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A new scheme for inrush identification in transformer protection
Electric Power Systems Research 63 (2002) 81 /86 www.elsevier.com/locate/epsr
A new scheme for inrush identification in transformer protection Hao Zhang a,*, Pei Liu a, O.P. Malik b a
Department of Electrical Power Engineering, Huazhong University of Science and Technology, Wuhan 430074, People’s Republic of China b Department of Electrical and Computer Engineering, The University of Calgary, Calgary, Alta., Canada T2N 1N4 Received 31 October 2001; accepted 19 December 2001
Abstract The second harmonic component is commonly used for blocking differential relay in power transformers. The altitudes of harmonics and fundamental are computed by discrete Fourier transform (DFT). However, this method is not effective in some cases. A new scheme to discriminate fault current and inrush current is presented in this paper. The ratio of the power spectrum (PS) of second harmonic to the PS of fundamental based on autoregressive process is used for inrush identification. Test results with the sampled data from a prototype device on a dynamic power system model verify the effectiveness of the proposed scheme. # 2002 Published by Elsevier Science B.V. Keywords: Power transformer protection; Power spectrum (PS); Autoregressive process
1. Introduction Differential relays are commonly used for the transformer protection. This approach compares the current at all terminals of the protected transformer by computing and monitoring a differential current. To avoid the needless trip by magnetizing inrush current, many novel restrain methods are proposed in recent years such as using wavelet transform [1,2], neural network [3], fuzzy logic [4] and so on. All these schemes are based on some special characteristics of advanced signal process techniques and are not mature enough to be used in power systems as the traditional methods. Although the second harmonic restrain principle is widely used in industrial application for many years, it often encounters some problems such as long restrain time when a long line is connected to the protected transformer. In the traditional method the altitude of second harmonic and fundamental are computed by discrete Fourier transform (DFT) and the ratio is used to judge whether the current is inrush or internal fault one. But it is well known that DFT is not accurate if the current is contaminated by harmonics that are not integer multiples of the fundamental, especially when the computation window is very short. * Corresponding author. Fax: /86-278-803-1477
In recent years, the modern spectrum analysis is getting much success in signal process area. Many mathematical models, such as autoregressive model (AR), moving average model (MA) and their mixed model (ARMA) are widely used for spectrum estimation. These methods are effective when the signal contains noise and the number of sampled data is small. In this paper, a new scheme is proposed based on AR PS analysis. Like the traditional method, the ratio of second harmonic PS to fundamental PS is employed as an index to differentiate inrush from internal fault. The results show that the algorithm is effective in improving the operation speed of the protection.
2. Principle of the scheme 2.1. Autoregressive model An autoregressive process of order P can be given by: xn
P X
ak xnk vn
(1)
k1
where xn is sampled data sequence, am , m /1. . .P , are the parameters of the filter modeling the signal. vn is white noise. Under the model, a signal within a short interval is described as the output of a time-invariant all-
0378-7796/02/$ - see front matter # 2002 Published by Elsevier Science B.V. PII: S 0 3 7 8 - 7 7 9 6 ( 0 2 ) 0 0 1 0 0 - 1
H. Zhang et al. / Electric Power Systems Research 63 (2002) 81 /86
82
pole filter of order P excited by white noise vn . The transfer function of the filter associated with the signal: 1
H(z) 1
P X
(2) ak zk
k1
Fig. 1. Dynamic power system model.
2.2. Estimation of parameters The estimation of parameters of AR model is widely discussed in [5,6]. The parametric estimation is formulated as a least squares. Burg’s lattice-based method is chosen to compute the least-squares AR model. The MATLAB 5.2 provides the burg method to estimate parameters that are used in this article. 2.3. Estimation of the power spectrum of data Noting that X (v) /H (v )*W (v ), the power spectrum (PS) of AR model is given by: 2
2
2
Px (v)jb(0)j jH(v)j
j
jb(0)j P X 1 ak ejkv k1
j
2
(3)
where jb (0)j2 /d2v is the variance of the white noise estimated from the model errors e (n ), satisfying the energy matching constraint between the time domain and the frequency domain.
