Transmission Lines Switching Overvoltages

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Transmission Lines Switching Overvoltages Evaluation Using. Radial Basis ... MATLAB/Simulink-based simulation tool [10], [11] is used for computation of both ...
Advances in Computational Mathematics and its Applications Vol. 1, No. 1, March 2012 Copyright © World Science Publisher, United States www.worldsciencepublisher.org

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Transmission Lines Switching Overvoltages Evaluation Using Radial Basis Function Neural Network *1,2

Iman Sadeghkhani, 3Nima Haratian, 1Arezoo Mortazavian, 4Seyed Abbas Taher 1

Department of Electrical Engineering, Islamic Azad University, Najafabad Branch, Najafabad, Iran Department of Electrical and Computer Engineering, Isfahan University of Technology, Isfahan, Iran 3 Department of Electrical Engineering, Allameh Feiz Kashani Institute of Higher Education, Kashan, Iran 4 Department of Electrical Engineering, University of Kashan, Kashan, Iran Email: [email protected], [email protected], [email protected], [email protected] 2

Abstract – In this paper, a radial basis function (RBF) neural network based approach is used to estimate transient overvoltages on transmission lines during power system restoration. In the early stages of the restoration, the transmission lines are lightly loaded; resonance therefore is lightly damped, which in turn means the resulting resonance voltages may be very high. Developed Artificial Neural Network (ANN) is trained with equivalent circuit parameters of the network as input parameters; therefore trained ANN has proper generalization capability. The simulated results for 39-bus New England test system, show that the proposed technique can estimate the peak values of switching overvoltages with acceptable accuracy. Keywords – Artificial neural networks, nonlinear input-output mapping, power system restoration, radial basis function (RBF), switching overvoltages, transmission lines energization.

1. Introduction In most countries, the main step in the process of power system restoration, following a complete/partial blackout, is energization of primary restorative transmission lines. In recent years, due to economic competition and deregulation, power systems are being operated closer and closer to their limits. At the same time, power systems have increased in size and complexity. Both factors increase the risk of major power outages. After a blackout, power needs to be restored as quickly and reliably as possible and, consequently, detailed restoration plans are necessary [1]-[5]. Switching overvoltage is a primary importance in insulation co-ordination for extra high voltage (EHV) lines. The objective of simulating switching overvoltage is to help for a proper insulation co-ordination and would lead to minimize damage and interruption to service as a consequence of steady state, dynamic and transient overvoltage [6]-[9]. One of the major concerns, especially at the beginning of a system restoration, is related to temporary overvoltages. During the early stages of the restoration procedures following a partial or complete blackout of the power system, the system is lightly loaded and resonance conditions are different from the ones at normal operation. The magnitude and shape of the switching overvoltages vary with the system parameters and network configuration. Even with the same system parameters and network configuration, the switching overvoltages are highly dependent on the characteristics

of the circuit breaker operation and the point-on-wave where the switching operation takes place. In this paper power system blockset (PSB), a MATLAB/Simulink-based simulation tool [10], [11] is used for computation of both switching and temporary overvoltages. This paper presents the artificial neural network (ANN) application for estimation of peak overvoltages under switching transients during transmission lines energization. A tool such as proposed in this paper that can give the maximum switching overvoltage will be helpful to the operator. It can be used as training tool for the operators. The proposed ANN is expected to learn many scenarios of operation. To give the maximum peak overvoltage in a shortest computational time that is the requirement during online operation of power systems. In this paper we have considered the most important aspects, which influence the transient overvoltages such as voltage at sending end of transmission line before switching, equivalent resistance, equivalent inductance, equivalent capacitance, switching angle, line length, line capacitance, and shunt reactor capacity. This information will help the operator to select the proper sequence of transmission lines to be energized safely with transients appearing safe within the limits. Since ANN is trained with equivalent circuit parameters, thus it's applicable to every studied system. In fact, proposed ANN is trained just once with a simple circuit that includes equivalent circuit parameters. Therefore, developed ANN can estimate overvoltage peak for every studied system. Results of the studies are presented for 39-bus New England test system to illustrate the proposed approach.

