temperature and the partial pressure of hydrogen, oxygen and water. Nernst voltage (E nernst ) represents the open-circuit voltage of the single fuel cell at the particular temperature and gas partial pressure. SOFC is studied as the example, and its Nernst voltage is given as RT 1 Enernst E0 ln( ph ) ln( p ) ln( ) 2 O p 2 H2O 2F 2 (5.27) where, E 0 is the standard referenced voltage at 1 atm pressure (V), F is Faraday constant (96485 C/mol), R is the universal constant of the gas (8.314 J/(K mol)), p H2, p O2 and p H2O are partial pressures of hydrogen, water vapor and oxygen (atm), T is cell absolute temperature (K), T ref is the referenced temperature (K). Activation over-voltage equivalent resistance (R act ) represents the losses of the activation of anode and cathode in the fuel cell. For SOFC, the activation over-voltage can be represented using Butler-Volmer equation, as J zfvact (1 ) zfvact J0[exp( ) exp( )] (5.28) RT RT where, α is the transmitting coefficient, z is the number of electrons transferred by every molecule fuel, J 0 is the exchange current density (A/m 2 ),J is the actual current 96

109 density (A/m 2 ). The activation over-voltages of the anode and cathode are described as RT J RT J J 1 2 Vact. i sinh ( ) ln[ ( ) 1] i a, c F 2J0. i F 2J0. i 2J0. i (5.29) Then, activation over-voltage equivalent resistance can be represented as R act V V I act. a act. c FC (5.30) Ohmic over-voltage resistance (R ohm ) is decided by the resistances of the anode, cathode, electrolyte and the connecting parts, and it can be expressed as R ohm ili A i (5.31) where, l i is the flowing distance when the current is flowing through resistances (cm), Ai is the flowing area when the current is flowing through resistances (cm 2 ), i is the resistivity of the the anode, cathode, electrolyte and the connecting parts ( cm ), which is affected much by the temperature. Concentration over-voltage equivalent resistance (R con ) represents the effects of the concentration of the reactant on the surface of the electrodes on the cell. The anodic and cathodic concentration overvoltages can be expressed as V V con. c con. a RT p p 2F p p RT 4F r H2 H2O ln( ) r H 2 H2O p r O2 ln( ) p O2 (5.32) Then, the concentration over-voltage equivalent resistance is 97

110 R con V V I con. a con. c FC (5.33) During the simulation study, it is noticed that the time constants of double-layer effect, changes in partial pressure and temperature differ a lot [89]: the time constant of doublelayer effect is usually less than 1 second and the changes in partial pressure are usually at tens of seconds to minutes, while the changes in temperature only appear after minutes to hours. Thus, during the short-term simulation study, we only consider the double-layer effect and assume partial pressures and temperature constant. Instead, for medium-term study, besides of double-layer effect the dynamics of partial pressure changes are also considered [90], and the fuel cell model is demonstrated as Fig The changes in temperature are only considered when the simulation time is long enough. u max stack I FC u min N 2K 2K in H2 r 2K u opt N r r Fuel valve control function in H2 N f 1 1 e s 1 1 f s Fuel processor delay r I FC Electric response delay Fuel Control in N H 2 r _ 1 H Current Measurement O 2K r Kr + - 1/ K 1 H 2 Electrochemical Dynamic s 1/ K 1 in NO 2 + H2O H 2 H2O O2 ph 2 p HO p 2 O2 1 RT 2 0 ln( H / ) 2 O2 H2O s 1 / K 1 N E p p p 2F - O2 s stack E nernst + - stack R con stack R act stack R ohm C Electric Part stack V FC Figure 5.15 Medium-term dynamic fuel cell model. Current measure part is to control the circuit current of the fuel cell stack I stack FC. Fuel utilization u is the ratio between the fuel flow that reacts and the fuel flow injected into the stack, described as 98

111 u N N 2KI r r H2 r FC in in H N 2 H2 (5.34) in N H 2 r N H 2 where, and represents the hydrogen input flow rates and hydrogen reactive flow rates respectively (mol/s), the constant K r N 4F, N is the number of the series cells, r I FC is the fuel cell feedback current (A). e is the electric response constant. Fuel control part is to control gas input flow rate N f (mol/s). The fuel valve is regulated by adjusting the operating current, and the control function is N in H 2 2K u opt r I r FC (5.35) where, u opt is the given optimal utilization value. Electrochemical dynamic part is most important in the medium-term dynamic model, which is to simulate the changing of gas partial pressure in the stack. The calculation methods of H 2, O 2 and H 2 O are similar. Taking H 2 as an example, the calculation process is introduced. Changes of the hydrogen partial pressure can be expressed as p V n RT H an H 2 2 (5.36) where, p is the hydrogen partial pressure (atm), is the anode volume (m 3 ), is H 2 V n an H 2 the number of moles of the hydrogen in the anode (mol), mol)). Then, it can be derived as R is gas constant (8.314 J/(K d RT d RT p n N N N dt V dt V in out r H2 H2 H2 H2 H2 an an (5.37) in N H 2 out N H 2 r N H 2 where,,, are the input, output and reacting flow rates of the hydrogen 99

112 fuel cell stack (mol/s) Since there is a proportional relation between the output rate of the reactants and the partial pressure of the reactants, shown as N p K out H2 H2 H2 (5.38) Substituting (5.38) into (5.37) and taking Laplace transform, we obtain 1/ K p s N K I H2 in r H ( ) 2 2 H 2 r FC 1 s H2 (5.39) where, V RTK. H2 an H Control System A DC/DC converter is generally connected to the fuel cell stack in order to increase the output voltage and thus reduce the number of fuel cells required. The output voltage and current at the terminal of the boost circuit are controlled, and the control system is similar to the one used for PV system, as shown in Fig Vdc Boost PWM Current Control PI Voltage Control Vdc,ref I fc PI Vdc Figure 5.16 Configuration and control for fuel cell generation system. 100

