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Artificial Neural Network for coordinated control of STATCOM, generator excitation and tap changing transformer
Electrical Power and Energy Systems 64 (2015) 536–541
Contents lists available at ScienceDirect
Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes
Artificial Neural Network for coordinated control of STATCOM, generator excitation and tap changing transformer S. Sumathi a,⇑, Bansilal b a b
RNS Institute of Technology, Bangalore, India The National institute of Technology, Mysore, India
a r t i c l e
i n f o
Article history: Received 29 September 2013 Received in revised form 29 June 2014 Accepted 14 July 2014
Keywords: STATCOM Tap changing transformer Generator excitation Artificial Neural Network (ANN)
a b s t r a c t Control of voltage in a power system under varying load conditions can be achieved by varying the generator excitation, changing the tap position of transformers and by varying the reactive power injection or absorption at the shunt compensated buses. Proper coordination of these controllers is essential for the effective operation of the power system. This paper deals with the development of Artificial Neural Network which gives the voltage controller settings, such that the voltage deviations at the load buses are minimum. Ó 2014 Elsevier Ltd. All rights reserved.
Introduction Voltage control is an important aspect in the day to day operation of power systems. The voltage control can be achieved by various reactive power controlling devices. Present day power systems use FACTS devices for the control of real and reactive power in the system. The shunt FACTS devices such as Static VAR Compensator (SVC), Static Synchronous Compensator (STATCOM) are the devices commonly used for the control of reactive power and hence used for the control of voltage in the system [1,2]. The coordinated control of these FACTS devices with the generator excitation system and tap changing transformers is essential for the control of voltages at the load buses. Hence the objective is to find the settings of these control devices so as to minimize the voltage deviations at the load buses. Generally non linear optimization techniques are used to find the controller settings [3]. Artificial Neural Network is one of the important artificial intelligence tools which can be used for non linear function mapping. A trained ANN can be used to model any function approximation in real time. In literature, we find many Artificial Neural Network applications for the monitoring and control of power system operation.
Artificial Neural Networks are used to detect the type and location of fault in distribution system [4]. Artificial Neural Networks find application in insulation failure detection in transformer windings [5]. ANN are also used in locating the phase of partial discharge in transmission line [6]. They are also used in evaluation of loadability limit of systems with TCSC [7]. Artificial Neural Networks find application in transient stability analysis of power system [8]. Artificial Neural Networks are developed even for protection co-ordination schemes [9]. In this paper ANNs are developed which give the controller settings for minimum voltage deviation under normal condition and under contingency condition. Prototype Artificial Neural Networks are developed for a 24 bus EHV power system. The single line diagram of the power system is shown in Fig. 1. The power system considered for analysis has 4 generators, 7 tap changing transformers at the load buses and a STATCOM connected at bus 24. The developed ANN take the load factor as input and gives the generator excitation, tap position of the transformers and the reactive power to be supplied by the STATCOM as output. The data for training the ANN is obtained by the conventional non linear optimization technique. Formulation of problem
⇑ Corresponding author. Tel.: +91 98801 29596. E-mail addresses: [email protected] (S. Sumathi), bansilal_nie@ rediffmail.com ( Bansilal). http://dx.doi.org/10.1016/j.ijepes.2014.07.056 0142-0615/Ó 2014 Elsevier Ltd. All rights reserved.
For the given loading condition the non linear optimization problem is to minimize the voltage deviations at the load buses. Hence the objective function is expressed as:
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S. Sumathi, Bansilal / Electrical Power and Energy Systems 64 (2015) 536–541
radial basis function neural networks are developed, corresponding to normal condition of the power system network and with line outage condition. The developed Artificial Neural Networks take the load factor as input and give the controller settings as output. The output includes the tap position of the transformers, reactive power injection by the STATCOM, and the voltages of the generator buses. The data for training the Artificial Neural Network is obtained by running the optimization program, for different load factors. Radial basis function neural network for normal operating condition Data for training the radial basis function neural network The load factor is varied from 0.9 to 1.1 in steps of 0.02. For the non linear least square optimization technique the tap position of tap changing transformers are initialized to 1.00. The value of reactive power injection by the STATCOM is initialized to 0.15pu and the generator excitations are initialized to 1.00pu. The values of control variables obtained from non linear optimization technique, are used for training the RBNN. Table 1 shows part of the data used for training the radial basis function network corresponding to normal operating condition of the power system. The developed RBNN has 11 neurons in the radial basis layer. It has 12 neurons in the output layer corresponding to 12 control variables.
Fig. 1. Single line diagram of 24 bus system.
Minimize
JðXÞ ¼
L X ½V iðdesÞ V iðactÞ 2
ð1Þ
i¼1
Where L is number of load buses; X is the vector of control variables; Vi(des) is the desired voltage at bus i; Vi(act) is the actual voltage at bus i. The non linear least square optimization technique is used for the solution of this non linear optimization problem as explained in Appendix. The control variables are tap position of the transformers, excitation of the generators and the reactive power injection by the STATCOM. Algorithm for solving non linear optimization problem 1. 2. 3. 4. 5. 6.