3. The restraint principle Like the traditional method, the second harmonic content is used to differentiate the inrush from the internal fault current. But here the restraint index is defined as the square root of ratio of the second harmonic PS to fundamental PS that is given by: sffiffiffiffiffiffiffiffiffiffiffiffiffi P(2v) ratio (4) P(v) where v is the fundamental frequency. So two steps need to be taken for inrush discrimination: Using sampled points in one cycle to compute the parameters of four-order autoregressive model. Compute the PS of second harmonic and fundamental. Because AR model has a small frequency shift, the PS at the frequency of v can be defined as: P(v)max(P(v2pn))
n Z; n3 to 3
(5)
The same is to the computation of PS at the frequency of 2v. The improved ratio is used as the restraint signal for inrush identification.
Fig. 2. B to ground internal fault on primary. (a) Internal fault current, (b) change of restraint percentage using DFT, (c) change of restraint percentage using AR model.
H. Zhang et al. / Electric Power Systems Research 63 (2002) 81 /86
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Fig. 3. B to phase C interval fault on primary. (a) Internal fault current, (b) change of restraint percentage using DFT, (c) change of restraint percentage using AR model.
Fig. 4. A to B internal fault on secondary. (a) Internal fault on current, (b) change of restraint percentage using DFT, (c) change of restraint percentage using AR model.
4. Results and analysis
Inter 8086 cpu. The sampling frequency is 1200 Hz, that is 24 points sampled in each cycle. Different kinds of internal faults and inrush currents are restored and analyzed with the proposed methods. The analyzed results are shown in Figs. 2/8. The tested transformer is connected with a long line and the system is loaded. Under this circumstance, the second harmonic ratio during faults is quite high, blocking the protection for a long time. With the PS
The experiment set-up consisted of a three-phase transformer bank of three 2 kVA, 462:200 V, 50 Hz single phase transformers, with a star connected primary and delta connected secondary. A model of a 500 kV, 340 km long line was connected on the primary side of the transformer as shown in Fig. 1. The six currents were sampled in real time by a single-board computer with
84
H. Zhang et al. / Electric Power Systems Research 63 (2002) 81 /86
Fig. 5. B 4.35% winding internal fault on primary. (a) Internal fault current, (b) change of restraint percentage using DFT, (c) change of restraint percentage using AR model.
Fig. 6. Energization with B to ground internal fault as primary. (a) Internal fault current, (b) change of restraint percentage using DFT, (c) change of restraint percentage using AR model.
ratio restraint principle, operation speed is enormously improved. The following examples are different kinds of internal faults that are analyzed by the proposed method and traditional method. The analyzed current is phase A /B current. The restraint ratio is 15%. Fig. 2 shows a B to ground internal fault on primary. The traditional restraint principle and the PS restraint principle are given by Fig. 2(b, c), respectively. The
traditional method does not open the operation until 80 ms, but the PS restraint principle opens the protection at 32 ms. Fig. 3 shows a B to phase C internal fault on primary. The operation time in Fig. 3(b) is 25 ms, while the transformer is allowed to operate at 90 ms using traditional second harmonic scheme. Fig. 4 shows an A to phase B internal fault on secondary. The operation time of second harmonic
H. Zhang et al. / Electric Power Systems Research 63 (2002) 81 /86
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Fig. 7. Inrush with no fault and no long line connected. (a) Inrush current, (b) change of restraint percentage using AR model.