113 5.5 Super-Capacitor Energy Storage System Super-capacitors are electrochemical capacitors that have unusually high energy density when compared with common capacitors, and they are widely used as energy storage device in DG applications. Fig shows the typical charging/discharging characteristic curves of the super-capacitor, as well as the curves of the battery [91]. Compared with batteries which are also widely used for energy storage applications, super-capacitors have energy densities that are approximately 10% of conventional batteries, while their power density is generally 10 to 100 times greater. Thus, supercapacitors have much shorter charge/discharge cycles and are more suitable for shortterm dynamic studies. Besides, the cycle life of super-capacitors is quite long, over 100,000 times. Figure 5.17 Typical charge/discharge characteristic curves of the super-capacitor and battery Mathematical Model Many equivalent circuits exist for modeling super-capacitors, such as classic equivalent circuit model, three branches model and ladder circuit model, etc. Classic equivalent circuit [92] is widely used because it is simple and effective, and it is shown as Fig The model consists of an ideal capacitor, a series resistance ESR and a parallel resistance EPR. ESR is very small, and simulates heat losses and charge/discharge 101

114 voltage transient mutation in the process of charging and discharging. EPR is a large resistance, which represents the current leakage effect and impact on long-term energy storage performance. ESR C EPR Figure 5.18 Classic equivalent circuit for ultra-capacitor. The three parameters in the model are formulated as V ESR I 2 1 t2 t1 EPR ln V / V C e v ESR i i d V C EPR 1 t2 C C C t C C _ init 1 (5.40) (5.41) (5.42) where, is the initial self-discharge at ; is the final self-discharge at t ; C is the V t 1 1 V2 2 rated capacitance; V is the change in voltage at turn on of load; I is the change in current at turn on of load; V is the initial capacitor voltage; i is the capacitor current. C _ init C Control System Super-capacitor energy storage system is composed of the super-capacitor, a bidirectional DC/DC converter and controllers, and it can be charged by the grid to store extra electric energy, and can also discharge electricity to the external grid. Supercapacitor energy storage system can operate as a compensation for some intermittent sources, such as wind farms or solar sources. In this manner, super-capacitors can be 102

115 considered as transition sources to maintain the DG system stable. Figure 5.19 gives the control system for the bi-directional converter [93]. The primary objective of the converter is to maintain the common dc-link voltage constant. In this way, no matter the ultra-capacitor is charging or discharging, the voltage at the dc bus can be stable and thus the ripple in the capacitor voltage is much less. When the voltage at DC bus is lower than the referenced voltage, switch S 2 is activated, and the converter works as a boost circuit; when the DC bus voltage is higher than the referenced voltage, switch S 1 is activated, and the converter works as a buck circuit. For both situations, the control scheme still includes two loops-external voltage control and internal current control. V dc PI I uc, ref V dc V dc, ref PI >= PWM NOT signal AND AND S 1 S 2 Iuc Ultracapacitor Luc V uc S 2 S 1 C dc V dc V dc, ref I uc Figure 5.19 Control for the bi-directional DC/DC converter. 103

116 AC Bus Gear Box DFIG PV Array Fuel Cell PMSG G Ultracapacitor Micro- Turbine Figure 5.20 A sketch of multiple distributed generation systems. 5.6 Operation of Grid-Connected / Islanded Distributed Generation Systems Fig shows a sketch of multiple distributed generation systems: each DG unit could operate separately, or work with other DG units under appropriate energy management strategy. All DG units can be integrated into the utility grid by implementing stable control strategy on the grid-tie inverter, and can also operate autonomously to supply electric power to loads directly. In general, during the gridconnected operation the output power from the DG unit is controlled, while during the islanded operation the voltage and frequency in the isolated network are regulated to be nominal. Detailed control strategy is discussed in the following. 104

117 Three-phase PWM inverter + v a i f L f L f v fa v fb i line R line R line L line L line v La v Lb Isolating Switches i g R g R g L g L g v ga v gb Grid V dc v b v c L f v fc R line L line v Lc R g L g v gc - AC Bus C f C f C f AC Loads Figure 5.21 The configuration of a distributed generation unit for grid-connected and islanded operations. In order to illustrate the development of the inverter controller, a general configuration of a distributed generation unit for both grid-connected and islanded operations is given as Fig The mathematic relations of the three-phase voltages and currents can be first obtained at the abc frame. The synchronous rotating frame (dq0 frame) with q-axis aligned to the grid voltage vector is used to design controllers. Applying the frame transformation, the relations of voltages and currents are written as (5.43)~(5.45), which provide the basis for designing the controllers for both grid-connected and autonomous systems. di L v v L i dt di L v v L i dt fd f d fd f fq fq f q fq f fd dv C i i C v dt dv C i i C v dt fd f fd line, d f fq fq f fq line, q f fd di L v v R i L i dt di L v v R i L i dt line, d line fd Ld line line, d line line, q line, q line fq Lq line line, q line line, d 105 (5.43) (5.44) (5.45)

118 5.6.1 Control System for Grid-Tie Inverter During grid-connected operation, the isolating switches are closed and v L is determined by the grid voltage as di L v v R i L i dt di L v v R i L i dt gd g Ld gd g gd g gq gq g Lq gq g gq g gd (5.46) where, * * v1 d vd v fd Lf i fq v1 q vq v fq Lf i fd * * id ifd iline, d C f vfq iq ifq iline, q C f vfd * v2 d vfd vld Rlineiline, d Llineiline, q * v2 q vfq vlq Rlineiline, q Llineiline, d * * v3d vld vgd Rgigd Lgigq v3q vlq vgq Rgigq Lgigd (5.47) Applying Laplace transformation to (5.43)~(5.45), then i fd ( s) i fq( s) 1 v fd ( s) v fq( s) 1 * * * * v1 d v1 q slf id iq sc f i () s i ( s) 1 i ( s) i ( s) 1 line, d line, q gd gq * * * * v2d v2q slline Rline v3d v3q slg Rg (5.48) During grid-connected operation, the ac load impedance is much larger than the line impedance, so i line i g. Thus, i i line, d line, q * * v4d v4q s Lline Lg Rline Rg 1 (5.49) where, v v v L L i v v v L L i * 4 d fd gd line g line, q * 4 q fq gq line g line, d (5.50) 106

