{"product_id":"graph-database-and-graph-computing-for-power-system-analysis-hardback-9781119903864","title":"Graph Database and Graph Computing for Power System Analysis (Hardback) 9781119903864","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eGraph Database and Graph Computing for Power System Analysis\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cfont size=\"4\"\u003eRenchang Dai (Author), Guangyi Liu (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781119903864, Wiley\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 28 September 2023\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e512 pages\u003cbr\u003e25.4 x 17.8 x 2.7 cm, 0.077 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e\u003cb\u003eGraph Database and Graph Computing for Power System Analysis\u003c\/b\u003e \u003cp\u003e\u003cb\u003eUnderstand a new way to model power systems with this comprehensive and practical guide\u003c\/b\u003e \u003c\/p\u003e\n\u003cp\u003eGraph databases have become one of the essential tools for managing large data systems. Their structure improves over traditional table-based relational databases in that it reconciles more closely to the inherent physics of a power system, enabling it to model the components and the network of a power system in an organic way. The authors’ pioneering research has demonstrated the effectiveness and the potential of graph data management and graph computing to transform power system analysis. \u003c\/p\u003e\n\u003cp\u003e\u003ci\u003eGraph Database and Graph Computing for Power System Analysis\u003c\/i\u003e presents a comprehensive and accessible introduction to this research and its emerging applications. Programs and applications conventionally modeled for traditional relational databases are reconceived here to incorporate graph computing. The result is a detailed guide which demonstrates the utility and flexibility of this cutting-edge technology. \u003c\/p\u003e\n\u003cp\u003eThe book’s readers will also find: \u003c\/p\u003e\n\u003cul\u003e\n\u003cli\u003eDesign configurations for a graph-based program to solve linear equations, differential equations, optimization problems, and more\u003c\/li\u003e \u003cli\u003eDetailed demonstrations of graph-based topology analysis, state estimation, power flow analysis, security-constrained economic dispatch, automatic generation control, small-signal stability, transient stability, and other concepts, analysis, and applications\u003c\/li\u003e \u003cli\u003eAn authorial team with decades of experience in software design and power systems analysis\u003c\/li\u003e\n\u003c\/ul\u003e \u003cp\u003e\u003ci\u003eGraph Database and Graph Computing for Power System Analysis\u003c\/i\u003e is essential for researchers and academics in power systems analysis and energy-related fields, as well as for advanced graduate students looking to understand this particular set of technologies.