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The algorithm for directional element without dead tripping zone based on digital phase comparator
Electric Power Systems Research 81 (2011) 377–383
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Electric Power Systems Research journal homepage: www.elsevier.com/locate/epsr
The algorithm for directional element without dead tripping zone based on digital phase comparator Zoran N. Stojanovic´ ∗ , Milenko B. Djuric´ Faculty of Electrical Engineering, University of Belgrade, Bulevar Kralja Aleksandra 73, 11120 Belgrade, Serbia
a r t i c l e
i n f o
Article history: Received 15 January 2009 Received in revised form 31 March 2010 Accepted 30 September 2010 Available online 27 October 2010 Keywords: Digital protection Directional element Digital phase comparator Dead tripping zone
a b s t r a c t This paper describes the algorithm for directional element without dead tripping zone. Instead of calculating phase angle between the phasors of voltage and current the algorithm uses digital phase comparator. The procedure is based on calculation of normalized average power within one semi-period of the input voltage and current signals. Before usage the samples are passed through the Fourier filter to remove high-order harmonics and/or direct component. The dead tripping zone is eliminated by introduction of a voltage delay which is used for determination of direction. In addition, special attention is paid to the problem of synchronization which appears when signal frequency deviates from the assumed value. Sensitivity of the algorithm can be easily adjusted in accordance with the parameters of the network in which a directional element is used. Performances of the method are tested by several computer-generated signals. Since the calculations used in this algorithm are based on simple mathematical operations, the high speed of operation is achieved. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Directional element appears in several types of protections (overcurrent, differential, distant, etc.) as an additional function which provides selectivity of protection. Directional element determines direction of the current with respect to a referent value which can be either a voltage or some other current. For alternating quantities, direction of the current with respect to a reference value is determined by the phase shift between the observed current and the reference value. Phase shifts between electrical variables for the purpose of digital relaying, can be determined by various methods. For example, for transmission lines for high or extremely high voltage, the methods based on increments of instantaneous electrical values or the traveling wave methods are applied [1–8]. These methods are characterized by high speed of response. When there is no need for a fast response, the methods based on phasors of electrical quantities [9,10] or on their increments [11,12] are applied. For determination of the amplitude and initial phase angle some of the well-known methods of signal processing are available, such as: zero-crossing [13], Fourier method [14], least error squares [15,16], Newton’s method [17–19] etc.
∗ Corresponding author. Tel.: +381 11 3218360; fax: +381 11 3248681. ´ [email protected] E-mail addresses: [email protected] (Z.N. Stojanovic), ´ (M.B. Djuric). 0378-7796/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.epsr.2010.09.013
In some specific cases, for determination of the fault direction it is possible to use only one electrical quantity [20–23]. It should be mentioned that recently in the algorithms for directional protection the wavelet transformation [24,25] and artificial neural network techniques [26,27] have been increasingly applied. A drawback of directional protections based on phasors of electrical quantities is the existence of a dead tripping zone. Namely, for faults close to the relay site the voltage becomes so low, that it is practically useless for proper operation of the relay. In this paper an algorithm for directional element without dead tripping zone is developed. Instead of calculating phase angle between the voltage and current phasors, the algorithm uses normalized average power within one semi-period of the voltage or current signal. Before usage the samples are filtered by the Fourier series to eliminate high-order harmonics and/or direct component. The dead tripping zone is eliminated by introduction of a voltage delay which is used for determination of direction. This delay is sufficiently long to ensure a reliable and clear determination of the current direction even for the nearby faults. In this process special attention is paid to the problem of synchronization which appears when the signal frequency deviates from the assumed value. Sensitivity of the algorithm is easily adjustable in accordance with the parameters of the network in which the directional element is used. Since the suggested procedure includes estimation of rms values of the voltage and current, the described algorithm could be used not only for a directional element but also for the overcurrent, differential, and distant relays without any additional modifications. The algorithm requires performing only simple mathematical opera-
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Fig. 1. Voltage and current signals are in phase.
tions, such as addition, multiplication and division, which results in a high speed of operation.
The algorithm for a directional element, based on average power calculated within one semi-period of the input signals, has the features of a phase comparator. If the phase shift between the voltage and current is within interval 90◦ > ϕ > 270◦ (−90◦ ), integral of the instantaneous power is positive. On the other hand, if the phase shift between the current and voltage is within interval 90◦ < ϕ < 270◦ (−90◦ ), integral of the instantaneous power is negative. Modulus of the average power is maximal if ϕ = 0◦ or 180◦ , i.e. the directional element is most sensitive when the current is in phase or counter-phase with the voltage. This represents a directional element of active power. However, this relay is not efficient in fault loops where the current is considerably delayed compared to the voltage (in practice in transmission lines this angle is 80◦ > ϕ > 60◦ ). For inductive loops, better solution is directional element of reactive power whose sensitivity is the highest when the phase angle between the voltage and current is 90◦ . The proposed algorithm is easily adjustable, i.e. its sensitivity could be made maximal for any phase shift between the current and voltage, what will be shown below. Since raw signals might contain high-order harmonics and/or direct component, it is convenient to filter samples before usage. If the cosine Fourier series is used, filtered samples of voltage and current are gained through Eqs. (1) and (2): uf (m) =
In the solutions for directional elements developed so far, phase angles of the current and reference voltage phasors were compared. The same result can be obtained when the average power of input signals (voltage and current) within one basic semi-period is calculated. Fig. 1 shows the waveforms of the current and voltage for the case when these quantities are in phase. In this case, the product of the voltage and current is positive at every time point observed, so the average power calculated for one semi-period of the frequency of the voltage or current signal is positive. Fig. 2 shows the voltage and current waveforms with a phase shift of 90◦ . In this case, multiplication of the voltage and current is positive within one fourth of the basic period, while within the other fourth it is negative. The average power within the first semi-period is equal to zero. Fig. 3 shows the voltage and current waveforms when they are shifted by 180◦ , i.e. when they are in the opposite phase. In this case the instantaneous power is negative, therefore its integral, as well as the average power, within one basic semi-period are negative.
if (m) =
Fig. 2. Current signal delayed by 90◦ compared to the voltage signal.
