Harold Kirkham works as a Research Engineer with the Advanced Power and Energy Systems Group at the Pacific Northwest National Laboratory. He is an internationally recognized expert and teacher on measurement in power systems.

Jan-Philipp Kitzig is a Research and Development Metrology Engineer with EA Elektro Automatik in Viersen, Germany.

David Laverty is a Reader in Electrical & Electronic Engineering at Queen's University Belfast.

Artis Riepnieks is an Electrical Research Engineer in Systems Engineering at Pacific Northwest National Laboratory.

Dani Strickland is a Senior Lecturer, Reader, and Professor at Loughborough University, United Kingdom.

Rod White is an Independent Researcher, formerly a Distinguished Scientist at the Measurement Standards Laboratory of New Zealand.

About the Authors xi

Preface xiii

Acknowledgments xix

1 Measurement: A New View 1

1.1 The Importance of Measurement 1

1.2 Power Factor and the AIEE-NELA Committee 4

1.3 The Joint Committee Failure 6

1.4 Three Kinds of Metrology 9

1.5 Legal Metrology 9

1.6 Scientific Metrology 13

1.7 Commercial Metrology 15

1.8 A New View Needed 16

1.9 Philosophy 17

1.10 The Conceptual and the Physical 18

1.11 Conceptual and Physical-More History 20

1.12 The Magical Role of the A/D Converter 23

1.13 A Perspective of This Book 24

1.14 Chapter Summary: History 24

1.15 Chapter Summary: Takeaways 25

References 25

2 Measurement: An Overview 27

2.1 Review 27

2.2 What Is Measurement? 28

2.3 The Real Number Line 31

2.4 Measurement Scales 33

2.5 Cauchy's Equation 34

2.6 Concatenation 37

2.7 Measurement Schemas 39

2.8 Sampling 42

2.9 Measuring 45

2.10 Reporting 45

2.11 Chapter Summary: History 47

2.12 Chapter Summary: Takeaways 47

2a Some Terms Used in the Field of Measurement 48

2a.1 Signal 50

2a.2 Reference 51

2a.3 Remarks on Clarity of Writing 52

References 53

3 Representational Measurements 55

3.1 Review 55

3.2 Directly Observable Quantities 56

3.3 The Measurement Model 57

3.4 Constraints on the Model: The GUM Revisited 58

3.5 Examples of Representational Measurement 60

3.6 Definitional Uncertainty 61

3.7 Concept Development and Appeal to Experiment 67

3.8 Chapter Summary: History 71

3.9 Chapter Summary: Takeaways 71

References 72

4 Operational Measurements 73

4.1 Review 73

4.2 You Can't Model Everything 74

4.3 The Operational Alternative 75

4.4 Human Experience 77

4.5 List of Operational Measurements 79

4.6 Hybrid Operational Measurements 81

4.7 Hybrid Measures: Summary 90

4.8 Value of the Hybrid Measure 90

4.9 Operational Power System Measurements 91

4.10 Representational and Operational Compared 93

4.11 Relationship to the Three Kinds of Metrology 98

4.12 Chapter Summary: History 99

4.13 Chapter Summary: Takeaways 100

4a Impulse Measurements 101

4a.1 Radio Influence Measurement 103

4A.2 Partial Discharge Measurement 108

References 111

5 Power Theories 113

5.1 Review 113

5.2 Chapter Organization 114

5.3 Introduction: Not Believing What We See 115

5.4 Reactive Power 116

5.5 NEMA Technical Report C12. 24 118

5.6 What is a Power Theory? 123

5.7 Power Theories 126

5.8 Czarnecki's Paradox Dooms Power Theories 128

5.9 Reactive Power: Last Words-Not Quite Last Rites 131

5.10 Apparent Power: Voisine's Paradox 132

5.11 Power Measurement 136

5.12 Kitzig's Power Paradox 139

5.13 Chapter Summary: History 144

5.14 Chapter Summary: Takeaways 145

5a Budeanu's Power Theory 146

5b Fryze's Power Theory 149

5b.1 The Three Voltmeter Method 151

5b.2 Relation to Fryze's Hope for Interpretation 154

5b.3 Where Did Fryze Go Wrong? 155

5c Reification 156

5d Ongoing Reification? 158

5e Logical Fallacies 160

References 163

6 Degrees of Freedom 167

6.1 Review 167

6.2 Signal Complexity 170

6.3 Symmetrical Components 174

6.4 Physical Meaning 176

6.5 Do Negative-Sequence Currents Exist? 179

6.6 Harmonic Effects and Phase-Sequence Components 181

