Phasor Measurement Unit Testing

Transcription

1 Delft University of Technology Faculty of Electrical Engineering, Mathematics and Computer Science Master of Science Thesis Phasor Measurement Unit Testing by Nhi Nguyen Delft, The Netherlands August 212 Copyright c 212 by Nhi Nguyen. All rights reserved.

2 Committee members Prof. ir. Lou van der Sluis Delft University of Technology, the Netherlands Dr. ir. Marjan Popov (supervisor) Delft University of Technology, the Netherlands Dr. ir. Dhiradj Djairam Delft University of Technology, the Netherlands Dr. ir. Gert Rietveld (supervisor) VSL, the Netherlands

3 Preface The thesis is the result of my 9 months working in the PMU project. It includes the study into PMU behavior and IEEE Synchrophasor standards through simulation and measurements. Simulation is done on a software platform whereas measurement is performed at a company, VSL, to test a PMU on its measurement quality. First of all, I would like to express my special thanks to my supervisors, Dr. Marjan Popov and Dr. Gert Rietveld, for their enthusiastic guidance and valuable suggestions and comments. I highly appreciate all their supevision, explanation, suggestions, and advice. I also would like to thank all staff members of the EPE group for providing me with important and useful knowledge and skills throughout my two years of studying. I wish to thank Alicja Lojowska, my officemate, for her kindness and her support during the time I have been working on my thesis. I would like to thank her for teaching me how to use Latex and for her lovely smile and sense of humor, which always makes me feel more positive. Finally, I thank my family and friends for their understanding and supporting during my study here. 1

4 Contents 1 Introduction Literature review Research objectives Research methodology Organization of the Thesis IEEE C Standards and Test signals IEEE C Standards Synchrophasor definition Measurement reporting rate Measurement reporting time Measurement evaluation Measurement compliance Test signals Steady state test signals Dynamic test signals Faulted test signals PMU simulation Simulation with steady state test signals Simulation with signal frequency Simulation with signal magnitude Simulation with signal phase angle Simulation with harmonic distortion Simulation with dynamic test signals Simulation with modulated test signals Simulation with frequency ramp signals Simulation with input step change signals Simulation with fault signals

5 CONTENTS 3 4 PMU test setup Test principle Test setup The Digitizer NI PXI The amplifiers The current shunt and the voltage divider The PMU under test Time source PMU test results PMU Window functions Window function properties Test on Window functions Test on Raised Cosine estimator algorithm Test with steady state test signals Test with signal frequency Test with signal magnitude Test with signal phase angle Test with harmonic distortion Test with dynamic test signals Test with modulated test signals Test with frequency ramp signals Test with step change signals Test with fault signals Conclusions and Recommendations Conclusions Recommendations for future work Appendices 91 A IEEE Synchrophasor Standard C compliance 92 B An example of PMU output phasors saved in *.txt file 96 C An example of the DG measurement of reference signals saved in *.txt file 98

6 List of Figures 2.1 Synchrophasor Synchrophasor Combined modulated test signal at 5 Hz modulation frequency (k x =.1; k a =.1; f=5hz) and phase modulated test signal at 1 Hz modulation frequency (k x = ; k a =.1; f=1hz) Frequency ramp test signals Magnitude and phase step test signals Fault currents of a single phase short circuit at phase A, 11 kv voltage bus Fault voltages of a single phase short circuit at phase A, 11 kv voltage bus PMU errors with signal frequencies PMU phase angle at 45Hz PMU errors with signal magnitudes PMU errors with signal phase angles PMU errors with harmonics PMU and reference magnitude and phase for 2 Hz combined modulated signals PMU errors with 2 Hz combined modulated signals PMU errors with 2 Hz phase modulated signals PMU errors with -1Hz/s ramp signal PMU errors with +1Hz/s ramp signal PMU responses for magnitude step signal PMU responses for phase step signal PMU responses and errors with fault signals PMU test procedure

7 LIST OF FIGURES PMU test setup diagram PMU test setup picture DG Filter delay PMU Hann, Hamming, and Blackman rolloff and rejection charateristics at window length 4 cycles PMU Rectangular, Flat Top, and Raised Cosine rolloff and rejection charateristics at window length 4 cycles PMU Triangular, Kaiser, and Nutall 4 Term rolloff and rejection charateristics at window length 4 cycles PMU errors as a function of window length for voltage test signal PMU errors as a function of window length for current test signal PMU errors as a function of window length with Raised Cosine window for voltage test signal PMU errors as a function of window length with Raised Cosine window for current test signal Rejection characteristic of Raised Cosine window at different window lengths PMU phase angle at 45Hz PMU errors as a function of power system frequency for voltage test signal PMU errors as a function of power system frequency for current test signal PMU errors as a function of signal magnitudes PMU errors as a function of signal phase angles PMU errors as a function of signal harmonic distortion PMU errors for 1 Hz modulated voltage test signal PMU errors for 2 Hz modulated voltage test signal PMU errors for 5 Hz modulated voltage test signal PMU errors for 2 Hz modulated current test signal PMU errors for ±1 Hz frequency ramp test signal PMU response delay and overshoot for magnitude step voltage signal PMU responses for magnitude and phase step voltage test signal PMU errors for step voltage test signal PMU errors for fault signal PMU responses for fault signal

8 List of Tables 2.1 PMU reporting rates PMU frequency range for signal frequency test PMU modulation frequency range A.1 Steady-state synchrophasor measurement requirements 93 A.2 Steady-state frequency and ROCOF measurement requirements A.3 Synchrophasor measurement bandwidth requirements using modulated test signals A.4 Frequency and ROCOF performance requirements under modulation tests A.5 Synchrophasor measurement requirements under frequency ramp tests A.6 Frequency and ROCOF performance requirements under frequency ramp tests A.7 Phasor performance requirements for input step change 95 A.8 Frequency and ROCOF performance requirements for input step change A.9 Response time for M-class phasor, Frequency and ROCOF for input step change

9 LIST OF TABLES 7 Acronyms GPS Global Positioning System PMU Phasor Measurement Unit SCADA Supervisory Control And Data Acquisition WAMPAC Wide Area Monitoring Protection And Control WAVI Wide Area Voltage stability Index NIST National Institute of Standard and Technology DUT Device Under Test CET Centre for Electric Technology DTU Technical University of Denmark VSL Dutch Metrology Institute UTC Universal Time Coordinated ROCOF Rate Of Change Of Frequency TVE Total Vector Error FE Frequency Error RFE Rate of change of Frequency Error MagE Magnitude Error PhaE Phase Error THD Total Harmonic Distortion DFT Discrete Fourier Transform DG Digitizer I/O Input/Output 1 PPS 1 Pulse Per Second FFT Fast Fourier Transform

10 Chapter 1 Introduction Power systems often operate close to their stability limit which means that any disturbances or faults may cause power oscillations and lead power systems to a cascade outage. It is, therefore, necessary to make correct decisions on how to take actions to stabilize power systems. With the advent of clock synchronization via Global Positioning Systems (GPSs), phasor measurement units (PMUs) have been introduced. PMUs are devices which produce synchronized phasor, frequency and rate of change of frequency estimates from voltage and/or current and a time synchronizing signal [1]. The key driver for PMU technology is the use of the precise time sources provided by GPS satellites to accurately measure the relative voltage and current phase angles at buses across interconnected grids [2]. This technology is capable of directly measuring the phase angles across an interconnected power grid, which is the main advantage that PMUs have over traditional SCADAs. PMUs are increasingly being deployed in power systems with various applications such as state estimation, angle and frequency monitoring, model derivation and validation, wide-area monitoring, protection and control, etc. Real-time data from PMUs provides significant improvements in such power system applications. For instance, it provides real-time monitoring and control of power systems, enhancement in state estimations, real-time congestion management, adaptive protection, power system restoration, etc. The requirements for PMU performance are defined in the IEEE Synchrophasor Standard C [3] and then C [1]. The former standard only introduces requirements for PMU steady state performance. Requirements for dynamic performance has been revised and incorporated into the later standard C In both standards, the measurement qual- 8

11 1.1. LITERATURE REVIEW 9 ity of PMUs is evaluated on the basis of the Total Vector Error (TVE) concept and benchmark tests, including the step tests on magnitude, phase and frequency. TVE is defined as the measure of error between the theoretical phasor value of the signal being measured and the phasor estimate [4]. The standard requires TVE to be less than 1 % under any conditions [1], [3]. 1.1 Literature review The first prototype PMU was developed in 1988 by a Virginia Tech research team starting from the Symmetrical Component Distance Relay algorithm. PMUs were then commercially manufactured and several innovations were added such as an internal GPS receiver, analog-to-digital converter data concentrators, and modem interfaces for remote access to the PMU. After the introduction of this new measurement device, research effort was made to develop PMU applications in power systems. Initial PMU applications were related to state estimations [4]. One piece of research into state estimations using PMU deals with the placement of minimal sets of PMUs in order to make the system measurement model observable and, therefore, linear. Different algorithms have been developed to solve this problem, such as integer linear programming, topology based or placement strategy against loss of a single PMU, etc. Simulation results have shown that about one fourth to one third of the system buses need to be provided with PMUs for complete observability [5]. Fault detection/location using PMU measurement has also been researched. References[6] and[7] propose an adaptive technique for fault detection/location. The papers indicate that by combining a robust fault detection/location index, parameter estimation algorithm, a special filtering technique and a well-designed PMU, the proposed technique will be an adaptive, high performance and low-cost fault detection/location technique with an accuracy of up to 99.9 %. Additional research has been performed about the usage of PMUs in widearea monitoring, protection and control (WAMPAC) of power networks. In [8], an overview of PMU applications in a large-scale WAMPAC system is described. The paper in question presents a typical WAMPAC architecture with its main building blocks. It notes that the architecture depends on specific system needs, its topology, generation profile, and the quality of the communication infrastructure.

