TOWARDS RESILIENT SMART GRIDS: ROBUST CONTROL FRAMEWORK DESIGN TO ENHANCE TRANSIENT STABILITY

Transcription

1 TOWARDS RESILIENT SMART GRIDS: ROBUST CONTROL FRAMEWORK DESIGN TO ENHANCE TRANSIENT STABILITY By MUHARREM AYAR A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2017

2 c 2017 Muharrem Ayar 2

3 To my lovely wife Ozlem, my beloved son Omer Selim and my parents 3

4 ACKNOWLEDGMENTS I would like to express my deepest respect and most sincere gratitude to my advisor, Dr. Haniph A. Latchman, for his encouragement, guidance, and support. He did not spare any effort to improve my research and teaching skills. His constructive criticism and invaluable suggestions throughout my graduate study have helped my research and enabled me to develop a better understanding of the subject. I am extremely privileged to have been a student under his supervision. I hope that I could become as good an advisor to my students as Dr. Latchman in the future. I extend my gratitude to my co-advisor, Dr. Janise McNair, for her guidance and support. She also assisted me greatly to improve my research and complete my doctoral dissertation. She is a dedicated advisor, and I have benefited tremendously from having been a student in her research group. I also express my appreciation to Dr. Arturo Bretas for his extraordinary guidance and support to improve my doctoral research. Also, I want to thank Dr. Norman Fitz-Coy for accepting to serve on my dissertation committee and his recommendations. A very special appreciation to my friend Dr. Serhat Obuz for his collaboration and fruitful discussions we held throughout my research, and for his contributions to the success of our joint research work. Finally, and most importantly, I would like to thank my family. My parents have been undeniably my pillar of strength and a constant source of motivation. Their prayers for me were what sustained me hereto. I cannot thank my lovely wife enough; without her understanding, patience, and support, I would not have been able to continue and succeed. My beloved son, your innocence was my fuel and your smile was my remedy. Special thanks also to my sisters, for their prayers for me. 4

5 TABLE OF CONTENTS page ACKNOWLEDGMENTS LIST OF TABLES LIST OF FIGURES ABSTRACT CHAPTER 1 INTRODUCTION Challenges in Smart Grids Cyber-Physical Security Stability and Resiliency Communication Research Motivation Research Contributions Dissertation Organization SMART GRID STABILITY AND CONTROL Smart Grid Stability Rotor Angle Stability Transient Stability Small-Signal Stability Frequency Stability Voltage Stability Controls for Smart Grid Transient Stability Decentralized Control Centralized Control Distributed Control Summary A ROBUST DECENTRALIZED CONTROL FRAMEWORK WITH CONSTANT TIME DELAY COMPENSATION Dynamic Model of Synchronous Machines Robust Nonlinear Controller Design Lyapunov Stability Analysis Simulation and Results Summary

6 4 CYBER-ENABLED DECENTRALIZED CONTROL FRAMEWORK WITH UN- KNOWN TIME-VARYING INPUT DELAY COMPENSATION Dynamic Model and Properties of Synchronous Machines Control Objective and Development Stability Analysis State Estimator Simulation and Results Summary A DISTRIBUTED NONLINEAR CONTROL STRATEGY FOR ENHANCING SMART GRID TRANSIENT STABILITY Distributed Control Framework Dynamic Model of Synchronous Machines Control Development Lyapunov Stability Analysis Simulation and Results Case Study under Practical Limitations Summary AN ADAPTIVE MAC PROTOCOL DESIGN FOR SMART GRID HOME AREA NETWORKS Literature Review Research Motivation HomePlug/IEEE 1901 CSMA/CA MAC Protocol Backoff Procedure Priority Resolution Adaptive Contention Window based CSMA/CA MAC Performance Evaluation with Prioritized Traffic Summary CONCLUSIONS AND FUTURE WORK Summary Future Work A Cross-Layer Strategy for Cyber-Physical Security of Smart Grids Saturated Robust Controller REFERENCES BIOGRAPHICAL SKETCH

7 Table LIST OF TABLES page 3-1 Decentralized controller gain settings for known constant time delay case Adjusted controller gain values for unknown time-varying constant time delay case Distributed controller gain settings Default simulation parameters Contention resolution parameters of the standard HomePlug MAC protocol HomePlug 1.0 MAC parameters

8 Figure LIST OF FIGURES page 1-1 Evolution of power girds: Past, Today and Future A satellite image of the Northeastern cities in US during 2003 blackout An overview of smart grid An overview of smart grid communication networks Classification of power system stability The dynamic model of synchronous machines An overview of decentralized control framework for transient stability Rotor angle and speed deviation of synchronous machines during and after three phase fault Stabilization time versus varying DESS capacity and time delay Stabilization time versus clearing time Stabilization time versus additive time-varying disturbance PMUs and synchrophasor data flows in the North American power grid Data flow of the proposed cyber-physical control strategy Rotor speed and angle deviation of synchronous machines during and after three phase fault Representation of varying actual time delay and its constant estimate Comparative simulation results under practical limitations An overview of designed distributed control framework for smart grids Rotor angle deviation and rotor speed oscillation over time during and after three-phase fault inception Stabilization performance of the distributed controller under practical limitations The MAC throughput comparison of wireless (IEEE ) and wired (HomePlug) networking technologies Operational flow chart of HomePlug/IEEE 1901 CSMA/CA MAC protocol Backoff resolution of HomePlug/IEEE 1901 CSMA/CA MAC protocol

9 6-4 Markov chain model for adaptive contention window based CSMA/CA MAC protocol Numeric and analytic solution for p o Estimating number of contending nodes over a changing network traffic Simulation results to evaluate MAC efficiency of the proposed MAC protocol when the number of nodes is given and estimated Case study to compare the MAC efficiency of the designed controller with the standardized HomePlug MAC Case study to compare the channel access delay performance of the designed controller with the standardized HomePlug MAC Cross-layer cyber-physical security framework for smart grid

10 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy TOWARDS RESILIENT SMART GRIDS: ROBUST CONTROL FRAMEWORK DESIGN TO ENHANCE TRANSIENT STABILITY By Muharrem Ayar August 2017 Chair: Haniph A. Latcman Cochair: Janise McNair Major: Electrical and Computer Engineering Smart grids use digital communications, signal processing, sensing, and control systems technologies to enhance the efficiency, reliability, and security of electrical power systems and contribute to the sustainability of energy with the large penetration of renewable energy sources. Increasing integration of the cutting-edge digital technologies has become the source of new challenges such as cybersecurity and uncertainties, while at the same time being the cornerstone of new opportunities such as real-time control and monitoring systems to enhance the power system stability. Maintaining the stability of power systems has become an even more challenging problem with the increasing complexity by enabling two-way power flow through active loads and energy storage systems. Fortunately, making real-time data exchange between sensors and control units possible through communication networks allows designing advanced control systems. However, communication delay which is inherent in communication systems limits the capacity of the control systems and introduce uncertainty to the system. On the other hand, cyber-attacks to the various segments of smart grids threat the stability and security of power systems by leading to malfunction of underlying protection and control systems. In today s world, isolating systems by deploying private networks cannot entirely protect them from cyber-attacks and penetration. The Stuxnet case, for example, led to 10

11 the malfunctioning of control systems in Iranian s nuclear power station, despite being physically isolated from the global network. Therefore, addressing various form of cyberattacks requires defense-in-depth strategies whereby enabling multiple layers of security in the underlying communication and control systems. This dissertation presents distributed and decentralized robust control frameworks that aim at enhancing the transient stability and resiliency of smart grids in the face of cyber-physical disturbances by employing phasor measurement units (PMU) and distributed energy storage systems (DESS). Robust controllers introduce a novel time delay compensation technique to mitigate the effect of communication and control input time delay. In addition, uncertainties arising from varying plant parameters and errors in sensor measurements are considered in the robust controller design. Furthermore, the communication delay is addressed in network layer by developing an adaptive medium access control (MAC) protocol to reduce the channel access delay and improve the data throughput with respect to increasing numbers of connected intelligent devices. The success of robust controllers is proven by conducting several comparative case studies based on IEEE 39 bus 10 machines test power system. The enhanced resiliency to the large time delay and uncertainties highlights the success of robust controllers in comparison to the state-of-the-art controllers. To illustrate, while the parametric feedback linearization (PFL) controller can tolerate up to 160ms communication delay, the designed distributed controller can stabilize a perturbed power system even in the existence of 1s communication delay. Similarly, comparisons between decentralized controller and the well-known multi-band power system stabilizer (MB-PSS) controller shows that decentralized controller can reduce the stabilization time by 80% when the delay is known and by 60% if the delay is unknown with respect to the MB-PSS. It is evident that the robust controller owes this success to the designed novel time delay compensation technique. Moreover, the simulation results with respect to uncertainty in sensor measurements show that the robust controller is resilient up to 10% deviation. 11

12 Whereas, the measurement uncertainty affect the stabilization performance of the PFL controller significantly. In addition, the designed MAC protocol is tested in a home area network (HAN) which hosts large numbers of nodes with various applications. Simulation results demonstrate that an 80% MAC efficiency is maintained for up to 100 nodes while the efficiency of standardized HomePlug MAC protocol, for example, reduces down to 10%. Similarly, an 80% reduction in channel access delay is achieved by the adaptive MAC protocol with respect to the HomePlug MAC protocol. It is asserted that tailoring the adaptive MAC protocol for other communication networks such as neighborhood area network (NAN) and wide area networks (WAN) can reduce the channel access delay and improve data throughput. 12

13 CHAPTER 1 INTRODUCTION Electricity is one of the ground-breaking discoveries of the 19th century that has made a great impact on the socioeconomic development of nations. Reliable delivery of electricity plays a crucial role in nation s economy, security, and even in the health and safety. However, the current electric infrastructures are aging and they are being pushed to do more than they were originally designed to do. Fundamental changes in both demand and supply side cause electrical power system to face increasing stress. On the demand side, increasing world energy consumption has been forcing capacity of electrical power systems to work on their physical limits. The International Energy Agency has recently released 2016 World Energy Outlook Report, that projects 30% rise in world energy consumption by 2040 [1]. Similarly, the International Energy Outlook 2016 (IEO2016) of the U.S. Energy Information Administration estimates that the energy consumption will grow by 48% between 2012 and 2040 [2]. In order to meet the current energy demand and preparing the power system for future, advanced technologies such as demand response (DR) and smart metering have been used to manage energy consumption and generation. On the supply side, concerns about energy security and sustainability, environmental effects of fossil fuel emission, and sustained long-term energy prices have led a shift from bulk energy generation to distributed generation by increasingly integrating renewable energy sources (RES) which are abundant in the form of solar, hydro, wind, geothermal, and biomass. According to the IEO2016, harvesting energy from renewables is growing at a rapid pace all over the world. Since renewables are eco-friendly and economic, many countries including the United States have been promoting green energy generation by adopting new energy policies and incentives [3]. In the United States, energy generation from renewables in the form of wind, solar, and geothermal has been doubled since 2008 and 20% growth has been targeted by 2020 [4]. China 13

14 Figure 1-1. Evolution of power girds: Past, Today and Future [7]. targeted to achieve 20% renewable by 2020 [3] and more ambitiously set the target of 86% renewable by 2050 [5]. Similarly, European Commission asserted 20% renewable target of Europe by 2020 [6]. The conventional power system architecture was based on bulk energy generation remotely located from consumers, hierarchical control systems with minimal feedback, and passive loads. The capacity, flexibility, reliability, and security of the traditional system is far more behind the need for meeting the emerging trends, such as increasing integration of relatively low inertia generation source, large penetration of distributed generation, and the need for better resiliency. It is expected from the today s electrical grids that dynamically optimize operation and sources, integrate diverse generation sources, integrate demand response, quickly detect and mitigate disturbances and provide robust protection against cyber-physical threats. Incorporating all these features transforms the conventional electric grids to the future s modern smart grids as illustrated in Figure 1-1. The targeted benefits from the smart grids includes: Increasing integration of renewable energy systems, Improving the efficiency of energy transmission, Engaging end-users in power systems management, Optimizing operation and management costs, 14

15 Quicker restoration or self-healing power systems after a disturbance, Enhancing the security. The modernization of the traditional power systems requires the use of cutting-edge technologies such as advanced metering infrastructures (AMI), wireless and fiber optic networks, and energy storage systems and advanced control that communicate and collaborate to enable safe and reliable two-way electricity and data flow. Enabling advanced technologies can greatly decrease the frequency and duration of power outages, reduces the impact of natural disasters, and accelerates the restoration service [2, 8]. Grid modernization must encompass the technologies that offer cybersecurity protections and innovative control system architectures. Smart grids are one of the critical infrastructures of the nations and must be protected well to avoid major blackouts which may cause socioeconomic disasters by damaging and even worse seizing the operation of banks, telecommunication, traffic, etc. A smarter grid should, therefore, enhance the resiliency of power systems in order to prepare them to address emergencies such as natural disasters and terrorist attacks. In addition to the resiliency of electrical grids, power system stability is vital for the reliable and sustainable operation of electrical grids that is maintained by enabling centralized, decentralized or distributed control architectures. Traditional control systems with minimal local feedback suffer from lack of situational awareness and the need for human intervention. The Northwestern blackouts in 2003 [9] and the Italy blackout in 2003 [10], for example, were the result of a cascading failure that occurred very fast due to the lack of advanced automation and global feedback for control. These two unhindered major blackouts affected over 50 million people and over 400 generators and caused a considerable amount of economic loss [11]. In the Figure 1-2, a satellite image of the US Northeastern cities in 2003 illustrates the blackout. 15

16 Figure 1-2. A satellite image of the Northeastern cities in US during 2003 blackout. The two-way interactive communication capacity of the smart grids equipment allows advanced digital control architectures with a real-time global feedback to enhance the stability and resiliency of electrical power grids. Current power systems has been relatively interacted with information and communication technologies and keep increasing interaction and to support automation, protection and control application as depicted in Figure 1-3. In today s smart grid, wide-area control systems (WACS) are employed throughout generation and transmission systems. However, their centralized architecture emerges several challenges such as increasing communication traffic and data volume with large penetration of advanced sensors, and cybersecurity risk due to their dependence on a central controller. Thus, the current trend for future smart grid control systems shifts to distributed architectures rather than centralized ones. The cybersecurity of smart grids is paramount for national security and need to be investigated and treated carefully. The National Institute of Standards and Technology (NIST) advocates that cybersecurity of electrical power grids requires a defense-indepth strategies by enabling multiple security throughout communication, protection and control systems. In this dissertation, several control frameworks that take in consideration of cyber-physical disturbances to enhance the transient stability are presented. Moreover, a communication protocol is presented that aims at improving the data throughput and the channel access delay for smart grid application within home 16

17 Figure 1-3. An overview of smart grid [8]. area networks. An adaptive medium access control (MAC) protocol has been designed to leverage the efficiency of highly populated networks. The major contributions of this dissertation includes: Decentralized and distributed control frameworks design, Developing model-free based robust nonlinear controllers, Implementing novel time delay compensation techniques to overcome effects of known and unknown time-varying delay, Using distributed energy storage systems (DESS) for transient stability enhancement, Designing an adaptive MAC protocol for smart grid home-area network Cyber-Physical Security 1.1 Challenges in Smart Grids Electrical energy is the major driver of social and economic dynamic of nations and thus securing the energy is critical. It is evident as the US has designated electrical power system as one of the top 16 critical infrastructures [12]. Concerns about the security of electrical grids have raised recently because of increasingly connecting grid equipment to communication networks that provides multiple entry points for the intrusion of adversary. Cyber-physical security, thus, has become one of the top 17

18 priorities of nations and many initiatives and research activities have been supported by governments. The US government, for example, allocated $14 billion budget for funding cybersecurity research and initiatives in FY 2016 [13]. Smart grids are one of the critical cyber-physical architectures comprised of a broad range of technologies implemented throughout the generation, transmission, and distribution systems that are owned and regulated by numerous owners. The large diversity in incorporated technological equipment and varying regional regulations across the countries requires consensus to address cyber-physical security. In the US, for example, several organizations including the Department of Energy (DoE), The National Electric Sector Cybersecurity Organization (NESCO), the National Institute of Standards (NIST), and the Nort American Electric Reliability Corporation (NERC) take on a mission with regard to the electrical power sector cybersecurity and resiliency. The NIST advocates that cybersecurity of intelligent electrical grids need defensein-depth strategies that utilize multiple layer security throughout the communication, protection and restoring systems [14]. Adaptive and dynamic nature of cyber-attacks threatens the various layer of power systems. The Stuxnet, for example, is a virus first identified in 2010 that caused a substantial damage in Iran s nuclear program [15]. This particular malware does not have a domain-specific design and an architecture which could be tailored as a platform for attacking modern supervisory control and data acquisition (SCADA) and PLC systems that are highly utilized in power system protection and control. It is evident that boosting only the cybersecurity of communication system or isolating SCADA systems from global networks may not be enough to protect smart grids as it was experienced by the Stuxnet that was introduced to the systems via a USB drive. Because of these reasons, cybersecurity needs to be considered throughout the entire grid operations and functions including communication, protection and control systems. 18

19 Electrical power grids are highly interconnected and a local failure or a cyberattack, which can lead a cascaded fault that may result in major blackouts. As an example, Ukrainian blackout in 2015 caused by a cyber-attack to a substation and culminated with a major power outage that affected over 225,000 people in Ukraine [16]. Quadrennial Energy Review report of US Department of Energy reveals the significance of smart grid cybersecurity by stating that electricity system faces imminent danger from cyber-attacks [17]. To draw attention towards cybersecurity of smart grid, many warnings [18 20] and some guidelines have been published, such as NISTIR 7628 [14] and NIST SP 1108 [21]. Since there is no single security measure that could counter all types of threats in smart grids, there is a need for cross-layer security solutions among communication, protection and control systems as suggested by the NIST. Communications systems need to be leveraged to detect and protect grid equipment from intrusions, malicious data injection, and intentionally occupation to increase latency. If communication layer fails, protection systems such as state estimation (SE) must be able to detect and correct malicious parameters to prevent systems from malfunctioning because of disturbances. On the other hand, control systems must be resilient to either failure of communication and protection system or inability to provide a totally reliable feedback to maintain the stability of systems or recovering the system that subjected to a major disturbance Stability and Resiliency Smart grid must address not only deliberate cyber-attacks but also inadvertent compromises of utilized cyber-physical infrastructures due to user errors, equipment failures and natural disasters to maintain the stability of systems. The power systems stability has always been a major concern for sustaining their reliable and secure operation. However, increasing integration of low inertia generations from renewables, large penetration of distributed energy generations at the distribution level, and introducing 19

