Thesis director
:Prof. Jean-‐Claude Maun President of the committee: Prof. Michel Kinnaert Members of the committee: Prof. Johan Gyselinck Prof. Liisa Haarla Dr. Tevfik Sezi
Prof. Thierry Van Cutsem Faculty of Applied Sciences
Bio-‐, Electro-‐, and Mechanical Systems
February 2013 Thèse présentée en vue de l’obtention du titre de
Docteur en Sciences de l’Ingénieur
Dot
From the Measurement of Synchrophasors to the Identification of Inter-‐Area Oscillations in Power Transmission Systems
Jacques Warichet
In the early 1980s, relaying engineers conceived a technology allowing a huge step forward in the monitoring of power system behavior: thesynchrophasor, i.e. the estimation of a phasor representation - amplitude and phase - of a sinusoidal waveform at a given point in time thanks to highly accurate time synchronization of a digital relay. By measuring synchrophasors across the power system several times per second, and centralizing the appropriate information in a hierarchical way through a telecommunication network link, it is now possible to continuously monitor the state of very large systems at a high refresh rate.
At the beginning, the phase angle information of synchrophasors was used to support or improve the performance of classic monitoring applications, such as state estimation and post- mortem analysis. Later, synchrophasors were found to be valuable for the detection and analysis of phenomena that were not monitored previously, such as system islanding and angular stability.
This allows a better understanding of system behavior and the design of remedial actions in cases where system security appears to be endangered. Early detection and even prediction of instabil- ities, as well as validation and improvement of the dynamic models used for studies, have thus become possible.
However, a power system is rarely stationary and the assumptions behind the definition of
“phasor” are not completely fulfilled because the waveforms’ frequency and amplitude are not constant over a signal cycle at fundamental frequency. Therefore, accuracyof synchrophasor measurements during dynamic events is an important performance criterion. Furthermore, when discontinuities (phase jumps and high magnitude variations) and harmonics disturb the measured analog signals as a consequence of switching actions or external disturbances, measurements provided to the “user” (the operator or the algorithms that will take decisions such as triggering alarms and remedial actions) require a certainrobustness.
The efforts underpinning this thesis have lead to the development of a method that ensures the robustness of the measurement. This scheme is described and tested in various conditions. In order to achieve a closer alignment between required and actual measurement performance, it is recommended to add anonline indicator of phasor accuracyto the phasor data.
Fast automated corrective actions and closed-loop control schemes relying on synchrophasors are increasingly deployed in power systems. The delay introduced in the measurement and the telecommunication can have a negative impact on the efficiency of these schemes. Therefore, measurementlatencyis also a major performance indicator of the synchrophasor measurement.
This thesis illustrates the full measurement chain, from the measurement of analog voltages and currents in the power system to the use of these measurements for various purposes, with an emphasis on real-time applications: visualization, triggering of alarms in the control room or remedial actions, and integration in closed-loop controls. It highlights the various elements along this chain, which influence the availability, accuracy and delay of the data.
The main focus is on the algorithm to estimate synchrophasors and on thetradeoff between accuracy and latencythat arises in applications for which measurements are taken during dynamic events and the data must be processed within a very limited timeframe.
If bothfastphasors andslower, more accuratephasors are made available, the user would be able to select the set of phasors that are the most suitable for each application, by giving priority to either accuracy or a short delay.
A specific application, the continuous monitoring of oscillatory stability, was selected in or- der to illustrate the benefits of synchrophasors for the monitoring, analysis and control of power system behavior. This application requires a good phasor accuracy but can allow for some mea- surement delay, unless phasor data are used in an oscillation damping controller. In addition, it also relies onmodal estimators, i.e. techniques for the online identification of the characteristics of oscillatory modes from measurements. This field of ongoing research is also introduced in this thesis.
The development of this thesis started in October 2004 and capitalized on the work performed previously by Xavier Robe (2003) in the field of Power Quality monitoring and on the first inquiries of St´ephane Roos (2004) into phasor measurement units (PMUs) and their applications. My work and that of my predecessors have been sponsored by SIEMENSand benefitted from the heritage of the IRAM (innovation in microprocessor relays) team, set up by the Universit´e Libre de Bruxelles (ULB) in the ’90s to perform research in the field of microprocessor relaying in partnership with SIEMENS. For SIEMENS, PMUs were the next natural step towards real-time applications, in order to complete their inventory of solutions ranging from digital relays, substation automation and tools for power system planning.
This research was initially performed in cooperation with the relay development team, led by Dr.
Andreas Jurisch. The focus was on the algorithm for synchrophasor estimation and this explains why a good part of this thesis is dedicated to the measurement of synchrophasors. In parallel to my work, SIEMENSdeveloped a prototype of PMU based on the SIPROTEC relay family. One exemplar was also given to the University in order to test it.
When the development and commercialization of a PMU became a clear priority for SIEMENS, the focus moved from the measurement of phasors to their applications for utilities. The Simeas R PMU was ready to be launched but other, more experienced manufacturers were struggling to justify the added value of phasor measurement units. SIEMENS decided to develop an application platform for PMUs, the SIGUARD Phasor Data Processor, that would include the function of data concentration and a portfolio of modular applications. My fellow researcher Benjamin Genet and myself then investigated a few possibilities before focusing on the monitoring of voltage stability and angle stability, respectively. During this second phase, our work was supervised and followed by Dr.
Tevfik Sezi. The research coupled with nearly immediate practical application brought about many interesting questions and requirements. For each method developed, we needed indicators and visual facilities to demonstrate its use. Our team also participated actively in workshops with SIEMENSin order to develop and improve the first versions of SIGUARD. As soon as the Simeas R PMU was available, SIEMENSgave us two exemplars. They proved to be useful for my work, and facilitated a more in-depth study of phasor estimation.
This thesis contains both literature reviews and my personal contribution. A large part of the work was done before September 2008, when my scholarship at the University ended and I became a full-time staff member at Elia, the Belgian Transmission System Operator. I could have submitted my thesis manuscript at that time, but I decided to perform additional practical tests in the laboratory in order to establish a link between the two parts of my work: the phasor measurement and the monitoring of oscillations. Therefore, I dedicated substantial time to the creation of good conditions in the laboratory for the tests in order to complete my studies. Unfortunately, the equipment available was old and the electrical machines and their controllers did not provide for the accuracy required to
obtain reliable results that could be replicated. Despite this setback, I did not want to deliver a thesis without establishing a clear link between measurement and applications. However, I hesitated on the next step, as it was not clear which course of action would be the most likely to allow me to submit a thesis that completes the circle. I continued reading the latest papers on related topics and noticed that most ideas we developed and shared during my time at University were becoming known and accepted by the community and that they had led - without any paternity links - to industry practices.
Therefore this area of study is maturing, and while this thesis could be developed further, I consider it important to defend and to publish it at this point in time, as it still provides a contribution to our understanding of this developing field. I hope this thesis reflects and rewards not only my efforts but also those of the people who contributed directly or indirectly to my work.
