Adaptive Phasor and Frequency-Tracking Schemes for ... - IEEE Xplore

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IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 26, NO. 2, APRIL 2011

Adaptive Phasor and Frequency-Tracking Schemes for Wide-Area Protection and Control Innocent Kamwa, Fellow, IEEE, Ashok Kumar Pradhan, Member, IEEE, and Geza Joos, Fellow, IEEE

Abstract—The steady-state performance of phasor measurement units (PMUs) is well standardized in the recently issued revised IEEE Std. C37.118. The Western Electricity Coordinating Council (WECC) has developed dynamic performance requirements for PMU filters as a means to guarantee better, uniform PMU response under dynamic conditions, such as power swings and changing harmonics. These have been endorsed by North American Synchrophasor Initiative (NASPI) for its wide-area monitoring infrastructure. The main purpose of this paper is to present a new framework for designing PMU filtering algorithms capable of meeting or exceeding the WECC/NASPI requirements, while achieving an optimum transient response time. To this end, an adaptive complex bandpass filter derived from the exponentially modulated filter bank theory has been devised. It is built from freely chosen low-pass filter prototypes that fulfill the WECC requirements. The static and dynamic performances of two specific schemes dedicated to control and monitoring with 4- and 7-cycle response-time, respectively, are ascertained under noisy waveforms and changing harmonics with system frequency varying from 40 to 80 Hz. The center-frequency adaptation approach is shown to be intrinsically superior to the frequency compensation scheme, especially under fast varying frequency and changing harmonics. Index Terms—Adaptive complex bandpass filtering, changing harmonics, frequency estimation, phasor measurement unit (PMU), power system oscillations, synchrophasor, wide-area measurement systems (WAMS), wide-area protection and control (WAPC).

I. INTRODUCTION

HE synchrophasor technology is now mature enough for practical real-time monitoring of multi-area networks spread over large geographical distances [1], [2]. A major step toward ensuring the interoperability of phasor measurement unit (PMU) devices from different vendors was recently achieved by the issuing of the revised IEEE Standard C37.118-2005 [2]. Compliance with this standard requires making phasor measurements that meet the synchrophasor definition within one

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Manuscript received August 30, 2009; revised November 02, 2009. First published February 05, 2010; current version published March 25, 2011. Paper no. TPWRD-00656-2009 I. Kamwa is with Power System and Mathematics, Hydro-Québec/IREQ, Varennes, QC J3X 1S1, Canada (e-mail: [email protected]). A. K. Pradhan is with the Department of Electrical Engineering, Indian Institute of Technology, Kharagpur 721302, India. (e-mail: [email protected]. ernet.in). G. Joos is with the Department of Electrical and Computer Engineering, McGill University, Montreal, QC H3A 2A7, Canada (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPWRD.2009.2039152

of two accuracy classes and conforming to the communication protocol for reporting measurements. The standard, rightly, made no attempt to set normative performance requirements from PMUs under dynamic conditions, although it recognizes that a particular PMU may have additional capabilities in the realm of accuracy, communication, reporting rates, frequency range, noise suppression, etc. In the same way the speed transducer is fully integrated with the power system stabilizer (PSS) and changes from one manufacturer to another without impacting the overall PSS functionality, original and innovative wide-area control schemes cannot be developed without revisiting the PMU dynamic performance requirements. On-board filtering will be ultimately specified in conjunction with the expected applications functionalities and the PMUs equipped with advanced capabilities (above and beyond those required for compliance with standard C37.118) will certainly have an edge when wide-area control and protection systems become a reality under the thrust of smart grid technology. In a pioneering effort to enhance the quality of the measurements from wide-area measurement systems (WAMS), the WECC in 2004 [3], introduced a signal filtering standard which for the first time provided vendors with a utility perspective on the minimal requirements for monitoring applications. These requirements have recently been endorsed by NASPI [4]. To sum up, the frequency response of a NASPI/WECC compliant PMU: dB or greater at 5 Hz; • is • does not exceed 40 dB at frequencies above the Nyquist frequency (a limit of 60 dB is preferred); • does not exceed 60 dB at frequencies that are harmonics of the actual power system frequency; • does not produce excessive ringing in records for step disturbances. Fig. 1 represents the filtering requirements in graphical form and assumes a sixth order Butterworth filter, with a 6 Hz bandwidth and an output rate of 30 sps. While these specifications are relatively explicit about noise and harmonic filtering, they do not consider the important issue of phasor distortion during fault and switching events [5], [6]. In the extreme case, the voltage could drop to zero during a three-phase-to-ground fault leaving the phase angle temporarily undefined. In view of control and protection applications, the phasor should therefore be tagged at the PMU level with respect to the transmission line status (fault, outage, switching transient, etc.). Otherwise, the user could mistakenly take strong actions based on the wrong information [5], [6]. This paper is aimed at developing a signal processing framework that results in phasor and frequency tracking schemes that meet/exceed the NASPI/WECC PMU filtering requirements [3],