6.7 Example of Fourier-Fortescue 183

6.8 Voltage and Current Harmonic Analysis 183

6.9 Current Phase-Sequence Analysis 183

6.10 Power and Reactive Calculations 185

6.11 Are Harmonic Phase-Sequence Values Useful? 187

6.12 Chapter Summary: History 187

6.13 Chapter Summary: Takeaways 188

References 189

7 Frequency 191

7.1 Background 191

7.2 Chapter Overview 197

7.3 Challenges of a Changing "Frequency" 197

7.4 Carson, Frequency Modulation 199

7.5 Van der Pol, Frequency Modulation 201

7.6 Rutman, Barnes, Frequency Stability 201

7.7 Cohen, Boashash, Time/Frequency Distribution 203

7.8 Summary So Far 204

7.9 Frequency Measurement Must Be (At Least Partly) Operational 205

7.10 Measuring in Distorted Conditions: Operationalism 207

7.11 Phase Locking, Alternate Methods 210

7.12 Fnet 211

7.13 Chapter Summary: History 217

7.14 Chapter Summary: Takeaways 217

References 218

8 Phasors and the PMU 221

8.1 Background and Chapter Overview 221

Part 1 The History of the PMU 222

8.2 The PMU as a New Kind of Measurement 222

8.3 The Northeast Blackout and the PMU 227

8.4 Three Revolutions in Measurement 229

8.5 The Second Revolution in Measurement 231

8.6 The PMU-The Third Revolution in Measurement 232

Part 2 Concepts Underlying PMU Measurement 233

8.7 The Meanings of "Phase" and "Phasor" 233

8.8 From Phase to Phasor 236

8.9 A Different Notation 239

8.10 Measuring a Signal to Express the Result as a Phasor 240

8.11 Initial Phase 242

8.12 Initial Phase: A Cautionary Tale 247

8.13 Rate of Change of Frequency 249

8.14 Chapter Summary: History 251

8.15 Chapter Summary: Takeaways 252

8a On the Definition of a Phasor 252

8a.1 Clement and Johnson 253

8a.2 Nau 254

8a.3 Scharf and Behrens 256

8a.4 Moura and Darwezeh 257

8a.5 Benedict 259

8a.6 Comment on Appendices, Sections 8A.1-8A.5 260

8b Problems in the PMU Standards 261

8b.1 Disclaimer 261

8b.2 Nostra Culpa 262

8b.3 Making a PMU 262

8b.4 The Standard Explanations of the PMU 265

8b.5 The Reference Model 267

8b.6 Evident Confusion 270

8b.7 Two Rotators 273

8b.8 The Delay Problem 276

8b.9 Repairing the Standard 277

References 279

9 An Exciting Future 283

9.1 Introduction 283

9.2 Artificial Intelligence 284

Part 1 Framework for R&D 285

9.3 Technology Readiness: Background 285

9.4 Technology Readiness for the Grid 286

9.5 An Assessment of Present Technology 290

9.6 The Example of IEEE Standard 1459 291

9.7 Digital Implementation of Analog Method 294

9.8 Determining the Period 295

Part 2 Some Ideas 296

9.9 Step Back and Examine the Needs 296

9.10 Increasing Capability 297

9.11 Understanding All the Information in the Power System 299

9.12 Probing the System 301

9.13 Probing the System: Parallel Substations 302

9.14 Probing the System: The Chief Joseph Brake 306

9.15 Probing the System: Low Energy 309

9.16 A Real-Time Trust Metric 310

9.17 Real-World Examples of the Trust Metric 315

9.18 A Real-Time No-Trust Metric 318

9.19 A Real-World Example of No-Trust Metric 318

9.20 Applying the No-Trust Metric 319

9.21 Matched Filters 320

9.22 Conclusion 324

9a An Impulse Problem? 325

9a.1 Background 325

9a.2 Explanation 326

References 328

Appendix A Error, Uncertainty, and Trust 331

A.1 Background 331

A.2 Review of Some Relevant History 332

A.3 BIPM Questionnaire 336

A.4 The GUM 337

A.5 A Brief Statistics Background 339

A.6 A "Type A" Worked Example 343

A.7 Are More Measurements Worthwhile? 345

A.8 Uncertainty: Type B Evaluation 346

A.9 A "Type B" Worked Example 347

A.10 Combining and Propagating Uncertainties 349

A.11 A Reminder 351

A.12 Real-world Considerations 352

A.13 The International Infrastructure 353

A.14 Uncertainty of Operational Measurements 354

A.15 Conditional Accuracy 355

A.16 An Aside on the Matter of Noise Floor 356

A.17 Appendix Summary 357

References 358

Chapter Summaries 361

Index 375