It is worth mentioning that PMUs and their applications are still part of my professional work.
As soon as I started at Elia, I managed to spark the interest of my colleagues in wide area measure- ment systems (WAMS) and my hierarchy found an appropriate framework that allowed us to use my knowledge and to extend it to practice. We are now in the last year of “Twenties”, a highly challeng- ing project within the 7th Framework Programme, and I am very glad to be in charge of the studies related to WAMS, for which the ULB is our major partner. This thesis has benefitted substantially from my experience in the “Twenties” project and, in general, from my work at Elia. Therefore, while the submission of this thesis has been delayed, this time has also given me a wider perspective of the subject of study, which I hope is also reflected in the thesis itself.
Before diving into the subject matter, I would like to thank a few people who contributed to this work. First of all, my thesis director, Professor Jean-Claude Maun. It was (and still is) a pleasure to work with him. His ability to understand any problem or situation combined with his limitless imagination and innovative thinking remain a source of inspiration for me.
I am also grateful to our partners at SIEMENSand to my colleagues at the University. Some of the researchers and assistants have become my close friends. I need to extend special thanks to the permanent personnel of the Electrical department: Ariane, Pascal and Christophe, as all of them were helpful and contributed to my work in their own way
I also thank Marc Stubbe and Karim Karoui from Tractebel Engineering whose passion for power systems lit the initial spark of inspiration in me. They gave me a fantastic chance when they accepted me as astagiaireand supervised my Master thesis. Moreover, they provided us with Eurostag licenses and always showed an interest in the discussion of technical matters.
My colleagues at Elia deserve a special acknowledgement. I was hired in 2008 with the assump- tion that I would soon hold a PhD. I am in their debt for their patience and support, and would in particular like to thank Wim Michiels (my current superior), Dounia Berger (my previous superior) and Director Hubert Lemmens. They gave me the freedom necessary and managed to provide me with a suitable framework to facilitate the completion of this thesis.
I am also grateful to the jury, for accepting being part of what is a crucial step for me. All of them are experts in their fields and it means a lot to me that they have accepted to dedicate their precious time to me. President Professor Michel Kinnaert was kind enough to understand and to accept my periodic requests to delay the finalization of this thesis.
And, last but not least, I would like to express my gratitude towards my family and my close friends. They have supported me throughout these years and were always understanding when I preferred spending time with my books, papers and my computer rather than with them. I hope I will be able to repay the time I owe them in the future.
Brussels, February 2013
Executive summary 3
Foreword 5
1 Introduction 13
1.1 Context . . . 13
1.2 Motivation of this work . . . 15
1.2.1 How this thesis materialized . . . 15
1.2.1.1 Phasor measurement accuracy and robustness . . . 15
1.2.1.2 Phasor measurement latency . . . 16
1.2.1.3 A missing link between phasor estimation and applications . . . . 16
1.2.2 Main contribution . . . 16
1.3 Outline of the thesis . . . 16
I About synchrophasors and wide area measurement systems 19 2 Wide area measurement systems and the synchrophasor technology 21 2.1 Introduction . . . 21
2.2 History of synchrophasor technology . . . 21
2.3 Wide area measurement systems . . . 22
2.3.1 Phasor measurement units . . . 23
2.3.2 Time synchronization . . . 24
2.3.2.1 Synchronization requirements . . . 24
2.3.2.2 Satellite broadcasts and GPS . . . 24
2.3.2.3 Accuracy of PMU synchronization . . . 25
2.3.3 Telecommunications and infrastructure . . . 27
2.3.3.1 Data concentrators . . . 27
2.3.3.2 Data transfer parameters . . . 27
2.3.3.3 WAMS architecture . . . 28
2.3.4 PMU placement . . . 29
2.4 The synchrophasor measurement chain . . . 30
2.4.1 Inaccuracies, delays and unavailabilities introduced along the chain . . . 32
2.4.2 Order of magnitude of error sources . . . 32
2.5 Discussion . . . 33
3 Principles and techniques for synchrophasor estimation 35
3.1 Introduction . . . 35
3.2 Definition . . . 35
3.3 The Fourier estimator . . . 36
3.3.1 Mathematical background . . . 36
3.3.2 Frequency response of theN-cycle Fourier estimator . . . 38
3.3.3 Phasor estimation error . . . 41
3.3.3.1 Frequency deviations . . . 41
3.3.3.2 Amplitude modulation . . . 44
3.3.4 Windowing functions for the Fourier estimator . . . 44
3.3.4.1 Boxcar or averaging filter . . . 44
3.3.4.2 Raised cosine filter . . . 45
3.3.5 Derivations of the Fourier estimator . . . 48
3.3.5.1 Two-step approach . . . 48
3.3.5.2 Phasorlets . . . 48
3.3.5.3 Taylor-Fourier transform . . . 48
3.4 Other estimation techniques . . . 49
3.4.1 Iterative algorithms . . . 49
3.4.2 Least mean squares estimators . . . 49
3.5 Frequency measurement . . . 50
3.5.1 Frequency in the phasor estimation process . . . 50
3.5.2 Characteristics of power system frequency . . . 50
3.5.3 Techniques for frequency estimation . . . 50
3.5.3.1 Demodulation technique . . . 51
3.5.3.2 Signal decomposition technique . . . 54
3.6 Phasor measurement unit architecture . . . 56
3.7 Variable rate processing (resampling) . . . 58
3.7.1 Classical sampling rate conversion method . . . 58
3.7.1.1 Classical oversampling . . . 58
3.7.1.2 Drawbacks of the classical sampling rate conversion method . . . 59
3.7.2 Oversampling and linear interpolation . . . 59
3.7.2.1 Oversampling . . . 59
3.7.2.2 Linear interpolation . . . 60
3.7.2.3 Practical implementation . . . 60
3.7.2.4 Interpolation filter design . . . 61
3.8 Discussion . . . 64
4 Standard for synchrophasors 65 4.1 Introduction . . . 65
4.2 History of the standard for synchrophasor . . . 66
4.3 Scope of the standard . . . 66
4.3.1 Phasor characterization . . . 66
4.3.2 Data and configuration frames . . . 67
4.3.3 Synchrophasor measurement error . . . 67
4.3.3.1 Synchronization error . . . 67
4.3.3.2 Total Vector Error . . . 67
4.3.4 Testing of PMUs . . . 70
4.4 Beyond the standard . . . 70
4.4.1 PMU testing . . . 70
4.4.1.1 PMU testing during dynamics and transients . . . 70
4.4.1.2 Testing procedures . . . 71
