Stability Enhancement Methods of Inverters Based on Lyapunov Function, Predictive Control, and Reinforcement Learning

175 Pages·2022·8.195 MB·English

by  Xin Zhang, Jinsong He, Hao Ma, Zhixun Ma, Xiaohai Ge

Xin Zhang · Jinsong He · Hao Ma ·
Zhixun Ma · Xiaohai Ge
Stability Enhancement
Methods of Inverters
Based on Lyapunov
Function, Predictive
Control, and
Reinforcement
Learning
Stability Enhancement Methods of Inverters Based
on Lyapunov Function, Predictive Control,
and Reinforcement Learning
· · · ·
Xin Zhang Jinsong He Hao Ma Zhixun Ma
Xiaohai Ge
Stability Enhancement
Methods of Inverters Based
on Lyapunov Function,
Predictive Control,
and Reinforcement Learning
Xin Zhang Jinsong He
College of Electrical Engineering Power Dispatching and Control Center
Zhejiang University of China Southern Power Grid
Hangzhou, Zhejiang, China Guangzhou, Guangdong, China
School of Electrical and Electronic
Hao Ma
Engineering
College of Electrical Engineering
Nanyang Technological University
Zhejiang University
Singapore, Singapore
Hangzhou, Zhejiang, China
Zhixun Ma
Xiaohai Ge
National Maglev Transportation
College of Electrical Engineering
Engineering R&D Center
Zhejiang University
Tongji University
Hangzhou, Zhejiang, China
Shanghai, China
ISBN 978-981-19-7190-7 ISBN 978-981-19-7191-4 (eBook)
https://doi.org/10.1007/978-981-19-7191-4
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Preface
Power inverters become more and more important and popular in our life. For
instance, in the smart grid, the power inverters transfer the solar/wind energy to the
AC grid; in the more electric aircraft (MEA), the power inverters can connect the DC
bus and AC bus in its hybrid AC/DC microgrid; in the shipboard power system (SPS),
the power inverters can transfer the DC bus energy to the AC loads, etc. However, the
power inverters still have stability problems, including the instability of the power
inverter itself, as well as the instability problem due to the interaction between the
inverters and the other power electronic units (i.e., weak grid, the electromagnetic
interference (EMI) filter, upstream/downstream power converters). So far, most of
the stability analyses and solutions are focused on small-signal stability technologies.
Unfortunately, in practice, most of the real instability issues in the power inverters
system are large-signal stability problem. Note that large-signal stability problems
typically cause severer damage to electrical equipment compared to the small-signal
counterpart.
Motivated by the above discussion, this book aims to propose a family of advanced
control strategies to improve the larger-signal stability of the power inverters system-
atically. This book first reviews the classifications of existing power inverters and
their applications. Then, this book introduces a family of our proposed control strate-
gies of power inverters for the applications of MEA, smart grid, SPS, etc. Also, the
large-signal stability issues are analyzed within the scope of stand-alone inverters,
grid-connected inverters, and these inverters interfaced with input EMI filters. From
this book, different large-signal stability problems of the power inverters may find
their corresponding control-based solutions.
This book offers comprehensive self-contained knowledge on the large-signal
stability study from Prof. Xin Zhang’s research group. This book introduces several
modified control schemes for the power inverters to improve their large-signal
stability, including the improved Lyapunov-based control method, the improved
backstepping control method, the improved finite control set model predictive control
method, etc. This book is suitable for all the levels of people related to power inverters.
For the junior-level people who are the first time to know the power inverters, this
book can help them to understand the concept, control logic, and large-signal stability
v
vi Preface
problem of the power inverters. For middle-level people having some background
in the control and design of power inverters, this book can help them to improve
their knowledge on the power inverters’ control strategy, which lets them find the
tips to fix the large-signal stability problem of the power inverters from a control
point of view. For the top-level people who are very familiar with power inverters,
this book may offer them certain inspirations. In this case, this book can be treated as
undergraduate textbooks, graduate textbooks, industrial design instruction books in
the field of power electronics, power systems, control engineering, which can bring
benefits to both academic and industrial sectors.