119 Outer-Level v gd Middle-Level i line, d i line, d vgd Inner-Level * * * * * v i + fd k i k pcs k v 1 i pvs k v d + fd + ic 1d fd iv + - -, k v ps k i 2d fd s sl + s s - f sc f R R s - - L L + line g line g C f vfq Cf vfq L line Lg iline, q L line Lg iline, q * i line d Figure 5.22 Three-level controller block diagram in d-axis for the grid-tie inverter. From (5.48) and (5.49), the control system can be decomposed into three levels, with PI controllers used in each level. Fig shows the block diagram of the control system for d-axis components with the control variables i f, v f and i line. The control system for the q-axis components is designed using the same method. For the grid-tie inverter, the objective is to manage the active and reactive power outputs of the DG system, and the reference values for the line current are given by (5.51). In sum, the entire controller for the grid-tie inverter is given as Fig i line, d P v Q v i P v Q v i * ref fd ref fq line, d vfd vfq * ref fq ref fd line, q vfd vfq (5.51) Pref Qref * ref fd i ref fq line, d P v Q v 1.5 v v 2 2 fd fq + i line,d - 1 k p L line ki s L g vgd + * v fd v fd - 3 iline,d k + iv k pv s + C f - * i fd + i fd - 5 k pc k s L f ic vfd * v d Pref Qref * ref fq i ref fd line, q P v Q v 1.5 v v 2 2 fd fq i line,q L k line p L g ki s vgq * v fq v fq C f k pv k s iv iline,q * i fq + i fq - 6 k L f pc k s ic vfq * v q Figure 5.23 The complete controller for the grid-tie inverter Control System for Islanded Inverter When the isolating switches are opened, the DG system is operating autonomously as a microgrid. Different from grid-connected operation, the line current is determined by 107

120 (5.52) assuming the AC loads are constant-impedance loads. di L v R i L i dt di L v R i L i dt line, d load Ld load line, d load line, q line, q load Lq load line, q load line, d where, R load and L load represent the accumulated load impedance. (5.52) Similarly, the control system for the islanded inverter can be designed as three levels. During the islanded operation, the voltage and frequency of the isolated system are controlled based on the frequency/active power droop and voltage/reactive power droop, as f f m P P V V m Q Q * * P inv * * Q inv (5.53) Thus, both the middle and inner levels are similar to the grid-tie inverter, but the outmost level is changed to the droop controller. The outputs form the droop controller are used to compute the reference values of voltages at d-q frame. Fig gives the complete controller for the autonomous inverter during islanded operation. Pinv + - P* 3 m P + f* - f * v fd + v fd - 3 k pv C f iline,d k + iv s + - * i fd + i fd - 5 k pc k s L f ic vfd * v d Q inv Q* m Q V* + - V * v fq v fq C f k pv k + iv + s + iline,q * i fq + i fq - 6 k L f pc k s ic vfq * v q Figure 5.24 Three-level controller block diagram in d-axis for the autonomous inverter Small-Signal Stability Analysis Based on the above analysis, the state-space model of an entire distributed generation system including the three-level control system can be obtained for both grid-connected 108

121 and autonomously operating systems. The grid-connected operation is studied as the example. For the outer-level, let φ 1 = i line,d i line,d, φ 2 = i line,q i line,q and define the state vector x = [ 1, 2 ] T, input vectors u 1 = [P ref, Q ref, v gd, v gq ] T and u 2 = [v fd, v fq, i line,d, i line,q ] T, and output vector y = [v fd, v fq ] T, then the state-space model is given as x A1 x B 1 u1 B 1 u2 y C x Du D u (5.54) The representations of the state matrix A 1, input matrix B 1 and B 2, output matrix C 1 and feedforward matrices D 1 ', D 1 '' can be easily obtained from (5.46)~(5.50). Similarly, the state-space representations of the middle-level and inner-level controllers are obtained as (5.55) and (5.56). x A2 x B 2 u1 B 2 u2 y C x D u D u (5.55) where, φ 3 = v fd v fd, φ 4 = v fq and u 2 = [v fd, v fq, i line,d, i line,q ] T. v fq, x = [φ 3, φ 4 ] T, y = [i fd, i fq ] T, u 1 = [v fd, v fq ] T x A3 x B 3 u1 B 3 u2 y C x D u D u (5.56) where, φ 5 = i fd u 2 = [i fd, i fq, v fd, v fq ] T. i fd, φ 6 = i fq i fq, x = [φ 5, φ 6 ] T, y = [v d, v q ] T, u 1 = [i fd, i fq ] T, For the ac-side system from the inverter terminal to the grid, we consider the filter inductance currents i fd, i fq, line currents i line,d, i line,q, and the PCC voltages v fd, v fq as both states and outputs. Two input vectors are defined as u 1 = [v d, v q ] T and u 2 = [v gd,v gq ] T. 109

122 Then the state-space model is x A4 x B 4 u1 B 4 u2 y C x D u D u (5.57) Based on (5.54)~(5.57), the state-space model of the entire system is concluded as (5.58) with the state vector, input vector, output vector are respectively defined as x 1, 2, 3, 4, 5, 6, i fd, i fq, v fd, v fq, iline, d, i line, q T u Pref, Qref, vgd, vgq T y i fd, i fq, v fd, v fq, iline, d, iline, q T x Ax Bu y C x D u (5.58) where, A A 0 0 B M C BC A 0 BD M C B M C B 3D 2C1 B 3C2 A3 B 3D 2D 1 M1C4 B 3D 2 M 2C4 B 3 M 3C 4 B4D 3D 2C1 B 4D 3C2 B 4C3 A4 B 4 D 3D 2D 1 M1 D 3D 2 M 2 D 3 M 3 C4, M 1 = M 2 = , M 3 =, B B BD BDD BDDD B N, C=[0 0 0 C 4 ], D= Finally, the block diagram for the state-space model of the grid-connected DG system can be concluded as Fig The state-space model for the islanded system can be obtained in the same way as the above procedures, and also its block diagram has the same form as Fig. 5.25, but the parameters of inputs, states and outputs are different. T 110