4.4.2 Online measure of the phasor accuracy . . . 71
4.4.3 Trade-off in responsiveness and accuracy of the measurement . . . 72
4.4.3.1 Causality of the algorithm . . . 72
4.4.3.2 Towards a user-selectable phasor with high accuracy or low latency? 74 4.5 The 2011 update of the standard . . . 75
4.6 Discussion . . . 77
5 An algorithm for robust synchrophasor measurement 79 5.1 Introduction . . . 79
5.2 Real-time estimate of the error . . . 80
5.2.1 One-cycle residue . . . 80
5.2.2 One-cycle residue vs. Total Vector Error . . . 80
5.2.3 Thresholds for residues . . . 84
5.3 Window flagging and frequency processing . . . 86
5.3.1 Window flags . . . 86
5.3.1.1 Coming from initialization . . . 88
5.3.1.2 Coming from stationary . . . 88
5.3.1.3 Coming from dynamic . . . 88
5.3.1.4 Coming from transient . . . 89
5.3.2 Frequency processing . . . 89
5.3.2.1 Processing in initialization . . . 89
5.3.2.2 Processing in stationary . . . 89
5.3.2.3 Processing in dynamic . . . 90
5.3.2.4 Processing in transient . . . 91
5.4 PMU performance testing and validation . . . 94
5.4.1 Testing equipment . . . 94
5.4.2 Results illustration . . . 94
5.4.2.1 Noise rejection . . . 96
5.4.2.2 Smooth dynamic events and frequency tracking . . . 101
5.4.2.3 Dynamic and transient events . . . 110
5.5 Conclusion on the flag management algorithm . . . 115
5.6 Discussion . . . 115
6 Conclusions of Part I 117 6.1 Main contributions . . . 117
6.2 Conclusions . . . 117
6.3 Future work and perspectives . . . 119
II About the use and applications of synchrophasors 121 7 Requirements for applications of synchrophasors 123 7.1 Classification of PMU applications . . . 123
7.1.1 Hierarchical classification . . . 124
7.1.2 Classification based on the density of telecommunication links . . . 125
7.1.3 Classification based on the timeframe of subsequent actions . . . 126
7.1.4 Classification based on the available phasor accuracy . . . 126
7.2 Discussion . . . 128
8 Electromechanical inter-area oscillations in power systems 129 8.1 Introduction . . . 129
8.2 Power system angular stability . . . 131
8.2.1 Transient stability . . . 132
8.2.2 Small-signal stability . . . 132
8.2.3 Oscillation modes . . . 133
8.3 Physical background and consequences of inter-area oscillations . . . 134
8.3.1 Sources of power system damping . . . 134
8.3.2 Voltage control and power system stabilizers . . . 134
8.3.3 Probability of occurrence of oscillatory instabilities . . . 135
8.3.4 Consequences of undamped oscillations . . . 136
8.4 Mathematical description of oscillatory stability . . . 136
8.4.1 Modeling of a synchronous generator . . . 136
8.4.1.1 The swing equation . . . 137
8.4.1.2 Generators and their controls . . . 137
8.4.2 Load modeling . . . 139
8.4.3 Dynamic system model . . . 139
8.4.3.1 Dynamic equations . . . 141
8.4.3.2 Grid equations . . . 141
8.4.3.3 FACTS and HVDC . . . 141
8.4.4 Power system response to small disturbances . . . 141
8.4.5 Small-signal (or linear) analysis . . . 144
8.4.5.1 Linearized system . . . 144
8.4.5.2 Oscillation modes characterization . . . 145
8.4.5.3 Observability and Controllability . . . 147
8.4.6 Mechanical equivalent . . . 147
8.5 Inter-area oscillations in planning and operations . . . 148
8.5.1 Inter-area oscillations in planning studies . . . 150
8.5.2 Online modal identification . . . 150
8.5.2.1 Purpose of modal identification . . . 150
8.5.2.2 Experience with modal identification . . . 151
8.5.2.3 Identifying sources of the oscillations . . . 151
8.5.2.4 Statistical approach . . . 153
8.5.3 Visualization and alarm criteria for electromechanical oscillations . . . 153
8.5.3.1 Oscillatory stability indicators . . . 155
8.5.3.2 Alarms . . . 155
8.5.3.3 Displaying oscillatory stability indicators . . . 156
8.6 Control of inter-area oscillations . . . 157
8.6.1 Power oscillation dampers . . . 157
8.6.2 Wide area power system stabilizers . . . 160
8.6.3 Corrective actions . . . 161
9 Identification of inter-area oscillations from measurements 163
9.1 Introduction . . . 163
9.2 The identification problem . . . 164
9.2.1 Mathematical formulation . . . 164
9.2.2 The modal estimation process . . . 166
9.3 Damping estimation . . . 167
9.3.1 Principles . . . 167
9.3.2 Assessing the error on the damping estimate . . . 168
9.3.3 Extracting single-mode signals . . . 168
9.3.3.1 Intrinsic mode functions . . . 168
9.3.3.2 Empirical mode decomposition . . . 168
9.3.4 About window placement issues for damping estimation . . . 171
9.4 Techniques for modal identification . . . 173
9.4.1 Ringdown analyzers . . . 174
9.4.1.1 Prony analysis . . . 174
9.4.1.2 Other ringdown methods . . . 176
9.4.2 Ambient mode-meters . . . 176
9.4.2.1 Nonparametric methods . . . 176
9.4.2.2 Parametric methods . . . 180
9.4.2.3 The assumption of Gaussian excitation . . . 183
9.4.3 Probing methods . . . 183
9.5 How to choose a modal estimator? . . . 184
9.5.1 Errors from estimates . . . 184
9.5.2 Testing and benchmarking modal estimators . . . 185
9.6 Estimation of mode shapes . . . 185
9.7 Signals for modal estimation . . . 186
9.7.1 Use of local signals . . . 187
9.7.2 Physical signals . . . 188
9.7.3 Discussion . . . 192
10 Conclusions of Part II 193 10.1 Conclusions . . . 193
10.2 Future work and perspectives . . . 195
A Publications 197 B Mathematical background 199 B.1 Least squares problems . . . 199
B.2 Dynamical systems . . . 200
B.2.1 State-space representations . . . 200
B.2.2 Linearization . . . 201
B.2.3 Modal form of a linear system . . . 202
B.2.4 Input-output descriptions of linear systems . . . 204
B.3 Random signals and their stochastic properties . . . 205
B.3.1 Random variables . . . 205
B.3.2 Random signals . . . 208
B.3.3 Stationarity and linearity . . . 209
B.3.4 Properties of signals in the frequency domain . . . 211
B.4 System identification . . . 216
B.4.1 Prediction-error parametric model estimation . . . 217
B.4.2 Subspace model identification . . . 219
B.4.2.1 Subspaces . . . 219
B.4.2.2 System matrix factorizations . . . 219
B.4.2.3 Subspace identification . . . 220
C Practical guide for the deployment of a WAMS ... 223
C.1 Business case and choice of applications . . . 223
C.2 Design of the WAMS . . . 224
C.3 Implementing and operating the WAMS . . . 225
References 227
List of Figures 239
List of Tables 243
Index 245
List of abbreviations 247
Introduction
1.1 Context
MODERN POWER SYSTEMS
Electric power systems have dramatically changed over time and it is reasonable to think that what we know today is not what the system will look like decades from now.