12 1.1. LITERATURE REVIEW 1 There has also been much research into the problem of voltage stability using PMUs. In [9], a Wide Area Voltage stability Index (WAVI) for dynamic situations is proposed. In [1], an algorithm for fast detection via Thevenin equivalents is described. Reference [11] deals with measuring devices. In [12], a contingency analysis and a model are proposed. Reference [13] develops an index for a transmission corridor, which is based on the transmission line capability. Reference [14] studies how PMUs can define a problem in the network to obtain voltage regulation. Many tests and calibrations have been performed on PMUs. Reference [15] describes the calibration system and dynamic test system for PMUs at the National Institute of Standards and Technology (NIST). The calibration system covers all conditions that satisfy the Standard requirements according to several hundred individual tests. It consists of a GPS clock and a device under test (DUT) connected to antennas to receive the GPS signal. The dynamic test system has a similar basic design to the calibration system. The test signals generated have linearly varying magnitude and frequency, as well as sinusoidal and damped sinusoidal magnitude and frequency. Reference [16] presents the plans and process towards the development of the dynamic PMU performance test system at NIST. An analysis model and an algorithm for taking time-synchronized signals and calculating dynamic parameters are proposed. Several test patterns for the dynamic testing of PMUs including linearly changing magnitudes or frequencies are presented. In [17], a report on the results of PMU laboratory development and testing done at the Centre for Electric Technology (CET), Technical University of Denmark (DTU) is made. According to this report, the university s PMU named DTU-PMU is tested and compared with a commercial PMU. Three main tests, including a steady-state test, a modulation test, and a dynamic test and harmonic rejection have been done. The dynamic tests are performed with the amplitude scan, phase angle scan and amplitude step signals. The steady state tests are implemented conforming to the IEEE standard C and the test results confirm the validation of the test setup and the performance of the DTU-PMU. Reference [18] lists initial results using TVE to investigate PMU performance conforming to the IEEE C standard. Two PMUs were tested with the signal magnitude test, signal phase angle test, amplitude modulation test, harmonic rejection test and frequency ramping test. However, the TVE standard for frequency ramping test at this time (21) is still under development (but not now in 212). It states that TVE error is mostly influenced by frequency and angle measurement. It also notes that a more generalized and accurate descrip-

13 1.2. RESEARCH OBJECTIVES 11 tion of phasor is necessary for amplitude modulation test. In [19], there is a description of several methods for analyzing dynamic power signals sent to a PMU. These methods, Taylor Expansion and Three-Waveform method, allow these signals to be accurately characterized in terms of their amplitude, phase, and frequency at specific time stamps synchronized to a PMU. This, in turn, allows PMUs with a wide range of dynamic signals to be accurately characterized. Paper [2] describes the equations for combined phase and amplitude modulated signals as test signals. It also describes a method for analyzing such modulated signals and for providing accurate phasor estimation. 1.2 Research objectives The research objectives of the thesis include: Understanding the behavior of PMUs through simulation and measurement; getting used to the new standard for PMU operation, i.e IEEE C [1]; learning how to evaluate the measurement quality of PMUs with the requirements mentioned in the IEEE C Standard; defining test signals that could be used for testing PMUs. Testing a PMU according to the IEEE C Standard in steady state and dynamic conditions; evaluating the quality of the PMU as well as the source of errors contributing to TVE errors of the PMU with a series of test signals and different PMU setting parameters. The thesis first discusses background knowledge on PMU and the field of PMU research, then going on to present the procedures and results in testing the Arbiter PMU. It begins with a literature review on PMU research and PMU testing and calibrating. It continues with a summary of the test signals to be used for testing the PMU. The rest will constitute a description of all steady state and dynamic tests together with results and conclusions. 1.3 Research methodology The testing of the PMU is done in three steps. Firstly, the IEEE C Standard has to be studied carefully to gain a general knowledge on how to estimate the measurement quality of PMUs and define which requirements and which test conditions should be included in the test. Next,

14 1.4. ORGANIZATION OF THE THESIS 12 a series of test signals, both steady state and dynamic, are generated in compliance with the standard. Then, a high accuracy test setup is prepared. This test setup is responsible for the generation and measurement of continuous test signals within a given test period. The generated test signals will be supplied for the inputs of the PMU and the measured test signals will provide the reference signals for calculating the errors of the PMU. After all the tests have been done, the analysis will be performed by comparing the output phasor of the PMU and the reference phasor in terms of their magnitude, phase, frequency and rate of change of frequency (RO- COF). The total vector error (TVE) is then calculated on the basis of the magnitude and phase of both phasors. 1.4 Organization of the Thesis Chapter 1: Introduction This chapter contains a literature review on post PMU research generally and on PMU testing and calibrating specifically. It continues with the research objectives and research methodology of the thesis and ends up with outlining the structure of the thesis. Chapter 2: IEEE C Standards and Test signals This chapter deals with all the test signals that will beused duringthe PMU test. These signals are generated as described in the IEEE C Standard. This chapter also discusses the requirements on PMU operation in the IEEE C Standard. Chapter 3: PMU simulation This chapter discusses the simulation results of the test signals with the help of a Software Platform provided by VSL. It provides initial insight into PMU operation and measurement quality evaluation. Chapter 4: PMU test setup This chapter describes in detail the procedure of PMU testing and the measurement setup. Chapter 5: PMU test results This chapter represents the body of the work done for the thesis. It shows the results of all measurements. It also includes discussions and evaluations on the obtained results.

15 1.4. ORGANIZATION OF THE THESIS 13 Chapter 6: Conclusions and Recommendations This chapter describes the thesis conclusions and recommendations for future work.

16 Chapter 2 IEEE C Standards and Test signals 2.1 IEEE C Standards The IEEE Synchrophasor Standards C [3] and C [1] provide a tool for defining PMU performance requirements and standardizing PMU measurement quality. The original Synchrophasor standard was IEEE This standard was then reviewed and developed into IEEE C [3]. The second standard provides a measurement convention definition, introduces a method of determining measurement precision, improves the time stamping method defined in the previous version, and provides requirements for measurement under steady state conditions [21]. In compliance with the IEEE C , many tests on PMU performance under steady state conditions have been developed. However, the ability of PMU to operate under dynamic conditions of the electric power grid has become increasingly important. Therefore, the need for dynamic PMU testing has required additional information to be included into the current standard. The IEEE C was again reviewed and replaced by the IEEE C [1], which is the current standard. In this standard, additional clarification for the phasor and synchronized phasor definitions has been provided. The concepts of TVE and compliance tests have been retained and expanded. Temperature variation tests have also been added. Above all, requirements for dynamic tests have been introduced and limits on frequency measurement and rate of change of frequency (ROCOF) 14

17 2.1. IEEE C STANDARDS 15 measurement have been provided [1] Synchrophasor definition The synchrophasor or synchronized phasor measurement is the representation of a sinusoidal signal with a phase angle relative to a cosine function at the nominal system frequency synchronized to the Universal Time Coordinated (UTC). In other words, the UTC provides a common time base for all PMUs. Accordingly, all PMU phase angle measurements are directly comparable. This provides invaluable information for wide area monitoring, protection and control of the electric power networks. The phasor measurement is done at a particular instant of time represented by the phasor time tag. The PMUs will receive a one pulse per second (1 PPS) GPS signal or a UTC secondrollover along with this time tag. If the time tag coincides with the peak of the cosinusoidal signal (Figure 2.1a), then the phase angle will be (Figure 2.1b), whereas a time tag occurring at the positive zero crossing of the signal (Figure 2.2a) will result in a phase angle of -9 (Figure 2.2b) Xm t= (1PPS) X=(X m / 2)e j (a) Waveform (b) Phasor Figure 2.1: Synchrophasor 1 The time tag occurring at the peak of the cosinusoidal signal leads to a synchrophasor with zero phase angle. A phasor estimation is made by sampling the waveform over a window of observation, which represents an average of the parameters that may be

18 2.1. IEEE C STANDARDS Xm t= (1PPS) X=(Xm/ 2)e j (a) Waveform (b) Phasor Figure 2.2: Synchrophasor 2 The time tag occurring at the positive zero crossing of the cosinusoidal signal leads to a synchrophasor with -9 phase angle. changing during that window. In most cases, a phasor is best estimated by a time tag at the center of the estimation window [1] Measurement reporting rate The measurement reporting rate F s is estimated in number of frames per second (frames/s). or data frame is a set of synchrophasor, frequency, and ROCOF measurements that corresponds to the same single time stamp [1]. Table 2.1: PMU reporting rates System frequency 5Hz 6Hz Reporting rates (Fr/s) A PMU provides data reporting rate at sub-multiples of the nominal power frequency [1], from 1 frames/s up to the system nominal frequency (5 or 6 frames/s). This is the rate at which TVE, FE and RFE estimates will be made. The actual rate to be used will be user selectable.

