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1 Chapter 1Figure 1.1 Structure of the book.

2 Chapter 2Figure 2.1 Examples of divisive opinions in a democratic society. (a) 2016 UK ...Figure 2.2 The sinusoid‐locked loop (SLL) that explains the inherent synchroni...Figure 2.3 Approximate electricity consumption in the US.Figure 2.4 A two‐port virtual synchronous machine (VSM).Figure 2.5 SYNDEM grid architecture based on the synchronization mechanism of ...Figure 2.6 A SYNDEM home grid.Figure 2.7 A SYNDEM neighbourhood grid.Figure 2.8 A SYNDEM community grid.Figure 2.9 A SYNDEM district grid.Figure 2.10 A SYNDEM regional grid.Figure 2.11 The iceberg of power system challenges and solutions.Figure 2.12 The frequency regulation capability of a VSM connected the UK publ...

3 Chapter 3Figure 3.1 Illustrations of the imaginary operator and the ghost operator. (a)...Figure 3.2 The system pair that consists of the original system and its ghost....Figure 3.3 Illustration of the ghost power theory.

4 Chapter 4Figure 4.1 Structure of an idealized three‐phase round‐rotor synchronous gener...Figure 4.2 The power part of a synchronverter is a basic inverter.Figure 4.3 The electronic part of a synchronverter without control.Figure 4.4 The electronic part of a synchronverter with the function of freque...Figure 4.5 Operation of a synchronverter under different grid frequencies (lef...Figure 4.6 Experimental setup with two synchronverters. (a) System structure. ...Figure 4.7 Experimental results in the set mode: output currents with 2.25 kW ...Figure 4.8 Experimental results in the set mode: output currents (left column)...Figure 4.9 Experimental results in the droop mode: primary frequency response.Figure 4.10 Experimental results: the currents of the grid, VSG, and VSG2 unde...Figure 4.11 Real power and reactive power during the change in the operati...Figure 4.12 Transient responses of the synchronverter. (a) Transfer from grid‐...

5 Chapter 5Figure 5.1 Structure of an idealized three‐phase round‐rotor synchronous motor...Figure 5.2 The model of a synchronous motor.Figure 5.3 PWM rectifier treated as a virtual synchronous motor.Figure 5.4 Directly controlling the power of a rectifier.Figure 5.5 Controlling the DC‐bus voltage of a rectifier.Figure 5.6 Simulation results when controlling the power. (a) Grid and interna...Figure 5.7 Simulation results when controlling the DC‐bus voltage. (a) Grid an...Figure 5.8 Experimental results when controlling the power. (a) Grid and inter...Figure 5.9 Experimental results when controlling the DC‐bus voltage. (a) Grid ...

6 Chapter 6Figure 6.1 Integration of a PMSG wind turbine into the grid through back‐to‐ba...Figure 6.2 Controller for the RSC.Figure 6.3 Controller for the GSC.Figure 6.4 Dynamic response of the GSC. (a) Full simulation process. (b) Volta...Figure 6.5 Dynamic response of the RSC. (a) Full simulation process. (b) Volta...Figure 6.6 Real‐time simulation results with a grid fault appearing at s for...

7 Chapter 7Figure 7.1 Conventional (DC) Ward Leonard drive system.Figure 7.2 AC Ward Leonard drive system. (a) Natural implementation. (b) Virtu...Figure 7.3 Mathematical model of a synchronous generator.Figure 7.4 Control structure for an AC WLDS with a speed sensor.Figure 7.5 Control structure for an AC WLDS without a speed sensor.Figure 7.6 An experimental AC drive.Figure 7.7 Reversal from a high speed without a load. (a) Speed. (b) Torque of...Figure 7.8 Reversal from a high speed with a load. (a) Speed. (b) Torque of th...Figure 7.9 Reversal from a low speed without a load. (a) Speed. (b) Torque of ...Figure 7.10 Reversal from a low speed with a load. (a) Speed. (b) Torque of th...Figure 7.11 Reversal at an extremely low speed without a load. (a) Speed. (b) ...Figure 7.12 Reversal from a high speed without a load (without a speed sensor)...Figure 7.13 Reversal from a high speed with a load (without a speed sensor). (...

