Robust Nonlinear Control of Power Systems with Voltage Source Converters

Abstract

This thesis focuses on design of a robust nonlinear control for power systems with voltage source converter (VSC) to improve power quality, reliability and efficiency. VSCs are widely used in smart grid, flexible AC transmission systems (FACTS), high-voltage direct current (HVDC) systems, and renewable energy sources (wind, photovoltaic, and fuel cells, etc.) due to its higher efficiency, lower noise and fatigue. At first, an overview of the mathematical models of the VSCs' applications in power systems is presented. Static synchronous compensator (STATCOM) system based VSC is modeled in synchronous rotating frame. In order to control instantaneous active and reactive powers directly without any inner-loop current regulators, a power model of a grid-connected voltage source inverter (VSI) is described. A type of VSC-HVDC called back-to-back static synchronous compensator (BTB STATCOM) system with asymmetrically structured converters is modeled in state-space. Finally, a mathematical model for a type of symmetrical structure back-to-back VSCs such as permanent-magnet synchronous generator (PMSG) wind turbine (WT) is represented. As a typical shunt FACTS device, STATCOM is installed at the point of common coupling (PCC) to improve the voltage quality of PCC through absorbing or injecting the certain reactive power. Three nonlinear control methods for the STATCOM system are presented to improve transient performance. First one is a passivity based control, which is designed based on a Lyapunov function by considering dissipation. An additional nonlinear damping term is designed to improve transient performance. It is guaranteed that the equilibrium point of the closed-loop system is locally exponentially stable in the operating range. The performance of the proposed method is validated via a 100 Mvar STATCOM system connected to the 345-kV grid system in SimPowerSystems, MATLAB/Siumlink. The second one is a dynamic extension algorithm (DEA) method for the STATCOM system. In order to conveniently design a reference output, the dynamics of the STATCOM system is put into the form of port-controlled Hamiltonian (PCH) to apply a tracking controller. The dynamic extended system becomes an input affine system so that the tracking controller is obtained in IOL framework. The tracking control law is generated considering the stability and performance of the input output linearized dynamics. Simulation results show that the proposed method improves the transient performance of the system over the previous results even in the lightly damped operating range. The last one is sliding mode control (SMC). Taking the reactive current as the output, the STATCOM system is represented in the normal form through the DEA method to apply SMC for regulating the tracking error of reactive current. Stability of internal dynamics is also shown by using a composite Lyapunov equation. Locally asymptotic stability of the tracking error is proved. The proposed method reduces the ripple of active current and DC voltage without sacrificing reactive current. Simulation results are illustrated to show the effectiveness of the proposed method. For a grid-connected VSI system, a grid voltage modulated direct power control (GVM-DPC) strategy is proposed to directly control the instantaneous active and reactive powers. The GVM-DPC method represents the system in $d$-$q$ frame without using a phase-lock loop. Another advantage is that the GVM method converts the grid-connected VSI system into a linear time-invariant system. The GVM-DPC is designed to obtain two separately second-order systems for not only the convergence rate of the instantaneous active and reactive powers