I. Sadeghkhani, et al., ACMA, Vol. 1, No. 1, pp. 17-22, March 2012

2. Study System Modeling

2.8 2.4 2

Voltage [p.u.]

In this paper the simulations are carried out employing PSB [10]. The simulation tool has been developed using state variable approach and runs in the MATLAB/Simulink environment. This program has been compared with other popular simulation packages (EMTP and Pspice) in [11]. The user friendly graphical interfaces of PSB enable faster development for power system transient analysis.

1.6 1.2 0.8 0.4 0 -0.4 -0.8 -1.2 -1.6 -2

2.1. Generator Model In [12] generators have been modeled by generalized Park’s model that both electrical and mechanical part are thoroughly modeled, but it has been shown that a simple static generator model containing an ideal voltage source behind the sub-transient inductance in series with the armature winding resistance can be as accurate as the Park model. Thus in this work, generators are represented by the static generator model. Phases of voltage sources are determined by the load flow results.

18

-2.4

0

All of the loads and shunt devices are modeled as constant impedances.

3. Switching Overvoltages during Restoration The sample system considered for explanation of the proposed methodology is a 400 kV EHV network shown in Fig. 1. The normal peak value of any phase voltage is 400 2/ 3 kV and this value is taken as base for voltage p.u. In the system studies 400 kV line-to-line base voltage and 100 MVA as a base power is considered. Fig. 2 shows the switching transient at bus 3 when transmission line is energized.

0.06

0.08

0.1

Figure 2. Transient overvoltage at bus 3 after switching of transmission line.

In practical system a number of factors affect the overvoltages factors due to energization or reclosing. In this paper following parameters is considered: Voltage at sending bus of transmission line before switching Equivalent resistance of the network Equivalent inductance of the network Equivalent capacitance of the network Closing time of the circuit breaker poles Line length Line capacitance Shunt reactor capacity Source voltage affects the overvoltage strongly. Fig. 3 shows the effect of source voltage on overvoltage at different line capacitance. Fig. 4 shows the effect of line length on overvoltages at different equivalent inductance. Also, Fig. 5 shows the effect of switching angle on overvoltage at different equivalent resistance. Controlled switching of high-voltage AC circuit breakers has become a commonly accepted means of controlling switching transients in power systems [5]. Fig. 6 shows the effect of shunt reactor capacity on overvoltage at different equivalent capacitance.

2.75 CLine = 1.1875e-8 F/k m 2.65 Voltage [p.u.]

2.3. Load and Shunt Devices Model

0.04

Time [s]

2.2. Transmission-Line Model Transmission lines are described by the distributed line model. This model is accurate enough for frequency dependent parameters, because the positive sequence resistance and inductance are fairly constant up to approximately 1 KHz [13] which cover the frequency range of harmonic overvoltages phenomena.

0.02

CLine = 1.2865e-8 F/k m

2.55 2.45 2.35 2.25 0.95

Figure 1. Study system for transmission line energization. G: generator, Reqv: equivalent resistance, Leqv: equivalent inductance, and Ceqv: equivalent capacitance.

1 1.05 Source Voltage [p.u.]

1.1

Figure 3. Overvoltage peak at bus 3 as source voltage while equivalent resistance 0.003 p.u., equivalent inductance 0.03 p.u., equivalent capacitance 1.2825 p.u., switching angle 54°, line length 300 km, and shunt reactor capacity 10 MVAR. C Line is line capacitance.

I. Sadeghkhani, et al., ACMA, Vol. 1, No. 1, pp. 17-22, March 2012

3.2 Leqv = 0.02 p.u.

Voltage [p.u.]

3.1 3

Leqv = 0.035 p.u.