2 2 u(k) · cos k · m m m
2. The algorithm for directional element based on digital phase comparator
,
(1)
k=1
2 2 i(k) · cos k · m m m
,
(2)
k=1
where u(k) – raw voltage samples, uf (m) – the m-th filtered voltage sample, i(k) – raw current samples, if (m) – the m-th filtered current sample, m – number of samples within the basic period of the signals. For the purpose of realization of the algorithm, two data windows of length m are needed (uf and if ). The filtered samples of voltage are stored in the first one, while the filtered samples of current are stored in the second: uf = [uf (1)uf (2) . . . uf (m − 1)uf (m)],
(3)
if = [if (1)if (2) . . . if (m − 1)i(m)].
(4)
Fig. 3. The voltage and current signals are in the opposite phase.
Z.N. Stojanovi´c, M.B. Djuri´c / Electric Power Systems Research 81 (2011) 377–383
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After each sample is read-in, the left shift for one position is taking place in the data windows (the second sample becomes first, while the new sample becomes the m-th sample). The average power within one semi-period of signals can be determined by the sum (integral): 2 P= m
3m/4
uf (k + s) · if (k),
(5)
where s – preset sensitivity of the relay expressed by the number of samples. If s = 0 sum (5) is calculated by using the central m/2 samples from both data windows, therefore the directional element of active power is obtained because sum (5) will be maximal if the current and voltage are in phase. If s = −m/4 sum (5) is calculated by using the central m/2 samples from the current data window and voltage samples having indexes 1 ≤ k ≤ m/2, so a directional element of the reactive-inductive power is obtained because sum (5) will be maximal and positive if the current is delayed by 90◦ compared to the voltage. If s = m/4 sum (5) is calculated by using the central m/2 samples from the current data window and voltage samples having indexes m/2 ≤ k ≤ m, so the directional element of reactive-capacitive power is obtained because sum (5) will be maximal and positive if the current is ahead by 90 ◦ compared to the voltage. On the other hand, for backward faults modules of the corresponding sums are maximal but the sums are negative. Numerical value of the average power within one semi-period of the signals depends upon the voltage and current amplitudes. It would be very difficult to estimate the distance from the directional limit, if the absolute values of the integral (sum) are taken into account. Therefore, it is convenient to somehow normalize the average power of the signals so it can change only within a limited interval, e.g. between −1 and 1. A logical solution is division of the average power with the apparent power of the signals. In that case, their ratio is the indicator of direction (id), i.e. the indicator is cos ϕ of the signals:
3m/4
id =
2/m P = S
u (k k=m/4+1 f
+ s) · if (k)
Urms · Irms
,
(6)
where Irms – rms value of the current, Urms – rms value of the voltage, S – apparent power. The algorithm for directional element should be adjusted by selecting sensitivity s so that modulus of the indicator id is maximal in the operating regime when direction is measured. Positive value of indicator id designates forward faults, while negative value corresponds to backward faults. Because of the limited sampling frequency of the A/D converter, continuous adjustment of sensitivity s is not possible. The minimum step of adjusting the sensitivity of the algorithm, expressed in degrees, is given by equation: ı=
Fig. 4. The current and voltage data window.
k=m/4+1
360◦ . m
Fig. 5. The current data window.
lengths of these windows are established according to Eqs. (8) and (9): bi =
m , 2
(8)
bu = 3 · m,
(9)
where bi – size of the current data window, bu – size of the voltage data window. The data window of current samples (Fig. 5) serves for determination of fault direction by using marker id given by formula (6). The same samples are used for estimation of the rms current by the method of average values:
· Iav if (k) , √ = √ 2· 2 2·m m/2
Irms =
where Iav – average value of the current within the semi-period. The data window of voltage samples is shown in Fig. 6. In the case when the phase angle between the voltage and current is 0◦ (directional element of active power), samples with indexes from m/2+1 till m are used for determination of the fault direction by calculating id. The subsequent m/4 samples from the left and right sides are used for adjustment of the relay sensitivity through variable s, as explained in the previous section (directional element of reactive power). The same voltage samples are also used for estimation of the rms voltage Urms which is contained by formula (6): Urms =
· Uav √ = √ 2· 2 2·m
m uf (k + s) ,
(11)
k=m/2+1
where Uav – average voltage value within the semi-period. Groups of samples designated as reserves (Fig. 6) are used for correction of the preset sensitivity s which is required when the frequency deviates from the assumed value. Starting from the left end
(7)
3. Elimination of the dead tripping zone of the directional element In order to eliminate the dead tripping zone, it is necessary to modify the voltage and current data windows mentioned in the previous section, by modulating their lengths (Fig. 4). The modified
(10)
k=1
Fig. 6. The voltage data window.
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of the window, 2m samples are used for a rough frequency estimation of the voltage signal by zero-crossing method. The application of this method is entirely valid since the filtered voltage samples are used and there is no possibility of multiple zero crossings due to voltage distortion. Since parts of the current and voltage registers, envisaged for calculation of indicator id, are shifted by 2m samples (Fig. 4), it is possible to use counted samples from two basic periods of the voltage signal for estimation of the frequency. This is very convenient from the point of view of the precision of the estimated frequency, since in the case of frequency deviation, the number of counted samples in two subsequent periods could be different. Having this in mind, the corrected sensitivity is calculated according to (12): sc = s − ns + 2 · m,
(12)
where sc – corrected sensitivity of the relay expressed by the number of samples, in the case when signal frequency deviates from the assumed (rated) value, s – preset relay sensitivity expressed by the number of samples, ns – number of counted samples in two subsequent periods of the voltage signal. Introduction of the voltage delay has no observable effect on the speed of the algorithm convergence. However, by this approach, the insensitivity zone of the directional element is eliminated. Namely, when a voltage smaller than usable appears, there are still enough “healthy” samples for evaluation of the fault direction. Marker id is still valid 50 ms plus additional time after occurrence of a fault. The mentioned time of 50 ms includes the time delay introduced by the Fourier filter (20 ms). On the other hand, additional time depends upon adjusted and corrected sensitivity of the relay. Assuming that for the sensitivity correction all ±m/4 samples (±5 ms) are used, additional time for a relay of active power is 10 ± 5 ms, for a relay of reactive-inductive power 15 ± 5 ms, and for a relay of reactive-capacitive power 5 ± 5 ms. It should be noted that the sensitivity correction with all ±m/4 samples implies frequency deviation of ± 6 Hz, which can hardly appear. Altogether, these data indicate that in every case marker id lasts long enough to determine reliably fault direction. The convergence time of the proposed algorithm approximately corresponds to the time delay of the Fourier filter. As already mentioned, this convergence takes 20 ms (one basic period), which is simultaneously the speed of response of the proposed algorithm. By the described algorithm, both forward and backward directional elements could be realized. The tripping condition of the forward directional element is id ≥ idp (idp ≈ 1), while that of the reverse direction is id ≤ idp (idp ≈ − 1), where idp is a preset value.
