Efficient Frequency-Adaptive Amplitude Tracking Algorithms for Protection Purposes Waldemar Rebizant, Member, IEEE, and Bartosz Rusek, Non-member, IEEE
Abstract—The new, fast and adaptive algorithms for measurement of signal amplitude for protection and control purposes are presented. The algorithms are intended for amplitude tracking of the distorted sinusoidal signals with varying frequency. Contradictory requirements of selective measurement of the fundamental frequency component parameters and algorithm application in off-nominal frequency conditions become reconciled due to introduction of the adaptivity idea. Wide frequency band features of the estimators are obtained by adaptive on-line changes of the orthogonal filter parameters (data window length) and coefficients in the measurement equations according to the observed actual frequency being tracked with special but simple digital procedure. The developed algorithms have been tested with MATLAB and EMTP-ATP generated signals. Practical implementation of the adaptive scheme on the TMS signal processor is also described. Index Terms— Amplitude estimation, protective relaying, adaptive signal processing, frequency independent algorithms.
I. INTRODUCTION
C
ontemporary protection and control devices or units used in power systems realize their functions nowadays in digital technique. Most of the digital measurement algorithms used for power system relaying purposes are designed to operate at fixed nominal frequency of input signals since frequency deviations in normal power system operating conditions are very small allowing to get proper accuracy of estimation. There are situations, however, when protections have to operate in serious off-nominal frequency conditions (e.g. during start up of a generator) and, if their measuring algorithms are not designed properly, they have sometimes to be interlocked [1] thus impairing protection system reliability. Similarly the relaying systems based on fault impedance estimation methods may maloperate if a fault occurs during off-nominal frequency conditions. In digital protection systems the signals which the decision whether to trip the faulty power line is based on are usually determined from orthogonal components of current and voltage phasors obtained by use of non-recursive digital filters. Selective frequency response of the filters and resulting selective features of estimators make them inadequate for W. Rebizant is with the Institute of Electrical Power Engineering, Wroclaw University of Technology, Poland (e-mail:
[email protected]). B. Rusek is with the Institute of Electrical Power Systems, Darmstadt University of Technology, Germany (e-mail:
[email protected]).
application in off-nominal frequency conditions. Contradictory requirements to be selective (suppression of noise) and unselective (to have all-pass unity frequency response insensitive to frequency changes) call for adaptive features of the estimators. The idea of adaptive estimation has already been suggested in papers [1-5]. In this paper a new approach to the problem of signal amplitude measurement in off-nominal frequency conditions is presented. Two different versions of adaptive estimators based on frequency deviation and signal period estimation are described and compared. According to the frequency measurement results the orthogonal filters are tuned up to the new frequency band by modification of their data window length and coefficients. The proposed method of adaptive measurement is simple and effective in use. II. ALGORITHM DESCRIPTION Within this section both basic amplitude measurement equations and their extension for the adaptive scheme are described. Two versions of the adaptation procedure are presented and compared one with another. A. Basic measurement equations For measurement of power system signal amplitudes (e.g. voltage |U|) the following digital algorithms are usually used: U U
2
=
2
= u c2 (n) + u s2 (n)
1 (u c (n − k )u s (n) − u s (n − k )u c (n) ) sin( kω1Ts )
(1) (2)
where u c , u s are voltage phasors at the orthogonal filter outputs (for instance full-wave Fourier cosine and sine ones), ω1 is the angular fundamental frequency, Ts is the sampling period and k is a number of delay samples (chosen from the range 1 ... N/4, with N being number of signal samples in one period of the actual fundamental frequency component). The features of algorithms (1) and (2), including their frequency responses are thoroughly discussed in [6]. It is obvious that the estimators in both versions (with and without delay) deliver correct values of measured quantities only when the signal frequency is equal to its nominal value for which the estimators were designed. When the frequency changes, certain measurement errors appear, either constant or oscillatory, depending on the estimator type. This is a result of inadequate filter gains that had been set for other signal frequency. The frequency responses of the algorithms for full-
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where d is certain time delay (d>0). It can be shown that g (ω) is proportional to the frequency deviation, i.e.: g (ω) ≅ −kTs ∆ω . The value of k is then updated according to the procedure:
1 Signal Amplitude (pu)
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g (ω ) < −δ increment k by 1 If g (ω ) ≤ δ then no change of k g (ω ) > δ decrement k by 1
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Fig. 1. Frequency response of the amplitude estimators: 1 – (1), 2 – (2).
