Foreword and Acknowledgements xiii
1 Basics of Reactive Power 1
1.1 Chapter Overview 1
1.2 Phasors and Vector Diagrams 1
1.3 Definition of Different Types of Power 4
1.4 Definition of Power for Non-Sinusoidal Currents and Voltages 6
1.5 Equivalent Mechanical Model for Inductance 9
1.6 Equivalent Mechanical Model for Capacitance 11
1.7 Ohmic and Reactive Current 12
1.8 Summary 13
References 13
2 Reactive Power Consumers 15
2.1 Chapter Overview 15
2.2 Reactive Energy Demand 15
2.3 Simplified Model: Series Reactive Power Consumer 16
2.4 Realistic Model: Mixed Parallel and Series Reactive Power 16
2.5 Reactive Power Demand of Consumers 17
2.5.1 Asynchronous Motors 17
2.5.2 Transformers 18
2.5.3 Control Gear (Ballast) for Gas Discharge Lamps 18
2.6 Summary 21
3 Effect of Reactive Power on Electricity Generation, Transmission and Distribution 23
3.1 Chapter Overview 23
3.2 Loading of Generators and Equipment 23
3.3 Power System Losses 24
3.4 Generators 27
3.5 Voltage Drop 28
3.5.1 General 28
3.5.2 Transferable Power of Lines and Voltage Drop 29
3.5.3 Transformer Voltage Drop 32
3.6 Available Power of Transformers 34
3.7 Summary 35
4 Reactive Power in Standard Energy Contracts 37
4.1 Chapter Overview 37
4.2 Introduction 37
4.3 Reactive Energy to be Considered in Standardized Contracts of Suppliers 38
4.3.1 Pricing Dependent on Consumed Reactive Energy (kvarh) 38
4.3.2 Pricing Dependent on Consumed Apparent Energy (kVAh) 40
4.4 Importance of Reactive Power in Determining the Costs of Connection 42
4.5 Summary 42
Reference 42
5 Methods for the Determination of Reactive Power and Power Factor 43
5.1 Chapter Overview 43
5.2 Methods 43
5.2.1 Determination of Power Factor in Single-Phase Grids 43
5.2.2 Direct Indication of Power Factor by Means of Bruegers Device 44
5.2.3 Determination of Power Factor in Three-Phase System 44
5.2.4 Determination of Power Factor Using Portable Measuring Equipment 46
5.2.5 Determination of Power (Factor) via Recorded Data 48
5.2.6 Determination of Power Factor by Means of an Active Energy Meter 48
5.2.7 Determination of Power Factor by Means of an Active and Reactive Energy Meter 49
5.2.8 Determination of Power Factor via the Energy Bill 50
5.3 Summary 51
6 Improvement of Power Factor 53
6.1 Chapter Overview 53
6.2 Basics of Reactive Power Compensation 53
6.3 Limitation of Reactive Power without Phase Shifting 55
6.4 Compensation of Reactive Power by Rotational Phase-Shifting Machines 55
6.5 Compensation of Reactive Power by Means of Capacitors 56
6.6 Summary 58
7 Design, Arrangement and Power of Capacitors 61
7.1 Chapter Overview 61
7.2 Basics of Capacitors 61
7.3 Reactive Power of Capacitors 64
7.4 Different Technologies in Manufacturing Capacitors 65
7.4.1 Capacitors with Paper Insulation 65
7.4.2 Capacitors with Metallized Paper (MP Capacitor) 65
7.4.3 Capacitors with Metallized Plastic Foils 66
7.5 Arrangements and Reactive Power of Capacitors 66
7.5.1 Capacitors Connected in Parallel 67
7.5.2 Capacitors Connected in Series 67
7.5.3 Star and Delta Connection of Power Capacitors 68
7.6 Design of MV Capacitors 69
7.7 Long-Term Stability and Ageing of Capacitor Installations 69
7.7.1 General 69
7.7.2 Influence of Operating Voltage 70
7.7.3 Ageing in the Case of Detuned Capacitors 72
7.7.4 Ageing due to Switching Operations 73