The first power systems were built in the late 19th century to power a few houses for lighting pur- poses. Very soon, the systems extended to supply industrial applications of electricity. Transformation to higher voltage levels for long distance transmission, together with the transition towards meshed networks, improved the efficiency and reliability of these systems. Today these complex structures span over thousands of kilometers and provide a commodity modern societies cannot live without.
However, it is only at the turn of the 21st century that the power industry has entered a completely new landscape. Before that, the industry was vertically integrated: one single company - mostly, at the national or regional level - was generating power, operating the grid, and distributing power to the final consumer. The interconnections between countries or regions were meant to improve the stability of the system1 and the costs associated to a given reliability2. Interconnections also had a socio-political meaning, allowing to integrate far-away regions and improving people’s lifestyle.
The dimensioning of interconnection lines (ortie lines) was therefore based on the principle that these lines would be used for emergency support and weakly loaded on a general basis. Since then, the paradigm has completely changed and transits across tie lines have significantly increased.
First of all, a free market has been installed in several places (for example, North America and Europe): the activities of generating, buying and selling energy have been liberalized. Network activ- ities have been kept under the hand of a limited number of parties because of their status of natural monopoly. Balance responsible parties are in charge of managing their portfolio of consumers and matching their consumption with generation at any time, by injecting or buying the needed energy within the interconnected system. Large consumer centers and generating plants are not always lo- cated close-by. Moreover, due to geographical differences and different national policies (especially regarding support of renewable energy sources), resources might be cheaper or available in bigger quantities abroad.
Also, the power generation from renewable sources - especially wind and solar - is only partially
1A bigger system, made of more rotating masses, has an increased inertia and as a consequence a more stable frequency.
2Operational reserves, especially spinning reserve, can be shared by several systems in order to cover forced outages, especially the loss of the biggest generating unit. Deterministic dimensioning of the reserve - through the (N-1) principle - requires a fixed amount of reserves that can be very costly for small systems.
controllable, and large dependent on weather conditions. Making the best use of this “marginally cheap”3 power requires a network able to feed the consumers with this power. This new paradigm leads to large power transfers across the system, through tie lines or corridors that were not built for this purpose.
Building new transmission infrastructure takes time4and Transmission System Operators (TSOs) need to achieve more flexibility in operating the grid. The installation of power flow control devices, such as Phase-Shifting Transformers (PSTs) or, more generally, Flexible AC Transmission Systems (FACTS), allows improving flows management across the system. In addition, the transmission lines capacities are also increased by the installation of high performance conductors and the progressive penetration of Dynamic Line Rating (DLR) techniques. These developments allow moving away thermal constraints and congestion issues, and have as consequence a higher grid loading. This means that the power system is now operated closer to stability limits that it used to be.
Another consequence of the increasing penetration of power electronics in the system (present in HVDC and FACTS, as well as in the connection technology of latest generation renewable energy sources) is the advent of faster dynamics in the system. Time constants of power electronics is an order of magnitude smaller than that of classical equipment. Therefore, there is a growing need for monitoring the system behavior more closely and to implement means to control it on a wider scale.
ANEW ERA FOR SYSTEM MONITORING,PROTECTION AND CONTROL
Fortunately, tools to monitor the power system have also improved with time. Conventional mon- itoring was (and still is) performed by gathering measurements from all around the grid at a rate between the second and tens of seconds. Not to overload communication channels between the sub- stations and the control room, measurements are typically sent only when the monitored variable changes by a given threshold (in the range of one percent). Therefore, all measurements are not taken at the same moment and the best snapshot of the system can only be available after the process of state estimation. This computation gives the most likely state of the system and takes several seconds to a few minutes, depending on the size of the mathematical model describing the system.
In the years 1970s, some engineers thought of adding a time synchronization device to protection relays in substations in order to improve their performance. Very soon they also realized the potential for monitoring. Thephasor measurement unit(PMU) was born. With the synchronization of the mea- surements, an instantaneous snapshot of the system is available, without (in theory, at least) the need for computationally intensive state estimation: what we get is astate measurement. With the progress in telecommunication technology, it is now possible to send data to the control room at a fixed rate, several times per second. This is the principle behindwide area measurement systems(WAMS). A major benefit is that it is finally possible to observe the system’s slow (or electromechanical) dynamics in real-time.
Recently, the interest of engineers and potential of the technology have turned these systems into wide area measurement, protection and control systems(WAMPAC): these system integrate triggering of preventive and corrective actions, system protection and even closed-loop controls.
3Generation from wind and solar requires very little operational and generating costs. However, the operational costs on the system operation are not negligible.
4The biggest constraints today are the ecological impact and people’s resistance (the so-called NYMBY-effect, standing forNot in my backyard).
1.2 Motivation of this work
1.2.1 How this thesis materialized
The work performed and reported here was initiated by SIEMENSin 2003. Not yet active on the WAMS scene, SIEMENSwas interested in an investigation about the issues faced by their customers that could be better solved with a solution involving PMUs.
The literature reported already numerous applications, at the stage of prototype [1, 2, 3, 4, 5, 6, 7]
or already implemented [8, 9, 10, 11, 12, 13, 14]. After having established a long list of actual and potential applications for PMUs, it became necessary to focus on some of them and to demonstrate their feasibility and added value.
1.2.1.1 Phasor measurement accuracy and robustness
The monitoring of steady-state flows and waveform angles - with its various classic applications to dynamic line rating, state estimation, (slow) voltage instability detection and load modeling - ac- commodates performance requirements stated in the 2005 standard for synchrophasors.
However, it appeared soon that the requiredaccuracy and robustnessof phasor estimation were not sufficient for monitoring applications dealing with electromechanical and transient dynamics, such as small-signal stability assessment, detection of islanded networks, identification of line parameters and event or fault analysis. The subjacent phenomena were not monitored or fully understood by operators in the control room, and PMUs could bring an added value by adding a new set of information for both operators and planners, so that better decisions could be taken, as illustrated in Figure 1.1.
Power System
Decision Processes
Measurement Based Information
System Information
Automatic control System operation System planning
Disturbances
Unobserved response
Observed response
Figure 1.1: Use of measurement-based information in decision processes for power system planning and operation.
The idea came to develop a basic signal processing scheme for phasor measurement in order to understand the accuracy of synchrophasors: how does this accuracy depend on the power system conditions and the associated input signals, and how does this accuracy influence the results of the subsequent applications?
The robustness of phasor measurements was also questioned: phasor measurements could be available (translating the reliability of the measurement chain) but what tells us that their accuracy is appropriate for the applications in mind of the user?
1.2.1.2 Phasor measurement latency
It also appeared to us that some applications required very quick reaction times or even automated actions: for example, transient stability, system integrity protection schemes. In addition, the idea of implementing automatic controls and feedback systems to improve the security of the system became more and more popular.
As a consequence, new questions were raised:how much delay is introduced by the measurement and the feedback loop, and is it compatible with the control system requirements? Performance re- quirements were thus extended to thelatencyof the measurement. A tradeoff (analog to the classic filtering problem) appeared between how fast one can obtain a measurement and how accurate this measurement can be.
