Evaluation of Steady-State and Dynamic Performance of a Synchronized Phasor Measurement Unit

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1 01 IEEE Electrical Power and Energy Conference Evaluation of Steady-State and Dynaic Perforance of a Synchronized Phasor Measureent Unit Dinesh Rangana Gurusinghe, Graduate Student Meber, IEEE, Athula D. Rajapakse, Senior Meber, IEEE, and Krish Narendra, Senior Meber, IEEE Abstract It is critically iportant to understand steadystate and dynaic perforance of phasor easureent units (PMUs) to ensure reliable and secure operation of the synchrophasor based wide area onitoring, control, and protection systes. The recently published IEEE Standard C provides necessary guidelines to characterize both steady-state and dynaic perforance of a PMU. This paper presents a perforance evaluation ethodology according to the IEEE Standard C and discusses the practical issues in the test environent. Results of the steady-state and dynaic responses tests on an actual PMU are also presented. The PMU perforance evaluation approach of this paper is siple, repeatable, and can be perfored at any facility with coonly available standard signal playback equipent. The ethod is based upon using test signals that are atheatically generated fro a signal odel and play backed into the PMU with precise global position syste (GPS) synchronization. Index Ters Discrete Fourier transfor, finite ipulse response, global position syste (GPS), phasor easureent unit (PMU), playback device, step response, total vector error (TVE). A I. INTRODUCTION synchronized phasor easureent or synchrophasor is a phasor value (agnitude and phase angle) obtained fro a voltage or a current wavefor, precisely referenced to a coon tie frae. Phasor easureent unit (PMU) is a device, which can extract phasor values as well as the frequency and the rate of change of frequency (ROCOF) of the easured wavefor [1]. PMU can be a stand-alone unit or a functional unit within another physical unit such as a protection relay or power syste data recorder. PMUs have any potential applications in power syste onitoring, protection, operation and control including iproved state estiation, frequency estiation, instability prediction, adaptive relaying, and wide area protection and control (WAPAC) []. Different applications of PMUs can be classified into two ain categories naely online (real tie) applications and offline applications. The online applications require faster data transfer rates that depend on the particular application. For exaple, voltage stability is a slower phenoenon and thus the onitoring voltage stability can be achieved with a slower data rate while an application such as D. R. Gurusinghe and A. D. Rajapakse are with the Dept. of Electrical and Coputer Engineering, University of Manitoba, Winnipeg, MB, R3T5V6, Canada (e-ail: ugurusi@cc.uanitoba.ca; rajapaks@cc.uanitoba.ca). K. Narendra is with ERLPhase Power Technologies Ltd, Winnipeg, MB, R3Y1G4, Canada (e-ail: knarendra@erlphase.co). frequency stability control, where a faster response is expected requires faster data transfer rate [3]. In contrast, the speed of data transfer over counication channels is less critical in the case of the offline applications. Most power utilities install PMUs at the iportant substations, targeting various aspects of power grid including steadystate and dynaic applications [4]. They use dedicated counications to send the data to their load dispatch center (LDC) in real tie. A phasor data concentrator (PDC) at the LDC collects the data fro different PMUs, tie align the, and send the data to local applications and archives. These systes ay be further linked to other power utilities to provide a wide area view of the power syste [5]. Data reporting rates for these online applications range fro 10 to 60 fraes per second (fps) [6]. Applications of PMU deand high accuracy and consistency in both steady-state and dynaic perforance to ensure PMU accurately reflects syste behavior. With growing PMU vendors, it is very iportant to establish the interoperability between different PMUs as different vendors typically use different algoriths [7]. Thus, PMU perforance evaluation plays a vital role. The recently published IEEE Standard C [6] provides necessary guidelines to assure both steady-state and dynaic characterization of phasor easureents. It defines two classes of perforances naely, P class and M class. P class is preferred for applications requiring fast response while M class is intended for applications