Abstract
This paper describes a scheme to improve theoverall performance of Phasor Measurement Units (PMU),such that the estimated phasors can be used for a wide rangeof applications in real-time. The main concern is the accuracyand robustness of the phasor estimation outside steadystate,which is strongly influenced by the accuracy of thefrequency estimation. The need to complement the phasordata with information about the phasor quality is also emphasized.Keywords - Phasor measurement, phasor quality assessment,on-line power system stability assessment.
1 Introduction
Phasor Measurement Units ability to measure thephase angle of input signals makes them particularly suitablefor dynamic events monitoring [1]. However, duringserious dynamic events (e.g. losses of synchronism andinterarea oscillations), large swings in active power, frequencyand other system variables can occur. In that case,the strict definition of a phasor representation is no morevalid and measurement accuracy is inevitably lower thanin steady-state.
1.1 PMU accuracy specificationsAccording to the IEEE standard on Synchrophasors[2], the maximum phase-shift accuracy one may needfor state estimation, monitoring, control, and relaying ofpower systems is 0.1±. The deviation in amplitude is usuallyless critical. For that purpose, a Total Vector Error(TVE) has been defined to designate the quality of PMUs:TVE =q(Xrf ¡ Xr)2 + (Xif ¡ Xi)2X2r + X2i(1)where Xrf and Xif are the measured values of the phasorreal and imaginary parts, as given by the measuringdevice, and Xr and Xi are the corresponding theoreticalvalues of the input signal at the instant of measurement.The standard requires the TVE to be measured in steadystateand to be lower than 1%. Levels 0 and 1 are thengiven to the devices depending on the range (in frequencydeviations, amplitude and harmonic distortion) where thiscondition is fullfilled.
1.2 Phasor Measurement and Dynamic Applications
The standard does not include information concerningthe accuracy of the estimated phasors in the messagessent to the Phasor Data Concentrator (PDC) and hence tothe downstreams applications. Furthermore, it suggeststhat even outside steady-state, the error on the frequencymeasurement can be neglected and thus an on-line computationof the TVE would prove to be satisfying for allwell-designed devices that belong to levels 0 and 1.The authors of this paper do not agree with this statement.Real-time measurement of the frequency may notbe free of errors if the frequency varies inside the considereddata window, as it is the case for interarea oscillations,where slopes reaching 0.1 to 0.8 Hz/s are possible.Since phasor measurements have a high added value outsidesteady-state with respect to other measurement techniques,errors in frequency and thus on the phasor mustbe considered for dynamic applications. Therefore, theauthors strongly advise to assess the quality of the computedphasors on-line. Unfortunately, the TVE as definedby equation 1 cannot be computed on the field, since thetheoretical phasor is unknown. Another indicator of thephasor quality is thus needed.
1.3 Paper contents
The content of this paper is as follows. Section 2 remindsthe definition of the phasor and the errors in phasormeasurement. Section 3 focuses on frequency measurement,an essential stone in phasor measurement. Section4 introduces the scheme that aims at improving the PMUaccuracy and robustness. Section 5 covers the phasor qualityissue and the conclusions come at section 6.
2 Phasor Measurement
For a discrete signal x(k), if the DFT (Discrete FourierTransform) data window contains exactly one cycle ofsamples, the phasor of fundamental frequency is given bywhere N is the number of samples and the subscript krepresents the last sample index in the data window. Theresulting phasor rotates on the complex plane with an angularspeed determined by the signal frequency, which canbe taken as instantaneous frequency

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