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KAMWA et al.: ADAPTIVE PHASOR AND FREQUENCY-TRACKING SCHEMES

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Fig. 2. DFT-based bandpass filtering of the space phasor.

After some algebraic manipulations of (2), we obtain (4)

Fig. 1. A sixth Butterworth filter with a 6-Hz bandwidth versus WECC filtering standard (sample rate = 30 sps) (cf. [4] at www.naspi.org).

This shows that the space phasor consists of the superposition of the negative and positive symmetrical components. When the contain positive and negative sequence waveforms harmonics, the space phasor can be generalized as follows:

[4]. An adaptive bandpass filter whose center frequency is adjusted online using an accurate frequency estimator is designed using Taylor windows of appropriate length. The bandpass filter possess attractive properties like linear phase, steep stopband, fast decaying side-lobes and a unit gain and zero phase at the center frequency which is confirmed through numerous tests.

(5)

II. DYNAMIC PHASOR EMBEDDED IN CHANGING HARMONICS For the sake of generality, let us consider the basic waveforms incoming to the PMU as a combination of positive and negative sequence components at fundamental frequency

(1) and represent the positive Let and negative symmetrical components, respectively. The corresponding space phasor is defined as [7]

(2) where and and of the instantaneous waveforms

are the Clarke’s components

(3)

Interharmonics and white noise can be similarly added to (5). The objective of a tracking scheme is to extract the fundamental space phasor from the space instantaneous phasor without any harmonics or negative sequence interference. The most intuitive approach to solving this problem, therefore, consists in bandor in passing the phasor around the center frequency order to obtain the positive and negative sequence phasors, respectively. This is classically done using the discrete Fourier transform DFT as illustrated in Fig. 2. The one cycle box-car window-based DFT is naturally centered at the nominal fundamental frequency and allocates perfect notches at the harmonic frequencies in positive and negative sequence. However, due to a non flat-top magnitude response and relatively high sidelobes, the DFT-extracted phasor suffers from two well-documented fundamental problems [8]: 1) amplitude loss and phase offset at off-nominal frequency and during power swings; 2) high sensitivity to interharmonics and deterioration of the harmonic and negative sequence rejection when the fundamental frequency is changing over a large interval. Recently, considerable research has been directed towards improving the Fourier-based phasor extraction [9], [10]. One approach uses frequency compensation based on a mixed time-frequency domain approximation of the Fourier phasor [9], but the achieved accuracy will still depend on the accuracy of the frequency estimator. Another approach uses a flat-top windowed DFT to avoid the amplitude loss. The windows were designed for the fundamental frequency only, by fitting the phasor to a second-order Taylor polynomial using the least-squares method [10]. In both cases, the analysis band-pass filters are of fixed coefficients and no performance assessment under changing harmonics is provided. Parametric approaches have been attempted to deal with the first mentioned issue above [12]–[14]. They were successful as long as the assumed model was close to the actual signal, which is not always the case (e.g., when interhamonics are present).