deanding greater precision. Synchrophasor tests perfored and discussed in this paper are to deterine the PMU perforance and confir its accuracy under a variety of conditions that are specified in [6]. Signal frequency, agnitude, phase angle, haronic distortion and out-of-band interference tests are perfored to evaluate steady-state perforances while easureent bandwidth, linear syste frequency rap and step response assessents are executed to assess dynaic copliances. The practical issues in test environent are also discussed with each test case, including reedial actions. Test cases were defined to satisfy requireents of both P class and M class. This paper is organized as follows. In Section II, basic concept of phasor easureent technology is stated. The phasor easureent setup of the paper is discussed in Section III. Section IV is devoted to analysis of results. It assesses different PMU test cases with practical issues. Finally, in Section V, the ain contributions of this paper are highlighted /1/$30 01 IEEE 6

2 II. PHASOR MEASUREMENT TECHNOLOGY A phasor is an equivalent representation of a pure sinusoidal wavefor, which is fully characterized by agnitude, phase angle, and frequency. For a given frequency, representation only requires agnitude and phase angle, that can be represented by a coplex nuber as shown in Fig. 1. Fig. 1. Sinusoidal wavefor with equivalent phasor representation on the coplex plane The sinusoidal wavefor can be written as, X cos t X cos ft (1) The corresponding phasor can be represented in (). X j X X X ( e cos jsin ϕ () In the general case, where both the aplitude, X ( and the sinusoidal frequency, f( are functions of tie, the sinusoid can be written as, X ( cos f ( dt (3) f ( f0 f ( (4) where f 0 is the noinal angular syste frequency (60 Hz) and Δf( is an offset fro the noinal frequency. The odified sinusoid can be written as, X ( cos f 0 t f ( t (5) Thus, the general phasor can be siply represented as, X ( jf ( t X ( X ( e f ( t (6) X (, Δf( and ϕ can be replaced with suitable atheatical functions so that different steady-state and dynaic test cases can be generated. PMUs use coplex atheatical algoriths to estiate phasor and syste frequency fro data saples. Typically, the input signal passes through a traditional anti-aliasing lowpass filter followed by an analogue to digital (A/D) converter, where the signal is sapled at fixed frequency. The discrete Fourier transfor is applied for sapled data to extract phasor estiates. The syste frequency estiate ethods vary fro vendor to vendor, where zero-crossing and rate of change of phasor angle approaches are popular. In [6], it is proposed to apply weighted average of last four phasor angles to deterine the syste frequency. Use of different algoriths can result in phasor and frequency values that differ fro the expected response for a particular condition. Thus, it is necessary to assess perforances fro different PMU vendors under the sae test conditions to evaluate their steady-state and dynaic perforances. III. PMU TEST SETUP The tests are perfored with a real tie playback device using recorded coon forat for transient data exchange (COMTRADE) files [8] of precisely generated test signals fro atheatical equations. The test setup provides input signals at a level and forat suitable for input to a PMU that accurately reproduces the COMTRADE signals in both signal aplitude and tiing. The recorded signals include both voltage and current wavefors and they are fed to the PMU, which calculates agnitude, phase angle and frequency easureents. The operational flowchart of test setup is shown in Fig.. The test setup basically consists of: - A COMTRADE generator that precisely produces voltage and current playback files with signals fro atheatical equations. - A real tie playback device that supplies real voltage and current signals at their appropriate levels (69 V voltage and 5 A current inputs). - A global position syste (GPS) receiver that generates the tie synchronization signal eployed to tie stap easured values. The GPS receiver chosen for the investigations supports a pulse-per-second (PPS) signal. The signal playback unit is also synchronized to GPS and the playing back of a signal file is started exactly at a specified tie. The analog test signals generated by the playback unit are thus referenced to a known tie. - Instruent transforers inside the PMU converts the generated test voltages and currents into low level signals that are within the range of its internal A/D converter. - The digitized signals are used to extract agnitude, phase angle and frequency easureents using discrete Fourier transfor (DFT). Fig.. Operational flowchart of test setup The PMU calculated easureents are evaluated against the actual test signals generated fro the atheatical equations, which were already used to produce COMTRADE files. Total vector error (TVE) and frequency error (FE) are deterined according to (7) and (8) respectively as per [6]. x ( ) ( ) x x a n x n a TVE( n) (7) xa xa where x a (n) is actual synchrophasor and x (n) is easured synchrophasor. FE fa f (8) where f a (n) is actual frequency and f (n) is easured fre- 63

