ARTIFICIAL NEURAL NETWORK BASED DYNAMIC COMPENSATION OF CURRENT TRANSFORMER ERRORS M. Lukowicz, E. Rosolowski Institute of Electrical Power Engineering Wroclaw University of Technology ul. Wybrzeze Wyspianskiego 27, 50-370 Wroclaw tel. (+48 71) 320 38 76 - fax (+48 71) 320 34 87 e-mail:
[email protected]. correction of CTs have been reported [1].
ABSTRACT - The paper presents application of neural corrector intended for dynamic compensation of a Current Transformer (CT) used for current measurement in high voltage power systems. After the problem and the model of the used transformer description the results obtained for different network parameters are presented. The non-linear multilayer Artificial Neural Network (ANN) structures with feedback connections have been investigated. The problem of correct application of such a novel method in real protection systems has been discussed.
MODELLED SYSTEM DESCRIPTION The considered fragment of 400kV system simulated in EMTP-ATP program is shown in figure 1. It consists of one overhead transmission line of 150km length supplied from generators UA and UB. The line is 3-phase continuously-transposed one divided into three parts. Two of them are of 25km length and the third of 100km. Such a division has been chosen in order to make possible carrying out simulations of short circuits at three locations: at the bus-bars, 25km and 50km from the point of CTs installation. ZSA and ZSB, modelled as normal mutually coupled RL elements represent the residual part of the 400kV system. The phase displacement between the sources UA and UB of 8deg forced the power flow of about 350MVA from the system SA to SB through the considered line. The line parameters (zero and positive sequence values) are listed at the figure.
INTRODUCTION In order to assure rapid and reliable operation of the power system control valid information on the state of the electrical elements is needed. One of the most important part of the electrical system is power system protection. Using phase voltages and currents the protection relays estimate the state of the controlled plant and make a decision: to trip, or not-to-trip the faulted circuit. Current and voltage transformers are elements that influence the criterion values measurement particularly during disturbances in the system. Certain construction limitations of the instrument transformers may in some cases cause meloperation or substantial delay in tripping of the protective relays. CT saturation and discharging of the capacitive voltage transformer internal energy during short circuits on an associated transmission line are the most important phenomena influencing quality of voltage and current magnitude measurement. Presentation of the dynamic correction of CT errors is the goal of the paper. Till now many studies on the 6$ 8$
=$
/ NP
/
/
NP NP
=%
THE MODEL OF A CT Fig. 2 presents the model of a CT used in simulations. The CTs have been modelled by means of standard block - type 98 described in the EMTP guide [2]. The CTs with regard to their nonlinear magnetising characteristics are the most interesting part of the measurement circuit connecting the protective relay with controlled plant. The flux/current curve of investigated CTs is shown in fig. 3. (Ω
6%
Ω
(Ω =/
8%
Fig. 1. The structure of the modelled system. L1(2,3)- R0=0.275Ω/km L0=3.2675mH/km C0=0.013uF/km R1=0.0276Ω/km L1=1.003mH/km C1=0.0085uF/km
Fig. 2. Diagram of CTs modelled
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testing process should be carried out with use of data not presented during training, some additional simulations has been prepared with following parameters:
$ 9V
)/8; Φ >9V@
• systems impedances Four combinations of 10Ω and 20Ω values have been used as impedances of the SA and SB systems. Argument of each impedance had the random value from the 80-89deg range and the |Z0|/|Z1| ratio had random value from the 1.2-2.0 range.
0$*1(7,6,1* &855(17 , >$@
• type of short circuit a) R-T
Fig. 3. Magnetising characteristic of the CT core
The saturation point (2.5A, 3.8Vs) has been selected to be used in EMTP auxiliary subroutine HYSDAT [2] for generation of the CT's magnetising characteristic curve.
SIMULATION CONDITIONS
b) R-S-T
• fault resistance
a) 3.5Ω b) 7.5Ω c) 13.5Ω
• fault location
a) 0km b) 12km c) 37.5km
• CT’s load
a) 10Ω b) (8+6j)Ω
• fault angle a) 2ms b) 8ms after phase R voltage maximum reaching
Taking into consideration the parameters which influence the level of CT saturation the following conditions to be changed at each simulations run have been chosen:
• remanent flux was chosen in the same manner as for training cases The sampling rate of 20 samples per cycle has been chosen.