2.9 2.8 2.7 2.6 2.5 2.4 2.3 2.2 150

200

250 Line Length [km]

300

350

Figure 4. Overvoltage peak at bus 3 as line length while equivalent source voltage 1.1 p.u., equivalent resistance 0.003 p.u., equivalent capacitance 1.2825 p.u., switching angle 54°, line capacitance 1.237e8 F/km, and shunt reactor capacity 10 MVAR. XLeqv is equivalent inductance. 2

Voltage [p.u.]

1.9 1.8 1.7 Reqv = 0.003 p.u.

1.6

Reqv = 0.006 p.u. 1.5

0

10

20

30 40 50 60 Switching Angle [deg.]

70

80

90

Figure 5. Overvoltage peak at bus 3 as switching angle while equivalent source voltage 1 p.u., equivalent inductance 0.025 p.u., equivalent capacitance 1.8912 p.u., line length 250 km, line capacitance 1.237e-8 F/km, and shunt reactor capacity 40 MVAR. Reqv is equivalent resistance.

1.9

Voltage [p.u.]

4. Radial Basis Function Neural Network Fig. 7 shows the structure of the RBF neural network, which comprises of three layers. The hidden layer possesses an array of neurons, referred to as the computing units. The number of such units can be varied depending on user’s requirement [15], [16]. Different basis functions like spline, multiquadratic, and Gaussian functions have been studied, but the most widely used one is the Gaussian type. In comparison to the other types of neural network used for pattern classification like back propagation feedforward networks, the RBF network requires less computation time for learning and has a more compact topology. The Gaussian RBF is found not only suitable in generalizing a global mapping but also in refining local features without altering the already learned mapping. Each hidden unit in the network has two parameters called a center ( ) and a width ( ) associated with it. The response of one such hidden unit to the network input is expressed as xn

1

exp

2 k

xn

2 k

(1)

Ceqv = 2.5 p.u.

1.7 1.6 1.5 1.4 20

regarded independently from the other important influencing factors. The magnitude of the overvoltages normally does not depend directly on any single isolated parameter and a variation of one parameter can often alter the influence of another parameter, in other words there exists an interaction between the various system and breaker parameters. This forbids the derivation of precise generalized rule of simple formulae applicable to all cases [14]. So an ANN can help to estimate the peak values of switching overvoltages generated during transmission line energization. An ANN is programmed by presenting it with training set of input/output patterns from which it then learns the relationship between the inputs and outputs.

k

Ceqv = 0.065 p.u. 1.8

19

30 40 50 60 70 Shunt Reactor Capacity [MVAR]

80

Figure 6. Overvoltage peak at bus 3 as shunt reactor capacity while equivalent source voltage 1 p.u., equivalent resistance 0.004 p.u., equivalent inductance 0.025 p.u., switching angle 18°, line length 250 km, and line capacitance 1.237e-8 F/km. Ceqv is equivalent capacitance.

As discussed above for an existing system the main factors witch affect the peak values of switching overvoltage are at voltage at sending bus of transmission line before switching, equivalent resistance, equivalent inductance, equivalent capacitance, switching angle, line length, line capacitance, and shunt reactor capacity. Here it should be mentioned that a single parameter often cannot be

where k is the center vector for kth hidden unit, k is the width of the Gaussian function, and || || denotes the Euclidean norm. The output layer comprises a number of nodes depending on the number of fault types to be classified which perform simple summation. The response of each hidden unit (1) is scaled by its connecting weights ( ’s) to the output nodes and then summed to produce the overall network output. The overall network output is expressed as N

f m ( xn )

mk k ( x n )

mo

(2)

k 1

where k indicates the total number of hidden neurons in the network, mk is the connecting weight of the kth hidden unit to mth output node, and mo is the bias term for the corresponding mth output neuron. The learning process of the RBFNN involves with the allocation of new hidden units and tuning of network parameters. The learning process is terminated when the output error goes under the defined threshold [17].