3 quency. As the PMU easureents are copared with atheatical equations, errors include both easureent and operational errors of COMTRADE file, playback device aplifier, GPS receiver, and so on. COMTRADE file error occurs due to conversion of analogue into integer values and it can be iniized by selecting a scale with proper precision and suitable tie step. Therefore, 16-bit A/D precision and 50 µs tie step is used in the tests reported in this paper. Playback device aplifier precision is set accordingly. The accuracy of the GPS receiver used is ±1 µs (a ±6 µs tiing error causes 1 % TVE in 60 Hz syste). The influence of these errors can be iniized by properly calibrating the instruentation using the known voltage and/or current wavefors. It is iportant to calibrate both agnitudes and tie delays. IV. RESULTS AND DISCUSSION Perforance tests need to be perfored over the entire ranges of interest and include a range of operating conditions. The M class operating range is considered in this paper as the P class range is always a subset of the M class range. Test results illustrate perforances of the highest reporting rate of 60 fps. It is experienced that if a PMU satisfies perforances at the highest reporting rate it also fulfills deand at lower reporting rates. However, it is necessary to evaluate PMU perforances at each reporting rate according to [6]. Steady-state tests confir easureent in constant conditions where agnitude, phase angle and frequency of test signal, and all other influence quantities are fixed for the period of easureent. They include signal frequency, agnitude, phase angle, haronic distortion and out-of-band interference tests. Each steady-state test continues over 5 seconds of test duration. Maxiu TVE and FE are copared with specified values in [6] so as to verify whether a PMU satisfies the guidelines required. A. Steady-state Signal Frequency As discussed in section II steady-state signal can be represented fro (1). Under the signal frequency test, the frequency, f is varied fro 55 Hz to 65 Hz with a step resolution of 1 Hz while all other quantities are kept constant. The axiu, iniu and ean values of percentage TVE are shown in Fig Signal Frequency (Hz) Fig. 3. Steady-state signal frequency response at 60 fps It is iportant to note that the phasor rotates with tie as the signal frequency deviates fro the noinal frequency. This phasor rotation should be taken into account when deterining TVE as per (6); otherwise calculations ay show abnoral TVE values. Frequency of the signal is easured in each case and FEs are deterined. The PMU satisfies signal frequency TVE copliance as the axiu TVE is less than 1% for frequencies between 55 Hz to 65 Hz. B. Steady-state Signal Magnitude : Voltage The per unit (pu) agnitude of voltage signal, X in (1) is varied fro 0.1 to 1. with a step resolution of 0.1 pu while all other quantities are kept constant. The axiu, iniu and ean values of percentage TVE are shown in Fig. 4. The PMU satisfies voltage signal agnitude TVE copliance as the axiu TVE is less than 1% for agnitudes between 0.1 pu to 1. pu Signal Magnitude (pu) Fig. 4. Steady-state signal agnitude response for voltage at 60 fps C. Steady-state Signal Magnitude : Current The pu agnitude of current signal, X in (1) is varied fro 0.1 to.0 with a step resolution of pu while all other quantities are kept constant. The axiu, iniu and ean values of percentage TVE are shown in Fig. 5. The PMU satisfies current signal agnitude TVE copliance as the axiu TVE is less than 1% for agnitudes between 0.1 pu to.0 pu Signal Magnitude (pu) Fig. 5. Steady-state signal agnitude response for current at 60 fps D. Steady-state Phase Angle The phase angle, ϕ in (1) is varied fro π to +π radians with a step resolution of π/6 radians while all other quantities are kept constant. The axiu, iniu and ean values of percentage TVE are shown in Fig. 6. The PMU satisfies phase angle TVE copliance as the axiu TVE is less than 1% for phase angles between π to +π radians Phase Angle (deg) Fig. 6. Steady-state phase angle response at 60 fps 64