Read the system data and the load multiplier. Initialize control variables. Form network matrices. Perform power flow with controller settings. Compute the voltage error, and the objective function. If the value of objective function is within the specified tolerance go to step 8. 7. Else solve for control variables and adjust it for suitable step size and go to step 3. 8. Print the results. Development of Artificial Neural Network An Artificial Neural Network (ANN) is an important artificial intelligence tool, which gives fast and acceptable solution in real time. ANNs are composed of simple elements operating in parallel. It is composed of a large number of highly interconnected processing elements that are analogous to neurons and are tied together with weighted connections that are analogous to synapses. Once trained the Artificial Neural Network is able to provide sufficiently accurate recommendations in a very short time suitable for on-line applications in energy control centers. A Radial Basis function Neural Networks (RBNN), one of the standard ANN which has one input layer, one hidden layer and an output layer. The hidden layer uses radial symmetric activation function such as Gaussian activation function. In this paper two
Validation of the radial basis function neural network CASE 1: load factor of 0.95. Table 2 shows the recommendations for different controller settings, provided by the non linear least square optimization technique and the predictions made by the developed radial basis function neural network for a load factor of 0.95. It can be observed from Table 2 that the recommendations provided by the radial basis function neural network is comparable with the results obtained from conventional non linear least square optimization technique. The recommendations provided by the radial basis function neural network for the reactive power injection is 0.1720 against 0.1500 provided by the optimization technique. The error in the recommendations of the neural network is just 0.022pu (2.2MVar). It can be seen that the recommendations provided by the radial basis function neural network for generator excitations are comparable with that of optimization technique. The error is found to be maximum in the recommendation of excitation of generator 1 (V1). And this error is just 0.0029pu. In case of transformer tap settings, a small variation in the recommendations has no significant effect on the system operation, because the transformer taps are varied in steps. Table 3 shows the voltage profile at all the load buses with the controller settings provided by optimization technique and radial Table 1 Data for training the radial basis function neural network under normal operating condition. Control variable
T5 T6 T7 T8 T9 T10 T11 Qstatcom V1 V2 V3 V4
Load factor 0.92
0.96
1.00
1.04
1.08
0.9625 0.9875 1.0000 1.0000 1.0000 0.9875 1.0000 0.1500 1.0150 0.9850 0.9950 1.0000
0.9875 0.9875 1.0000 1.0000 1.0000 0.9875 1.0000 0.2000 1.0050 0.9950 1.0000 1.0000
0.9750 0.9875 1.0000 1.0000 1.0000 0.9875 1.0000 0.2500 1.0100 0.9900 1.0000 1.0000
0.9500 0.9875 1.0000 1.0000 1.0000 0.9875 1.0000 0.3500 1.0200 0.9800 1.0000 1.0000
0.9500 1.0000 1.0000 1.0000 1.0000 0.9750 1.0000 0.8000 1.0250 0.9600 1.0100 1.0000
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S. Sumathi, Bansilal / Electrical Power and Energy Systems 64 (2015) 536–541
Table 2 Controller setting recommendations for load factor of 0.95. Control variable
T5 T6 T7 T8 T9 T10 T11 Qstatcom V1 V2 V3 V4
Load factor of 0.95 OPT tech
RBNN
0.9875 0.9875 1.0000 1.0000 1.0000 0.9875 1.0000 0.1500 1.0050 0.9950 1.0000 1.0000
0.9804 0.9875 1.0000 1.0000 1.0000 0.9859 1.0000 0.1720 1.0079 0.9932 0.9999 1.0000
Table 3 Voltage profile at the load buses for a load factor of 0.95. Load bus
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 P
(ViVdes)2
Voltages (load factor 0.95) OPT tech
RBNN
0.9863 0.9673 0.9407 1.0138 1.0251 1.0346 1.0411 1.0063 0.9969 1.0184 1.0142 0.9972 1.0158 0.9975 1.0050 0.9971 1.0160 1.0096 1.0153 1.0004 0.0100
0.9907 0.9708 0.9518 1.0161 1.0255 1.0357 1.0427 1.0088 0.9996 1.0209 1.0157 0.9987 1.0181 0.9998 1.0067 1.0005 1.0170 1.0122 1.0179 1.0033 0.0092
Table 4 Controller setting recommendations for load factor of 1.05. Control variable
T5 T6 T7 T8 T9 T10 T11 Qstatcom V1 V2 V3 V4
CASE 2: load factor 1.05. Table 4 shows the recommendations for different controller settings, provided by the non linear least square optimization technique and the recommendations provided by the developed radial basis function neural network for a load factor of 1.05. It can be seen from Table 4 that the recommendations provided by the RBNN for the reactive power injection is 0.5052pu against 0.4000pu provided by the optimization technique. The error in the recommendations of the neural network is just 0.1052pu. It can be seen that the recommendations provided by the neural network for generator excitations are comparable with that of optimization technique. The error is maximum in the excitation of generator 2 (V2). And this error is just 0.0052pu. In case of transformer tap settings, a small variation in the recommendations has no significant effect on the system operation, because the transformer taps are varied in steps. Table 5 shows the voltage profile at all the load buses with the controller settings provided by optimization technique and Artificial Neural Network for the load factor of 1.05. Table 5 also shows that the minimum value of objective function achieved with the controller settings given by non linear optimization technique is 0.0097 where as the value of objective function obtained with the controller settings predicted by the developed radial basis function neural network is 0.0090, indicating better voltage control of the power system network. Radial basis function neural network for line outage condition Another radial basis function neural network to recommend the various controller settings to achieve minimum voltage deviation under contingency condition is also developed. Here the line outage of transmission line connected between bus 12 and bus 17 is considered as it is found to be one of the critical contingency. Non linear least square optimization technique is used to obtain the various controller settings at various loading conditions with line outage. Data for training the radial basis function network under line outage (12–17) condition The data obtained from optimization technique is used to develop an Artificial Neural Network based on radial basis function.
Table 5 Voltage profile at the load buses for a load factor of 1.05.
Load factor 1.05 OPT tech
RBNN
0.9500 0.9875 1.0000 1.0000 1.0000 0.9875 1.0000 0.4000 1.2050 0.9750 1.0000 1.0000
0.9509 0.9941 1.0000 1.0000 1.0000 0.9855 1.0000 0.5052 1.0217 0.9698 1.0015 1.0000
basis function neural network for the load factor of 0.95. Table 3 also shows that the minimum value of objective function achieved with the controller settings given by non linear optimization technique is 0.0100 where as the value of objective function obtained with the controller settings predicted by the developed radial basis function neural network is 0.0092, indicating better voltage control of the power system.