20 active loads in electrical grid to enable bi-directional power flow have fueled the power system instability problems. In conventional electrical power systems, stability has been treated by conducting local control actions with a minimal feedback signals from associated equipment. The emerging instability problem with the increasing complexity in power system environment and growing interdependency between cyber and physical components reveal the need for advanced robust control system architectures. Fortunately, the ability of information technology to enable real-time two-way communication between widely dispersed sensors such as PMU and control systems provides an opportunity to design real-time monitoring and control systems such as wide-area monitoring systems (WAMS) and wide-area control systems (WACS). The WACS proposes a centralized control architecture that aggregates system information at a central point via remotely installed sensors, calculate control signals and actuates remote devices in the case of disturbances. The increased visibility of grid through distributed sensors helps control systems to command the entire grid effectively. However, concerns about scalability and security of centralized control architectures have been arising because of the increasing communication burden and security risk of being dependent on a single control center. Emerging uncertainties that may stem from the communication delay and the loss or the failure of sensors contribute to the instability of power systems. On the other hand, the coexistence of a variety of low inertia energy generators with bulk energy generators adversely affect the physical dynamics of the electrical power system [22]. Distributed generation units such as inverter-connected wind turbines and PV, which do not have rotational inertia, have been effectively displacing the rotating conventional generators. This transformation results in changes in electromechanical 20

21 dynamics of synchronous machines and affects the power system stability [23]. Moreover, the fast frequency dynamics with low rotational inertia make frequency control and power system stability even more challenging. Taking into account all these challenges, new robust control architectures are explicitly required to enhance the stability and resiliency power systems in the face of cyber-physical disturbances. It is concluded that controller that is required must be able to withstand to uncertainties that arise from cyber treats and compromises of the cyber and physical infrastructures, and changing nonlinear dynamics coupled with reducing overall rotational inertia Communication Figure 1-4. An overview of smart grid communication networks [24]. Communication technologies are the key enablers of the smart grid applications such as demand response, real-time monitoring, automation, and control, etc. Smart grid communication networks (SGCN) are typically comprised of several segments, each of which operates within a specific region of electrical power systems to ensure information and control message exchange among entities. The communication characteristics of these segments differ from each other in terms of operation region, supported application, delay, and bandwidth requirements. In general, the SGNC are decomposed into three representative networks that are home area networks (HAN), 21

22 neighborhood area networks (NAN) and wide area networks (WAN), as illustrated in Figure 1-4. Home Area Networks (HAN) A HAN is utilized in residential dwellings to support a range of applications such as smart meters, smart appliances, charging and control of Plug-in Hybrid Electric Vehicles (PHEVs), and IP multimedia. Typically, HANs need to cover areas of up to 200m 2. Heterogeneity is the biggest challenge in HAN because of different needs of supported applications such as various data rate and delay requirements. HANs tailor wireless, wired or hybrid networking technologies such as PLC, Zigbee and Wi-Fi to support smart applications within the premises. Neighborhood Area Networks (NAN) The NAN enables information exchange between a cluster of smart meters at customer premises and utility company s WANs. The population of each NAN varies from a few hundred to a few thousand of smart meters depending on the power grid topology and the deployed communications technology and protocol. The required data rate varies depending on deployed applications. While a simple demand meter reading application only needs a few bps, supporting sophisticated applications such as advanced distribution automation, fault detection and restoration may require higher data rates, e.g., a few tens of kbps per meter. It is worth to note that the NAN is responsible for transporting a huge volume of different types of data and distributing control signals between utility companies and a large number of devices installed at customer premises [25]. The NAN can be formed by using power line communication (PLC), Wi-Fi and cellular technologies. Wide Area Network (WAN) WAN is responsible for long-haul communications such as delivering aggregated data of multiple NANs to utility company s private networks and ensuring data exchange among different data concentrators of power generation plants, distributed energy 22

23 resource stations, transmission and distribution grids, control centers, etc [25]. The WAN may cover a very large area, i.e., thousands of square kilometers and could aggregate a large number of supported devices and thus require hundreds of megabits per second (Mbps) of data transmission. WANs are usually enabled by using cellular networking technology such as WiMaX, 3G, and LTE and fiber optical solutions for the given long distances among entities. Installation cost of fiber optical networks and operational cost of cellular network emerge as a problem from utility & business perspective. The seamless collaboration of all these segments reveals the need for interoperability of various communications technologies to coexist and to meet the requirements of each applications in terms of data rates, communications latency, deployment/maintenance costs. The Electric Power Research Institute (EPRI) and the National Institute of Standards and Technology (NIST) emphasize that communication between each component in the smart grid is extremely important to secure the energy generation and consumption in an efficient way [26]. Currently standardized wireless (e.g., cellular, satellite, microwave, WiMAX, WiFi, and Zigbee) and wired (e.g, copper cable, fiber optic cable, and power line carrier) network technologies have been designed specifically for internet communication but tailored for SGCN. It must be noted that, the internet and smart grid communication networks pose fundamental differences in terms of bandwidth, latency, and security requirements. While, the data rate and the fairness, for example, are the key metrics for internet communication, latency requirements are more stringent in smart grids. For instance, load shedding for under frequency has a delay allowance of only 10 ms [25]. 1.2 Research Motivation This dissertation looks for answers for following questions arises in smart grid control and communications: 23

24 1. How to enhance the resiliency of smart grids by addressing transient stability problem? 2. How to address the negative influence of large penetration of distributed generations? 3. How to mitigate the effect of uncertainties such as delay, erroneous sensor measurement, and varying plant parameters in control systems? 4. How to improve the channel access delay and throughput performance of the smart grid communication networks at the medium access control layer? 1.3 Research Contributions The contributions of the research can be summarized as follows: 1. A decentralized control framework has been developed to enhance the transient stability margin of synchronous generators (SG) when a large disturbance such as loss of large loads or generators occurs. The designed control framework employs PMU to obtain local measurements and DESS to provide external power for damping the frequency oscillation quickly when SG are perturbed. A modelfree based nonlinear robust controller with a novel constant and known input delay compensation technique has been developed and the proposed framework has been validated on IEEE 39 bus 10 machine test power system via Matlab- Simulink. 2. The delay compensation technique applied to decentralized control framework has been leveraged to take care of unknown time-varying delay. Also, the control framework has been boosted by enabling state estimation function to filter out the PMU measurement before entering the controller. 3. A distributed control framework has been designed to enhance the transient stability of smart grids by enabling situational awareness. In addition to the local measurements, remote data from adjacent buses are considered to calculate control signal. In contrast to the centralized control architectures such as WACS, 24

25 the distributed control framework reduces the communication burden while partially maintaining situational awareness. Also, the distributed controller is advantageous over WACS in terms of cybersecurity. For example, a cyber-attack to the centralized controller may result in failure of the entire system, however, a cyber-attack to a distributed controller can only effect a particular area in the power grid and this area can be isolated to prevent the system from cascaded failures. 4. An adaptive medium access control protocol for smart grid home area networks have been developed to enhance the throughput and delay performance for the highly congested network. The increasing traffic throughout network might be because of either high connectivity or cyber attacks such as denial-of-service. The proposed MAC protocol maintains the throughput and delay characteristics of the network even for highly congested networks. Analytical and numerical studies demonstrate the success of the proposed MAC protocol with respect to the state-of-art models. 1.4 Dissertation Organization The rest of the dissertation is organized as follows. Chapter 2 presents a detailed review on power systems stability and control systems. In Chapter 3, a decentralized control framework has been introduced to address the transient stability issue of smart grids. In Chapter 4, the proposed decentralized controller has been extended by considering cyber-physical limitations and developing a new nonlinear robust controller to compensate for unknown time-varying time delay. In Chapter 5, a distributed control framework has been developed to enhance the stability and resiliency of synchronous generators. In Chapter 6, an adaptive channel access protocol is presented that has been developed to enhance the throughput and delay performance of HAN. The conclusion and final remarks are given in Chapter 6. 25

26 CHAPTER 2 SMART GRID STABILITY AND CONTROL In the conventional power systems, generally organized as generation, transmission, distribution and end-users (customers), the electrical power is generated through bulk energy sources that are located far away from end-users and first transformed to high voltage (HV) by step-up transformers before transmitting through long distances. At the distribution side, the high voltage is reduced to medium voltage (MV) or low voltage (LV) to provide electrical power to the residential customers and industry. The smart grid has drastically changed the classical power systems by enabling two-way power and communication data flow with the increasing integration of distributed generations (DG) and advanced digital technologies. The large penetration of DG distribution system is shifting distribution systems from being a passive network, containing only loads, to an active network. However, the intermittent and inertia-less nature of distributed energy sources such as wind power, photo voltaic (PV) impacts the stability of the power systems. Furthermore, equipping the power system components with intelligent electronic devices to connect them to data network raises cybersecurity issues besides their advantageous in terms of enhancing operation and management power systems. This chapter investigates the existing stability problems in smart grids and discusses control systems that have been developed for addressing the instability of power systems. Furthermore, contributions of the state-of-the-art controllers to the resiliency and the cyber-physical security of the smart grid are studied and the existing problems that are remained open are presented. 2.1 Smart Grid Stability Stability of power systems has been considered as critical for secure and reliable operation of system since 1920s [27] and has been defined by IEEE/CIGRE Joint Task 26

27 Figure 2-1. Classification of power system stability. Force in [28] as the ability of electrical power systems to regain a state of operation point after being subjected to a physical disturbance. Instability of smart grids is a complex problem as it can emerge in various forms depending on numerous factors. Throughout the history, maintaining the transient stability has been the dominant issue on most systems including electrical power grids. With the continuous evolution of power systems through increasing interconnections, integration of renewable energy sources, and deployment of digital technologies, various forms of power systems stability have emerged such as frequency stability, voltage stability, and rotor angle stability. It should be noted that instability of the power systems must be carefully identified before treating. In [28], the power systems stability has been defined and categorized as in Figure 2-1 by considering the physical nature of the resulting mode of instability, the size of the disturbances, and the devices, process and time spans to assess stability Rotor Angle Stability Rotor angle stability is the ability of the interconnected synchronous machines (generators) to remain in synchronism being subjected to a large or a small disturbance. Multiple synchronous machines run parallel and deliver active power to the loads depends on the rotor angle of the machines. Power system faults such as losing a large load lead to a sudden changes on the generator electrical power output. However, the mechanical power input to generators cannot response instantaneously. In steady-state 27

28 condition, there is an equilibrium between the input mechanical power and the electrical output power of all synchronous machines in interconnected power systems and speed of the machines remain same. During a fault, synchronous machines lose the equilibrium which results in the acceleration or deceleration of the machines. If a synchronous machine temporarily moves faster relative to the other machines, the rotor angle of the machine will advance with respect to slow machine. The resulting angular difference lead to increase load delivered by faster machine and decrease load delivered by slow machine in order to reduce the speed difference and hence the angular separation. Also, after a certain point, an increase in angular separation will be followed by decreasing the power transfer by fast machine which further increases the angular separation. If the kinetic energy corresponding to the angular separation cannot be absorbed, then instability occurs and synchronization of a machine or a group of machines will be lost. The power system stability depends on the existence of synchronizing torque and damping torque for each synchronous machine. Lack of synchronizing torque causes non-oscillatory instability and lack of damping torque lead to oscillatory instability. Rotor angle stability is divided into two subcategories: transient stability and small-signal stability which are the concern of power system when subjected to a large disturbance and small disturbance respectively Transient Stability Transient stability is the ability of synchronous machines to return to stable condition and maintaining synchronism after being subjected larges disturbances come out of switching ON and OFF of the circuit breakers to isolate and clear the faults in perturbed area in interconnected power systems. Since power systems often experience these type of faults, the transient stability needs to be studied carefully. The transient stability depends on the initial states and the severeness of the disturbances. Instability may take place in the form of angular separation due to insufficient synchronizing torque, that 28

29 Figure 2-2. The dynamic model of synchronous machines. is also called as first swing instability. In large systems, transient stability may occur as a result of superposition of a slow inertia swing mode and local plant swing mode leading a large excursion of rotor angle beyond the first swing [29]. The transient stability is a short term phenomena, that is, the target time frame for transient stability studies is usually 3 to 5 seconds following a disturbance. However, the time frame may extend to seconds for very large systems with dominant inter-area swings [28]. In order to study the transient stability of a synchronous generators using swing equation, a synchronous machine, as illustrated in Figure 2-2, can be examined. A synchronous machine supplied with input mechanical power P M produces a mechanical torque equal to T S that rotates the machine at a speed of ω rad/sec and outputs electromagnetic torque T E and electrical power P E on the receiving end. In steady state condition, if the synchronous machine is supplied from one end and a constant load connected to the other end, a relative angular displacement,, known as load angle δ, occurs between rotor axis and stator magnetic field in proportional to the loading of the machine. A sudden change in loading (add or remove), leads to deceleration or acceleration of the rotor accordingly with respect to the stator magnetic field and causes swinging of the rotor speed relative to the stator magnetic field. The relative motion of the load angle and stator magnetic field is known as swing equation for transient stability of power system [29 31]. There are numbers of factors that may influence the transient stability of power systems including generator inertia, generator loading, generator power output during 29

30 fault, and fault clearing time [29]. The inertia have become even critical with increasing penetration of inertialess renewable energy generations. The decreasing overall inertia makes transient stability a challenging issue for interconnected smart grid power systems Small-Signal Stability Small-disturbance or small-signal stability is associated with the ability of power system to resist small disturbances such that the linearization of the system dynamic model is allowable for stability analysis [29]. Small-signal stability problems can be resolved into local and global instability problems. Local problems are associated with only a small part of the power system and depends on the rotor angle oscillation of a single machine with respect to the rest of the power systems. Damping these oscillations rely on the strength of the transmission system. excitation control system and plant output [29]. On the other hand, global problems arises from inter area oscillations where oscillation of a group of machine in one area of swinging against a group of machines in another area. The characteristics of the global instability problems are very complicated and load characteristics are the major effects on the inter area stability mode. The time span for small-signal stability is on the order of 10 to 20 seconds following a disturbances [28] Frequency Stability Frequency stability stands for maintaining the steady frequency of power systems after being subjected to large disturbances perturbing the load and generation balance. The frequency instability causes tripping of generating units and/or loads. In general, large disturbances end up with excursion of frequency, power flows, voltage, hence advanced control and protection schemes that are required but not included in conventional transient stability and voltage stability studies. Frequency stability requires to maintain an equilibrium between loads and generators with a minimum unintentional loss of loads. In interconnected power systems, this 30

31 instability condition emerges during islanding power networks and arises the questions of whether or not each island will reach the equilibrium with minimum unintentional loss of load. The frequency stability problems generally stems from the poor response of the incorporated equipment and lack of coordination between control and protection systems [28]. During frequency excursion, the response time of the activated process and devices range from a fraction of seconds for the response of load shedding, generator control, and protections, to a several minutes for the response time of the devices such as load voltage controller and prime mover energy supply systems Voltage Stability Voltage stability aims at maintaining steady voltages at all buses after power system being subjected to a disturbance from a given initial operating points. Voltage instability occurs when the equilibrium between load and supply is lost, because the load tends to restore more power than the capacity of generation [29]. The voltage instability may end up with losing load or tripping transmission lines and so cascaded outages. Also, some generators may lose synchronism because of outages or operating conditions that violate field current limit [28, 32]. The voltage stability is analyzed under two subcategories as shown in Figure 2-1 that are small disturbance stability and large disturbance stability. Small-disturbance voltage stability aims at maintaining steady voltages after power systems being subjected to small disturbances such as load variations. Whereas, large-disturbance voltage stability targets sustaining all bus voltages within an allowable level following a large disturbance such as loss of generation, systems faults, presence of contingencies [28, 32]. Also, it is worth to note that the time span for voltage stability problem ranges from a few seconds that corresponds to short-term, to tens of minutes that corresponds to long-term voltage stability. The short-term voltage stability comprise of fast acting load components such as electronically controlled loads, induction motors, 31

32 and HVDC converters. Whereas, the long-term voltage stability includes slow acting components such as generator current limiters and tap-changing transformers [28]. 2.2 Controls for Smart Grid Transient Stability Reliability is the major concern of the power system design and operation. Maintaining reliability depends on security of the power system. To be secure, the power system must be stable and also must be secure against intentional or unintentional cyber physical disturbances at all level. In conventional power systems, various control and protection systems have been employed to enhance the reliability, security and stability of the electrical power grid. However, the power grids have experienced a big changes with the integration of digital technologies, distributed energy generation and various smart applications such as demand response, real-time monitoring and control. The rapid transformation of the power systems into smart grid emerges new security and stability problems beside numerous advantageous. The growing complexity of the power systems has left the conventional control systems insufficient in terms of security and stability. Transient stability, for instance, has been taken care of local excitation controllers in traditional power system. However, the increasing penetration of low inertia or inertia-less power generations arises and fuels the transient stability problem once again. In order to maintain the transient stability with respect to reducing rotational inertia in power system, robust control architectures are required. Due to the fact that smart grid has a cyber-physical nature, the proposed controllers need to be studied with a particular focus on cyber-physical effects and limitations. In the literature, control architectures for stability of power systems are categorized into three groups: i) decentralized (local) controllers, ii) centralized controllers, and iii) distributed controllers. In this section, different control schemes that fall in these groups are reviewed. 32

33 2.2.1 Decentralized Control Decentralized controllers are distributed all over the power systems that operates locally and perform its own objective rather than global objectives. Most of the excitation controllers in conventional power systems fall into this category. In decentralized control, each local controller situated near synchronous generators observes the rotor speed and rotor angle of its generator and calculate the control signal. Little or no communication need in decentralized control systems reduces the cost but lack of information exchange decreases the overall system performance. Conventional power system stabilizers (PSS) are an excellent example of the local linear controllers [33 35]. However, PSS are designed to respond to small disturbances, caused by small load variations, thus their contribution for transient stability is marginal. Over the last few years, advanced excitation control schemes have been developed to enhance the robustness of power systems by using nonlinear techniques or linearization techniques such as direct feedback linearization (DFL). The DFL method has been proposed in [36 39] to linearize the nonlinear dynamic model of multi-machine power systems in order to make it possible to use linear control techniques. Even though these DFL techniques provide a stabilization in large extent, they all require the exact knowledge of the power system plant parameters which is usually unavailable in practice [40]. Also, unexpected faults in system and external disturbances could degrade the stabilizing capability of a controller that is designed for a specific model Centralized Control Centralized controllers are considered advantageous over decentralized controllers in terms of situational awareness since centralized controllers enable information exchange globally. The integration of information communication systems makes possible monitoring the power system components in real-time through sensors and communication networks and control the entire systems with a broad knowledge. Widearea control systems (WACS) are currently implemented centralized control approaches. 33

34 WACS are implemented implemented in addition to the local primary controllers. It is envisioned that WACS can effectively address the inter-area oscillation problem since information exchange is enabled [41]. WACS are developing in parallel to the advancement in communication, sensor and digital signal processing technologies. Phasor measurement units (PMU), for instance, are one of the advanced sensor technologies deployed to the power systems in order to measure and transmit the real-time phasor data with a high precision and in real-time accordingly. Besides all advantages of WACS structures, the increasing number of PMU deployment for enhancing observability leads an exponential rise in data volume and arises communication problems such as time delay. Aggregating information at a central point to calculate the control action and transmitting control signal back to local actuators significantly increase the communication overhead. Moreover, the reliability of centralized controller is low, because communication systems are vulnerable to cyber-attacks and rely on a single point which increases the risk that any possible attack may lead the system to instability. In addition, communication latency is another issue that centralized controller hold due to the long communication distances. Transient stability, for example, is a short term phenomena and need to be circumvent quickly. If the latency goes beyond the acceptable rate, it becomes one of the key disturbance by itself for centralized controller Distributed Control The distributed controller have been a rising trend for multi-agent systems because of their efficiency in terms of processing and capability of enabling coordination between agents. The rising communication and security problems in centralized controllers and lack of information exchange in classical decentralized controller make distributed control strategies promising for power system stability. In distributed power system control strategies, first the entire system is divided into small regions and the interaction 34