123 u 1 ' u 1 '' B 1 ' B 1 '' A 1 s -1 x 1 D 1 ' D 1 '' C 1 u 2 '' y 1 (u 2 ') B 2 ' B 2 '' A 2 s -1 x 2 D 2 ' D 2 '' C 2 y 2 u 3 '' (u 3 ') B 3 ' B 3 '' A 3 s -1 x 3 D 3 ' D 3 '' C 3 y 3 (u 4 ') B 4 ' A 4 u 2 '' B 4 '' s -1 x 4 M 1 M 2 M 3 D 4 ' D 4 '' C 4 y 4 Figure 5.25 Block diagram of the state-space model for the grid-connected DG system. 5.7 Case Study Fig shows the configuration of a distribution system with multiple grid-connected distributed energy resources, including wind turbine, microturbine, PV cells, fuel cells and supercapacitor energy storage. System voltage is 400 V. There are fifteen nodes in the network, with five different loads connected to nodes A MT generation unit and a wind farm are located at nodes 12 and 13, respectively. The PV generation unit, fuel cell generation unit and energy storage are all connected to node 14 via a mutual inverter. Each distributed energy resource can also be disconnected from the grid and the control strategy should be changed from the grid-connected operation control to islanded operation control. PV generation unit, fuel cell generation unit and supercapacitor energy storage are accumulated together, which finally consists of a DC generation system. At first, the grid-connected operation of multiple distributed generation systems is simulated, and different scenarios are studied, including steady state, faults on the line, 111

124 changes in wind speed and solar irradiance. For each scenario, the dynamic behaviors of all DG units are analyzed. Then, the islanded operation of the DC generation system, i.e. DC microgrid is studied with the implementation of the autonomous inverter control. 20kV 0.4kV 3 40 Line 1 35m 1 3+N kw Wind Farm Wind Power System Load 1 Load Line 6 30m 30m Load Line 3 Line 5 30m 2 35m 35m 35m Line 2 30m kw Line 4 17 MT Load 5 Micro-Gas-Turbine System Load Line 6 30m Line m AC DC Load 6 DC DC PV System PV Cells DC Micro-grid DC DC Ultra- Capacitor DC DC Fuel Cells Electro -lyzer Fuel Cell Generation System Figure 5.26 Configuration of the distribution system with multiple distributed energy resources Grid-Connected Operation The model of the complete grid-connected hybrid AC/DC microgrid system is built 112

125 using MATLAB/Simulink. The capacities of wind power unit and MT generation unit are 90 kw and 30 kw, respectively. The wind turbine operates at a nominal wind speed of 15 m/s, with a generator rotor speed of 1.2 pu. SOFC is used as the energy resource in the fuel cell generation unit and its capacity is 18 kw. PV generation unit has a maximum power rating of 9.8 kw with solar irradiance of 1000 W/m 2 and an operating temperature of 298K. (1) Steady State Operation and Line Faults At steady state, all distributed generation units are controlled to operate under their rated conditions, and supply power to loads and grid. Then, two faults respectively occur at 5 s and 9 s, and both last for 1 second. Fig gives the types and locations of two faults. All simulation results are given in Fig Fault-1: 4s-5s phase-a line grounding fault Fault-2: 9s-10s 3-phase line grounding fault 30m 35m 35m 35m m Load Figure 5.27 Two faults occurred at the system. All distributed generating units reach steady-state operation after a short period of transient time. At steady state, since the PV generation system and fuel cell system can supply sufficient power for the load demands, the super-capacitor energy storage system is inactive, i.e. neither charging nor discharging. The pitch angle controller maintains the pitch angle to fix at eight degree so that the rotational speed of wind generator is 1.2 p.u.. The rotational speed of MT generator finally stays at 0.96 p.u. during steady-state 113

126 operation. Two line faults both affect all bus voltages and currents. Single-phase fault has little influence on the side of each distributed generation unit because of the isolation effect from the power electronics. During 3-phase grounding fault, WT and MT system are significantly affected by fluctuations in rotational speed, and the DC microgrid is not stable since it is actually disconnected from the grid by the fault. After clearing the fault, the entire system regains stability gradually. 114

127 Figure 5.28 Simulation results for the system at steady-state. (2) Changes in Wind Speed and Solar Irradiance Fig shows the changes happened in both wind speed and solar irradiance. At t=5s wind speed has a step change from 15m/s to 20m/s, and then at t=12s wind speed changes again from 20m/s to 12m/s. Solar irradiance increases from 1000 W/m 2 to 1500 W/m 2 at t=8s, and then decreases greatly to 500 W/m2 at t=15s. Total simulation time is 20 s. Fig gives simulation results for the wind power unit and DC generation unit. 115

128 time solar irradiance wind speed 0-5s s-8s s-12s s-15s s-20s Figure 5.29 Changes in wind speed and solar irradiance. Figure 5.30 Simulation results for wind power unit and DC generation unit. When the wind speed jumps to 20 m/s, the pitch angle controller increases pitch angle to about 19 degrees to limit output power to ~90 kw; when wind speed decreases to 12 m/s, the pitch angle is kept at 0 to allow the wind turbine to extract maximum power, ~70 116

129 kw. In the DC generation system, MPPT controller enables the PV system to work at its MPPs for various environmental conditions. Super-capacitor energy storage system can track the power difference between sources and load demands by charging and discharging Islanded Operation DC generation unit can be disconnected from the grid and work as a microgrid to supply power for Load 5, which is 25 kva with 0.9 power factor. Now the control strategy for the islanded inverter is switched to droop control so that system voltage and frequency in the microgrid could be maintained to be nominal as 400 V and 60 Hz, respectively. Fig shows simulation results of the microgrid. It proves that the proposed droop controller can maintain the entire microgrid operate stably: voltage and frequency are maintained nominal; all DC energy resources operate stably and generate constant power; voltages and currents at the terminal of the autonomous inverter are three-phase sinusoidal; and the ac load gets fully served by the microgrid with enough generation. 117