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and frequency of the stationary phasor are then computed as shown in the figure. Additional low-pass filtering may be required to comply with specific filtering requirements of the application. The frequency value used in both compensation and adaption is derived through a separate frequency estimator using the demodulation method in [17] or any other proven accurate frequency measurement algorithm [18]. This allows more freedom independently from the in adjusting the frequency filter WECC filters. However, if the latter are sufficiently effective, value can be used in a feedback loop (with one sample the delay to avoid any algebraic loop problem). The second option reduces the computational burden of the overall scheme by removing the “slow frequency tracking” block. To design the bandpass filter, let us consider the following filter bank definition which comes from the exponentially modulated (EM) filter bank theory [19]:

Fig. 3. Overview of the proposed exponentially modulated (EM) bandpass filter-based adaptive phasor tracking scheme.

Parametric methods are effective in smoothing white noise and tracking the amplitude and phase of the fundamental phasor during power swings [14], but they do not properly address the issue of changing harmonics under large frequency shifts.

III. ADAPTIVE BANDPASS FILTER DESIGN TO MEET WEEC/NASPI FILTERING SPECIFICATIONS It was pointed out in [15] that an effective way to extract a phasor embedded in changing harmonics was by adaptive bandpass Kalman filtering. This approach solved the two problems before at the expense of a high-order state space complicated , when harmonics are included), which model (of order even then will not match the underlying signal behavior at times. To avoid this pitfall we have revisited the adaptive bandpass approach in a non-parametric framework. A related idea was tried in [16] using a tunable infinite-impulse-response (IIR) complex bandpass filter. However, the proposed design was coupled to a specific low-pass prototype making it very hard to adapt to other applications such as WECC-compliant filtering for monitoring. Fig. 3 provides an overview of the proposed phasor and frequency scheme. The voltage space phasor is the main input, sampled at a constant rate (e.g., 48 samples/cycle of the nominal frequency). Given an efficient bandpass filter (to be described later), we have two possible routes [6] as follows. 1) Keep the filter fixed and proceed to frequency compensation of its output. 2) Adapt the filter center frequency online so that there is no need for frequency compensation of its output. The time-varying phasor is then made stationary by frequency shifting based on a local reference phasor. The amplitude, phase

(6) where and is the impulse response coefficients of a linear-phase low-pass FIR proof filter cells is setotype filter. Furthermore, the number is the length of the prototype filter. If properly lected so that chosen, the scaling factor and the center frequency of the ith filter can be located at the fundamental frequency. Assuming a samples per cycle of the fundamental sampling rate of

(7) and signs define the positive and negative where the sequence filters, respectively (i.e., the bandpass filter required to extract the corresponding symmetrical component from the space-phasor). A similar filter bank can be defined with real coefficients as follows:

(8) The final impulse response data of the th bandpass filter, after rescaling for a unit magnitude and zero phase at the center frequency, are (9) is the nominal frequency response of where the th filter cell at the fundamental frequency. To illustrate this band-pass filter design, a few typical prototype low-pass filters are shown in Fig. 4. The same sixth-


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Fig. 5. Example of an exponentially modulated filter bank from a 4-cycles Taylor window-based low-pass prototype.

Fig. 4. Candidate low-pass FIR prototype filters for use in bandpass filter-based phasor extraction.

order Butterworth filter which appeared previously in Fig. 1 is reproduced here for reference purposes. The Kay window is defined as follows [20]:

(10) while the Taylor window [20] is given by

(11) with the filter coefficients being

and . According to Fig. 4, the Taylor window-based 7-cycle lowpass filter prototype has its 3 dB bandwith at 6 Hz with its 60 dB stop-band at 20 Hz. The corresponding 4-cycle filter has a 10 Hz bandwith and 30 Hz stopband. The first filter thus meets the WECC requirements for a 30 Hz PMU reporting rate while the second can report the phasor at a 60 Hz sampling rate without violating the WECC requirement on Nyquist frequency attenuation. The phase response highlights the large delay introduced by a Butterworth solution which is obviously incompatible with control and protection objectives. For instance, its phase delay at 2 Hz while the 4 and 7-cycles FIR filter introduces, is 22 and 42 phase lag, respectively. As shown in the bottom of Fig. 4, the proposed prototype filters have constant group delays, in a sharp contrast with the six-order discrete Butterworth filter whose group delay is variable. In fact, giving that all filters involved in the scheme of Fig. 3 are derived from low-pass finite impulse response (FIR) prototypes with symmetrical impulse response (as for example in (11)), their phase is always linear over the pass band and it is possible to establish that their group delay is [26]

where is the phase of the filter frequency response, while is the length of the filter expressed in the number of cycles of the fundamental frequency. Whatever the sampling rate, the group delay is always half the length of the symmetrical FIR filter. The filter bank resulting from the exponential modulation of a 4-cycles Taylor window-based low-pass prototype is shown in Fig. 5, where the fundamental center frequency is assigned to cell No. 3 (blue). The scaling in (9) forces the bandpass to a unit gain and zero phase shift at the center frequency. Also, the filter linear phase property is evident on the second panel. Fig. 6 illustrates the magnitude response of the centered bandpass for different low-pass prototypes. The 7-cycle optimized low-pass was obtained using the method in [21] whose optimum

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Fig. 6. Bandpass filter magnitude response for various prototypes low-pass filters.

solution is less narrow but has far greater stopband attenuation (80 dB). This example demonstrates how flexible the proposed method is. It is not dependent on any specific low-pass filter design method as in [16]. The only requirement is that the prototype should be a linear-phase FIR filter. In real-time, once an is available, the center freaccurate frequency estimate quency can be updated as follows:

(12) The filter coefficients are then updated in real-time by substituting this new value of in (6). This modification can be done at a slower rate, typically that of which is decimated by a according to Fig. 3. With 4-cycle Taylor filtering, factor variable can be refreshed at one point per cycle the giving its good attenuation at the 30-Hz Nyquist frequency. In the frequency compensation approach, a static frequency dependent model of the magnitude and phase of the bandpass filter around its center can be built off-line at the design stage. Giving the computational capabilities of today computers, highorder polynomials can be used in the fitting process without a significant penalty in real-time. Fig. 7 illustrates the accuracy of a sample polynomial fitting over a wide frequency range with an order 6 for the box-car window and 10 for the 4-cycle Taylor windows. Let us define the correction factor as follows:

(13) ( Hz) is the frequency offset from the where and are the fitting polybandpass center frequency; nomial functions for the amplitude and phase of the bandpass frequency responses, respectively (Fig. 5). Then, the estimated should be corrected as follows: phasor

(14) is the running estimated frequency value for use in where the frequency compensation scheme. For the one-cycle box-car

Fig. 7. Polynomial fitting of the magnitude response around the center frequency for various windows.

window shown in Figs. 6–7 and with nitude polynomial is

given in Hertz, the mag-

while the phase polynomial (in deg.) is a simple linear function . with negative slope: In many windowed DFT [22]–[24], advantage is taken of the analytic expression of the cosine-windows expressed as in (11) to develop simplified analytic formulations which speed-up the real-time frequency compensation process [15]. IV. STANDARDIZED PARAMETRIC TEST SIGNALS To demonstrate the effectiveness of the algorithms, standard tests signals are generated in Matlab using the “discrete 3-phase Programmable Source” available in the SimPowerSystems package (Fig. 8). In the example shown, the base voltage is 735 kV (or 600.125 kV phase-ground). The source will therefore generate a sum of second and third harmonics between 0 and 50 s, in the negative and positive sequence, respectively, with a 10% magnitude. The fundamental amplitude is zero but its frequency is ramping from 40 to 80 Hz over the time frame of 4 to 40 s, with the harmonics frequency changing accordingly. The programmable three-phase source is used to generate parametric test signals as follows. 1) Changing harmonics: fundamental frequency ramp from 40 to 80 Hz (1.1 Hz/s) with simultaneous addition of 10% harmonics from 2nd to 11th. Even and odd harmonics are in positive and negative sequence, respectively. A 10% magnitude interharmonics is added as in [16] at a Hz ( 330.6 Hz). frequency of 5.51 2) Amplitude ramp from 0.9 to 1 p.u. (1.1 p.u./s) at a fixed fundamental frequency with 10% of all harmonics from 2nd to 11th and 20 dB white noise added on phase-a. Amplitude (0.1 p.u.), frequency(0.1 Hz), and phase (5 ) steps applied separately at fundamental frequency 3) Additive single sinusoidal interference (0.1 p.u.) over the frequency range 0.5 to 500 Hz.