cycle Fourier filters used for signal orthogonalisation are presented in Fig. 1. Either a band-type or unique-curve characteristic is obtained, which illustrates how the estimator equation itself modifies the frequency features of the entire digital measurement chain. B. Adaptive Solution In order to remove or minimize estimation errors in case of application of estimators (1) and/or (2) for wide-frequency measurements (e.g. for generator protection), it is necessary to adapt the orthogonal filters to the actual frequency of the signals. It is realized by the following procedure: • determine the number of samples in one period of input signals N (directly or by signal frequency estimation), • set the filter data window length to N and modify filter coefficients (i.e. the filter impulse response). Additionaly, in case of estimator (2), the value of k resulting from the currently estimated signal frequency is sent to the measurement block, thus on-line updating the previously used delay value. The procedure of adaptive measurement can be represented by the block diagram shown in Fig. 2.
where δ is a discrimination threshold assumed for the expected range of frequency changes. The value of delay k may be any fraction of N, however, once defined, determines clearly the actual value of N. For instance, if k was initially chosen to be equal to N/4, the current value of N is set to be 4 times k. Consequently, the data window length of the filters used is always extended (or compressed) to the actual value of N (for full cycle filters). More details on this approach may be found in [3]. D. The New ∆N – Based Adaptive Scheme The new approach presented in this section uses similar principles to the method presented before. The difference lies in the manner of adapting the filter window lengths and in frequency calculation algorithm. The amplitude estimation scheme is illustrated by Fig. 3. Instead of determining the deviation from power frequency, here the signal frequency itself is coarsely estimated according to the formulae [3]: f =
ADAPTIVE ORTHOGONAL FILTERS
uc(n) us(n)
Nm =
k
MEASURING ALGORITHMS
|U|
(6))
ESTIMATION of f and Nm (5), (6)
Yes 4 CONS. CHANGES of N (in one direction) ?
Fig. 2. Block scheme of the adaptive amplitude measurement.
C. Frequency Deviation – Based Adaptive Scheme The first version of the adaptive estimator studied is based on calculation of the following function (written here for an arbitrary voltage signal) [3]: g(ω) = 0.5
f T = s Ts f
∆ N>1 or ∆ N 1 decrement N by 1
(8)
Provided the algorithm (2) is further used for amplitude calculation, the actual value of delay k has to be newly set as well. Keeping in mind that k should be an integer number, its updating is only possible after four consecutive changes of N in one direction (up or down), i.e. only when N/4 becomes integer. This principle is illustrated schematically in Fig. 4. N=84
N=83
change of k=21
N=81
actual frequency. The amplitude measurement results are correct for both algorithm (1) and (2) when the adaptation procedure is active, regardless of the signal frequency value (with some distortions observed after the change of frequency - from constant value to linear increasing). Significant measurement errors for all off-nominal frequencies are seen when the standard algorithm without adaptation is used (here – shown for the algorithm (2) only). The other tests of the proposed adaptive estimation algorithms were conducted with use of EMTP – generated signals. The power system configuration used for tests (Fig. 7) was previously presented in [2]. At time t=200 ms the switch to the infinite bus is opened (the system becomes isolated). Additionally at t=1.0 s a three-phase fault in the middle of the line Q-R was modelled. Transients in generators P and Q $PSOLWXGHDOJ QRDGDSW
$PSOLWXGH SX )UHTXHQF\ SX
Determined number Nm is usually not a discrete value and thus can not be directly used for updating the filters’ DW length N. The direction of frequency changes can be known by calculating the difference between previously set discrete value of N and obtained number of Nm:
$FWXDO DPSOLWXGH
$PSOLWXGHDOJ ZLWKDGDSW
N=80
change of k=20
N=79
7LPH VHF
1 Frequency (pu)
A. Samples of Simulation Study Results A number of various signals have been prepared for testing purposes. Both accuracy and dynamics of the adaptive estimators have been tested. Full-cycle sine and cosine filters were applied for signal filtering. Using MATLAB program, the test signals were generated with two following scenarios: 1. step change of frequency from 50 to 40 Hz and at the same time a step change of amplitude from 1.0 to 2.0 pu, 2. linear change of frequency form 5 to 50Hz (changing rate 50Hz/sec) with constant amplitude. The measurement results for the first testing scenario are presented in Fig. 5. The difference between the adaptive and non-adaptive algorithms is significant and well seen. Adaptive algorithm is slower (longer filter DW is set by adaptive procedure) but reaches proper value of signal amplitude (2 pu). The response of standard algorithm is smoother and faster, however, the steady-state value reached is inaccurate. The situation for continuously increasing frequency (starting at t=0.6 sec) is shown in Fig. 6. The estimated frequency keeps up with the actual frequency of the signals with total delay of estimation not exceeding two periods of
Fig. 5. Dynamic properties of the adaptive and standard algorithms during the step change of frequency and of amplitude.
