Power Systems Analysis

__Power Systems Analysis, Second Edition,__ describes the operation of the interconnected power system under steady state conditions and under dynamic operating conditions during disturbances. Written at a foundational level, including numerous worked examples of concepts discussed in the text, it provides an understanding of how to keep power flowing through an interconnected grid. The second edition adds more information on power system stability, excitation system, and small disturbance analysis, as well as discussions related to grid integration of renewable power sources. The book is designed to be used as reference, review, or self-study for practitioners and consultants, or for students from related engineering disciplines that need to learn more about power systems. Cover Power Systems Analysis Copyright Dedication Preface 1 Introduction 1.1 The Electrical Power System 1.2 Network Models 1.3 Faults and Analysis 1.4 The Primitive Network 1.5 Power System Stability 1.6 Deregulation 1.7 Renewable Energy Resources 2 Graph Theory 2.1 Introduction 2.2 Definitions 2.3 Tree and Cotree 2.4 Basic Loops 2.5 Cut-Set 2.6 Basic Cut-Sets Worked Examples Problems Questions 3 Incidence Matrices 3.1 Element-Node Incidence Matrix 3.2 Bus Incidence Matrix 3.3 Branch-Path Incidence Matrix K 3.4 Basic Cut-Set Incidence Matrix 3.5 Augmented Cut-Set Incidence Matrix B ̃ 3.6 Basic Loop Incidence Matrix 3.7 Augmented Loop Incidence Matrix 3.8 Network Performance Equations Worked Examples Questions Problems 4 Network Matrices 4.1 Introduction 4.2 Network Matrices 4.2.1 Network Matrices by Singular Transformations 4.2.1.1 Bus Admittance Matrix and Bus Impedance Matrix 4.2.1.2 Branch Admittance and Branch Impedance Matrices 4.2.1.3 Loop Impedance and Loop Admittance Matrices 4.2.2 Network Matrices by Nonsingular Transformation 4.2.2.1 Branch Admittance Matrix 4.2.2.2 Loop Impedance and Loop Admittance Matrices 4.3 Bus Admittance Matrix by Direct Inspection Worked Examples Questions Problems 5 Building of Network Matrices 5.1 Introduction 5.2 Partial Network 5.3 Addition of a Branch 5.3.1 Calculation of Mutual Impedances 5.3.2 Calculation of Self-Impedance of Added Branch Zab 5.3.3 Special Cases 5.4 Addition of a Link 5.4.1 Calculation of Mutual Impedances 5.4.2 Computation of Self-Impedance 5.4.3 Removal of Elements or Changes in Element 5.5 Removal or Change in Impedance of Elements with Mutual Impedance Worked Examples Problems Questions 6 Symmetrical Components 6.1 The Operator “a” 6.2 Symmetrical Components of Unsymmetrical Phases 6.3 Power in Sequence Components 6.4 Unitary Transformation for Power Invariance 7 Three-Phase Networks 7.1 Three-Phase Network Element Representation 7.1.1 Stationary Network Element 7.1.2 Rotating Network Element 7.1.3 Performance Relations for Primitive Three-Phase Network Element 7.2 Three-Phase Balanced Network Elements 7.2.1 Balanced Excitation 7.2.2 Transformation Matrices 7.3 Three-Phase Impedance Networks 7.3.1 Incidence and Network Matrices for Three-Phase Networks 7.3.2 Algorithm for Three-Phase Bus Impedance Matrix 7.3.2.1 Performance Equation of a Partial Three-Phase Network 7.3.2.2 Addition of a Branch 7.3.2.3 Addition of a Link Summary of the Formulae Worked Examples Questions Problems 8 Synchronous Machine 8.1 The Two-Axis Model of Synchronous Machine 8.2 Derivation of Park’s Two-Axis Model 8.3 Synchronous Machine Analysis 8.3.1 Voltage Relations—Stator or Armature 8.3.1.1 Field or Rotor 8.3.1.2 Direct Axis Damper Windings 8.3.1.3 Quadrature Axis Damper Windings 8.3.2 Flux Linkage Relations 8.3.2.1 Armature 8.3.2.2 Field 8.3.2.3 Direct Axis Damper Winding 8.3.2.4 Quadrature Axis Damper Winding 8.3.3 Inductance Relations 8.3.3.1 Self-Inductance of the Armature Windings 8.3.3.2 Mutual Inductances of the Armature Windings 8.3.3.3 Mutual Inductances Between Stator and Rotor Flux 8.3.4 Flux Linkage Equations 8.3.4.1 Field 8.3.4.2 Direct Axis Damper Winding 8.3.4.3 Quadrature Axis Damper Winding 8.4 The Transformations 