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xiii | |
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xxv | |
Preface |
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xxvii | |
Acronyms |
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xxxi | |
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1 Definitions objectives and background |
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1 | (10) |
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1 | (1) |
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1.2 Classification of electromagnetic transients |
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2 | (1) |
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3 | (1) |
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4 | (2) |
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1.4.1 State variable analysis |
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5 | (1) |
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1.4.2 Method of difference equations |
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5 | (1) |
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1.5 Historical perspective |
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6 | (2) |
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1.6 Range of applications |
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8 | (1) |
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8 | (3) |
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2 Analysis of continuous and discrete systems |
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11 | (24) |
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11 | (1) |
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11 | (18) |
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2.2.1 State variable formulations |
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12 | (8) |
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2.2.2 Time-domain solution of state equations |
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20 | (1) |
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2.2.3 Digital simulation of continuous systems |
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21 | (8) |
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29 | (2) |
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2.4 Relationship of continuous and discrete domains |
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31 | (1) |
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31 | (2) |
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33 | (2) |
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3 State variable analysis |
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35 | (32) |
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35 | (1) |
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3.2 Choice of state variables |
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35 | (2) |
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3.3 Formation of the state equations |
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37 | (5) |
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3.3.1 The transform method |
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37 | (3) |
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40 | (2) |
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42 | (2) |
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3.5 Transient converter simulation |
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44 | (15) |
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45 | (1) |
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45 | (4) |
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49 | (1) |
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49 | (4) |
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3.5.5 Effect of automatic time-step adjustments |
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53 | (3) |
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3.5.6 TCS converter control |
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56 | (3) |
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59 | (4) |
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63 | (1) |
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64 | (3) |
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4 Numerical integrator substitution |
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67 | (32) |
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67 | (1) |
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4.2 Discretisation of R, L, C elements |
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67 | (7) |
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67 | (1) |
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68 | (1) |
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69 | (2) |
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4.2.4 Components reduction |
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71 | (3) |
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4.3 Dual Norton model of the transmission line |
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74 | (2) |
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76 | (12) |
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4.4.1 Example: conversion of voltage sources to current sources |
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77 | (1) |
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4.4.2 Network solution with switches |
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78 | (2) |
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4.4.3 Example: voltage step applied to RL load |
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80 | (8) |
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4.5 Non-linear or time varying parameters |
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88 | (4) |
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4.5.1 Current-source representation |
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88 | (1) |
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4.5.2 Compensation method |
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89 | (2) |
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4.5.3 Piecewise linear method |
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91 | (1) |
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92 | (2) |
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4.7 Sparsity and optimal ordering |
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94 | (3) |
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4.8 Numerical errors and instabilities |
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97 | (1) |
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97 | (1) |
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98 | (1) |
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5 The root-matching method |
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99 | (22) |
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99 | (1) |
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5.2 Exponential form of the difference equation |
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99 | (3) |
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5.3 z-Domain representation of difference equations |
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102 | (2) |
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5.4 Implementation in EMTP algorithm |
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104 | (7) |
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5.5 Family of exponential forms of the difference equation |
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111 | (6) |
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113 | (2) |
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5.5.2 Steady-state response |
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115 | (1) |
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116 | (1) |
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117 | (2) |
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119 | (1) |
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120 | (1) |
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6 Transmission lines and cables |
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121 | (34) |
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121 | (1) |
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121 | (6) |
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6.2.1 Multi-conductor transmission lines |
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124 | (3) |
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6.3 Frequency-dependent transmission lines |
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127 | (8) |
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6.3.1 Frequency to time-domain transformation |
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130 | (5) |
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135 | (1) |
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6.4 Overhead transmission line parameters |
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135 | (3) |
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6.4.1 Bundled sub-conductors |
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137 | (1) |
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138 | (1) |
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6.5 Underground cable parameters |
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138 | (5) |
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143 | (10) |
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153 | (1) |
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153 | (2) |
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7 Transformers and rotating plant |
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155 | (36) |
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155 | (1) |
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7.2 Basic transformer model |
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155 | (7) |