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Fig. 9. Response of the adaptive and frequency compensated schemes to test signal # 1: Changing harmonics. Taylor-based 4-cycle low-pass prototypes.

TABLE I MAXIMUM AND STANDARD DEVIATION OF AMPLITUDE ERRORS UNDER CHANGING HARMONICS—4-CYCLE TAYLOR WINDOW PROTOTYPE

Fig. 8. Three-phase programmable source configuration in Matlab.

4) Additive white noise on phase-a with a fixed fundamental frequency of nominal magnitude and frequency: signal-tonoise ratio ranging from 80 dB to 10 dB. 5) Sinusoidal amplitude (0.1 p.u.), frequency (0.1 Hz) and phase modulation (5 ) over the frequency range 0.5 to 500 Hz. The objective of the next section is to verify that the proposed schemes not only comply with the Std C37.118 but also exceed the expectations of the WECC filtering standards. V. RESULTS OF PARAMETRIC TESTS Unless stated otherwise, the configurations analyzed in the sequel consists of a 4-cycle Taylor bandpass phasor tracking at a sampling rate of 1440 Hz, followed by a one cycle smoothing at the 960 Hz sampling rate. A. Dynamic Responses to Ramp and Steps In the first experiment, signal #1 is applied to the new scheme and corresponding results are shown in Fig. 9. Due to the scale of the plot, the filtered frequency (Fwecc) seems perfect, but it is actually lagging behind the set frequency deviation. The amplitude error on the bottom plot illustrates the superiority of frequency adaptation over frequency compensation when the frequency changes. Table I summarizes the magnitude errors in the different time frames: signal between 1 and 50s, initial steady state at 40 Hz (1 to 4s) and final steady state at 80 Hz (40 to 50s). Both the frequency compensation and adaptation schemes are based on the same frequency measurement and the same 4-cycle Taylor windows for bandpass filtering of the instantaneous space phasor. Since the adaptive scheme is most reliable, this will be the focus of the rest of this paper. Its performance for the second

Fig. 10. Response of the 4-cycle adaptive schemes to the test signal no 2-amplitude ramp in white noise and harmonics.

test signal is shown in Fig. 10. The steady-state amplitude errors are within 0.05% but the errors increase slightly during the amplitude ramping. Under the stated conditions of the 2nd test signal, the frequency errors are independent of the amplitude ramping (1.1 p.u./s) and stay within 5 mHz. The step responses presented in Fig. 11 illustrate the good linear behavior of the phasor and frequency tracking schemes. The Taylor windows-based seven-cycle scenario is built by combining a 4-cycle-based adaptive bandpass filter with a 3-cycles low-pass post-processing filter. Table II provides more details about the step responses characteristics computed using

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Fig. 11. Response of the 4- and 7- cycle adaptive schemes to test signal #3-Step responses harmonics.

Fig. 12. Static responses of the 4- and 7-cycles adaptive schemes to test signal # 5—Additive sinusoidal interference.