Load bus
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 P
(ViVdes)2
Voltages (load factor 1.05) OPT tech
RBNN
0.9956 0.9595 0.9676 1.0044 1.0040 1.0074 1.0105 0.9763 0.9636 0.9939 0.9908 0.9707 0.9926 0.9717 0.9799 0.9679 1.0004 0.9838 0.9817 0.9683 0.0097
0.9928 0.9579 0.9649 1.0039 1.0016 1.0064 1.0105 0.9784 0.9665 0.9947 0.9920 0.9720 0.9932 0.99723 0.9806 0.9707 1.0011 0.9847 0.9847 0.9723 0.0090
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S. Sumathi, Bansilal / Electrical Power and Energy Systems 64 (2015) 536–541 Table 6 Data for training the radial basis function neural network under line outage (12–17) condition. Control variable
T5 T6 T7 T8 T9 T10 T11 Qstatcom V1 V2 V3 V4
T5 T6 T7 T8 T9 T10 T11 Qstatcom V1 V2 V3 V4
Load bus
Load factor 0.92
0.96
1.00
1.04
1.08
0.9625 1.0000 1.0000 1.0000 1.0000 0.9875 1.0000 0.7000 1.0150 0.9600 1.0000 1.0000
0.9625 1.0000 1.0000 1.0000 1.0000 0.9875 1.0000 1.0500 1.0200 0.9650 1.0000 1.0000
0.9500 1.0000 1.0000 1.0000 1.0000 0.9875 1.0000 1.4500 1.0200 0.9650 1.0050 1.0000
0.9500 1.0000 1.0000 1.0000 1.0000 0.9750 1.0000 1.8500 1.0200 0.9650 1.0150 1.0000
0.9500 1.0000 1.0000 1.0000 1.0000 0.9750 1.0000 2.1000 1.0250 0.9650 1.0250 1.0050
Table 7 Controller setting recommendations for load factor of 0.95. Control variable
Table 8 Voltage profile at the load buses for a load factor of 0.95 with line outage.
Load factor 0.95 OPT tech
RBNN
0.9625 1.0000 1.0000 1.0000 1.0000 0.9875 1.0000 0.9000 1.0200 0.9650 1.0000 1.0000
0.9642 1.0000 1.0000 0.9995 0.9995 0.9865 1.0000 0.9441 1.0179 0.9638 0.9995 1.0004
To obtain the input data for the neural network the load factor of the system is varied from 0.9 to 1.1 in steps of 0.02. Table 6 shows the data used for training the network corresponding to line outage condition of the network.
Validation of the radial basis function neural network CASE 1: load factor of 0.95. Table 7 shows the recommendations for different controller settings, provided by the optimization technique and the recommendations provided by the developed radial basis function neural network for line outage conditions for a load factor of 0.95. It can be seen from Table 7 that the recommendations provided by the radial basis function neural network is comparable with the recommendations provided by the optimization technique. The maximum error is in the recommendations for reactive power injection by the STATCOM. The maximum error is only 0.021pu (2.1MVAR). The maximum value of error in the recommendations of generator excitation is 0.0021pu corresponding to generator 1. In case of transformer tap settings, a small variation in the recommendations has no significant effect on the system operation, because the transformer taps are varied in steps. Table 8 shows the voltage profile at all the load buses with the controller settings provided by optimization technique and Artificial Neural Network for the load factor of 0.95 with line outage. It can be observed from Table 8 that the value of objective function achieved with the controller settings given by optimization technique is 0.0098, whereas the value of objective function obtained with the controller settings predicted by radial basis function neural network is 0.0103. The error in the value of objective function is 5.1%.
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 P
(ViVdes)2
Voltages (load factor 0.95) OPT
RBNN
0.9963 0.9675 0.9675 1.0068 0.9974 0.9991 1.0071 0.9692 0.9524 0.9871 0.9905 0.9729 0.9976 0.9789 0.9869 0.9783 1.0021 0.9780 0.9759 0.9651 0.0098
0.9943 0.9658 0.9638 1.0056 0.9949 0.9949 0.9963 0.9723 0.9564 0.9881 0.9922 0.9752 0.9967 0.9785 0.9869 0.9655 1.0029 0.9790 0.9679 0.9699 0.0103
Table 9 Controller setting for load factor of 1.05. Control variable
Load factor 1.05 OPT
RBNN
T5 T6 T7 T8 T9 T10 T11 Qstatcom V1 V2 V3 V4
0.9500 1.0000 1.0000 1.0000 1.0000 0.9750 1.0000 1.8500 1.0250 0.9650 1.0200 1.0000
0.9495 1.0000 1.0000 1.0003 1.0003 0.9756 1.0000 1.8479 1.0221 0.9665 1.0179 1.0022
Table 10 Voltage profile at the load buses for a load factor of 1.05. Load bus
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 P
(ViVdes)2
Voltages (load factor 1.05) OPT
RBNN
0.9970 0.9636 0.9722 1.0098 0.9990 1.0019 1.0063 0.9723 0.9601 0.9862 0.9860 0.9658 0.9930 0.9720 0.9771 0.9781 0.9976 0.9761 0.9887 0.9819 0.0090
0.9941 0.9610 0.9699 1.0078 0.9990 1.0019 1.0063 0.9725 0.9603 0.9851 0.9870 0.9665 0.9917 0.9704 0.9773 0.9776 0.9989 0.9750 0.9887 0.9820 0.0095
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S. Sumathi, Bansilal / Electrical Power and Energy Systems 64 (2015) 536–541
CASE 2: load factor of 1.05. Table 9 shows the controller setting recommendations under line outage conditions given by neural network and optimization technique for a load factor of 1.05. It can be seen from Table 9 that the maximum error in the recommendations by the neural network is in excitation of generator 1 and the error is 0.0029pu. In case of transformer tap settings, a small variation in the recommendations has no significant effect on the system operation, because the transformer taps are varied in steps. Table 10 shows the voltage profile at all the load buses with the controller settings provided by optimization technique and Artificial Neural Network for the load factor of 1.05 with line outage. Table 10 shows that the objective function value obtained by the optimization technique is 0.0090, whereas the value of objective function obtained with the controller setting given by radial basis function neural network is 0.0095 which is comparable with the recommendations provided by optimization technique. The error in the value of objective function is 5.5%.
Defining
2 @V gþ1 @T
6 1 6 H ¼ 6 ... 4
@V n @T 1
@V gþ1 @T t
@V gþ1 @V 1
.. .
.. .
.. .