Fig. 7. The first test: Uf = 0.2 pu, ϕpf = 0, ϕf = /2, f = 50 Hz, s = −m/4 without highorder harmonics.
f = 50 Hz – frequency of the input signals. It has been assumed that a fault occurs 0.2 s after the beginning of the simulation, while the simulation lasts for 0.5 s. Since the fault loop is inductive, preset sensitivity of the relay is s = −m/4. The results of the test which simulates a distant fault (Uf > 0) are shown in Fig. 7. The convergence time of rms values of current and voltage is 30 ms:20 ms is necessary for the Fourier filter and 10 ms for the method of average values. Furthermore, the calculation of rms voltage is shifted for 45 ms (2 14 m samples) because the relay of reactive-inductive power is read in. It can be observed in Fig. 7 that the direction indicator id converges faster then rms values. This time approximately corresponds to the delay caused by the Fourier filter which is 20 ms (one basic period). In the second test, an unfavorable case when the voltage during the fault decreases below the limit of usability, i.e. Uf = 0 pu is considered. The results of the test in which a nearby fault is simulated are shown in Fig. 8. It can be noted that duration of indicator id lasts long enough (around 45 ms) to establish precisely direction of the fault. In the next test (Fig. 9) to already mentioned signals, high-order harmonics are added. In order to make distortions more visible the following values of high-order harmonics are adopted: U2 = 10%U1 ,
4. Testing of the algorithm For evaluation of performance of the proposed algorithm, a series of tests by the computer-generated voltage and current signals were performed. Let us assume that the sampling frequency of the A/D converter is set to fs = 3000 Hz [28]. In the first test, the voltage and current signals are applied to a relay having the following characteristics: Ipf = 1 pu – rms value of the pre-fault current, If = 3 pu – rms value of the fault current, Upf = 1 pu – rms value of the pre-fault voltage, Uf = 0.2 pu – rms value of the voltage during the fault, ϕpf = 0 – phase shift of the pre-fault voltage and current, ϕf = /2 – phase shift of the voltage and current during the fault,
Fig. 8. The second test: Uf = 0 pu, ϕpf = 0, ϕf = /2, f = 50 Hz, s = −m/4 without highorder harmonics.
Z.N. Stojanovi´c, M.B. Djuri´c / Electric Power Systems Research 81 (2011) 377–383
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Fig. 9. The third test: Uf = 0 pu, ϕpf = 0, ϕf = /2, f = 50 Hz, s = −m/4 with high-order harmonics.
Fig. 11. The fifth test: Uf = 0 pu, ϕpf = 0, ϕf = /2, f = 53 Hz, s = −m/4 with high-order harmonics.
U3 = 30%U1 , U4 = 10%U1 , U5 = 30%U1 , I2 = 10%I1 , I3 = 30%I1 , I4 = 10%I1 , and I5 = 30%I1 . Phase angles of high-order harmonics before and after the fault are chosen arbitrarily. From Fig. 9 it can be observed that high-order harmonics in input signals have no effect on marker id calculation. These results are expected since discrete Fourier transform is applied before calculation. In the fourth test, signals from the third test but with the frequency f = 47 Hz are generated. The results are shown in Fig. 10. Since the real signal frequency deviates from assumed, the algorithm performs the correction of adjusted sensitivity s by zerocrossing method. It could be noticed that waving of marker id is the lowest around the value which determines relay tripping (≈1). The lower id the higher is waving. Therefore, this change of indicator id enables accurate determination of the fault direction without any additional “ironing” of variable id. In the fifth test, the relay inputs are signals from the third test but of the frequency f = 53 Hz. The results are shown in Fig. 11 and implicate the conclusions similar to the previous case. In the next test, a capacitive fault loop (ϕf = −/2) is read in, and the adjusted sensitivity of the relay is changed to m/4, so that
the relay would trip properly. The frequency of the input signals remained 53 Hz. The results of the test are given in Fig. 12. Since the capacitive relay is read in (s = m/4) and the sensitivity correction exists (f = 53 Hz), the indicator id is valid around 30 ms during the fault what is enough for reliable determination of fault direction. In the sixth test a backward directional element is tested (ϕpf = − or ϕpf = ) for an inductive fault loop (ϕf = 3/2 or ϕf = −/2) and frequency of 47 Hz. As already stated, now the tripping condition is id ≈ −1, while the preset sensitivity remains the same as in the forward directional element of the inductivereactive power (s = −m/4). The results of the test are given in Fig. 13. Finally, for the purpose of generating realistic input signals, the network on Fig. 14 is modeled by using additional Matlab module Power System Blockset. Four different faults are analyzed: k1 – distant “backward” fault, k2 – nearby “backward” fault, k3 – nearby “forward” fault, and k4 – distant “forward” fault. To both active networks high-order harmonics are added until order 5 with the following features: U2 = 0.3U1 , 2 = /2 rad, 3 = 0 rad, U4 = 0.3U1 , 4 = /4 rad, U5 = 0.3U1 , U3 = 0.3U1 , 5 = /3 rad. Furthermore, on the measuring site, the white
Fig. 10. The fourth test: Uf = 0 pu, ϕpf = 0, ϕf = /2, f = 47 Hz, s = −m/4 with high-order harmonics.
Fig. 12. The sixth test: Uf = 0 pu, ϕpf = 0, ϕf = −/2, f = 53 Hz, s = m/4 with high-order harmonics.
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Fig. 16. Nearby “backward” fault (k2 ).
Fig. 13. The sixth test: Uf = 0 pu, ϕpf = , ϕf = 3/2, f = 47 Hz, s = −m/4 with high-order harmonics.