8 Chapter 8Figure 8.1 Typical control structures for a grid‐connected inverter. (a) When ...Figure 8.2 A compact controller that integrates synchronization and voltage/fr...Figure 8.3 The per‐phase model of an SG connected to an infinite bus.Figure 8.4 The controller for a self‐synchronized synchronverter.Figure 8.5 Simulation results: under normal operation. (a) Frequencies and Figure 8.6 Simulation results: connection to the grid. (a) and . (b) .Figure 8.7 Comparison of the frequency responses of the self‐synchronized sync...Figure 8.8 Dynamic performance when the grid frequency increased by 0.1 Hz at Figure 8.9 Simulation results under grid faults: when the frequency dropped by...Figure 8.10 Experimental results: when the grid frequency was lower (left colu...Figure 8.11 Experimental results of the original synchronverter: when the grid...Figure 8.12 Voltages around the connection time: when the grid frequency was l...

9 Chapter 9Figure 9.1 Controlling the rectifier DC‐bus voltage without a dedicated synchr...Figure 9.2 Controlling the rectifier power without a dedicated synchronization...Figure 9.3 Simulation results when controlling the DC bus voltage. (a) Frequen...Figure 9.4 Grid voltage and control signal. (a) Uncontrolled mode. (b) PWM‐con...Figure 9.5 Grid voltage and input current. (a) Uncontrolled mode. (b) When =0...Figure 9.6 Simulation results when controlling the real power. (a) Frequencies...Figure 9.7 Experiment results: controlling the DC‐bus voltage. (a) Frequencies...Figure 9.8 Experiment results: controlling the power. (a) Grid and internal fr...

10 Chapter 10Figure 10.1 Typical configuration of a turbine‐driven DFIG connected to the gr...Figure 10.2 A model of an ancient Chinese south‐pointing chariot (WIKIpedia 20...Figure 10.3 A differential gear that illustrates the mechanics of a DFIG, wher...Figure 10.4 The electromechanical model of a DFIG connected to the grid.Figure 10.5 Controller to operate the GSC as a GS‐VSM.Figure 10.6 Controller to operate the RSC as a RS‐VSG.Figure 10.7 Connection of the GS‐VSM to the grid.Figure 10.8 Synchronization and connection of the RS‐VSG to the grid.Figure 10.9 Operation of the DFIG‐VSG.Figure 10.10 Experimental results of the DFIG‐VSG during synchronization proce...Figure 10.11 Experimental results during the normal operation of the DFIG‐VSG.

11 Chapter 11Figure 11.1 Three typical earthing networks in low‐voltage systems.Figure 11.2 Generic equivalent circuit for analyzing leakage currents.Figure 11.3 Equivalent circuit for analyzing leakage current of a grid‐tied co...Figure 11.4 A conventional half‐bridge inverter. (a) Topology. (b) Average cir...Figure 11.5 A transformerless PV inverter. (a) Topology. (b) Average circuit m...Figure 11.6 Controller for the neutral leg.Figure 11.7 Controller for the inverter leg.Figure 11.8 Real‐time simulation results of the transformerless PV inverter in...

12 Chapter 12Figure 12.1 STATCOM connected to a power system. (a) Sketch of the connection....Figure 12.2 A typical two‐axis control strategy for a PWM based STATCOM using ...Figure 12.3 A synchronverter based STATCOM controller.Figure 12.4 Single‐line diagram of the power system used in the simulations.Figure 12.5 Detailed model of the STATCOM used in the simulations.Figure 12.6 Connecting the STATCOM to the grid. (a) . (b) . (c) Real power. ...Figure 12.7 Simulation results of the STATCOM operated in different modes. (a)...Figure 12.8 Transition from inductive to capacitive reactive power when the mo...Figure 12.9 Simulation results of the STATCOM operated with a changing grid fr...Figure 12.10 Simulation results of the STATCOM operated with a changing grid v...Figure 12.11 Simulation results with a variable system strength. (a) . (b) ....