130 Figure 5.31 Simulation results of the microgrid. 118

131 + m Pinv P + - * P m Qinv Q - * Q * f * V V m V ref + + ref Figure 5.32 Designed scheme of the synchronization. Besides, the disconnected microgrid can be reconnected to the grid. But before conducting the reconnection, the magnitudes and phases of the voltages at the point of common coupling (PCC) in both microgrid and the grid should be synchronized. Fig shows a simple scheme of synchronization: detect the grid-side voltage and microgrid voltage, and compute both voltage magnitude difference V m and phase difference θ, which are then added into the reference values of the controller for the autonomous inverter. When both voltage magnitudes and phase angles of the microgrid and bulk grid are exactly same, the connecting switch between the microgird and grid is closed so that the microgrid is reconnected to the distribution grid. Fig shows the simulation results of the synchronization process. At the beginning, there are slight magnitude difference and significant phase difference between microgrid voltage and grid voltage. When t = 2 s, the synchronization is implemented, and after about 1 second the magnitudes and phases of the voltages in the microgrid and the grid get exactly synchronized with zero difference. 119

132 Figure 5.33 Simulation results of the synchronization process. 120

133 Chapter 6 Distribution Network Reconfiguration and Energy Management of Distributed Generation Systems The mathematical modeling, primary control and simulation studies of multiple distributed generation (DG) units were studied in chapter 5. From the perspective of a distribution system, the integration of these DGs can help improve the voltage profile, provide uninterrupted power supply and also reduce power losses. The locations and outputs of DERs also affect system voltages and power losses directly, and it is necessary to choose the optimal locations and to determine the capacity of DG units first in order to improve voltages and reduce losses during distribution system operation. All previous studies on network reconfiguration are based on balanced system assumption with the application of single-phase equivalents. However, distribution systems are generally unbalanced because of non-uniform load distribution and nonsymmetrical conductor spacing on three-phase lines. With the expected growth in the numbers and sizes of single-phase DERs integrated into the grid and the increasing power demands for charging plug-in electric vehicles, unbalance issues, developing efficient and robust algorithms for reconfiguration of unbalanced distribution networks is essential. 6.1 Three-Phase Power Flow and Power Loss Minimization Three-Phase Unbalanced System Modeling Fig. 6.1 shows the components between two buses in an unbalanced distribution system, and voltages and currents are related as (6.1). 121

134 Bus-i a V i b V i c V i I a L,i I b c L,i I L,i I i a b I i c I i z aa z bb z cc z ab z bc Bus-j a V z j ca b V j c V j Figure 6.1 Components between two buses in an unbalanced distribution system. a a a V V i j I aa ab ac i z z z b b b Vi V j zba zbb z bc Ii c c z c Vi V ca zcb zcc j i Ii (6.1) Loads can be modeled as negative current injections at buses for both Wye and Delta connections. Each load is assumed to be a linear combination of constant power component, constant impedance component and constant current component, thus the three-phase current injection at bus-i is computed as IL,i 1, i IP,i 2, i IZ,i 3, i II,i abc abc abc abc (6.2) where, [I P,i ] abc, [I Z,i ] abc, [I I,i ] abc are three-phase current injections of the constant power, constant impedance and constant current loads connecting at bus-i, respectively. The DG unit locating at bus-i can be modeled as positive current injection, as a a b b c c PDG, i jqdg, i PDG, i jqdg, i PDG, i jq DG, i I DG,i a* b* c* abc Vi Vi Vi T (6.3) where, P p p DG,i, Q DG,i are phase-p active and reactive power generated from the DG unit locating at bus i. V i p =e i p + jf i p is phase-p voltage at bus i. If a DG unit works at constant power mode, the equivalent current injection could be computed directly as (6.3) because the values of active and reactive power are specified. However, if a DG unit works at constant voltage mode, a two-loop computation is needed to obtain the equivalent current injection. The inner-loop calculates the reactive power output of the DG unit that is necessary to keep the bus voltage magnitude at the specified 122

135 value, and the outer-loop calculates the current injection with the initially specified active power and the solved reactive power. It is noted that although two-phase or single-phase branches usually exist in the unbalanced network, (6.1) is still true while the values of the corresponding phase impedances for the missing phases become zeros, and the voltages and currents for the missing phases are then deleted from the results. Similarly, for the single-phase or twophase loads and DG units, the output power of the missing phase is set to zero without changing the formulations of (6.2) and (6.3) Power Flow Equations Network reconfiguration is generally indicated as feeder reconfiguration, thus it is supposed that only three-phase feeder branches are reconfigurable. Besides, it is assumed that each feeder branch is equipped with a three-phase switch, and the state of the switch is defined as S j 1, switch j is closed and directionis same astheinitial 0, switch jisopen 1, switch j is closed and directionis opposite (6.4) where, direction refers to the direction of current flow. The connectivity of a network can be represented using node-branch incidence matrix. If the system is ideally three-phase balanced, single-phase equivalents are adopted and the node-branch incidence matrix is denoted as A balanced, which varies for different system structures. The calculation starts from the assumption that all switches are initially closed, and the node-branch incidence matrix for the closed-loop system is A 0 balanced, which is constant for a specific system. Then A balanced can be computed using A 0 balanced and switch states, as 123

136 a ij = a ij 0 S j (6.5) where, a ij, a 0 ij are the ij-th elements of A balanced and A 0 balanced respectively. If the system is unbalanced, three-phase representations of the node-branch incidence matrix must be used, which can be acquired by multiplying each element in A balanced with a 3 3 unit matrix, as 0 a ij a ij A( i, j) 0 a 0 0 a 0 S 0 0 a 0 ij 0 0 a ij 0 ij ij j (6.6) It is known that T bus branch bus bus bus I = A Y A V Y V (6.7) where, V bus is bus voltage vector. I branch and I bus are branch current vector and node injection current vector, respectively. Z branch is branch reactance diagonal matrix. Y branch and Y bus are branch admittance diagonal matrix and node admittance matrix, respectively. And, it is known that I bus = IDG IL (6.8) where, I DG and I L are DG injection current vector and load injection current vector, respectively. According to (6.7) and (6.8), power flow algorithm is developed as: with initial voltage V (k 1) bus (k is the iteration time) given, node injection current I (k) bus is computed from (6.8), and the results are used to compute new bus voltages V (k) bus using (6.7). The iteration goes on until meeting the stop criteria, and finally system voltages and currents are solved iteratively. Further, from (6.7) the current injection at bus-i is given as 124