Fig. 8. Inrush with a long line but no fault. (a) Inrush current, (b) change of restraint percentage using AR model.
restrain principle is 58 ms while the proposed result shows it has a quicker operation speed operating at 16 ms. A 4.35% winding internal fault of B-phase is shown in Fig. 5(a). It can be seen from the figure that for internal winding fault, the harmonic content is comparatively low, so after 25 ms the protection is allowed to operate. For PS ratio, the protection responds more quickly to operate at 20 ms. The most serious condition is energization with fault. At this moment, the current is enormously distorted and the traditional method will restrain the protection for a long time. Seen from Fig. 6(b), the operation time is 80 ms while the operation time of PS restraint principle is 38 ms. For inrush currents, the protection should differentiate them from internal fault currents. Fig. 7(a) shows an inrush with no fault and no long line connected, while Fig. 8(a) shows an inrush with no fault but a long line connected. It is shown in Fig. 7(b) and Fig. 8(b) that the restraint percentages using the proposed method always stay above the restraint ratio 15% we set in this paper, so the protection will be prohibited from operation successfully.
5. Conclusions A novel PS ratio restraint principle has been proposed in this paper. The principle can improve the operation speed during internal fault and restrain the protection effectively while energization without fault. The PS is estimated by AR model that is widely used for short window PS estimation. The scheme is tested by data obtained from a dynamic model. Simulation results show that this algorithm is effective in distinguishing inrushes from different kinds of transformer internal faults with or without transmission lines.
References [1] X. Lin, P. Liu, S. Cheng, A wavelet transform based scheme for power transformer inrush identification, WM PWRD, 2000. [2] F. Jiang, Z. Q.Bo, Power transformer protection based on transient detection using discrete wavelet transform (DWT), WM PWRD, 2000. [3] J. Pihler, B. Grcar, D. Dolinar, Improved operation of powr transformer protection using artificial neural network, IEEE Trans. Power Deliv. 12 (3) (1997).
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H. Zhang et al. / Electric Power Systems Research 63 (2002) 81 /86
[4] B. Kasztenny, E. Rosolowski, et al., A self-organizing fuzzy logic based protective relay */an application to powr transformer protection, IEEE Trans. Power Deliv. 12 (3) (1997).
[5] S. Shon, K. Mehrota, ‘Performance comparisons of autoregressive estimation methods’, in: Proceeding of IEEE International Conference ASSP, 14.3.1 /14.3.4, 1984. [6] S.L. Marple, Jr, Digital Spectral Analysis with Applications (Chapter 8), Prentice Hall, Englewood Cliffs, 1987.
A new scheme for inrush identification in transformer protection Hao Zhang a,*, Pei Liu a, O.P. Malik b a
Department of Electrical Power Engineering, Huazhong University of Science and Technology, Wuhan 430074, People’s Republic of China b Department of Electrical and Computer Engineering, The University of Calgary, Calgary, Alta., Canada T2N 1N4 Received 31 October 2001; accepted 19 December 2001
Abstract The second harmonic component is commonly used for blocking differential relay in power transformers. The altitudes of harmonics and fundamental are computed by discrete Fourier transform (DFT). However, this method is not effective in some cases. A new scheme to discriminate fault current and inrush current is presented in this paper. The ratio of the power spectrum (PS) of second harmonic to the PS of fundamental based on autoregressive process is used for inrush identification. Test results with the sampled data from a prototype device on a dynamic power system model verify the effectiveness of the proposed scheme. # 2002 Published by Elsevier Science B.V. Keywords: Power transformer protection; Power spectrum (PS); Autoregressive process
1. Introduction Differential relays are commonly used for the transformer protection. This approach compares the current at all terminals of the protected transformer by computing and monitoring a differential current. To avoid the needless trip by magnetizing inrush current, many novel restrain methods are proposed in recent years such as using wavelet transform [1,2], neural network [3], fuzzy logic [4] and so on. All these schemes are based on some special characteristics of advanced signal process techniques and are not mature enough to be used in power systems as the traditional methods. Although the second harmonic restrain principle is widely used in industrial application for many years, it often encounters some problems such as long restrain time when a long line is connected to the protected transformer. In the traditional method the altitude of second harmonic and fundamental are computed by discrete Fourier transform (DFT) and the ratio is used to judge whether the current is inrush or internal fault one. But it is well known that DFT is not accurate if the current is contaminated by harmonics that are not integer multiples of the fundamental, especially when the computation window is very short. * Corresponding author. Fax: /86-278-803-1477
In recent years, the modern spectrum analysis is getting much success in signal process area. Many mathematical models, such as autoregressive model (AR), moving average model (MA) and their mixed model (ARMA) are widely used for spectrum estimation. These methods are effective when the signal contains noise and the number of sampled data is small. In this paper, a new scheme is proposed based on AR PS analysis. Like the traditional method, the ratio of second harmonic PS to fundamental PS is employed as an index to differentiate inrush from internal fault. The results show that the algorithm is effective in improving the operation speed of the protection.