Fig. 14. The network modeled by Power System Blockset.
noise is injected simulating interferences in power system. Before sampling and digital processing, signals are passed through analog first order low-pass filter. Assigned frequency of the system is 53 Hz. Since the inductive fault loop is considered, the relay of reactive power (s = −m/4) is read in. The waveforms of current, voltage and marker id for the faults k1 , k2 , k3 and k4 are shown on Figs. 15–18. It can be observed from Figures that aside from distinctive highorder harmonics and noise in input signals, in the current signal there is also decaying direct component. However, even in these conditions marker id indicates unambiguously and reliably the fault direction with no regard to the fault distance.
Fig. 17. Nearby “forward” fault (k3 ).
Fig. 18. Distant “forward” fault (k4 ).
5. Conclusions
Fig. 15. Distant “backward” fault (k1 ).
The algorithm for directional element without the dead tripping zone, based on digital phase comparator is developed. Instead of calculating the phase angle between the voltage and current pha-
Z.N. Stojanovi´c, M.B. Djuri´c / Electric Power Systems Research 81 (2011) 377–383
sors, the algorithm uses normalized average power of the signals over the interval equal to one basic semi-period. Before usage the samples are passed through the Fourier filter to remove high-order harmonics and/or direct component. The dead tripping zone is eliminated by introducing voltage delay which is used for determination of direction. This delay is of sufficient duration, therefore it enables an accurate and unambiguous determination of the current direction when a close fault occurs. The response of the directional element is very fast, around one basic period. Special attention is paid to the problem of synchronization which appears when the signal frequency deviates from the assumed (rated) value. The described problem is efficiently solved through application of the zero-crossing method. This has been verified by several performed tests. Sensitivity of the algorithm is easily adjustable in accordance with the network parameters where the directional element is used. Since the suggested procedure includes estimation of the rms values of the voltage and current, the described algorithm could be used, not only for directional elements but also, for the overcurrent, differential, and distant relays without any additional modifications. The algorithm uses only simple mathematical operations such as addition, multiplication and division which results in a high speed of operation. References [1] M. Chamia, S. Liberman, Ultra high speed relay for EHV/UHV transmission lines—development, design and application, IEEE Transactions on Power Apparatus and Systems 97 (1978) 2104–2116. [2] M. Vitins, A fundamental concept for high speed relaying, IEEE Transactions on Power Apparatus and Systems 100 (1981) 163–173. [3] F. Engler, O.E. Lanz, M. Hanggli, G. Bacchini, Transient signals and their processing in an ultra high-speed directional relay for EHV/UHV transmission line protection, IEEE Transactions on Power Apparatus and Systems 104 (1985) 1463–1473. [4] A.T. Johns, M.A. Martin, A. Barker, E.P. Walker, P.A. Crossley, A new approach to E.H.V. direction comparison protection using digital signal processing techniques, IEEE Transactions on Power Systems 1 (1986) 24–34. [5] E.H. Shehab-Eldin, P.G. McLaren, Traveling wave distance protection-problem areas and solutions, IEEE Transactions on Power Delivery 3 (1988) 894–902. [6] K.S. Prakash, O.P. Malik, G.S. Hope, Amplitude comparator based algorithm for directional comparison protection of transmission lines, IEEE Transactions on Power Delivery 4 (1989) 2032–2041. [7] K.S. Prakash, O.P. Malik, G.S. Hope, G.C. Hancock, K.K. Wong, Laboratory investigation of an amplitude comparator based directional comparison digital protection scheme, IEEE Transactions on Power Delivery 5 (1990) 1687–1694. [8] Gabriel Benmouyal, Simon Chano, Characterization of phase and amplitude comparators in UHS directional relays, IEEE Transactions on Power Systems 12 (1997) 646–653. [9] He Jia-li, Zhang Yuan-hui, Yang Nian-ci, New type power line carrier relaying system with directional comparison for EHV transmission lines, IEEE Transactions on Power Apparatus and Systems 103 (1984) 429–436. [10] Moustafa Mohammed Eissa, Evaluation of a new current directional protection technique using field data, IEEE Transactions on Power Delivery 20 (2005) 566–572. [11] P.G.S.M. McLaren, G.W.S.M. Swift, Z. Zhang, E. Dirks, R.P. Jayasinghe, I. Fernando, A new directional element for numerical distance relays, IEEE Transactions on Power Delivery 10 (1995) 666–675. [12] Gabriel Benmouyal, Jean Mahseredjian, A combined directional and faulted phase selector element based on incremental quantities, IEEE Transactions on Power Delivery 16 (2001) 478–484. [13] Milenko B. Djuric, Zeljko R. Djurisic, Frequency measurement of distorted signals using Fourier and zero crossing techniques, Electric Power Systems Research 78 (2008) 1407–1415.
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Electric Power Systems Research journal homepage: www.elsevier.com/locate/epsr
The algorithm for directional element without dead tripping zone based on digital phase comparator Zoran N. Stojanovic´ ∗ , Milenko B. Djuric´ Faculty of Electrical Engineering, University of Belgrade, Bulevar Kralja Aleksandra 73, 11120 Belgrade, Serbia
a r t i c l e
i n f o
Article history: Received 15 January 2009 Received in revised form 31 March 2010 Accepted 30 September 2010 Available online 27 October 2010 Keywords: Digital protection Directional element Digital phase comparator Dead tripping zone
a b s t r a c t This paper describes the algorithm for directional element without dead tripping zone. Instead of calculating phase angle between the phasors of voltage and current the algorithm uses digital phase comparator. The procedure is based on calculation of normalized average power within one semi-period of the input voltage and current signals. Before usage the samples are passed through the Fourier filter to remove high-order harmonics and/or direct component. The dead tripping zone is eliminated by introduction of a voltage delay which is used for determination of direction. In addition, special attention is paid to the problem of synchronization which appears when signal frequency deviates from the assumed value. Sensitivity of the algorithm can be easily adjusted in accordance with the parameters of the network in which a directional element is used. Performances of the method are tested by several computer-generated signals. Since the calculations used in this algorithm are based on simple mathematical operations, the high speed of operation is achieved. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Directional element appears in several types of protections (overcurrent, differential, distant, etc.) as an additional function which provides selectivity of protection. Directional element determines direction of the current with respect to a referent value which can be either a voltage or some other current. For alternating quantities, direction of the current with respect to a reference value is determined by the phase shift between the observed current and the reference value. Phase shifts between electrical variables for the purpose of digital relaying, can be determined by various methods. For example, for transmission lines for high or extremely high voltage, the methods based on increments of instantaneous electrical values or the traveling wave methods are applied [1–8]. These methods are characterized by high speed of response. When there is no need for a fast response, the methods based on phasors of electrical quantities [9,10] or on their increments [11,12] are applied. For determination of the amplitude and initial phase angle some of the well-known methods of signal processing are available, such as: zero-crossing [13], Fourier method [14], least error squares [15,16], Newton’s method [17–19] etc.