4 E. Steady-state Haronic Distortion A 10% haronic is introduced into the test signal where (1) is odified with (9) Haronic No. Fig. 7. Steady-state 10% haronic distortion response at 60 fps f t 0.1cos af t X cos (9) 0 The haronic nuber, a is varied fro to 50 (integer values only) while all other quantities are kept constant. The haronic coponent can either be in phase or out of phase with the fundaental coponent. The haronic coponent is ignored when deterining TVE where only the fundaental coponent is used for calculations. The axiu, iniu and ean values of percentage TVE are shown in Fig. 7. Frequency of the signal is easured in each case and FEs are deterined. The PMU satisfy haronic distortion TVE copliance as the axiu TVE is less than 1 % for a 10% haronic for signals between the second and the fiftieth haronic. F. Steady-state Out-of-Band Interference A 10% out-of-band interference is introduced into the test signal where (1) is odified with (10). X cos f0 t 0.1cos fobt (10) The frequency of an interference signal, f ob is varied fro 10 Hz to 10 Hz (second haronic) while all other quantities are kept constant. The interference signal should be in phase with the fundaental coponent. For a 60 fps reporting rate the frequency band requireent is fro 30 Hz to 90 Hz. The test frequencies are 10 Hz to 30 Hz and 90 Hz to 10 Hz. The interference coponent is ignored when deterining TVE where only the fundaental coponent is used for calculations. The axiu, iniu and ean values of percentage TVE are shown in Fig. 8. Frequency of the signal is easured in each case and FEs are deterined. The PMU does not satisfy out of band interference TVE copliance as the axiu TVE is greater than 1.3 % for a 10% out of band interference signal Frequency of Interference (Hz) Fig. 8. Steady-state 10% out of band interference response at 60 fps It is noted that FE copliance is not a part of agnitude and phase angle test. Further, the out-of-band interference test 0 1 does require for P class. The steady-state TVE and FE results of the PMU are suarized in Table I. The PMU satisfies both P class and M class TVE copliance of steady-state except out-of-band interference. TABLE I SUMMARY OF STEADY-STATE TVE AND FE RESULTS Influence Reference Max Max FE Range quantity condition TVE (%) (Hz) Signal frequency 60 Hz ± 5.0 Hz 8 17 Signal agnitude 10% to 10% 69 V voltage rated 0.94 N/A Signal agnitude 10% to 00% 5 A current rated 8 N/A Phase angle constant ± π radians 0.18 N/A Haronic < % 10% any harhonic distortion (THD) upto 50 th 6 01 Out-of-band < % of input interfering signal signal agnitude % of input signal agnitude Signal Frequency (Hz) Fig. 9. Magnitude and phase angle odulation response at 60 fps Dynaic copliances include easureent bandwidth, linear syste frequency rap and step response assessents. G. Measureent Bandwidth Test signals for easureent bandwidth are priarily 60 Hz wavefors that are aplitude or/and phase angle odulated with a sine wave. They could, however, be any kind of signal odulation or other cobination that could be input to a PMU to deterine a specific type of response characteristic. Modulation level is kept at 10% while odulation frequency is varied over a range that will deonstrate the PMU response characteristics. The tests at each odulation frequency step continue for at least two full cycles of odulation. The input test signal is represented in (11) as, X 1 kx cos ft.cos f0 t ka cos ft (11) The agnitude odulation level, k x and phase angle odulation level, k a are kept for 10% while the odulation frequency f is varied fro 0.1 to 5 Hz. The axiu, iniu and ean values of percentage TVE are shown in Fig. 9. Frequency of the signal is easured in each case and FEs are deterined. It is necessary to repeat the sae test with only the phase angle odulated signal where k x = 0 and k a = 0.1. It is iportant to allow an adequate settling tie to prevent paraeter change transient effects fro distorting the easureent. The PMU satisfies easureent bandwidth TVE copliance up to odulation frequency of Hz as axiu TVE is less than 3% but it does not coply TVE requireent beyond the odulation frequency of Hz. Thus, the PMU satisfies P class copliance but violates M class copliance. 65