\u003c\/p\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cp\u003eAbout the Authors xiii\u003c\/p\u003e \u003cp\u003ePreface xv\u003c\/p\u003e \u003cp\u003eAcknowledgments xvii\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart I Theory and Approaches 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction 3\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Power System Analysis 6\u003c\/p\u003e \u003cp\u003e1.1.1 Power Flow Calculation 6\u003c\/p\u003e \u003cp\u003e1.1.2 State Estimation 6\u003c\/p\u003e \u003cp\u003e1.1.3 Contingency Analysis 7\u003c\/p\u003e \u003cp\u003e1.1.4 Security-Constrained Automatic Generation Control 7\u003c\/p\u003e \u003cp\u003e1.1.5 Security-Constrained ED 8\u003c\/p\u003e \u003cp\u003e1.1.6 Electromechanical Transient Simulation 9\u003c\/p\u003e \u003cp\u003e1.1.7 Photovoltaic Power Generation Forecast 10\u003c\/p\u003e \u003cp\u003e1.2 Mathematical Model 10\u003c\/p\u003e \u003cp\u003e1.2.1 Direct Methods of Solving Large-Scale Linear Equations 10\u003c\/p\u003e \u003cp\u003e1.2.2 Iterative Methods of Solving Large-Scale Linear Equations 11\u003c\/p\u003e \u003cp\u003e1.2.3 High-Dimensional Differential Equations 11\u003c\/p\u003e \u003cp\u003e1.2.4 Mixed Integer-Programming Problems 11\u003c\/p\u003e \u003cp\u003e1.3 Graph Computing 12\u003c\/p\u003e \u003cp\u003e1.3.1 Graph Modeling Basics 13\u003c\/p\u003e \u003cp\u003e1.3.2 Graph Parallel Computing 14\u003c\/p\u003e \u003cp\u003eReferences 14\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Graph Database 17\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Database Management Systems History 17\u003c\/p\u003e \u003cp\u003e2.2 Graph Database Theory and Method 18\u003c\/p\u003e \u003cp\u003e2.2.1 Graph Database Principle and Concept 18\u003c\/p\u003e \u003cp\u003e2.2.1.1 Defining a Graph Schema 19\u003c\/p\u003e \u003cp\u003e2.2.1.2 Creating a Loading Job 20\u003c\/p\u003e \u003cp\u003e2.2.1.3 Graph Query Language 21\u003c\/p\u003e \u003cp\u003e2.2.2 System Architecture 25\u003c\/p\u003e \u003cp\u003e2.2.3 Graph Computing Platform 25\u003c\/p\u003e \u003cp\u003e2.3 Graph Database Operations and Performance 26\u003c\/p\u003e \u003cp\u003e2.3.1 Graph Database Management System 26\u003c\/p\u003e \u003cp\u003e2.3.1.1 Parallel Processing by MapReduce 27\u003c\/p\u003e \u003cp\u003e2.3.1.2 Graph Partition 29\u003c\/p\u003e \u003cp\u003e2.3.2 Graph Database Performance 35\u003c\/p\u003e \u003cp\u003eReferences 38\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Graph Parallel Computing 41\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Graph Parallel Computing Mechanism 41\u003c\/p\u003e \u003cp\u003e3.2 Graph Nodal Parallel Computing 44\u003c\/p\u003e \u003cp\u003e3.3 Graph Hierarchical Parallel Computing 46\u003c\/p\u003e \u003cp\u003e3.3.1 Symbolic Factorization 47\u003c\/p\u003e \u003cp\u003e3.3.2 Elimination Tree 51\u003c\/p\u003e \u003cp\u003e3.3.3 Node Partition 56\u003c\/p\u003e \u003cp\u003e3.3.4 Numerical Factorization 57\u003c\/p\u003e \u003cp\u003e3.3.5 Forward and Backward Substitution 58\u003c\/p\u003e \u003cp\u003eReferences 59\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Large-Scale Algebraic Equations 61\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Iterative Methods of Solving Nonlinear Equations 61\u003c\/p\u003e \u003cp\u003e4.1.1 Gauss–Seidel Method 61\u003c\/p\u003e \u003cp\u003e4.1.2 PageRank Algorithm 62\u003c\/p\u003e \u003cp\u003e4.1.2.1 PageRank Algorithm Mechanism 63\u003c\/p\u003e \u003cp\u003e4.1.2.2 Iterative Method 66\u003c\/p\u003e \u003cp\u003e4.1.2.3 Algebraic Method 67\u003c\/p\u003e \u003cp\u003e4.1.2.4 Convergence Analysis 69\u003c\/p\u003e \u003cp\u003e4.1.3 Newton–Raphson Method 72\u003c\/p\u003e \u003cp\u003e4.2 Direct Methods of Solving Linear Equations 75\u003c\/p\u003e \u003cp\u003e4.2.1 Introduction 75\u003c\/p\u003e \u003cp\u003e4.2.2 