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7.2.1 Numerical implementation |
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157 | (1) |
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7.2.2 Parameters derivation |
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158 | (2) |
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7.2.3 Modelling of non-linearities |
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160 | (2) |
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7.3 Advanced transformer models |
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162 | (10) |
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7.3.1 Single-phase UMEC model |
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162 | (4) |
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7.3.2 UMEC implementation in PSCAD/EMTDC |
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166 | (2) |
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7.3.3 Three-limb three-phase UMEC |
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168 | (3) |
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7.3.4 Fast transient models |
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171 | (1) |
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7.4 The synchronous machine |
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172 | (15) |
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7.4.1 Electromagnetic model |
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172 | (7) |
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7.4.2 Electro-mechanical model |
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179 | (2) |
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7.4.3 Interfacing machine to network |
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181 | (4) |
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7.4.4 Types of rotating machine available |
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185 | (2) |
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187 | (1) |
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187 | (4) |
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191 | (24) |
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191 | (1) |
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8.2 Transient analysis of control systems |
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191 | (2) |
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8.3 Control modelling in PSCAD/EMTDC |
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193 | (10) |
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196 | (7) |
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8.4 Modelling of protective systems |
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203 | (8) |
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203 | (3) |
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8.4.2 Electromechanical relays |
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206 | (1) |
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207 | (1) |
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8.4.4 Microprocessor-based relays |
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207 | (1) |
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208 | (1) |
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209 | (2) |
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211 | (1) |
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212 | (3) |
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9 Power electronic systems |
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215 | (34) |
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215 | (1) |
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9.2 Valve representation in EMTDC |
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215 | (2) |
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9.3 Placement and location of switching instants |
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217 | (1) |
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9.4 Spikes and numerical oscillations (chatter) |
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218 | (9) |
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9.4.1 Interpolation and chatter removal |
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220 | (7) |
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227 | (4) |
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9.6 Example of HVDC simulation |
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231 | (1) |
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231 | (10) |
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9.7.1 The static VAr compensator |
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231 | (8) |
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9.7.2 The static compensator (STATCOM) |
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239 | (2) |
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9.8 State variable models |
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241 | (5) |
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9.8.1 EMTDC/TCS interface implementation |
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241 | (3) |
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9.8.2 Control system representation |
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244 | (2) |
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246 | (1) |
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246 | (3) |
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10 Frequency-dependent network equivalents |
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249 | (28) |
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249 | (1) |
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250 | (1) |
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10.3 Extent of system to be reduced |
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250 | (1) |
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250 | (1) |
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10.5 System frequency response |
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251 | (9) |
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10.5.1 Frequency-domain identification |
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252 | (8) |
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10.5.2 Time-domain identification |
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260 | (1) |
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10.6 Fitting of model parameters |
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260 | (4) |
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260 | (2) |
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262 | (2) |
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264 | (1) |
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10.8 Model implementation |
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264 | (1) |
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265 | (8) |
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273 | (2) |
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275 | (2) |
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11 Steady-state assessment |
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277 | (18) |
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277 | (1) |
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11.2 Phase-dependent impedance of non-linear device |
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278 | (3) |
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11.3 The time-domain in an ancillary capacity |
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281 | (4) |
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11.3.1 Iterative solution for time invariant non-linear components |
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281 | (1) |
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11.3.2 Iterative solution for general non-linear components |
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282 | (2) |
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11.3.3 Acceleration techniques |
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284 | (1) |
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11.4 The time-domain in the primary role |
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285 | (5) |
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11.4.1 Harmonic assessment historically |
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285 | (1) |
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11.4.2 Basic time-domain algorithm |
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286 | (1) |
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287 | (1) |
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11.4.4 Dc System representation |
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287 | (1) |
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11.4.5 Ac System representation |
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287 | (3) |
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290 | (2) |
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292 | (3) |
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12 Mixed time-frame simulation |
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295 | (20) |
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295 | (2) |
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12.2 Description of the hybrid algorithm |
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297 | (2) |
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12.2.1 Individual program modifications |
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299 | (1) |
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299 | (1) |
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299 | (6) |
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12.3.1 Equivalent impedances |
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300 | (2) |
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12.3.2 Equivalent sources |
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302 | (1) |