2. Principle of the scheme 2.1. Autoregressive model An autoregressive process of order P can be given by: xn
P X
ak xnk vn
(1)
k1
where xn is sampled data sequence, am , m /1. . .P , are the parameters of the filter modeling the signal. vn is white noise. Under the model, a signal within a short interval is described as the output of a time-invariant all-
0378-7796/02/$ - see front matter # 2002 Published by Elsevier Science B.V. PII: S 0 3 7 8 - 7 7 9 6 ( 0 2 ) 0 0 1 0 0 - 1
H. Zhang et al. / Electric Power Systems Research 63 (2002) 81 /86
82
pole filter of order P excited by white noise vn . The transfer function of the filter associated with the signal: 1
H(z) 1
P X
(2) ak zk
k1
Fig. 1. Dynamic power system model.
2.2. Estimation of parameters The estimation of parameters of AR model is widely discussed in [5,6]. The parametric estimation is formulated as a least squares. Burg’s lattice-based method is chosen to compute the least-squares AR model. The MATLAB 5.2 provides the burg method to estimate parameters that are used in this article. 2.3. Estimation of the power spectrum of data Noting that X (v) /H (v )*W (v ), the power spectrum (PS) of AR model is given by: 2
2
2
Px (v)jb(0)j jH(v)j
j
jb(0)j P X 1 ak ejkv k1
j
2
(3)
where jb (0)j2 /d2v is the variance of the white noise estimated from the model errors e (n ), satisfying the energy matching constraint between the time domain and the frequency domain.
3. The restraint principle Like the traditional method, the second harmonic content is used to differentiate the inrush from the internal fault current. But here the restraint index is defined as the square root of ratio of the second harmonic PS to fundamental PS that is given by: sffiffiffiffiffiffiffiffiffiffiffiffiffi P(2v) ratio (4) P(v) where v is the fundamental frequency. So two steps need to be taken for inrush discrimination: Using sampled points in one cycle to compute the parameters of four-order autoregressive model. Compute the PS of second harmonic and fundamental. Because AR model has a small frequency shift, the PS at the frequency of v can be defined as: P(v)max(P(v2pn))
n Z; n3 to 3
(5)
The same is to the computation of PS at the frequency of 2v. The improved ratio is used as the restraint signal for inrush identification.
Fig. 2. B to ground internal fault on primary. (a) Internal fault current, (b) change of restraint percentage using DFT, (c) change of restraint percentage using AR model.
H. Zhang et al. / Electric Power Systems Research 63 (2002) 81 /86
83
Fig. 3. B to phase C interval fault on primary. (a) Internal fault current, (b) change of restraint percentage using DFT, (c) change of restraint percentage using AR model.
Fig. 4. A to B internal fault on secondary. (a) Internal fault on current, (b) change of restraint percentage using DFT, (c) change of restraint percentage using AR model.
4. Results and analysis
Inter 8086 cpu. The sampling frequency is 1200 Hz, that is 24 points sampled in each cycle. Different kinds of internal faults and inrush currents are restored and analyzed with the proposed methods. The analyzed results are shown in Figs. 2/8. The tested transformer is connected with a long line and the system is loaded. Under this circumstance, the second harmonic ratio during faults is quite high, blocking the protection for a long time. With the PS
The experiment set-up consisted of a three-phase transformer bank of three 2 kVA, 462:200 V, 50 Hz single phase transformers, with a star connected primary and delta connected secondary. A model of a 500 kV, 340 km long line was connected on the primary side of the transformer as shown in Fig. 1. The six currents were sampled in real time by a single-board computer with
84
H. Zhang et al. / Electric Power Systems Research 63 (2002) 81 /86
Fig. 5. B 4.35% winding internal fault on primary. (a) Internal fault current, (b) change of restraint percentage using DFT, (c) change of restraint percentage using AR model.