@V n @T t
@V n @ r1
@V n @V g
2
@V gþ1 @Q stat
3
7 .. 7 . 7 5
ðA:3Þ
@V n @Q stat
3 V gþ1ðacsÞ 7 .. 7 . 5 V nðactÞ
V gþ1ðdesÞ
6 rn JðXÞ ¼ 2Ht 6 4 V nðdesÞ
ðA:4Þ
To make rn JðXÞ ¼ 0, the correction to be applied to the control variable using Newton method are
DX ¼
1 @ rx JðXÞ ½rx JðXÞ @X
ðA:5Þ
The jacobian of rX JðXÞ is calculated by assuming H as a constant matrix.
2
3 V gþ1ðcalÞ 7 .. 7 . 5
V gþ1ðdesÞ
6 @ rX JðXÞ @ ¼ ½2Ht 6 4 @X @X V nðdesÞ
ðA:6Þ
V nðcalÞ
@ rX JðXÞ ¼ 2½Ht ½H @X
ðA:7Þ
Hence substituting Eqs. (A.6) and (A.7) in Eq. (A.5), we obtain,
2
2
V gþ1ðdesÞ
6 1 6 t6 DX ¼ ½2½Ht ½H 6 42½H 4 V nðdesÞ 2
V gþ1ðdesÞ
6 ½Ht HDX ¼ ½Ht 6 4
Appendix
@V gþ1 @V g
We have
Conclusion Prototype Artificial Neural Networks are developed for the coordinated control of voltage controlling devices, to achieve minimum voltage deviation in the power system. One Radial Basis function Neural Network is developed for normal operating condition of the power system and the other neural network is developed for the power system under single transmission line outage. The performances of both the networks are evaluated under different loading conditions. Since neural networks are trained off line, networks can be developed for critical contingency conditions of the system. Such Artificial Neural Networks can be used as decision aid tool by the operators of the power system in Energy Control Centers.
V nðdesÞ
33 V gþ1ðcalÞ 77 .. 77 . 55
V nðcalÞ
3 V gþ1ðcalÞ 7 .. 7 . 5
ðA:8Þ
ðA:9Þ
V nðcalÞ
Least square optimization technique The optimization technique used is Least Square Minimization. The control variable considered are, reactive power injection by the STATCOM, Tap positions of OLTC transformers and generator excitation. Let
2
The objective function is to minimize the voltage deviations from the desired value. Hence the objective function is expressed as: N X
ðV iðdesÞ V iðactÞ Þ2
ðA:1Þ
i¼gþ1
½X ¼ ½DT 1 ; DT 2 ; . . . DT t ; DV 1 ; DV 2 ; . . . DV g ; DQ stat
ðA:10Þ
where
½DQ G ¼ ½DQ 1 ; . . . ; DQ g t ½DQ s ¼ ½DQ stat t ½DQ r ¼ ½DQ gþ2 ; . . . ; DQ n t ½DT T ¼ ½DT 1 ; . . . ; DT t t ½DV G ¼ ½DV 1 ; . . . ; DV g t
where X is the vector of control variable. t
The elements of H matrix cannot be defined directly and so is evaluated as a sensitivity matrix. The relation between the net reactive power change at any bus due to change in the transformer tap setting and voltage magnitudes can be written as,
3 2 3 2 3 DT T DQ G A1 A2 A3 A4 6 7 6 7 6 7 6 DV G 7 A7 A8 56 7 4 DQ s 5 ¼ 4 A5 A6 4 DV s 5 A9 A10 A11 A12 DQ r DV r
n – Total number of the buses in the system. 1,2,. . ., g – Generator buses. g + 1 – STATCOM bus. g + 2,. . ., n – Remaining load buses. t – Number of OLTC transformers.
Min JðXÞ ¼
Computation of H matrix
½DV S ¼ ½DV stat t ðA:2Þ
where DTi – change in transformer tap; DVi – change in generator excitation; DQstat – change in reactive power injection by STATCOM. The condition for minimization of J(X) is Dn JðXÞ ¼ 0
½DV r ¼ ½DV gþ2 ; . . . ; DV n t The sub matrices A1 to A12 are the corresponding terms of the partial derivatives @Q =@T and @Q =@V. Transferring the control variable to RHS and the dependent variables to LHS we obtain,
S. Sumathi, Bansilal / Electrical Power and Energy Systems 64 (2015) 536–541
2
3
2 3 DQ G DT T S1 S2 6 7 6 7 4 DV s 5 ¼ 4 DV G 5 S3 S4 DV r DQ s
ðA:11Þ
541
matrix of size (s)(s). Matrices S3 and S4 are voltage sensitivities of load busses and matrices S1 and S2 are sensitivities of generator Q injections to different reactive power controllers. References
where
S1 ¼ ½B1 þ ½B2½B41 ½B3 S2 ¼ ½B2½B41 ½B5 H ¼ ½S3 S4 S3 ¼ ½B41 ½B3 S4 ¼ ½B41 ½B5 B1 ¼ ½A1 A2 B2 ¼ ½A3 A4 A5 A6 B3 ¼ A9 A10 A7 A8 B4 ¼ A11 A12 1 B5 ¼ 0 Matrix S1 is of size (g)(t+g), S2 is of size (g)(s), S3 is of size (s+r)(t+g), S4 is of size (s+r)(s), H is of size (s+r)(t+g+s), B1 is of size (g)(t+g), B2 is of size (g)(s+r), B3 is of size (s+r)(t+g), B4 is of size (s+r)(s+r), B5 is of size (s+r)(s) and I is an identity
[1] Hingorani Narain G, Gyugyi Laszlo. Understanding FACTS: concepts and technology of flexible AC transmission systems. IEEE Press; 2000. [2] Zhang Xiao-Ping, Rehtanz Christian, Pal Bikash. Flexible AC transmission systems modeling and control. Springer – Verlag Heidelberg; 2006. [3] Thukaram Bansilal D, Parthasarathy K. Optimal reactive power dispatch algorithm for voltage stability improvement. Electr Power Energy Syst 1996;18(7):461–8. [4] Rafinia Ali, Moshtagh Jamal. A new approach to fault detection in three phase underground distribution system using combination of wavelet analysis with ANN and FLS. Int J Electr Power Energy Syst 2014;55:261–74. [5] Rahmatian M, Vahidi B, Ghanizadeh AJ, Gharehpetian GB, Alehosseini HA. Insulation failure detection in transformer winding using cross correlation technique with ANN and k-NN regression method during impulse test. Electr Power Energy Syst 2013;53:209–18. [6] Su Ming-shou, Chen Jiann-Fuh, Lin Yu-Hsun. Phase determination of partial discharge source in three phase transmission line using discrete wavelet transform and probabilistic neural network. Electr Power Energy Syst 2013;51:27–34. [7] Nagalakshmi S, Kamaraj N. Online evaluation of lodability limit for pool model with TCSC using back propagation neural network. Electr Power Energy Syst 2013;47:52–60. [8] Karami A, Esmaili SZ. Transient stability assessment of power system described with detailed model using neural networks. Electr Power Energy Syst 2013;45:279–92. [9] Zayandehroodi Hadi, Mohmed Azah, Shareef Hussain, Farhoodnea Masoud. A novel neural network and backtracking based protection co-ordination scheme for distribution system with distributed generation. Electr Power Energy Syst 2013;43:868–79.