35 between these regions are maintained through distributed controllers. Since sensors only transmit data to the associated controller, communication burden is relieved. Utilizing distributed control approaches do not only ease the communication burden and decrease latency but also enhance the power system security in contrast to centralized scheme. For example, if a distributed control agent experience a cyberattack, other distributed controllers can sustain their operation by isolating the attacked controller from the system. Furthermore, distributed controller are usually secondary controller, hence even if their operation perturbed, the primary local controller will continue to treat the system. Distributed controls for networked multi-agent systems have attracted many researchers because of their advantages in reducing communication load while enhancing the system performance. In [42, 43], authors present distributed consensus controllers for networked multi-agent systems. A distributed model predictive control (MPC) is presented in [44] and Venkat et al., uses distributed MPC strategy for power system automatic generation controller in [45, 46]. Furthermore, a distributed control strategy was designed to address transient stability problem by using parametric feedback linearization (PFL) technique to actuate external storage sources (ESS) in [47, 48]. Authors aim at damping the oscillation after power system being subjected a large disturbance by absorbing or injecting power from generator buses via fast acting EES such as flywheels or batteries. However, the proposed model is inconsistent with the distributed approach since it explicitly considers the knowledge of all generator angles and voltages in calculation of power flow. In addition, the proposed PFL based control requires exact model knowledge of the dynamic system which is unrealistic for highly nonlinear smart grid power systems. Furthermore, a distributed frequency control algorithm that is capable of restoring system frequency after a disturbance is presented in [49]. This method uses a PI-like controller to actuate the mechanical power input of generators to damp oscillations of 35

36 power systems. Technological limitations of the generator turbine and valve actuation speeds and time constants may limit the performance and effectiveness of this kind of approach for system stabilization. One limitation of this method is that it considers linearized power flow equations, which may introduce errors when generator angles largely deviate from the equilibrium point during severe disturbances. Time delay is still an issue even for distributed controllers since even a small time delay may significantly affect the control performance. Time delay systems have been thus a major interest in many studies [50]. In recent decades, efforts focused on designing controllers which are subjected to time delay for linear dynamics [51, 52] and nonlinear dynamics [53 59]. Compensating the time delay problem has been addressed for linear systems in [60 64] and for nonlinear systems in [65 68] with exact model knowledge. In [66 68], predictor based controllers are designed to compensate for an arbitrary long input time delay by transforming the input delay as a transport partial differential equation. However, the predictor-based controllers require the exact model knowledge of the dynamics and do not consider uncertainties in field parameters and external disturbances. Uncertainties in field parameters and external disturbances are inevitable in many nonlinear systems such as smart grids. In order to abstain from the exact model knowledge requirement of the dynamics, several nonlinear controllers are designed [59, 69 71]. Hence, there is a need for designing controllers that can compensate for the time delay and external disturbances for uncertain nonlinear dynamics. The designed controllers [59, 69, 70] consider single-agent systems and do not consider the communication delay. Therefore, there is a need for distributed controllers that are robust to communication and control input delay and also external disturbances for uncertain nonlinear dynamics such as smart grids. 2.3 Summary In this chapter, the emerging and existing power systems stability problems with their causes and effects are discussed for current smart grid power systems. Also, the 36

37 state-of-art control systems that are already implemented or proposed for addressing power system instability are presented. Since the major interest of this thesis is to develop control systems to enhance the the transient stability of smart grid, the literature review is extended for controllers that have been developed for the same purposes. In conclusion, we assert that the transient stability problem is becoming even more critical with the rapid penetration of inertia-less renewable energy sources. Also, the integration of information and communication systems has transformed the power system into cyber-physical system, hence cyber security emerges another challenging problem. Therefore, we advocate that in order to enhance the resiliency of the smart grid, advanced control strategies that are robust to cyber disturbances such as communication delay, contingent sensor measurement and-cyber attacks, and physical disturbances such as losing loads or generators are required. 37

38 CHAPTER 3 A ROBUST DECENTRALIZED CONTROL FRAMEWORK WITH CONSTANT TIME DELAY COMPENSATION Reliability is the key to the success of power system that invokes robust control systems for enhancing the stability margin. The large penetration of distributed generations with their inertia-less generation units leads to a transient stability problem, which refers to the ability of synchronous generators to return back to their nominal operation frequency after being subjected a large disturbance. Transient instability has always been a major problem in multi-machine interconnected power systems with respect to varying network configuration, loading, and power flow condition and become even more dynamic with the integration of intermittent renewable energy sources. Current excitation control systems implemented for transient stability of power systems are insufficient to maintain stability during inter-area oscillations. Therefore, in this chapter, a new nonlinear controller for the synchronous machine excitation system is presented that uses a novel control input time delay compensation technique and distributed energy storage sources (DESS) to enhance the transient stability of smart grids. The designed control framework, shown in Figure 3-1, uses local measurements (rotor angle and rotor speed) obtained by phasor measurement units connected at the generator buses and actuates fast acting DESS such as flywheels or batteries to inject or absorb damping power to the system. The objective is to return the perturbed synchronous machines back to synchronism as quick as possible. DESS are currently being deployed in power systems to perform zero-energy ancillary services, such as load following and regulation, especially due to the increasing penetration of intermittent solar and wind power sources [72]. The presented control framework adds a function to DESS by using them for transient stability. PMU sensors are employed because of their capability in providing real-time data to controller and other power system functions to enhance visibility of entire system. 38

39 Figure 3-1. An overview of decentralized control framework for transient stability. As the designed decentralized control framework can be used to address transient instability problem by itself, it can also be used as a backup controller to Wide-area control systems (WACS). Due to the centralized nature of WACS, they may suffer from large communication delay, cyber disturbances and loss of remote sensors. Hence, a backup controller like primary excitation controllers is needed to enhance the resiliency of the smart grids. Time delay is inherent for all systems and significantly affects the performance of the incorporated applications. The time delay in the proposed control framework arises from the communication between sensor and controller, processing in controller and response time of the DESS. To mitigate the effect of time delay and uncertainties arise from varying plant parameters and cyber disturbances, the proposed nonlinear robust controller is leveraged by developing a novel delay compensation technique and considering the time-varying additive disturbances in the dynamic model. The Lyapunov stability analysis proves that all error tracking signals are globally uniformly ultimately bounded (GUUB) and the decentralized nonlinear controller can guarantee the system stability over the whole operating region regardless of fault locations or parameter uncertainties of the transmission network. Furthermore, the designed decentralized control framework was implemented on IEEE 39 bus 10 machine test 39

40 power system through Matlab/Simulink and validated with respect to varying fault locations, DESS capacity, control input time delay and parametric uncertainties. Simulation results demonstrate the success of the proposed control framework in damping the post-fault frequency oscillation very quickly. 3.1 Dynamic Model of Synchronous Machines Multi-machine power systems consist of n synchronous generators, which are interconnected through a transmission network. The transient stability of synchronous generators are studied by using swing equations defined in [29 31, 73] as: δ i = ω i, ω i = 1 M i ( D i ω i + P m,i P e,i ), (3 1) where ω i R is the rotor speed deviation from the synchronous rotating reference of generator i in radian per second (rad/s), which is the difference between electrical actual rotor speed ω act i R (rad/s) and synchronous rotor speed ω o R (rad/s), ω i = ω act i ω 0 and ω i R is the acceleration of the generator i. The δ i R denotes the rotor angle deviation from the synchronous rotating reference of the generator i in radian, equivalent to the transient internal voltage angle of the machine [29]. D i is per unit damping constant and M i denotes the normalized inertia constant, given in s 2 /rad. The difference between mechanical power input (P m,i ) and electrical power output (P e,i ), both are in p.u, is defined as the accelerating power (P a,i ), that is, (P a,i = P m,i P e,i ). P m,i can be assumed as constant for transient stability analysis and P e,i can be calculated by using the following power flow equation. P e,i = κ E i E k (G ik cos (δ i δ k )+B ik sin (δ i δ k )), (3 2) k=1 where κ R is the set of buses connected to bus i, G ik R denotes the equivalent conductance between the buses i and k, while B ik R is the equivalent susceptance 40

41 between the buses i and k. E i, E k C are the voltages of buses i and k, respectively, while δ i R and δ k R are their respective angles. 3.2 Robust Nonlinear Controller Design By considering the external damping power absorbed or injected through DESS, the swing equation (3 1) modifies as follows: ω i = 1 M i ( D i ω i + P a,i + d i (t) + u i (t τ i )), (3 3) where, u i (t τ i ) R represents the external generalized delayed input control signal which corresponds to the DESS power output. τ i R is a known constant non-negative time delay and t 0 R is the initial time. Also, d i : [t 0, ) R denotes uncertain time-varying exogenous disturbance stems from uncertainties in power system. The controller is developed based on the following assumptions: Assumption 1. The rotor angle (δ i ) and rotor speed (ω i ) are measurable. Assumption 2. M i is bounded by known, positive, constants such that m i M i m i, where m i, m i R. D i and P e,i are also bounded by a known constants. Assumption 3. The unknown nonlinear exogenous disturbance and its first time derivative exist and are bounded by known positive constants [74]. Assumption 4. δ id R, is designed such that the δ id refers to the pre-fault value of δ i. Assumption 5. The input delay is a known non-negative constant. Also, it is assumed that the system in (3 1) does not escape to infinity during the time interval [t 0, t 0 + τ i ] [59]. The objective of the control design is to ensure that the actual rotor angle of each generator (δ i ) tracks its desired rotor angle (δ id ) despite a known constant input 41

42 delay, additive disturbances and uncertainties in the dynamics. To quantify the control objective, a measurable auxiliary tracking error, denoted by e 0i R is defined as e 0i = t 0 (δ i (θ) δ d,i (θ)) dθ. (3 4) where the first time derivative of e 0i quantifies the control objective. To facilitate the subsequent analysis, auxiliary tracking errors, denoted by e 1i R, defined as e 1i = ė 0i + α i e 0i (3 5) where α i R is an adjustable, positive, constant control gain. In order to compensate the input delay, an auxiliary error signal denoted by e ui R is developed to to inject a delay-free input signal and cancel the delayed input signal in the closed-loop error system as follows: e ui = t t τ i u i (θ) dθ. (3 6) Furthermore, an auxiliary tracking errors, denoted by r i R, defined as r i = ė 1i + β i e 1i + η i e ui, (3 7) where β i, η i R are adjustable, positive, constant control gains. Based on the subsequent stability analysis, the following continuous robust controller is is designed as u i = k i r i, (3 8) where k i R are positive, adjustable, constant control gains. Taking the time derivative of (3 7) and using (3 3)-(3 5), (3 6), and (3 8), the closed-loop dynamics for r i can be obtained as ṙ i = ( α i + β i D ) i ω i + 1 P a,i + d ) i (η i 1Mi u i (t τ i ) M i M i M i +α i β i (e 1i α i e 0i ) η i k i r i. (3 9) 42

43 To facilitate the stability analysis, the expressions in (3 9) can be segregated as terms that can be upper bounded by a state-dependent function and by a constant, such that ṙ i = Ñi + N i e 1i + (η i 1Mi ) k i r i (t τ i ) η i k i r i (3 10) where the auxiliary terms Ñi, N i R can be defined as ( Ñ i α i + β i D ) i ω i + α i β i (e 1i αe 0i ) (3 11) M i N i 1 M i P a,i + d i M i. (3 12) Remark 3.1. By using Assumption 2, an upper bound can be obtained for (3 11) as Ñi ψ 1i z i, (3 13) where ψ 1i R is a known positive constant and z i R 4 is the vector of error signals defined as z i [e 0i, e 1i, r i, e ui ] T. (3 14) Remark 3.2. N i is upper bounded by a known constant, by Assumptions 2, where ψ 2i R is a known positive constant. sup N i ψ 2i, (3 15) t R To facilitate the subsequent stability analysis, auxiliary bounding positive constants σ i, Ω i R are defined as (αi ) ( σ i min{ 1 2, Ω i min { σi 2, ω 2ik 2 i 3, 1 3τ i β i η2 i 2ε 1i 1 2 } ), ( ) } ω 2i 3τ i ε 1i, η ik i 8 (3 16) (3 17) 43

44 where ɛ 1i, ω 2i R are known, positive constants. It should be noted that ɛ 1i, ω 2i R are not implemented in the control law but will be used for stability analysis. Also, σ i and Ω i will be used as bounding constants (for convergence decay rate and definition of the domain of attraction) in Section 3.3. As a conclusion, the result is global in the sense that D = S D = R Lyapunov Stability Analysis Theorem 3.1. Given the dynamics in (3 1), the controller given in (3 8) ensures globally uniformly ultimately bounded tracking in the sense that e i (t) ɛ 0i exp ( ɛ 1i t) + ɛ 2i, (3 18) where ɛ 0i (1 + α i ) 2V i (t 0 ) 2λ 2iΦ 2 i Ω i m i η i k i, ɛ 1i Ω i 2λ2i Φ λ 2i (t t 0 ) and ɛ 2i (1 + α i ) 2 i Ω i m i η i k i. The control gains are selected sufficiently large relative to the initial conditions of the system such that the following conditions are satisfied. α i > 1 2, (3 19) β i > η2 i 2ε 1i + 1 2, (3 20) η i < 1 m i + ψ 3i, (3 21) k i 2ψ 1i η i σ i, (3 22) ω 2i >3τ i ε 1i, (3 23) τ i η i 8 (2φ2 i ɛ 1i + ψ2 3i η i ) (3 24) Proof. Let V : D R be a continuously differentiable Lyapunov function candidate defined as V i 1 2 et 0ie 0i et 1ie 1i rt i r i + φ i 2 et iue iu + Q 1i + Q 2i, (3 25) 44

45 where Q 1i, Q 2i R are defined as ( ψ 2 Q 1i 3i ki 2 η i k i Q 2i ω 2i t t ) t + φ2 i k i r i (θ) 2 dθ, (3 26) ε 1i t τ i u 2 i (θ) dθds, (3 27) and let y i R 5 be defined as t τ i [ y i s z i, Q 1i, Q 2i ] T. (3 28) The following inequalities can be obtained for (3 25) as λ 1i y i 2 V i λ 2i y i 2, (3 29) where λ 1i min{ 1, φ i } andλ 2 2 2i max{ φ i, 1}. The time derivative of (3 26), (3 27) and 2 using (3 5)-(3 6), (3 10), the time derivative of (3 25) can be obtained as V i = e T 0i (e 1i αe 0i ) + e T 1i (r i β i e 1i η i e iu ) + φ i e T uik i (r i r i (t τ i )) ( ) ) + ri T Ñ i + N i e 1i + (η i 1Mi k i r i (t τ i ) η i k i r i ( ) ψ 2 + 3i ki 2 + φ2 i k i (r 2 i ri 2 (t τ i ) ) t + ω 2i τ i ki 2 ri 2 u 2 i (θ) dθ (3 30) η i k i ε 1i t τ i After completing the squares for r i with r T i Ñ i, r T i N i, applying Young Inequality for cross terms in (3 30), the following upper bound can be obtained for (3 30) as ( V i α i 1 ) ( e 2 0i β i η2 i 2 ( ( ηi k i φ 2 8 i k i + ψ2 3iki 2 ε 1i η i k i 2ε 1i φ2 i k i ε 1i ) e 2 1i + ε 1i e 2 ui + ψ 1i z i ψ2i 2 η i k i η i k i )) t + ω 2i τ i ki 2 ri 2 ω 2i u 2 i (θ) dθ (3 31) t τ i 45

46 The Cauchy-Schwartz inequality is used to develop the following upper bound for e 2 ui. t e 2 ui τ i u 2 i (θ) dθ. (3 32) t τ i The following upper bound can be obtained for Q 2i as Q 2i ω 2i τ i sup sɛ[t τ i,t] t s u 2 i (s) ds ω 2i τ i t t τ i u 2 i (θ) dθ. (3 33) Using (3 8), (3 26), (3 32), (3 33) and the gain condition (3 24), the following upper bound can be obtained for (3 30) as ( V i α i 1 ) ( e 2 0i β i η2 i 1 ) e 2 1i η ( ) ik i ω2i 2 2ε 1i 2 8 r2 i ε 1i e 2 ui 3τ i + ψ 1i η i k i z i 2 ω 2ik 2 i 3 Q 1i Q 2i 3τ i + 1 η i k i ψ 2 2i (3 34) Using the definitions of z i in (3 14) and σ i in (3 16), and the gain conditions (3 19), (3 20), (3 23) an upper bound can be obtained for (3 34) as ( σi V i 2 ψ ) 1i z i 2 σ i η i k i 2 z i 2 ω 2iki 2 3 Q 1i Q 2i + 1 ψ2i 2 (3 35) 3τ i η i k i Using the definition of Ω i in (3 17), the gain condition in (3 22), the definition of y i and (3 29), an upper bound can be obtained for (3 35) as V i Ω i λ 2i V i + 1 η i k i ψ 2 2i (3 36) The solution of the differential equation in (3 36) can be obtained as V i (t) Λ i (3 37) 46

47 where Λ i ( ) V i (t 0 ) e Ω i (t t λ 0 ) 2i + ψ2 2i λ 2i δ i η i k i 1 e Ω i (t t λ 0 ) 2i. Using (3 25) and (3 37), the following inequalities can be obtained for e 0i, e 1i, r i and e ui as e 0i 2Λ i, e 1i 2Λ i, r i 2Λ i, e ui 2 φ Λ i. By using the time derivative of (3 4) and (3 5), δ i δ id can be upper bounded as δ i δ d,i (1 + α i ) 2Λ i, By using (3 1), (3 4) and (3 5), ω i ω d,i can be upper bounded as ω i ω d,i ( 1 + β i + η ) 2Λi i. φ i It is concluded that by using the Theorem 4.18 in [75], y is semi-globally uniformly ultimately bounded where uniformity in initial time can be concluded from the independence of δ i and the ultimate bound from t o. Since e 0i, e 1i, r i and e ui L, then from (3 8), u i L. Analysis of the closed-loop system shows that the remaining signals are bounded. 3.4 Simulation and Results The developed control framework has been implemented and validated on the IEEE 39 bus 10 machines test power system via Matlab-Simulink. The model parameters of test power system were obtained from [31, 76] and given in Appendix A. The power output capacity of each connected DESS (P DESS ) is rated to the mechanical power output of the associated generator, that is, ( P DESS = ρp m ). Also, desired rotor angles values (δ d,i ) are set to their own pre-fault values for the sake of easiness as suggested in [48]. In addition, The controller gains, given in Table 3-1, are found with respect to the gain conditions given in (3 19) - (3 24). 47