• systems impedances Four combinations of 5Ω and 25Ω values have been used as impedances of the SA and SB systems. Argument of each impedance had the random value from the 80-89deg range and the |Z0|/|Z1| ratio had random value from the 1.2-2.0 range.
NEURAL APPROACH TO THE PROBLEM OF CT COMPENSATION The application of CT’s inverse transfer function GCOR in the artificial neural network form is the base of the idea of CT compensation presented in the paper. The function GCOR and the transfer function of CT (GCT) set up in series should assure identity of CT primary and compensated secondary currents. Since the CT’s transfer function is nonlinear, usage of the nonlinear artificial multilayer neural network structure, as presented in figure 4, is required. The sigmoidal tangent activation function has been assigned to neurons in hidden layers and the linear one to the output neuron of the selected ANN architecture. In order to assure the independence of compensation quality from the magnitude value of considered signal, input patterns were dynamically standardised during the training and testing process. The standardisation process and realised function are described by eq. 1 and figure 4.
• type of short circuit a) R-G b) R-S-T-G • fault resistance
a) 0Ω
• fault location
a) 0km b) 25km c) 50km
• CT’s load
a) 10Ω b) (8+6j)Ω
b) 10Ω c) 20Ω
• fault angle a) 0° b) 90° (phase R voltage the zero and maximum value crossing) • remanent flux was chosen randomly from the range of (-2.8÷2.8)Vs The current waveforms obtained from simulations have been used for preparation of training patterns. The data generated with above parameters have been intended for ANN training. As the reliable ANN
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The next three indices have been introduced to define the usefulness of the corrected signals for the magnitude, resistance and reactance estimation:
L Q V Q Z
L Q1 V Q Z
Z
L Q1 V Q F
L Q
G
Z
L Q1 V Q F
G
L Q1 1 V Q F
G
F
1
1
1
Fig. 4. ANN compensator’s architecture
LF ] − 1 = V Q ∗ ) LZ LZ V Q LZ ] − 1 + V Q −1 − −1 −1 + LF ] V Q LF ] V Q G
G
Z
G
where: V Q = PD[ _ L Z Q _ _ L Z Q − _
F
(1)
_ L Z Q
The secondary current and compensated ANN's output samples dynamically scaled with s(n) factor and the recently inquired sample of the secondary current have been used for forming the network input patterns.
In order to determine the performance of CTs correctors we introduced four types of quality indices. The first one measures the ability of reconstruction of the secondary current: =
M
− ′
L ′S Q M
LF Q M
,S M
=
= 5 S Q M − 5F Q M HUU5 Q = ∑ = 5 S Q M M =
(4)
= ; S Q M − ; F Q M HUU; Q = ∑ = ; S Q M M =
(5)
Full-cycle digital sine and cosine filters have been used for estimation of orthogonal components of considered voltage and current signals. They in turn have been used for estimation of U, I, R, X quantities. It is evident that the lower the performance indices are, the better the compensated signals correspond to the target ones.
THE PERFORMANCE INDICES
= ∑=
(3)
where: j - number of considered current waveshapes from faulted phases, Z - number of considered fault currents, n - number of current sample, I’p(n,j) - magnitude of the primary current referred to the secondary side (estimated at n-th instant), c,p - subscripts indicating currents used for criteria quantities estimation (c-compensated, pprimary currents), R, X - resistance and reactance, respectively.
− _
iw - sample of secondary current, ic - sample of compensated current, Nw, Nc - shift register lengths, Nd - structural delay of compensation
HUU Q 6
= , ′S Q M − , F Q M HUU $ Q = ∑ = , ′S Q M M =
COMPENSATION OF THE CT -PARAMETERS SELECTION
(2)
Table 1. Values of the performance indices. Compensation made with the ANNs of 8-8-1 structure (Nw=4, Nc=8) with Nd parameter
∑ HUU Q @
being changed. (CT’s burden ZL = (8+6j)Ω); { HUU = >
- indices averaged over two cycles of the fundamental fre-
Q =
quency}
without com. Nd=0 Nd =1 Nd =2 Nd =3
errS [%] 8.43 4.84 4.23 2.16 2.07
TRAINING DATA errA [%] errR [%] 7.87 160.27 3.38 47.23 4.04 34.83 1.98 6.52 1.96 6.73
errX [%] 378.27 69.74 122.61 33.67 31.24
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errS [%] 6.05 5.02 3.61 1.91 2.01
TESTING DATA errA [%] errR [%] 6.77 20.79 3.74 12.44 3.73 10.53 2.02 4.03 1.92 7.04
errX [%] 242.82 112.52 80.08 56.07 54.62
Table 2. Values of the performance indices. Compensation made with the ANNs of 8-8-1 structure and Nw, Nc parameters being changed. (Nd=2); (CT’s load - ZL = (8+6j)Ω).