Amplitude (pu);
The developed adaptive measurement scheme has been thoroughly tested with MATLAB and EMTP-ATP generated test signals. The algorithm was also implemented on a signal processor to check possibility of its real-time application.
$FWXDOIUHTXHQF\
Fig. 4. Illustration of updating the delay value k.
III. VALIDATION AND TESTS
(VWLPDWHGIUHTXHQF\
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Fig. 6. Adaptive measurements of amplitude during linear frequency changes from 5 to 50 Hz. GP
S
P
j19 Ω 70km 750MVA H=3,5
17,5/400kV
R
opened at t=0,2s
fault at t=1,0 s GQ
70km
Q 70km
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Fig.7. Fragment of test power system modelled in EMTP.
Load 1128 MVA cos φ =0,88
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Fig. 8. Transient signals picked up at busbar GP (Fig. 7): a) rotor’s speed of generators P and Q, b) phase A current, c) phase A voltage.
rotors’ speed accompanying this sudden load variation and following fault inception are shown in Fig. 8a. The current and voltage waveforms at GP busbar are shown in Fig. 8b and Fig 8c, respectively. In consequence of new loading conditions the system frequency decreases. At the moment of fault inception the system frequency was equal to 48.5 Hz. Since in the simulated case the fault is not cleared within a reasonable period of time, both generators accelerate reaching speed values far beyond acceptable limits. The amplitudes of voltage signal (picked up at the GP busbar) measured by non-adaptive and adaptive algorithms are shown in Figs. 9a and 9b-c, respectively. The biggest differences are seen for larger frequency deviations when the filters used become untuned if the adaptation procedure is off. Then non-adaptive algorithms deliver improper value of signal amplitude (constant deviation, alg. (2)) or oscillate around
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Fig. 9. Amplitude estimation with algorithms: a) non-adaptive, b) adaptive with ∆ω – based tuning , c) adaptive with ∆N – based tuning.
proper value (alg. (1)). Small ripples on the measurement curves seen in Fig. 9b-c are a result of slightly inadequate filter gains between consecutive on-line adjusting of the filter DW lengths. They disappear when the system frequency satisfies equation (6) and Nm is a discrete value. It can be observed that the algorithm (2) possesses higher level of frequency independence (seen here as a kind of error averaging feature) resulting in smoother and more accurate amplitude measurement. Comparing Figs. 9b and 9c one can assess the quality of adaptation procedure used. Better results (two times smaller ripples) are obtained for the tuning scheme due to much finer step of filter DW length changing.
The operation of both ∆ω and ∆N – based adaptive estimators for current signals are presented in Fig. 10. The frequency value needed for algorithms’ adaptation was determined from the phase voltage signal. One can notice that the observations made for voltage measurement are valid also for current amplitude estimation.
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Fig. 10. Operation of the new ∆N – based adaptive estimators for current signals picked up at busbar GP: a) , b) and c) – as in Fig. 9.
3URJUDPPDEOHIXQFWLRQJHQHUDWRU 56&
,6$ &RPSXWHU,%03&
6LJQDO3URFHVVRUERDUG ZLWK$'FRQYHUWHU
Fig. 11. Layout of the laboratory stand with TMS Signal Processor.
B. Technical Implementation The technical implementation of the developed algorithm has been performed. The layout of the laboratory stand is shown in Fig. 11. The IBM PC computer is used as a supervisory programming and control unit. The EVM board with TMS320C30 signal processor (Texas Instruments family, 30MHz clock, 32-bit, floating-point) and A/D converter (14bit, with low-pass anti-aliasing filters) is connected to the ISA PC bus. The testing signals are delivered from the Programmable Function Generator HAMEG 8131, capable of generating any desired voltage waveform defined by the user with 12-bit resolution. Its programming is done from the PC (signals defined in MATLAB or EMTP) via the RS232C serial interface. Two versions of signal processor programming were tested: a) hardware programs written in assembler, while algorithm equations given in C language (optimal for testing purposes), b) as before, with filtering part of the algorithm written also in assembler language. The real-time tests have shown that in case of the programming version a) the required time for execution of all equation of the adaptive estimator within one time-step was equal to 0.4ms. Deeper entry in assembler (version b), filter equations) brought about considerable shortening of the algorithm execution time – to 0.14ms, which allows to work with the sampling frequency set to 7kHz. With faster signal processors (available at present above 200MHz) and the entire program code written in the machine language even 10-time higher sampling rates could be set. That means that practical implementation of the adaptive algorithm for estimation of magnitude of both currents and voltages (three-phase signals) is utterly attainable. In Fig. 12 the process of real-time voltage amplitude measurement with the ∆ω – based adaptive estimator is shown and compared with the off-line estimation in MATLAB simulated environment. The results of amplitude estimation off-line (Fig. 12a) and on-line (Fig. 12b) are almost identical. Higher level of “noise” accompanying real-time measurements results from the non–ideal 14–bit A/D conversion and lower accuracy of calculations with 32–bit floating point signal processor. Fig. 12c illustrates the process of the filter adaptation according to the procedure (4). The on-line upgrading of the filter DW length N makes the filter center frequency follow signal frequency changes with resolution resulting from the value of parameter δ. Transient state of signal frequency assessment may be observed at (and after) the points of sudden change of voltage signal, i.e. after opening of the tie connection RS and after fault inception.