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12.3.3 Phase and sequence data conversions |
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302 | (1) |
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12.3.4 Interface variables derivation |
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303 | (2) |
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12.4 EMTDC to TS data transfer |
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305 | (1) |
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12.4.1 Data extraction from converter waveforms |
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305 | (1) |
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12.5 Interaction protocol |
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306 | (2) |
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308 | (1) |
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12.7 Test system and results |
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309 | (2) |
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311 | (1) |
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312 | (3) |
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13 Transient simulation in real-time |
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315 | (14) |
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315 | (3) |
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13.2 Simulation with dedicated architectures |
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318 | (5) |
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319 | (2) |
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321 | (2) |
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13.3 Real-time and near real-time on standard computers |
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323 | (2) |
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13.3.1 Example of real-time test |
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324 | (1) |
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325 | (1) |
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325 | (4) |
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329 | (106) |
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329 | (2) |
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14.1.1 Modelling considerations |
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330 | (1) |
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14.1.2 Time-step and plot-step |
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330 | (1) |
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14.1.3 Avoiding singularities |
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331 | (1) |
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331 | (1) |
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331 | (10) |
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332 | (4) |
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14.2.2 Back-flashover modelling |
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336 | (1) |
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14.2.3 Surge arrester modelling |
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337 | (1) |
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14.2.4 Direct lightning strike to phase conductor |
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338 | (1) |
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14.2.5 Lightning strike to ground wire or tower |
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338 | (3) |
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14.3 Capacitor switching studies |
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341 | (22) |
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342 | (9) |
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14.3.2 Back-to-back switching |
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351 | (5) |
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14.3.3 Voltage magnification |
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356 | (7) |
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14.4 Transformer energisation |
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363 | (10) |
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14.4.1 Parallel sympathetic interaction |
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367 | (5) |
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372 | (1) |
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372 | (1) |
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372 | (1) |
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14.5 Transient recovery voltage studies |
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373 | (11) |
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384 | (4) |
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385 | (3) |
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14.7 Voltage fluctuations |
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388 | (5) |
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14.7.1 Modelling of flicker penetration |
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390 | (3) |
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393 | (2) |
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395 | (9) |
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398 | (2) |
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400 | (4) |
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14.10 Solar photovoltaic farm |
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404 | (5) |
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409 | (10) |
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410 | (6) |
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416 | (3) |
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419 | (5) |
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14.13 Electric vehicle charging |
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424 | (2) |
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14.14 Heat-pumps/air-conditioners |
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426 | (3) |
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429 | (3) |
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432 | (1) |
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432 | (3) |
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Appendix A System identification techniques |
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435 | (10) |
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A.1 s-Domain identification (frequency-domain) |
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435 | (2) |
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A.2 z-Domain identification (frequency-domain) |
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437 | (2) |
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A.3 z-Domain identification (time-domain) |
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439 | (1) |
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440 | (2) |
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A.5 Recursive least-squares curve-fitting algorithm |
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442 | (3) |
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Appendix B Numerical integration |
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445 | (8) |
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B.1 Review of classical methods |
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445 | (3) |
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B.2 Truncation error of integration formulae |
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448 | (2) |
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B.3 Stability of integration methods |
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450 | (3) |
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Appendix C Test systems data |
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453 | (8) |
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C.1 CIGRE HVDC benchmark model |
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453 | (1) |
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C.2 Lower South Island (New Zealand) system |
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453 | (8) |
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Appendix D Developing difference equations |
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461 | (8) |
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D.1 Root-matching technique applied to a first-order lag function |
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461 | (1) |
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D.2 Root-matching technique applied to a first-order differential pole function |
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462 | (1) |
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D.3 Difference equation by bilinear transformation for RL series branch |
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463 | (1) |
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D.4 Difference equation by numerical integrator substitution for RL series branch |
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463 | (3) |
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D.5 Equivalence of trapezoidal rule and bilinear transform |
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466 | (3) |
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Appendix E MATLAB® code examples |
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469 | (16) |
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E.1 Voltage step on RL branch |
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469 | (1) |
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470 | (2) |
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E.3 General version of example E.2 |
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472 | (9) |
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E.4 Frequency response of difference equations |
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481 | (4) |
Index |
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485 | |