but also the steady-state performance. In addition, the closed-loop system is exponentially stable in the whole operating range. The proposed method is validated by using MATLAB/Simulink and PLECS blockset. The simulation results show that the proposed method has not only a good tracking performance in both active and reactive powers but also a lower current total harmonic distortion than that of the sliding mode control DPC method. Finally, the proposed method is validated by using hardware-in-the-loop (HIL) system with a digital signal processor. The experimental results are similar to simulation results. Moreover, the proposed method provides less total harmonic distortions and more robustness to the line impedance variation and grid voltage sag. For BTB STATCOM system, which employs a pulse width modulation (PWM) technology for a rectifier station and a multipulse technology for an inverter station, a PBC using PCH form is proposed to improve robustness and simplify controller design. The PBC, which consisted of the desired control input and a new control input considering the performance of all states, is designed based on error dynamics. By using the Lyapunov theorem. the control input guarantees the exponential stability of equilibrium point of the closed-loop system. The proposed method is validated through a simulation and its effectiveness is compared with an IOL controller. Simulation results show that PBC enhances the performances of the states of the inverter and DC voltage. For PMSG WT system, a nonlinear feedback controller based on a PCH system is presented to enhance the low voltage ride through (LVRT) capability. For the simplification, this thesis focuses on the nonlinear control law of the grid side converter (GSC) that is directly connected to the grid and affected during network disturbances. The proposed controller is designed through the analysis of PMSG GSC model from the passivity viewpoint in order to regulate the reference of the DC voltage and track the reference of the reactive current. The exponential stability of the equilibrium point of the error dynamics at the origin is guaranteed by using Lyapunov theory. Finally, the proposed method is validated through simulation. The simulation results show that the performance has smaller overshoot and faster convergence when the proposed method is used than when the conventional method is used. | 본 학위 논문에서는 전력의 품질, 신뢰도와 효율을 향상하기 위하여 전압형 컨버터 기반인 전력시스템에 대한 비선형 강인 제어기를 제안하였다. VSC는 높은 효율성, 낮은 소음과 피로도의 장점으로 스마트 그리드, 유연송전시스템, 초고압직류송전과 신재생에너지(풍력, 태양광, 연료전지 등) 다양한 분야에서 널리 사용하고 있다. 우선 본 학위 논문에서는 각종 VSC를 적용한 전력 시스템의 수학적 모델을 소개합니다. 첫전쨰 순서는 VSC 기반인 무효전력보상기(STATCOM)을 동기 좌표계에서 모델링한다. 순간 유$\cdot$무효 전력을 직접적으로 제어하기 위하여 계통 연계형 전압형 인버터의 모델을 정지 좌표계($\alpha$-$\beta$ frame)에서 표현한다. 초고압직류송전 종료의 하나인 백투백 무효전력보상기(BTB STATCOM)은 비대칭의 컨버터 구조를 갖고 있으면 이 논문에서는 그의 상태 공간 모델을 보여 주엇다. 마지막으로는 대칭구조인 백투백 VSC 즉 영구자석 풍력발전기의 수학적 모델을 보여주었다. STATCOM은 전형적인 병렬연결 FACTS 장치로서 접속점에 설치하여 뮤효전력을 흡수 생한하는 방식으로 접속점의 전압 품질을 향상시키는 역할을 한다. STATCOM의 과도성능을 향상하기 위하여 세가지 비선형 제어알고리즘을 소개한다. 첫번째로는 수동성 기반 제어기, 이는 시스템의 소실을 고려하여 Lyapunov 함수 기반에서 설계 된것이다. 과도성능을 향상하기 위하여 비선형 댐핑을 추가적으로 설계한다. 폐 루우프 시스템의 평형점이 운전구간내에서 지수적 안정화(exponentially stable) 된다는것을 확인 할수 있다. 제안한 제어기는 SimPowerSystems, MATLAB/Siumlin을 이용하여 345-kV 전력 시스템에 연결된 100Mvar STATCOM에서 검증 하였다. 두번째로는 동력학 화장 방법을 STATCOM에 고안 하였다. Tracking 제어기를 설게하기 위하여 STATCOM의 동력학을 확장하여 PCH 시스템 유형에 대입한다. 확장된 동력학 시스템은 input affine 시스템으로 변화하고 tracking 제어기는 입출력 선형화 프레임워크에서 얻어진다. 설계 된 tracking 제어기법은 안정도와 입출력 선형화의 성능을 보장한다. 시뮬레이션 결과에서 lightly damped 운전구역에서 설계된 제어기법은 보다 낳은 성능을 보여준다. 마지막으로는 SMC이다. DEA 방법을 이용하여 STATCOM 시스템을 normal form으로 표시하고 무효 전류를 출력으로 하여 tracking error가 조절하는 SMC을 설계 한다. Internal dynamics의 안정도는 composite Lyapunov 수식을 이용하여 보여 주었고 tracking error의 locally asymptotic 안정도를 증명 하였다. 