19 2.1. IEEE C STANDARDS Measurement reporting time For a reporting rate N frames/s(n is a positive interger), the reporting times will be evenly spaced through each second with frame number (numbered from to N-1) coincides with the UTC secondrollover or the 1 PPS signal provided by GPS. These reporting times are to be used for determining the instantaneous values of the synchrophasor [1] Measurement evaluation A synchrophasor measurement is evaluated using TVE. The standard defines TVE as the difference between a perfect sample of a theoretical synchrophasor and the estimated phasor given by the unit under test at the same instant of time. To put it more simply, TVE is the relative difference between a measured phasor at the output of the PMU and a reference phasor: ( TVE = X r (n) X r (n)) 2 +( X i (n) X i (n)) 2 X r (n) 2 +X i (n) 2 [1] (2.1) Where: Xr (n) and X i (n) are sequences of estimates given by the unit under test and X r (n) and X i (n) are sequences of theoretical values of the input signal at the instants of time (n) assigned by the unit to those values. TVE represents a combination of two possible errors, i.e the magnitude error and the phase error. For instance, if a given PMU that perfectly synchronized with the reference time has no phase error, 1 % of TVE means thatthistotalvectorerroriscausedby1%ofthemagnitudeerror. Similarly, with a zero magnitude error, 1 % of the TVE is due to 1 % of the phaseerror which is.1 rador.57. Thiscorrespondsto atime errorof approximately ±31 µs for a 5 Hz system. The standard requires a limit of 1 % for both performance classes (explained in the next part) under all test conditions except the modulated test. For modulated tests, this limit is 3 % in both classes. Frequency and rate of change of frequency (ROCOF) measurement accuracy are also specified in the standard. Frequency error (FE) and ROCOF error (RFE) are defined in the standard as the absolute value of the difference between the theoretical values and the estimated values at the same time

20 2.1. IEEE C STANDARDS 18 instant given in Hz and Hz/s respectively: FE = f true f measured = f true f measured [1] (2.2) RFE = (df/dt) true (df/dt) measured [1] (2.3) A time source frequency error of.1 mhz in a 5 Hz system will cause an error of.5 Hz ROCOF. The standard requires that the maximum allowed FE and RFE during steady state test conditions are 5 mhz and.1 Hz/s respectively. During dynamic test conditions, these values are higher depending on each specific test. Experience has shown that PMUs are among the best frequency transducers available, delivering a frequency accuracy of a few milihertz (typically 1-3 mhz) with a measurement window of a few cycles [21]. TVE, FE and RFE are calculated for every data frame of a PMU. A PMU having a reporting rate of 5 frames/s, for example, will have its TVE, FE and RFE calculated in each of those 5 frames. It is also mentioned in the standard that the TVE, FE and RFE for each measurement will be the average, RMS, or maximum values observed over a minimum of 5 seconds of test duration, depending on specific tests. Besides, there are definitions and requirements on measurement response time and delay time, measurement reporting latency and measurement and operational errors. Measurement response time is the time to transition between two steady state measurements before and after a step change is applied to the PMU inputs. It can be determined as the difference between the time that the measurement leaves a specified accuracy limit and the time it re-enters and stay within that limit when a step change is applied to the PMU inputs [1]. Measurement delay time, on the other hand, is defined as the time interval between the instant that a step change is applied to the input of a PMU and the measurement time that the stepped parameter achieves a value that is haft way between the initial value and final steady state values [1]. These response time and delay time will be determined through tests with input step change test signals and fault test signals. Measurement reporting latency is the time delay from when an event occurs on the power system to the time that it is reported in data [1]. Measurement and operational errors are the internal problems encountered by the PMU during the measurement process, which will be indicated by a flag assigned by the PMU. In later simulation and testing, the PMU is not tested on these measurement reporting latency, and measurement and operational errors.

21 2.2. TEST SIGNALS Measurement compliance The standard requires all compliance measurements to be evaluated by a class of performance. There are two classes of PMU performance defined in the standard: the P class and the M class. The P class refers to Protection application, which requires fast response while the M class stands for Measurement application which requires greater precision and does not require the quickest reporting rate. This class of performance is provided by the vendor or it can be user selectable if the vendor provides both P and M classes. All compliance tests are to be performed with all the parameters set to standard reference conditions, except those being varied during each specific test [1]. Such reference conditions for all tests are nominal voltage; nominal current; nominal frequency; constant voltage, current, phase and frequency; signal THD of less than.2 % of the fundamental. 2.2 Test signals To prepare for PMU simulation and measurement, a series of test signals including steady state and dynamic signals have been generated in compliance with the IEEE C standard. These test signals are used for testing the accuracy and response of PMUs under steady state and dynamic conditions. The steady state test signals consist of frequency, magnitude, phase and harmonic distortion test signals. The dynamic test signals include modulation, frequency ramp and step test signals. A short circuit current has also been generated to test the ability of the PMU during fault conditions. This fault current test signal is not required by [1]. Since the PMU used in later simulation and testing is single phase, all test signals will be generated for 1 phase, i.e phase A. Specific requirements, reference condition as well as range of influence quantity over which the PMU will be within its limits for each steady state and dynamic test signals provided in the standard are presented in Appendix A. The PMU used in the later simulation and testing will be of performance class M and reporting rate 5 frames/s. Each test signal is, therefore, produced in conformity with the reference condition and the range defined for class M and reporting rate 5 frames/s in the standard. Additionally, most parameters of the steady state and dynamic test signals will be varied following the testing guide for steady state and dynamic performance tests

22 2.2. TEST SIGNALS 2 described in [22] Steady state test signals Basically, a single-phase steady state test signal are generated with a cosinusoidal form, nominal magnitude, nominal frequency and constant phase angle: Where: X m : nominal magnitude ω =2πf : nominal frequency in rad/s ϕ: phase angle X = X m cos(ω t+ϕ) (2.4) The generated test signals have the nominal rms voltage and nominal rms current of the Dutch power grid, i.e 1/ (3) Vrms and 1 Arms, nominal frequency of 5 Hz, and nominal phase angle of. Each test signal is generated using Matlab for a duration of 1 second and a sampling frequency of 2 khz (time step of sec or 5 µs). The idea of the steady state test is to change one fundamental parameter around its nominal value while keeping others constant. The fundamental parameters of a sinusoidal waveform are magnitude, phase angle, and frequency. Therefore, each steady state test signal corresponds to the variation of each of these parameters. In addition, according to the standard, another steady state test signal which includes 1 % each harmonic is used for testing the harmonic rejection capability of the PMU. In Table A.1 and A.2 of Appendix A, measurement requirements by the standard for steady state conditions are described. It can be seen in these tables that there are requirements for signal frequency test, signal magnitude test, signal phase angle test, harmonic distortion test, and out of band interference test, which means 5 steady state tests should be done with the PMU. However, due to time limit, only the first 4 tests will be performed and thus the corresponding first 4 test signals will be generated. For signal frequency testing: According to the standard, for class M at reporting rate F s 25 frames/s, frequencies of the test signals have to be varied around the nominal frequency by ±5 Hz. All other parameters of the signal are kept at nominal conditions. In [22], the frequency in a signal frequency test of a 5 Hz system is suggested to be varied as follows:

23 2.2. TEST SIGNALS 21 Table 2.2: PMU frequency range for signal frequency test 4-45 Hz Hz Hz Hz 1 Hz.2 Hz.1 Hz.2 Hz The signal frequency is then decided to be varied with a step of 1 Hz for the whole instants from (5-5) Hz or 45 Hz to (5 + 5) Hz or 55 Hz. For signal magnitude testing: In this test, all other parameters kept at nominal values while the magnitudes of the test signals are changed. The standard has defined a magnitude range of (1-12) % of the nominal magnitude for voltage signals and (1-12) % of the nominal magnitude for current signals. These test signals are then generated with their magnitudes being varied as presented in [22]. Voltage: Nominal, ±1 %, ±2 %, and 1 % of the nominal value. Current: Nominal, 15 %, 75 %, 5 % and 1 % of the nominal value. For signal phase angle testing: With nominal magnitude and nominal frequency, the test signals should have their phase angles varied within ±π as mentioned in the standard. Correspondingly, the test signals have the following phase angles as proposed in [22]:, ±45, ±9, ±135, and ±18. For signal harmonic distortion testing: For this test, the standard requires signals with 1 % harmonic and up to 5 th harmonic. Nevertheless, due to time reason, only test signals with 1 % of the 3 rd harmonic and/or the 5 th harmonic components have been generated Dynamic test signals Dynamic test signals are used for validating PMU accuracy and response under dynamic variation of signal parameters. In compliance with the standard, modulated test signals, frequency ramp test signals and input step change test signals are listed as dynamic test signals. For modulated test signals, one or two fundamental parameters are varied with slow dynamics