13 Chapter 13Figure 13.1 Per‐phase diagram with the Kron‐reduced network approach.Figure 13.2 Phase portraits of the controller. (a) The frequency dynamics. (b)...Figure 13.3 The controller to achieve bounded frequency and voltage.Figure 13.4 surface (upper) and surface (lower) with respect to and .Figure 13.5 Illustration of the areas characterized by lines and lines.Figure 13.6 Illustration of the area where a unique equilibrium exists. (a) Wh...Figure 13.7 Real‐time simulation results comparing the original (SV) with the ...Figure 13.8 Phase portraits of the controller states in real‐time simulations....

14 Chapter 14Figure 14.1 The controller of the original synchronverter.Figure 14.2 Active power regulation in a conventional synchronverter after dec...Figure 14.3 Properties of the active power loop of a conventional synchronvert...Figure 14.4 VSM with virtual inertia and virtual damping.Figure 14.5 The small‐signal model of the active‐power loop with a virtual ine...Figure 14.6 Implementations of a virtual damper. (a) Through impedance scaling...Figure 14.7 A VSM in a microgrid connected to a stiff grid.Figure 14.8 Normalized frequency response of a VSM with reconfigurable inertia...Figure 14.9 Effect of the virtual damping ( s).Figure 14.10 A microgrid with two VSMs.Figure 14.11 Two VSMs operated in parallel with s.Figure 14.12 Two VSMs operated in parallel with s and s.Figure 14.13 Simulation results under a ground fault with s. (a) Normalized ...Figure 14.14 Experimental results with reconfigurable inertia and damping. (a)...Figure 14.15 Experimental results from the original synchronverter for compari...Figure 14.16 Experimental results showing the effect of the virtual damping wi...Figure 14.17 Experimental results when two VSMs with the same inertia time con...Figure 14.18 Experimental results when two VSMs with the same inertia time con...Figure 14.19 Experimental results when two VSMs with different inertia time co...Figure 14.20 Experimental results when the two VSMs operated as the original S...

15 Chapter 15Figure 15.1 Block diagrams of a conventional PLL. (a) Operational concept. (b)...Figure 15.2 Enhanced phase‐locked loop (EPLL) or sinusoidal tracking algorithm...Figure 15.3 Power delivery to a voltage source through an impedance.Figure 15.4 Conventional droop control scheme for an inductive impedance. (a) ...Figure 15.5 Conventional droop control strategies. (a) For resistive impedance...Figure 15.6 Linking the droop controller in Figure 15.4(b) and the (inductive)...Figure 15.7 Droop control strategies in the form of a phase‐locked loop. (a) W...Figure 15.8 The conventional droop controller shown in Figure 15.4(a) after ad...Figure 15.9 The synchronization capability of the droop controller shown in Fi...Figure 15.10 Connection of the droop controlled inverter to the grid.Figure 15.11 Regulation of the grid frequency and voltage in the droop mode.Figure 15.12 Robustness of synchronization against DC‐bus voltage changes. (a)...Figure 15.13 System response when the operation mode was changed.

16 Chapter 16Figure 16.1 A single‐phase inverter. (a) Used for physical implementation. (...Figure 16.2 Controller to achieve a resistive output impedance.Figure 16.3 Controller to achieve a capacitive output impedance.Figure 16.4 Typical output impedances of L‐, R‐, and C‐inverters.Figure 16.5 Two R‐inverters operated in parallel.Figure 16.6 Conventional droop control scheme for R‐inverters.Figure 16.7 Experimental results: two R‐inverters in parallel with conventio...Figure 16.8 Robust droop controller for R‐inverters.Figure 16.9 Experimental results for the case with a linear load when invert...Figure 16.10 Experimental results for the case with a linear load when inver...Figure 16.11 Experimental results for the case with the same per‐unit impeda...Figure 16.12 Experimental results with a nonlinear load: with the robust dro...Figure 16.13 Robust droop controller for C‐inverters.Figure 16.14 Experimental results of C‐inverters (left column) and R‐inverte...Figure 16.15 Experimental results of C‐inverters (left column) and R‐inverte...Figure 16.16 Robust droop controller for L‐inverters.Figure 16.17 Experimental results of L‐inverters with a linear load: with th...Figure 16.18 Experimental results of L‐inverters with a nonlinear load: with...