∗ Corresponding author. Tel.: +381 11 3218360; fax: +381 11 3248681. ´ [email protected] E-mail addresses: [email protected] (Z.N. Stojanovic), ´ (M.B. Djuric). 0378-7796/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.epsr.2010.09.013
In some specific cases, for determination of the fault direction it is possible to use only one electrical quantity [20–23]. It should be mentioned that recently in the algorithms for directional protection the wavelet transformation [24,25] and artificial neural network techniques [26,27] have been increasingly applied. A drawback of directional protections based on phasors of electrical quantities is the existence of a dead tripping zone. Namely, for faults close to the relay site the voltage becomes so low, that it is practically useless for proper operation of the relay. In this paper an algorithm for directional element without dead tripping zone is developed. Instead of calculating phase angle between the voltage and current phasors, the algorithm uses normalized average power within one semi-period of the voltage or current signal. Before usage the samples are filtered by the Fourier series to eliminate high-order harmonics and/or direct component. The dead tripping zone is eliminated by introduction of a voltage delay which is used for determination of direction. This delay is sufficiently long to ensure a reliable and clear determination of the current direction even for the nearby faults. In this process special attention is paid to the problem of synchronization which appears when the signal frequency deviates from the assumed value. Sensitivity of the algorithm is easily adjustable in accordance with the parameters of the network in which the directional element is used. Since the suggested procedure includes estimation of rms values of the voltage and current, the described algorithm could be used not only for a directional element but also for the overcurrent, differential, and distant relays without any additional modifications. The algorithm requires performing only simple mathematical opera-
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Fig. 1. Voltage and current signals are in phase.
tions, such as addition, multiplication and division, which results in a high speed of operation.
The algorithm for a directional element, based on average power calculated within one semi-period of the input signals, has the features of a phase comparator. If the phase shift between the voltage and current is within interval 90◦ > ϕ > 270◦ (−90◦ ), integral of the instantaneous power is positive. On the other hand, if the phase shift between the current and voltage is within interval 90◦ < ϕ < 270◦ (−90◦ ), integral of the instantaneous power is negative. Modulus of the average power is maximal if ϕ = 0◦ or 180◦ , i.e. the directional element is most sensitive when the current is in phase or counter-phase with the voltage. This represents a directional element of active power. However, this relay is not efficient in fault loops where the current is considerably delayed compared to the voltage (in practice in transmission lines this angle is 80◦ > ϕ > 60◦ ). For inductive loops, better solution is directional element of reactive power whose sensitivity is the highest when the phase angle between the voltage and current is 90◦ . The proposed algorithm is easily adjustable, i.e. its sensitivity could be made maximal for any phase shift between the current and voltage, what will be shown below. Since raw signals might contain high-order harmonics and/or direct component, it is convenient to filter samples before usage. If the cosine Fourier series is used, filtered samples of voltage and current are gained through Eqs. (1) and (2): uf (m) =
In the solutions for directional elements developed so far, phase angles of the current and reference voltage phasors were compared. The same result can be obtained when the average power of input signals (voltage and current) within one basic semi-period is calculated. Fig. 1 shows the waveforms of the current and voltage for the case when these quantities are in phase. In this case, the product of the voltage and current is positive at every time point observed, so the average power calculated for one semi-period of the frequency of the voltage or current signal is positive. Fig. 2 shows the voltage and current waveforms with a phase shift of 90◦ . In this case, multiplication of the voltage and current is positive within one fourth of the basic period, while within the other fourth it is negative. The average power within the first semi-period is equal to zero. Fig. 3 shows the voltage and current waveforms when they are shifted by 180◦ , i.e. when they are in the opposite phase. In this case the instantaneous power is negative, therefore its integral, as well as the average power, within one basic semi-period are negative.
if (m) =
Fig. 2. Current signal delayed by 90◦ compared to the voltage signal.
2 2 u(k) · cos k · m m m
2. The algorithm for directional element based on digital phase comparator
,
(1)
k=1
2 2 i(k) · cos k · m m m
,
(2)
k=1
where u(k) – raw voltage samples, uf (m) – the m-th filtered voltage sample, i(k) – raw current samples, if (m) – the m-th filtered current sample, m – number of samples within the basic period of the signals. For the purpose of realization of the algorithm, two data windows of length m are needed (uf and if ). The filtered samples of voltage are stored in the first one, while the filtered samples of current are stored in the second: uf = [uf (1)uf (2) . . . uf (m − 1)uf (m)],
(3)
if = [if (1)if (2) . . . if (m − 1)i(m)].
(4)
Fig. 3. The voltage and current signals are in the opposite phase.
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After each sample is read-in, the left shift for one position is taking place in the data windows (the second sample becomes first, while the new sample becomes the m-th sample). The average power within one semi-period of signals can be determined by the sum (integral): 2 P= m
3m/4
uf (k + s) · if (k),
(5)
where s – preset sensitivity of the relay expressed by the number of samples. If s = 0 sum (5) is calculated by using the central m/2 samples from both data windows, therefore the directional element of active power is obtained because sum (5) will be maximal if the current and voltage are in phase. If s = −m/4 sum (5) is calculated by using the central m/2 samples from the current data window and voltage samples having indexes 1 ≤ k ≤ m/2, so a directional element of the reactive-inductive power is obtained because sum (5) will be maximal and positive if the current is delayed by 90◦ compared to the voltage. If s = m/4 sum (5) is calculated by using the central m/2 samples from the current data window and voltage samples having indexes m/2 ≤ k ≤ m, so the directional element of reactive-capacitive power is obtained because sum (5) will be maximal and positive if the current is ahead by 90 ◦ compared to the voltage. On the other hand, for backward faults modules of the corresponding sums are maximal but the sums are negative. Numerical value of the average power within one semi-period of the signals depends upon the voltage and current amplitudes. It would be very difficult to estimate the distance from the directional limit, if the absolute values of the integral (sum) are taken into account. Therefore, it is convenient to somehow normalize the average power of the signals so it can change only within a limited interval, e.g. between −1 and 1. A logical solution is division of the average power with the apparent power of the signals. In that case, their ratio is the indicator of direction (id), i.e. the indicator is cos ϕ of the signals:
3m/4
id =
2/m P = S
u (k k=m/4+1 f
+ s) · if (k)
Urms · Irms
,
(6)
where Irms – rms value of the current, Urms – rms value of the voltage, S – apparent power. The algorithm for directional element should be adjusted by selecting sensitivity s so that modulus of the indicator id is maximal in the operating regime when direction is measured. Positive value of indicator id designates forward faults, while negative value corresponds to backward faults. Because of the limited sampling frequency of the A/D converter, continuous adjustment of sensitivity s is not possible. The minimum step of adjusting the sensitivity of the algorithm, expressed in degrees, is given by equation: ı=
Fig. 4. The current and voltage data window.