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Figure 7. The structure of RBF neural network. 2.5

error(%)

ANN

PSB

PSB

100

Results for a sample test data are presented in Table 1 and Figs. 8 and 9. Table 1 contains the some sample result of test data. Data in column VPSB are the absolute values of peak voltage at bus 3 calculated by PSB program where the VRBF values are those obtained from simulated trained network. Fig. 8 shows the overvoltage peak bus 3 against the shunt reactor capacity at different switching angle. Also, Fig. 9 shows the overvoltage peak at bus 3 against the equivalent inductance at different line capacitance. The proposed model tested with portions of 39-bus New England test system. Various cases of line energization are taken into account and corresponding peak values estimated from trained model.

2.3 2.2 Voltage [p.u.]

All experiments have been repeated for different system parameters. After learning, all parameters of the trained networks have been frozen and then used in the retrieval mode for testing the capabilities of the system on the data not used in learning. The testing data samples have been generated through the PSB program by placing the parameter values that are not used in learning, by applying different parameters. A large number of testing data have been used to check the proposed solution in the most objective way at practically all possible parameters variation. Percentage error is calculated as:

S.A.=27 S.A.=27 S.A.=81 S.A.=81

2.4

4.1. Training Artificial Neural Network

-PSB -ANN -PSB -ANN

2.1 2 1.9 1.8 1.7 1.6 1.5

0

10

20 30 40 50 60 Shunt Reactor Capacity [MVAR]

70

80

Figure 8. Overvoltage peak vs. shunt reactor capacity at bus 3 simulated by ANN and PSB while equivalent source voltage 1.025 p.u., equivalent resistance 0.0055 p.u., equivalent inductance 0.025 p.u., equivalent capacitance 1.5869 p.u., line length 250 km, and line capacitance 1.237e-8 F/km. S.A. is switching angle.

5. Case Study In this section, the proposed algorithm is demonstrated for two case studies that are a portion of 39-bus New England test system, of which its parameters are listed in [18]. The simulations are undertaken on a single phase representation. In the proposed method, first, studied system must be converted to equivalent circuit of Fig. 1, i.e., values of equivalent resistance, equivalent inductance, and equivalent capacitance are calculated by using equivalent circuit theory. These values are used in trained artificial neural network to estimate overvoltages peak.

I. Sadeghkhani, et al., ACMA, Vol. 1, No. 1, pp. 17-22, March 2012

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Table 1. Some Sample Testing Data and Output V

Reqv

Leqv

Ceqv

L.L.

CLine

S.A.

R

VPSB

VRBF

errorV

0.907 0.003 0.022 1.28 175 1.19e-8 54 10 2.1105 2.0834 1.2851 0.932 0.003 0.022 1.28 325 1.19e-8 54 10 2.2415 2.2775 1.6041 0.953 0.003 0.027 1.28 325 1.24e-8 54 10 2.4057 2.4152 0.3955 0.945 0.003 0.037 1.28 275 1.29e-8 54 10 2.2544 2.2855 1.3795 0.976 0.003 0.032 1.28 225 1.27e-8 54 10 2.3064 2.3238 0.7529 0.997 0.003 0.032 1.28 375 1.22e-8 54 10 3.0053 2.9395 2.1901 1.031 0.003 0.022 1.28 275 1.29e-8 54 10 3.0372 3.0201 0.5618 1.065 0.003 0.027 1.28 375 1.24e-8 54 10 2.3213 2.2921 1.2579 1.003 0.0035 0.025 0.36 250 1.23e-8 45 70 1.7102 1.7422 1.8726 1.006 0.0035 0.025 1.58 250 1.23e-8 81 30 2.0231 2.0852 3.0674 1.002 0.0045 0.025 1.58 250 1.23e-8 27 30 1.9062 1.8542 2.7283 1.007 0.0045 0.025 2.8 250 1.23e-8 27 50 1.7478 1.7139 1.9406 1.004 0.0055 0.025 2.19 250 1.23e-8 63 10 2.1745 2.1917 0.7916 1.001 0.0055 0.025 0.97 250 1.23e-8 9 50 1.5126 1.5095 0.2064 1.005 0.0065 0.025 2.8 250 1.23e-8 45 70 1.7745 1.7296 2.5301 0.999 0.0065 0.025 0.36 250 1.23e-8 81 10 2.2733 2.2925 0.8445 V = voltage at sending bus of transmission line before switching [p.u.], Reqv = equivalent resistance [p.u.], Leqv = equivalent inductance [p.u.], Ceqv = equivalent capacitance [p.u.], L.L. = line length [km], CLine = line capacitance [F/km], S.A. = switching angle [°], R = shunt reactor capacity [MVAR], and errorV = voltage error [%].

