Optimal Capacitor placement in Distribution Systems with Distributed Generators for Voltage Profile improvement by Particle Swarm Optimization

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1 Optimal Capacitor placement in Distribution Systems with Distributed Generators for Voltage Profile improvement by Particle Swarm Optimization G. Balakrishna 1, Dr. Ch. Sai Babu 2 1 Associate Professor, Department of Electrical and Electronics Engg., Intell Engineering Collge, Anantapur(AP), INDIA 2 Professor, Department of Electrical and Electronics Engg., JNTU College of Engg., Kakinada(AP), INDIA ABSTRACT To ensure the good quality of power in electrical distribution systems, voltages at the different nodes should be within reasonable limits. Shunt capacitors banks installed in the distribution feeders can supply part of the reactive power required by the inductive loads and hence reduces the voltage drops. Further Distributed Generators (DGs) also supplies the reactive power and hence improves the voltage profile and also provides the local real power generation. The improvement in voltage profile in the system is very much sensitive to the locations of the Shunt capacitor banks as well as Distributed Generators. In this paper, an optimization method based on Particle Swarm Optimization is proposed to solve for optimal placement of shunt capacitor banks along with the DG units for a distribution system for voltage profile improvement. The proposed method is tested on IEEE 41 bus radial distribution system and results are presented. Keywords: Distribution systems, Distributed Generators, Shunt Capacitor Banks, Particle Swarm Optimization 1. INTRODUCTION In a practical power system network especially in distribution system the system operators are always obligated with voltage levels of each customer bus within the satisfied limits. To ensure good voltage profile in distribution systems, several standards have been established to provide recommendations and stipulations. In general many electrical power supply companies try to maintain/control the distribution voltage variations within the range of. One of the most commonly used methods to improve the voltage profiles of distribution systems is connecting shunt capacitor banks along the feeders. Due to the recent advances DGs came into picture to better the voltage profiles further. Distributed Generators (DGs) and Shunt capacitor bank modifies and improves the voltage profile by changing the power flow patterns. Therefore locations of DGs and Shunt capacitor banks have a significant role and impact on the enhancement of voltage profile. In the past two decades, great effort has been contributed to solve the optimal capacitor placement problem that utilizes different methods/algorithms that is based on different objectives. The optimal capacitor placement problem generally be formulated as a mixed integer optimization problem. Several algorithms can help in getting the solution of optimal capacitor placement problem. For instance, a heuristic constructive algorithm (HCA) is presented in [2] where in the integer variable are denoted by a sigmoid function. Another heuristic method is used in [3] to get a near optimal solution for realistic sized systems with a objective function of minimizing harmonic levels, capacitance costs and losses. This method is extended to unbalanced loads in [4]. Ant colony search algorithm (ACSA) is usd in [5] to get solution to optimal capacitor placement problem and network reconfiguration problem. The Optimal Capacitor placement and its sizing problem in [6] has an objective function of minimizing the cost subjected to voltage profile limits, capacitor sizes at each bus and power quality limits of harmonics. The effect of placement of capacitor on distribution system reliability is considered in [7] by defining multi objective function i.e. reliability cost, investment cost and cost of losses. Considerable amount of research has also been done on optimal placement of DG as well. An analytical method is presented in [8] to obtain the optimal location of DG units in radial and networked systems to minimize the losses. Optimal placement of DGs in [9] is fixed by using exhaustive search to optimize the efficiency and system reliability. In this work the system SAIDI is used to represent the reliability. An iterative based algorithm is given in [10], where in continuous power flow is used to find the most sensitive bus to voltage collapse or maximum loading for DG installation. The objective functions of this include the power loss reduction, power transfer capability improvement and to increase the voltage stability margins. Genetic algorithm (GA) is used in [11], to find the optimal DG location with various load models. The objective function here is base on multi objective index that considers real and reactive power losses, voltage profile and capacity of DG. Immune Volume 2, Issue 12, December 2014 Page 21