Hangzhou, China Xin Zhang
Contents
1 Introduction ................................................... 1
1.1 Significance of DG in MGs .................................. 1
1.2 Categories of MGs .......................................... 3
1.2.1 AC MG ............................................. 3
1.2.2 DC MG ............................................ 4
1.2.3 Hybrid MG ......................................... 5
1.3 The Cornerstone of MGs: Power Inverters ...................... 5
1.3.1 Grid-Connected Inverters: L or LCL Filtered Inverters ..... 6
1.3.2 Standalone Inverters: LC-Filtered Inverter ............... 7
1.3.3 Grid-Connected and Standalone Inverters Cascaded
with LC Input Filters ................................. 8
1.4 The Necessity of Large-Signal Stability Analysis in Control
of Inverters ................................................ 9
1.4.1 Stability Problems of Inverters and the Existing
Small-Signal Stability Analysis ........................ 9
1.4.2 The Necessity of Large-Signal Stability Analysis ......... 10
1.4.3 Existing Large-Signal Stability Analysis of Inverters
Via Lyapunov’s Theory ............................... 11
1.4.4 The Motivation of This Book: Advanced Control
Strategies for the Power Inverter to Improve Its
Large-Signal Stability ................................ 12
References ..................................................... 13
2 Adaptive Backstepping Current Control of Single-Phase
LCL-Grid-Connected Inverters to Improve Its Large-Signal
Stability in the Presence of Parasitic Resistance Uncertainty ........ 19
2.1 Introduction ............................................... 19
2.2 Mathematical Modelling ..................................... 21
2.3 Derivation of Proposed Control Scheme ....................... 22
2.3.1 Step I: Derivation of Pseudo Reference x (t)
2ref
and Adaptive Law 1 .................................. 22
vii
viii Contents
2.3.2 Step II: Derivation of Pseudo Reference x (t)
3ref
and Adaptive Law 2 .................................. 24
2.3.3 Step III: Derivation of Control Law μ(t) and Adaptive
Law 3 .............................................. 26
2.4 Test Results ............................................... 28
2.5 Conclusion ................................................ 30
References ..................................................... 31
3 An Adaptive Dual-Loop Lyapunov-Based Control Scheme
for a Single-Phase Stand-Alone Inverter to Improve Its
Large-Signal Stability .......................................... 33
3.1 Introduction ............................................... 34
3.2 Mathematical Modelling ..................................... 35
3.2.1 Average Model of the Investigated System ............... 35
3.2.2 Load Voltage Reference ............................... 35
3.2.3 Current-Loop Reference .............................. 36
3.2.4 Model of the Load Current ............................ 36
3.3 Proposed Adaptive Dual-Loop Lyapunov-Based Control
Scheme ................................................... 36
3.3.1 The Proposed Lyapunov Function ...................... 36
3.3.2 Derivation of the Adaptive Dual-Loop Control Law ....... 37
3.3.3 Implementation of Proposed Control Scheme ............ 39
3.4 Stability Analysis and Robustness Verification .................. 39
3.4.1 Stability Analysis .................................... 39
3.4.2 Robustness Against Plant Parametric Variations .......... 42
3.5 Test Results ............................................... 43
3.5.1 Steady-State and Dynamic Performance Evaluation ....... 43
3.5.2 Overload and Recovery Scenario ....................... 43
3.6 Conclusion ................................................ 44
References ..................................................... 45
4 Lyapunov-Based Control of Three-Phase Stand-Alone
Inverters to Improve Its Large-Signal Stability with Inherent
Dual Control Loops and Load Disturbance Adaptivity ............. 47
4.1 Introduction ............................................... 48
4.2 Preliminary of the Proposed Adaptive Dual-Loop
Lyapunov-Based Control: Mathematical Modelling .............. 50
4.2.1 Average Model of the Investigated System ............... 50
4.2.2 Load Voltage References v , v , and Inductor
odref oqref
Current References i , i ......................... 51
Ldref Lqref
4.2.3 Model of the Load Currents and Proposed Adaptive
Laws ............................................... 51
4.2.4 Modified Inductor Current References i , i
Ldref Lqref
Incorporated with Adaptive Laws ...................... 52
4.3 Derivation of Proposed Adaptive Decoupled Dual-Loop
Lyapunov-Based Control Scheme ............................. 52
Contents ix
4.3.1 Proposed Weighted All-in-One Lyapunov Function V ..... 52
4.3.2 Derivation of the Switching Functions and Adaptive
Laws ............................................... 53
4.4 Implementation of Proposed Control Scheme and Its Resulted
dq Decoupled Error Dynamics ............................... 56