24 2.2. TEST SIGNALS 22 while others are kept constant. For frequency ramp test signals, a linear ramp is applied to the frequency while the other two parameters are constant at nominal values. For input step change test signals, a sudden change in magnitude or phase angle occurs at a certain time while other fundamental parameters remain constant. In the standard, these dynamic test signals are formulated for three phases. For the purpose of simulating and testing, however, only single-phase test signal is needed and hence only single-phase dynamic test signals, i.e. test signals phase A, are generated. Table A.3 to A.7 of Appendix A represent the requirements for PMU dynamic tests, including modulated test, frequency ramp test and step change test. Modulated test signals: These test signals are used for evaluating PMU responses to different types of power signal modulation. It includes combined magnitude and phase modulated signals and phase modulated signals with different modulation frequencies. The standard requires TVE, FE and RFE to be measured over at least two full cycles of modulation. A three-phase modulated test signal can be mathematically expressed as [1]: X a = X m [1+k x cos(ωt)] cos[ω t+k a cos(ωt π)] (2.5) X b = X m [1+k x cos(ωt)] cos[ω t 2π/3+k a cos(ωt π)] (2.6) X c = X m [1+k x cos(ωt)] cos[ω t+2π/3+k a cos(ωt π)] (2.7) Where: X a, X b, X c : modulated signals of phase A, phase B, phase C X m : nominal magnitude of the test signal ω = 2πf : nominal power system frequency (rad/s) ω = 2πf: modulation frequency (rad/s) k x : amplitude modulation factor k a : phase angle modulation factor. For combined modulated signal: k x =.1; k a =.1 (rad) For phase modulated signal: k x =; k a =.1 (rad) According to the standard, for performance class M, the modulation frequency should be varied from.1 Hz to less than F s /5 Hz (1 Hz) or 5 Hz. The test signal is then generated with modulation frequency varied between.1 Hz and 1 Hz as depicted in [22] as follows:

25 2.2. TEST SIGNALS 23 Table 2.3: PMU modulation frequency range.2 Hz to 2 Hz 2 Hz to 1 Hz Every.2 Hz Every.5 Hz Modulated signal Sinusoidal signal X X Time(s) (a) 5 Hz combined modulated signal Time(s) (b) 1 Hz phase modulated signal Figure 2.3: Combined modulated test signal at 5 Hz modulation frequency (k x =.1; k a =.1; f=5hz) and phase modulated test signal at 1 Hz modulation frequency (k x = ; k a =.1; f=1hz) Examples of modulated test signals can be seen on Figure 2.3a and 2.3b. Frequency ramp test signals: ThesetestsignalshavealinearrampfrequencywitharamprateofR f =df/dt. Other fundamental parameters are kept constant. The standard states that for a frequency ramp test, the allowed TVE, FE and RFE may be exceeded during a transition period before and after a sudden change in ROCOF. Mathematically, the three-phase test signal is represented by [1]: X a = X m cos(ω t+πr f t 2 ) (2.8) X b = X m cos(ω t 2π/3+πR f t 2 ) (2.9) X c = X m cos(ω t+2π/3+πr f t 2 ) (2.1) Where: X a, X b, X c : frequency ramp signals of phase A, phase B, phase C X m : nominal magnitude of the signal ω : nominal power system frequency (rad/s)

26 2.2. TEST SIGNALS 24 R f : frequency ramp rate (Hz/s), R f =±1 Hz/s. The standard states that the signal frequency ramp rate is +1 Hz/s or -1 Hz/s and the signal frequency can be varied in a range F s /5 Hz (1 Hz) or ±5 Hz. Two test signals have been generated with ramp rates +1 Hz/s and - 1 Hz/s in the frequency range from (5-1) Hz or 49 Hz to (5 + 1) Hz or 51 Hz. It means that one test signal has its frequency changed from 49 Hz to 5 Hz while the other has its frequency changed from 5 Hz to 51 Hz. Figure 2.4 is an example of frequency ramp test signals at ±1 Hz/s ramp rate. Frequency ramp test signal at ramp rate +1 Hz/s: Rf = Freq ramp signal Sinusoidal signal Frequency ramp test signal at ramp rate 1 Hz/s: Rf = Freq ramp signal Sinusoidal signal X X Time(s) (a) +1 Hz/s frequency ramp test signal Time(s) (b) -1 Hz/s frequency ramp test signal Input step change test signals: Figure 2.4: Frequency ramp test signals This test signal represents a transition between two steady states used for determining response time, delay time, and overshoot in a measurement [1]. The three-phase test signal is formulated as [1]: X a = X m [1+k x f 1 (t)] cos[ω t+k a f 1 (t)] (2.11) X b = X m [1+k x f 1 (t)] cos[ω t 2π/3+k a f 1 (t)] (2.12) X c = X m [1+k x f 1 (t)] cos[ω t+2π/3+k a f 1 (t)] (2.13) Where: X a, X b, X c : step change signals of phase A, phase B, phase C X m : nominal magnitude of the signal ω : nominal power system frequency (rad/s) k x : magnitude step size

27 2.2. TEST SIGNALS 25 k a : phase step size f 1 (t): unit step function and f 1 (t t 1 ) = { if t < t 1 1 if t > t 1 (2.14) The standard defines the signal to have a ±1 % step in magnitude and ±1 step in phase. A ±1 % step in magnitude occurs when k x =±.1 and k a = whereas a ±1 step in phase corresponds to k x = and k a =±π/18. The test signals for PMU measurement are generated with steps of ±1 % in magnitude and ±1 in phase at time t 1 =.2s and t 2 =.7s. Figure 2.5a and Figure 2.5b shows examples of magnitude and phase step signals Signal with a step of ±1% in magnitude Signal with a step of 1 in phase Phase step signal Sinusoidal signal X X Time (s) (a) Magnitude step (k x = ±.1; k a = ) Time (s) (b) Phase step (k x = ; k a = ±π/18) Figure 2.5: Magnitude and phase step test signals Faulted test signals A test signal is generated to simulate a single-phase short circuit of phase A of an 11 kv voltage bus. Though this test signal is not proposed in the standard, it represents a real situation that any PMU may have to deal with. During the fault occurrence, the current of the faulted phase increases to

28 2.2. TEST SIGNALS 26 approximately 2 ka while those of the other two phases only show small steps. The voltages of all three phases also have small steps in this period. These small step signals are similar to the above mentioned step test signals. In Figure 2.6 and Figure 2.7, the faulted current and voltage waveforms of phase A and phase B are shown. 2 Faulted current Ia 5 Faulted current Ib Ia (A) Ib (A) Time(s) (a) Fault current Ia Time(s) (b) Fault current Ib Figure 2.6: Fault currents of a single phase short circuit at phase A, 11 kv voltage bus Va (V) x Faulted voltage Va Time(s) (a) Fault voltage Va Vb (V) x Faulted voltage Vb Time(s) (b) Fault voltage Vb Figure 2.7: Fault voltages of a single phase short circuit at phase A, 11 kv voltage bus

29 Chapter 3 PMU simulation Before performing tests on a PMU, it is necessary to have an idea about its behavior with different input signals and how its measurement quality is evaluated through TVE, FE and RFE. Simulations are performed for this purpose. In this context, the PMU is simulated by a simple PMU algorithm represented in PMU 4P D.m c, which is provided by VSL. This PMU algorithm performs phasor estimation through a centered time-tag window. All simulation results presented in this chapter is only for this particular simple PMU algorithm. Any deviating results may be due to such imperfections of the PMU algorithm as incorrect ROCOF estimation for the first frame and problems with response to rapid variations. Even though the algorithm is not perfect, the simulation results give some ideas on PMU behaviors. Reference phasors are obtained by performing Discrete Fourier Transform (DFT) of the test signals mentioned in Chapter 2 by means of Discrete Fourier Matlab Simulink block. This block calculates the reference phasors over a running window of 1 cycle of the fundamental frequency. PMU errors are then calculated using the TVE calculator function in TVE- Calculator.m c, provided by VSL. This calculator receives the estimated phasors of the PMU and the reference phasors, compares the two sets of parameters in time (in every time frame) and evaluates the differences [27]. Apart from TVE, FE and RFE, the calculator also determines PMU magnitude error (MagE) and phase error (PhaE), which will be helpful for analyzing sources of errors contributing to TVE. 27

30 3.1. SIMULATION WITH STEADY STATE TEST SIGNALS 28 In all simulations, the PMU algorithm performs phasor estimation with window length 1 cycle, PMU reporting rate 5 frames/s, and PMU class M. It means only standards for this specific reporting rate and PMU type are included. The simulation is done for steady state, dynamic, and fault signals. 3.1 Simulation with steady state test signals The measurement quality of the PMU algorithm at steady state conditions is evaluated through all steady state test signals described in part Simulation with signal frequency This simulation deals with the test signals at different power system frequencies, from 45 Hz to 55 Hz. The resultant maximum PMU errors at each frequency are then plotted. For this test, with PMU class M and reporting rate 5 frames/s, the IEEE standard requires a maximum TVE of 1 %, a maximum FE of.5 Hz, and a maximum RFE of.1 Hz/s [1]. The simulation results show a perfect PMU with almost zero errors (Figure 3.1). Most PMU errors are smallest at nominal frequency (5 Hz), and at off-nominal frequencies, they are slightly higher. This means the PMU algorithm used in this simulation satisfies the standard and it could perform well at both nominal and off-nominal power system frequencies. Figure 3.2 is the phase angle of the test signal measured by the PMU at power system frequency of 45 Hz. It can be seen that the PMU phase angle has a continuous, linear change of 36 per frame. The same behavior can be observed in the reference phase angle. In general, if the frequency f of input signals is different from the nominal frequency f and f < 2 f, the phase angles estimated by the PMU will change uniformly with a step of (2 pi (f f )/f ) 18/pi (deg) until reaching +18 or 18, then they wrap around to 18 or +18 and keep changing (synchrophasors are commonly reported in angles 18 or +18 rather than to 36 ) [1] Simulation with signal magnitude In this part of the simulation, the current and voltage test signals with various magnitudes, from 1 % to 15 % of the nominal, are used. It is required in the IEEE standard for reporting rate 5 frames/s and PMU class

31 3.1. SIMULATION WITH STEADY STATE TEST SIGNALS 29 7 x x 1 6 PMU Frequency error ( Hz ) PMU ROCOF error ( Hz/s ) Frequency ( Hz ) (a) Frequency error Frequency ( Hz ) (b) ROCOF error 1 x 1 7 PMU TVE error ( % ) Frequency ( Hz ) (c) TVE error Figure 3.1: PMU errors with signal frequencies M that TVE in this test should not exceed 1 %. There is no requirement for FE and RFE [1]. In Figure 3.3, simulation results have been shown with very small PMU errors. MagEs and TVEs for voltage signals are a little less than that for current signals at the same percentage (1 % and 1 %) of the nominal magnitudes Simulation with signal phase angle In signal phase angle test, the maximum acceptable TVE for PMU class M at reporting rate 5 frames/s is 1 % according to the IEEE standard. There is no requirement for FE and RFE [1].