TABLE II STEP RESPONSES INFORMATION

the Matlab “StepInfo.m” utility function. The rise time is defined as the duration between 5% and 95% of the final response, while the settling time is the time taken by the response to stabilize within 99.5% of its final value. The reference column corresponds to the step response of the sixth-order Butterworh filter shown in Figs. 1 and 4. The 4-cycle solution results in a satisfactory dynamic performance for wide-area control, with flat and well-damped responses. Even if the settling time is relatively slow, due to the adaptation mechanism, the rise time is very fast and the final phasor and frequency response are unbiased. For monitoring purposes, the proposed 7-cycle solution clearly outpaces the 6th order Butterworth in term of settling time. B. Static Responses The algorithms responses to additive interference of sinusoidal and white noise types, respectively, are presented in Figs. 12 and 13. The magnitude error response confirms that the 4-cycles solution can achieve a reporting rate of 60 Hz while complying with the 1% C37.118 out-of band level 1 rejection requirement. Likewise, the 7-cycle scheme is capable of a 30 Hz reporting rate with no harmonic or negative sequence sensitivity. Fig. 14 presents the frequency responses of the overall phasor and frequency tracking schemes. It is seen that the frequency and amplitudes errors are negligible under a purely sinusoidal amplitude and frequency modulation, respectively. The phase response is not shown but we have verified that they closely

Fig. 13. Static responses of the 4-cycle adaptive schemes to test signal # 5-Additive noise on phase-a in nominal conditions.

match the phase of the corresponding 4- or 7-cycles low-pass prototypes shown in Fig. 4. VI. TYPICAL PERFORMANCE UNDER FAULT CONDITIONS Two sets of signals are studied in sequel to illustrate some problems facing PMU filtering for wide-area control. A. EMTP Simulation The first set of signals resulted from EMTP simulation of a sudden three-phase fault at the LG2 power-plant in the HydroQuebec’s grid. The results obtained with the 4-cycle scheme are shown in Fig. 15. The upper panel confirms the effectiveness of the fast phasor tracking scheme on these relatively clean signals. A fault flag, shown in dashed orange, was separately determined by pattern analysis of the low level signals in a way similar to [5]. It is very helpful to tag the phasor estimates as suspect during a temporary voltage dip. The lower panel of Fig. 15 illustrates how to use such a flag to remove fault-induced spikes from the frequency estimates. The raw estimate unrealistically


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Fig. 14. Response of the 4- and 7- cycle adaptive schemes to the test signal no 6-Sinusoidal Amplitude/Frequency modulation. Fig. 15. Responses of the 4-cycle adaptive scheme to EMTP simulated threephase fault signals in Hydro-Québec’s grid.

exceeds 1.75 Hz, but by using the flag the frequency is considerably smoothened (i.e., orange and dashed orange vs black). In fact, any action taken for protection or control purposes based on the spiky estimate will be worse that doing nothing. Therefore, qualifying the phasor and frequency using a status description flag (such as Fault, Transient, Open, etc.) should really be a full component of the PMU data collection and dissemination process [5], [6]. B. Actual Recording at a Nuclear Power Station The second set of signals is actual data recorded at the Gentilly nuclear power station during a minor fault event in the Hydro-Quebec’s system. The phasor results from the 7-cycle filtering scheme are shown in Fig. 16. Everything seems fine from this viewpoint but, looking at the frequency estimates in Fig. 17, it is observed that the 7-cycle filter did not eliminate all the noise on the signal, despite the substantial attenuation compared to the raw estimate in the lower panel of the plot. The (in orange), did a much better backup frequency estimate, smoothing job in this case. To understand the limitation of the WECC specification in this case, we performed the spectral and Prony analyses [25] of the raw frequency estimates. The results are shown in Fig. 18. In addition to a local mode with a frequency of 1.43 Hz, the 675 MW turbine-generator displays poorly damped torsional modes at 9.95 Hz and 17.8 Hz. One way to deal with this issue is to supplement the WECC/ NASPI requirements with notch filters when the situation requires more rejection at specific frequencies. For example, we

Fig. 16. Phasor estimates by the 7-cycle adaptive scheme following an actual fault at a nuclear power plant in the Hydro-Québec’s grid.