k=m/4+1
360◦ . m
Fig. 5. The current data window.
lengths of these windows are established according to Eqs. (8) and (9): bi =
m , 2
(8)
bu = 3 · m,
(9)
where bi – size of the current data window, bu – size of the voltage data window. The data window of current samples (Fig. 5) serves for determination of fault direction by using marker id given by formula (6). The same samples are used for estimation of the rms current by the method of average values:
· Iav if (k) , √ = √ 2· 2 2·m m/2
Irms =
where Iav – average value of the current within the semi-period. The data window of voltage samples is shown in Fig. 6. In the case when the phase angle between the voltage and current is 0◦ (directional element of active power), samples with indexes from m/2+1 till m are used for determination of the fault direction by calculating id. The subsequent m/4 samples from the left and right sides are used for adjustment of the relay sensitivity through variable s, as explained in the previous section (directional element of reactive power). The same voltage samples are also used for estimation of the rms voltage Urms which is contained by formula (6): Urms =
· Uav √ = √ 2· 2 2·m
m uf (k + s) ,
(11)
k=m/2+1
where Uav – average voltage value within the semi-period. Groups of samples designated as reserves (Fig. 6) are used for correction of the preset sensitivity s which is required when the frequency deviates from the assumed value. Starting from the left end
(7)
3. Elimination of the dead tripping zone of the directional element In order to eliminate the dead tripping zone, it is necessary to modify the voltage and current data windows mentioned in the previous section, by modulating their lengths (Fig. 4). The modified
(10)
k=1
Fig. 6. The voltage data window.
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of the window, 2m samples are used for a rough frequency estimation of the voltage signal by zero-crossing method. The application of this method is entirely valid since the filtered voltage samples are used and there is no possibility of multiple zero crossings due to voltage distortion. Since parts of the current and voltage registers, envisaged for calculation of indicator id, are shifted by 2m samples (Fig. 4), it is possible to use counted samples from two basic periods of the voltage signal for estimation of the frequency. This is very convenient from the point of view of the precision of the estimated frequency, since in the case of frequency deviation, the number of counted samples in two subsequent periods could be different. Having this in mind, the corrected sensitivity is calculated according to (12): sc = s − ns + 2 · m,
(12)
where sc – corrected sensitivity of the relay expressed by the number of samples, in the case when signal frequency deviates from the assumed (rated) value, s – preset relay sensitivity expressed by the number of samples, ns – number of counted samples in two subsequent periods of the voltage signal. Introduction of the voltage delay has no observable effect on the speed of the algorithm convergence. However, by this approach, the insensitivity zone of the directional element is eliminated. Namely, when a voltage smaller than usable appears, there are still enough “healthy” samples for evaluation of the fault direction. Marker id is still valid 50 ms plus additional time after occurrence of a fault. The mentioned time of 50 ms includes the time delay introduced by the Fourier filter (20 ms). On the other hand, additional time depends upon adjusted and corrected sensitivity of the relay. Assuming that for the sensitivity correction all ±m/4 samples (±5 ms) are used, additional time for a relay of active power is 10 ± 5 ms, for a relay of reactive-inductive power 15 ± 5 ms, and for a relay of reactive-capacitive power 5 ± 5 ms. It should be noted that the sensitivity correction with all ±m/4 samples implies frequency deviation of ± 6 Hz, which can hardly appear. Altogether, these data indicate that in every case marker id lasts long enough to determine reliably fault direction. The convergence time of the proposed algorithm approximately corresponds to the time delay of the Fourier filter. As already mentioned, this convergence takes 20 ms (one basic period), which is simultaneously the speed of response of the proposed algorithm. By the described algorithm, both forward and backward directional elements could be realized. The tripping condition of the forward directional element is id ≥ idp (idp ≈ 1), while that of the reverse direction is id ≤ idp (idp ≈ − 1), where idp is a preset value.
Fig. 7. The first test: Uf = 0.2 pu, ϕpf = 0, ϕf = /2, f = 50 Hz, s = −m/4 without highorder harmonics.
f = 50 Hz – frequency of the input signals. It has been assumed that a fault occurs 0.2 s after the beginning of the simulation, while the simulation lasts for 0.5 s. Since the fault loop is inductive, preset sensitivity of the relay is s = −m/4. The results of the test which simulates a distant fault (Uf > 0) are shown in Fig. 7. The convergence time of rms values of current and voltage is 30 ms:20 ms is necessary for the Fourier filter and 10 ms for the method of average values. Furthermore, the calculation of rms voltage is shifted for 45 ms (2 14 m samples) because the relay of reactive-inductive power is read in. It can be observed in Fig. 7 that the direction indicator id converges faster then rms values. This time approximately corresponds to the delay caused by the Fourier filter which is 20 ms (one basic period). In the second test, an unfavorable case when the voltage during the fault decreases below the limit of usability, i.e. Uf = 0 pu is considered. The results of the test in which a nearby fault is simulated are shown in Fig. 8. It can be noted that duration of indicator id lasts long enough (around 45 ms) to establish precisely direction of the fault. In the next test (Fig. 9) to already mentioned signals, high-order harmonics are added. In order to make distortions more visible the following values of high-order harmonics are adopted: U2 = 10%U1 ,
4. Testing of the algorithm For evaluation of performance of the proposed algorithm, a series of tests by the computer-generated voltage and current signals were performed. Let us assume that the sampling frequency of the A/D converter is set to fs = 3000 Hz [28]. In the first test, the voltage and current signals are applied to a relay having the following characteristics: Ipf = 1 pu – rms value of the pre-fault current, If = 3 pu – rms value of the fault current, Upf = 1 pu – rms value of the pre-fault voltage, Uf = 0.2 pu – rms value of the voltage during the fault, ϕpf = 0 – phase shift of the pre-fault voltage and current, ϕf = /2 – phase shift of the voltage and current during the fault,
Fig. 8. The second test: Uf = 0 pu, ϕpf = 0, ϕf = /2, f = 50 Hz, s = −m/4 without highorder harmonics.