32 3.1. SIMULATION WITH STEADY STATE TEST SIGNALS pmu reference Va phase angles (deg) Time (s) Figure 3.2: PMU phase angle at 45Hz This simulation is done with the test signals of different phase angles, from 18 to +18. All PMU errors are also very small, almost zeros for all phase angles ±18, ±135, ±9 and ±45 (Figure 3.4) Simulation with harmonic distortion In harmonic distortion test, the IEEE standard requires a maximum TVE of 1 %, a maximum FE of.25 Hz, and a maximum RFE of 6 Hz/s for PMU class M and reporting rate 5 frames/s [1]. The test signals contain the 3 rd harmonic, 5 th harmonic and 3 rd and 5 th harmonics. PMU errors are shown in Figure 3.5. ROCOF and PhaE are almost zero. FE, MagE, and TVE of these test signals are much higher than those of other steady state test signals. MagE and TVE are still far below their limits in the standard while FE has exceeded its requirement. The maximum FE is -.4 Hz with the signal containing the 5 th harmonic (Figure 3.5a). The signal containing both the 3 rd and 5 th harmonics causes highestmage(.17%), TVE(approximately.17%), andphae( deg) while signal containing only the 3 rd harmonic causes less errors than those of signal containing both the 3 rd and 5 th harmonics and more errors than those of signal containing only the 5 th harmonic.

33 3.2. SIMULATION WITH DYNAMIC TEST SIGNALS 31 PMU Frequency error ( Hz ) 3.5 x Current Voltage PMU ROCOF error ( Hz/s ) 7 x Current Voltage Percentage of nominal magnitude ( % ) (a) Frequency error Percentage of nominal magnitude ( % ) (b) ROCOF error PMU TVE error ( % ) 3.5 x Current Voltage PMU Magnitude error ( % ) 14 x Current Voltage Percent of nominal magnitude ( % ) (c) TVE error Percentage of nominal magnitude ( % ) (d) Magnitude error Figure 3.3: PMU errors with signal magnitudes 3.2 Simulation with dynamic test signals All dynamic test signals mentioned in part will be applied for estimating PMU performance under such dynamic conditions as modulation, frequency ramp or step change in magnitude and phase angle. The expected simulation results should meet the requirements for dynamic tests, PMU class M and reporting rate 5 frames/s in the standard. Regarding modulated test, a maximum TVE of 3 %, a maximum FE of.3 Hz, and a maximum RFE of 3 Hz/s are required. As for frequency ramp test, TVE should be less than 3 %, FE should be less than.5 Hz, and RFE should not be more than.1 Hz/s. For step change in magnitude and phase test, the standard requires a maximum delay time of 1/(4*F s ) or 5 ms, a maximum overshoot of 1 % of step magnitude, a maximum TVE response time

34 3.2. SIMULATION WITH DYNAMIC TEST SIGNALS 32 1 x x 1 4 PMU Frequency error ( Hz ) PMU ROCOF error ( Hz/s ) Phase angle ( deg ) (a) Frequency error Phase angle ( deg ) (b) ROCOF error 1 x x 1 4 PMU TVE error ( % ) PMU Phase error ( deg ) Phase angle ( deg ) (c) TVE error Phase angle ( deg ) (d) Phase error Figure 3.4: PMU errors with signal phase angles of.199 s, a maximum FE response time of.13 s, and a maximum RFE response time of.134 s [1] Simulation with modulated test signals The simulation is done with combined and phase modulated test signals with modulation frequencies of.2 Hz,.4Hz, 1Hz, 2 Hz, and 5 Hz. In Figure 3.6, the magnitude and phase angle of the PMU output and the reference for 2 Hz combined modulated signals can be seen. In Figure 3.7 and 3.8 the errors between the PMU and the reference for combined and phase modulated test signals at modulation frequency 2 Hz are shown respectively.

35 3.2. SIMULATION WITH DYNAMIC TEST SIGNALS x 1 9 PMU Frequency error ( Hz ) PMU ROCOF error ( Hz/s ) rd 5th 3rd and 5th Harmonics (a) Frequency error 3rd 5th 3rd and 5th Harmonics (b) ROCOF error PMU TVE error ( % ) PMU Magnitude error ( % ) rd 5th 3rd and 5th Harmonics (c) TVE error.4 3rd 5th 3rd and 5th Harmonics (d) Magnitude error 8 x PMU Phase error ( deg ) rd 5th 3rd and 5th Harmonics (e) Phase error Figure 3.5: PMU errors with harmonics

36 3.2. SIMULATION WITH DYNAMIC TEST SIGNALS 34 Magnitude PMU ref Phase angle ( deg ) PMU ref Time (a) Magnitudes Time (b) Phase angles Figure 3.6: PMU and reference magnitude and phase for 2 Hz combined modulated signals It can be seen from the plotted PMU errors that MagEs, PhaEs, FEs and TVEs follow the modulation of the signals. In other words, within 5 time frames (1 sec), these errors make up approximately two full sinusoidal cycles which are also the modulation cycle of the signals. For combined modulated signals(figure 3.7), the maximum FE and RFE are.2 Hz and 2.4 Hz/s respectively. These values are within the requirement, which is.3 Hz for FE and 3 Hz/s for RFE. The maximum TVE is only about.23% while the standard requires a maximum TVE of 3 %. This error is dueto boththemage (maximum.125 %) andthephae (maximum.123 or.22 %). For phase modulated signals (Figure 3.8), FE and RFE remain the same as those of combined modulated signals whereas all other errors are much smaller. The maximum TVE is now.1 %. Besides, the maximum MagE is quite small (.1 %) and maximum PhaE is.578 (.1 %). In this case, PhaE contributes more to the TVE. It can be observed in Figure 3.7b, 3.7e, and Figure 3.8b and 3.8e that there is a jump of ROCOF errors and phase errors in the first frames. This weird behavior may be due to the above mentioned limitations of the PMU algorithm, in which the PMU does not provide correct ROCOF estimation for first frames and has problem with response to rapid variations.

37 3.2. SIMULATION WITH DYNAMIC TEST SIGNALS 35 PMU Frequency error ( Hz ) (a) Frequency error PMU ROCOF error ( Hz/s ) (b) ROCOF error PMU TVE error ( % ) PMU Magnitude error ( % ) (c) TVE error (d) Magnitude error PMU Phase error ( deg ) (e) Phase error Figure 3.7: PMU errors with 2 Hz combined modulated signals

38 3.2. SIMULATION WITH DYNAMIC TEST SIGNALS 36 PMU Frequency error ( Hz ) (a) Frequency error PMU ROCOF error ( Hz/s ) (b) ROCOF error PMU TVE error ( % ) PMU Magnitude error ( % ) (c) TVE error (d) Magnitude error.6 PMU Phase error ( deg ) (e) Phase error Figure 3.8: PMU errors with 2 Hz phase modulated signals

39 3.2. SIMULATION WITH DYNAMIC TEST SIGNALS 37 The highest modulation frequency that the PMU algorithm could keep all errors within the limits is 3 Hz. Beyond this frequency, TVE is still far below its standard but FE and RFE have exceeded their limits Simulation with frequency ramp signals Inthispart, test signalswith frequencyramp±1hz/s areto beused. Figure 3.9 and Figure 3.1 represent PMU errors for signals with frequency ramp -1 Hz/s and +1 Hz/s respectively. As can be seen from Figure 3.9, for a ramp of -1 Hz/s, the maximum FE is.15 Hz and the maximum RFE is.13 Hz/s. These values are quite good compared to the requirement of.5 Hz for FE and.1 Hz/s for RFE as proposed in the standard. The maximum TVE (.425 %) is even more than 1 times better than the limit. MagE is quite small (maximum of.1 %) compared to PhaE (maximum of.243 or.43 %). Similar results can be seen for +1 Hz/s ramp signal in Figure 3.1. The frequency ramp has caused a jump in the first frame of frequency error, TVE error, and phase error, and a jump in the first two frames of ROCOF errors. Consequently, to make the plots clearer, in both figures (Figure 3.9 and 3.1), the first frame of FE, TVE, and PhaE, and the first two frames of RFE have been removed Simulation with input step change signals The test signals according to the IEEE standard [1] have 1 % step in magnitude or 1 step in phase at.2 s and.7 s. Simulation with these step signals is done to evaluate response time, delay time, and overshoot in the measurement of the PMU. Figure 3.11 and Figure 3.12 show PMU magnitude and phase responses as well as its TVEs for signals with 1 % step in magnitude and 1 step in phase. These figures also illustrate how response delay and response time are determined. Response delay is the time from the occurrence of the step to the time when 5 % of the final step value is reached. Response time, on the other hand, is the time when PMU error starts exceeding the limit of 1 % to the time when it start going back to values below this limit. There is no overshoot observed in the PMU responses for these magnitude and phase step signals.