2 Algorithm (IA) is used in [13] to optimize the voltage profiles by changing the location of DGs with the constraints of bus voltage limits and line current limits. 2. PROBLEM FORMULATION The primary objective of Optimal DG placement and Optimal Shunt Capacitor banks is to improve the voltage profile satisfying all practical constrains. The main objective function defined in this work is to maximize the minimum voltage in the distribution system by installing DGs and Shunt capacitor banks at its optimal locations. Distributed Generators installed in Electrical power distribution systems can generate active power as well as reactive power to meet the requirements of local demands and hence reduces the voltage drop in a radial distribution system. At the same time Shunt capacitors installed in distribution systems generate the lagging reactive powers to meet the reactive power demands of the lagging inductive loads and thereby decreasing the voltage drops and hence helps in maintaining the good voltage profile. However, there are some criterions to evaluate how good a voltage profile is. It is difficult to develop a mathematical formulation of voltage profile for any optimization problem. In this section, formulas which will deal with the goodness of voltage profile in an optimization model is presented and hence the optimal locations of DGs as well as optimal locations of Shunt capacitor banks can be obtained for a better voltage profile. The most difficult issue in optimizing voltage profile of a distribution system is to ensure the lowest bus voltage in the system greater than the lower voltage limit. Generally in radial distribution system the voltage drops along the line thereby the loads far away from the substation end experiences low voltage problems. The objective function in this modeling is focused on the maximization of lowest bus voltage magnitude which can be written as (1) Where is an unknown variable, which can be fixed by observing voltage magnitude at all load buses of the distribution system and is subjected to the following constraints. (i) Power Flow Constraints: If shunt capacitor banks are used to connect in the system these equation will be (2) (3) (ii) Voltage magnitude Constraints The voltage at all buses should be within the range allowable minimum voltage value and maximum voltage i.e., for i all the load buses.(6) At the same time the voltage should be always greater than the minimum allowable bus voltage Here the objective function to maximize the (iii) Distributed Generator Constraints: In this model, optimal locations of DGs and its active and reactive power output are to be found. DG units can be installed at any bus except substation bus of the system. If a DG unit is installed at bus, its active and reactive power generations should be within the DG unit s capacity limits i.e., 3. APPLICATION OF PSO In this section, an approach is proposed to implement the PSO algorithm in solving the optimal network reconfiguration. The step by step procedure for PSO algorithm can be summarized as Step 1 : Initialization of population at random Step 2 : Velocity and position update Step 3 : updating P best and G best Step 4 : Goto step 2 until satisfying the terminating criterion Volume 2, Issue 12, December 2014 Page 22

3 3.1. INITIALIZATION It is the process of generating a particle at random. The particle consists of optimal location of DG, its real power output and reactive power output for mere DG placement problem(for case-1 to case-3). For case 4 and case 5 the locations of DG units is fixed and Optimal location of shunt capacitor banks are to found that is why the particle consists of optimal location list of shunt capacitor banks and real and reactive power output of DG units. Generation of a particle: For case-1 to case-3, the individual particle consists of the optimal location of DG unit, real power output and reactive power output of the DG as given in (10) X i 0 =(LDG, P