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Fig. 9. The third test: Uf = 0 pu, ϕpf = 0, ϕf = /2, f = 50 Hz, s = −m/4 with high-order harmonics.
Fig. 11. The fifth test: Uf = 0 pu, ϕpf = 0, ϕf = /2, f = 53 Hz, s = −m/4 with high-order harmonics.
U3 = 30%U1 , U4 = 10%U1 , U5 = 30%U1 , I2 = 10%I1 , I3 = 30%I1 , I4 = 10%I1 , and I5 = 30%I1 . Phase angles of high-order harmonics before and after the fault are chosen arbitrarily. From Fig. 9 it can be observed that high-order harmonics in input signals have no effect on marker id calculation. These results are expected since discrete Fourier transform is applied before calculation. In the fourth test, signals from the third test but with the frequency f = 47 Hz are generated. The results are shown in Fig. 10. Since the real signal frequency deviates from assumed, the algorithm performs the correction of adjusted sensitivity s by zerocrossing method. It could be noticed that waving of marker id is the lowest around the value which determines relay tripping (≈1). The lower id the higher is waving. Therefore, this change of indicator id enables accurate determination of the fault direction without any additional “ironing” of variable id. In the fifth test, the relay inputs are signals from the third test but of the frequency f = 53 Hz. The results are shown in Fig. 11 and implicate the conclusions similar to the previous case. In the next test, a capacitive fault loop (ϕf = −/2) is read in, and the adjusted sensitivity of the relay is changed to m/4, so that
the relay would trip properly. The frequency of the input signals remained 53 Hz. The results of the test are given in Fig. 12. Since the capacitive relay is read in (s = m/4) and the sensitivity correction exists (f = 53 Hz), the indicator id is valid around 30 ms during the fault what is enough for reliable determination of fault direction. In the sixth test a backward directional element is tested (ϕpf = − or ϕpf = ) for an inductive fault loop (ϕf = 3/2 or ϕf = −/2) and frequency of 47 Hz. As already stated, now the tripping condition is id ≈ −1, while the preset sensitivity remains the same as in the forward directional element of the inductivereactive power (s = −m/4). The results of the test are given in Fig. 13. Finally, for the purpose of generating realistic input signals, the network on Fig. 14 is modeled by using additional Matlab module Power System Blockset. Four different faults are analyzed: k1 – distant “backward” fault, k2 – nearby “backward” fault, k3 – nearby “forward” fault, and k4 – distant “forward” fault. To both active networks high-order harmonics are added until order 5 with the following features: U2 = 0.3U1 , 2 = /2 rad, 3 = 0 rad, U4 = 0.3U1 , 4 = /4 rad, U5 = 0.3U1 , U3 = 0.3U1 , 5 = /3 rad. Furthermore, on the measuring site, the white
Fig. 10. The fourth test: Uf = 0 pu, ϕpf = 0, ϕf = /2, f = 47 Hz, s = −m/4 with high-order harmonics.
Fig. 12. The sixth test: Uf = 0 pu, ϕpf = 0, ϕf = −/2, f = 53 Hz, s = m/4 with high-order harmonics.
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Fig. 16. Nearby “backward” fault (k2 ).
Fig. 13. The sixth test: Uf = 0 pu, ϕpf = , ϕf = 3/2, f = 47 Hz, s = −m/4 with high-order harmonics.
Fig. 14. The network modeled by Power System Blockset.
noise is injected simulating interferences in power system. Before sampling and digital processing, signals are passed through analog first order low-pass filter. Assigned frequency of the system is 53 Hz. Since the inductive fault loop is considered, the relay of reactive power (s = −m/4) is read in. The waveforms of current, voltage and marker id for the faults k1 , k2 , k3 and k4 are shown on Figs. 15–18. It can be observed from Figures that aside from distinctive highorder harmonics and noise in input signals, in the current signal there is also decaying direct component. However, even in these conditions marker id indicates unambiguously and reliably the fault direction with no regard to the fault distance.
Fig. 17. Nearby “forward” fault (k3 ).
Fig. 18. Distant “forward” fault (k4 ).
5. Conclusions
Fig. 15. Distant “backward” fault (k1 ).