Basic Concepts 76\u003c\/p\u003e \u003cp\u003e4.2.2.1 Data Structures of Sparse Matrix 76\u003c\/p\u003e \u003cp\u003e4.2.2.2 Matrices and Graphs 78\u003c\/p\u003e \u003cp\u003e4.2.3 Historical Development 80\u003c\/p\u003e \u003cp\u003e4.2.4 Direct Methods 81\u003c\/p\u003e \u003cp\u003e4.2.4.1 Solving Triangular Systems 81\u003c\/p\u003e \u003cp\u003e4.2.4.2 Symbolic Factorization 82\u003c\/p\u003e \u003cp\u003e4.2.4.3 Fill-Reducing Ordering 82\u003c\/p\u003e \u003cp\u003e4.3 Indirect Methods of Solving Linear Equations 83\u003c\/p\u003e \u003cp\u003e4.3.1 Stationary Methods 83\u003c\/p\u003e \u003cp\u003e4.3.1.1 Jacobi Method 83\u003c\/p\u003e \u003cp\u003e4.3.1.2 Gauss–Seidel Method 85\u003c\/p\u003e \u003cp\u003e4.3.1.3 SOR Method 86\u003c\/p\u003e \u003cp\u003e4.3.1.4 SSOR Method 86\u003c\/p\u003e \u003cp\u003e4.3.2 Nonstationary Methods 88\u003c\/p\u003e \u003cp\u003e4.3.2.1 CG Method 88\u003c\/p\u003e \u003cp\u003e4.3.2.2 Gmres 89\u003c\/p\u003e \u003cp\u003e4.3.2.3 BCG (bi-CG) 90\u003c\/p\u003e \u003cp\u003eReferences 91\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 High-Dimensional Differential Equations 95\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Integration Methods 95\u003c\/p\u003e \u003cp\u003e5.1.1 An Overview of Integration Methods and their Accuracy 95\u003c\/p\u003e \u003cp\u003e5.1.1.1 One-Step Methods 96\u003c\/p\u003e \u003cp\u003e5.1.1.2 Linear Multistep Methods 99\u003c\/p\u003e \u003cp\u003e5.1.2 Integration Methods for Power System Transient Simulations 100\u003c\/p\u003e \u003cp\u003e5.1.3 Transient Analysis Accuracy 100\u003c\/p\u003e \u003cp\u003e5.1.4 Transient Analysis Stability 101\u003c\/p\u003e \u003cp\u003e5.1.4.1 Absolute Stability 101\u003c\/p\u003e \u003cp\u003e5.1.4.2 Stiff Stability 102\u003c\/p\u003e \u003cp\u003e5.2 Time Step Control 103\u003c\/p\u003e \u003cp\u003e5.2.1 Adaptive Time Step 104\u003c\/p\u003e \u003cp\u003e5.2.1.1 Change by Iteration Number 105\u003c\/p\u003e \u003cp\u003e5.2.1.2 Change by Estimated Truncation Error 105\u003c\/p\u003e \u003cp\u003e5.2.1.3 Change by State Variable Derivative 106\u003c\/p\u003e \u003cp\u003e5.2.2 Multiple Time Step 106\u003c\/p\u003e \u003cp\u003e5.2.3 Break Points 109\u003c\/p\u003e \u003cp\u003e5.3 Initial Operation Condition 110\u003c\/p\u003e \u003cp\u003e5.4 Graph-Based Transient Parallel Simulation 115\u003c\/p\u003e \u003cp\u003e5.5 Numerical Case Study 117\u003c\/p\u003e \u003cp\u003e5.6 Summary 123\u003c\/p\u003e \u003cp\u003eReferences 124\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Optimization Problems 125\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Optimization Theory 125\u003c\/p\u003e \u003cp\u003e6.2 Linear Programming 125\u003c\/p\u003e \u003cp\u003e6.2.1 The Simplex Method 127\u003c\/p\u003e \u003cp\u003e6.2.1.1 Basic Feasible Solution 127\u003c\/p\u003e \u003cp\u003e6.2.1.2 The Simplex Iteration 128\u003c\/p\u003e \u003cp\u003e6.2.2 Interior-Point Methods 132\u003c\/p\u003e \u003cp\u003e6.3 Nonlinear Programming 138\u003c\/p\u003e \u003cp\u003e6.3.1 Unconstrained Optimization Approaches 139\u003c\/p\u003e \u003cp\u003e6.3.1.1 Line Search 140\u003c\/p\u003e \u003cp\u003e6.3.1.2 Trust Region Optimization 141\u003c\/p\u003e \u003cp\u003e6.3.1.3 Quasi-Newton Method 141\u003c\/p\u003e \u003cp\u003e6.3.1.4 Double Dogleg Optimization 142\u003c\/p\u003e \u003cp\u003e6.3.1.5 Conjugate Gradient