DG, Q DG ) (10) Where X i 0 is the i th particle in 0 th iteration LDG is the location of DG P DG is the real power output of the DG Q DG is the reactive power output of the DG For case-4 and case-5, the individual particle consists of the location list of Capacitor units (it may be for 2 or 4 or 6 or 8 capacitor banks), real power output and reactive power output of the DG X i 0 =(LCB1,LCB2,..LCBn, P DG, Q DG ) (11) Where X i 0 is the i th particle in 0 th iteration, LCB1 is the location of first capacitor bank, LCBn is the location of n th capacitor bank, n is the number of capacitor banks used, P DG is the real power output of the DG, Q DG is the reactive power output of the DG, The velocity of individual particle i can be observed as V i 0 = (V il,, V in ) 3.2. THE PSO ALGORITHM: Step1. Initialization-initialize all particles Step2. Set iteration count=0 Step3. Evaluate the fitness function i.e. the minimum voltage in the system and fix the individual particles minimum voltage to individuals Pbest and find the maximum value from minimum voltages of all the particles and fix it as Gbest for this iteration Step4. Evaluate the velocity of each population by using the equation Step5. Update the position of each population by using the equation.(12) (13) Step6. Find the new values of fitness function for each of the population and replace Pbest with it if it is greater than the former value and also fix the maximum value of Pbest among all the population to Gbest Step7. Increase the iteration count by 1 Step8. Check the stopping criterion, if not satisfied go to step3 Finally the optimum solution can be obtained through Gbest 4. EXAMPLE The performance of the proposed PSO algorithm for Optimal Capacitor placement and Optimal DG placement is verified on IEEE-41 bus system, consisting of 41 buses, 40 lines with a total real power load of 4635 kw and total reactive power load of 3250 kvar. For this test system five cases are considered: Case-1: Optimal DG placement of capacity about of total load without Shunt Capacitor Banks. Case-2: Optimal DG placement of capacity that can meet total load of the system without Shunt Capacitor Banks. Case-3: Optimal DG placement of capacity of total load of the system and DG is operated in islanding mode, without Shunt Capacitors Banks. Case-4: Optimal Capacitor placement in Grid connected mode with DG Case-5: Optimal Capacitor placement in Island operation mode of DG. In case-1, the rating of the DG used is of 1/3 rd of total load of the distribution system which is approximately equal to 1500 kw and 1200 kvar. The simulation results for this case are given in Table 1. In case-2, the real and reactive power capacities of DG unit are increased to 5000 kw and 4000 kvar and is sufficient to feed all the loads of the system. Therefore DG can be operated either in grid connected mode or in islanding mode. For case-2 the DG is operated in Grid connected mode. The simulation results for case-2 are given in Table 1. Volume 2, Issue 12, December 2014 Page 23

4 In case-3, also the real and reactive power capacities of DG unit used are 5000 kw and 4000 kvar and is sufficient to feed all the loads of the system. When the entire distribution system suffers from the power outage then it is completely disconnected from the substation and is connected to DG unit. The operation of DG in such case is called as Islanding operation of DG. In this case also only one DG is used in the system. The simulation results for case-3 are given in Table 1. Table 1: Simulation Results for case-1, case-2 and case-3 and minimum voltage comparison From case-1 to case-3, better results are observed for case-2 where the capacity of the DG is sufficient to meet the entire load and is to be operated in grid connected mode. Figure 1 shows the voltage profile of a distribution system for case- 1, case-2 and case CASE-1 CASE-2 CASE Voltage (p.u) Bus Number Figure 1: The voltage profile of a distribution system In case-4 also the real and reactive power capacities of DG unit used are 4000 kw and 2500 kvar and is sufficient to feed all the loads of the system. In addition to the DG units Shunt capacitors are also used to improve the voltage profile. The total number capacitors used in this case are 2 to 8 and the reactive power rating of each capacitor is fixed at 400 kvar. In this case the distribution system is operated in grid connected mode. The DG unit in this case is located at bus number 9 which is as found in case -2. The simulation results and comparison of results with existing method for case-4 is given in Table 2. Table 2: Simulation Results for case-4 and minimum voltage comparison Volume 2, Issue 12, December 2014 Page 24

