Modeling and Control of Modern Electrical Energy Systems

Description

Modeling and Control of Modern Electrical Energy Systems A step-by-step approach to the modeling, analysis, and control of modern electronically controlled energy systems In Modeling and Control of Modern Electrical Energy Systems, distinguished researcher Dr. Masoud Karimi-Ghartemani delivers a comprehensive discussion of distributed and renewable energy resource integration from a control system perspective. The book explores various practical aspects of these systems, including the power extraction control of renewable resources and size selection of short-term storage components. The interactions of distributed energy resources (DERs) with the rest of the electric power system are presented, as is a discussion of the ability of the DER to ride through grid voltage faults and frequency swings. Readers will also discover how to derive mathematical models of different types of energy systems and build simulation models for those systems. Modeling and Control of Electrical Energy Systems provides end-of chapter examples and problems, as well as: A thorough introduction to power electronic conversion, including power electronics and standard power electronic convertersAn in-depth treatment of feedback control systems, including frequency-domain (transfer function) approaches and time-domain (state space) approachesComprehensive discussions of direct current DERs and single-phase alternating current DERsFulsome explorations of three-phase distributed energy resources Perfect for researchers, practitioners, and professors with an interest in electronically interfaced modern energy systems, Modeling and Control of Modern Electrical Energy Systems will also earn a place in the libraries of senior undergraduate and graduate students of electrical engineering. Cover Title Page Copyright Contents Author Biography Preface Acknowledgments Acronyms Symbols Introduction Part I Power Electronic Conversion Chapter 1 Power Electronics 1.1 Power Electronics Based Conversion 1.1.1 Advantages of Power Electronics 1.2 Power Electronic Switches 1.3 Types of Power Electronic Converters 1.4 Applications of Power Electronics in Power Engineering 1.4.1 Power Quality Applications 1.4.2 Power System Applications 1.4.3 Rectifiers and Motor Drive Applications 1.4.4 Backup Supply and Distributed Generation Applications 1.5 Summary and Conclusion Exercises Problems Reference Chapter 2 Standard Power Electronic Converters 2.1 Standard Buck Converter 2.1.1 Analysis of Operation 2.1.2 Switching Model 2.1.3 Average (or Control) Model 2.1.3.1 Current Control Model 2.1.3.2 Output Voltage Control Model 2.1.3.3 Input Voltage Control Model 2.1.4 Steady‐State Analysis 2.1.5 Sensitivity Analysis 2.1.5.1 Sensitivity to R 2.1.5.2 Sensitivity to vB 2.1.5.3 Sensitivity to vA 2.1.6 Virtual Resistance Feedback 2.1.7 Input Feedback Linearization 2.2 Standard Boost Converter 2.2.1 Analysis of Operation 2.2.2 Steady‐State Analysis 2.2.3 Switching Model 2.2.4 Average (or Control) Model 2.2.4.1 Current Control Model 2.2.4.2 Input Voltage Control 2.2.4.3 Output Voltage Control 2.3 Standard Inverting Buck‐Boost Converter* 2.3.1 Analysis of Operation 2.3.2 Steady‐State Analysis 2.3.3 Switching Model 2.3.4 Average (or Control) Model 2.3.4.1 Current Control Model 2.4 Standard Four‐Switch Buck‐Boost Converter* 2.4.1 Analysis of Operation 2.4.2 Steady‐State Analysis 2.4.3 Switching Model 2.4.4 Average (or Control) Model 2.4.4.1 Current Control Model 2.5 Standard Bidirectional Converter 2.6 Single‐Phase Half‐Bridge VSC 2.6.1 Analysis of Operation 2.6.2 Switching Model 2.6.3 Average (or Control) Model 2.6.4 Sensitivity Analysis and Role of Feedback 2.6.4.1 Sensitivity to R 2.6.5 Synchronized Sampling 2.7 Full‐Bridge VSC 2.7.1 Bipolar PWM Operation 2.7.2 Unipolar PWM Operation 2.8 Three‐Phase VSC 2.8.1 Modeling in Stationary Domain 2.8.2 Modeling in