137 n c l lp p bus, i ik k k1 pa I t V, l phase a, b, c. (6.9) where, lp = t ik m (a 0 lp j=1 ij a kj. 0 y lp j ) S 2 j g lp ik + jb ik [y j aa, y j ab, y j ac ; y j ba, y j bb, y j bc ; y j ca, y j cb, y j cc ] is the conjugate inverse matrix of the phase impedance matrix for the j th branch. Besides, since I l l l Pinject, i j Qinject, i bus, i l l ei j fi (6.10) p p where, P inject,i, Q inject,i are actual phase-p active and reactive power injections at bus i. Finally, we can obtain power flow equations as ik k ik k i ik k ik k P e g e b f f g f b e Q f g e b f e g f b e n c l l lp p lp p l lp p lp p inject, i i k1 pa ik k ik k i ik k ik k n c l l lp p lp p l lp p lp p inject, i i k1 pa (6.11) Power Loss Minimization In unbalanced systems, the power loss at a branch is computed as the difference (by phase) of the input power minus the output power. Because T A V Z I bus branch branch (6.12) According to (6.1), (6.6) and (6.12), total active power losses in the system is obtained as P V V a a y S n c n c m k* p 0 0 pk 2 loss Re j i il jl l l j1 ka i1 pa l1 n c n c j1k a i1 pa k p pk p pk k p pk p pk j i ij i ij j i ij i ij e e g f b f f g e b (6.13) 125

138 In (6.13), the results of voltages depend on system topology and output power of DG units, which are decision variables in the optimization problem of minimizing power loss. Besides, these constraints are required when minimizing power loss: (1) Voltage Limits All voltage magnitude deviations be within 5% of the norminal value V norm V a i, V b i, V c i 1.05 V norm, i=1, 2,..., N. (6.14) Voltage unbalance or imbalance in short is often expressed as the negative sequence component of the voltage divided by the positive sequence component according to the IEEE Standard [94]. Alternative definitions consider the unbalance as the maximum deviation divided by the average of the three phases [95]. Voltage unbalance is an undesired attribute that can cause excessive heating in motors and result in unbalanced currents and noncharacteristic harmonics for electronic equipment such as adjustable speed drives. Imbalance in phase currents may furthermore lead to excessive levels of neutral currents, which may cause nuisance line trips. The ANSI C standard recommends that voltage unbalance be limited to 3%. V p c i avgi p i i avgi pa 3%, where, avg V 3, p a, b, c (6.15) (2) Current Limits Branch currents are computed using (6.12), and each current is limited by I p branch, i I i,max (6.16) where, I max i is the ampacity of branch i. (3) DG Capacity Limits p max p max DG, i DG, i, DG, i DG, i P P Q Q (6.17) 126

139 unit. where, P max max DG,i, Q DG,i are the maximum active power and reactive power for the i th DG (4) System Structure Constraints System structure constraints are same as those used in balanced system study. First, the distribution system is radial without meshes, thus M k1 S N d k (6.18) All loads are served without disconnections, so In addition, at least one branch is open in each loop, so rank(a) = N d (6.19) M k i1 S i M k 1 (6.20) 6.2 Optimal Planning of DG Units Hour t System Data Acquisition Reconfigure Decide the Optimal Locations and Capacity of DG Units... P 1 Q 1 P 2 Q P K Q K Opened Switches Determine system topology and the actual output power of all DG units for the current operation time window Figure 6.2 The framework of the strategy. According to the above study, the factors to affect system power losses include system topology and the amount, locations and output power of DG units in the system. A study framework is proposed to take all these factors into consideration to minimize power 127

140 losses, shown as Fig The penetration of DG units is defined as the ratio of the buses connecting with DG units to the total amount of buses in the system and its value is pregiven. All DG units connecting at the same bus could be aggregated into a single cluster, so it is assumed that each bus only has one aggregated DG unit installed. Then, in order to determine the optimal results of switch states and DG output power during real-time operation, the optimal locations and capacity of all DG units in the system are solved primarily Optimal Locations of DG Units The sensitivity of power losses with respect to the active power injection at each bus is computed to determine the most sensitive buses for installing DG units. Since the integration of DG units will add positive active power injections, so the best location is the one with the most negative sensitivity in order to get the largest power loss reduction. First, we can denote (6.13) as P loss = g ( e, f ) (6.21) Voltage vectors and power injections are related by (6.11), as h( e,f,p inject,q inject ) = 0 (6.22) If a small change [ P, Q] T is added into the power injection vector [P inject, Q inject ] T, the change in voltage vector is solved from h h e h h Pinject 0 e f f inject inject x P Q Qinject 0 x 0 (6.23) Further, the induced changes in power losses are 128

141 g g e e f f Ploss (6.24) Finally, the sensitivity vector of the power losses with respect to the power injection at each bus is obtained as M S 1 g g h h h h [ ] e f e f Pinject Qinject (6.25) With the sensitivity vector solved, the sensitivity of total power losses with respect to each phase of the power injection at each bus can be obtained. It is assumed that only three-phase buses are considered as candidate locations, and the sensitive index of a bus is computed as the average value of three phases. Thus, the sensitivity vector is first formed as (6.25) but only the results of the sensitivity for three-phase buses are computed to analyze Optimal Capacity of DG Units The optimal capacities of DG units are solved in order to minimize power losses in the unbalanced distribution system with the initial topology. This case can be considered as the worst scenario in the reconfiguration study because DG units must generate the maximal power into the grid without the additional support of reconfiguring the network. The optimization problem can be formulated as min J P u loss x,u f(x,u) = 0 st.. g(x,u) 0 (6.26) where, x = [e, f] T, u = [P DG, Q DG ] T. f (x, u) is power flow equations. g (x, u) represents the constraints (6.14)~(6.17). 129