Contents lists available at ScienceDirect
Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes
Artificial Neural Network for coordinated control of STATCOM, generator excitation and tap changing transformer S. Sumathi a,⇑, Bansilal b a b
RNS Institute of Technology, Bangalore, India The National institute of Technology, Mysore, India
a r t i c l e
i n f o
Article history: Received 29 September 2013 Received in revised form 29 June 2014 Accepted 14 July 2014
Keywords: STATCOM Tap changing transformer Generator excitation Artificial Neural Network (ANN)
a b s t r a c t Control of voltage in a power system under varying load conditions can be achieved by varying the generator excitation, changing the tap position of transformers and by varying the reactive power injection or absorption at the shunt compensated buses. Proper coordination of these controllers is essential for the effective operation of the power system. This paper deals with the development of Artificial Neural Network which gives the voltage controller settings, such that the voltage deviations at the load buses are minimum. Ó 2014 Elsevier Ltd. All rights reserved.
Introduction Voltage control is an important aspect in the day to day operation of power systems. The voltage control can be achieved by various reactive power controlling devices. Present day power systems use FACTS devices for the control of real and reactive power in the system. The shunt FACTS devices such as Static VAR Compensator (SVC), Static Synchronous Compensator (STATCOM) are the devices commonly used for the control of reactive power and hence used for the control of voltage in the system [1,2]. The coordinated control of these FACTS devices with the generator excitation system and tap changing transformers is essential for the control of voltages at the load buses. Hence the objective is to find the settings of these control devices so as to minimize the voltage deviations at the load buses. Generally non linear optimization techniques are used to find the controller settings [3]. Artificial Neural Network is one of the important artificial intelligence tools which can be used for non linear function mapping. A trained ANN can be used to model any function approximation in real time. In literature, we find many Artificial Neural Network applications for the monitoring and control of power system operation.
Artificial Neural Networks are used to detect the type and location of fault in distribution system [4]. Artificial Neural Networks find application in insulation failure detection in transformer windings [5]. ANN are also used in locating the phase of partial discharge in transmission line [6]. They are also used in evaluation of loadability limit of systems with TCSC [7]. Artificial Neural Networks find application in transient stability analysis of power system [8]. Artificial Neural Networks are developed even for protection co-ordination schemes [9]. In this paper ANNs are developed which give the controller settings for minimum voltage deviation under normal condition and under contingency condition. Prototype Artificial Neural Networks are developed for a 24 bus EHV power system. The single line diagram of the power system is shown in Fig. 1. The power system considered for analysis has 4 generators, 7 tap changing transformers at the load buses and a STATCOM connected at bus 24. The developed ANN take the load factor as input and gives the generator excitation, tap position of the transformers and the reactive power to be supplied by the STATCOM as output. The data for training the ANN is obtained by the conventional non linear optimization technique. Formulation of problem
⇑ Corresponding author. Tel.: +91 98801 29596. E-mail addresses: [email protected] (S. Sumathi), bansilal_nie@ rediffmail.com ( Bansilal). http://dx.doi.org/10.1016/j.ijepes.2014.07.056 0142-0615/Ó 2014 Elsevier Ltd. All rights reserved.
For the given loading condition the non linear optimization problem is to minimize the voltage deviations at the load buses. Hence the objective function is expressed as:
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S. Sumathi, Bansilal / Electrical Power and Energy Systems 64 (2015) 536–541
radial basis function neural networks are developed, corresponding to normal condition of the power system network and with line outage condition. The developed Artificial Neural Networks take the load factor as input and give the controller settings as output. The output includes the tap position of the transformers, reactive power injection by the STATCOM, and the voltages of the generator buses. The data for training the Artificial Neural Network is obtained by running the optimization program, for different load factors. Radial basis function neural network for normal operating condition Data for training the radial basis function neural network The load factor is varied from 0.9 to 1.1 in steps of 0.02. For the non linear least square optimization technique the tap position of tap changing transformers are initialized to 1.00. The value of reactive power injection by the STATCOM is initialized to 0.15pu and the generator excitations are initialized to 1.00pu. The values of control variables obtained from non linear optimization technique, are used for training the RBNN. Table 1 shows part of the data used for training the radial basis function network corresponding to normal operating condition of the power system. The developed RBNN has 11 neurons in the radial basis layer. It has 12 neurons in the output layer corresponding to 12 control variables.
Fig. 1. Single line diagram of 24 bus system.
Minimize
JðXÞ ¼
L X ½V iðdesÞ V iðactÞ 2
ð1Þ
i¼1
Where L is number of load buses; X is the vector of control variables; Vi(des) is the desired voltage at bus i; Vi(act) is the actual voltage at bus i. The non linear least square optimization technique is used for the solution of this non linear optimization problem as explained in Appendix. The control variables are tap position of the transformers, excitation of the generators and the reactive power injection by the STATCOM. Algorithm for solving non linear optimization problem 1. 2. 3. 4. 5. 6.