Rotating Synchronous Frame 2.8.3 Compact Modeling Using Complex Transfer Functions* 2.9 Modeling of Converter Delays 2.10 Summary and Conclusion Exercises Problems References Part II Feedback Control Systems Chapter 3 Frequency‐Domain (Transfer Function) Approach 3.1 Key Concepts 3.1.1 Transfer Function 3.1.1.1 Differential Equation 3.1.1.2 Definition of Zeros and Poles of a TF or an LTI System 3.1.1.3 Partial Fraction Expansion (PFE) 3.1.2 Stability 3.1.3 Disturbance 3.1.4 Uncertainty 3.1.5 Statement of Control Problem 3.2 Open‐Loop Control 3.3 Closed‐Loop (or Feedback) Control 3.3.1 Feedback Philosophy 3.3.2 Stability Margins 3.3.2.1 Case I: Proportional Control C(s)=Kp 3.3.2.2 Case II: Proportional‐Derivative Control C(s)=K(s+z)=Kds+Kp 3.3.2.3 Case III: Proportional‐Integrating Control C(s)=Ks+zs=Kp+Kis 3.3.2.4 Case IV: PID Control C(s)=K(s+z1)(s+z2)s=Kds+Kp+Kis 3.4 Some Feedback Loop Properties 3.4.1 Removal of Steady‐State Error 3.4.2 Pole Location and Transient Response 3.5 Summary and Conclusion Problems Chapter 4 Time‐Domain (State Space) Approach 4.1 State Space Representation and Properties 4.1.1 Relationship between SS and TF 4.1.2 Facts 4.2 State Feedback 4.2.1 Concept of Controllability 4.2.2 Concept of Stabilizability 4.2.3 Removing Steady‐State Error 4.2.4 Challenges with State Feedback Method 4.3 State Estimator 4.3.1 How to Choose the Estimator's Poles? 4.3.2 Separation Property 4.3.3 Conditions for Existence of Estimator Gain H 4.3.4 Concept of Observability 4.3.5 Concept of Detectability 4.4 Optimal Control 4.4.1 Linear Quadratic Regulator (LQR) 4.4.2 Linear Quadratic Tracker (LQT) 4.4.2.1 LQT Without Direct Output Feedback 4.4.2.2 Robust LQT with Direct Output Feedback 4.4.2.3 Elementary Design Approach (Unstable!) 4.4.2.4 LQT Design for Step Commands and Step Disturbances 4.4.2.5 LQT Design for Sinusoidal References and Disturbances 4.5 Summary and Conclusion Problems References Part III Distributed Energy Resources (DERs) Chapter 5 Direct‐Current (dc) DERs 5.1 Introduction 5.1.1 System Description 5.1.2 General Statement of Control Objectives 5.2 Overview of a Solar PV Conversion System 5.2.1 Photovoltaic Effect and Solar Cell 5.2.2 General PV Converter Structures 5.3 Power Control via Current Feedback Loop 5.3.1 Control Objectives 5.3.2 Control Approach 5.3.2.1 Robust Tracking and Current Limiting 5.3.2.2 Soft Start Control 5.3.3 Design of Feedback Gains Using TF Approach 5.3.4 LQT Approach and Design 5.3.5 Control Design Requirements for Current Limiting 5.4 Grid Voltage Support 5.4.1 Explanation on Concept of Inertia 5.4.2 Conflict of Inertia Response and Current Limiting 5.4.3 Inertia Response Using Capacitor Emulation 5.4.4 Full State Feedback of Power Loop 5.4.5 Static Grid Voltage Support (Droop Function) 5.4.6 Inertia Power Using Grid Voltage Differentiation 5.4.7 Common Approach: Nested Control Loops 5.5 Analysis of Weak Grid Condition 5.6 Load Voltage Control 5.6.1 Control Structure and Optimal Design 5.6.2 Current Limiting 5.7 Grid‐Forming Converter Controls 5.7.1 Grid‐Forming Control Without a dc‐Side Capacitor 5.7.2 Grid‐Forming Controller with a dc‐Side Capacitor 5.7.2.1 Full State Feedback 5.8 Control Scenarios in a PV Converter 5.8.1 PV Voltage Control 5.8.2 MPPT via PV Voltage Control 5.8.3 Mathematical Modeling of MPPT Algorithm 5.8.3.1 Calculation of ddvpvppv: Method 1 5.8.3.2 Calculation of ddvpvppv: Method 2 5.8.4 PV Power Control 5.9 LCL Filter* 5.9.1 Passive Damping of Resonance Mode 5.9.2 Full‐State Feedback with Active Damping 5.9.3 Delay Compensation Technique Using LQT Approach 5.10 Summary and Conclusion Problems References Chapter 6 Single‐Phase Alternating‐Current (ac) DERs 6.1 Power Balance in a dc/ac System 6.1.1 Power Decoupling 6.2 Power Control Method via Current Feedback Loop (CFL) 6.2.1 Input Linearization and Feedforward Compensation 6.2.2 Control Structure 6.2.3 Calculating and Limiting Reference