1.2.1.3 A missing link between phasor estimation and applications
It soon became obvious that the requirements (accuracy, robustness and latency) for synchropha- sors were crucial for a wide range of applications, and that there was a value in the study of the relationship between phasor estimation and the subsequent applications. At that time, the literature was divided in two groups: one group, made of power system engineers, was dealing with PMU applications while another group, mainly populated by signal processing specialists, was handling synchrophasor measurements. Few were the authors considering both at the same time.
The identification of inter-area oscillations was chosen as main application investigated in this work, but the principles and algorithms were developed with the scope to understand and improve performance of synchrophasor estimation, and can serve a wide range of applications.
1.2.2 Main contribution
The main contribution of this work is related to the link between the process of phasor estimation and the various applications. Along this work, the emphasis was put on the need to (i) test PMUs not only in steady-state but also in dynamic conditions, and (ii) assess online the phasor accuracy and include this value in the data frame, and (iii) consider the measurement latency.
The outcome of this work was published in 2008 [15] and 2009 [16]. Soon after, when industry started updating the IEEE Standard for synchrophasors, Dr. Tevfik Sezi (our principal partner at SIEMENS) joined the drafting team. Since he followed closely the work reported here, we can say that this work contributed to discussions surrounding the latest update of the standard in 2011.
This contribution is concentrated in Section 4.4 and Chapter 5, while the consequence for appli- cations is discussed in Chapter 7.
1.3 Outline of the thesis
This dissertation is divided in two parts. The first part is dedicated to the measurement of syn- chrophasors and their role in wide area measurement systems. In Chapter 2, the reader is introduced to the concept of wide area measurement systems and to the technology of phasor measurement units.
The emphasis of this chapter is on the place of the PMU in the measurement chain and the various sources of errors along this whole chain. Telecommunication issues are briefly discussed. Chapter 3 provides details about synchrophasor measurement: the algorithms used, their theoretical background, their strengths and weaknesses. This chapter is a collection of known subjects from signal processing theory and its application to phasor measurements. Chapters 4 and 5 contain the main contribution
of this work. In Chapter 4, we discuss the standard for synchrophasors: its history and evolution, the main contents and why the 2005 version was insufficient to handle dynamic and transient applications.
Our initial suggestions and improvements of the latest update, in 2011, are also highlighted. In Chap- ter 5, we propose an online measure of the phasor accuracy and introduce an algorithm to illustrate means to achieve robust synchrophasor measurement. Computer simulations and laboratory experi- ments are shown in order to support the performance improvements. Finally, Chapter 6 summarizes the findings and conclusions from the first part.
The second part of the dissertation is about the use and applications of synchrophasors. Chap- ter 7 introduces a few applications of phasor measurements and classifies them according to various relevant parameters. Among the most interesting parameters are those influencing the requirements for accuracy and latency of measurements. Chapter 8 provides a general introduction to electrome- chanical inter-area oscillations in power systems. This application of PMUs is a good illustration of a phenomenon that was not monitored continuously before the advent of this technology. The moni- toring of inter-area oscillations imposes rather high requirements for synchrophasor accuracy and, in case of closed-loop control to improve the damping of these oscillations, limits to the measurement latency are also necessary. Chapter 9 is dedicated to the identification of inter-area oscillations from real-time measurements. It summarizes the literature on the topic and ends with a discussion on the input signals used for this purpose. Finally, a conclusion on the applications of synchrophasors is drawn in Chapter 10.
About synchrophasors and wide area
measurement systems
Wide area measurement systems and the synchrophasor technology
2.1 Introduction
This chapter gives a general overview about phasor measurement technology and its use within wide area applications for power systems. After a few words about the history of phasor measure- ments, we will introduce wide area measurement systems (WAMS) and the complete measurement chain.
SOURCES OF ERRORS
From the analog waveforms of voltages and currents in the system to the estimation of a syn- chrophasor, several sources of error are present. The first error is related to the first part of the word synchrophasor, it is the error of synchronization. It is caused by inaccuracies in the time synchroniza- tion signal from GPS and, mostly, to the processing of this time synchronization by the measurement device. To this first error source, we must add the errors in the measurement equipment (transformers, wiring) and the errors induced by the phasor estimation device (filtering, analog to digital conversion, and phasor estimation). With today’s technology, the order of magnitude of the errors of measurement equipment is comparable to that of the estimation device, and both are one order of magnitude bigger than synchronization error.
2.2 History of synchrophasor technology
Power system engineers have always been interested in the phase angle of voltage phasors. The reason is that many processes in planning and operation of the power system are concerned by the power flow, and the power flow on a transmission line is linear with the sine of the angle difference between voltages at the two ends of the line according to the simplifiedpower-angle relationship(see Figure 8.3):
P= E1E2
X sin∆δV (2.1)
Therefore engineers have always looked for ways to measure the voltage phase angle differences.
Thestate estimationprocess computes themost likely1 voltage magnitude and phase of all nodes in
1Thestate estimationin power systems is an algorithm determining the system state from a model of the network and redundant measurements. It is typically formulated as a weighted least-squares problem. Thestatevector is the magnitude
the network but, due to the related computation burden, it cannot be performed in real-time for large systems. In the early 1980s, some systems were developed to measure the phase by counting the time needed to the next zero-crossing of the voltage waveform after some reference instant. The inaccuracy of the reference and the effects of noise and harmonics in the voltage waveform led to poor results.
The foundations of phasor measurements is in the field of power system relaying, when in the early 1970s microprocessor-based protection devices started to appear [17]. First of all, there was a limitation in computational power to compute all the required equations at every sample to verify that none of the type of faults supervised was present in the three-phase transmission line. The introduction of symmetrical components-based algorithms in 1977 allowed decreasing the amount of equations [18]. Efficient algorithms for computing positive-sequence components of three-phase systems were developed and it was soon recognized by Phadke that the positive-sequence voltage on its own had some value for power system applications [19] (1983). This can be considered as the starting point of modern synchrophasor measurement. At the same time, the Global Positioning System (GPS) was being fully deployed and the synchronization of devices started to reach accuracies sufficient for all industrial applications.
The first prototype of modern phasor measurement unit (PMU) using GPS was built by Phadke at Virginia Tech in the early 1980s and was deployed in the United States in some substations of the Bonneville Power Administration, among others. The first commercial manufacturing of PMUs was started by Macrodyne in 1991 in collaboration with Virginia Tech [20, 21].
Figure 2.1: Schematic view of a wide area measurement and control system.
2.3 Wide area measurement systems
Figure 2.1 shows a schematic view of awide area measurement system(WAMS). WAMS is the name given to an ensemble of PMUs feeding in real-time a central server (or several of them) with synchrophasors measured at a high rate for the monitoring of a large system. The main constituents of a WAMS are the PMUs and the server(s), calledphasor data concentrator(s)(PDC), but the whole
and phase angle of the voltage at each bus of the network, and should not be confused with the state-space model of the system, described in details in Appendix B.2.
infrastructure around it, telecommunication channels and synchronization source, are also of prime importance.
