Preface and Acknowledgments |
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xiii | |
Chapter 1 Winding Distribution in an Ideal Machine |
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1 | (76) |
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1 | (1) |
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2 | (6) |
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1.3 Calculation of the Winding Function |
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8 | (13) |
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1.4 Multipole Winding Configurations |
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21 | (4) |
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1.5 Inductances of an Ideal Doubly Cylindrical Machine |
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25 | (4) |
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1.6 Calculation of Winding Inductances |
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29 | (3) |
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1.7 Mutual Inductance Calculation - An Example |
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32 | (7) |
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1.8 Winding Functions for Multiple Circuits |
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39 | (7) |
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1.9 Analysis of a Shorted Coil - An Example |
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46 | (3) |
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1.10 General Case for C Circuits |
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49 | (4) |
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1.11 Winding Function Modifications for Salient-Pole Machines |
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53 | (11) |
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1.12 Leakage Inductances of Synchronous Machines |
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64 | (6) |
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1.12.1 The Synchronous Machine Stator |
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64 | (5) |
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1.12.2 The Synchronous Machine Rotor |
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69 | (1) |
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1.13 Practical Winding Design |
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70 | (6) |
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76 | (1) |
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76 | (1) |
Chapter 2 Reference Frame Theory |
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77 | (60) |
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77 | (1) |
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2.2 Rotating Reference Frames |
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78 | (3) |
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2.3 Transformation of Three-Phase Circuit Variables to a Rotating Reference Frame |
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81 | (15) |
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2.3.1 Vector Approach Applied to r-L Circuits |
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81 | (4) |
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2.3.2 Transformation Equations |
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85 | (7) |
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2.3.3 System Equations in the d-q-n Coordinate System |
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92 | (3) |
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2.3.4 Power Flow in the d-q-n Equivalent Circuits |
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95 | (1) |
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2.4 Stationary Three-Phase r-L Circuits Observed in a d-q-n Reference Frame |
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96 | (18) |
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104 | (10) |
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2.5 Matrix Approach to the d-q-n Transformation |
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114 | (7) |
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117 | (4) |
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2.6 The d-q-n Transformation Applied to a Simple Three-Phase Cylindrical Inductor |
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121 | (5) |
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2.7 Winding Functions in a d-q-n Reference Frame |
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126 | (5) |
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2.8 Direct Computation of d-q-n Inductances of a Cylindrical Three- Phase Inductor |
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131 | (3) |
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134 | (1) |
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134 | (3) |
Chapter 3 The d-q Equations of a Synchronous Machine |
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137 | (56) |
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137 | (1) |
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137 | (1) |
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3.3 Synchronous Machine Equations in the Phase Variable or as-, bs-, cs- Reference Frame |
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138 | (5) |
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140 | (2) |
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3.2.2 Flux Linkage Equations |
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142 | (1) |
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3.4 Transformation of the Stator Voltage Equations to a Rotating Reference Frame |
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143 | (1) |
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3.5 Transformation of Stator Flux Linkages to a Rotating Reference Frame |
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144 | (2) |
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3.6 Winding Functions of the Three-Phase Stator Windings in a d-q-n Reference Frame |
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146 | (2) |
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3.7 Winding Functions of the Rotor Windings |
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148 | (12) |
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3.7.1 The d-Axis Amortisseur Winding Function |
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148 | (7) |
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3.7.2 The q-Axis Amortisseur Circuit Winding Function |
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155 | (4) |
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3.7.3 The Field Circuit Winding Function |
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159 | (1) |
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3.8 Calculation of Stator Magnetizing Inductances |
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160 | (4) |
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3.9 Mutual Inductances Between Stator and Rotor Circuits |
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164 | (3) |
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3.10 d-q Transformation of the Rotor Flux Linkage Equation |
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167 | (1) |
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168 | (1) |
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169 | (2) |
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3.13 Summary of Synchronous Machine Equations Expressed in Physical Units |
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171 | (1) |
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3.14 Turns Ratio Transformation of the Flux Linkage Equations |
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172 | (8) |
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3.15 System Equations in Physical Units Using Hybrid Flux Linkages |
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180 | (1) |
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3.16 Synchronous Machine Equations in Per Unit |
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181 | (9) |
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181 | (2) |
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183 | (1) |
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3.16.3 Flux Linkage Equations |
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184 | (1) |
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3.16.4 Electromagnetic Torque Equation |
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185 | (1) |
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186 | (1) |
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187 | (1) |
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187 | (3) |
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190 | (1) |
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190 | (3) |
Chapter 4 Steady State Behavior of Synchronous Machines |
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193 | (72) |
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193 | (1) |
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193 | (3) |
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4.3 Steady State Form of Park's Equations |