without com. Nw=2 Nc=10 Nw=4 Nc=8 Nw=6 Nc=6 Nw=8 Nc=4 Nw=10 Nc=2 Nw=12 Nc=0
TRAINING DATA errA [%] errR [%] 7.87 160.27 4.28 10.40 1.98 6.52 2.27 14.82 4.11 19.7 5.62 38.25 7.32 130.3
errS [%] 8.43 2.91 2.16 2.32 3.05 5.83 8.41
errX [%] 378.27 49.16 33.67 32.77 63.32 123.42 150.42
errS [%] 6.05 2.99 1.91 2.72 3.12 5.73 6.01
TESTING DATA errA [%] errR [%] 6.77 20.79 2.99 13.34 2.02 4.03 2.56 7.42 3.27 18.83 5.64 19.81 6.32 20.7
errX [%] 242.82 72.34 56.07 75.42 83.4 110.3 132.84
Nc=8 have been selected. The first row in table 1 shows values of performance indices computed for secondary currents without compensation and the last row - values of indices computed after compensation process made with the feedforward ANN (Nc=0). Introductory research has shown that ANN compensation structures fed with signals from short shift registers (e.i. those of low sum of Nw and Nc parameters) revealed poor performance features. For that reason the variants of compensators with sum Nw+Nd=12 were investigated.
Utilising the algorithm intended for real-time recurrent neural network training [3] many alternative compensators have been prepared. Parameters Nd, Nw, Nc and size of an ANN were changed during investigations. The goal of research was determination of the optimal mentioned parameters which would guarantee the best performance of obtained compensators. The time delay selection (Nd) Table 1 presents the relationship of performance of obtained networks with respect to the structural time delay Nd. Presented indices have been averaged over two cycles of the fundamental frequency. Research of ANNs ability to CT compensation has shown that CT with complex R-X load could be corrected with ANN. However, compensation process had to be delayed for 0 to 2ms. The required time delay depends on timeconstant of secondary circuit of CT model [4]. The greater time-constant, the longer delay should be introduced.
Selection of the optimal size of the ANN Table 3 shows values of performance indices computed for training and testing data. Secondary current waves have been compensated with ANN consisted of various number of neurons in hidden layers. Investigations have been curried out for ANN fed from shift registers of Nw=4 and Nc=8 lengths and with 2ms time delay introduced to compensation process. As can be seen, ANN of 5-5-1 structure shows good performance and requires small number of computation units.
Selection of the length of the shift registers Table 2 includes values of performance indices computed for training and testing secondary currents compensated with ANN under Nw and Nc parameters being changed. The best suited values of Nw=4 and
Compensation of a CT with purely resistive load The ANN of 8-8-1 size has been selected for com-
Table 3. Values of the performance indices. Compensation made with the ANNs of different sizes (Nd=2, Nw=4, Nc=8) (CT’s load ZL = (8+6j)Ω)
without comp. 3-3-1 5-5-1 7-7-1 9-9-1
errS [%] 8.43 6.37 2.26 2.12 1.91
TRAINING DATA errA [%] errR [%] 7.87 160.27 6.15 78.3 2.14 6.52 2.07 6.32 1.95 6.03
errX [%] 378.27 56.23 33.67 42.75 39.71
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errS [%] 6.05 5.84 2.34 4.17 2.34
TESTING DATA errA [%] errR [%] 6.77 20.79 6.35 17.86 2.22 4.13 3.78 20.72 4.01 17.01
errX [%] 242.82 87.32 62.07 65.77 59.21
Table 4. Values of performance indices. Compensation made with the ANNs of 8-8-1 size. (Nd=0, Nw=4, Nc=8); (CT’s load ZL = 10Ω)
TRAINING DATA errA [%] errR [%] 5.79 405.66 1.51 10.79
errS [%] 10.74 2.31
without com. 8-8-1
errX [%] 562.68 35.92
TESTING DATA errA [%] errR [%] 4.67 26.07 1.69 8.11
errS [%] 7.91 2.48
errX [%] 243.26 27.09
ZLWKRXW FRP ZLWK FRP
HUU;
HUU5
HUU6
HUU$
W >PV@
W >PV@
W >PV@
W >PV@
Fig. 5. Graphs of the performance indices in the time domain (the resistive-inductive load). Compensation carried out with the 5-5-1 ANN.(Nd=2; Nw=4; Nc=8)
ZLWKRXW FRP
HUU5
HUU$
HUU6
ZLWK FRP
HUU;
t [ms]
W >PV@
W >PV@
W >PV@