Optimization 143\u003c\/p\u003e \u003cp\u003e6.3.2 Constrained Optimization Approaches 145\u003c\/p\u003e \u003cp\u003e6.3.2.1 Karush–Kuhn–Tucker Conditions 145\u003c\/p\u003e \u003cp\u003e6.3.2.2 Linear Approximations of Nonlinear Programming with Linear Constraints 145\u003c\/p\u003e \u003cp\u003e6.3.2.3 Linear Approximations of Nonlinear Programming with Nonlinear Constraints 147\u003c\/p\u003e \u003cp\u003e6.4 Mixed Integer Optimization Approach 147\u003c\/p\u003e \u003cp\u003e6.4.1 Branch-and-Bound Approach 148\u003c\/p\u003e \u003cp\u003e6.4.2 Machine Learning for Branching 150\u003c\/p\u003e \u003cp\u003e6.5 Optimization Problems Solution by Graph Parallel Computing 151\u003c\/p\u003e \u003cp\u003e6.5.1 Simplex Method Based on Graph Parallel Computing 151\u003c\/p\u003e \u003cp\u003e6.5.2 Interior-Point Method Based on Graph Parallel Computing 154\u003c\/p\u003e \u003cp\u003eReferences 156\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Graph-Based Machine Learning 159\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 State of Art on PV Generation Forecasting 159\u003c\/p\u003e \u003cp\u003e7.2 Graph Machine Learning Model 160\u003c\/p\u003e \u003cp\u003e7.3 Convolutional Graph Auto-Encoder 162\u003c\/p\u003e \u003cp\u003e7.3.1 Auto-Encoder 162\u003c\/p\u003e \u003cp\u003e7.3.2 Auto-Encoder on Graphs 163\u003c\/p\u003e \u003cp\u003e7.3.3 Probability Distribution Function Approximation 164\u003c\/p\u003e \u003cp\u003e7.3.4 Convolutional Graph Auto-Encoder 167\u003c\/p\u003e \u003cp\u003e7.3.5 Graph Feature Extraction Artificial Neural Network (R(G)) 169\u003c\/p\u003e \u003cp\u003e7.3.6 Encoder (Q) and Decoder (P) 170\u003c\/p\u003e \u003cp\u003e7.3.7 Estimation of P(V∗\/ π) 171\u003c\/p\u003e \u003cp\u003eReferences 171\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart II Implementations and Applications 175\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Power Systems Modeling 177\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Power System Graph Modeling 177\u003c\/p\u003e \u003cp\u003e8.2 Physical Graph Model and Computing Graph Model 178\u003c\/p\u003e \u003cp\u003e8.3 Node-Breaker Model and Graph Representation 180\u003c\/p\u003e \u003cp\u003e8.4 Bus-Branch Model and Graph Representation 189\u003c\/p\u003e \u003cp\u003e8.5 Graph-Based Topology Analysis 190\u003c\/p\u003e \u003cp\u003e8.5.1 Substation-Level Topology Analysis 190\u003c\/p\u003e \u003cp\u003e8.5.2 System-Level Network Topology Analysis 196\u003c\/p\u003e \u003cp\u003eReferences 198\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 State Estimation Graph Computing 199\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Power System State Estimation 199\u003c\/p\u003e \u003cp\u003e9.2 Graph Computing-Based State Estimation 201\u003c\/p\u003e \u003cp\u003e9.2.1 State Estimation Graph Computing Algorithm 201\u003c\/p\u003e \u003cp\u003e9.2.1.1 Build Node-Based State Estimation 201\u003c\/p\u003e \u003cp\u003e9.2.1.2 Graph-Based State Estimation Parallel Algorithm 203\u003c\/p\u003e \u003cp\u003e9.2.2 Numerical Example 209\u003c\/p\u003e \u003cp\u003e9.2.3 Graph-Based State Estimation Implementation 215\u003c\/p\u003e \u003cp\u003e9.2.3.1 Graph-Based State Estimation Graph Schema 215\u003c\/p\u003e \u003cp\u003e9.2.3.2 Nodal Gain Matrix Formation 216\u003c\/p\u003e \u003cp\u003e9.2.3.3 Build RHS 219\u003c\/p\u003e \u003cp\u003e9.2.4 