Current 6.2.4 Single‐Phase ePLL 6.2.4.1 Linear Analysis of ePLL 6.2.4.2 Two Modifications to the ePLL 6.2.5 Controller Formulation and LQT Design 6.2.6 Impact of Grid Voltage Harmonics 6.2.7 Harmonics and dc Control Units 6.2.8 Weak Grid Condition and PLL Impact* 6.2.8.1 Short‐Circuit Ratio (SCR) 6.2.8.2 LTI Model of Reference Current Generation 6.2.8.3 Controller and Its Design 6.3 Grid‐Supportive Controls 6.3.1 Static (or Steady‐State) Support 6.3.2 Dynamic (or Inertia) Support 6.3.3 Power Controller with Grid Support 6.3.4 Virtual Synchronous Machine (VSM) 6.3.4.1 Stability Analysis and Design of VSM 6.3.4.2 Start‐up Synchronization 6.3.4.3 Grid‐Connection Synchronization 6.4 dc Voltage Control and Support 6.4.1 System Modeling 6.4.2 Control Structure and Design 6.4.3 Removing 2‐f Ripples from Control Loop* 6.4.3.1 Notch Filtering Method 6.4.3.2 Direct Ripple Cancellation Method 6.4.4 Obtaining Inertia from Capacitor* 6.4.4.1 Non‐VSM Approach 6.4.4.2 VSM Approach 6.5 Load Voltage Control and Support 6.5.1 Direct Voltage Control Approach 6.5.2 Voltage Control Loop with Current Limiting 6.5.3 Deriving Grid‐Forming Controllers 6.5.3.1 Power Droops Strategy 6.5.3.2 Swing Equation Strategy (VSM Approach) 6.5.3.3 Analogy Between the Two Approaches 6.5.3.4 Damping Strategies 6.5.4 Discussion 6.6 DERs in a Hybrid ac/dc Network 6.7 Summary and Conclusion Problems References Chapter 7 Three‐Phase DERs 7.1 Introduction 7.1.1 Symmetrical Components 7.1.2 Powers in a Three‐Phase System 7.1.2.1 Balanced Situation 7.1.2.2 Unbalanced Situation 7.1.3 Space Phasor Concept and Notation 7.1.3.1 Space Phasor of a Positive‐Sequence Signal 7.1.3.2 Space Phasor of a Negative‐Sequence Waveform 7.1.3.3 Power Definitions and Expressions Using Space Phasor 7.2 Three‐Phase PLL 7.2.1 SRF‐PLL 7.2.1.1 Principles of Operation 7.2.1.2 Approximate Linear Analysis and Design 7.2.1.3 Alternative Presentations 7.2.2 Three‐Phase Enhanced PLL (ePLL) 7.2.2.1 Basic ePLL Structure 7.2.2.2 Analysis of Basic ePLL 7.2.3 ePLL with Negative‐Sequence Estimation 7.2.4 ePLL with Negative‐seq and dc Estimation 7.3 Vector Current Control in Stationary Domain 7.3.1 Controller Structure 7.3.2 Current Reference Generation and Limiting 7.3.2.1 Balanced Current 7.3.2.2 Unbalanced Current 7.3.3 Harmonics, Higher‐Order Filters, System Delays 7.3.4 Weak Grid Conditions and Including PLL in Controller* 7.4 Vector Current Control in Synchronous Reference Frame 7.4.1 Control Structure 7.4.2 Current Reference Generation and Limiting 7.4.2.1 Balanced Current 7.4.2.2 Unbalanced Current 7.4.3 SISO and MIMO Control Approaches 7.4.4 Optimal Design of PI Controller Gains 7.4.4.1 SISO Design 7.4.4.2 MIMO Design 7.4.5 Optimal Design of PIR Controller Gains 7.4.5.1 SISO Design 7.4.5.2 MIMO Design 7.4.6 Harmonics, Higher‐Order Filters, Control Delays* 7.4.7 Weak Grid Conditions and Including PLL in Controller* 7.4.8 Remarks on VCC in αβ and dq Frames 7.5 Grid‐Supportive Controls 7.5.1 Power Controller with Grid Support 7.5.2 Virtual Synchronous Machine (VSM) 7.5.3 Stability Analysis and Design of VSM 7.5.3.1 Start‐up Synchronization 7.5.3.2 Grid‐Connection Synchronization 7.5.3.3 Comment on Adaptive Parameters 7.6 dc Side Voltage Control and Support 7.6.1 System Modeling 7.6.2 Control Structure and Design 7.6.3 Obtaining Inertia from dc Side Capacitor* 7.6.3.1 Non‐VSM Approach 7.6.3.2 VSM Approach 7.7 Load Voltage Control and Support 7.7.1 Direct Voltage Control Approach 7.7.1.1 DVC in Stationary Frame 7.7.1.2 DVC in Rotating Frame 7.7.2 Voltage Control with Current Limiting 7.7.2.1 Active Damping of Resonance Mode 7.7.3 Deriving Grid‐Forming Controllers* 7.7.3.1 Power Droops Strategy 7.7.3.2 Swing Equation Strategy (VSM Approach) 7.7.3.3 Analogy Between Filtered‐Powers Droop and VSM Approaches 7.7.3.4 Damping Strategies 7.7.3.5 Discussion 7.8 Summary and Conclusion Problems References Chapter 8 Summary and Conclusion Index EULA