48 Table 3-1. Decentralized controller gain settings for known constant time delay case. α i β i η i k i Generator Generator Generator Generator Generator Generator Generator Generator Generator Generator The objective of the control framework is to recover the perturbed synchronous generators after a major disturbance. Therefore, a solid three-phase fault is applied at bus 17 in line at t o =0.5 s in order to test the stabilization performance of the controller. Afterwards, the fault is cleared by opening circuit breakers within clearing time that is set to 100 ms unless otherwise specified. The controller takes action and actuates the DESS to inject or absorb power according to the control signal after 100 ms. The performance of the proposed control framework is quantified in terms of stabilization time that is calculated as the time between fault inception and convergence of all generators speed to the synchronous frequency of 60 Hz within a tolerance of 0.1%, that is, [ ] Hz. This stabilization criterion is inspired by the Frequency Trigger Levels of 0.05 Hz deviation by North American Electric Reliability Corporation [77]. Finally, the simulation time was set to 20 ms and beyond that time limit refers to losing stability and failure of controller. The frequency oscillation and rotor angle deviation of all generator during and after fault, shown in Figure 3-2 over time, demonstrate the stabilization performance of the proposed controller when the control input delay and maximum capacity of DESS are 48

49 Angle -δ (Degree) Time (seconds) δ 1 δ 2 δ 3 δ 4 δ 5 δ 6 δ 7 δ 8 δ 9 Speed ( ω ) Hz * * Time (seconds) ω 1 ω 2 ω 3 ω 4 ω 5 ω 6 ω 7 ω 8 ω 9 ω 10 Figure 3-2. Rotor angle and speed deviation of synchronous machines during and after three phase fault. set to τ i =10 ms and ρ i =0.2 respectively. Furthermore, the response of the controller with respect to varying control input delay, DESS power output capacity and the magnitude of additive disturbance were evaluated. It should be noted that all PSS controllers were disabled in this simulation to make the condition more aggressive. First, the performance of the designed control framework was demonstrated in Figure 3-3 with respect to varying DESS capacity and control input time delay. The simulation results show that the proposed control framework can stabilize the frequency oscillation within [6-8] s based on the time delay (τ i ) when Stabilization time [s] τ i =10ms τ i =50ms τ i =100ms τ i =130ms DESS power output capacity - ρ Figure 3-3. Stabilization time versus varying DESS capacity and time delay. 49

50 Stabilization time [s] Decentralized (τ i =10ms) Decentralized (τ i =50ms) Decentralized (τ i =100ms) Decentralized (τ i =130ms) MBPSS Fault clearing time [s] Figure 3-4. Stabilization time versus clearing time. ρ=5%. The stabilization time decreases in response to the increasing DESS capacity. It is worth to note that time delay arises as a factor that deteriorates the stability of the system. However, the effect of the time delay is diminished by enabling the time delay compensation technique in the control development. As can be seen in Figure 3-3, stabilization can be maintained for up to 130 ms control input time delay. Fault clearing time is critical for transient stability and refers to the time between fault inception and clearing the fault by opening circuit breakers. The proposed control framework shows robustness to the increasing fault clearing time. In Figure 3-4, stabilization time of the designed control is demonstrated with respect to increasing fault clearing time for various control input delay cases. Furthermore, the developed controller is compared with well-known PSS controllers as implemented in [76]. The first is the Multi-band PSS (MBPSS), which was capable of stabilizing the system for fault clearing times inferior to 225 ms. Both ωpss and P apss were not capable of stabilizing the system for most cases, therefore we omitted their results. The results illustrated in Figure 3-4 show that the designed controller is less sensitive to variations in fault clearing time than MBPSS. In the case where the clearing time is 200 ms, the proposed method can return the system to stability at least two times faster than 50

51 Stabilization time [s] Decentralized (τ i =10ms) Decentralized (τ i =50ms) Decentralized (τ i =100ms) Decentralized (τ i =130ms) MBPSS Signal-to-noise Ratio [db] Figure 3-5. Stabilization time versus additive time-varying disturbance. MBPSS. However, the proposed control framework fails if clearing time goes beyond 200 ms. Resiliency of the power system is paramount to the reliability of the power system. Therefore, the sensitivity of the proposed controller to additive Gaussian white noise disturbance was assessed in Figure 3-5. The power of white noise, denoted by d(t) in (3 3), is rated to the electrical power of each generators P e,i in order to model uncertainty from measurements and injected to the swing equation. The ratio of the actual P e, i/n oise is given in decibels and denoted as signal-to-noise ratio (SNR). We have considered that the maximum power output of each DESS is set to ρ=20%, unless otherwise specified. Simulation results show that the proposed method presents superior robustness to this type of disturbances in comparison to the MBPSS, as shown in Figure 3-5. The stabilization time achieved by the nonlinear controller is practically unchanged for the whole SNR range, while the performance of the MBPSS is immensely degraded for lower SNR. The results also show that the controller presents small sensitivity to time delay variations. As shown in Figure 3-3, 3-4 and 3-5, there is only a slight improvement of performance for lower controller input time delays. 51

52 3.5 Summary In this chapter, a robust nonlinear control framework to enhance the transient stability margin of synchronous machines by using DESS is presented. Performance of the designed controller is validated through a Matlab-Simulink simulation environment. Simulation results demonstrate that the proposed controller can achieve better transient stability performance than conventional PSS methods. In particular, the controller introduced in this article is highly resilient to the constant known time delay because of the novel time delay compensation technique nonlinear implemented in nonlinear controller. The designed control framework also enhances the resiliency of the smart grid to uncertainties. Although, the proposed controller can improve the transient stability margin for the given conditions, a further amendment is required to make it practical for realistic smart grid controls. One of the drawback is the assumption taken that the time delay is a known constant. The changing network dynamics and using system components manufactured differently may lead to expose various time delay characteristics for each control agents. Hence, leveraging the controller for unknown delay cases would be realistic. 52

53 CHAPTER 4 CYBER-ENABLED DECENTRALIZED CONTROL FRAMEWORK WITH UNKNOWN TIME-VARYING INPUT DELAY COMPENSATION Power systems are very complex and highly nonlinear interconnected systems that show changes in network structures over time. Integration digital technologies have a great influence in fueling the complexity of the smart grid power system besides all of their advantages for enhancing the energy efficiency, reliability, and security. In order to take advantage of all deployed intelligent technologies, their seamless integration and cooperation are key to the success of smart gird technology. Interdependency between cyber and physical components in smart grids requires particular attention while designing or upgrading a subsystem, such as control systems, protection schemes, etc. To enhance the resiliency of the smart grid, this interdependency must be studied well by considering limitations and requirement of all incorporated systems. In this chapter, the decentralized control framework has been extended to further enhance the cyber-physical security, resiliency, and reliability of multi-machine power system along with contributing to the transient stability. In addition to employing the PMU sensor at every generator buses and DESS to provide external damping power, a State Estimation (SE) function has been added to filter out the sensor data before arriving to the controller. Following the American Recovery and Reinvestment Act of 2009, the number of PMUs connected to the US power grid increased from 166 in 2005 to more than 1700 in 2015 as illustrated in Figure 4-1 [78]. This large deployment of advanced sensors enables monitoring of the power grid in a level that could not be achieved in the past. Synchronized time-stamped voltage and current phasors from PMUs allows the use of linear power system state estimators that can obtain the states of the system in a much faster way than traditional nonlinear state estimators, such as weighted least squares state estimator (WLS-SE). While linear state estimators are solved using linear algebra, nonlinear power system state estimators usually require the solution of an iterative 53

54 Figure 4-1. PMUs and synchrophasor data flows in the North American power grid. algorithm, such as Newton-Raphson, whose solution is not guaranteed to converge to the global optimum nor the necessary number of iterations known. In this paper, we assume that PMUs that measure both voltage and current are deployed in buses nearby a given generator, thus enabling the use of linear state estimators to obtain the angle of a given generator. More importantly, once this data is obtained by the means of a decentralized linear state estimator, we assume it can be obtained quickly enough to allow real-time operation and has redundancy enough to deal with bad data from those measurements. Communications among PMUs, SE, and DESS expose control systems to time delay that might be uncertain because of changing distance between nodes and experiencing cyber disturbances such as DoS on PMU nodes. In order to address all these contingencies in the control development, robust control systems with unknown and time-varying delay compensation emerges as a need to enhance the transient stability of smart grid despite cyber-physical disturbances. To compensate the delay at the control input, designing a delayed control signal is required to use the future state of the feed-forward terms in the closed-loop dynamics. 54

55 Figure 4-2. Data flow of the proposed cyber-physical control strategy. The predicted-based control techniques are needed to obtain the future state of the dynamics and implementing in the actuator. However, prediction of future states requires the exact model knowledge of dynamics and so the prediction-based control scheme is not efficient in the presence of unknown time-varying input delay. Such difficulties, thus, motivated us to design a controller that can compensate for the the time-varying input delay without using the exact model knowledge of the dynamics. Lyapunov stability analysis guarantees that all error tracking signals are globally uniformly ultimately bounded. Furthermore, the proposed model has been validated through IEEE 39 bus 10 machine power test systems by considering the physical limitations of employed technologies such as DESS and unknown-time delay at the control input and additive time-varying disturbance. Elapsed time to recover perturbed synchronous machines from transient instability is taken as a performance metric and the simulation results demonstrate the success of the developed cyber-enabled decentralized control framework. The presented control framework combines a nonlinear robust decentralized controller that can compensate unknown time delay and additive time-varying disturbance 55

56 with a linear state estimator which is capable of detecting, identifying and correcting bad data in real time. The following contribution have been made in this chapter: Extension of the innovation-based bad data detection, identification and correction methods previously developed for the nonlinear WLS-SE [79 81] to an all-pmu linear State Estimator. A novel control input time delay compensation method to mitigate the effect of unknown time-varying delay that stem from communications despite the parametric and dynamical uncertainties by developing a model-free robust controller. 4.1 Dynamic Model and Properties of Synchronous Machines The objective of this controller is to maintain the transient stability of the interconnected synchronous generators after being subjected to a large disturbance such as 3-phase fault, losing generator or large loads. The transient stability can be studied by using the swing equation given in [29, 30]: δ i = ω i, ω i = 1 M i ( D i ω i + P a,i ), (4 1) where P a,i = P m,i P e,i represents the accelerating power, which is the difference between the mechanical power, P m,i R, and electrical power, P e,i R, of generator i, all in p.u. δ i R is the rotor angle and ω i R is rotor speed deviation from synchronous speed, ω 0 R, of the generator i, both in rad/s. D i R is per unit damping constant and M i R denotes the normalized inertia constant, given in s 2 /rad. The electrical output power P e,i can be calculated by using the following electrical equation P e,i = Φ E i E k (G cos(δ i δ k ) + B ik sin(δ i δ k )), (4 2) k=1 where Φ R is the set of buses connected to bus i, G ik R denotes the equivalent conductance between the buses i and k, while B ik R is the equivalent susceptance between the buses i and k. E i, E k C are the voltages of buses i and k, respectively, 56

57 while δ i R and δ k R are their respective angles. The rotor angle of the generator, δ i, also represents the voltage angle of the generator internal bus. Transient stability is related with whether there is enough restorative power (synchronizing power) to overcome an initial acceleration/deceleration following a large disturbance. An external energy source, thus, can be employed to achieve a faster transient stability in conjunction with a controller. The external power source input (u i ) can be represented in swing equation (4 1) as follows: M i δi = D i δi + P a,i + d i (t) + u i (t τ i ), (4 3) where, d i : [t 0, ) R is an uncertain time-varying additive disturbance. u i (t τ i ) R represents the external generalized delayed input control where τ i : [t 0, ) R is an unknown time-varying delay. In the rest of the paper, all time-delayed functions will be written in the form of x(t τ) = x τ (t) for t τ t 0 and x(t τ) = 0 for brevity. The following assumptions are utilized for subsequent analysis. Assumption 6. The rotor angle (δ i ) and the rotor speed (ω i ) are measurable [82]. Assumption 7. The generalized inertia of the generator i, M i, is bounded such that m i M i m i, where m i, m i R are known positive constants. The damping coefficient of generator i, D i, is bounded by some constants such that D i D i D i where D i, D i R are known positive constants. Assumption 8. The unknown time-varying additive disturbance term is bounded by known positive constants. Assumption 9. The input delay is bounded such that τ i (t) < τ i for all t R, where τ i R, are positive constants. Also, a sufficiently accurate constant estimate ˆτ i R of τ i is available such that τ i τ i where τ i τ i ˆτ i, and τ i is a positive constant 1. 1 Since the maximum tolerable error ( τ), and the estimate of actual delay (ˆτ) are known, the maximum tolerable input delay can be determined. 57

58 Furthermore, it is assumed that the system in (4 1) does not escape to infinity during the time interval [t 0, t 0 + τ i ] [71]. 4.2 Control Objective and Development The objective of the control design is to ensure that the actual rotor angle of each generator δ i tracks its desired rotor angle. The reference set point for the generator i, δ id R is chosen as equal to i-th generator s steady state rotor angle (δ i,d = δ i pre fault ). δ id R despite an unknown input delay and an unknown time-varying bounded additive disturbances. A measurable auxiliary tracking error, denoted by e 0i R, is defined as e 0i = t 0 (δ i (θ) δ id (θ)) dθ, (4 4) where ė 0 quantifies the control objectives. To facilitate the subsequent analysis, auxiliary tracking errors, denoted by e 1,i R, is defined as e 1i = ė 0i + α 1i e 0i (4 5) where α 1i R is adjustable, positive, constant control gain and another subsequent tracking error signal, denoted by r i R, is defined as r i = ė 1i + α 2i e 1i + α 3i e ui, (4 6) where α 2i, α 3i R are adjustable, positive, constant control gains. The absence of delayfree control signal in the closed-loop dynamics induces to use predictor-based controller. However, the lack of exact plant parameter knowledge encourage to avoid predictorbased control design techniques. To overcome the difficulties in predictor-based input delay compensation method, an auxiliary error signal is designed to inject delay-free control signal in the closed-loop dynamics and denoted by e ui R where, e ui t t ˆτ i u i (θ) dθ, (4 7) 58

59 Substituting time derivatives of (4 3) - (4 5), and (4 7) into the time derivative of (4 6) and multiplying both side with M i yields the open-loop dynamics, M i ṙ i = D i δi + P a,i + u i (t τ i ) + d i + M i α 1i ë 0i + M i α 2i ė 1i + M i α 3i ė ui (4 8) The open-loop error system in (4 8) can be segregated by terms that can be upper bounded by a state-dependent function S i and a constant S i where S i, S i R. Substituting (4 7), S i and S i into (4 8) yields M i ṙ i = S i + S i + (u i (t τ i ) u i (t ˆτ i )) + M i α 3i u i + (1 M i α 3 ) u i (t ˆτ i ) e 1i (4 9) where, S i D i δi + M i α 1i ë 0 + M i α 2i ė 1i + e 1i (4 10) S i P a,i + d i, (4 11) and there exist a constant η i R such that η i > (1 M i α 3i ). It should be noted that to provide sufficient gain conditions η i should be chosen sufficiently small by selection of α 3i. Remark 4.1. S i is upper bounded by a known positive constant C 1i R, by using the Assumptions 8, sup S i C 1i. (4 12) t R Remark 4.2. S is upper bounded by a linearly state-dependent vector. Using Lemma 5 in [83] and Assumption 7, an upper bound for (4 10) can be obtained as S i C2i z i, (4 13) where C 2i R is a known positive constant and z i R is the vector of error signals defined as [ z i e 0i e 1i r i e ui ] T. (4 14) 59

60 Based on the subsequent stability analysis, a continuous robust controller is designed as u i = k i r i, (4 15) where k i R is a positive, adjustable, constant control gain. Substituting (4 15) into (4 9), the closed-loop error dynamics for r i can be written as Mṙ i = S i + S i + (u i (t τ i ) u i (t ˆτ i )) k i r i M i α 3i (1 M i α 3i ) k i r i (t ˆτ i ) e 1i (4 16) To facilitate the subsequent stability analysis, auxiliary bounding constants σ i, β i R, are defined as {( σ i min α 1i 1 ) (, α 2i 2 β i 1 { 2 min σ i, 2µ 3i, 2µ } 3i 3µ 2i 3ˆτ i ( α )) 3i, 2 µ 3i 6ˆτ i k 2 i, mα } 3ik i 4 (4 17) (4 18) where µ 2i, µ 3i R are known, adjustable, positive constants. 4.3 Stability Analysis Theorem 4.1. The designed controller in (4 15) guarantees that all tracking error signals are globally uniformly ultimately bounded for the power system dynamics given in (4 3) in the sense that where Λ i constant such that υ i δ i δ id (1 + α 1i ) 2Λ i ( ) ( ) V i (t 0 ) λ 2iυ i β i exp β i λ 2i (t t 0 ) + λ 2iυ i β i C2 1i m i α 3i k i and υ i R is a known positive + K2 i 4 τ i. Also, the control gains are chosen sufficiently large relative to the initial conditions of the system in order to satisfy the following conditions. α 1i >0.5 (4 19) α 2i >0.5 (α 3i + 1) (4 20) 60

61 α 3i 2ω 3i 3τ i ki 2 τ i 1 ( mα3i ) (η i + µ 1i ) 2k i 2 2µ 1i k i (4 21) µ 2i µ 3iˆτ i k 2 i (4 22) k i 2C2 2i mα 3i σ i, (4 23) µ 2i > k i (η i + µ 1i ) 2 where µ 1i R is a known, adjustable, positive constant. Proof. Let the Lyapunov function candidate V i defined as (4 24) where Q 1i, Q 2i R are defined as V i 1 2 e2 0i e2 1i M ir 2 i + µ 1i 2 e2 ui + Q 1i + Q 2i (4 25) t Q 1i µ 2i ri 2 (θ) dθ (4 26) t ˆτ i t t Q 2i µ 3i ri 2 (θ) dθds (4 27) t ˆτ i and the first time derivatives of (4 26), (4 27) are obtained by means of Leibniz rule as follows: s Q 1i =µ 2i r 2 i µ 2i r 2 iˆτi (4 28) Q 2i =µ 3iˆτ i r 2 i µ 3i t The Lyapunov function in (4 25) satisfies the following inequalities where Ψ i R 5 are defined as: { 1 min 2, m i 2, µ } { 1i Ψ i 2 V i (Ψ i ) max 1, 2 Ψ i t ˆτ i r 2 i (θ) dθ. (4 29) m i 2, µ } 1i Ψ i 2 (4 30) 2 [ z i, Q 1i, Q 2i ] T. (4 31) 61