40 3.2. SIMULATION WITH DYNAMIC TEST SIGNALS 38 PMU Frequency error ( Hz ) Frequency ( Hz ) (a) Frequency error PMU ROCOF error ( Hz/s ) Frequency ( Hz ) (b) ROCOF error PMU TVE error ( % ) PMU Magnitude error ( % ) Frequency ( Hz ) (c) TVE error Frequency ( Hz ) (d) Magnitude error.23 PMU Phase error ( deg ) Frequency ( Hz ) (e) Phase error Figure 3.9: PMU errors with -1Hz/s ramp signal

41 3.2. SIMULATION WITH DYNAMIC TEST SIGNALS 39 PMU Frequency error ( Hz ) PMU ROCOF error ( Hz/s ) Frequency ( Hz ) (a) Frequency error Frequency ( Hz ) (b) ROCOF error PMU TVE error ( % ) PMU Magnitude error ( % ) Frequency ( Hz ) (c) TVE error Frequency ( Hz ) (d) Magnitude error PMU Phase error ( deg ) Frequency ( Hz ) (e) Phase error Figure 3.1: PMU errors with +1Hz/s ramp signal

42 3.2. SIMULATION WITH DYNAMIC TEST SIGNALS Signal magnitude Response delay 5% of the step value PMU TVE error ( % ) Response time Time (s) (a) Response delay (b) Response time Figure 3.11: PMU responses for magnitude step signal 1 1 Signal phase angle ( deg ) Response delay X:.2 Y: % of the step value PMU TVE error ( % ) Response time Time (s) (a) Response delay (b) Response time Figure 3.12: PMU responses for phase step signal For magnitude step signal, since the 11 th frame is exactly at 5 % of the step value, the response delay in magnitude is almost ms (Figure 3.11a). The standard requires this response delay to be below 1/(4 Fs) or 5 ms. From Figure 3.11b, the response time of TVE is calculated approximately from the 1 th to the 12 th sample, which is.4 s. This value should be less than.199 s as required in the standard. The response time for FE and RFE are also quite small compared to the standard. Furthermore, except transition instants, TVE, FE and RFE during steady state periods are almost zero. Similar responses for phase step signal can be seen in Figure 3.12a and

43 3.3. SIMULATION WITH FAULT SIGNALS 41 Figure 3.12b. Since the 11 th (at ) is quite close to 5 % of the step value (5 ), the response delay is very small compared to the limit of.5 ms. The response time is also.4 s. 3.3 Simulation with fault signals The PMU deals with the single phase short circuit current I a. This fault current is similar to the previous magnitude step signal. In this case, however, the current changes from a small steady state value (42 A) to a huge value (1391 A) during the fault. Figure 3.13c, 3.13d and 3.13e represent FE, RFE and TVE for the fault current I a. These errors are almost zero during steady state condition. At the transition between steady state and fault periods, huge errors are observed. The overshoot, delay time and TVE response time can be seen in Figure 3.13a and 3.13b. PMU overshoot is A. The maximum overshoot required by the Standard is 1 % of the step magnitude, which is 1 % of ( ) A or 97.1 A. This overshoot, therefore, meets the standard. The response delay is the time step between the 1th and 11th sample, i.e..2 s. The TVE response time is 3.5 times more than the time step between 2 samples or.7 s whereas it is required to be lower than.199 s according to the standard. Similarly, for FE and RFE, the response time are also much smaller than their limits. The currents I b and I c and the voltages of 3 phases only suffer from small changes during the fault. They are, in fact, magnitude step signals as described in part

44 3.3. SIMULATION WITH FAULT SIGNALS 42 PMU Magnitude Overshoot Response delay (a) Overshoot and response delay PMU TVE error ( % ) 2 15 Response time (b) Response time PMU Frequency error ( Hz ) (c) Frequency error PMU ROCOF error ( Hz/s ) (d) ROCOF error 12 1 PMU TVE error ( % ) (e) TVE error Figure 3.13: PMU responses and errors with fault signals

45 Chapter 4 PMU test setup 4.1 Test principle The basic principle of testing the PMU is generating a test signal, supplying it into the PMU input and comparing the resulting PMU output with the expected result known as the reference. It is important that the reference and the PMU output are measured at the same instant of time so that their values are comparable. A test setup satisfying this must provide an accurate time source with precise time synchronization to the UTC time. Figure 4.1: PMU test procedure 43

46 4.2. TEST SETUP 44 According to the C Standard[1], it is highly recommended that a time source should reliably provide time, frequency, and frequency stability at least 1 times better than those values corresponding to 1 % TVE, which are ±31 µs for time and.1 mhz for frequency, respectively [1]. The test procedure is summarized as in Figure Test setup With the above mentioned principle and procedure of PMU testing, a test setup with high accuracy has been built: Figure 4.2: PMU test setup diagram The test setup (Figure 4.2 and 4.3) performs the generation of test signals and the measurement of reference signals. First, sampled test signals of 1 second, both currents and voltages, are acquired by the Digitizer. At the output channels (Generation CH and CH1), continuous voltage signals in the range of 1 mv to 1 V are generated. These signals will be the input of the PMU as well as the reference for calculating PMU errors. The voltage signal from output CH (Generation CH) is then supplied to the current amplifier which creates a current at its output. This current is both fed

47 4.2. TEST SETUP 45 Figure 4.3: PMU test setup picture 1 : NI PXI-4461; 2 : Atomic Clock 1 PPS signal; 3 : Model 1133A Power Sentinel PMU; 4 : Current amplifier 1A/1V; 5 : Shunt; 6 : Voltage amplifier 25V/1V; 7 : Transformer; 8 : RD-33 Dytronic Three-Phase Reference Standard; 9 : PZ-4 Power Analyzer directly to the input of the PMU and fed to the input CH (Measurement CH) of the Digitizer through a current shunt for measurement. In a similar way, the voltage signal from output CH1 (Generation CH1) is transformed into a voltage signal at Dutch distribution low voltage grid level, which is 23 V,byavoltage amplifierandatransformer. Thisvoltage signalisagain both directly supplied to the PMU input and to the input CH1 (Measurement CH1) through a voltage divider for measurement The Digitizer NI PXI-4461 The NI PXI-4461 Digitizer (DG) is a high accuracy data acquisition device for making precision measurements [23]. It is specially designed for applications with very large dynamic ranges. With either two inputs and two outputs or four inputs, the device is ideal for applications requiring simultaneous generation and acquisition of signals. The inputs and outputs have 24-bit resolution.

48 4.2. TEST SETUP 46 In the PMU test setup, the DG is used for both generating and measuring test signals. The generating function is performed through D/A converters with two high-fidelity analog output channels (Generation CH and CH1). These analog output channels have a voltage range of ±1 mv to 1V and an update rate up to 24.8 ks/s. During the PMU tests, when a 1sec 2 khz sampled test signal is acquired at the input channels, a 1 Vrms voltage signal will be generated repeatedly at the analog output channels. The measurement is done through 24-bit resolution A/D converters with two analog input channels (Measurement CH and CH1). The voltage range of these channels is ±316 mv to 42.4V and the update rate can also reach 24.8 ks/s. The analog output channels have analog and digital anti-imaging filters. Analog filters will remove unexpected interharmonic components generated when an analog signal is produced from digital data. Digital filters will limit the bandwidth of the output signal to half the original conversion rate, thus reject images caused by the 8-times oversampling process. The generated signals, as a result, are low-distortion, low noise and flat-frequency. Similarly, there are both analog and digital filters in the analog inputs for antialiasing. Analog filters help filter out from input signals all frequency components beyond the range of the A/D converters while digital filters automatically adjust their cut-off frequency to remove any frequency components above half the programmed sampling rate. The DG also provides analog and digital triggering channel for signal acquisition The amplifiers There are two amplifiers in the test setup, i.e the current amplifier and the voltage amplifier. The current amplifier is used for transforming a voltage signal into a current signal with the transforming ratio of 1A/1V. The voltage amplifier increases voltage signals to higher values with an amplifying ratio of 25V/1V. However, the exact behavior of the amplifiers is not relevant since we are measuring the signal applied to the PMU with the reference system. In the test setup, a 24V/25V transformer is also employed to convert the voltage signal at the output of the voltage amplifier to the Dutch distribution low voltage grid level.