5 Case-5 is similar to case-4 but in case-5 the DG is used to operate in island mode. The DG unit in this case is located at bus number 8 which is as found in case -3. The simulation results and comparison of results with existing method for case-5 is given in Table 3 Table 3: Simulation Results for case-4 and minimum voltage comparison From the simulations results of case-4 and case-5, it is observed that better voltage profile is obtained when the DG has the capacity of supplying the total load of the system and it can be either operated in grid connected mode or island mode when the distribution system is connected simultaneously with capacitors. 4.CONCLUSIONS In this paper, a Particle Swarm Optimization algorithm has been proposed to find the optimal locations of shunt capacitor bank in the distribution network in the presence of DG units. The problem here is formulated as a non-linear optimization problem with an objective function of maximizing the minimum voltage subject to a set of constraints. Test results has been presented, that shows that using PSO the optimal capacitor placement problem with DG units can be solved effectively for loss reduction when compared to existing algorithm. REFERENCES [1] I. American National Standards Institute, "American National Standard For Electric Power Systems and Equipment Voltage Ratings (60 Hertz)," National Electrical Manufacturers Association, [2] I. C. da Silva, S. Carneiro, E. J. de Oliveira, J. de Souza Costa, J. L. Rezende Pereira, and P. A. N. Garcia, "A Heuristic Constructive Algorithm for Capacitor Placement on Distribution Systems," IEEE Transactions on Power Systems, vol. 23, pp , [3] B. Gou and A. Abur, "Optimal capacitor placement for improving power quality," proceedings of IEEE Power Engineering Society Summer Meeting, 1999, pp , vol.1. [4] G. Carpinelli, P. Varilone, V. Di Vito, and A. Abur, "Capacitor placement in three-phase distribution systems with nonlinear and 6 unbalanced loads," Generation, Transmission and Distribution, IEE Proceedings-, vol. 152, pp , [5] C. Chung-Fu, "Reconfiguration and Capacitor Placement for Loss Reduction of Distribution Systems by Ant Colony Search Algorithm," IEEE Transactions on Power Systems, vol. 23, pp , [6] M. Ladjavardi and M. A. S. Masoum, "Genetically Optimized Fuzzy Placement and Sizing of Capacitor Banks in Distorted Distribution Networks," IEEE Transactions on Power Delivery, vol. 23, pp , [7] A. H. Etemadi and M. Fotuhi-Firuzabad, "Distribution system reliability enhancement using optimal capacitor placement," Generation, Transmission & Distribution, IET, vol. 2, pp , [8] W. Caisheng and M. H. Nehrir, "Analytical approaches for optimal placement of distributed generation sources in power systems," IEEE Transactions on Power Systems, vol. 19, pp , [9] D. Zhu, R. P. Broadwater, T. Kwa-Sur, R. Seguin, and H. sgeirsson, "Impact of DG placement on reliability and efficiency with time-varying loads," IEEE Transactions on Power Systems, vol. 21, pp , [10] H. Hedayati, S. A. Nabaviniaki, and A. Akbarimajd, "A Method for Placement of DG Units in Distribution Networks," IEEE Transactions on Power Delivery, vol. 23, pp , Volume 2, Issue 12, December 2014 Page 25

6 [11] D. Singh and K. S. Verma, "Multiobjective Optimization for DG Planning With Load Models," IEEE Transactions on Power Systems, vol. 24, pp , [12] W. Prommee and W. Ongsakul, "Optimal multi-distributed generation placement by adaptive weight particle swarm optimization," International Conference on Control, Automation and Systems, ICCAS 2008, pp [13] M. R. Aghaebrahimi, M. Amiri, and S. H. Zahiri, "An immune-based optimization method for distributed generation placement in order to optimize voltage profile," International Conference on Sustainable Power Generation and Supply, SUPERGEN '09., [14] T. Jen-Hao, L. Tain-Syh, and L. Yi-Hwa, "Strategic distributed generator placements for service reliability improvements," in proceeding of IEEE Power Engineering Society Summer Meeting, 2002, pp , vol.2. [15] M. E. Baran and F. F. Wu, "Network reconfiguration in distribution systems for loss reduction and load balancing", IEEE Transations on Power Delivery, vol. 4, pp , Volume 2, Issue 12, December 2014 Page 26