62 The time derivative of (4 25) can be obtained by using the time derivative of (4 6), (4 7), (4 16), (4 26), and (4 27) as ( ) V i =e 0i (e 1i α 1i e 0i ) + e 1i (r i α 2i e 1i α 3i e ui ) + r i Si + S i + r i (k i (r i (t τ i ) r i (t ˆτ i )) k i r i M i α 3i (1 M i α 3i ) k i r i (t ˆτ i ) e 1i ) µ 1i e ui (k i r i k i r i (t ˆτ i )) + µ 2i r 2 i µ 2i r 2 i (t ˆτ i ) + µ 3iˆτ i r 2 i µ 3i t t ˆτ i r 2 i (θ) dθ (4 32) By using the Young s inequality for the cross terms in (4 32), the following inequalities are written as e 2 0i 2 + e2 1i e 0i e 1i r i r 2 r iˆτi i r2 i (t ˆτ i), 2 e ui r i e 2 ui 2 + r2 i 2, e 2 1i e ui e ui r iˆτi e 2 1i + e2 ui 2 2 e 2 ui + r2 i (t ˆτ i) 2 2 (4 33) Using (4 33), Remark 4.1 and Remark 4.2 yields to the following upper bound for (4 32) as V i ( α 1i 1 ) ( e 2 0i (α 3i + 2µ 1i k i ) e 2 ui+ ) e 2 1i α 2i 1 + α 3i 2 ( ki 2 (η i + µ 1i ) + µ 2i ) r 2 i + C 2i r i z i + C 1i r i m i α 3i k i r i + k i r i r i (t τ i ) r i (t ˆτ i ) t + µ 3iˆτ i ri 2 µ 3i ri 2 (θ) dθ (4 34) t ˆτ i It should be noted that provided z i (.) K i for all. [t o, t], using (4 15) and the fact that the closed-loop dynamics defined in (4 16) can be used to conclude that ṙ K i where K i R is a known constant. Using mean value theorem, the following inequality can be obtained as r i k i r i (t τ i ) r i (t ˆτ i ) k i r i τ i ṙ i (Θ (t, τ i, ˆτ i )) k i τ i r i K i (4 35) 62

63 where Θ (t, τ i, ˆτ i ) is a point between t τ i and t ˆτ i. After completing the square, the following upper bound can be obtained as k i τ i r i K i K2 i 4 τ i + k 2 i τ i r 2 i (4 36) The Cauchy-Schwartz inequality can be used to develop the following upper bounds e 2 ui ˆτ i k 2 i t t ˆτ i r 2 i (θ) dθ (4 37) Furthermore, an upper bound for Q 2i can be obtained as Q 2i ˆτ i sup s (t,t ˆτ i ) ( t s ) t ri 2 (θ) dθ ω 3ˆτ i ri 2 (θ) dθ (4 38) t ˆτ i Completing the square for r i, using (4 15), (4 5),(4 37), (4 38) and gain conditions in (4 22), (4 23), (4 34)can be found upper bounded as V i ( α 1i 1 ) e 2 0i 2 ( 2α2i α 3i 1 2 ) e 2 1i µ 3i 6τ i k 2 i e 2 ui m iα 3i k i ri K2 i 4 τ i + C2 2i z i 2 + C2 1i µ 3i Q 1i µ 3i Q 2i (4 39) m i α 3i k i m i α 3i k i 3µ 2i 3ˆτ i By using the definition of z i in (4 14), and σ i in (4 17), and the gain conditions defined in (4 19)-(4 21), an upper bound can be obtained for (4 39) as V i σ i 2 z i 2 µ 3i Q 1i µ 3i Q 2i + C2 1i + K2 i 3µ 2i 3ˆτ i m i α 3i k i 4 τ i (4 40) Furthermore, using the definition of Ψ i in (4 31), β i in (4 18) and the gain condition defined in (4 23), σ i 2C2 2i mα 3i k i, an upper bound for (4 40) can be obtained as V i β i Ψ i 2 + C2 1i + K2 i m i α 3i k i 4 τ i (4 41) By using (4 30), an upper bound can be obtained for (4 41) V i β i λ 2i V i + υ i (4 42) 63

64 where υ i Let C2 1i mα 3i k i + K2 i τ 4 i. The solution of (4 42) yields ( V i (t 0 ) λ 2iυ i V i ( ) ( V i (t 0 ) λ 2iυ i β i exp β i λ 2i (t t 0 ) β i ) ) ( exp β ) i (t t 0 ) + λ 2iυ i. (4 43) λ 2i β i + λ 2iυ i β i is denoted by Λ i. Upper bounds can be obtained for the absolute value of e 0i, e 1i, e ui, and r i by using (4 25) and (4 43) as e 0i 2Λ i e 1i 2Λ i 2 e ui Λ i µ 1i 2 r i Λ i. m i By using the time derivative of (4 4)-(4 5), δ i δ id can be upper bounded as δ i δ id (1 + α 1i ) 2Λ i (4 44) Additionally, an upper bound for ω i ω 0, can be obtained as ω i ω 0 ( 1 + α 2i + α ) 2Λi 3i. (4 45) µ 1i It can be concluded that Ψ i is uniformly ultimately bounded. Provided Ψ i (t 0 ) S D, where uniformity in initial time can be concluded from the independence of δ i and the ultimate bound from t 0. Since e oi, e 1i, r i, e ui L, from (4 15), u i L and the remaining signals are bounded. 4.4 State Estimator A state estimator with bad data detection, identification and correction is leveraged as a means of providing increased robustness to the control scheme against malicious data injection in measurements or bad data resulting from other causes as, for instance, meter malfunction. Given that enough redundancy is provided for number of measurements affected by an adversarial attack or other sources of gross errors in 64

65 measurements, those can be corrected by the proposed method. Once we assumed that PMU measurements are available for all the buses of the system, a linear state estimator will be used. The state estimation will be presented and implemented by splitting the complete power system in contiguous regions, each one of which will provide a state estimation of its local variables. For a power system with n buses, the problem of estimating the vector of states x C N based on the set of measurements y C m, where m N, is described by (4 46) [84]. y = Hx + ε (4 46) In (4 46), H is the projection matrix that maps the states to the measurements and ε models the error of this mapping as a uncorrelated random value that follows a Gaussian distribution. The solution to (4 46) is the state vector x that minimizes the cost function J(x). J(x) = y Hx 2 R 1 = [y Hx] R 1 [y Hx] (4 47) where ( ) denotes the complex conjugate transpose of a matrix. Geometrically, the J(x) index is a norm in the vector space of the measurements C m, given by the inner product u, v = u T R 1 v, where R is a positive definite symmetric matrix. Let ˆx be the solution of this minimization problem, thus, the estimated measurements vector is given by ŷ = H ˆx and the vector of residuals ρ is defined as the difference between y and ŷ. If the system represented by (4 46) is observable, then, the vector space C m of the measurements can be decomposed in a direct sum of two vector sub-spaces, as shown by (4 48). C m = R (H) R (H) (4 48) The range space of H, given by R (H), is a N-dimensional vector sub-space that belongs to C m and R (H) is its orthogonal complement, i.e., if u R (H), and v R (H), then, u, v = u T R 1 v = 0. The solution of the linear state estimator can 65

66 be interpreted as the projection of the vector of measurements y in R (H). Let P be the linear operator that projects the vector y in R (H), i.e. ŷ = Py. The operator P that minimizes the norm J(x) is the orthogonal projection of y in R (H), which means that the vector ŷ = H ˆx is orthogonal to the vector of residuals, as shown by (4 49). ŷ, ρ = (H ˆx) R 1 (y H ˆx) = 0 (4 49) The solution of (4 49) for ˆx yields (4 50). ˆx = (H R 1 H) 1 H R 1 y (4 50) Since ŷ = H ˆx, the projection matrix P that maps y to ŷ is given by (4 51). P = H(H R 1 H) 1 H R 1 (4 51) The solution to the classical WLS-SE can be interpreted as a projection matrix P acting on of the vector of measurements y to minimize the vector of residuals ρ given the inner product as defined previously. Another way to visualize the state estimation is seeing the geometrical position of the measurement error related to the range space R (H). Then, decomposing the space of the vector of measurements into a direct sum between R (H) and R (H), it is possible to decompose the vector of measurements error ε into two components: undetectable (ε U ) component and detectable (ε D ) component. where ε U R (H) and ε D R (H). Therefore: ε = }{{} Pε + (I P)ε (4 52) }{{} ε U ε D ε 2 R = ε U 2 1 R + ε D R (4 53) The difference between the two previous components is that they belong to different spaces, the first pertaining to the R (H) and the other pertaining to the R (H), consequently having different properties. Two main differences between the error component 66

67 and the residual will be enumerated: i) Degrees of freedom m and m n respectively; ii) The first is a random variable by the hypothesis of SE formulation, having m residuals in a m-dimensional space and the second is not a random variable (m residuals in a space of dimension m n). One should be aware that ε U is undetectable, at lights of the classical WLS, because it looks only for the error component which is orthogonal to the range space of H, that is, ε D. That statement is because the WLS state estimation objective function minimizes the distance from the measurement y to the range space of H. This error component turns out to be therefore, the measurement residual. In order to estimate the error one needs also to estimate the error component ε U. With that purpose, the innovation of a measurement, related to the other measurements, is defined as the information it contains, and not the others measurements of the measurement set [80]. This definition suggests that the innovation is contained in the portion of the measurement that is independent of the other measurements of the system, i.e., the portion that cannot be obtained from linear combinations of rows of the matrix H. Therefore, the new information of a measurement is its part that is orthogonal to the range space of H, i.e., belonging to R (H). If a measurement has an error, its component orthogonal to the range space of H will show the error through its residual, the other component, however, will have its error completely masked. Thus, the vector of masked error, in the state estimation process, is the vector belonging to the range space of the Jacobian matrix. Since the residual ε D and the other error component ε U are orthogonal to each other, it is possible to compose the measurement error vector; that is, for the i-th measurement: ε i 2 = ε i U 2 + ε i D 2 (4 54) This error vector is called Composed Measurement Error (CME). In order to find the masked error and compose the measurement s total error, the II is used, as proposed 67

68 by [80]: II i = εi D ε i U = 1 Pi i Pi i A measurement with low Innovation Index (II) indicates that a large component of its error is not reflected in its residual as obtained by the classical WLS estimator. Consequently, even when those measurements have gross errors, their residuals will be relatively small. Knowing that the vector spaces R (H) and R (H) are orthogonal (4 55) to each other, then, it is possible to recalculate the composed error of the i-th measurement. Thus, (4 54)becomes: ( ε i 2 = ) ε i IIi 2 D (4 56) Since ε D is equal to the residual ρ, (4 56) becomes: ε i 2 = ( ) ρ 2i CME IIi 2 i = ρ i IIi 2 (4 57) where ρ i is the residual of the i-th measurement and II i is the innovation index of this same measurement, both known quantities once an initial state is chosen. If instead we work with the normalized residual one obtains the Composed Normalized Error (CNE), given by: CNE i = ρ N i II 2 i (4 58) where ρ N i is the normalized residual of the i-th measurement. Otherwise, if one normalizes the error one obtains: CME N i = CME i /si = ρ i /si II 2 i (4 59) where s i is the standard deviation of i-th measurement. 68

69 4.5 Simulation and Results The proposed cyber-physical control framework, shown in Figure 4-2, has been tested on IEEE 39 Bus 10 machines test power system via Matlab-Simulink as implemented by [76]. The system data for test power grid such as were obtained from [31]. The controller gains, given in Table 4-1, are found with respect to the gain conditions given in ( ). In addition, the post fault desired rotor angles of machines (δ i,d ) are set to their pre-fault values at the steady-state as suggested by [48]. Furthermore, Multi Band Power System Stabilizer (MB-PSS) as implemented in [76] was also tested and optionally run in parallel with the proposed controller for the purpose of comparison. We have limited the simulation time to 10s. A three-phase fault was applied at bus 17 in line at t o =0.5 s and cleared six cycles later at t 1 =0.6 s. The decentralized controllers start taking action with a delay of 100 ms with respect to the action of the protection relay that tripped the transmission line between buses 16 and 17 at t 3 =0.7 s. If no stabilizing control scheme is applied for this case, the system becomes unstable. The system is stabilized at the time t s when Table 4-1. Adjusted controller gain values for unknown time-varying constant time delay case. Index α 1,i α 2,i α 3,i k i Generator Generator Generator Generator Generator Generator Generator Generator Generator Generator

70 Figure 4-3. Rotor speed and angle deviation of synchronous machines during and after three phase fault. all generators speed (ω i ) reach to the synchronous speed within the range of 0.1%, that is, [ ] Hz. In order to measure the performance of the proposed control framework, the stabilization time is defined as the time elapsed between t 1 and t s. This stabilization criterion was inspired by the Frequency Trigger Levels of 0.05 Hz deviation used by the North American Electric Reliability Corporation (NERC) [77]. First of all, all PSS control systems have been disabled to make stabilization more difficult for the proposed controller. The simulation results presented in Figure 4-3 show the convergence of all perturbed synchronous generators to the synchronism with the help of proposed decentralized controller within 2 s. Furthermore, various case studies have been conducted to evaluate resiliency and robustness of the controller Figure 4-4. Representation of varying actual time delay and its constant estimate. 70

71 to cyber and physical limitations such as time-varying delay, maximum power capacity of flywheels, and time-varying disturbances in Figure 4-5. The time-varying actual delay (τ iact ) in the system is modeled as a sinusoidal function where (τ iact = τ imean + sin(τ imean /0.1) but the estimated delay (τ iest ) is used for control action that is assumed as 0 τ iest τ iact. Figure 4-4 illustrates how the actual delay (τ iact ) and the estimated delay (τ iest ) are designed for the simulation when the τ imean =80 ms. Figure 4-5A shows the performance of the decentralized controller with and without PSS controller with respect to varying control input delay (τ imean ). It is evident that the proposed controller is able to stabilize the dispersed power system within about 2 s in the presence of peak 100 ms time delay and maintain stabilization for up to peak 140 ms time delay. Running the PSS in parallel provides minor contribution to improve stability performance but then fails for the time delays beyond 160 ms. The power output capacity of the utilized DESS is directly correlated with the stabilization ability of the decentralized controller. Thus, in the Figure 4-5B, the simulation is extended to test the performance of the proposed control framework with respect to various DESS capacity denoted by (γ i ). The capacity of the DESSs are rated to their associated generator mechanical power, namely, ( P max,i = γ i P m,i /100) where the DESS capacity percentile (γ i ) is set to 20% initially and remained same throughout the simulation unless otherwise is specified. The simulation result shows that the stabilization performance improves as (γ i ) increases. Also, activating PSS controller help to improve stabilization of synchronous machines especially when there is no enough power at the DESS. Furthermore, the resiliency of the proposed controller to the time-varying disturbance has been evaluated by injecting an additive Gaussian white noise disturbance, denoted by d(t) in (4 3), to the synchronous machine dynamics. This disturbance stands for uncertainties in the system that may stem from failure of sensors, maliciously changed measurements and varying plant parameters. In the simulation, the power of 71

72 12 10 Decentralized Decentralized+PSS Decentralized Decentralized+PSS Stabilization time [s] Stabilization time [s] Mean communication delay [s] Flywheel maximum power output [% of Mechanical power] A B Decentralized Decentralized+PSS Only PSS 2.14 Mean Time delay Estimation Error Stabilization time [s] Stabilization time [s] Signal to Noise Ratio [db] C Estimation Error (τ mean -τ est ) D Figure 4-5. Comparative simulation results under practical limitations. A) Stabilization time with respect to control input delay, B) Stabilization time versus maximum DESS power output capacity, C) Stabilization time in regard to signal-to-noise ratio, D) Robustness to error in estimation of varying time delay. the d(t) is rated to the mechanical power of each generators. The ratio of the actual P m,i /Noise is given in decibels and denoted as SNR. The default SNR value is set to 20 db unless otherwise specified. In Figure 4-5C, a comparative study is presented to evaluate the performance of the proposed controller and PSS controller exclusively, and when they collaborate. The proposed controller explicitly improves the stability 72

73 margin for synchronous generator in comparison to the PSS controllers. It can also be seen that cooperation with PSS controller helps a little bit when disturbance is severe. When SNR< 3dB, neither proposed controller nor combination with PSS can return generators back to synchronization. However, the stabilization time reduces in proportion to increasing SNR. Cooperation of PSS with decentralized controller significantly helps to enhance stabilization performance when the SNR is below 10dB, but for larger disturbances the increase in performance is only marginal. Finally, we investigate the effect of estimation error in time delay. In Figure 4-5D, the stabilization performance is evaluated with respect to estimation error in time delay where the error is calculated by (Error = τ imean τ iest ). The simulation result demonstrates that the performance of the controller remains unaffected by changing the time delay estimation. Therefore, it is concluded that the proposed controller is robust to time delay estimation error. 4.6 Summary In this chapter, a cyber-physical control framework with a state estimation algorithm has been introduced to enhance the transient stability of smart grids in the face of cyber and physical limitations and disturbances. The proposed controller has been simulated and evaluated on IEEE 39 bus 10 machines test power system through Matlab-Simulink. Furthermore, a well-known MB-PSS controller model has been implemented to conduct a comparative study. As a result of simulations, it is concluded that the proposed decentralized controller significantly improves the transient stability margins of the synchronous generators in the presence of cyber and physical disturbances despite given limitations. The resiliency of the proposed control framework to the time-varying delay and disturbances makes it attractive for future smart grid control systems. Also, the model-free based design of nonlinear controller makes it more suitable for cyber-physical power systems that are highly nonlinear and experience variation in dynamic plant parameters over time. 73

74 CHAPTER 5 A DISTRIBUTED NONLINEAR CONTROL STRATEGY FOR ENHANCING SMART GRID TRANSIENT STABILITY Visibility is a crucial concept in smart grid power system to improve the situational awareness and eliminating human factor by fully integrating automation and control systems. It is envisioned that increasing situational awareness can protect power system from cascading failure and major blackout as occurred in Northeastern, A manageable local blackout cascaded into massive widespread distress on the electric grid because human fault in control center, lack of situational awareness and poor automation systems. The lesson learned from this blackout has promoted centralized control system by using massive amount of remote sensors to monitor the grid and report to a central controller. Furthermore, the advancement in sensor technologies such as PMU has given an opportunity to obtain more precise information with a high frequency, currently up to 60 samples per second [85]. At the beginning, centralized control approach was a brilliant idea since it promotes visibility of the grid by exploiting advanced sensors and communication networks across the grids. However, the increasing deployment of PMU sensors has emerges scalability issues. To illustrate, currently, 1700 PMU have been installed across the North American electrical power grids [78]. The long distance between PMU and control center and growing data volume have emerged communication delay which has a negative influence in real-time monitoring and control. Furthermore, controlling the entire grid arises cybersecurity problems since highly connected nature of smart grids provides multiple entry point for adversaries. For example, Ukrainian power grid attack in 2015, is one of the recent example that adversaries targeted power grid remotely and left 225,000 customers out power [16]. Also, some other cyber attacks have been reported in [15, 86 88]. Emerging cyberphysical problems in centralized control systems have lead to develop distributed control strategies to reduce communication overload and make smart 74

75 Figure 5-1. An overview of designed distributed control framework for smart grids. grid systems more secure to cyber threats. The use of distributed versus centralized and decentralized controllers is a present trend in power systems control [89]. Thus, a novel distributed controller framework is presented in this chapter to address transient stability of smart grids. 5.1 Distributed Control Framework The designed distributed control treats the power grid as a multi-agent system where each synchronized machine is modeled as an agent that comprises of a PMU, a fast acting (DESS), the distributed controller. The control framework is illustrated on IEEE 39 bus 10 machine test power system in Figure 5-1 where all generator buses and neighboring buses are equipped with a PMU to provide real-time measurements to the control agents. Upon receiving PMU measurements and given the desired operation set points, distributed controller computed the required oscillation damping power that is injected or absorbed through a fast acting external storage source. The designed 75