• Fine tuning of the filter DW length with the ∆N procedure reduces instantaneous measurement errors due to inaccurate filter settings when compared to the ∆ω scheme. • The adaptive amplitude estimation scheme can be applied for measurement purposes when signal frequency may vary in wide range, e.g. for generator protection and control A successful attempt to the practical implementation of the new adaptive estimator on a digital signal processor with sampling rate of a few kHz is also described.
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V. ACKNOWLEDGMENT 0
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The authors gratefully acknowledge the contribution of J. Staszewski (WUT, Wroclaw, Poland) for his work on the hardware implementation of the adaptive estimator algorithms.
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VI. REFERENCES Voltage (kV)
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VII. BIOGRAPHIES
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W. Winkler and A. Wiszniewski: "Adaptive protection - potential and limitation", CIGRE SC34 Colloqium, Stockholm, 1995, Rep. 34-206. W. Fromm, A. Halinka and W. Winkler: "Accurate measurement of wide-range power system frequency changes for generator protection", Developments in Power System Protection, 25-27 March 1997, IEE Conference Publication No 434, pp. 53-57. W. Rebizant, J. Szafran and M. Michalik: "Adaptive estimation of wide range frequency changes for power generator protection and control purposes", IEE Proc. – Generation, Transmission and Distribution, vol. 146, no. 1, pp. 31-36, Jan. 1999. P.J. Moore, R.D. Carranza and A.T. Johns: "A new numeric technique for high-speed evaluation of power system frequency", IEE Proc.Generation, Transmission and Distribution, vol. 141, no. 5, pp. 529-536, Sept. 1994. I. Brncic, B. Hillstrom, E. Nilsson and J. Zakonjsek: "A mathematical module for protection and control purposes", in Proc. of 10th Int. Conf. on Power System Protection, Bled, Slovenia, Oct. 1996, pp. 179-188. W. Rebizant and J. Szafran: "Frequency response of relaying algorithms based on orthogonal components", in Proc. of 13th Int. Conf. on Power System Protection, Bled, Slovenia, Sept. 1996, pp. 161-166.
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Fig. 12. Results of: a) simulations, b) real-time measurement of voltage amplitude, c) on-line upgrading of filter DW length.
IV. CONCLUSIONS In the paper the theoretical analysis and simulative investigations of the new adaptive scheme for signal amplitude estimation are described. The adaptation procedure based on determination of the difference between actually measured period of the signal fundamental frequency component and current filter DW length is compared to the frequency deviation – based scheme. The following features of the new estimator are worth to be pointed out: • The proposed adaptive scheme is capable of tracking signal amplitude with high dynamics even if the signal frequency is varying in wide range and with changing rates up to a few Hz per second. • Proper measurement results with the adaptive algorithms are not only quantitatively but also qualitatively better than those with use of standard non-adaptive estimators.
Waldemar Rebizant (M’2000) was born in :URFáDZ 3RODQG LQ +H UHFHLYHG KLV M.Sc. and Ph.D. degrees (both with honors) from Wroclaw University of Technology, Poland in 1991 and 1995, respectively. Since 1991 he has been a faculty member of Electrical Engineering Faculty at the WUT. In June 1996 he was awarded Siemens Promotion Prize for the best dissertation in electrical engineering in Poland in 1995. In 1999 he was granted a prestigious Humboldt research scholarship for the academic year 1999/2000. In the scope of his research interests are: digital signal processing and artificial intelligence for power system protection purposes. Bartosz Rusek (Non-member) was born in 1977 in Pulawy, Poland. He graduated from the Faculty of Electrical Engineering of Wroclaw University of Technology, Poland in 2002. At present he is an assistant at the Institute of Electrical Power Systems of the Darmstadt University of Technology, Germany. His research interests include: digital protection and control systems, digital signal processing and digital modeling of CB.