verified that the following notch filters effectively smooth out the torsional modes from the signal, with less phase lag : in the useful band than

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result from selecting Taylor windows of appropriate length as low-pass FIR prototypes. The bandpass filter is then automatically derived using the exponential- or cosine-modulated filter bank theory. Numerous parametric test signals are used to prove the effectiveness of the filters, including changing harmonics with fundamental frequency varying from 40 to 80 Hz and phase, amplitude and frequency step responses. Static responses to sinusoidal amplitude/frequency modulation and additive interference up to 500 Hz, confirm that the 4- and 7-cycle Taylor windows-based solutions comply with both the WECC/NASPI and C37.118-2005 requirements for 60 and 30 Hz reporting rates, respectively. However, initial experiments with simulated and actual system responses in fault conditions point to the need for additional research in tagging the phasor when it is unreliable, and to more targeted notch-filtering of torsional or within-band interference as required by the application. REFERENCES Fig. 17. Frequency estimates by the 7-cycle adaptive scheme following an actual fault at a nuclear power plant in the Hydro-Québec’s grid. (a) Filtered frequency estimate. (b) Raw frequency estimate.

Fig. 18. Spectral and Prony analysis of the raw frequency estimates in the bottom panel of Fig. 17.

This example shows that there will be no easy way for a single filtering solution addressing all wide-area control applications. The filter requirements are so specific to the actual situation that the best approach may possibly be to provide a flexible framework as presented in this paper which will allow the vendor and the utility to jointly fine-tune the PMU filtering performance within the specifics of the plan, the grid and the target application (e.g., see [8]). VII. CONCLUSION We have presented a design method for PMU filtering schemes capable of matching or exceeding the WECC/NASPI requirements for wide-area monitoring applications. We discovered that the best compromise is achieved using an adaptive bandpass filter whose center frequency is adjusted online using an accurate and slow frequency estimator. The bandpass filter has attractive prescribed properties such as linear phase, steep stopband, fast decaying side-lobes and, more important, a unit gain and zero phase at the center frequency. These properties

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Innocent Kamwa (S’83–M’88–SM’98–F’05) received the Ph.D. degree in electrical engineering from Laval University, Laval, QC, Canada, in 1988. He is with the Hydro-Québec Research Institute (IREQ), Power System Analysis, Operation and Control, Varennes, QC, Canada, where he is currently a Principal Researcher in bulk system dynamic performance. He has been an Associate Professor of Electrical Engineering at Laval University since 1990. Dr. Kamwa has been active for the last 13 years on the IEEE Electric Machinery Committee, where he is presently the Standards Coordinator. A member of CIGRÉ and a registered professional engineer, Dr. Kamwa is a recipient of the 1998, 2003, and 2009 IEEE Power Engineering Society Prize Paper Awards and is currently serving on the Adcom of the IEEE System Dynamic Performance Committee.

Ashok Kumar Pradhan (M’94) received the Ph.D. degree in electrical engineering from Sambalpur University, India, in 2001. He has been with the Department of Electrical Engineering, Indian Institute of Technology, Kharagpur, since 2002. Currently, he is Associate Professor. His research interests include power system dynamics and relaying.

Geza Joós (M’82–SM’89–F’06) received the M.Eng. and Ph.D. degrees from McGill University, Montreal, QC, Canada. He has been a Professor with McGill University since 2001, where he holds a Canada Research Chair in Power Electronics applied to Power Systems. He is involved in fundamental and applied research related to the application of high-power electronics to power conversion, including distributed generation and wind energy, and to power systems. He was previously with ABB, the Ecole de technologie supérieure and Concordia University. He is involved on a regular basis in consulting activities in power electronics and power systems. He is active in a number of IEEE Industry Applications Society committees and in IEEE Power Engineering Society working groups and in CIGRE working groups. He is a Fellow of the Canadian Academy of Engineering and of the Engineering Institute of Canada.