76 controller is distributed in the sense that the entire grid is divided into agents and each agent relies on local and adjacent PMUs. The objective of this control strategy to enhance the transient stability and resiliency to cyber-physical uncertainties. Even though the distributed approach helps decreasing the communication delay (latency), it cannot be totally avoided in the presence of communication. Hence, there is a need for designing controller system that can compensate for the time delay. Moreover, the control system must be robust to cyber disturbances such as cyberattacks and sensor measurement errors, since they may lead to malfunctioning of the controller. Stuxnet is one of the well-known malicious computer worms that was originally designed to cease Iran s nuclear activity by infecting the industrial control systems [15]. Stuxnet compromised Iranian programmable logic controllers (PLCs) to collect data and cause the fast-spinning centrifuges to tear apart. However, Stuxnet could be tailored as a platform for attacking modern supervisory control and data acquisition (SCADA) systems implemented for smart grids. It should be noted that Stuxnet is introduced to the target environment that is isolated from global network, via a USB flash drive. In this point of view, the US government designated the electrical power grid as one of the most critical infrastructures [88] and allocated $14 billion to support research and development on cyber-physical security in FY 2016 [13]. The strengths of the proposed distributed nonlinear robust controller can be summarized as: Model-free based control design that does not require exact model knowledge of the systems Delay compensation technique implemented to mitigate the negative effect of excessive time delay Resilient to time-varying additive disturbances stemming from uncertainties. 76

77 Lyapunov-Krasovskii functionals are used in the Lyapunov-based stability analysis to prove that tracking error signals are globally uniformly ultimately bounded. In addition, the proposed control framework has been validated by implementing on IEEE 39 bus 10 machine test power systems in Matlab-Simulink. Numerical simulation results demonstrate the resiliency of the designed distributed robust controller to time delay and uncertainty under physically practical limitations. It is concluded that the proposed distributed control strategy is capable of enhancing the transient stability margin of synchronous generators and contributes to the resiliency of smart grid by enabling multiple layer security in addition to the protection in communication layer and state estimation in detection and correction layer Dynamic Model of Synchronous Machines The dynamic model of the multi-machine power systems has been defined by the swing equation in [29 31, 73] as follows: δ i = ω i, ω i = 1 M i ( D i ω i + P m,i P e,i ), (5 1) where ω i R is the rotor speed deviation from the synchronous rotating reference of generator i in radian per second (rad/s), which is the difference between electrical actual rotor speed ω act i R (rad/s) and synchronous rotor speed ω o (rad/s), ω i = ω act i ω 0 and ω i R is the acceleration of the generator i. The δ i R denotes the rotor angle deviation from the synchronous rotating reference of the generator i in radian, equivalent to the transient internal voltage angle of the machine [29]. M i denotes the normalized inertia constant, given in s 2 /rad. The difference between mechanical power input (P m,i R) and electrical power output (P e,i R), both are in p.u, is defined as the accelerating power (P a,i R), that is, (P a,i = P m,i P e,i ). P m,i can be assumed as constant for transient stability analysis and P e,i can be calculated by using the following 77

78 power flow equation. κ P e,i = E i E k (G ik cos (δ i δ k )+B ik sin (δ i δ k )), (5 2) k=1 where κ R is the set of buses connected to bus i, G ik R denotes the equivalent conductance between the buses i and k, while B ik R is the equivalent susceptance between the buses i and k. E i, E k C are the voltages of buses i and k, respectively, while δ i and δ k are their respective angles Control Development The proposed nonlinear distributed controller aims at frequency synchronization of all generators in the presence of time delay and disturbance. In order to damp the postfault frequency oscillation, DESSs are employed to accelerate stabilization by injecting or absorbing power at the generator buses. Including an external power input (u i ), calculated by distributed controller based on local and neighboring PMU measurements, modifies the swing equation defined in (5 1) as follows: ω i = 1 M i ( D i ω i + P a,i + d i (t) + u i (t τ i )), (5 3) where, u i (t τ i ) R represents the external generalized delayed input control vector, τ i R is a known constant non-negative time delay and t 0 is the initial time. d i : [t 0, ) R is an uncertain time-varying exogenous disturbance due to uncertainties. The control development is based on the assumptions that the rotor phase angle and speed are measurable and also the dynamics of the generator i in (5 1) satisfies the following assumptions. Assumption 10. The generalized inertia of the generator i, M i, is bounded by known, positive, constants such that m i M i m i, where m i, m i R. The damping coefficient of generator i, D i, is bounded by some constants. Assumption 11. The unknown nonlinear exogenous disturbance and its first time derivative exist and are bounded by known positive constants [74]. 78

79 Assumption 12. The reference set point for the generator i, δ i,d R, is designed such that the δ i,d refers to the value of δ i as in the steady-state. Assumption 13. The input delay is a known non-negative constant. Additionally, it is assumed that the system in (5 1) does not escape to infinity during the time interval [t 0, t 0 + τ i ] [59]. The objective of the control design is to ensure that the actual rotor angle of each generator (δ i ) tracks its desired rotor angle δ i,d despite a known constant input delay and bounded disturbances. To quantify the control objective, a measurable auxiliary tracking error, denoted by e 0i R is defined as e 0i = t 0 (δ i (θ) δ i,d (θ)) dθ, (5 4) where the first time derivative of e 0i quantifies the control objective. To facilitate the subsequent analysis, auxiliary tracking error signals, denoted by e 1,i, r i R, defined as e 1i =ė 0i + α i e 0i (5 5) r i =ė 1i + β i e 1i + η i e ui, (5 6) where α i, β i, η i R are adjustable, positive, constant control gains. Furthermore, a novel tracking error signal is defined to inject a delay-free control input signal to the closed-loop dynamic by using the past states in a finite integral over a constant delay interval and denoted by e ui R. e ui where ξ i R is an adjustable, positive, constant control gain. t t τ i e ξ i(θ t) u i (θ) dθ, (5 7) By multiplying the time derivative of (5 6) by M i and using (5 3), (5 4), (5 5), and (5 7), the open-loop dynamics for r i can be obtained as ( M i ṙ i = D i δi + P a,i + d i (t) + u i (t τ i ) M i δi,d + M i (α i + β i ) δi δ ) i,d 79

80 + M i α i β i (δ i δ i,d ) M i ξ i η i e ui + M i η i u i M i η i e ξ iτ i u i (t τ i ). (5 8) Based on the subsequent stability analysis, the following continuous robust controller is obtained: u i = k i r i 1 υ i (1 e ξ iτ i) ηi P a,i (t τ p,i ), (5 9) where k i, υ i R are positive, adjustable, constant control gains, and τ p R is a known constant non-negative communication delay. Substituting (5 9) into (5 8), the closed-loop error dynamics for r can be written as ( M i ṙ i = D i δi + P a,i + d i (t) + u i (t τ i ) M i δi,d + M i (α i + β i ) δi δ ) i,d M i η i +M i α i β i (δ i δ i,d ) M i ξ i η i e ui M i η i k i r i υ i (1 e ξ iτ i) P a,i (t τ p,i ) + M ie ξ iτ i υ i (1 e ξ iτ i) P a,i (t (τ p,i + τ i )) + M i η i e ξ iτ i k i r i (t τ i ). (5 10) The closed-loop error system for r i in (5 10) can be segregated by terms that can be upper bounded by a state-dependent function and a constant such that, M i ṙ i = e 1i + M i η i k i e ξ iτ i r i (t τ i ) + Ñi + N i + S 1i + S 2i M i η i k i r i, (5 11) where the auxiliary terms Ñi, N i, S 1i, S 2i R can be defined as ( Ñ i D i δi + D i δi,d + M i (α i + β i ) δi δ ) i,d + e 1i + M i α i β i (δ i δ i,d ) M i ξ i η i e ui, (5 12) N i D i δi,d M i δi,d + d i (t), (5 13) S 1i P a,i P a,i (t τ p,i ), (5 14) M i S 2i υ i (1 e ξ iτ i) (P a,i (t τ p,i ) P a,i (t (τ p,i + τ i ))). (5 15) 80

81 Remark 5.1. N i, S 1i and S 2i are upper bounded by known constants as given in Assumptions 10, sup N i N i, sup S 1i S 1i, sup S 2i S 2i, (5 16) t R t R t R where N i, S 1i, S 2i R are known positive constants. Remark 5.2. Ñ i is upper bounded by a state-dependent function, by using Lemma 5 in [83] and Assumption 10. The upper bound for (5 12) can be obtained as Ñi ψ i z i, (5 17) where ψ i R is a known positive constant and z i R 4 is the vector of error signals defined as [ z i e 0i e 1i r i e ui ] T. (5 18) To facilitate the subsequent stability analysis, auxiliary bounding positive constants 1 σ i, Ω i R are defined as {( σ i min α i 1 ) (, β i η i 2 ), ξ iµ i 2, k } im i η i, (5 19) 8 { σi } Ω i min 2, ξ i, (5 20) where µ i R is a known, selectable, positive constant. Theorem 5.1. Given the dynamics in (5 1), the controller given in (5 9) ensures that all error tracking signals are globally uniformly ultimately bounded in the sense that δ i δ i,d ɛ 0i exp ( ɛ 1i (t t 0 )) + ɛ 2i, (5 21) 1 σ i and Ω i will be used as bounding constants (for convergence decay rate and definition of the domain of attraction) in the Appendix. 81

82 where ɛ 0i, ɛ 1i, ɛ 2i R are known positive constants. The control gains are selected sufficiently large relative to the initial conditions of the system such that the following conditions are satisfied 2 α i > 1 2, (5 22) β i > 1 + η i 2, (5 23) ) (1 + 1mi, (5 24) ξ i > η i ( + k i 1 + e ξ i τ i ) 1 + µ i η i µ i < m ( ) iη i 1 2e ξ i τ i 8, (5 25) k i > 8 m i η i σ i ψ 2 i. (5 26) Lyapunov Stability Analysis Proof. Let V i : D R be a Lyapunov function candidate defined as where the functionals Q i : R R be defined as V i 1 2 e2 0i e2 1i M ir 2 i + µ i 2 e2 ui + Q i, (5 27) Q i k t i 2 (µ i + m i η i ) e ξi(θ t) ri 2 (θ) dθ, (5 28) t τ i Let y i R 5 be defined as [ y i z i, Q i, ] T. (5 29) The Lyapunov function candidate defined in (5 27) can be bounded as Ξ imin y i 2 V i Ξ imax y i 2 (5 30) 2 The control gain conditions can be provided by selecting sufficiently large k i, ξ i and sufficiently small µ i. 82

83 where Ξ imin, Ξ imax R are known positive constants and defined as Ξ imin min{ 1 2, m 2, µ i }, (5 31) 2 Ξ imax max{1, m 2, µ i }. (5 32) 2 Using (5 4)-(5 7), (5 11), and by applying the Leibniz Rule for (5 28), the time derivative of (5 27) can be determined V i e 0i (e 1i α i e 0i ) + e 1i (r i β i e 1i η i e ui ) +r i ( e1i + M i η i k i e ξ iτ i r i (t τ i ) ) + r i (Ñi + N i + S 1i + S 2i M i η i k i r i ) ( + µ i e ui ξi e ui k i r i + k i e ξ iτ i r i (t τ i ) ) ( 1 + µ i e ui P a,i (t (τ i,p + τ i )) 1 ) S 2i υ i η i η i M i ξ i Q 1i + k i 2 (µ i + m i η i ) r 2 i k ie ξ iτ i 2 (µ i + m i η i ) r 2 i (t τ i ). (5 33) By using Assumption (10), (5 16), (5 17) and canceling common terms in (5 33), (5 33) can be upper bounded as V i e 0i e 1i α i e 2 0i β i e 2 1i + η i e 1i e ui + m i η i k i e ξ iτ i r i r i (t τ i ) m i η i k i r 2 i + ρ i r i z i + r i N i + r i S 1i + r i S 2i ξ i µ i e 2 ui + k i µ i e ui r i + k i e ξ iτ i µ i e ui r i (t τ i ) + µ i e ui P a,i (t (τ i,p + τ i )) + µ i e ui S 2i υ i η i η i m i ξ i Q 1i + k i 2 (µ i + m i η i ) r 2 i k ie ξ iτ i 2 (µ i + m i η i ) r 2 i (t τ i ). (5 34) 83

84 Using Young s Inequality and completing the squares for r i, by nonlinear damping, the following inequalities can be obtained for (5 34) as ( V ) ( e 2 0i β i 1 2 η i 2 ) e 2 1i ξ iµ i α i e2 ui k im i η i 8 ( ξi µ i 2 η i 2 k )) iµ i ( 1 + e ξ i τ i ) µ i (1 + 1mi e 2 ui 2 2η i k ( i mi η i ( 1 2e ξ i τ i ) ) 2µi ri ρ 2 i z i ( ( N i 2 + m i η i k i m i η i k S 1i 2 + S 2i k )) iµ i i 2 µ i ξ i Q 1i + 2υi 2η Pa,i 2 (t (τ i,p + τ i )). (5 35) i By using the definition σ i in (5 19) and the gain conditions in ( ), (5 35) can r 2 i be upper bounded as ( σi V i 2 4 ) ρ 2 i z i 2 σ i m i η i k i 2 z i 2 ξ i Q 1i + Φ i, (5 36) where Φ i 1 m i η i k i ( N 2 i + S 2 1i + S 2 2i ( 1 + k i µ i )) 2 + µ i P 2 2υi 2η i a,i (t (τ i,p + τ i )) 3, and P a,i R is a known constant such that sup t R P a,i P a,i. Using (5 26) and the definition of Ω i in (5 20), the expression in (5 36) reduces to V Ω i y i 2 + Φ i, (5 37) Using (5 30) and (5 37), an upper bound can be obtained for (5 37) as V i Ω i Ξ max V i + Φ i. (5 38) 3 It shlould be noted that larger k i, υ i and smaller µ i provide smaller Φ i. 84

85 The solution of the differential inequality in (5 38) can be obtained as V i (t) Λ i, (5 39) where, ( Λ i V i (t 0 ) Ξ ) ( maxφ i exp Ω ) i (t t 0 ) + Ξ maxφ i Ω i Ξ max Ω i By using (5 27) and (5 39), the following upper bounds can be obtained for the absolute values of e 0i, e 1i, r i, e ui, e pi as e 0i 2Λ i, e 1i 2Λ i, r 2 e ui Λ i. µ i 2 m i Λ i, By using the time derivative of (5 4) and (5 5), δ i δ id can be upper bounded as δ i δ id (1 + α i ) 2Λ i, By using (5 1), (5 4), (5 5), and (5 7), ω i ω id can be upper bounded as ω i ω id 2Λ i 1 m i + (1 + α i ) α i +β i + It can be concluded that y is globally uniformly ultimately bounded, where uniformity in initial time can be concluded from the independence of Ω i and the ultimate bound from t 0 [75]. Since e 0i, e 1i, r i, e ui, L, P a,i L, and from (5 9), we can conclude that u L and that the remaining signals are bounded. Remark 5.3. Let V i : D R be a Lyapunov function, where D R 5 is the domain that contains the origin, satisfies the following inequality 1 µ i η i Ξ imin y i 2 V i Ξ imax y i 2. (5 40) In addition, the equation (5 37) can be used to obtain the following inequality 85

86 V i Ω i 2 y i 2, y i (t) D with y i (t) ( 2Φi Ω i ) 1 2, t t0. with 2Φ i Ω i Ξ i Ξ imax, where Ξ i R is a positive constant. Then, the set S Ξi {V i (y i ) Ξ i } is a positively invariant for (5 3) and y i (t 0 ) S Ξi. By using the Theorem 4.15 in [90], ( ) 1 2Φ 2 the following inequality holds for any initial state y i (t 0 ) without any limitation on i Ω i such that y i (t) Ξ imax Ξ imin ( Ω i 2Φi max{ y (t 0 ) exp( (t t 0 )), 4Ξ imax Ω i ) 1 2 }, i 1, 2,..., n. Using definition of Theorem 4.5 in [90], it can be concluded that y i is globally uniformly ultimately bounded. 5.2 Simulation and Results The designed distributed control framework has been implemented on IEEE 39 bus 10 machine test power system by using the Matlab-Simulink with the model parameters given in [31, 76]. The power system model developed by [76] is modified to test the proposed distributed control strategy. Communication time delay (τ p ) and Table 5-1. Distributed controller gain settings. α i, β i η, υ i, ξ i k i P ref (p.u) Generator Generator Generator Generator Generator Generator Generator Generator Generator Generator

87 Table 5-2. Default simulation parameters. Parameter Description Default ρ DESS maximum power output ratio (P max,i /P m,i ) 10 % τ p Communication delay, latency 100 ms τ i Control input delay 20 ms SNR Signal to noise ratio (P m,i /Noise) 20 db τ s Sampling period of controller output 10 ms response time of the controller and flywheel (τ i ) are artificially introduced to mimic the communication layer. The controller gains are experimentally obtained by following the gain conditions defined in (5 26) and provided in Table 5-1. The desired operation set points of generators such as rotor angle (δ d,i ) are set to their pre-fault values in steady as suggested in [48]. Finally, the initial simulation parameters are fixed to the values given in Table 5-2 unless otherwise specified. In order to assess the performance of the designed controller in treating the transient instability problem, a three-phase fault is applied at bus 17 in line at t=0.5 s. Shortly after within the critical clearing time, the fault is cleared at t=0.6 s and the controller is activated at the time t=0.7 s. Angle deviation and frequency oscillation have been monitored and the stabilization time is calculated to evaluate the controller performance. Our definition for stabilization was inspired by the Frequency Trigger Levels of 0.05 Hz deviation used by the North American Electric Reliability Corporation (NERC) [77]. Hence, the stabilization time is defined as the time passed after fault inception to convergence of all generator speeds to the synchronous frequency within a tolerance of 0.1 %, namely, [ ] Hz. Figure 5-2 shows the frequency oscillation and rotor angle deviation for synchronous machines over time after a fault inception. When a fault applied at t=0.5 s, rotor speed starts swinging and at the time of t=0.7 s, the proposed control framework takes action to damp the oscillation. The right-hand side of Figure 5-2 shows that all 10 generators can converge to the synchronized speed region, highlighted by dashed lines at Hz and Hz, at about 3.5 s or earlier for the given initial conditions in Table 87