8.5 Stator Voltage Equations 8.6 Steady-State Equation 8.7 Steady-State Vector Diagram 8.8 Reactances 8.9 Equivalent Circuits and Phasor Diagrams 8.9.1 Model for Transient Stability 8.10 Transient State Phasor Diagram 8.11 Power Relations 8.12 Synchronous Machine Connected Through an External Reactance Worked Examples Questions Problems 9 Lines and Loads 9.1 Lines 9.1.1 Short Lines 9.1.2 Medium Lines 9.1.3 Long Lines 9.2 Transformers 9.2.1 Transformer with Nominal Turns Ratio 9.2.2 Phase Shifting Transformers 9.3 Load Modeling 9.3.1 Constant Current Model 9.3.2 Constant Impedance Model 9.3.3 Constant Power Model 9.4 Composite Load 9.4.1 Dynamic Characteristics 9.5 Induction Machine Modeling 9.6 Model with Mechanical Transients 9.6.1 Power Torque and Slip 9.6.2 Reactive Power and Slip 9.6.3 Synchronous Motor 9.7 Rectifiers and Inverter Loads 9.7.1 Static Load Modeling for Load Flow Studies 9.7.2 Voltage Dependence of Equivalent Loads 9.7.3 Derivation for Equivalent Load Powers Worked Examples Questions Problems 10 Power Flow Studies 10.1 Necessity for Power Flow Studies 10.2 Conditions for Successful Operation of a Power System 10.3 The Power Flow Equations 10.4 Classification of Buses 10.5 Bus Admittance Formation 10.6 System Model for Load Flow Studies 10.7 Gauss–Seidel Method 10.8 Gauss–Seidel Iterative Method 10.8.1 Acceleration Factor 10.8.2 Treatment of a PV Bus 10.9 Newton–Raphson Method 10.9.1 Rectangular Coordinates Method 10.9.2 The Polar Coordinates Method 10.10 Sparsity of Network Admittance Matrices 10.11 Triangular Decomposition 10.12 Optimal Ordering 10.13 Decoupled Methods 10.14 Fast Decoupled Methods 10.15 Load Flow Solution Using Z-Bus 10.15.1 Bus Impedance Formation 10.15.2 Addition of a Line to the Reference Bus 10.15.3 Addition of a Radial Line and New Bus 10.15.4 Addition of a Loop Closing Two Existing Buses in the System 10.15.5 Gauss–Seidel Method Using Z-Bus for Load Flow Solution 10.16 Convergence Characteristics 10.17 Comparison of Various Methods for Power Flow Solution Worked Examples Problems Questions 11 Short Circuit Analysis 11.1 Per Unit Quantities 11.2 Advantages of Per Unit System 11.3 Three-Phase Short Circuits 11.4 Reactance Diagrams 11.5 Percentage Values 11.6 Short Circuit kVA 11.7 Importance of Short Circuit Currents 11.8 Analysis of R–L Circuit 11.9 Three-Phase Short Circuit on Unloaded Synchronous Generator 11.10 Effect of Load Current or Prefault Current 11.11 Reactors 11.11.1 Construction of Reactors 11.11.2 Classification of Reactors Worked Examples Problems Questions 12 Unbalanced Fault Analysis 12.1 Sequence Impedances 12.2 Balanced Star Connected Load 12.3 Transmission Lines 12.4 Sequence Impedances of Transformer 12.5 Sequence Reactances of Synchronous Machine 12.6 Sequence Networks of Synchronous Machines 12.6.1 Positive Sequence Network 12.6.2 Negative Sequence Network 12.6.3 Zero Sequence Network 12.7 Unsymmetrical Faults 12.8 Assumptions for System Representation 12.9 Unsymmetrical Faults on an Unloaded Generator 12.10 Line-to-Line Fault 12.11 Double Line-to-Ground Fault 12.12 Single Line-to-Ground Fault with Fault Impedance 12.13 Line-to-Line Fault with Fault Impedance 12.14 Double Line-to-Ground Fault With Fault Impedance Worked Examples Problems Questions 13 Power System Stability 13.1 Elementary Concepts 13.2 Illustration of Steady State Stability Concept 13.3 Methods for Improcessing Steady State Stability Limit 13.4 Synchronizing Power Coefficient 13.5 Short Circuit Ratio and Excitation System 13.6 Transient Stability 13.7 Stability of a Single Machine Connected to Infinite Bus 13.8 The Swing Equation 13.9 Equal Area Criterion and Swing Equation 13.10 Transient Stability Limit 13.11 Frequency of Oscillations 13.12 Critical Clearing Time and Critical Clearing Angle 13.13 Fault on a Double-Circuit Line 13.14 Transient Stability When Power Is Transmitted During the Fault 13.15 Fault Clearance and Reclosure in Double-Circuit System 13.16 First Swing Stability 13.17 Solution to Swing Equation Step-by-Step