Read the system data and the load multiplier. Initialize control variables. Form network matrices. Perform power flow with controller settings. Compute the voltage error, and the objective function. If the value of objective function is within the specified tolerance go to step 8. 7. Else solve for control variables and adjust it for suitable step size and go to step 3. 8. Print the results. Development of Artificial Neural Network An Artificial Neural Network (ANN) is an important artificial intelligence tool, which gives fast and acceptable solution in real time. ANNs are composed of simple elements operating in parallel. It is composed of a large number of highly interconnected processing elements that are analogous to neurons and are tied together with weighted connections that are analogous to synapses. Once trained the Artificial Neural Network is able to provide sufficiently accurate recommendations in a very short time suitable for on-line applications in energy control centers. A Radial Basis function Neural Networks (RBNN), one of the standard ANN which has one input layer, one hidden layer and an output layer. The hidden layer uses radial symmetric activation function such as Gaussian activation function. In this paper two
Validation of the radial basis function neural network CASE 1: load factor of 0.95. Table 2 shows the recommendations for different controller settings, provided by the non linear least square optimization technique and the predictions made by the developed radial basis function neural network for a load factor of 0.95. It can be observed from Table 2 that the recommendations provided by the radial basis function neural network is comparable with the results obtained from conventional non linear least square optimization technique. The recommendations provided by the radial basis function neural network for the reactive power injection is 0.1720 against 0.1500 provided by the optimization technique. The error in the recommendations of the neural network is just 0.022pu (2.2MVar). It can be seen that the recommendations provided by the radial basis function neural network for generator excitations are comparable with that of optimization technique. The error is found to be maximum in the recommendation of excitation of generator 1 (V1). And this error is just 0.0029pu. In case of transformer tap settings, a small variation in the recommendations has no significant effect on the system operation, because the transformer taps are varied in steps. Table 3 shows the voltage profile at all the load buses with the controller settings provided by optimization technique and radial Table 1 Data for training the radial basis function neural network under normal operating condition. Control variable
T5 T6 T7 T8 T9 T10 T11 Qstatcom V1 V2 V3 V4
Load factor 0.92
0.96
1.00
1.04
1.08
0.9625 0.9875 1.0000 1.0000 1.0000 0.9875 1.0000 0.1500 1.0150 0.9850 0.9950 1.0000
0.9875 0.9875 1.0000 1.0000 1.0000 0.9875 1.0000 0.2000 1.0050 0.9950 1.0000 1.0000
0.9750 0.9875 1.0000 1.0000 1.0000 0.9875 1.0000 0.2500 1.0100 0.9900 1.0000 1.0000
0.9500 0.9875 1.0000 1.0000 1.0000 0.9875 1.0000 0.3500 1.0200 0.9800 1.0000 1.0000
0.9500 1.0000 1.0000 1.0000 1.0000 0.9750 1.0000 0.8000 1.0250 0.9600 1.0100 1.0000
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S. Sumathi, Bansilal / Electrical Power and Energy Systems 64 (2015) 536–541
Table 2 Controller setting recommendations for load factor of 0.95. Control variable
T5 T6 T7 T8 T9 T10 T11 Qstatcom V1 V2 V3 V4
Load factor of 0.95 OPT tech
RBNN
0.9875 0.9875 1.0000 1.0000 1.0000 0.9875 1.0000 0.1500 1.0050 0.9950 1.0000 1.0000
0.9804 0.9875 1.0000 1.0000 1.0000 0.9859 1.0000 0.1720 1.0079 0.9932 0.9999 1.0000
Table 3 Voltage profile at the load buses for a load factor of 0.95. Load bus
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 P
(ViVdes)2
Voltages (load factor 0.95) OPT tech
RBNN
0.9863 0.9673 0.9407 1.0138 1.0251 1.0346 1.0411 1.0063 0.9969 1.0184 1.0142 0.9972 1.0158 0.9975 1.0050 0.9971 1.0160 1.0096 1.0153 1.0004 0.0100
0.9907 0.9708 0.9518 1.0161 1.0255 1.0357 1.0427 1.0088 0.9996 1.0209 1.0157 0.9987 1.0181 0.9998 1.0067 1.0005 1.0170 1.0122 1.0179 1.0033 0.0092
Table 4 Controller setting recommendations for load factor of 1.05. Control variable
T5 T6 T7 T8 T9 T10 T11 Qstatcom V1 V2 V3 V4
CASE 2: load factor 1.05. Table 4 shows the recommendations for different controller settings, provided by the non linear least square optimization technique and the recommendations provided by the developed radial basis function neural network for a load factor of 1.05. It can be seen from Table 4 that the recommendations provided by the RBNN for the reactive power injection is 0.5052pu against 0.4000pu provided by the optimization technique. The error in the recommendations of the neural network is just 0.1052pu. It can be seen that the recommendations provided by the neural network for generator excitations are comparable with that of optimization technique. The error is maximum in the excitation of generator 2 (V2). And this error is just 0.0052pu. In case of transformer tap settings, a small variation in the recommendations has no significant effect on the system operation, because the transformer taps are varied in steps. Table 5 shows the voltage profile at all the load buses with the controller settings provided by optimization technique and Artificial Neural Network for the load factor of 1.05. Table 5 also shows that the minimum value of objective function achieved with the controller settings given by non linear optimization technique is 0.0097 where as the value of objective function obtained with the controller settings predicted by the developed radial basis function neural network is 0.0090, indicating better voltage control of the power system network. Radial basis function neural network for line outage condition Another radial basis function neural network to recommend the various controller settings to achieve minimum voltage deviation under contingency condition is also developed. Here the line outage of transmission line connected between bus 12 and bus 17 is considered as it is found to be one of the critical contingency. Non linear least square optimization technique is used to obtain the various controller settings at various loading conditions with line outage. Data for training the radial basis function network under line outage (12–17) condition The data obtained from optimization technique is used to develop an Artificial Neural Network based on radial basis function.
Table 5 Voltage profile at the load buses for a load factor of 1.05.