Graph-Based State Estimation Computation Efficiency 220\u003c\/p\u003e \u003cp\u003e9.3 Bad Data Detection and Identification 223\u003c\/p\u003e \u003cp\u003e9.3.1 Chi-Squares Test 224\u003c\/p\u003e \u003cp\u003e9.3.2 Advanced Bad Data Detection 224\u003c\/p\u003e \u003cp\u003e9.3.3 Bad Data Identification 228\u003c\/p\u003e \u003cp\u003e9.3.3.1 Normalized Residual 228\u003c\/p\u003e \u003cp\u003e9.3.3.2 Largest Normalized Residual for Bad Data Identification 229\u003c\/p\u003e \u003cp\u003e9.4 Graph-Based Bad Data Detection Implementation 229\u003c\/p\u003e \u003cp\u003eReferences 231\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Power Flow Graph Computing 233\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Power Flow Mathematical Model 233\u003c\/p\u003e \u003cp\u003e10.2 Gauss–Seidel Method 234\u003c\/p\u003e \u003cp\u003e10.3 Newton–Raphson Method 242\u003c\/p\u003e \u003cp\u003e10.3.1 Build Jacobian Graph 245\u003c\/p\u003e \u003cp\u003e10.3.2 Graph-Based Symbolic Factorization 247\u003c\/p\u003e \u003cp\u003e10.3.3 Graph-Based Elimination Tree Creation and Node Partition 249\u003c\/p\u003e \u003cp\u003e10.3.4 Graph Numerical Factorization 251\u003c\/p\u003e \u003cp\u003e10.3.5 Build Right-Hand Side 253\u003c\/p\u003e \u003cp\u003e10.3.6 Graph Forward and Backward Substitution 254\u003c\/p\u003e \u003cp\u003e10.3.7 Graph-Based Newton–Raphson Power Flow Calculation 255\u003c\/p\u003e \u003cp\u003e10.4 Fast Decoupled Power Flow Calculation 257\u003c\/p\u003e \u003cp\u003e10.4.1 Build B_P and B_PP Graphs 259\u003c\/p\u003e \u003cp\u003e10.5 Ill-Conditioned Power Flow Problem Solution 261\u003c\/p\u003e \u003cp\u003e10.5.1 Introduction 261\u003c\/p\u003e \u003cp\u003e10.5.2 Determine the Feasibility of the Power Flow 262\u003c\/p\u003e \u003cp\u003e10.5.3 Problem Formulation for Determining the Feasibility of Power Flow 263\u003c\/p\u003e \u003cp\u003e10.5.4 Power Flow Feasibility Verification 264\u003c\/p\u003e \u003cp\u003e10.5.5 Find a Feasible Solution for the Power Flow Problem 266\u003c\/p\u003e \u003cp\u003eReferences 271\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Contingency Analysis Graph Computing 273\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 dc Power Flow 273\u003c\/p\u003e \u003cp\u003e11.2 Bridge Search 276\u003c\/p\u003e \u003cp\u003e11.3 Conjugate Gradient for Postcontingency Power Flow Calculation 282\u003c\/p\u003e \u003cp\u003e11.4 Contingency Analysis Using Convolutional Neural Networks 294\u003c\/p\u003e \u003cp\u003e11.4.1 Convolutional Neural Network 295\u003c\/p\u003e \u003cp\u003e11.4.2 Convolutional Neural Network Components 297\u003c\/p\u003e \u003cp\u003e11.4.2.1 Convolutional Neural Network Input 297\u003c\/p\u003e \u003cp\u003e11.4.2.2 Convolutional Neural Network Output 297\u003c\/p\u003e \u003cp\u003e11.4.2.3 Convolutional Neural Network Convolutional Layer 297\u003c\/p\u003e \u003cp\u003e11.4.2.4 CNN Pooling Layer 298\u003c\/p\u003e \u003cp\u003e11.4.2.5 CNN Fully Connected Layer 299\u003c\/p\u003e \u003cp\u003e11.4.3 Evaluation Metrics 299\u003c\/p\u003e \u003cp\u003e11.4.3.1 Accuracy 299\u003c\/p\u003e \u003cp\u003e11.4.3.2 Precision 300\u003c\/p\u003e \u003cp\u003e11.4.3.3 Recall 300\u003c\/p\u003e \u003cp\u003e11.4.4 Implementation of Convolutional Neural Network 300\u003c\/p\u003e \u003cp\u003e11.5 Contingency Analysis Graph Computing Implementation 302\u003c\/p\u003e \u003cp\u003eReferences 306\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Economic Dispatch and Unit Commitment 309\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Classic Economic Dispatch 309\u003c\/p\u003e \u003cp\u003e12.1.1 Thermal Unit Economic Dispatch 309\u003c\/p\u003e \u003cp\u003e12.1.2 Hydrothermal Power Generation System Economic Dispatch 315\u003c\/p\u003e \u003cp\u003e12.2 Security-Constrained Economic Dispatch 320\u003c\/p\u003e \u003cp\u003e12.2.1 Generation Shift Factor Matrix 323\u003c\/p\u003e \u003cp\u003e12.2.2 Graph-Based SCED Modeling 325\u003c\/p\u003e \u003cp\u003e12.2.3 Graph-Based SCED 327\u003c\/p\u003e \u003cp\u003e12.2.3.1 Buildup Simplex Graph 328\u003c\/p\u003e \u003cp\u003e12.2.3.2 Graph-Based Simplex Method 331\u003c\/p\u003e \u003cp\u003e12.2.3.3 Update Power Flow 331\u003c\/p\u003e \u003cp\u003e12.2.3.4 Graph-Based SCED Implementation 333\u003c\/p\u003e \u003cp\u003e12.3 Security-Constrained Unit Commitment 334\u003c\/p\u003e \u003cp\u003e12.3.1 SCUC Model 334\u003c\/p\u003e \u003cp\u003e12.3.2 Graph-Based SCUC 335\u003c\/p\u003e \u003cp\u003e12.4 Numerical Case Study 336\u003c\/p\u003e \u003cp\u003e12.4.1 Graph-Based SCED Modeling 336\u003c\/p\u003e \u003cp\u003e12.4.2 Basic Feasible Solution 340\u003c\/p\u003e \u003cp\u003e12.4.3 Economic Dispatch Optimal Solution 342\u003c\/p\u003e \u003cp\u003eReferences 342\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Automatic Generation Control 345\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Classic Automatic Generation Control 345\u003c\/p\u003e \u003cp\u003e13.1.1 Speed Governor Control 345\u003c\/p\u003e \u003cp\u003e13.1.2 Speed Droop Function 347\u003c\/p\u003e \u003cp\u003e13.1.3 Frequency Supplementary Control 353\u003c\/p\u003e \u003cp\u003e13.1.4 Fundamentals of Automatic Generation Control 355\u003c\/p\u003e \u003cp\u003e13.2 Network Security-Constrained Automatic Generation Control 358\u003c\/p\u003e \u003cp\u003e13.3 Security-Constrained AGC Graph Computing 361\u003c\/p\u003e \u003cp\u003eReferences 364\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Small-Signal Stability 365\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 Small-Signal Stability of a Dynamic System 365\u003c\/p\u003e \u003cp\u003e14.2 System Linearization 366\u003c\/p\u003e \u003cp\u003e14.3 Small-Signal Stability Mode 367\u003c\/p\u003e \u003cp\u003e14.4 Single-Machine Infinite Bus System 367\u003c\/p\u003e \u003cp\u003e14.4.1 Classical Generator Model 367\u003c\/p\u003e \u003cp\u003e14.4.2 Third-Order Generator Model 369\u003c\/p\u003e \u003cp\u003e14.4.3 Numerical Case Study 373\u003c\/p\u003e \u003cp\u003e14.4.3.1 Stable Case 373\u003c\/p\u003e \u003cp\u003e14.4.3.2 Instable Case 376\u003c\/p\u003e \u003cp\u003e14.5 Small-Signal Oscillation Stabilization 378\u003c\/p\u003e \u003cp\u003e14.6 Eigenvalue Calculation 379\u003c\/p\u003e \u003cp\u003e14.6.1 Graph-Based Small-Signal Stability Analysis 382\u003c\/p\u003e \u003cp\u003e14.6.2 Buildup Small-Signal Stability Graph 383\u003c\/p\u003e \u003cp\u003e14.6.3 Numerical Example 383\u003c\/p\u003e \u003cp\u003eReferences 388\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 Transient Stability 391\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e15.1 Transient Stability Theory 391\u003c\/p\u003e \u003cp\u003e15.1.1 Stability Region and Boundary 391\u003c\/p\u003e \u003cp\u003e15.1.2 