설계된 제어기법은 무효전류의 성능을 보장하면서 유효전류와 직류 접압의 리플을 줄이는 것을 시뮬레이션 결과에서 확인 할수 있었다. 계통연계형 전압형 인버터에 대하여 순간 유$\cdot$무효 전력을 직접적으로 에어하기 위하여 GVM-DPC 기법을 고안하였다. GVM-DPC 방법은 위상동기루프를 이용하지 않고 시스템을 동기 좌표계에서 표현하였다. 또 다른 장점은 GVM-DPC 방법은 계통연계형 VSI 시스템을 선형 시불변 시스템으로 표현하였다. 순간 유$\cdot$무효 전력의 수렴도과 정상상태의 성능을 모두 보장하기 위하여 GVM-DPC 방법은 2개의 분리된 2차 시스템으로 설계 되였다. 또한, 페류프 시스템이 전체 운전 영역에서 exponentially stable하다는것을 확인하였다. 설계된 제어기법은 MATLAB/Simulink과 PLECS blockset를 이용하여 검증하였다. 시뮬레인션 결과에서는 설게된 제어기법은 SMC-DPC 기법보다 유$\cdot$무효 전력의 좋은 추정성능과 적은 THD을 갖는 것을 보여주었다. 마지막으로는 HIL 시스템과 디지털 신호 처리기=을 이용하여 제언된 제어기법을 검증하였다. 실험결과는 시뮬레이션 결과와 비슷한 성향이 나타났다. 또한, 설계된 제어기법은 line impedance 변화와 계통 전압 sag에 강인 하다는것을 보여 주었다. BTB STATCOM은 rectifier station에 PWM 기법을 사용하고 inverter station에 multipulse technology를 사용하는 시스템이다. 강인성 향상과 제어기를 간단히 설게하기 위하여 PCH form을 이용한 수동성 기반 제어기를 고안하였다. Desired 제어 입력과 모든 상태의 성능을 보장하는 새로운 입역으로 구성된 PBC는 error dynamics 기반으로 설계 되엿다. Lyapunov theorem을 이용하여 폐 루우프 시스템의 평형점이 exponential stability를 보장한다. 설계된 제어기법은 시뮬레이션을 통하여 IOL controller과 비교하며 검증하였다. 시뮬레이션 결과에서는 PBC가 인버터와 직류 전압의 성능을 향상하는것을 확인하핬다. PMSG WT 시스템에 LVRT 능력을 향상하기 위하여 PCH 기반인 비선형 피드백 제어기를 설게하였다. 계통 disturbances에 영향 받는 계통과 직접 연결괸 GSC에 대하여 비선형 제어기법을 설게하는것에 초점을 가졌다. 직류 전압의 regulation과 뮤효전류의 reference를 추종하기 위하여 PMSG GSC의 모델을 수동성 관전에서 제안한 제이기법을 설계하였다. Lyapunov theory을 이용하여 error dynamics의 평형점이 exponential stability를 보장한다. 설계된 제어기법은 SimPowerSystems, MATLAB/Siumlin을 이용하여 검증하였고 기존 제어기법보다 작은 오버슈트와 빠른 수렴도를 가지는것을 보여주었다.; This thesis focuses on design of a robust nonlinear control for power systems with voltage source converter (VSC) to improve power quality, reliability and efficiency. VSCs are widely used in smart grid, flexible AC transmission systems (FACTS), high-voltage direct current (HVDC) systems, and renewable energy sources (wind, photovoltaic, and fuel cells, etc.) due to its higher efficiency, lower noise and fatigue. At first, an overview of the mathematical models of the VSCs' applications in power systems is presented. Static synchronous compensator (STATCOM) system based VSC is modeled in synchronous rotating frame. In order to control instantaneous active and reactive powers directly without any inner-loop current regulators, a power model of a grid-connected voltage source inverter (VSI) is described. A type of VSC-HVDC called back-to-back static synchronous compensator (BTB STATCOM) system with asymmetrically structured converters is modeled in state-space. Finally, a mathematical model for a type of symmetrical structure back-to-back VSCs such as permanent-magnet synchronous generator (PMSG) wind turbine (WT) is represented. As a typical shunt FACTS device, STATCOM is installed at the point of common coupling (PCC) to improve the voltage quality of PCC through absorbing or injecting the certain reactive power. Three nonlinear control methods for the STATCOM system are presented to improve transient performance. First one is a passivity based control, which is designed based on a Lyapunov function by considering dissipation. An additional nonlinear damping term is designed to improve transient performance. It is guaranteed that the equilibrium point of the closed-loop system is locally exponentially stable in the operating range. The performance of the proposed method is validated via a 100 Mvar STATCOM system connected to the 345-kV grid system in SimPowerSystems, MATLAB/Siumlink. The second one is a dynamic extension algorithm (DEA) method for the STATCOM system. In order to conveniently design a reference output, the dynamics of the STATCOM system is put into the form of port-controlled Hamiltonian (PCH) to apply a tracking controller. The dynamic extended system becomes an input affine system so that the tracking controller is obtained in IOL framework. The tracking control law