Frequency and Voltage Control of a Grid of Microgrids by Baheej Alghamdi A thesis presented to the University of Waterloo in fulfillment of the thesis requirement for the degree of Doctor of Philosophy in Electrical and Computer Engineering Waterloo, Ontario, Canada, 2021 © Baheej Alghamdi 2021 Examining Committee Membership The following served on the Examining Committee for this thesis. The decision of the Examining Committee is by majority vote. Supervisor: Claudio Ca~nizares Professor, Department of Electrical and Computer Engineering, University of Waterloo Internal Member: Kankar Bhattacharya Professor, Department of Electrical and Computer Engineering, University of Waterloo Internal Member: John Simpson Adjunct Assistant Professor, Department of Electrical and Computer Engineering, University of Waterloo Internal-External Member: Roydon Fraser Professor, Department of Mechanical and Mechatronics Engineering, University of Waterloo External Examiner: Amir Yazdani Professor, Department of Electrical, Computer, and Biomedical Engineering, Ryerson University ii Author's Declaration I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. iii Abstract The rapid proliferation of Distributed Energy Resources (DERs) in recent years has resulted in significant technical challenges for power system operators and planners, mainly due to the particular characteristics of some of these systems that are interfaced with converters that alter the dynamic behavior of typically power systems. To accommodate the increasing penetration of DERs in power systems, microgrids have been formed to facilitate their integration. The operation of these microgrids could be further enhanced by interconnecting them to satisfy the overall system demand, and improve their stability if suitable control schemes are implemented. The control of microgrids has been extensively studied; however, coordinated operation, dynamics, and control of a grid that includes interconnected microgrids have not been sufficiently addressed in the literature, and thus this is the focus of this thesis. In the first stage of the thesis, a new microgrid interface based on Virtual Synchronous Generators (VSGs) is proposed to control the power exchange of interconnected ac and dc microgrids, and provide frequency support, voltage regulation, and virtual inertia for individual microgrids and the host grid as required, to improve both frequency and voltage dynamics for the overall system. Thus, a hierarchical distributed control technique is proposed, where the primary control of interfacing VSGs provides adaptive inertia for the ac systems, while a secondary distributed control of the system regulates the frequency and the voltages of the host grid and the interconnected microgrids, based on a consensus technique with limited information about the overall system. The proposed controller shares the total system load among the grid and microgrids, while minimizing the overall frequency and voltage deviations in all interconnected systems. The proposed interface and the controller are implemented, tested, and validated in detailed simulations for a grid-of-microgrids system. In the second stage of the thesis, an adaptive active power droop controller and voltage setpoint control in isolated microgrids for optimal frequency response and stability after disturbances is first proposed and presented, and then applied to the coordinated control of interconnected microgrids. The control scheme involves an optimal and model predictive control approach, which continuously adjusts the active power droop gains and the voltage setpoints of Distributed Energy Resources (DERs) to maintain the frequency of the system within acceptable limits, and enhance the primary frequency response of the system, while taking into account the active power sensitivity of the microgrid loads to the system's operating voltage. The proposed approach is also implemented, tested, validated, and compared via detailed simulations in a microgrid benchmark system and the developed grid-of-microgrids test system. iv The results demonstrate that the proposed VSG controlled interfaces limit severe fre- quency deviations during disturbances, and allow proper power sharing among the mi- crogrids without causing significant power transients for the ac/dc systems, compared to existing techniques. Furthermore, the proposed secondary distributed and centralized fre- quency and voltage controllers maintain the power balance of the interconnected systems and regulate the microgrids' frequencies and dc voltages to nominal values, compared to conventional frequency controllers; however, the distributed control approach shows bet- ter overall