88 Rotor Angle ( δ ) - Degree Gen. 1 Gen. 2 Gen. 3 Gen. 4 Gen. 5 Gen. 6 Gen. 7 Gen. 8 Gen. 9 Rotor Speed (ω) - Hz Gen. 1 Gen. 2 Gen. 3 Gen. 4 Gen. 5 Gen. 6 Gen. 7 Gen. 8 Gen. 9 Gen Time (seconds) Time (seconds) Figure 5-2. Rotor angle deviation and rotor speed oscillation over time during and after three-phase fault inception Similarly, the left-hand side of Figure 5-2 illustrates the convergence of rotor angles of machines to the pre-fault values accordingly, in about the same time frame. Machine 10 is the angular reference. 5.3 Case Study under Practical Limitations The practical maximum efficiency of the proposed controller is affected by the inherent limitations of the employed communication, sensor and DESSs technologies such as latency through communication network, accuracy and reporting frequency of PMUs and maximum power limit of the DESSs. In addition to these restrictions, cyber-attacks introduce external limitations and uncertainties to the smart grid systems which severely affect the controller performance. The controller, thus, must be resilient to both internal and external limitations. In this section, we evaluate the proposed controller under practical limitations and compare that with the PFL controller, described in [48]. The parameters used in the PFL controller are 1 for the frequency control (noted α in [48]) and 0.5 for the phase cohesiveness for all machines (noted β in [48]). This controller was also implemented in the same Matlab-Simulink New England 39-bus test system [76]. The governor, as implemented in [76], is activated for all simulations, while the PSS is always disabled. To make a reasonable comparison, we adopted the limitations defined in [48] which are: i) maximum power injection/absorption 88

89 A B C D E F Figure 5-3. Stabilization performance of the distributed controller under practical limitations. A) Stabilization time versus maximum DESS power output capacity, B) Stabilization time versus varying communication delay, C) Stabilization time versus signal-to-noise ratio, D) Stabilization time with respect to varying sampling rate, E) Robustness to the deviation in sensor measurement, F) Robustness to the deviation in sensor measurement when the latency is fixed at 100 ms. 89

90 capacity of DESS (P max ), ii) communication delay (latency, τ p ), iii) sensor noise, and iv) sampling of the controller output. Since the control input signal (u i ) represents the actual power need to be injected or absorbed, P max determines the upper and lower limit of the controller signal that can be realized by DESS having limited power output. Thus, we set the P max to a percentage of mechanical power of each generator, that is, P max,i = ρp m,i /100. PMUs sample the time-stamped phasors before transmitting through the communication channel and typically the maximum sampling rate is up to 60 samples per second. Sensor noise affect the PMU measurements and add uncertainties to the controller operation. Latency is inherent due to processing and propagation of data through communication layers and channel are usually considered to be in the order of 10 ms [91]. In addition to these inherent limitations, in this paper, we consider time delay due to response time of DESSs and controller which is considered 20 ms. The proposed controller and the PFL controller are comparatively evaluated in Figure 5-3 in terms of stabilization time for different types of practical limitations. The values for each tested parameter are given in 5-2 unless otherwise noted. First, the stabilization time against varying percentage of the P max is evaluated in the presence of different latency cases. As shown in Figure 5-3A, the proposed controller can stabilize the system in all latency cases for values of ρ larger than 4%. As expected, the stabilization time decreases as ρ increases until it reaches a plateau for ρ>10%. The PFL controller is not equally robust to latency. For cases where τ p >50 ms it cannot stabilize the system. The stabilization time of PFL is similar to the proposed controller when the latency is 50 ms but the PFL controller shows abnormal behaviors for larger values of latency. Thus, we can infer that the PFL controller is not robust to latency. In Figure 5-3B, stabilization time as a function of latency is shown for different maximum power limits of DESSs (ρ). Both controller schemes could only stabilize the system for ρ 5%The plots of the PFL controller for ρ >5% were omitted because they 90

91 only show stabilization for τ p =50 ms and for larger latency, stability is not reached. If latency is greater than 100 ms, the PFL controller cannot stabilize the generators. Our approach can stabilize the system for all cases where ρ >5% and also stabilize the system for ρ =5% and τ p <800 ms. Since the resiliency to latency is very important for cyber physical systems, the proposed controller may be considered a candidate controller for practical implementations. Furthermore, the robustness of both controllers is evaluated in the presence of uncertainties. An additive Gaussian white noise disturbance, d(t), is injected to the systems dynamics as shown in (5 3). The power of the d(t) is given relatively to the mechanical power of each generator (P m,i ) to add uncertainty to PMU measurements. This injected error models noisy PMU measurements or maliciously distorted measurements that lead to changes in the calculation of P e,i in (5 2). The ratio of noise was calculated using the default mechanical power as P m,i /Noise is given in decibels (db) and denoted as signal-to-noise ratio (SNR). Figure 5-3C demonstrates the ability of the proposed and PFL controllers to mitigate the effects of uncertainties. As expected, the performance of both controllers is harmed by larger disturbances, i.e., smaller values of SNR. The results show that the proposed controller can stabilize all generators for all cases tested while the PFL controller can only reach stability when τ p =50 ms. Moreover, the stabilization is tested for different values of sampling period for different latency, as shown in Figure 5-3D. It is expected that extending the sampling period results in degraded performance since the controller receives less frequent state feedback updates from the sensors. PMUs can provide up to 60 samples per second and so that the minimum sampling period can be s. Thus, a controller should achieve transient stability for a sampling period of at least s. As illustrated in Figure 5-3D, the proposed controller can achieve transient stability within around 3.2 s with respect to varying sampling rate and latency. The PFL controller achieves the same 91

92 performance as the proposed controller when the latency is 50 ms, while for other cases it fails. Finally, the robustness of the distributed controller is assessed in Figure 5-3E with respect to the sensor measurement deviation from 1% to 5%. While the robust controller can tolerate up to 5% deviation in measurements, the performance of PFL controller collapse under the same conditions. To make it more clear, in Figure 5-3F, the resiliency of both controllers to sensor errors is tested when the communication delay is fixed at 100 ms. It is evident that the proposed nonlinear control can resist errors in sensor measurements without losing stabilization performance in terms of time. Whereas, increasing deviation in sensor measurement effects the stabilization performance of the PFL significantly. From the perspective of the numerical results, we conclude that the proposed control outperforms the PFL controller under large latencies in communications. Although, the performance of the PFL controller can approach that of the proposed controller for lower latency, it fails for increasing latency. Robustness to time delay and uncertainty are two key metrics in cyber-physical systems. Hence, we consider various latency cases when evaluating the performance of the controller for sampling rate, noise and maximum power percentage. As a result, the proposed controller can compensate up to 130 ms latency plus 20 ms control input delay due to response time of DESS and controller. 5.4 Summary In this paper, we present a novel nonlinear distributed control design for transient stability of cyber-physical smart grids. The performance of the designed controller is validated through a Matlab-Simulink simulation environment. To present a comparative study, the most recently developed PFL based controller is simulated under practical limitations. The simulation results, as discussed in Section 5.3, demonstrate that the proposed controller can achieve better transient stability performance under the same practical limitations. In particular, the controller introduced in this article becomes most 92

93 attractive in showing better resilience to the time delay. Since the proposed controller presents a novel nonlinear technique capable of performing time delay compensation, the results validates its correctness. The success of this controller as being resilient to cyber disturbances (delay and uncertainty in measurements) may provide solutions for future robust cyber-physical systems. Additionally, while DESS technologies currently deployed to support the integration of renewable energy sources into the Grid are considered costly, the additional function of improving system transient stability margins may increase the value of the services they currently provide to the Grid. Consequently, the adoption of our approach could help expand the capability of the Power Grid to assimilate renewable power sources by economically enabling a larger installation of grid-connected DESSs. 93

94 CHAPTER 6 AN ADAPTIVE MAC PROTOCOL DESIGN FOR SMART GRID HOME AREA NETWORKS Smart grid refers to a set of technologies including two-way communication technologies, control systems, sensors, and computer processing that utilize advanced functions such as demand response, smart metering, energy management systems, and real-time monitoring and control to enhance the reliability, sustainability, quality, and efficiency of electrical power systems. Maintaining the seamless operations of all these functions highly depend on the performance of the underlying smart grid communication networks (SGCN). Ensuring the information exchange between smart grid components while meeting the application-specific latency and data rate requirements are the key to success in the SGCN. The SGCN can be basically decomposed into home area networks (HAN), neighborhood area networks (NAN), and wide area networks (WAN), each of which has different coverage areas and supports various applications that require various data rate, delay tolerance, security. The WAN are established for long-haul communication between the NANs and utility systems to support automation, control, protection applications. The NAN connects multiple smart meters within a region to the WAN to deliver metering data to utilities. HAN operates within a residential and supports a variety of applications such as smart meters, home power generation, smart appliances, electrical vehicle charging, and multimedia. There are a variety of technologies to establish these networks such as HomePlug, G3, ITU-T, PRIME for power line communication (PLC), cellular 3G-4G, Zigbee, WiMAX, IEEE x, IEEE , proprietary networks for wireless communications, and fiber optical communications. Current SGCN solutions tailor these modern wireless and wired networking technologies depending on delay constraints, the amount of data to be transmitted, transmission environment, and the cost. 94

95 These networking solutions differ from each other by means of technologies implemented in sub-layers such as modulations, error coding, error correction, etc. However, in the medium access control (MAC) layer, contention based or reservation based channel access protocols are used. PLC standards mostly define their MAC protocol with the contention-based Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA) technique exclusively or in combination with the reservation-based Time Division Multiple Access (TDMA) method. HomePlug 1.0, HomePlug AV and IEEE 1901 use CSMA/CA with optional TDMA in the MAC layer, while HPGP adopted exclusively CSMA/CA. MAC layer protocols are critical to guarantee an efficient and fair resource (bandwidth) allocation for contending network users. Thus, a special attention should be drawn to MAC layer protocols for highly populated networks such as smart grid HANs. Enhancing the accessibility to medium while meeting required data rate and delay characteristics of each contending users is crucial for maintaining the seamless operation of underlying applications. Recently, with the increasing numbers of connected smart devices and multimedia applications, the population of the HANs has been growing quickly. In addition, the diversity in supported applications with their varying data rate requirements and sensitivity to delay emerges as a challenge for MAC protocol design. Smart appliances, for example, do not require high data rates but the multi-media applications such as IP TV require high data rates. Similarly, smart meters are not delay-sensitive applications but multimedia applications. HANs must support a wide range of applications in the same network while guaranteeing their data rate and delay requirements without sacrificing the performance of any of the applications. The state-of-the-art MAC protocols such as IEEE x and HomePlug are not able to maintain a high efficiency for highly populated networks. As shown in Figure 6-1, 95

96 IEEE for CW [32:1024] HomePlug/P1901 for CA0 or CA1 HomePlug/P1901 for CA2 or CA3 0.7 MAC Efficiency Number of Nodes Figure 6-1. The MAC throughput comparison of wireless (IEEE ) and wired (HomePlug) networking technologies both IEEE and HomePlug protocols suffer in terms of MAC efficiency in the face of increasing network population. Thus, an enhancement in MAC efficiency is needed. An adaptive channel access mechanism, based on Markov chain model, has been developed to enhance the efficiency and delay performance of highly populated networks. As part of the MAC layer protocol development for smart grid communication, the proposed adaptive approach is tailored for HomePlug MAC protocol and tested by conducting a numerical studies in Matlab in this chapter. The simulation results show that the designed adaptive MAC protocol maintains the efficiency at around 80% MAC for up to 100 nodes. Whereas the MAC efficiency reduces down to 10% with the standard HomePlug MAC protocol. Also, an 80% reduction in channel access delay is achieved in comparison to the HomePlug MAC protocol. It should be noted that the adaptation and implementation of the proposed channel access scheme to the other communication technologies such as wireless and fiber optical as being other options to be explored in further work. 6.1 Literature Review Optimizing the performance of networking technologies has received a great deal of interest leading to better understanding of their characteristics. For example, in recent years, several interesting research results have been reported in the performance 96

97 analysis of standard IEEE MAC and HomePlug MAC. Performance analysis of the standard IEEE MAC was studied in [92]. Later on, several authors have proposed an enhancement to DCF by means of finding an optimal contention window (CW) and changing the backoff resolution of the conventional DCF. Cali et al. found the number of nodes to compute the optimal CW [93, 94]. Bianchi at al. used a Kalman filter method to estimate the numbers of contending nodes [95]. Heusse et al. defined a method to enhance throughput and fairness by computing the number of consecutive idle slots between two transmission attempts instead of estimating the number of nodes [96]. Although, estimating the number of a consecutive idle slot is relatively easier than estimating the number of nodes, [96] does not show a remarkable improvement with respect to the standard DCF. Along the same lines, several authors have extensively analyzed the performance of HomePlug MAC [97 99] and some improvements have been presented through [ ]. All of these consisted of adaptive CW adjustments. However, the proposed models have only been analyzed in terms of MAC throughput and under the assumption that there is only one type of traffic presented. Furthermore, the Markov chain model that is used to define the proposed model in [100, 101] did not consider the time spent for a successful transmission or collision during which a node must freeze its backoff counter until the ongoing transmission attempt terminates, that is, as long as the node senses the channel idle. The defined problem was addressed in [103] by redefining the Markov chain model of [101]. Most of these studies are largely confined to throughput analysis and enhancement without any priority classes and with no attention to delay performance. The rising popularity of delay sensitive (QoS) applications (video, voice, etc.) reveals the need also for improving the delay performance of MAC protocols as well as for considering different simultaneous priority classes. Medium access delay is a crucial problem when the MAC protocol is taken into off all priority consideration since all of the users share the channel resource, which may cause longer access 97

98 delay when the network is highly congested. In [97, 99], delay analysis of the standard HomePlug/IEEE 1901 has been done but [97] did not consider the 4 different CAs contending at the same time. Furthermore, the results reported in [99] shows that the throughput and the medium access delay performance of standard HomePlug/IEEE 1901 MAC degrade significantly when the number of active users increases. 6.2 Research Motivation The HPGP offers a potential 75% reduction in cost and power consumption, which makes it more affordable for smart grid applications while maintaining interoperability with the existing 45 million HPAV devices for HANs. The maximum data rate provided by HPGP is 10 Mbps but this is the maximum data rate and in some circumstances, it can be as low as 1 Mbps or even worse. In addition, the performance of HPAV may be adversely affected when HPGP devices operate in the presence of high-speed HomePlug AV products. Thus, the distributed bandwidth control (DBC) mechanism has been defined in HPGP to help to avoid any performance degradation for HPAV devices. As a result, the DBC limits the channel access time of HPGP devices to approximately 7% in the presence of HPAV devices which reduces the maximum coded PHY data rate to 700 kbps. If we consider the MAC efficiency of the standard MAC protocol, that reduces 10% when the number of connected devices is 100, the overall data rate drops down to 70 kbps. Given that the minimum data rate to support smart grid application is ~250 kbps, the standard HomePlug MAC no more meets the data rate requirements [104]. From the view of presented issues so far, we proposed a new CSMA/CA MAC layer protocol based on adaptive contention window technique. The proposed model includes the priority resolution for the sake of quality of service (QoS) and aims to improve the MAC throughput while keeping the channel access delay within the tolerable limit. The designed MAC protocol has been tested under saturation conditions and results published in [103, 105]. The saturation condition results without enabling the priority 98

99 Table 6-1. Contention resolution parameters of the standard HomePlug MAC protocol. Priority CA0 & CA1 CA2 & CA3 BPC CW DC CW DC > resolution mechanism in [103] demonstrates that the MAC efficiency is maintained at about 80% for up to 100 contending users while the efficiency of the standard HomePlug MAC falls to 10% with the same number of users. In addition, the delay and throughput performance of the proposed model with priority resolution mechanism were evaluated in [105]. The simulation results show that the proposed MAC protocol outperforms the standard HomePlug MAC protocol in terms of MAC throughput and channel access latency. 6.3 HomePlug/IEEE 1901 CSMA/CA MAC Protocol HomePlug and IEEE 1901 uses the same CSMA/CA MAC protocol defined in the HomePlug 1.0 standard and consists of two main segments that are a random backoff resolution and a priority resolution. The backoff resolution is similar to the IEEE CSMA MAC but two new counters, a Defer Counter (DC) and a backoff procedure counter (BPC) have been introduced. The priority mechanism provides channel differentiation by defining 4 different channel access priorities in order to provide QoS, which guarantees different traffic types Backoff Procedure The backoff resolution runs as described in Figure 6-2. Each time a node has a frame to transmit, the BPC and the DC are set to the initial values given in Table 6-1 and the BC is chosen randomly between [0, CW]. The BC decreases by one in each time slot when the channel is sensed as idle. The BC freezes but the DC starts decreasing 99

100 by one when the channel is sensed as busy and the packet is transmitted when the BC becomes zero. After a successful acknowledgment (ACK) message exchange, the transmission is inferred as successful or as a failure otherwise. If the BC of multiple nodes expire simultaneously, a collision occurs and counters are reinitialized. If the DC becomes negative before the BC expires, then the DC and the BC are reset instead of waiting for the BC to expire. The purpose of the DC is to decrease the collision rate and associated MAC access delay when the network is highly congested Priority Resolution In order to provide a channel access differentiation, data traffic in the PLC MAC is classified into 4 different Channel Access priorities, CA0-CA3. Two priority slots, called PRS0 and PRS1, are defined after a successful frame transmission as shown in Figure 6-3. In each of these PRS slots, nodes are allowed to announce the priority of their pending packets by asserting a 1 or 0. CA3, CA2 and CA1, CA0 share the same contention parameters as seen in Table 6-1. The highest priority packet (CA3) asserts in both PRS0 and PRS1, CA2 packets are announced only in PRS0. CA1 announces in PRS1 and the CA0 does not signal in any of these slots. By using these priority slots, each node knows whether there is a pending transmission attempt from a higher priority category and thus, lower priority class nodes do not contend for the channel. The Figure 6-2. Operational flow chart of HomePlug/IEEE 1901 CSMA/CA MAC protocol. 100

101 Figure 6-3. Backoff resolution of HomePlug/IEEE 1901 CSMA/CA MAC protocol. Figure 6-4. Markov chain model for adaptive contention window based CSMA/CA MAC protocol. priority resolution scheme is enabled right after a successful transmission and disabled after, i) a collision, ii) erroneous reception and iii) if the channel is detected as idle for longer than the maximum length of a frame transmission time [104, 106]. 6.4 Adaptive Contention Window based CSMA/CA MAC The proposed MAC protocol redefines the backoff resolution scheme of HomePlug MAC by using the bi-dimensional Markov chain model shown in Figure 6-4. The operational flow chart of the adaptive contention window size based MAC protocol is very similar to that of standard HomePlug MAC with the exception that the DC value is kept fixed and the contention window (CW) size is updated based on the network population. Thus, Table 6-1 is not used for choosing DC and so the BPC is no longer needed. 101

102 The bi-dimensional Markov chain model represents the event sequence of a single node during backoff procedure. Each box in Figure 6-4 denotes the state probability of a node. The state probability is a function of backoff counter (BC) and the defer counter (D) where can be represented by (D, BC). The probability that the node senses the medium as idle is denoted by p i and also serves as the transition probability to the adjacent states in which the backoff counter is one less. The transition probability to the state in which defer counter is one less is denoted by 1 p i. The probability of transition to top row states, for the nodes that run their BC to zero, is 1/CW. The BC is reset to a random value between [0, CW 1] when the nodes reach to a top row state. Finally, transition probability to the top row states if the defer counter becomes less than zero is (1 p i )/CW. The probability that a node starts transmission (p o ) and the probability that a node finds the medium idle (p i ) have been found to be D p o = (i, 0) (6 1) i=0 p i =(1 p o ) n 1 (6 2) The numerical solution of these equations gives the p o corresponding to n. Also the p o can be calculated as the ratio of the number of states in which BC is zero to the total number of states in Markov chain model. The number of states wherebc is zero is D + 1 and the total number of states is (D + 1)/CW. Taking the ratio of these yields p o = 1 CW (6 3) The efficiency of the MAC protocol may be defined as: η = P S T Data P s T s + P I T I + P C T C (6 4) 102