5 H. Rap of Syste Frequency The input signal frequency is linearly raped to test perforances during power syste frequency changes. The input test signal is represented in (1) as, Rap Rate (Hz/s) Fig. 10. Linear frequency rap response at 60 fps 0 X cos f t R t (1) f The signal frequency rap rate, R f is varied fro negative rap ( Hz/s) to positive rap (+ Hz/s) while the rap range is fro 55 Hz to 65 Hz. The axiu, iniu and ean values of percentage TVE are shown in Fig. 10. Frequency of the signal is easured in each case and FEs are deterined. It is iportant to exclude easureents during the first two reporting intervals before and after a change in the frequency rap. For exaple, period of 33 s before and after a transition should be discarded in the reporting rate of 60 fps. The PMU satisfies frequency rap TVE copliance of both P class and M class as the axiu TVE is less than 1 % for rap rate between Hz/s to + Hz/s while the rap range is fro 55 Hz to 65 Hz. The easureent bandwidth and rap of syste frequency results are suarized in Table II. TABLE II SUMMARY OF MEASUREMENT BANDWIDTH AND LINEAR FREQUENCY RAMP TVE AND FE RESULTS Reference Max Max FE Influence quantity Range condition TVE (%) (Hz) Measureent bandwidth 69 V, 60 Hz Mod. Freq k x = 0.1, k a = 0.1 radian 0.1 to 5 Hz Linear frequency rap Rap rate of ± Hz/s 69 V, 60 Hz ± 5.0 Hz/s 9 58 I. Step Response Step responses provide a siple and easily observed ethod of coparing the PMU response to a sudden input change. They also eulate what ay be observed during load switching and faults. Step responses include agnitude and phase angle steps. Steps include positive and negative steps of 10% agnitude and 10% phase angle. The step is initiated by a signal at a precise tie, which allows deterining the response tie, delay tie and axiu overshoot/undershoot. As PMU response tie and delay tie are sall copared to the PMU reporting interval it is difficult to characterize the response of a single step. Therefore, the equivalent sapling approach explained in [5], [6] should be used to achieve the required easureent resolution. A unit step function u( is applied to the input signal agnitude and phase angle and it is represented in (13) as, X 1 k u(.cos f0t k u( (13) a The agnitude step size, k and the phase angle step size, k a are taken as 0.1 and +0.1 for negative and positive steps respectively. Fig. 11 represents agnitude positive step wavefors of input test signal, actual and easured agnitude response, and TVE response in the sae tieline. Phase angle positive step response wavefors of input test signal, actual and easured phase angle response, and TVE response are illustrated in Fig. 1. Current Input (A) Magnitude (A) Tie (s) Fig. 11. Wavefors of agnitude positive step response at 60 fps Current Input (A) Phase angle (deg) Actual Measured Tie (s) Fig. 1. Wavefors of phase angle positive step response at 60 fps Actual Measured 66

6 Reported values of a single step are represented by the dots on the continuous response curve, which is obtained by the equivalent tie sapling approach. In agnitude step, the PMU fails to coply P class TVE deand as response tie exceeds 1.7/f 0 (8) seconds but it coplies M class as the response tie is less than 79 seconds. Furtherore, axiu overshoots/undershoots of the PMU is zero but the delay tie is higher than 04 seconds at 60 fps reporting rate. In phase angle step, the PMU fails to coply both P class and M class TVE deand as response tie of TVE exceeds P class requireent of 1.7/f 0 (8) seconds and M class requireent of 79 seconds. Furtherore, axiu overshoots/undershoots of the PMU exceeds 10 % of step agnitude and the delay tie is also higher than 04 seconds at 60 fps reporting rate. Table III is suarized step perforances of the actual PMU. Step change k x = 0.1 k a = 0 k x = k a = 0 k x = 0, k a = π/18 k x = 0, k a = + π/18 TABLE III STEP CHANGE PERFORMANCE OF ACTUAL PMU Max Response Delay Reference overshoot / tie tie condition undershoot (sec.) (sec.) (% of step) A A A A Frequency Response tie (sec.) V. CONCLUSION This paper reviewed the PMU perforance tests specified in the IEEE Standard C [6], developed a test ethodology, and discussed soe practical issues in the test environent. The PMU evaluation ethod used in this paper is siple, repeatable, and can be perfored at any facility with coonly available standard signal playback equipent. The approach is based on the atheatically generated signals played back into the PMU using playback equipent with precise GPS synchronization. An actual PMU was tested using the proposed ethod and soe saple test results were presented. In dynaic tests, the signal is not purely sinusoidal and