frequency and dc-voltage dynamics and regulation than the centralized control approach. v Acknowledgements I would like to express my sincere gratitude to Professor Claudio A. Ca~nizaresfor his guidance, patience, and support throughout my PhD studies. It has been a great honor for me to have completed my research under his supervision, where I have learned many valuable skills that will help me in my academic career. I would like to acknowledge the following members of my PhD thesis Examination com- mittee for their valuable comments and input: Professor Kankar Bhattacharya from the Electrical and Computer Engineering Department at the University of Waterloo; Profes- sor Roydon Fraser from the Mechanical and Mechatronics Engineering Department at the University of Waterloo; Professor John Simpson from the Electrical and Computer Engi- neering Department at the University of Waterloo; and Professor Amir Yazdani from the Department of Electrical, Computer, and Biomedical Engineering at Ryerson University. I wish to acknowledge King Abdulaziz University, the Saudi Government, and NSERC for fully funding my PhD studies at the University of Waterloo. vi Table of Contents List of Tables xi List of Figures xii Nomenclature xv List of Acronyms xxi 1 Introduction1 1.1 Research Motivation..............................1 1.2 Literature Review................................3 1.2.1 Gird of MGs...............................3 1.2.1.1 Energy Management.....................3 1.2.1.2 Frequency and DC-Voltage Control.............4 1.2.1.3 Voltage Control........................8 1.2.1.4 Stability............................9 1.2.2 Discussion................................ 10 1.3 Research Objectives............................... 11 1.4 Outline of the Proposal............................. 12 vii 2 Background Review 14 2.1 MG Overview.................................. 14 2.1.1 MG Definition and Components.................... 14 2.1.2 Modeling................................ 14 2.1.2.1 Synchronous Generators (Diesel Units)........... 14 2.1.2.2 BESS............................. 15 2.1.2.3 Wind Generator Model................... 19 2.1.2.4 Load Model.......................... 19 2.2 MG Control................................... 19 2.2.1 Frequency Control........................... 20 2.2.1.1 Decentralized Primary Frequency Control......... 20 2.2.1.2 Centralized Frequency Control............... 21 2.2.2 Voltage-Frequency Control....................... 22 2.2.3 Voltage Control............................. 23 2.2.3.1 Decentralized primary Voltage Control........... 23 2.2.3.2 Centralized Voltage Control................. 23 2.2.4 DC MGs................................. 24 2.2.4.1 DC-DC Converters...................... 25 2.2.4.2 DC Loads........................... 25 2.3 MMG System.................................. 26 2.3.1 Architectures and Layouts....................... 26 2.3.2 Centralized Control........................... 27 2.3.3 Distributed Control........................... 28 2.4 Virtual Synchronous Generators........................ 29 2.4.1 VSG Governor and AVR model.................... 30 2.4.2 Virtual Synchronous Impedance and Voltage Control Loops.... 31 2.4.3 Current Control Loop......................... 32 2.5 Summary.................................... 32 viii 3 Distributed Control of Interconnected MGs 33 3.1 Distributed Droop-Free DC Voltage Controller............... 34 3.1.1 DC MG Configuration......................... 34 3.1.2 Communication Graph Algebraic Theory............... 35 3.1.3 Proposed Distributed Controller.................... 36 3.1.4 Case Studies and Results........................ 38 3.1.4.1 Validation and Comparison................. 39 3.1.4.2 Stability Analysis....................... 41 3.1.4.3 Communication Link Failure and Islanding Mode..... 43 3.1.4.4 Communication Delay.................... 44 3.2 Distributed Control of MMG.......................... 45 3.2.1 Proposed AC Micorgrid Interface................... 45 3.2.1.1 B2B VSG Interface...................... 46 3.2.1.1.1 DC-Link Voltage Regulation............ 46 3.2.1.1.2 VFC......................... 48 3.2.1.1.3 Adaptive Inertia.................. 49 3.2.1.2 DC MG Interface....................... 51 3.2.2 Proposed Distributed Control System................. 53 3.2.2.1 Adaptive Distributed Control................ 54 3.2.2.2 Rule Based Controller.................... 55 3.2.3 Case Studies and Results........................ 56 3.3 Summary.................................... 64 4 Frequency Regulation Through Optimal Droop Gain and Voltage Con- trol 65 4.1 Droop and Voltage Control for Optimal Frequency Regulation....... 66 4.1.1 Optimization Model.........................