7.8 Summary 73
References 73
8 Determination of Required Power of Capacitors 75
8.1 Chapter Overview 75
8.2 Basics of Calculation 75
8.3 Determination of Compensation at New Projected Plants 79
8.4 Summary 85
Reference 85
9 Types of Reactive Power Compensation 87
9.1 Chapter Overview 87
9.2 Single-Type Compensation 87
9.2.1 Single-Type Compensation in Asynchronous Motors 88
9.2.2 Single-Type Compensation of Transformers 97
9.2.3 Single-Type Compensation of Reactive Power for Welding Transformers 99
9.2.4 Single-Type Compensation of Fluorescent Lamps 103
9.3 Bulk-Type Compensation 108
9.4 Central-Type Compensation 111
9.5 Mixed Compensation 112
9.6 Advantages and Disadvantages of Different Types of Compensations 113
9.7 Summary 115
Reference 115
10 Compensation of Existing Installations 117
10.1 Chapter Overview 117
10.2 Methods of Determining the Reactive Power for Extension 117
10.3 Calculation of the Extension Unit by Means of Energy Invoices 118
10.4 Summary 121
11 Control of Reactive Power 123
11.1 Chapter Overview 123
11.2 General 123
11.2.1 Reactive Power Compensation Units 124
11.3 Control of Reactive Power by Automatic Reactive Power Controllers 124
11.3.1 General 124
11.3.2 Number of Steps and Reactive Power of the Capacitor Steps 125
11.3.3 Threshold Level C/k Value 131
11.3.4 Reverse Control Scheme (cos d Line) 133
11.3.5 Automatic Reactive Power Control 135
11.3.6 No-Volt Release Function 137
11.4 How to Wire a Power Factor Relay 137
11.5 Reactive Power Control by Mixed Measurement 138
11.6 Reactive Power Control with Multiple Feed-ins 140
11.6.1 Measuring by Means of Summation Current Transformer 140
11.6.2 Parallel Operation of Compensation Banks for Each Incoming Supply 142
11.7 Performances of Automatic Compensation Banks 144
11.8 Summary 146
12 Discharging Devices for Power Capacitors 147
12.1 Chapter Overview 147
12.2 Basis at LV Applications 147
12.2.1 Rapid Discharging with Additional Resistances Switched in 150
12.2.2 Discharging Capacitors by Means of Reactors 150
12.3 Discharging Devices in MV Capacitors 152
12.3.1 MV Capacitors to be Discharged by Resistances 152
12.3.2 MV Capacitors to be Discharged by Reactors 154
12.4 Calculation of the Electric Charge to be Stored on an MV Capacitor 154
12.5 Summary 156
13 Protection of Capacitors and Compensations 157
13.1 Chapter Overview 157
13.2 Protection against Overcurrent and Short Circuit 157
13.3 Overvoltage Protection 158
13.4 Protection against Overtemperatures 158
13.5 Protection against Internal Faults 158
13.5.1 Protection against Voltage Flashover 159
13.5.2 Self-healing Technology 159
13.5.3 Protection against Overheating and Internal Overpressure 159
13.6 Protection by Balance Observation at Single-Phase MV Capacitors 162
13.7 Summary 163
Reference 163
14 Switching of Capacitors 165
14.1 Chapter Overview 165
14.2 General 165
14.3 Selection of Switchgear 167
14.3.1 Air Contactors 168
14.3.2 Circuit Breakers 169
14.3.3 Switch Fuses and Magnetic Trips 169
14.4 Switching by Semiconductors (Thyristor Modules) 169
14.4.1 General 169
14.4.2 Static Contactors for Switching Capacitors up to 415 V 171
14.4.3 Static Contactors for Switching Capacitors of Rated Voltage Higher than 500 V 173
14.4.4 Power Factor Relays for Static Contactors 173
14.4.5 Dynamic Reactive Power Compensation (Ready to Install) 174