undergoes changes in its aplitude, phase angle, and frequency over a given interval. Even during steady-state tests, haronics and noise superiposed on the signal are changing. Therefore, it is necessary to continue steady-state tests for over 5 seconds and the odulation tests over at least two full cycles of odulation. In the case of step response evaluation, proper resolution should be aintained to enable accurate deterination of the response and delay ties. The actual PMU tested in the paper satisfied steady-state TVE copliance tests of both P and M classes except the outof-band interference test. In dynaic tests, the PMU satisfied the easureent bandwidth test of P class, and the linear frequency rap test and the overshoot/undershoot requireents of the agnitude step response of both perforance classes. The PMU, which has been designed according to the previous synchrophasor standards, did not satisfy the other dynaic requireents. However, the perforances of the actual PMU can be enhanced by ipleenting backend low-pass finite ipulse response filters as provided in [6]. VI. REFERENCES [1] A. G. Phadke, J. S. Thorp and M. G. Adaiak, A new easureent technique for tracking voltage phasors, local syste frequency, and rate of change of frequency, IEEE Trans. Power Engineering Review, vol. PER-3, pp. 3, May [] A. G. Phadke, Synchronized phasor easureents in power systes, IEEE Coputer Applications in Power, pp , Apr [3] P. Kundur, J. Paserba, V. Ajjarapu, G. Andersson, A. Bose, C. Canizares, N. Hatziargyriou, D. Hill, A. Stankovic, C. Taylor, T. Cutse and V. Vittal, Definition and classification of power syste stability, IEEE Trans. Power Systes, vol. 19, pp , May 004. [4] Z. Huang, B. Kasztenny, V. Madani, K. Martin, S. Meliopoulos, D. Novosel and J. Stenbakken, Perforance evaluation of phasor easureent systes, in Proc. 008 Power and Energy Society General Meeting, 0-4 July 008. [5] K. Martin, T. Faris and J. Hauer, Standardized testing of phasor easureent units, in Proc. 006 Fault and Disturbance Analysis Conf., Georgia Tech, Atlanta, GA, pp [6] IEEE standard for synchrophasor easureents for power systes, IEEE Standard C , Dec [7] K. E. Martin, J. F. Hauer and T. J. Faris, "PMU testing and installation considerations at the Bonneville Power Adinistration," in Proc. 007 IEEE Power Engineering Society General Meeting, 4-8 June 007. [8] IEEE standard for coon forat for transient data exchange (COMTRADE) for power systes, IEEE Standard C37.111, Oct VII. BIOGRAPHIES Dinesh Rangana Gurusinghe (S 11) received the B.Sc. (Eng.) degree fro the University of Moratuwa, Katubedda, Sri Lanka, in 003, and the M.Eng. degree fro the Asian Institute of Technology, Bangkok, Thailand, in 010. Currently, he is pursuing the Ph.D. degree in the Departent of Electrical and Coputer Engineering at the University of Manitoba, Winnipeg, MB, Canada. He is a Corporate Meber and Charted Engineer in the Institution of Engineers, Sri Lanka. His ain research areas are synchrophasor easureents and their applications in power syste, power syste protection, power syste stability, power syste optiization, and power syste operation and control. Athula D. Rajapakse (M 99-SM 08) received the B.Sc. (Eng.) degree fro the University of Moratuwa, Katubedda, Sri Lanka, in 1990, and the M.Eng. degree fro the Asian Institute of Technology, Bangkok, Thailand, in 1993, and the Ph.D. degree fro the University of Tokyo, Tokyo, Japan, in Dr. Rajapakse is a Registered Professional Engineer in the province of Manitoba, Canada. Currently, he is an Associate Professor at the University of Manitoba, Winnipeg, MB, Canada. His research interests include power syste protection, transient siulation of power and power-electronic systes, and distributed and renewable energy systes. Krish Narendra obtained his B.E. (Electrical Engineering) in 1986 fro University Visweswaraiah College of Engineering (UVCE), and M.Sc. (E.E), Ph.D. (E.E) with a specialization in High Voltage Engineering fro Indian Institute of Science, India in 1989 and 1993 respectively. He is now the VP-Technology and Quality and is a eber of the core corporate anageent tea of ERLPhase Power Technologies Ltd, Canada. Dr. Narendra is actively participating in the IEEE PRSC working groups and is a eber of the PRTT of NASPI. His areas of interests include Power Systes Disturbance Analysis, Protection, HVDC Controls, Neural Networks, Fuzzy logic, Phasor Technology (PMUs), and IEC application to protection and control. 67

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