49 4.2. TEST SETUP The current shunt and the voltage divider The current shunt is used for converting current signals to voltage levels of the Digitizer analog input channels. It is a low resistance operating by the principle of Ohm s law (V = R I) and AC or DC current can be measured from the voltage drop created by the current flowing across it. The nominal value of the current shunt in the PMU test setup is.9 Ohm but the real value after calibration is Ohm. Both analog input channels of the DG are not designed to directly measure voltages and currents up to levels needed for a power measurement. For this reason, voltages need to be scaled down to smaller values which are suitable for the DG to measure. This could be done with a resistive voltage divider. The nominal divider ratio of the voltage divider is 1. In fact, its real ratio after calibration is The PMU under test The PMU to be tested is the Model 1133A Power Sentinel provided by Arbiter Systems [24]. It consists of GPS receiver and synchronization, voltage and current inputs, programmable-gain amplifier, multiplexers and A/D converter, digital signal processor, display and keyboard, I/O functions, and power supply. With a twelve-channel GPS receiver, accurate time of up to a fraction of a microsecond anywhere in the world is made by comparing an internal 1- MHz crystal oscillator to a 1-PPS output of the GPS receiver. The PMU offers a wide range of window functions to optimize phasor outputs for different applications. The windowing function includes Estimator Algorithm and Window Length in cycles. This window function behaves as a low pass filter which filters out higher frequency components. The PMU measures voltage or current by making a number of separate measurements per second, depending on the reporting rate, of the square of the voltage or current samples. The square root of the resulting sum is proportional to the rms voltage or current value during that measurement interval. The PMU performs a fast Fourier transform (FFT) of the windowed voltage and current samples to calculate phase angle and frequency. Phase angles are calculated from the relationship between the real and imaginary parts

50 4.3. TIME SOURCE 48 of the fundamental-frequency bin of the FFT. The phase measurements are then compared to determine phase angle between voltages and currents or between any two voltages or currents. With the use of GPS synchronization, phase angle measurements are made comparable between different PMUs. Frequency is measured by taking the difference in phase angle between subsequent measurements based on f = dϕ/dt. Phasor data are formatted and output in accordance with IEEE Synchrophasor standard C A phasor consists of the real and imaginary components of voltage or current magnitude at a particular point in a power distribution system, along with suitable time synchronization fields and other information. This information is in real time, and is based on the measured fundamental voltage, current, and phase angle described above. In addition to phasor measurements, the PMU could also perform energy and power measurements, power quality measurements such as harmonic measurements, power interruptions and flicker. The PMU is connected to PC through a software named PSCSV provided by the vendor. Besides, the PMU has been selected to be of class M with the reporting rate of 5 frames/s during all tests, thus it should satisfy the standards for class M at 5 frames/s. The three phase current inputs of the PMU are connected in series and the three phase voltage inputs are connected in parallel so that the performance of all three phases of the PMU could be evaluated. 4.3 Time source In order to evaluate the measurement quality of the PMU through TVE, FE and RFE, the reference phasors have to be measured at the same instant of time as the estimated phasors of the PMU. Therefore, one of the most important issues in PMU testing is to provide a reliable time source with very high accuracy with respect to the UTC time. This can be done by synchronizing both the PMU measurements and the measurements of reference phasors to the UTC time. The PMU is synchronized by a built-in GPS satellite receiver to within 1 µs of the UTC time. As a result, each PMU measurement is assigned a time tag indicating the UTC time at which the measurement is done. A reporting rate of 5 frames/s is chosen for the PMU under test, thus each

51 4.3. TIME SOURCE 49 measurement of the PMU has 5 data frames in 1 second. To synchronize the measurement of the reference signals to the UTC time, an atomic clock 1 PPS signal is supplied through a 5 Ohm impedance to the triggering channel of the DG. This 1 PPS signal comes from the cesium atomic clock laboratory of VSL. The atomic clock provides a time source with an accuracy in the order of several nanoseconds with reference to the UTC time. Every measurement of reference signals is triggered by the 1 PPS signal and the time of the PC is recorded as the time at which each measurement is started. Since the PC has been accurately adjusted to the UTC time, the time of each measurement is actually the UTC time. From the time tag in PMU measurements and the time of reference signal measurements, estimated phasors of the PMU and reference phasors at the same instants of time can be known. The PMU measurement quality can then be evaluated by calculating TVE, FE and RFE of both phasors. The DG, however, has an output filter delay which is the time required for digital data to propagate through the D/A converter and interpolation digital filters [23]. This delay time varies with the sampling frequency of input signals. For instance, a 1 khz sampling frequency signal has a delay of samples or ms while a 2 khz sampling frequency signal is delayed by 63 samples or.315 ms (315 µs) [26]. In the PMU tests, all test signals are generated with a sampling frequency of 2 khz, which means that the expected filter delay is 315 µs. Signal Measurement of 1 PPS signal by Digitizer Time (s) x 1 4 (a) DG Filter delay in time Signal Measurement of 1 PPS signal by Digitizer Sample (b) DG Filter delay in samples Figure 4.4: DG Filter delay

52 4.3. TIME SOURCE 5 To exactly determine the filter delay of the DG in the test setup, a test on a 1 PPSsignal is done. Inthis test, an atomic clock 1PPS signal is suppliedto the triggering channel of the DG. Another atomic clock 1 PPS signal is fed into one of the two analog inputs, say, CH for measuring. The delay time will be the time from the first sample of the measured pulse to the sample in the middle of the rising edge of the pulse. The measurement result has shown an average filter delay of approximately 319 µs (Figure 4.4). An uncertainty of 3 µs is considered to take into account variations or jitter of the middle point of the signal due to some unknown behavior inside the DG. The filter delay now becomes (319±3) µs. A filter delay of 32 µs or 64 samples is then included for all the later PMU tests. For a particular test, a 2 samples (1 second) signal is measured 7 times in 7 seconds, in which the 1 second signal is running continuously and then 7 measurements are triggered by consecutive 1 PPS pulses. However, only the first 197 samples, instead of 2 samples, of the 1 second signal is selected for measuring so that there is time for data transfer between the digitizer and the PMU. If more samples are taken, the next trigger of the 1 PPS signal will be missed. The corresponding PMU measurements, therefore, should include only 49 instead of 5 frames in 1 second and TVE, FE and RFE will be calculated for these 49 frames.

53 Chapter 5 PMU test results The Model 1133A Power Sentinel PMU is tested using the steady state, dynamic and fault test signals described in chapter 2. The accuracy of the PMU in measuring such basic quantities as magnitude, phase angle and frequency can be tested through steady state test signals. Dynamic test signals are used for evaluating the dynamic PMU performance through the variation of signal magnitude, phase angle and frequency. The PMU measurement quality is also tested under fault conditions with the fault signals. Besides, the PMU provides a wide range of window functions for optimizing phasor outputs for individual applications. This window function consists of estimator algorithm and window length in cycles [24]. To choose a suitable window function for later PMU tests, a test has also been performed on different window functions. All tests are performed in such procedure and principle as depicted in chapter 4. The PMU is tested on both its current and voltage measurement quality. For each test signal, 7 measurements are done. The obtained data are then analyzed in Matlab under the reporting rate of 5 frames/s. First, the measurements of the PMU are aligned with the measurements of the reference signals on the basis of the time tag in each measurement. Next, the reference data are Discrete Fourier transformed with the use of the Discrete Fourier Matlab Simulink block to extract the magnitude and phase angle of the fundamental signal component. Afterward, the PMU phasors and reference phasors are compared for determining PMU errors. These errors, including FE, RFE, TVE, MagE and PhaE, are calculated by the function TVECalculator in TVECalculator.m. Then, in each time frame, PMU errors of all 7 measurements are averaged to get an average error. 51

54 5.1. PMU WINDOW FUNCTIONS 52 In each steady state test, the PMU has one value for each error (FE, RFE, TVE, MagE or PhaE) over 5 time frames. This error is resulted from the average of the errors over these 5 frames. In dynamic tests, PMU errors are not averaged over 5 time frames. Instead, they are plotted as a function of frame. 5.1 PMU Window functions Window function properties The PMU offers 9 window functions including Rectangular, Raised Cosine, Hann, Hamming, Blackman, Triangular, Flat Top, Kaiser and Nutall 4 Term and 8 window lengths from 1 to 8 cycles. The Discrete Fourier Matlab Simulink block, however, by default, only uses the Rectangular window, which can not be changable, for estimating the reference data. All the above window functions serve the same purpose as a low-pass filter and have the same basic working principle[25]. The main difference between them is the shape and magnitude of sideband lobes, which are peaks in the rejection band, the passband width, and flatness. A window function software tool, i.e. WindowFunction.exe, has been provided along with the PSCSV software. From this software tool, the rolloff (magnitude error) and rejection characteristics of all window functions of the PMU can be observed (Figure 5.1, 5.2, and 5.3). (a) Rolloff charateristic (b) Rejection charateristic Figure 5.1: PMU Hann, Hamming, and Blackman rolloff and rejection charateristics at window length 4 cycles

55 5.1. PMU WINDOW FUNCTIONS 53 (a) Rolloff characteristic (b) Rejection characteristic Figure 5.2: PMU Rectangular, Flat Top, and Raised Cosine rolloff and rejection charateristics at window length 4 cycles (a) Rolloff characteristics (b) Rejection characteristics Figure 5.3: PMU Triangular, Kaiser, and Nutall 4 Term rolloff and rejection charateristics at window length 4 cycles It can be seen in Figure 5.1a, 5.2a, and 5.3a that the differences in rolloff between window functions become larger as the frequency gets further from the nominal frequency (higher frequency offset). It is stated in [25] that the Rectangular window is equivalent to no window at all, which has the narrowest main lobe (passband) for any window length. It works well only when the signal is centered in the passband or at nominal system frequency. It performs worse than any other window for off-nominal and out-of-band signals.