The algorithm for directional element without the dead tripping zone, based on digital phase comparator is developed. Instead of calculating the phase angle between the voltage and current pha-
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sors, the algorithm uses normalized average power of the signals over the interval equal to one basic semi-period. Before usage the samples are passed through the Fourier filter to remove high-order harmonics and/or direct component. The dead tripping zone is eliminated by introducing voltage delay which is used for determination of direction. This delay is of sufficient duration, therefore it enables an accurate and unambiguous determination of the current direction when a close fault occurs. The response of the directional element is very fast, around one basic period. Special attention is paid to the problem of synchronization which appears when the signal frequency deviates from the assumed (rated) value. The described problem is efficiently solved through application of the zero-crossing method. This has been verified by several performed tests. Sensitivity of the algorithm is easily adjustable in accordance with the network parameters where the directional element is used. Since the suggested procedure includes estimation of the rms values of the voltage and current, the described algorithm could be used, not only for directional elements but also, for the overcurrent, differential, and distant relays without any additional modifications. The algorithm uses only simple mathematical operations such as addition, multiplication and division which results in a high speed of operation. References [1] M. Chamia, S. Liberman, Ultra high speed relay for EHV/UHV transmission lines—development, design and application, IEEE Transactions on Power Apparatus and Systems 97 (1978) 2104–2116. [2] M. Vitins, A fundamental concept for high speed relaying, IEEE Transactions on Power Apparatus and Systems 100 (1981) 163–173. [3] F. Engler, O.E. Lanz, M. Hanggli, G. Bacchini, Transient signals and their processing in an ultra high-speed directional relay for EHV/UHV transmission line protection, IEEE Transactions on Power Apparatus and Systems 104 (1985) 1463–1473. [4] A.T. Johns, M.A. Martin, A. Barker, E.P. Walker, P.A. Crossley, A new approach to E.H.V. direction comparison protection using digital signal processing techniques, IEEE Transactions on Power Systems 1 (1986) 24–34. [5] E.H. Shehab-Eldin, P.G. McLaren, Traveling wave distance protection-problem areas and solutions, IEEE Transactions on Power Delivery 3 (1988) 894–902. [6] K.S. Prakash, O.P. Malik, G.S. Hope, Amplitude comparator based algorithm for directional comparison protection of transmission lines, IEEE Transactions on Power Delivery 4 (1989) 2032–2041. [7] K.S. Prakash, O.P. Malik, G.S. Hope, G.C. Hancock, K.K. Wong, Laboratory investigation of an amplitude comparator based directional comparison digital protection scheme, IEEE Transactions on Power Delivery 5 (1990) 1687–1694. [8] Gabriel Benmouyal, Simon Chano, Characterization of phase and amplitude comparators in UHS directional relays, IEEE Transactions on Power Systems 12 (1997) 646–653. [9] He Jia-li, Zhang Yuan-hui, Yang Nian-ci, New type power line carrier relaying system with directional comparison for EHV transmission lines, IEEE Transactions on Power Apparatus and Systems 103 (1984) 429–436. [10] Moustafa Mohammed Eissa, Evaluation of a new current directional protection technique using field data, IEEE Transactions on Power Delivery 20 (2005) 566–572. [11] P.G.S.M. McLaren, G.W.S.M. Swift, Z. Zhang, E. Dirks, R.P. Jayasinghe, I. Fernando, A new directional element for numerical distance relays, IEEE Transactions on Power Delivery 10 (1995) 666–675. [12] Gabriel Benmouyal, Jean Mahseredjian, A combined directional and faulted phase selector element based on incremental quantities, IEEE Transactions on Power Delivery 16 (2001) 478–484. [13] Milenko B. Djuric, Zeljko R. Djurisic, Frequency measurement of distorted signals using Fourier and zero crossing techniques, Electric Power Systems Research 78 (2008) 1407–1415.
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[14] A. Gomez Exposito, J.A. Rosendo Macias, J.L. Ruis Macias, Discrete Fourier transform computation for digital relaying, International Journal of Electrical Power and Energy Systems 25 (2003) 229–233. [15] M.S. Sachdev, M. Nagpal, A recursive least error squares algorithm for power system relaying and measurement applications, IEEE Transactions on Power Delivery 6 (1991) 1008–1015. [16] V. Terzija, M. Djuric, B. Kovacevic, A new self-tuning algorithm for the frequency estimation of distorted signals, IEEE Transactions on Power Delivery 10 (1995) 1779–1785. [17] V. Terzija, M. Djuric, Direct estimation of voltage phasor, frequency and its rate of change using Newton’s iterative method, International Journal of Electrical Power and Energy Systems 16 (1994) 423–428. [18] M.B. Djuric, V.V. Terzija, An algorithm for frequency relaying based on the Newton-Raphson method, Electric Power Systems Research 31 (1994) 119–124. [19] Vladimir V. Terzija, Milenko B. Djuric, Nenad Z. Jeremic, A recursive Newton type algorithm for digital frequency relaying, Electric Power Systems Research 36 (67) (1996) 72. [20] M.I. Gilany, O.P. Malik, G.S. Hope, A digital protection technique for parallel transmission lines using a single relay at each end, Transactions on Power Delivery 7 (1992) 118–125. [21] M.I. Gilany, O.P. Malik, G.S. Hope, A laboratory investigation of a digital protection technique for parallel transmission lines, IEEE Transactions on Power Delivery 10 (1995) 187–193. [22] M.M. Eissa, O.P. Malik, A new digital directional transverse differential current protection, IEEE Transactions on Power Delivery 11 (1996) 1285–1291. [23] A.K. Pradhan, A. Routray, S. Madhan Gudipalli, Fault direction estimation in radial distribution system using phase change in sequence current, IEEE Transactions on Power Delivery 22 (2007) 2065–2071. [24] W. Chan, O.P. Malik, X. Yin, D. Chen, Z. Zhang, Study of wavelet based ultra high speed directional transmission line protection, IEEE Transactions on Power Delivery 18 (2003) 1134–1139. [25] T.M. Lai, L.A. Snider, E. Lo, D. Sutanto, High-impedance fault detection using discrete wavelet transform and frequency range and rms conversion, IEEE Transactions on Power Delivery 20 (2005) 2065–2071. [26] T.S. Sidhu, H. Singh, M.S. Sachdev, Design, implementation and testing of an artificial neural network based fault direction discriminator for protecting transmission lines, IEEE Transactions on Power Delivery 10 (1995) 697–706. [27] M. Sanaye-Pasand, O.P. Malik, High speed transmission system directional protection using an Elman network, IEEE Transactions on Power Delivery 13 (1998) 2065–2071. [28] P.G. McLaren, K. Mustaphi, G. Benmouyal, S. Chano, A. Girgis, C. Henville, M. Kezunovic, L. Kojovic, R. Marttila, M. Meisinger, G. Michel, M.S. Sachdev, V. Skendzic, T.S. Sidhu, D. Tziouvaras, Software models for relays, IEEE Transactions on Power Delivery 16 (2001) 238–245. Zoran N. Stojanovi´c was born in Poˇzarevac, Serbia on July 22, 1979. He finished High School in Svilajnac in 1998 and graduated from Faculty of Electrical Engineering, University of Belgrade in 2003. After graduation, he worked for a year at Department for Design at EnergoprojektHidroinzenjering in Belgrade. Since 2005, he has been working at Faculty of Electrical Engineering, University of Belgrade and holds a position of assistant. His main fields of interest are relay protection, monitoring of high voltage equipment and computer-aided design. Milenko B. Djuri´c (1948–Sarajevo) received the B.S.; M.Sc. and Ph.D. degrees in Electrical Engineering from the Faculty of Electrical Engineering (University of Belgrade/Serbia) in 1973, 1977 and 1985, respectively. A few years he spent in the Electric Power Company in Kraljevo/Serbia. In 1980 he jointed the Faculty of Electrical Engineering, Belgrade, where he is a full Professor. His main areas of scientific interests are power system protection and stability and digital signal processing applications in power system protection.