Load factor 1.05 OPT tech
RBNN
0.9500 0.9875 1.0000 1.0000 1.0000 0.9875 1.0000 0.4000 1.2050 0.9750 1.0000 1.0000
0.9509 0.9941 1.0000 1.0000 1.0000 0.9855 1.0000 0.5052 1.0217 0.9698 1.0015 1.0000
basis function neural network for the load factor of 0.95. Table 3 also shows that the minimum value of objective function achieved with the controller settings given by non linear optimization technique is 0.0100 where as the value of objective function obtained with the controller settings predicted by the developed radial basis function neural network is 0.0092, indicating better voltage control of the power system.
Load bus
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 P
(ViVdes)2
Voltages (load factor 1.05) OPT tech
RBNN
0.9956 0.9595 0.9676 1.0044 1.0040 1.0074 1.0105 0.9763 0.9636 0.9939 0.9908 0.9707 0.9926 0.9717 0.9799 0.9679 1.0004 0.9838 0.9817 0.9683 0.0097
0.9928 0.9579 0.9649 1.0039 1.0016 1.0064 1.0105 0.9784 0.9665 0.9947 0.9920 0.9720 0.9932 0.99723 0.9806 0.9707 1.0011 0.9847 0.9847 0.9723 0.0090
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S. Sumathi, Bansilal / Electrical Power and Energy Systems 64 (2015) 536–541 Table 6 Data for training the radial basis function neural network under line outage (12–17) condition. Control variable
T5 T6 T7 T8 T9 T10 T11 Qstatcom V1 V2 V3 V4
T5 T6 T7 T8 T9 T10 T11 Qstatcom V1 V2 V3 V4
Load bus
Load factor 0.92
0.96
1.00
1.04
1.08
0.9625 1.0000 1.0000 1.0000 1.0000 0.9875 1.0000 0.7000 1.0150 0.9600 1.0000 1.0000
0.9625 1.0000 1.0000 1.0000 1.0000 0.9875 1.0000 1.0500 1.0200 0.9650 1.0000 1.0000
0.9500 1.0000 1.0000 1.0000 1.0000 0.9875 1.0000 1.4500 1.0200 0.9650 1.0050 1.0000
0.9500 1.0000 1.0000 1.0000 1.0000 0.9750 1.0000 1.8500 1.0200 0.9650 1.0150 1.0000
0.9500 1.0000 1.0000 1.0000 1.0000 0.9750 1.0000 2.1000 1.0250 0.9650 1.0250 1.0050
Table 7 Controller setting recommendations for load factor of 0.95. Control variable
Table 8 Voltage profile at the load buses for a load factor of 0.95 with line outage.
Load factor 0.95 OPT tech
RBNN
0.9625 1.0000 1.0000 1.0000 1.0000 0.9875 1.0000 0.9000 1.0200 0.9650 1.0000 1.0000
0.9642 1.0000 1.0000 0.9995 0.9995 0.9865 1.0000 0.9441 1.0179 0.9638 0.9995 1.0004
To obtain the input data for the neural network the load factor of the system is varied from 0.9 to 1.1 in steps of 0.02. Table 6 shows the data used for training the network corresponding to line outage condition of the network.
Validation of the radial basis function neural network CASE 1: load factor of 0.95. Table 7 shows the recommendations for different controller settings, provided by the optimization technique and the recommendations provided by the developed radial basis function neural network for line outage conditions for a load factor of 0.95. It can be seen from Table 7 that the recommendations provided by the radial basis function neural network is comparable with the recommendations provided by the optimization technique. The maximum error is in the recommendations for reactive power injection by the STATCOM. The maximum error is only 0.021pu (2.1MVAR). The maximum value of error in the recommendations of generator excitation is 0.0021pu corresponding to generator 1. In case of transformer tap settings, a small variation in the recommendations has no significant effect on the system operation, because the transformer taps are varied in steps. Table 8 shows the voltage profile at all the load buses with the controller settings provided by optimization technique and Artificial Neural Network for the load factor of 0.95 with line outage. It can be observed from Table 8 that the value of objective function achieved with the controller settings given by optimization technique is 0.0098, whereas the value of objective function obtained with the controller settings predicted by radial basis function neural network is 0.0103. The error in the value of objective function is 5.1%.
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 P
(ViVdes)2
Voltages (load factor 0.95) OPT
RBNN
0.9963 0.9675 0.9675 1.0068 0.9974 0.9991 1.0071 0.9692 0.9524 0.9871 0.9905 0.9729 0.9976 0.9789 0.9869 0.9783 1.0021 0.9780 0.9759 0.9651 0.0098
0.9943 0.9658 0.9638 1.0056 0.9949 0.9949 0.9963 0.9723 0.9564 0.9881 0.9922 0.9752 0.9967 0.9785 0.9869 0.9655 1.0029 0.9790 0.9679 0.9699 0.0103
Table 9 Controller setting for load factor of 1.05. Control variable
Load factor 1.05 OPT
RBNN
T5 T6 T7 T8 T9 T10 T11 Qstatcom V1 V2 V3 V4
0.9500 1.0000 1.0000 1.0000 1.0000 0.9750 1.0000 1.8500 1.0250 0.9650 1.0200 1.0000
0.9495 1.0000 1.0000 1.0003 1.0003 0.9756 1.0000 1.8479 1.0221 0.9665 1.0179 1.0022
Table 10 Voltage profile at the load buses for a load factor of 1.05. Load bus
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 P
(ViVdes)2
Voltages (load factor 1.05) OPT
RBNN
0.9970 0.9636 0.9722 1.0098 0.9990 1.0019 1.0063 0.9723 0.9601 0.9862 0.9860 0.9658 0.9930 0.9720 0.9771 0.9781 0.9976 0.9761 0.9887 0.9819 0.0090
0.9941 0.9610 0.9699 1.0078 0.9990 1.0019 1.0063 0.9725 0.9603 0.9851 0.9870 0.9665 0.9917 0.9704 0.9773 0.9776 0.9989 0.9750 0.9887 0.9820 0.0095
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CASE 2: load factor of 1.05. Table 9 shows the controller setting recommendations under line outage conditions given by neural network and optimization technique for a load factor of 1.05. It can be seen from Table 9 that the maximum error in the recommendations by the neural network is in excitation of generator 1 and the error is 0.0029pu. In case of transformer tap settings, a small variation in the recommendations has no significant effect on the system operation, because the transformer taps are varied in steps. Table 10 shows the voltage profile at all the load buses with the controller settings provided by optimization technique and Artificial Neural Network for the load factor of 1.05 with line outage. Table 10 shows that the objective function value obtained by the optimization technique is 0.0090, whereas the value of objective function obtained with the controller setting given by radial basis function neural network is 0.0095 which is comparable with the recommendations provided by optimization technique. The error in the value of objective function is 5.5%.