14.5 Summary 175
Reference 175
15 Installation, Disturbances and Maintenance 177
15.1 Chapter Overview 177
15.2 Installation of Automatically Controlled Compensation Banks 177
15.3 Automatic Compensation Banks: Setting into Operation 178
15.3.1 Selection of Current Transformer (CT) and Determination of the CT Cable 178
15.3.2 Preset Switching Time Delay per Capacitor Step 183
15.4 Disturbances and How to Solve Them 184
15.5 Working and Maintenance 185
15.6 Summary 187
References 187
16 Reactive Power Compensation in Electrical Plants with Generators 189
16.1 Chapter Overview 189
16.2 General 189
16.3 Automatic Control of Reactive Power within Four Quadrants 190
16.3.1 Technical Considerations 190
16.3.2 Bargaining Considerations 192
16.4 Summary 193
References 194
17 Effects of Perturbation Considering Especially the Impact of Harmonics on Power Factor Correction Capacitors 195
17.1 Chapter Overview 195
17.2 Perturbations and Improved Power Quality for Business Customers 196
17.3 Measuring and Analysis 198
17.4 Summary 203
References 204
18 Resonances in Electrical Power Systems 205
18.1 Chapter Overview 205
18.2 Parallel Resonance Circuit 205
18.3 Series Resonance Circuit 208
18.4 Typical Resonances in Power Systems 208
18.4.1 Resonance due to Reactive Power Compensation in 6 kV System 208
18.4.2 Parallel Resonance in a 30 kV Industrial System 210
18.4.3 Impedance in Urban 10 kV System 212
18.5 Summary 212
Reference 212
19 Reactor-Protected Capacitors and Filter Circuits 213
19.1 Chapter Overview 213
19.2 Effect of Reactor-Protected Systems and System Configuration 214
19.2.1 Effect of Reactor-Protected Systems 214
19.2.2 System Configuration of Reactor-Protected Capacitor Banks 217
19.3 Notes on the Selection of Reactors 220
19.4 Influence of the Reactor Rate on the Capacitors Lifetime 222
19.5 Filter Effect with Detuned Filters 223
19.6 Filter Circuits 225
19.6.1 General 225
19.6.2 Active Filters 227
19.6.3 Passive Filters 229
19.6.4 Comparison of Active and Passive Filters 233
19.7 Neutral Line Harmonic Filtering 233
19.7.1 General 233
19.7.2 Special Features of the Third Harmonic 234
19.7.3 Network Relief by the Neutral Line Harmonic Filter 235
19.8 Summary 238
References 239
20 Dynamic Reactive Power Compensation Systems 241
20.1 Chapter Overview 241
20.1.1 Improvement of Power Quality via Dynamic Reactive Power Compensation Systems 242
20.2 Motor Startup Compensation 245
20.3 Flicker Compensation 245
20.4 Evaluation of Power Factor Correction Solutions as Seen by the Distribution System Operator (Power Utility) 251
20.5 Summary 252
References 252
21 Compensation Effects at Rectifiers 253
21.1 Chapter Overview 253
21.1.1 General 253
21.2 Compensation Bank at a Six-Pulse Rectifier 254
21.2.1 Time Courses of Voltage and Current at a Three-Phase Bridge-Connected Rectifier 256
21.2.2 How Compensation Banks Affect Three-Phase Bridge-Connected Rectifiers 257
21.3 Characteristic Behaviour of Reactive Power Controllers at Rectifiers 260
21.4 Summary 261
References 261
22 Environmental and Climate Protection Using Capacitors 263
22.1 Chapter Overview 263
22.2 PCB-Filled Capacitors 263
22.3 Climate Change and Energy Efficiency through Power Factor Correction 264
22.4 Summary 267
References 267
Symbols and Abbreviations 269
Index 273