2.3.1 Phasor measurement units
The PMUs are situated in the substations and provide measurements of time-stamped positive- sequence voltages and currents of all monitored buses and feeders, as well as frequency (and rate of change of frequency). The measurements can be stored in local data storage devices, which can later be accessed from remote locations for post-mortem analysis or diagnostic purposes. The PMU data is also available for real-time applications in a steady stream as soon as the measurements are made.
PMUs built by different manufacturers differ from each other in many aspects. However, we will introduce agenericPMU in order to illustrate its main components.
Anti-aliasing
filters A/D conv.
GPS receiver Phase-locked
oscillator Analog
Inputs
Phasor micro- processor
Modem One pulse
per second Second Of Century Counter
Figure 2.2: Major elements of a modern PMU [22].
The PMU shown in Figure 2.2 has a structure very similar to microprocessor-based relays. The analog inputs are currents and voltages obtained from the secondary windings of the current and voltage transformers. All three-phase currents and voltages are used in order to perform positive- sequence measurement. In contrast to relays, a PMU can be fed with currents and voltages coming from various feeders and buses in a substation.
The currents and voltages are converted into voltages with shunts or instruments transformers (in the range of±10 volts) to match the requirements of the analog-to-digital (A/D) converters. The sampling rate chosen for the sampling process dictates the frequency response of the anti-aliasing filters. These are in most cases analog-type filters with a cut-off frequency smaller than half the sampling rate in order to satisfy the Nyquist criterion. According to [22], many relay designs include a high sampling rate (thus with a high cut-off frequency of the analog filter) followed by a digital decimation in order to ensure a more stable response with respect to temperature and aging. Higher sampling rates also lead to improved phasor accuracy. This will be more detailed and exploited in Sections 3.6 and 3.7. Another advantage of the high sampling rate (and high-bandwidth) is the possibility to use the relay as a digital fault recorder.
The sampling clock is phase-locked with the GPS clock pulse (see Section 2.3.2). The micro- processor calculates, at least2, positive-sequence estimates of the voltages and currents using various techniques (discussed in details in Chapter 3) as well as frequency and rate of change of frequency measured locally. The output of the PMU includes the measurements and their time-stamp, as well as
2Most commercially available PMUs estimate also all single-phase phasors and can also be used for relaying applica- tions.
some other auxiliary messages (alarms, accuracy range). This output is transferred over communica- tion links through suitable modems to a higher level of hierarchy of the measurement system.
2.3.2 Time synchronization
The time-stamp associated with each message sent by a PMU identifies the Coordinated Universal Time (UTC) second as well as the instant related to the power frequency period as defined in the standard (for a 50Hz system, the minimal set of reporting rates include 10, 25 or 50 frames per second).
2.3.2.1 Synchronization requirements
We can classify synchronization requirements for microprocessor-based equipment, commonly called intelligent electronic device (IED), in three levels:
1. Synchronization of the clocks of IEDs in a substation: the goal is to have all IED records referenced to the same time. It is not important what is the reference and 1ms accuracy is generally suitable.
2. Synchronization of the clocks of IEDs in several substations: for this application, an additional requirement is that the source of synchronized time must be applied to all the considered sub- stations to create a common time reference.
3. Synchronization of data sampling across the power system: this application is the most con- straining and requests that all IEDs across the whole system are synchronized within 1µs or less of each other. This puts additional limitations on the distribution techniques to maintain this level of accuracy.
Measurement of synchrophasors falls into the last category and therefore requests the highest accuracy in time synchronization.
2.3.2.2 Satellite broadcasts and GPS
Today, the most accurate source of time synchronization is accessible through satellite broadcast.
With respect to terrestrial sources, it has the advantage of not being affected by the irregular terrain and only slightly by atmospheric and seasonal variations, and it offers a world-wide coverage. At the same time it is relatively cheap for the user because the satellite system sponsor provides the primary reference and time dissemination systems. As a consequence, the principal problem or risk with satellite broadcast isavailability. All satellite systems have been put up through individual or joint government efforts for purposes other than time dissemination. During crises, the primary purposes take priority, and timing functions may be suspended or intentionally degraded, resulting in reduced accuracy. Moreover, satellite systems are expensive to maintain and those using the system for timing purposes are at the mercy of funding provided for the primary function [23]. The consequence of a GPS signal loss on PMU accuracy has been investigated, for example, in [24].
The main systems currently in use are GOES, GPS and GLONASS. Several other potential sources include the GALILEO satellite system. We will now focus on the GPS system because it is the one used by currently commercially available PMUs.
The Global Positioning System (GPS) is a constellation of 24 Earth-orbiting satellites (24 are in operation and there are several satellites as backups) developed by the U.S. Department of Defense, initially as a military navigation system. Soon it was opened to everyone and in year 2000 theselected availability3was eliminated so that everyone can now benefit from the full accuracy of the system.
The satellites are moving in low-Earth orbiting, that is approximately 20,200 km above the Earth surface, with an orbit of 12 hours and emit a 1575MHz time signal that can be received by a simple omnidirectional antenna. The system guarantees coverage of at least four satellites at all times, even in sites with restricted sky view. In most places six to ten satellites are in range so that signal reception is unlikely to be lost. The signal is resistant to interferences but has a very low level requiring a sensitive receiver.
GPS receivers must know where the satellites actually are in order to correct for the propagation delay. This is possible because the satellites travel in very high and predictable orbits. Therefore, the GPS receiver stores an almanac that tells where every satellite should be at any given time. The U.S.
Department of Defense moreover constantly monitors the exact position of the satellites and transmits adjustments to all GPS receivers as part of the satellites’ signals.
Whereas the most common use of the GPS system is in determining coordinates of the receiver, the signal which is most important for PMUs is theone pulse-per-second(PPS). The GPS satellites keep accurate atomic clocks which provide the “GPS time”, that does not take into account the Earth rotation. The identity of the pulse is defined by the number of seconds since the time that the clocks began to count (January 6, 1980). The receivers then correct for the Earth rotation and provide the UTC clock time, which is today the standard time reference for industrial applications.
2.3.2.3 Accuracy of PMU synchronization
The IEEE Standard for synchrophasors C37.118 requires the time synchronization to be accurate to 1µs. This corresponds to an angular accuracy of 0.022◦ for a 60Hz system, and 0.018◦ for a 50Hz system. Commercially available PMUs are able to reach this level of accuracy, and even better accuracies, if some measures are taken.
GPS RECEIVER ERROR
The sources of inaccuracies of the time synchronization at the GPS receiver can be summarized as follows [23]:
• Time adjustments are made assuming that the radio signal propagation delays, based on the speed of light, are constant. In fact, the Earth’s atmosphere slows the radio signals down slightly.
The delay varies depending on what angle the received signal passes through the atmosphere.