Defining
2 @V gþ1 @T
6 1 6 H ¼ 6 ... 4
@V n @T 1
@V gþ1 @T t
@V gþ1 @V 1
.. .
.. .
.. .
@V n @T t
@V n @ r1
@V n @V g
2
@V gþ1 @Q stat
3
7 .. 7 . 7 5
ðA:3Þ
@V n @Q stat
3 V gþ1ðacsÞ 7 .. 7 . 5 V nðactÞ
V gþ1ðdesÞ
6 rn JðXÞ ¼ 2Ht 6 4 V nðdesÞ
ðA:4Þ
To make rn JðXÞ ¼ 0, the correction to be applied to the control variable using Newton method are
DX ¼
1 @ rx JðXÞ ½rx JðXÞ @X
ðA:5Þ
The jacobian of rX JðXÞ is calculated by assuming H as a constant matrix.
2
3 V gþ1ðcalÞ 7 .. 7 . 5
V gþ1ðdesÞ
6 @ rX JðXÞ @ ¼ ½2Ht 6 4 @X @X V nðdesÞ
ðA:6Þ
V nðcalÞ
@ rX JðXÞ ¼ 2½Ht ½H @X
ðA:7Þ
Hence substituting Eqs. (A.6) and (A.7) in Eq. (A.5), we obtain,
2
2
V gþ1ðdesÞ
6 1 6 t6 DX ¼ ½2½Ht ½H 6 42½H 4 V nðdesÞ 2
V gþ1ðdesÞ
6 ½Ht HDX ¼ ½Ht 6 4
Appendix
@V gþ1 @V g
We have
Conclusion Prototype Artificial Neural Networks are developed for the coordinated control of voltage controlling devices, to achieve minimum voltage deviation in the power system. One Radial Basis function Neural Network is developed for normal operating condition of the power system and the other neural network is developed for the power system under single transmission line outage. The performances of both the networks are evaluated under different loading conditions. Since neural networks are trained off line, networks can be developed for critical contingency conditions of the system. Such Artificial Neural Networks can be used as decision aid tool by the operators of the power system in Energy Control Centers.
V nðdesÞ
33 V gþ1ðcalÞ 77 .. 77 . 55
V nðcalÞ
3 V gþ1ðcalÞ 7 .. 7 . 5
ðA:8Þ
ðA:9Þ
V nðcalÞ
Least square optimization technique The optimization technique used is Least Square Minimization. The control variable considered are, reactive power injection by the STATCOM, Tap positions of OLTC transformers and generator excitation. Let
2
The objective function is to minimize the voltage deviations from the desired value. Hence the objective function is expressed as: N X
ðV iðdesÞ V iðactÞ Þ2
ðA:1Þ
i¼gþ1
½X ¼ ½DT 1 ; DT 2 ; . . . DT t ; DV 1 ; DV 2 ; . . . DV g ; DQ stat
ðA:10Þ
where
½DQ G ¼ ½DQ 1 ; . . . ; DQ g t ½DQ s ¼ ½DQ stat t ½DQ r ¼ ½DQ gþ2 ; . . . ; DQ n t ½DT T ¼ ½DT 1 ; . . . ; DT t t ½DV G ¼ ½DV 1 ; . . . ; DV g t
where X is the vector of control variable. t
The elements of H matrix cannot be defined directly and so is evaluated as a sensitivity matrix. The relation between the net reactive power change at any bus due to change in the transformer tap setting and voltage magnitudes can be written as,
3 2 3 2 3 DT T DQ G A1 A2 A3 A4 6 7 6 7 6 7 6 DV G 7 A7 A8 56 7 4 DQ s 5 ¼ 4 A5 A6 4 DV s 5 A9 A10 A11 A12 DQ r DV r
n – Total number of the buses in the system. 1,2,. . ., g – Generator buses. g + 1 – STATCOM bus. g + 2,. . ., n – Remaining load buses. t – Number of OLTC transformers.
Min JðXÞ ¼
Computation of H matrix
½DV S ¼ ½DV stat t ðA:2Þ
where DTi – change in transformer tap; DVi – change in generator excitation; DQstat – change in reactive power injection by STATCOM. The condition for minimization of J(X) is Dn JðXÞ ¼ 0
½DV r ¼ ½DV gþ2 ; . . . ; DV n t The sub matrices A1 to A12 are the corresponding terms of the partial derivatives @Q =@T and @Q =@V. Transferring the control variable to RHS and the dependent variables to LHS we obtain,
S. Sumathi, Bansilal / Electrical Power and Energy Systems 64 (2015) 536–541
2
3
2 3 DQ G DT T S1 S2 6 7 6 7 4 DV s 5 ¼ 4 DV G 5 S3 S4 DV r DQ s
ðA:11Þ
541
matrix of size (s)(s). Matrices S3 and S4 are voltage sensitivities of load busses and matrices S1 and S2 are sensitivities of generator Q injections to different reactive power controllers. References
where
S1 ¼ ½B1 þ ½B2½B41 ½B3 S2 ¼ ½B2½B41 ½B5 H ¼ ½S3 S4 S3 ¼ ½B41 ½B3 S4 ¼ ½B41 ½B5 B1 ¼ ½A1 A2 B2 ¼ ½A3 A4 A5 A6 B3 ¼ A9 A10 A7 A8 B4 ¼ A11 A12 1 B5 ¼ 0 Matrix S1 is of size (g)(t+g), S2 is of size (g)(s), S3 is of size (s+r)(t+g), S4 is of size (s+r)(s), H is of size (s+r)(t+g+s), B1 is of size (g)(t+g), B2 is of size (g)(s+r), B3 is of size (s+r)(t+g), B4 is of size (s+r)(s+r), B5 is of size (s+r)(s) and I is an identity
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