is generated considering the stability and performance of the input output linearized dynamics. Simulation results show that the proposed method improves the transient performance of the system over the previous results even in the lightly damped operating range. The last one is sliding mode control (SMC). Taking the reactive current as the output, the STATCOM system is represented in the normal form through the DEA method to apply SMC for regulating the tracking error of reactive current. Stability of internal dynamics is also shown by using a composite Lyapunov equation. Locally asymptotic stability of the tracking error is proved. The proposed method reduces the ripple of active current and DC voltage without sacrificing reactive current. Simulation results are illustrated to show the effectiveness of the proposed method. For a grid-connected VSI system, a grid voltage modulated direct power control (GVM-DPC) strategy is proposed to directly control the instantaneous active and reactive powers. The GVM-DPC method represents the system in $d$-$q$ frame without using a phase-lock loop. Another advantage is that the GVM method converts the grid-connected VSI system into a linear time-invariant system. The GVM-DPC is designed to obtain two separately second-order systems for not only the convergence rate of the instantaneous active and reactive powers but also the steady-state performance. In addition, the closed-loop system is exponentially stable in the whole operating range. The proposed method is validated by using MATLAB/Simulink and PLECS blockset. The simulation results show that the proposed method has not only a good tracking performance in both active and reactive powers but also a lower current total harmonic distortion than that of the sliding mode control DPC method. Finally, the proposed method is validated by using hardware-in-the-loop (HIL) system with a digital signal processor. The experimental results are similar to simulation results. Moreover, the proposed method provides less total harmonic distortions and more robustness to the line impedance variation and grid voltage sag. For BTB STATCOM system, which employs a pulse width modulation (PWM) technology for a rectifier station and a multipulse technology for an inverter station, a PBC using PCH form is proposed to improve robustness and simplify controller design. The PBC, which consisted of the desired control input and a new control input considering the performance of all states, is designed based on error dynamics. By using the Lyapunov theorem. the control input guarantees the exponential stability of equilibrium point of the closed-loop system. The proposed method is validated through a simulation and its effectiveness is compared with an IOL controller. Simulation results show that PBC enhances the performances of the states of the inverter and DC voltage. For PMSG WT system, a nonlinear feedback controller based on a PCH system is presented to enhance the low voltage ride through (LVRT) capability. For the simplification, this thesis focuses on the nonlinear control law of the grid side converter (GSC) that is directly connected to the grid and affected during network disturbances. The proposed controller is designed through the analysis of PMSG GSC model from the passivity viewpoint in order to regulate the reference of the DC voltage and track the reference of the reactive current. The exponential stability of the equilibrium point of the error dynamics at the origin is guaranteed by using Lyapunov theory. Finally, the proposed method is validated through simulation. The simulation results show that the performance has smaller overshoot and faster convergence when the proposed method is used than when the conventional method is used.