Method 13.18 Factors Affecting Transient Stability 13.18.1 Effect of Voltage Regulator 13.19 Excitation System and the Stability Problem 13.20 Dynamic Stability 13.20.1 Power System Stabilizer 13.21 Small Disturbance Analysis 13.22 Node Elimination Methods 13.23 Other Methods for Solution of Swing Equation 13.23.1 Modified Euler’s Method Worked Examples Problems Questions Index Back Cover Front Cover -- Power Systems Analysis -- Copyright Page -- Dedication -- Contents -- Preface -- 1 Introduction -- 1.1 The Electrical Power System -- 1.2 Network Models -- 1.3 Faults and Analysis -- 1.4 The Primitive Network -- 1.5 Power System Stability -- 1.6 Deregulation -- 1.7 Renewable Energy Resources -- 2 Graph Theory -- 2.1 Introduction -- 2.2 Definitions -- 2.3 Tree and Cotree -- 2.4 Basic Loops -- 2.5 Cut-Set -- 2.6 Basic Cut-Sets -- Worked Examples -- Problems -- Questions -- 3 Incidence Matrices -- 3.1 Element-Node Incidence Matrix -- 3.2 Bus Incidence Matrix -- 3.3 Branch-Path Incidence Matrix K -- 3.4 Basic Cut-Set Incidence Matrix -- 3.5 Augmented Cut-Set Incidence Matrix B̃ -- 3.6 Basic Loop Incidence Matrix -- 3.7 Augmented Loop Incidence Matrix -- 3.8 Network Performance Equations -- Worked Examples -- Questions -- Problems -- 4 Network Matrices -- 4.1 Introduction -- 4.2 Network Matrices -- 4.2.1 Network Matrices by Singular Transformations -- 4.2.1.1 Bus Admittance Matrix and Bus Impedance Matrix -- 4.2.1.2 Branch Admittance and Branch Impedance Matrices -- 4.2.1.3 Loop Impedance and Loop Admittance Matrices -- 4.2.2 Network Matrices by Nonsingular Transformation -- 4.2.2.1 Branch Admittance Matrix -- 4.2.2.2 Loop Impedance and Loop Admittance Matrices -- 4.3 Bus Admittance Matrix by Direct Inspection -- Worked Examples -- Questions -- Problems -- 5 Building of Network Matrices -- 5.1 Introduction -- 5.2 Partial Network -- 5.3 Addition of a Branch -- 5.3.1 Calculation of Mutual Impedances -- 5.3.2 Calculation of Self-Impedance of Added Branch Zab -- 5.3.3 Special Cases -- 5.4 Addition of a Link -- 5.4.1 Calculation of Mutual Impedances -- 5.4.2 Computation of Self-Impedance -- 5.4.3 Removal of Elements or Changes in Element -- 5.5 Removal or Change in Impedance of Elements with Mutual Impedance -- Worked Examples -- Problems Power Systems Analysis, Second Edition, describes the operation of the interconnected power system under steady state conditions and under dynamic operating conditions during disturbances. Written at a foundational level, including numerous worked examples of concepts discussed in the text, it provides an understanding of how to keep power flowing through an interconnected grid. The second edition adds more information on power system stability, excitation system, and small disturbance analysis, as well as discussions related to grid integration of renewable power sources. The book is designed to be used as reference, review, or self-study for practitioners and consultants, or for students from related engineering disciplines that need to learn more about power systems. Includes comprehensive coverage of the analysis of power systems, useful as a one-stop resource Features a large number of worked examples and objective questions (with answers) to help apply the material discussed in the book Offers foundational content that provides background and review for the understanding and analysis of more specialized areas of electric power engineering Power system analysis is a pre-requisite course for electrical engineering students. This book introduces concepts of a power system, network model faults and analysis and the primitive network stability. It also deals with graph theory relevant to various incidence matrices, building of network matrices and power flow studies. It further discusses with short circuit analysis, unbalanced fault analysis and power system stability problems, such as, steady state stability, transient stability and dynamic stability. Salient Features: Number of worked examples are followed after explaining theory