Energy Function Method 391\u003c\/p\u003e \u003cp\u003e15.1.2.1 Controlling UEP Method 392\u003c\/p\u003e \u003cp\u003e15.1.2.2 Stability-Region-Based Controlling UEP Method 393\u003c\/p\u003e \u003cp\u003e15.2 Transient Simulation Model 393\u003c\/p\u003e \u003cp\u003e15.2.1 Generator Rotor Model 393\u003c\/p\u003e \u003cp\u003e15.2.2 Generator Electro-Magnetic Model 394\u003c\/p\u003e \u003cp\u003e15.2.3 Excitation System Model 394\u003c\/p\u003e \u003cp\u003e15.2.4 Governor Model 396\u003c\/p\u003e \u003cp\u003e15.2.5 PSS Model 397\u003c\/p\u003e \u003cp\u003e15.3 Transient Simulation Approach 397\u003c\/p\u003e \u003cp\u003e15.3.1 Transient Simulation Algorithm 398\u003c\/p\u003e \u003cp\u003e15.3.2 Steady-State Equilibrium Condition 398\u003c\/p\u003e \u003cp\u003e15.3.3 Generator Injection Current 400\u003c\/p\u003e \u003cp\u003e15.4 Transient Simulation by Graph Parallel Computing 401\u003c\/p\u003e \u003cp\u003e15.4.1 Transient Simulation Graph 401\u003c\/p\u003e \u003cp\u003e15.4.2 Loading Data into Graph 403\u003c\/p\u003e \u003cp\u003e15.4.3 Graph-Based Transient Simulation Implementation 406\u003c\/p\u003e \u003cp\u003e15.5 Numerical Example 406\u003c\/p\u003e \u003cp\u003e15.5.1 Power Flow Data 406\u003c\/p\u003e \u003cp\u003e15.5.2 Dynamic Data 406\u003c\/p\u003e \u003cp\u003e15.5.3 Power Flow Results 409\u003c\/p\u003e \u003cp\u003e15.5.4 Steady-State Equilibrium Point 410\u003c\/p\u003e \u003cp\u003e15.5.5 Generator Injection Current Calculation 415\u003c\/p\u003e \u003cp\u003e15.5.6 Calculate Bus Voltage 416\u003c\/p\u003e \u003cp\u003e15.5.7 Simulation Results 416\u003c\/p\u003e \u003cp\u003eReferences 421\u003c\/p\u003e \u003cp\u003e\u003cb\u003e16 Graph-Based Deep Reinforcement Learning on Overload Control 425\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e16.1 Introduction 425\u003c\/p\u003e \u003cp\u003e16.2 DDPG Algorithm 426\u003c\/p\u003e \u003cp\u003e16.2.1 Terminology 426\u003c\/p\u003e \u003cp\u003e16.2.2 Q Function 427\u003c\/p\u003e \u003cp\u003e16.2.3 Q Value Approximation 427\u003c\/p\u003e \u003cp\u003e16.2.4 Policy Gradient 428\u003c\/p\u003e \u003cp\u003e16.3 Branch Overload Control 429\u003c\/p\u003e \u003cp\u003e16.3.1 States 429\u003c\/p\u003e \u003cp\u003e16.3.2 Actions 430\u003c\/p\u003e \u003cp\u003e16.3.3 Rewards 430\u003c\/p\u003e \u003cp\u003e16.4 Graph-Based Deep Reinforcement Learning Implementation 430\u003c\/p\u003e \u003cp\u003eReferences 433\u003c\/p\u003e \u003cp\u003e\u003cb\u003e17 Conclusions 435\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eAppendix 437\u003c\/p\u003e \u003cp\u003eIndex 481\u003c\/p\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Electronics \u0026amp; communications engineering [\u003ca title=\"See our other books on Electronics \u0026amp; communications engineering\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Electronics%20\u0026amp;%20communications%20engineering%20%5BTJ%5D%22\"\u003eTJ\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Wiley-IEEE Press","offers":[{"title":"Brand New","offer_id":52430994309400,"sku":"9781119903864","price":86.85,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9781119903864.jpg?v=1784768209","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/graph-database-and-graph-computing-for-power-system-analysis-hardback-9781119903864","provider":"Freshly Printed Books","version":"1.0","type":"link"}