56 5.1. PMU WINDOW FUNCTIONS 54 The Rectangular and Triangular windows, for most applications, are not recommended. They are mostly applied for experiment purposes [25]. The often-used Hann and Blackman windows both have desirable characteristics, in which the magnitude of their rejection sidelobes decreases with increasing frequency (Figure 5.1b). The Hamming window behaves similar to the Hann but its rejection sidelobes do not decrease as quickly as the Hann (Figure 5.1b). The Nutall 4 Term window is similar to the Hann and Blackman, with even better rejection characteristics (more than 9 db) (Figure 5.3b). The Hann and Hamming (2-term), Blackman (3-term) and Nutall (4-term) all belong to the Blackman-Harris window family [25]. The Kaiser also has similar performance as the Blackman-Harris family(figure 5.3b). The Flat Top window has broader passband than other windows but its rejection is not as good as that of the other windows (Figure 5.2). However, it is acceptable under many conditions and still much better than the Rectangular window [25]. The Raised Cosine window provides the broadest flat passband with the rejection comparable to the Hann window (Figure 5.2) Test on Window functions This test is done on 9 estimator algorithms (windows) at 3 window lengths, i.e. 1, 2 and 4 cycles. The test signal used in this test is the steady state test signal at nominal magnitude, nominal frequency and nominal phase angle. The resultant PMU errors are then plotted as a function of window length for all windows. Figure 5.4 and 5.5 represent PMU errors with window functions for PMU voltage phase A and current phase A measurements. FE are more than 1 times better than the standards for all windows at window length 1, 2, and 4 cycles. This error is lower for window length 2 cycles and lowest for window length 4 cycles. ROCOF error is quite high at window length 1 cycle. It even exceeds the standard of.1 Hz/s (Flat Top). At window length 2 cycles, many windows (Hann, Hamming, Triangular, Blackman, Kaiser, Raised Cosine) have ROCOF error more than 1 times better than the standard. At window length 4 cycles, ROCOF errors of all windows are almost zero. For voltage measurement, TVE is quite high at window length 1 cycle (the smallest error is.52 % and the highest is 1.8 %). At window length 2 cycles, TVE for

57 5.1. PMU WINDOW FUNCTIONS 55 Frequency error (Hz) 3.5 x Hann Hamming Rectangular Flat top Triangular Blackman Kaiser Cosine Nutall ROCOF error (Hz/s) 14 x Hann Hamming Rectangular Flat top Triangular Blackman Kaiser Cosine Nutall Window length (cycles) (a) Frequency error Window length (cycles) (b) ROCOF error TVE error (%) Hann Hamming Rectangular Flat top Triangular Blackman Kaiser Cosine Nutall Magnitude error (%) Hann Hamming Rectangular Flat top Triangular Blackman Kaiser Cosine Nutall Window length (cycles) (c) TVE error Window length (cycles) (d) Magnitude error Phase error (deg) Hann Hamming Rectangular Flat top Triangular Blackman Kaiser Cosine Nutall Window length (cycles) (e) Phase error Figure 5.4: PMU errorsas afunctionof window length forvoltage test signal

58 5.1. PMU WINDOW FUNCTIONS 56 Frequency error (Hz) 3.5 x Hann Hamming Rectangular Flat top Triangular Blackman Kaiser Cosine Nutall ROCOF error (Hz/s) 14 x Hann Hamming Rectangular Flat top Triangular Blackman Kaiser Cosine Nutall Window length (cycles) (a) Frequency error Window length (cycles) (b) ROCOF error TVE error (%) Hann Hamming Rectangular Flat top Triangular Blackman Kaiser Cosine Nutall Magnitude error (%) Hann Hamming Rectangular Flat top Triangular Blackman Kaiser Cosine Nutall Window length (cycles) (c) TVE error Window length (cycles) (d) Magnitude error Phase error (deg) Hann Hamming Rectangular Flat top Triangular Blackman Kaiser Cosine Nutall Window length (cycles) (e) Phase error Figure5.5: PMU errorsas afunctionofwindowlength for currenttest signal

59 5.2. TEST ON RAISED COSINE ESTIMATOR ALGORITHM 57 Flat Top, Kaiser and Nutall 4 Term and Blackman are much higher than the others. At window length 4 cycles, only Kaiser has TVE error up to 1 % whereas the others result in quite small errors (less than.2 %) (Figure 5.4c). In Figure 5.4e and 5.4d, it is found that Kaiser has higher PhaE than the others while Flat Top, Nutall 4 Term and Blackman have higher MagE than the others. The results of the current measurements are essentially equal to those of the voltage measurements, which can be seen in Figure 5.5. From these results we can make several conclusions. In the first place, window length 1 cycle is not suitable for accurate measurements. Window length 2 and 4 cycles, which provide more accurate measurements are, therefore, selected for doing PMU tests. In the second place, an estimator needs to be chosen among the five best routines, i.e. Hann, Hamming, Rectangular, Triangular and Raised Cosine for PMU testing. In [28], the four-cycle Raised Cosine has been proved to be efficient in dynamic phasor estimation for many reasons such as allowing to capture the behavior of an oscillation. Accordingly, the Raised Cosine estimator algorithm has been suggested for coming PMU steady state and dynamic tests. Finally, estimator algorithm Raised Cosine and window length 2 and 4 cycles will be used in all coming PMU tests. To clearly illustrate for this choice, another test has been done on the Raised Cosine at window length from 1 to 8 cycles. 5.2 Test on Raised Cosine estimator algorithm Average errors with standard deviation for 3 phases are shown in Figure 5.6 and 5.7 for voltage and current test signals. Standard deviation σ shows the variation of measurements from the average value. It is calculated using the following fomular: σ = 1 N (X i X) (N 1) 2 [29] (5.1) k=1 Where: N is the number of elements in the sample, X = 1 N average value. N X i is the k=1

60 5.3. TEST WITH STEADY STATE TEST SIGNALS 58 In PMU steady state tests, since each error is averaged over 49 frames and each frame is the average of 7 measurements, the standard deviation calculated for each error becomes: σ = σ 49 7 (5.2) It can be seen in Figure 5.6 and 5.7 that the PMU has better measurement quality at window length 2, 4, and 6 cycles. This can also be seen in the rejection characteristic of the Raised Cosine window at window length from 1 to 8 cycles (Figure 5.8). In Figure 5.8a, window length 1 cycle has the largest sidelobe amplitudes and poorly attenuated sidebands. Window length 2 cycles is slightly better than window length 3 cycles regarding sidelobe amplitudes and their attenuation. In figure 5.8b, window length 4 cycles has more attenuated sidebands than window length 3 and 5 cycles. Window length 6, 7, and 8 cycles all have small sidelobe amplitudes and attenuated sidebands (Figure 5.8c). For dynamic tests, smaller window length may track more accurately signal dynamics. Window length 2 and 4 cycles rather than window length 6 cycles, therefore, have been selected for PMU tests. The smallest TVE error is around.1 % at window length 4 cycles, which is 1 times better than the standard. At window length 2 and 3 cycles, TVE is partly from MagE and partly from PhaE. At window length 4, 5, 6, 7, and 8 cycles, since MagE is essentially small, TVE is mostly caused by PhaE. The standard deviation has shown that there is not much variation in the errors from their averages, which means that the measurements are stable. Similar results can be found in 3 phases of the PMU, thus the analysis for other tests will be done for only 1 phase, i.e phase A. 5.3 Test with steady state test signals All steady state test signals mentioned in will be applied for testing the PMU at steady state conditions. The standard for steady state test signals requires a maximum FE of 5 mhz, RFE of.1 Hz/s and TVE of 1 %.

61 5.3. TEST WITH STEADY STATE TEST SIGNALS 59 5 x Phase A Phase B Phase C Phase A Phase B Phase C Freq error (Hz) Window length (cycles) (a) Frequency error ROCOF error (Hz/s) Window length (cycles) (b) ROCOF error Phase A Phase B Phase C.15.1 Phase A Phase B Phase C TVE error (%) Magnitude error (%) Window length (cycles) (c) TVE error Window length (cycles) (d) Magnitude error Phase error (deg) Phase A Phase B Phase C Window length (cycles) (e) Phase error Figure 5.6: PMU errors as a function of window length with Raised Cosine window for voltage test signal

62 5.3. TEST WITH STEADY STATE TEST SIGNALS 6 5 x Phase A Phase B Phase C Phase A Phase B Phase C Freq error (Hz) Window length (cycles) (a) Frequency error ROCOF error (Hz/s) Window length (cycles) (b) ROCOF error TVE error (%) Phase A Phase B Phase C Magnitude error (%) Phase A Phase B Phase C Window length (cycles) (c) TVE error Window length (cycles) (d) Magnitude error Phase error (deg) Phase A Phase B Phase C Window length (cycles) (e) Phase error Figure 5.7: PMU errors as a function of window length with Raised Cosine window for current test signal

63 5.3. TEST WITH STEADY STATE TEST SIGNALS 61 (a) Window length 1, 2, and 3 cycles (b) Window length 3, 4, and 5 cycles (c) Window length 6, 7, and 8 cycles Figure 5.8: Rejection characteristic of Raised Cosine window at different window lengths Test with signal frequency This test deals with test signals with a range of power system frequencies, from 45 Hz to 55 Hz. PMU phase angle measurement for the signal at 45 Hz power system frequency, for example, can be seen in Figure 5.9. As already mentioned in the simulation, in this test, the PMU also has a continuous, linear change in phase angle of (2 pi (f f)/f 18/pi) per frame, which is 36 per frame for a frequency of 45 Hz. Average errors with standard deviation of voltage and current measurements