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196 | (4) |
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4.4 Steady State Torque Equation |
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200 | (2) |
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4.5 Steady State Power Equation |
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202 | (2) |
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4.6 Steady State Reactive Power |
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204 | (1) |
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4.7 Graphical Interpretation of the Steady State Equations |
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204 | (3) |
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4.8 Steady State Vector Diagram |
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207 | (3) |
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4.9 Vector Interpretation of Power and Torque |
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210 | (6) |
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4.10 Phasor Form of the Steady State Equations |
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216 | (1) |
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4.11 Equivalent Circuits of a Synchronous Machine |
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217 | (4) |
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4.12 Solutions of the Phasor Equations |
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221 | (2) |
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4.13 Solution of the Steady State Synchronous Machine Equations Using MathCAD |
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223 | (3) |
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4.14 Open-Circuit and Short-Circuit Characteristics |
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226 | (7) |
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4.15 Saturation Modeling of Synchronous Machines Under Load |
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233 | (5) |
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4.16 Construction of the Phasor Diagram for a Saturated Round-Rotor Machine |
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238 | (2) |
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4.17 Calculation of the Phasor Diagram for a Saturated Salient-Pole Synchronous Machine |
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240 | (1) |
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4.18 The Zero Power Factor Characteristic and the Potier Triangle |
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241 | (7) |
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4.19 Other Reactance Measurements |
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248 | (3) |
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4.20 Steady State Operating Characteristics |
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251 | (2) |
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4.21 Calculation of Pulsating and Average Torque During Starting of Synchronous Motors |
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253 | (9) |
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262 | (1) |
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263 | (2) |
Chapter 5 Transient Analysis of Synchronous Machines |
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265 | (50) |
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265 | (1) |
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5.2 Theorem of Constant Flux Linkages |
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265 | (1) |
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5.3 Behavior of Stator Flux Linkages on Short Circuit |
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266 | (1) |
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5.4 Three-Phase Short Circuit, No Damper Circuits, Resistances Neglected |
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267 | (3) |
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5.5 Three-Phase Short Circuit from Open Circuit, Resistances and Damper Windings Neglected |
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270 | (2) |
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5.6 Short Circuit From Loaded Condition, Stator Resistance and Damper Winding Neglected |
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272 | (3) |
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5.7 Three-Phase Short Circuit from Open Circuit, Effect of Resistances Included, No Dampers |
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275 | (7) |
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5.8 Extension of the Theory to Machines with Damper Windings |
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282 | (8) |
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5.9 Short Circuit of a Loaded Generator, Dampers Included |
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290 | (1) |
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5.10 Vector Diagrams for Sudden Voltage Changes |
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291 | (4) |
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5.11 Effect of Exciter Response |
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295 | (2) |
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5.12 Transient Solutions Utilizing Modal Analysis |
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297 | (9) |
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5.13 Comparison of Modal Analysis Solution with Conventional Methods |
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306 | (4) |
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5.14 Unsymmetrical Short Circuits |
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310 | (2) |
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312 | (1) |
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312 | (3) |
Chapter 6 Power System Transient Stability |
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315 | (34) |
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315 | (1) |
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315 | (3) |
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318 | (2) |
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6.4 Mechanical Acceleration Equation in Per Unit |
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320 | (2) |
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6.5 Equal Area Criterion for Transient Stability |
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322 | (1) |
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6.6 Transient Stability Analysis |
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323 | (8) |
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6.7 Transient Stability of a Two Machine System |
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331 | (2) |
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6.8 Multi-Machine Transient Stability Analysis |
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333 | (4) |
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6.9 Types of Faults and Effect on Stability |
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337 | (3) |
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6.10 Step-by-Step Solution Methods Including Saturation |
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340 | (2) |
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6.11 Machine Model Including Saturation |
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342 | (5) |
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6.12 Summary-Step-by-Step Method for Calculating Synchronous Machine Transients |
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347 | (1) |
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348 | (1) |
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348 | (1) |
Chapter 7 Excitation Systems and Dynamic Stability |
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349 | (46) |
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349 | (1) |
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7.2 Generator Response to System Disturbances |
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350 | (2) |
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7.3 Sources of System Damping |
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352 | (1) |
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7.4 Excitation System Hardware Implementations |
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353 | (12) |
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7.4.1 Basic Excitation System |
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353 | (1) |
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353 | (4) |
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7.4.3 Modeling of Saturation |
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357 | (5) |
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7.4.4 AC Excitation Systems |
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362 | (1) |
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7.4.5 Static Excitation Systems |
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363 | (2) |