142 With the introduction of penalty function into the objective function, inequality constraints can be eliminated, as min J P ( x,u) (, g ) uc loss i i i i1 H (6.27) where, H is the total amount of inequality constraints. Each penalty function is defined as 0, if gi 0 i ( i, gi) and 0. 2 i i gi, if gi 0 (6.28) The equality constraints f(x,u) is always true since the power flow computation is first solved to calculate power losses. As a result, (6.26) is changed into an unconstrained optimization problem, the minimizer of which is solved numerically using quasi-newton method. Primarily, this theorem is proved [96]: Let F: R n R n be continuously differentiable in an open convex set D R n. Assume that there exists u R n and r,β>0, such that N(u, r) D, F(u ) = 0, H(u ) 1 exists with H(u ) 1 β, and H Lip γ (N(u, r)). Then there exist ε > 0 such that for all u 0 N(u, r) the sequence u 1, u 2, generated by u k+1 = u k H(u k ) 1 F(u k ) is well defined, and converges to u. The derivative of (6.27) is given by Fu x,u x,u dj H uc dploss d i ( i, gi) du du du i1 (6.29) where, the first term at the rightmost side of the equation is same as the sensitivity matrix given in (6.25) with the columns representing for the buses connecting with DG units selected, and the second term could be obtained by differentiating (6.14)~(6.17). 130

143 Because the hessian matrix is hard to solve directly, the minimizer for (6.27) could be solved using secant method with positive definite secant update, as -1 k+1 k k k u u - H F u s = u - u, y = F u - F u k k+1 k k k+1 k T T k k k k k k y y H s s H H k+1 = H k + - T T y s s H s k k k k k (6.30) And, the initial value H 0 is set to be J uc (u 0 ) I. The approximated hessian matrix obtained is symmetric and positive definite. After using (6.30) to get a local Newton step, the backtracking line-search [97] is added to ensure the global convergence, and each next Newton step is chosen so that the Armijo condition is satisfied, as T J u J u F u u u uc k1 uc k k k1 k (6.31) 6.3 Network Reconfiguration and Optimal Operation of DG Units After installing DG units and scheduling their optimal capacity as the above procedures, system power loss has been minimal for the initial system structure. It is expected that the power loss could be reduced further if the system is reconfigured optimally. Besides, due to time-varying loads, power loss will not be always minimal for a fixed network structure and constant DG output power, so there is a need for reconfiguring the network and curtailing DG power from time to time. Thus, an optimization problem with the objective of minimizing the total costs of power losses and curtailing the output power of DG units is defined for each operation period, and the problem formulation is given as 131

144 min J w P, w P P K c p p S PQ DGact 1 loss 2 DG max, i DGact, i t i1 pa K c p p w3 QDG max, i QDGact, i T t i1 pa s. t. (6.14) ~ (6.20), and p p p p DGact, i DG max, i DGact, i DG max, i t t P P, Q Q, i 1 ~ K, p a, b, c, t 1 ~ 24. (6.32) where, T is the amount of tie-switches in the system. K is the amount of DG units in p the system. T is the planned operation period in hour. P DGmax,i p and Q DGmax,i are the optimal capacity of the i th p DG unit solved in (P DGact,i p ) and (Q t DGact,i ) are the t actual phase-p active and reactive output power of the i th DG unit for the operating time t, w 1 ~w 3 are electricity tariff in USD/kWh, and their values are assumed as 1 in the following study. A hierarchical, decentralized approach has been proposed to reconfigure balanced distribution systems in Chapter IV. With necessary improvements, this approach can be used to solve both optimal topology and DG outputs simultaneously for unbalanced distribution systems. Fig. 6.3 shows the flowchart of the revised hierarchical decentralized approach, and a timescale of 24 hours is included. (1) Network Decomposition The procedures to decompose the entire distribution network are same as those illustrated in Chapter IV. Decomposed subsystems are arranged layer by layer, and the lowest-layer subsystems form the basis of the entire system, and they include all buses and loads, as well as DG units. Each higher-layer subsystem is composed of several lower-layer subsystems and the highest-layer subsystem denotes the entire distribution system. 132

145 NO 1. Network decomposition 2. Apply multi-agent framework t = 1 Collect all useful system data at hour-t NO Any changes? YES 3. Enable the lowest-layer agents and use GA to solve the optimization problem. Initialization:pop_size, max_gen. Let gen=1, and encode the 1 st generation. Cross Over Mutation Select an offspring from all new chromosomes Satisfy all constraints? YES Keep this offspring in the population and compute its operating costs NO Delete this offspring from the population All offsprings are evaluated? YES Elitism selection from the remained feasible population NO k=k+1 k>max_gen YES STOP Generate the solutions. Wait until next operation time window arrives. 4. Move upwards to enable upper-layer agents and use the heuristic algorithm to find the optimal switching-pairs for the studied loops. 5. Move upwards until finishing studying all upper layers. NO (2) Apply Multi-Agent Framework t = t+1 t>24? YES STOP Figure 6.3 The flowchart of the proposed methodology. 133

146 An intelligent agent consisting of a data unit, a computation unit and a decision unit is assigned to each subsystem, and it is used to solve the sub-problem for the assigned subsystem and exchange information with other agents. Because of the possible existence of DG units in the lowest-layer subsystems, the lowest-layer agents should be capable to decide both optimal system topologies and optimal DG outputs for their local systems, so the optimization problem for each lowestlayer agent is formulated as (6.32) with refining all variables as those in its local subsystem. Differently, all higher-layer agents only need to determine whether the common tie-switches should be closed or not based on the decision plans solved in lowerlayer agents, so each embedded optimization problem is a pure reconfiguration problem, and it is formulated as min J P S, S, PQ T loss at the studied subsystem solved solved st.. (6.16) ~ (6.21). (6.33) where, S at the studied subsystem is the set of switch states to solve; S solved is the set of switch states that are already solved at the lower-layer agents; PQ solved is the actual output power of DG units determined at the lowest-layer agents. (3) Solve Optimization Problems at the Lowest-Layer Agents The optimization problems defined in lowest-layer agents are mixed-integer nonlinear ones with both switch states and DG outputs as decision variables. According to the discussions of three proposed methods in Chapter III, it is known that both the revised GA and the hybrid algorithm are able to solve DG outputs by adding DG power into the decision variables. However, it is also known that the revised GA has much better accuracy and computational speed than the hybrid algorithm. Thus, the revised GA is 134