4.4.1 Block Diagram of the Proposed Control Scheme .......... 56
4.4.2 Decoupled Error Dynamics in d Frame and q Frame ...... 56
4.4.3 Recommended Way to Set Load Voltage References ...... 57
4.5 Stability Analysis and Controller Design Guidelines ............. 58
4.5.1 Closed-Loop System Stability Proof .................... 58
4.5.2 Power Loss Analysis, Switching Frequency (f )
s
Selection and Output LC Filter Design .................. 60
4.5.3 Controller Gains Selection Via Poles Placement .......... 61
4.6 Test Results ............................................... 62
4.6.1 Performance of Proposed Approach .................... 62
4.6.2 Comparisons Between the Proposed Approach
and Existing Control Schemes ......................... 65
4.7 Conclusion ................................................ 67
References ..................................................... 69
5 An Ellipse-Optimized Composite Backstepping Control
Strategy for a Point-of-Load Inverter to Improve
Its Large-Signal Stability Under Load Disturbance
in the Shipboard Power System .................................. 71
5.1 Introduction ............................................... 72
5.2 Preliminary of the Ellipse-Optimized Composite
Backstepping Controller: Mathematical Modelling .............. 75
5.2.1 Dynamic Equations of the Investigated POL Inverter ...... 75
5.2.2 Control Objectives: Load Voltage References x *, x * ..... 76
1 3
5.3 Recursive Derivation and Implementation of the Proposed
Composite Backstepping Controller ........................... 76
5.3.1 Two-Step Backstepping Derivation in d Frame ........... 76
5.3.2 Two-Step Backstepping Derivation in q Frame ........... 78
5.3.3 Design of the Kalman Filter to Estimate
and Feedforward the Load Currents for Load
Disturbance Rejection ................................ 80
5.3.4 Implementation of the Proposed Composite
Backstepping Controller with a Kalman Filter ............ 82
5.4 Ellipse-Based Controller Gains Optimization, Feedback
Gains Matrix Selection, and Robustness Analysis ............... 83
5.4.1 Proposed Intuitive Ellipse-Based Strategy to Optimize
the Controller Parameters with Fully Consideration
of ξ and ω ......................................... 83
n
x Contents
5.4.2 Quantitative Selection of the Feedback Gain Matrix
G of the Kalman Filter Aided by Ellipse-Optimized
Strategy ............................................ 87
5.4.3 Robustness Analysis of the Proposed Control Scheme
Under Parametric Variations and Measurement Errors ..... 88
5.5 Test Results ............................................... 90
5.5.1 Effectiveness of the Proposed Ellipse-Optimized
Controller Gains Selection Strategy ..................... 90
5.5.2 Robustness Tests Under Plant Parametric Variations ....... 90
5.5.3 Performance Evaluation Under Linear/Nonlinear
Load Step, Reference Step, Overload and Recovery ....... 91
5.5.4 Comparisons Between Existing Lyapunov-Based
Approaches and the Proposed Control Scheme ........... 92
5.6 Conclusion ................................................ 94
References ..................................................... 96
6 Stability Constraining Dichotomy Solution Based Model
Predictive Control for the Three Phase Inverter Cascaded
with Input EMI Filter in the MEA ............................... 101
6.1 Introduction ............................................... 101
6.2 Instability Problem of the Researched AC Cascaded System
in MEA ................................................... 103
6.2.1 Instability Problem Description ........................ 103
6.2.2 The Instability Reason of CPL with LC Input Filter ....... 105
6.3 Preliminary of the SCDS-MPC Method: Mathematical
Modeling of the Researched AC Cascaded System in MEA ....... 107
6.3.1 Conventional Inverter Mathematical Model .............. 107
6.3.2 Improved Mathematical Model with Consideration
of the Inverter and Input EMI Filter for Stability
Analysis ............................................ 108
6.4 The Proposed SCDS-MPC Method ........................... 110
6.4.1 Conventional Model Predictive Control Scheme .......... 110
6.4.2 Proposed Dichotomy Solution (DS) Based Model
Predictive Control .................................... 111
6.4.3 Proposed System Stability Constraining Cost
Function Definition ................................... 112
6.4.4 Sensitivity Analysis of Model Parameters Variation ....... 117
6.5 Test Results ............................................... 120
6.6 Conclusion ................................................ 122
References ..................................................... 123
7 Composite-Bisection Predictive Control to Stabilize the Three
Phase Inverter Cascaded with Input EMI Filter in the SPS ......... 127
7.1 Introduction ............................................... 127
7.2 Mathematical Modeling ..................................... 130
7.3 Conventional FCS MPC and Problem Formulation .............. 131