Fig. 6. Graphs of performance indices in time domain (the purely resistive load). Compensation carried out with the 8-8-1 ANN.(Nd=0; Nw=4; Nc=8)
Figures 5-6 show graphs of the performance indices in the time domain computed for uncompensated and compensated secondary currents of CTs. The processed current waveshapes have been chosen from training and testing data sets. Figure 5 refers to compensation of the CT with resistive-inductive load and figure 6 with the purely resistive load. The time of 0ms meets the fault inception. Figures 7-9 show results of compensation and amplitude estimation based on uncompensated and compensated currents. It is well visible that ANN corrects
pensation of the CT with purely resistive load (10Ω). Lengths of the shift registers were the same as for resistive-inductive load, i.e. Nw=4 and Nc=8. Studies have shown that in the cases of resistive load no delay time in compensation algorithm is required, i.e. Nd=0. Table 4 contains values of performance indices computed for such a burden case. COMPENSATION RESULTS IN THE TIME DOMAIN
35,0$5$@
, >$@
>PV@
Fig. 8. a) Plot of phase T currents generated from simulation of
Fig. 7. a) Plot of phase S currents generated from simulation of R-
R-T fault at bus-bars (RF=3.5Ω) Compensation carried out by ANN of 5-5-1 structure. b) Amplitude estimation of primary, secondary and compensated current.
S-T fault at bus-bars (RF=0Ω). Compensation carried out by ANN of 5-5-1 structure. b) Amplitude estimation of primary, secondary and compensated current.
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D
D
35,0$5PV@
$03/,78'( (67,0$7,21
E
, >$@
, >$@
>PV@
Fig. 9. a) Plot of phase S currents generated from simulation of
Fig. 10. a) Plot of phase T currents generated from simulation of
R-S-T fault at distance 12.5km from bus-bars (RF=3.5Ω). Compensation carried out by ANN of 5-5-1 structure. b) Amplitude estimation of primary, secondary and compensated current.
R-G fault at bus-bars (RF=0Ω). Compensation carried out by ANN of 5-5-1 structure. b) Amplitude estimation of primary, secondary and compensated current.
shape of the secondary current which is similar to the shape of the primary current referred to the secondary side of the CT. Estimation of current amplitude after compensation is much more accurate than in the case of estimation based on the distorted secondary current. Figure 10 presents the result of compensation made on current from unfaulted phase. In that case compensation process is successful as well.
transformer energising can make possible that mentioned limitations will be omitted. Since proposed compensators are able to estimate the correct secondary current under different fault conditions, they can improve the sensitivity and maximise the stability of relays thus making the use of the CT with the reduced core cross section possible.
REFERENCES CONCLUSIONS [1] Y. Kang, J. Park, S. Kang, "An algorithm for Compensating Secondary Currents of Current Transformers", IEEE/PES Winter Meeting, January 21-25 1996, Baltimore. [2] EMTP Rule book, Leuven EMTP Centre, July 1987. [3] Haykin S., Neural Networks, A Comprehensive Foundation, Macmillan Publishing Company, 1994. [4] IEEE Power System Relaying Committee, "Transient Response of Current Transformers", IEEE Trans. PAS, vol. 96, no. 6, November/December 1977, pp. 1809-1814
The paper proposes the novel ANN based compensation technique for accurate measurement of the CT secondary current. It can successfully compensate the secondary current when a resistive and resistive-inductive CT's load is applied. Since the proposed compensators are intended for sine waveshapes correction, they can be only applied to improve currents at transmission lines. Authors believe that it is possible to prepare ANNs intended for correction of CTs used to power transformer current measurement. Enclosing in training data sets such current shapes as flowing during e.g.
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