147 chosen to solve the mixed-integer nonlinear optimization problem (6.32) defined in lowest-layer agents. Because of the existence of DG power in the decision variables, some changes are made in the algorithm. OS 1 ~OS T P 1a Q 1a P 1b Q 1b P 1c Q 1c... P K,a Q K,a P K,b Q K,b P K,c Q K,c Figure 6.4 The genes included in each chromosome. Each chromosome in a population is defined as Fig. 6.4 and it has T+6K genes in total: (a) The first T genes represent the opened switches. (b) The following 6K genes are the active and reactive power generated from K DG units. It is assumed that there are both half chance to apply the cross-over and mutation operators. The cross-over operator randomly selects two chromosomes (A, B) and then exchanges their information to create two new chromosomes (C, D) following the rule based on one-point technique and arithmetical operator: (a) Select a gene i from T+6K genes randomly. (b) If i T, C(1: i) = A(1: i), C(i + 1: T) = B(i + 1: T), and C(T + 1: T + 6K) = 0.2 A(T + 1: T + 6K) B(T + 1: T + 6K). (c) If i >T, C(1: T) = A(1: T), C(T + 1: i) = 0.8 A(T + 1: i) B(T + 1: i), andc(i + 1: T + 6K) = 0.2 A(i + 1: T + 6K) B(i + 1: T + 6K). The other chromosome D is obtained in the opposite way to C by reversing A and B in the above equations. The mutation operator randomly changes one gene in the selected chromosome to introduce new information into the offspring. If the selected gene denotes an opened 135

148 switch, it is replaced by another switch in the corresponding loop; otherwise, it is replaced by another feasible value within the capacity of DG units. Before evaluating fitness values of the new population, all repeated chromosomes are deleted and the feasibility of each offspring is evaluated by checking system structure constraints and voltage/current constraints in turn. Then, the fitness values of all feasible offsprings are computed and the elitism is used to select the best population. At last, the optimal topologies of all lowest-layer subsystems and the optimal outputs of DG units are solved. Coordination between agents is conducted when necessary, as explained in Chapter IV. Then, the final results are transferred into upper-layer agents to activate the computations in them. (4) Enable the Upper-Layer Agents and Move Upwards With switch states and DG outputs solved in lower-layer agents known, the proposed heuristic algorithm based on branch-exchange and single-loop optimization is used to solve the optimal topologies of upper-layer subsystems. Keep on until all layers are studied. Then the optimal topology of the entire distribution system and the actual output power of all DG units are both acquired for the present time window based on the timely system data. Thus, distribution feeders are reconfigured and the operations of DG units are regulated optimally, and such status will be kept same until the next time window arrives when the operation plan for next period is re-evaluated. 136

149 6.4 Case Study The proposed methodology to plan and operate DG units and reconfigure unbalanced distribution feeders are tested on two cases including a 25-bus unbalanced distribution system and the revised IEEE 123-bus test system Gaussian-Mixture Load Modeling Because time-variant loads could affect the result of sensitive matrix, Monte Carlo simulation is carried out to determine the most sensitive buses based on a great quantity of historical load data. A lot of statistical methods have been given to model the loads, such as Gaussian distribution [98], Weibull distribution [99], Beta distribution [100], etc. Gaussian-Mixture Model (GMM) [101] is used to model the load because it can fairly represent different types of load distributions as a convex combination of several normal distributions with respective means and variances. The probability density function (pdf) of a GMM is given by AM f z w i N (μ i, σ i ) (6.34) i1 where, AM is the amount of mixture components, and w i is the proportion of each component. With 2013 full-year load data of four different areas given in [102], four different GMMs of load pdfs with three mixture components are obtained as Fig. 6.5 and the critical parameters are also marked. In order to apply the GMM to different test systems, the horizontal axis is given as the per unit values. 137

150 Figure 6.5 GMM approximations of load pdfs Case I: 25-Bus Unbalanced Distribution System Fig. 6.6 shows the diagram of the 25-bus distribution system [103]. Both line impedance and load distribution are unbalanced. Total loads are kw and 792 kvar (phase-a), kw and 801 kvar (phase-b), and kw and 800 kvar (phase-c). The initial power losses at three phases are kw and the minimum voltage is 0.93 pu TS-1 TS TS Figure 6.6 Single-line diagram of the 25-bus unbalanced distribution system. (1) Optimal Planning of DG Units Each load is applied with a GMM randomly, so the actual load power is the initial value multiplied with the per unit value generated by GMM. Monte Carlo simulation is 138

151 conducted and it is shown that buses 11, 17, 10, 9, 15, 16, 14 and 8 are always the eight most sensitive buses for all 500 samples. In order to prove the effectiveness of reducing power losses through installing DG units at the most sensitive buses, the power loss of the initial system, the system with eight DG units installed at the above eight buses respectively, the system with eight DG units installed at the buses computed as [61] and the system with eight DG units installed at other buses randomly chosen are compared and the results are given in Fig If the sensitive buses are selected according to the method given in [61], the results are buses 2, 3, 4, 6, 7, 10, 18, 23. Each DG unit is assumed to be three-phase balanced and each phase is 40 kw. It clearly shows that the power losses are minimal if eight DG units are installed at the sensitive buses selected using the proposed approach. Figure 6.7 Power loss in the system with DG units installed at different locations. After the locations of DG units are confirmed, the optimal capacity of each DG unit could be solved. Three scenarios are studied: (1) only one DG unit is installed at the most sensitive bus 11; (2) two DG units are installed at buses 11 and 17 respectively; (3) three DG units are installed at buses 11, 17 and 10 respectively. The limits of DG sizes are also 500 kw/ 500kVA for each phase. The proposed quasi-newton algorithm converges quickly after 5~20 iterations for different scenarios. The optimal capacities of DG units for three scenarios are given in Table 6.1. Besides, the values of some key performance indicators (KPI) are also given. 139