17 Chapter 17Figure 17.1 The model of a single‐phase inverter.Figure 17.2 The closed‐loop system consisting of the power flow model of an ...Figure 17.3 Interpretation of transformation matrices and . (a) . (b) ....Figure 17.4 Interpretation of the universal transformation matrix .Figure 17.5 Universal droop controller.Figure 17.6 Rel‐time simulation results of three inverters with different ty...Figure 17.7 Experimental set‐up consisting of an L‐inverter, an R‐inverter, ...Figure 17.8 Experimental results with the universal droop controller. (a) ...

18 Chapter 18Figure 18.1 The self‐synchronized universal droop controller.Figure 18.2 Experimental results of self‐synchronization with the R‐inverter...Figure 18.3 Experimental results when connecting the R‐inverter to the grid....Figure 18.4 Experimental results with the R‐inverter: performance during the...Figure 18.5 Experimental results with the R‐inverter: regulation of system f...Figure 18.6 Experimental results with the R‐inverter: change in the DC‐bus v...Figure 18.7 Experimental results of self‐synchronization with the L‐inverter...Figure 18.8 Experimental results with the L‐inverter: connection to the grid...Figure 18.9 Experimental results with the L‐inverter: performance during the...Figure 18.10 Experimental results with the L‐inverter: regulation of system ...Figure 18.11 Experimental results with the L‐inverter: change in the DC‐bus ...Figure 18.12 Experimental results of self‐synchronization with the L‐inverte...Figure 18.13 Experimental results from the L‐inverter with the robust droop ...Figure 18.14 Experimental results from the L‐inverter with the robust droop ...Figure 18.15 Experimental results from the L‐inverter with the robust droop ...Figure 18.16 Experimental results with the L‐inverter under robust droop con...Figure 18.17 A microgrid including three inverters connected to a weak grid....Figure 18.18 Real‐time simulation results from the microgrid. (a) Real power...

19 Chapter 19Figure 19.1 A general three‐port converter with an AC port, a DC port, and a...Figure 19.2 DC‐bus voltage controller to generate the real power reference....Figure 19.3 The universal droop controller when the positive direction of th...Figure 19.4 Finite state machine of the droop‐controlled rectifier.Figure 19.5 Illustration of the operation of the droop‐controlled rectifier....Figure 19.6 The ‐converter.Figure 19.7 Control structure for the droop‐controlled rectifier. (a) Contro...Figure 19.8 Experimental results in the GS mode. (a) Real power , grid volt...Figure 19.9 Experimental results in the NS‐H mode. (a) Real power , grid vo...Figure 19.10 Experimental results in the NS‐L mode. (a) Real power , grid v...Figure 19.11 Transient response when the system starts up. (a) Real power ,...Figure 19.12 Transient response when a load is connected to the system. (a) ...Figure 19.13 Experimental results showing the capacity potential of the rect...Figure 19.14 Controller for the conversion leg.Figure 19.15 Comparative experimental results with a conventional controller...

20 Chapter 20Figure 20.1 A grid‐connected single‐phase inverter with an filter.Figure 20.2 The equivalent circuit diagram of the controller.Figure 20.3 The overall control system.Figure 20.4 Controller states. (a) and . (b) and .Figure 20.5 Implementation of the current‐limiting universal droop controlle...Figure 20.6 Operation with a normal grid. (a) Real and reactive power, RMS c...Figure 20.7 Transient response of the controller states with a normal grid. ...Figure 20.8 Operation under a grid voltage sag for 9 s. (a) Real and react...Figure 20.9 Controller states under the grid voltage sag for 9 s. (a) an...Figure 20.10 Operation under a grid voltage sag for 9 s. (a) Real and reac...Figure 20.11 Controller states under the grid voltage sag for 9 s. (a) a...