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7.5 IEEE Type 1 Excitation System |
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365 | (4) |
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7.6 Excitation Design Principles |
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369 | (5) |
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7.7 Effect of the Excitation System on Dynamic Stability |
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374 | (18) |
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7.7.1 Generator Operating with Constant Field Flux Linkages |
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374 | (6) |
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7.7.2 Generator with Variable Field Flux Linkages |
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380 | (6) |
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7.7.3 Closed Loop Representation |
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386 | (4) |
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7.7.4 Excitation Control of Other Terminal Quantities |
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390 | (2) |
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392 | (2) |
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394 | (1) |
Chapter 8 Naturally Commutated Synchronous Motor Drives |
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395 | (44) |
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395 | (1) |
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8.2 Load Commutated Inverter (LCI) Synchronous Motor Drives |
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395 | (2) |
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8.3 Principle of Inverter Operation |
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397 | (2) |
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8.4 Fundamental Component Representation |
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399 | (7) |
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399 | (2) |
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401 | (4) |
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8.4.3 Expression for Power and Torque |
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405 | (1) |
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8.5 Control Considerations |
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406 | (2) |
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8.5.1 Firing Angle Controller |
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406 | (2) |
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8.6 Starting Considerations |
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408 | (1) |
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8.7 Detailed Steady State Analysis |
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408 | (16) |
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8.7.1 Modes of Converter Operation |
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411 | (2) |
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413 | (1) |
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8.7.3 Conduction Mode 1 State Equations |
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414 | (3) |
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8.7.4 Commutation Mode 2 State Equations |
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417 | (4) |
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8.7.5 Calculation of Initial Conditions |
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421 | (3) |
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424 | (1) |
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425 | (2) |
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8.10 Torque Capability Curves |
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427 | (5) |
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8.11 Constant Speed Performance |
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432 | (2) |
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8.12 Comparison of State Space and Phasor Diagram Solutions |
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434 | (2) |
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436 | (1) |
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437 | (2) |
Chapter 9 Extension of d-q Theory to Unbalanced Operation |
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439 | (28) |
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439 | (1) |
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9.2 Source Voltage Formulation |
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439 | (4) |
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9.3 System Equations to Be Solved |
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443 | (3) |
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9.4 System Formulation with Non-Sinusoidal Stator Voltages |
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446 | (5) |
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9.5 Solution for Currents |
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451 | (2) |
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9.6 Solution for Electromagnetic Torque |
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453 | (9) |
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462 | (2) |
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464 | (3) |
Chapter 10 Linearization of the Synchronous Machine Equations |
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467 | (30) |
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467 | (1) |
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10.2 Park's Equations in Physical Units |
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467 | (2) |
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10.3 Linearization Process |
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469 | (5) |
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10.4 Transfer Functions of a Synchronous Machine |
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474 | (5) |
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10.4.1 Transfer Function Inputs |
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474 | (1) |
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10.4.2 Transfer Function Outputs |
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475 | (4) |
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10.5 Solution of the State Space and Measurement Equations |
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479 | (6) |
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10.6 Design of a Terminal Voltage Controller |
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485 | (5) |
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10.7 Design of a Classical Regulator |
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490 | (5) |
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495 | (1) |
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496 | (1) |
Chapter 11 Computer Simulation of Synchronous Machines |
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497 | (50) |
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497 | (1) |
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11.2 Simulation Equations |
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497 | (3) |
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11.3 MATLAB Simulation of Park's Equations |
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500 | (3) |
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11.4 Steady State Check of Simulation |
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503 | (4) |
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11.5 Simulation of the Equations of Transformation |
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507 | (11) |
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518 | (2) |
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11.7 Consideration of Saturation Effects |
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520 | (5) |
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525 | (4) |
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529 | (2) |
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11.10 Approximate Models of Synchronous Machines |
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531 | (12) |
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543 | (4) |
Appendix 1 Identities Useful in AC Machine Analysis |
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547 | (2) |
Appendix 2 Time Domain Solution of the State Equation |
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549 | (6) |
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A2.1 Reduction to Explicit Form |
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549 | (3) |
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552 | (1) |
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553 | (2) |
Appendix 3 Three-Phase Fault |
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555 | (8) |
Appendix 4 TrafunSM |
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563 | (8) |
Appendix 5 SMHB Synchronous Machine Harmonic Balance |
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571 | (12) |
Index |
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583 | |