Reactive Power Compensation
A Practical Guide

The area of reactive power compensation is gaining increasing importance worldwide. If suitably designed, it is capable of improving voltage quality significantly, meaning that losses in equipment and power systems are reduced, the permissible loading of equipment can be increased, and the over-all stability of system operation improved. Ultimately, energy use and CO₂ emisson are reduced.

This unique guide discusses the effects of reactive power on generation, transmission and distribution, and looks at the compensation of existing installations in detail. It outlines methods for determination of reactive power and answers the questions that arise when controlling it, for example, at parallel operation with generators. There is also a chapter devoted to installation, maintenance and disturbances.

Key features include:

• A concise overview as well as deep specific knowledge on the segment power factor regulation and network quality
• Theory of reactive power compensation coupled with typical application examples such as car manufacturing, metal rolling and chemical works
• Chapter summaries with charts explaining how to put the theory into practice
• Coverage on the cost-saving aspects of this technology, including the efficient use of energy and the reduction of CO₂

A practical guide for electrical engineers and technicians in utilities, this is also essential reading for maintenance engineers, designers, electrical contractors, manufacturing companies, and researchers, also those in industry and planning agencies. Insightful and clear, the book will also appeal to senior undergraduate and graduate electrical engineering students and professors.

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 Brueger’s 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 ϕd 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 Capacitor’s 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

Wolfgang Hofmann, Reactive Power Engineering, Munich, Germany

Jürgen Schlabbach, University of Applied Sciences, Bielefeld, Germany

Wolfgang Just, Engineering Consultant, Dorsten, Germany