• The propagation speed in the receiver antenna and antenna lead is different from free-space and the atmosphere. Therefore the delay through the antenna lead varies with length. Some receivers compensate for this by assuming an average antenna lead length, others allow the user to input a delay setting. For long distances between antenna and receiver, some manufacturers provide repeating amplifiers that create an inherent incremental signal delay.
• Problems can also occur when radio signals bounce off large objects, such as adjacent buildings, giving a receiver the impression that the satellite is further away than it actually is.
3Until May 2000, the U.S. military only could benefit from the actual GPS accuracy, while the public was limited to a lower degree of accuracy.
• Satellites occasionally send bad almanac data, misreporting their own position.
• Time jitter may occur when the satellite clock receiver looses lock with one satellite and achieves lock with another.
GPS satellite clock receivers compensate and adjust for many of these error sources, so that theerror at the receiveris in the range of less than 50ns.
TIME SYNCHRONIZATION DISTRIBUTION ERROR
The above holds forstratum 14 time synchronization. Once the stratum 1 signal is received, it is used directly by the clock in the receiving device to display accurate time anddisseminate a time signal to IEDs in the vicinity according to the IRIG-B format (the standard IRIG stands for Inter Range Instrumentation Group) [25]. The demodulated IRIG-B time code, used for PMUs, is a pulse train of positive pulses at the rate of 100 PPS. The rising edge of the reference pulse coincides with the seconds change in the clock and provides an accuracy of 1ns. The distribution of the IRIG-B time synchronization then suffers some latency, which is proportional to the cable length. It is estimated to be in the range of 5ns/m.
PPS PPS
tsample
0 tabs
tsample
+
_
PPS
oscillator offset
Figure 2.3: Synchronization of the internal oscillator of an IED with the PPS signal.
The last source of synchronization error is the IEDsynchronized time processing. IED typically use the IRIG signal to update their onboard clock and calendar in a background mode. The period between reading the signal may vary depending on how busy the processor is with higher priority functions. The onboard clock might then lose accuracy, depending on the stability of the clock oscil- lator. To achieve the highest possible IED clock accuracy, the IED must regularly read and process the IRIG time synchronization signal, for example every second. In most devices, the internal IED clock is locked with the incoming PPS through a phase-locked loop such as that depicted in Figure 2.3.
Each sample of the voltage and current digital waveforms is stamped with respect to the last received pulse. At every pulse, the offset between the pulse and the last sample at the sampling frequency is computed, and fed back to adjust the sampling rate.
4Stratum levels are used to indicate the traceability path from the atomic clocks operated by national standards organi- zations. They are stratum 0 clocks because they are the most accurate. However, stratum 0 time sources cannot be used on the network. Stratum 1 time sources are directly traceable to national standards. Stratum 1 time sources get their time by direct connection to atomic clocks, through GPS transmissions. Therefore, stratum 1 time sources act as the primary time standard. Stratum 2 time sources get their time from stratum 1 sources, and so on. Higher stratum levels are deemed less accurate than their source due to transmission delays (from a few to several ms per level) [23].
2.3.3 Telecommunications and infrastructure
PMUs are installed in power system substations. In most applications, however, the phasor data are used to make decision and initiate actions at locations remote from the measuring PMUs. There- fore, an appropriate infrastructure is required to transmit phasor data.
2.3.3.1 Data concentrators
The data stream from a PMU goes to servers where data from several PMUs are combined. The devices at this second level of hierarchy are commonly known asphasor data concentrators(PDC). A PDC gathers data from several PMUs, rejects bad data, aligns the time-stamps, and creates coherent sets of simultaneously recorded data from part or the whole power system. There are storage facilities at the PDC as well. The PDC application functions can be monitoring, feeding other tools or even real-time controls.
One may view the PDC as the level of data gathering of a utility (TSO or regional service centre).
On a systemwide scale, the utility can exchange data or information with another utility, at the level of PDCs. The advantage is that one can select which data to exchange and at what rate. An alternative to this decentralized approach is to have a super-PDC that gathers data from PDCs. It can be all data, or only some data needed for systemwide applications (oscillations monitoring), while local applications are performed at the utility PDC level (state estimation, voltage stability monitoring, event analysis) [26].
2.3.3.2 Data transfer parameters
Communication facilities are essential for applications requiring phasor data at remote locations.
The most critical parameters influencing the design of a network for WAMS are the bandwidth (or capacity), the latency, the reliability and investment [27].
The channel capacity is the measure of the data rate (in kilobits per second) that can be sus- tained on the available data link. It also often referred to as thebandwidth. The data volume created by PMUs is in the range of 20 to 80 kbit/s. In the rest of this work, we will consider that this is not a limiting factor.
The data latency is defined in [28] as the time between when the state occurred and when it was acted upon by an application. Each application has its own latency requirements depending upon the kind of system response it is dealing with. Among the other delays, communication delay also adds to the latency and needs to be minimized. The communication delays on the network are comprised of transmission delays, propagation delays, processing delays, and queuing delays.
An application where the time delay is crucial and given a lot of attention is the design of wide- area power system stabilizers (for more details, see Section 8.6.2). In [29], the tradeoff between performance (in the time-domain and frequency-domain) and delay tolerance is analyzed. Not sur- prisingly, time delay tolerance increases when system bandwidth increases while this latter improves the performance. The authors also compare approaches to increase the time delay tolerance while maintaining an acceptable performance.
The data transfer reliability is also an important parameter that influences the availability of the synchrophasor data for the applications. It takes into account the loss of data packets as well as
the loss of a communication link. Lost data packets depend on the used protocols and communication links, and on queuingissues in routers. The impact of a lost communication link depends on the network topology (redundancy).
2.3.3.3 WAMS architecture
The design and deployment of WAMS have been given a lot of attention in the literature, for example, [30, 2]. A first design choice is the choice of a centralized or decentralized topology, and is shown in Figure 2.4. In large power systems, the control strategy will most probably be a combination of centralization and decentralization, with various levels of hierarchy. This is well illustrated by the NASPI roadmap [31].
(a) (b)
Figure 2.4: Representation of a (a) centralized and (b) decentralized control strategy for WAMS [27].
In [27], two indices are used to identify the influence of a certain system architecture on the latency and reliability of the communication network: thenumber of routers - i.e. the number of nodes between given node and control centre, also known as network hops - and thelength of media.
For an equivalent cost, it is shown that a decentralized control strategy has the potential to decrease latency and improve reliability.
The approach presented in [28] consists in designing a WAMS infrastructure based on the power system specificities and the requirements in bandwidth and latency of the anticipated applications of the user. A few representative applications are listed for illustration (Figure 2.5) with the associated requirements for the WAMS: required data (or physical variables), number of PMUs, geographical location of the used PMUs and the length of a data window required.
Authors of [27] also emphasize that power grid transmission media can be either dependent and independent. Dependent media are part of power network elements (e.g. power line communication, broadband over power line), while independent media do not depend on the power system and may be of the type available to all users as an open access media (for instance, wireless communication media) or those owned by data service providing companies (such as leased line or dedicated data links). Dependent media can be co-optimally designed in conjunction with power system planning problems and offer an opportunity to manage infrastructures interdependency problems.