103 where P s is the probability of successful transmission, P I is the probability of idle channel, and P C is the collision probability. Also T I denotes a slot time duration, T C stands for time spent during a collision, T S represents time elapsed during a successful transmission and T Data gives the required time for prorogation of a data frame. Using the protocol definition and the statistical properties above, the following equations can be obtained as: P S =np o (1 p o ) n 1 P I = (1 p o ) n P I =(1 p o ) n P C =1 P S P I T S =P RS0 + P RS1 + T F rame + RIF S + T ACK + CIF S T C =P RS0 + P RS1 + T F rame + CIF S Since p o is a function of n, the optimal contention window size (W opt ) corresponding to n can be found by using the (6 4). Hence, po that maximizes the throughput becomes the optimal transmission probability p opt.taking the derivative of (6 4) with respect to p o and setting it to zero yields to the following equation for the p opt as a function of n. T I (P S p I dp o P I dp s dp o ) + T C (P S dp C dp o P I dp s dp o ) = 0 Assuming that p o 1, the approximation, 1 T I T c = 1 np o (1 p o ) n (6 5) simplifies the (6 5) and yields (1 p o ) n 1 np o + n(n 1) p 2 o 2 p o 1 n 2TI T C (6 6) 103

104 p o Numeric Solution Analytic Solution Number of User Figure 6-5. Numeric and analytic solution for p o In addition to this solution, a numeric solution without any assumption has been conducted through a simulation. Figure 6-5 shows a plot of the simulation and analytical results and confirms that (6 6) is a good approximation. Furthermore, using (6 3) in (6 6), the following linear relationship between CW and n can be obtained. CW = n T C (6 7) 2TI As it can be seen from (6 7), determining the optimal contention window (CW) size depends on the knowledge of n. Therefore, the practical application of the proposed model relies on estimating the number of contending nodes. For that purpose, many estimation algorithms have been carried out in literature. The carrier sense ability of CSMA/CA mechanism allows tracking the channel status and interpreting whether the channel is being used or idle. By using this feature of CSMA/CA, [100] proposed a stochastic model to predict network population, [95] used Kalman filter to improve the estimation correctness, and [107] used Bayesian estimation algorithm. However, the method given [100] is inadequate to estimate network population well and Kalman based solution defined in [95] and Bayesian estimation models given in [107] are very complicated solutions for a practical implementation. Therefore, we assert that there is a need for designing a new estimation algorithm. The estimation algorithm, given in [100], has been extended by developing a new estimation algorithm through the use of a nonlinear smoothing function in addition to 104

105 ARMA linear filter. The estimation algorithm relies on estimating the number of idle slots during a time slot interval. By exploiting the carrier sense ability of CSMA/CA protocol, the channal is observed over n o time slots and the number of idle time slots (n i ) and busy time slots (n b ) are calculated. Taking the ratio of n i to n o gives a stochastic approximation of the probability of finding the channel as idle, which is equal to p i. p i = n i n o (6 8) Approximating (6 2) by using the assumption that (p o 1) yields, p i 1 (n 1)p o (6 9) and substituting (6 8) into (6 9) gives an equation to estimate n as: n = CW (1 n i n o ) + 1 (6 10) For the case of fast traffic fluctuation, the following linear ARMA filter was used to avoid sharp changes in the estimated value of n. n t+1 = an t + 1 α i=1 n t 1 (6 11) After every 10 estimation attempts using a smoothing factor, α =.9, the estimated value of n was updated. In addition to the ARMA filter, the following nonlinear smoothing function was used to update the CW for flattening the estimation deviation and smoothing the estimating during an abrupt change in network population. s(n) = 1 + h n CW (n) = s(n)cw (n 1) (6 12) 105

106 Figure 6-6. Estimating number of contending nodes over a changing network traffic. Figure 6-7. Simulation results to evaluate MAC efficiency of the proposed MAC protocol when the number of nodes is given and estimated. To analyze the effectiveness of the estimation algorithm for n, we ran a discrete event simulation. In this simulation, n changes over 50x10 4 time slots and the estimation scheme was used to track the actual value of n. The performance of the proposed estimation algorithm can be assessed from Figure 6-6 where the estimation algorithm has been analyzed for only linear filter and with non-linear smoothing filter. The effect of the nonlinear filter design can be observed easily that the variation in estimation shrink with the help of the nonlinear smoothing filter. Although, there is still deviation between actual and estimated value of n, it was proved in Figure 6-7 that the deviation does not affect the MAC efficiency much. 106

107 6.5 Performance Evaluation with Prioritized Traffic The channel access delay and the MAC efficiency performance of the developed medium access protocol have been analyzed by conducting a discrete event simulation through Matlab. In order to determine the maximum achievable performance, the designed MAC protocol has been assessed under saturation condition which refers to the limit reached by network as the offered number of user increases and shows the maximum number of nodes that a network can support in stable conditions [92]. It is one of the fundamental metrics used in the performance analysis for MAC protocol. The number of nodes is assumed to be at least 2 and increases up to 100. Although, a hundred nodes is an extreme case for a HAN, in the future with the proliferation of Smart Grid devices and assigning a different IP addresses for many electric outlets, it may become a realistic case. The saturation conditions are defined as: i) all stations have frames to transmit immediately after a successful transmission, ii) large enough buffer size and re-transmission limit, iii) ideal channel conditions and iv) collision is detected if the BC of multiple nodes expire at the same time. Simulation parameters are given in Table 6-2. It is worth to note that optional features of the HomePlug MAC such as frame aggregation, frame bursting, contention free channel access have not been considered in this simulation. The MAC efficiency is defined in (6 4) and calculated by using the parameters given in Table 6-2 for priority classes CA0-CA3. Table 6-2. HomePlug 1.0 MAC parameters. Parameters Value in HomePlug 1.0 Data Rate (R) 14 Mbps Slot time (T slot = T I ) 35.84µs ACK transmission time (T ACK 72µs RIFS 26µs CIFS 35.84µs PRS0 and PRS µs T Data is fixed at 1500 byte µs 107

108 Furthermore, the medium access delay is defined as the total time elapsed from the beginning of a transmission attempt to the successfully completion. Due to the saturation condition, it can be assumed that each station always has a frame for transmission, and so the delay can be defined as the time between two contiguous frames in a station to be transmitted successfully. The designed adaptive MAC protocol has been compared with the state-of-the-art HomePlug MAC protocol by conducting two different cases: i) numbers of nodes that have lower channel access priority such as CA2-CA0 are set to 1, that is (n CA2 = n CA1 = n CA0 = 1), while the number of CA3 nodes (n CA3 ) varies, ii) numbers of nodes that have channel access priority of CA2-CA0 are fixed at 10, namely (n CA2 = n CA1 = n CA0 = 10), while n CA3 varies. The MAC efficiency of the proposed MAC protocol and the standard HomePlug MAC are compared in Figure 6-8 for both cases. Figure 6-8A and Figure 6-8C show the efficiency for highest priority nodes when n CA2 = n CA1 = n CA0 is fixed at 1 and 10 respectively. As shown in Figure 6-8A, the MAC efficiency of the proposed MAC protocol is maintained at about 80% when the number of CA3 nodes increases up to 100. However, the MAC efficiency of the standard HomePlug MAC decreases down to 40% for n CA3 =30 and reduces down to 10% when n CA3 with same network load. Although, n CA3 =100 is an extreme case for an usual HAN, it shows the deficiency of the HomePlug MAC in the face of growing network population. In Figure 6-8C, the MAC efficiency of the modified HomePlug for CA3 nodes begins at about 40% but gradually reaches 80% efficiency as CA3 nodes dominate the network. It is evident that the poor efficiency in the case number two is because of the high network population initially and the definition of the priority access mechanism. Since the priority resolution mechanism is activated right after a successful transmission and deactivated after a collision, at the beginning of the simulation priority resolution does not work. Therefore, lower priority nodes do not defer for transmission. However, 108

109 η MAC Efficiency CA3 Modified MAC CA3 HomePlug MAC η MAC Efficiency x CA2 Modified MAC CA1 Modified MAC CA0 Modified MAC CA2 HomePlug MAC CA1 HomePlug MAC CA0 HomePlug MAC Number of CA3 Nodes A Number of CA3 Nodes B η MAC Efficiency CA3 Modified MAC CA3 HomePlug Number of CA3 Nodes C η MAC Efficiency 10 x CA2 Modified MAC CA1 Modified MAC CA0 Modified MAC CA2 HomePlug CA1 HomePlug CA0 HomePlug Number of CA3 Nodes D Figure 6-8. Case study to compare the MAC efficiency of the designed controller with the standardized HomePlug MAC. the MAC efficiency of CA3 nodes reaches to 80% as n CA3 dominates the network. Also, as seen in Figure 6-9B and Figure 6-8D, lower priority (CA2-CA0) nodes will have a MAC efficiency that are different than zero due to the same reason explained above. When the priority resolution mechanism is deactivated, CA2-CA0 nodes will have a chance to transmit their pending packets. Furthermore, the standard HomePlug performs better than modified MAC for lower priority nodes. However, it should be noted that the efficiency of both the standard HomePlug MAC and the adaptive MAC are pretty close to zero under saturation condition. Thus, making a concrete comparison is not 109

110 MAC Access Delay [s] CA3 Modified MAC CA3 HomePlug MAC Number of CA3 Nodes A MAC Access Delay [s] CA2 Modified MAC CA1 Modified MAC CA0 Modified MAC CA2 HomePlug MAC CA1 HomePlug MAC CA0 HomePlug MAC Number of CA3 Nodes B 2 4 CA2 Modified MAC 3.5 CA1 Modified MAC MAC Access Delay [s] CA3 Modified MAC CA3 HomePlug MAC Access Delay [s] CA0 Modified MAC CA2 HomePlug MAC CA1 HomePlug MAC CA0 HomePlug MAC Number of CA3 Nodes C Number of CA3 Nodes D Figure 6-9. Case study to compare the channel access delay performance of the designed controller with the standardized HomePlug MAC. possible. The MAC efficiency comparison for CA2-CA0 nodes was left as a future work that needs to be deeply analyzed under unsaturated conditions. The delay performance of the modified and the standard HomePlug MAC is evaluated in Figure 6-9. Figure 6-9A- 6-9C show the delay that CA3 nodes encounter when n CA3 varies and the initial numbers of CA2-CA0 nodes are set to 1 and 10 respectively. Both the modified and the standard HomePlug MAC result in the same amount of delay for up to 20 high priority nodes but then the delay for the standard HomePlug MAC increases much faster than the delay of the modified MAC. The 110

111 maximum delay is recorded as 0.2 s for the modified HomePlug MAC whenn CA3 =100 but the standard HomePlug experiences 1 s delay for the same number of nodes. Unlike the high priority nodes, the lower priority nodes generally experience relatively high delay in both the modified and the standard HomePlug MAC protocol. A long delay is reasonable for lower priority nodes due to the aforementioned definition of priority resolution mechanism and saturation condition. Also, Figure 6-9B shows that the standard HomePlug MAC experiences slightly shorter delay in comparison to modified MAC when numbers of lower priority nodes are fixed at 1. However, the delay performance of the modified MAC degrades when numbers of lower priority nodes are set to 10. In general, for the performance of the modified MAC under saturation conditions, we can say that the modified MAC protocol outperforms the standard HomePlug MAC in both delay and MAC efficiency analysis for high priority packet transmission. Although, the standard HomePlug MAC shows slightly better performance than modified MAC for lower priority packet transmission, we cannot conclude that the modified MAC only outperforms the standard HomePlug for high priority packet transmission since saturation conditions does not allow lower priority nodes to use the channel fairly. The performance of MAC protocols should be examined under unsaturated conditions which is the more realistic condition for real applications, and this is the subject of our future work. 6.6 Summary In this chapter, an adaptive contention-based MAC protocol is presented that aims at enhancing the throughput and delay performance for smart grid HANs where a variety of smart grid applications in addition to bandwidth-hungry multimedia applications run together. The increasing numbers of connected devices in HANs leads to decrease in data rate and increase in channel access delay which are two critical metrics for network performance. The insufficient performance of state-of-the-art communication 111

112 protocols with current MAC layer solutions motivated use to develop an adaptive MAC layer protocol to guarantee high data throughput and low channel access delay in the face of increasing network diversity and population. The designed adaptive Markov chain based channel access scheme has been initially implemented into the PLC HomePlug protocol to update the current one. The adaptive HomePlug MAC protocol has been simulated to evaluate the efficiency and the delay performance with respect to increasing network population. Simulation results demonstrate that the adaptive MAC protocol can maintain the efficiency at around 80% with respect to increasing network population up to 100 nodes. Whereas w the MAC efficiency of standard HomePlug MAC protocol reduces down to 10% in the presence of 100 nodes. Also, the adaptive MAC protocol offers an 80% reduction in channel access delay relative to the standard HomePlug MAC protocol. The promising simulation results in throughput and delay performance enhancement encourage us to tailor the adaptive medium access scheme for other communication protocols used in smart grids. However, the adaptation and implementation of the proposed channel access scheme to the other communication technologies such as wireless and fiber optical have left a further work to be explored in the future. 112

113 CHAPTER 7 CONCLUSIONS AND FUTURE WORK 7.1 Summary Maintaining the stability of power systems has become even more challenging problem with the increasing integration of low-inertia and intermittent distributed generation (DG). The changing power system dynamic by enabling two-way power flow and introducing active loads have incapacitated conventional power system controllers. In Chapter 2, a detailed survey is given that discusses current and emerging stability problems with respect to changing smart grid environments and assesses state-of-art control system in the face of rising uncertainties and disturbances. It is apparent that underlying communication networks allow data exchange between remote entities which significantly enhance the performance of the control systems. However, the inherent communication delay adds uncertainty to the controllers which considerably effects the stability of the systems. In Chapter 3, a decentralized control framework is presented that uses distributed energy storage systems (DESS) and phasor measurement units (PMU) to activate the controller. A novel time delay compensation technique is developed in robust nonlinear control to mitigate the effect of known constant time delay. Also, robustness to additive time-varying disturbances is achieved. The simulation results, based on IEEE 39 bus 10 machine test power systems, demonstrate that the decentralized control framework can significantly enhance the transient stability of synchronous machines when a large disturbance occurs. The stabilization time with respect to different time delay, fault clearing time, and time-varying additive disturbance is used to show how the decentralized controller is able to outperform the state-of-art power systems stabilizer (PSS) controller. The robust controller improves stabilization time by 75% regarding the same fault-clearing time and by 80% with respect to time-varying disturbance in the presence up to 130ms time delay. 113

114 The varying communication delay because of different distances between sensor and control units and cyber-attacks such as denial-of-service (DoS) presents in smart grid systems. In Chapter 4, the robust nonlinear controller is further improved to make the controller design even more realistic and resilient by extending the time delay compensation technique for unknown time varying input delay. The numerical results shows the robust control can provide 60% improvement over PSS controller regarding to the additive time-varying disturbance even if the robust controller is subjected to unknown time-varying input delay. Situational awareness is a term introduced to power systems as a result of experiencing major blackouts caused by cascaded failures and stands for the ability of control systems being aware of the entire or a wide range of power grids. The lack of situational awareness in traditional local controllers lead to design centralized strategies to address instabilities arise from cascading effect. However, centralized control systems suffer from the increasing communication payload and being an easy target for adversaries. Distributed controllers, thus, are the new trend in power system control. In Chapter 5, a distributed control framework is presented that aims at receiving feedback from local and neighboring PMUs to actuate DESS. The nonlinear robust control with constant known time delay compensation technique is implemented on IEEE 39 bus test power system. The performance of the distributed controller is compared with a state-of-art controller which uses the same distributed settings but a parametric feedback linearization (PFL) controller. The simulation results are on the favor of the nonlinear controller in most of the cases. Resilience to the latency highlights the nonlinear controller as maintaining stability for up to 1s latency whereas PFL controller fails if the latency is more than 160ms. The nonlinear controller owed this success to the implemented novel time delay compensation technique. Challenges in smart grid communications constitute the other focus of this dissertation. Increasing numbers of connected devices in smart grids with various demands 114

115 from communication networks such as low delay, high data rate, require special attention to support heterogeneous applications by ensuring their needs. In addition to the controller development, an adaptive medium access control (MAC) protocol for smart grid communication is presented in Chapter 6 that targets enhancing the MAC efficiency and delay performance in Home Area Networks where smart meters, smart appliances, electrical vehicle and other multimedia applications are hosted. The numerical studies conducted by comparing with standardized protocols demonstrate that the adaptive MAC protocol can maintain the efficiency at around 80% with respect to increasing network population up to 100 while the MAC efficiency of standard HomePlug MAC protocol reduces down to 10% in the presence of 100 nodes. Also, the adaptive MAC protocol offers an 80% reduction in channel access delay relative to the standard HomePlug MAC protocol. 7.2 Future Work A Cross-Layer Strategy for Cyber-Physical Security of Smart Grids The demonstrated success of the proposed controllers motivates us to develop a complete system that may be implemented to future s smart grids. Smart grids are cyber-physical systems that pose a high interdependency between incorporated technologies and physical components. In order to enhance the resiliency and security of the electrical grids truly, neither control systems nor communication systems are adequate by itself. Therefore, a cross-layer strategy is required to enable interaction between layers to enhance the resiliency and security while optimizing their actions. A cross-layer framework has been envisioned as illustrated in Figure 7-1 to enhance the resiliency and cybersecurity of smart grids. The proposed framework basically consist of a physical layer where power flows and a cyber layer where information flows. In order to control the physical system, PMU sensors are deployed to monitor the system. The performance of the control systems depends on reliable feedback data, thus cyber layer must guarantee real-time and reliable data exchange. In the proposed 115

116 Figure 7-1. Cross-layer cyber-physical security framework for smart grid. framework, communication layer is defined based on Software Defined Network (SDN) and embedded machine learning techniques. The SDN is an emerging technology that adds flexibility to the networking systems and can be tailored to the smart grid applications easily. The objective of using the SDN is to redefine the PMU communication network by enabling communication between PMUs, unlike the traditional approach that allows only communication between PMU and data concentrator. Losing a PMU may lead to malfunctioning or failure of control systems. Thus, enabling communication between PMUs can help to reduce data loss by routing the PMU data throughout other PMUs when a communication link is down. By using the ability of SDN controller to monitor the network status, contingency in PMU networks can be detected before it causes a disturbance. In addition, the SDN can be boosted by utilizing machine learning techniques for detecting abnormal activities such as cyber-attack. By monitoring data links and using the historical data, anomalies can be detected by the machine learning function. If an anomaly is detected, it may be either corrected or the controller can be notified before facing the anomalies. 116