Fig. 6. Energization with B to ground internal fault as primary. (a) Internal fault current, (b) change of restraint percentage using DFT, (c) change of restraint percentage using AR model.
ratio restraint principle, operation speed is enormously improved. The following examples are different kinds of internal faults that are analyzed by the proposed method and traditional method. The analyzed current is phase A /B current. The restraint ratio is 15%. Fig. 2 shows a B to ground internal fault on primary. The traditional restraint principle and the PS restraint principle are given by Fig. 2(b, c), respectively. The
traditional method does not open the operation until 80 ms, but the PS restraint principle opens the protection at 32 ms. Fig. 3 shows a B to phase C internal fault on primary. The operation time in Fig. 3(b) is 25 ms, while the transformer is allowed to operate at 90 ms using traditional second harmonic scheme. Fig. 4 shows an A to phase B internal fault on secondary. The operation time of second harmonic
H. Zhang et al. / Electric Power Systems Research 63 (2002) 81 /86
85
Fig. 7. Inrush with no fault and no long line connected. (a) Inrush current, (b) change of restraint percentage using AR model.
Fig. 8. Inrush with a long line but no fault. (a) Inrush current, (b) change of restraint percentage using AR model.
restrain principle is 58 ms while the proposed result shows it has a quicker operation speed operating at 16 ms. A 4.35% winding internal fault of B-phase is shown in Fig. 5(a). It can be seen from the figure that for internal winding fault, the harmonic content is comparatively low, so after 25 ms the protection is allowed to operate. For PS ratio, the protection responds more quickly to operate at 20 ms. The most serious condition is energization with fault. At this moment, the current is enormously distorted and the traditional method will restrain the protection for a long time. Seen from Fig. 6(b), the operation time is 80 ms while the operation time of PS restraint principle is 38 ms. For inrush currents, the protection should differentiate them from internal fault currents. Fig. 7(a) shows an inrush with no fault and no long line connected, while Fig. 8(a) shows an inrush with no fault but a long line connected. It is shown in Fig. 7(b) and Fig. 8(b) that the restraint percentages using the proposed method always stay above the restraint ratio 15% we set in this paper, so the protection will be prohibited from operation successfully.
5. Conclusions A novel PS ratio restraint principle has been proposed in this paper. The principle can improve the operation speed during internal fault and restrain the protection effectively while energization without fault. The PS is estimated by AR model that is widely used for short window PS estimation. The scheme is tested by data obtained from a dynamic model. Simulation results show that this algorithm is effective in distinguishing inrushes from different kinds of transformer internal faults with or without transmission lines.
References [1] X. Lin, P. Liu, S. Cheng, A wavelet transform based scheme for power transformer inrush identification, WM PWRD, 2000. [2] F. Jiang, Z. Q.Bo, Power transformer protection based on transient detection using discrete wavelet transform (DWT), WM PWRD, 2000. [3] J. Pihler, B. Grcar, D. Dolinar, Improved operation of powr transformer protection using artificial neural network, IEEE Trans. Power Deliv. 12 (3) (1997).
86
H. Zhang et al. / Electric Power Systems Research 63 (2002) 81 /86
[4] B. Kasztenny, E. Rosolowski, et al., A self-organizing fuzzy logic based protective relay */an application to powr transformer protection, IEEE Trans. Power Deliv. 12 (3) (1997).
[5] S. Shon, K. Mehrota, ‘Performance comparisons of autoregressive estimation methods’, in: Proceeding of IEEE International Conference ASSP, 14.3.1 /14.3.4, 1984. [6] S.L. Marple, Jr, Digital Spectral Analysis with Applications (Chapter 8), Prentice Hall, Englewood Cliffs, 1987.