Figure 2.5: Survey about latency and data requirements for PMU applications [28].
2.3.4 PMU placement
The question of placement of PMUs is also an item receiving a lot of attention in the literature.
Several methodologies are used, either to reach a sufficient coverage to monitor the whole system or dedicated to a specific application.
Optimal placement techniques for system observability were developed in, for example, [32, 33, 34]. These authors have developed and applied various optimization and searching methods.
From their work, we can conclude thatcompletesystem observability is guaranteed by the placement of PMUs at about 1/5 to 1/4 of the number of network buses. This number is reduced further when acceptingincompleteobservability. In [35], the problem is posed to maximize the information content of the captured signals while minimizing the redundant information.
Placement methodologies for system dynamics monitoring - The first proposed methodolo- gies for dynamics monitoring [36, 37] used pilot pointslocated at the center of coherent regions of a system. These regions contain groups of stiffly interconnected machines with common modes of oscillations in the case of small-signal stability studies. Unfortunately, the system may not always be decomposable into meaningful clusters and this leads to monitoring all machine terminals. Fur- thermore, coherent regions are not stationary but exhibit also a dynamic behavior. Indeed, they may split or merge as the loading conditions of the system change. Consequently, apilotplacement that is optimal at a particular operating condition may perform poorly at another.
PMU placement for inter-area oscillations monitoring - For electromechanical oscillations (our target application in the second part of this thesis), the most common approach is theoretical and based on the model of the system (under the assumption that the model is accurate enough for this purpose). The eigenvectors of the dominant modes provided by linear analysis (see Section 8.4.5) are used to compute the observability of these modes. The substations where the observability is the highest are the best candidates for the installation of the PMUs. Similarly, if actuators (FACTS, HVDC, or even wide area PSS) are used to control or damp oscillations, the most efficient locations are given by the controllability of the modes.
In [38], Palmeret al. propose a method to choose the measurement sites in order to maximize their sensitivity to lightly damped inter-area modes while minimizing their sensitivity to local modes.
A deeper understanding of the propagation of electromechanical modes across the system vari- ables can also be used to select the ideal PMU locations. This approach was developed in [39] and extended in [40], where a closed-form expression for network sensitivities is provided.
2.4 The synchrophasor measurement chain
The previous sections provided details on all elements involved in the complete measurement chain for synchrophasors. We can now wrap up the collected information and assess the impact of each element on the accuracy, delay and availability of synchrophasors for the subsequent applications.
1. The voltage and current analog waveforms are acquired from the secondary windings ofmea- surement transformers. These measurement transformers are one of the main source of errors in the measurement chain.
(a) Accuracy class: Measurement transformers are characterized by an accuracy class. The class designation of a transformer is an approximate measure of the accuracy. It gives the amplitude error of a current, resp. voltage, transformer in % at rated current, resp.
voltage. While voltage is kept under normal operation in a small range around nominal value, the current depends on the loading of the network and the specific topology around the measurement location. Therefore, the relative error in current is mostly higher. The allowed phase error for a specified load impedance is also defined for each class in the IEC standard 60044.
For PMU applications, it is recommended to use metering transformers rather than re- laying transformers. Indeed, metering transformers are designed for billing and require a higher accuracy along the whole measurement scale than relaying transformers, used to identify specific or abnormal conditions to trip equipment.
In the power industry, it is common practice to use class 0.2 metering transformers. These have errors in the range of 0.2% in magnitude and 10 minutes in phase.
(b) Calibration and reclassification of relaying transformers: Errors from measurement transformers can be reduced by calibration but it is known to be expensive and time- consuming, and rarely performed on a system-wide basis. Phasor measurements can be used for calibration under the condition that access is given to a reference transformer [41]. Where no metering transformers are present, reclassification (i.e. upgrading) of a relay-class transformer into a metering-class transformer allows avoiding investment and optimizing equipment [42].
2. The synchronization accuracy influences essentially the phase error of the synchropha- sors. In order to measure a phasor or a phase angle difference at remote locations, a reference is required. This reference is available with thetime synchronizationfrom GPS. Synchronization was detailed in Section 2.3.2 and can be divided in four parts:
(a) GPS signal emission: very accurate, with an error in the range of nanoseconds.
(b) The error at theGPS receiveris in the range of 50 nanoseconds.
(c) The main contributor to synchronization error can be theGPS signal distribution within the substationif not taken care of. However, it is possible to keep it in the range of a few tens of nanoseconds.
(d) Synchronization of the internal clock of the measurement device: since synchroniza- tion is a high-priority task for PMUs, manufacturers ensure that the clock stability is high and that synchronization is verified at least every second to avoid any drift in the sampling rate.
Overall, the synchronization error of PMUs must be lower than 1µs to comply with the IEEE Standard C37.118. This is equivalent to 0.018◦ for a 50Hz system. In practice, most com- mercially available PMUs have better accuracies than this. If the synchronization chain is well established (moderate cable length between antenna and receiver, quality wiring, knowledge and compensation of latency), it is possible to keep this error within 200 to 500 nanoseconds.
3. Input filtering and conversion of the PMU introduces small errors and latency. The input analog waveforms of current and voltage pass through a hardware analog filter and an analog- to-digital (A/D) converter in order to create a digital signal at a high sampling rate for the electronic device. Know-how of manufacturers allows reducing and even neglecting this error with respect to others.
4. The estimation of the synchrophasor is a potential source of major errors and non-negligible latency. Once the sampled signals are made available, the device has to estimate the syn- chrophasor and to time-stamp it with respect to the synchronization signal. Many different phasor estimation algorithms exist and perform differently. They are the scope of Chapters 3-5.
(a) In most commercially available PMUs, off-nominal frequencies and the levels of noise and harmonics typical to transmission and distribution power system do not introduce errors.
(b) The major source of error is the non-stationarity of the signal within the measure- ment window and signal modulations. While in steady-state, the phasor accuracy is in the range of 0.01◦, this error can increase substantially during electromechanical oscilla- tions and can be higher than the requirement of the standard (phase angle errors of 0.1 to 0.5◦are typical).
(c) The latency introduced in the measurement is strongly dependent on the algorithm used. Its order of magnitude is in the range of tens of milliseconds, and is only critical for applications requiring very fast reaction times (transient stability). For applications involving closed-loop controls, knowledge of the latency can be used to improve the ef- fectiveness of control schemes.
The latency and errors differ from one processing method to another and a trade-off is possible.
For the user, it is also possible to privilege one parameter with respect to the other. This idea will be developed in Section 4.4.3.2.
5. The telecommunication infrastructure can influence strongly the availability and latency of synchrophasor data.
(a) While the length of the links influences in a proportional way the transfer delays, the routers in the network influence both the delay and availability of data. While pack- ets can be lost, queuing is the main sources of delays. In some cases, delays are such