21 Chapter 21Figure 21.1 Two systems with disturbances interconnected through .Figure 21.2 Two systems with disturbances and external ports interconnected ...Figure 21.3 Three‐phase grid‐connected converter with a local load.Figure 21.4 The controller for a cybersync machine with to be supplied as Figure 21.5 The mathematical structure of the system constructed to facilita...Figure 21.6 Blocks and implemented with the integral controller. (a) . ...Figure 21.7 A cybersync machine equipped with regulation and self‐synchroniz...Figure 21.8 Simulation results from a cybersync machine, where the detailed ...Figure 21.9 Experimental results from a cybersync machine. (a) Around synchr...

22 Chapter 22Figure 22.1 A photo of the SYNDEM smart grid research and educational kit.Figure 22.2 SYNDEM smart grid research and educational kit: main power circu...Figure 22.3 Implementation of DC–DC converters. (a) Buck (step‐down) convert...Figure 22.4 Implementation of uncontrolled rectifiers. (a) A single‐phase ha...Figure 22.5 Implementation of PWM‐controlled rectifiers. (a) A single‐phase ...Figure 22.6 Implementation of the ‐converter.Figure 22.7 Implementation of inverters. (a) A single‐phase inverter. (b) A ...Figure 22.8 Implementation of a DC–DC–AC converter.Figure 22.9 Implementation of a single‐phase back‐to‐back converter.Figure 22.10 Implementation of a three‐phase back‐to‐back converter.Figure 22.11 Illustrative structure of the single‐node system.Figure 22.12 Circuit of the single‐node system. (a) Wiring illustration with...Figure 22.13 Experimental results from the single‐node system equipped with ...Figure 22.14 Texas Tech SYNDEM microgrid built up with eight SYNDEM smart gr...

23 Chapter 23Figure 23.1 Illinois Tech SYNDEM smart grid testbed. (a) System structure. (...Figure 23.2 Topology of a ‐converter.Figure 23.3 Topology of a Beijing converter.Figure 23.5 Back‐to‐back converter formed by a ‐converter and a conversion ...Figure 23.4 Back‐to‐back converter formed by a Beijing converter and a conve...Figure 23.6 Operation of the energy bridge to black start the SYNDEM grid. (...Figure 23.7 Integration of the solar power node. (a) Responses of the solar ...Figure 23.8 Integration of the wind power node. (a) Responses of the wind po...Figure 23.9 Performance of the wind power node when the wind speed changes...Figure 23.10 Integration of the DC‐load node. (a) Responses of the DC‐load V...Figure 23.11 Integration of the AC‐load node. (a) Responses of the AC‐load V...Figure 23.12 Operation of the whole testbed. (a) Responses of energy bridge ...

24 Chapter 24Figure 24.1 The home field at the Texas Tech University Center at Junction, ...Figure 24.2 The home grid. (a) One‐line diagram. (b) Its backbone: five Synd...Figure 24.3 Black‐start and grid‐forming capabilities. (a) Whole process. (b...Figure 24.4 From islanded to grid‐tied operation. (a) Whole process. (b) Zoo...Figure 24.5 Seamless mode change when the public grid is lost and then recov...Figure 24.6 Power sharing and regulation of the voltage and frequency of the...Figure 24.7 The nonlinearity of the transformer. (a) With one inverter. (b) ...Figure 24.8 The nonlinearity of household loads.Figure 24.9 The large inrush current of the air‐conditioning unit.

25 Chapter 25Figure 25.1 Panhandle wind power system. (a) Geographical illustration. (b) ...Figure 25.2 Connection of a wind power generation system to the grid.Figure 25.3 VSM controller for each wind turbine. (a) Robust droop control f...Figure 25.4 Standard DQ controller for the GSC.Figure 25.5 Simulated panhandle wind farms.Figure 25.6 Simulation results from a single unit. (a) Dynamic response of t...Figure 25.7 The voltage, frequency, active power, and reactive power at 345 ...Figure 25.8 Panhandle wind power system: the voltage, frequency, active powe...

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