2.8 2.7

Voltage [p.u.]

2.6 2.5 2.4 CLine=1.2246e-8F/km-PSB 2.3

CLine=1.2246e-8F/km-ANN

2.2

CLine=1.2989e-8F/km-PSB CLine=1.2989e-8F/km-ANN

2.1 0.02

0.025 0.03 0.035 Equivalent Inductance [p.u.]

bus of transmission line before switching, equivalent resistance, equivalent inductance, and equivalent capacitance are calculated. In other words, this system is converted to equivalent system of Fig. 1. Values of equivalent resistance, equivalent inductance and equivalent capacitance are 0.00386 p.u., 0.02894, and 2.8031 p.u., respectively. For testing trained ANN, values of voltage at sending bus of transmission line before switching, switching angle, line length, and shunt reactor capacity are varied and in each state, overvoltage peak values are calculated from trained ANN and actual system (no equivalent). Table 2 contains the some sample result of test data of case 1.

0.04

Figure 9. Overvoltage peak vs. equivalent inductance at bus 3 simulated by ANN and PSB while equivalent source voltage 1.075 p.u., equivalent resistance 0.003 p.u., equivalent capacitance 1.2825 p.u., switching angle 54°, line length 325 km, and shunt reactor capacity 10 MVAR. C Line is line capacitance.

5.1. Case 1 Fig. 10 shows a one-line diagram of a portion of 39bus New England test system which is in restorative state. The generator at bus 35 is a black-start unit. In this case, line 16_19 must be energized. Shunt reactor installed at the receiving end of transmission line, reduces the maximum overvoltage.

5.2. Case 2 As another example, the system in Fig. 11 is examined. In the next step of the restoration, line 5_6 must be energized. After converting this system to equivalent circuit of Fig. 1, i.e., after calculating equivalent circuit seen from bus 5, various cases of transmission line energization are taken into account and corresponding peak overvoltages are computed from PSB program and trained ANN. In this case, Values of equivalent resistance, equivalent inductance and equivalent capacitance are 0.006408 p.u., 0.02375, and 1.4516 p.u., respectively. Summery of few result are presented in Table 3. It can be seen from the results that the ANN is able to learn the pattern and give results to acceptable accuracy.

Figure 10. Studied system for case 1.

First, equivalent circuit of this system, seen behind bus 16, is determined and values of voltage at sending

Figure 11. Studied system for case 2.

I. Sadeghkhani, et al., ACMA, Vol. 1, No. 1, pp. 17-22, March 2012

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Table 2. Case 1 Some Sample Testing Data and Output V [p.u.]

S.A. [deg.]

L.L. [km]

0.9086 30 0.9086 60 0.9577 60 0.9726 45 1.0068 90 1.0451 23 1.0559 75 1.0559 38 V = voltage at sending bus of transmission voltage error.

R [MVAR]

VPSB [p.u.]

VRBF [p.u.]

180 15 2.0164 180 15 2.1375 245 65 2.1571 290 23 2.3409 150 5 2.8534 400 87 2.3795 210 50 2.5172 210 33 2.7716 line before switching, S.A. = switching angle, L.L. = line length, R

errorV [%]

1.9736 2.1207 2.1626 1.1724 2.1957 1.7905 2.3313 0.4093 2.7472 3.7221 2.3586 0.8801 2.5585 1.6394 2.7312 1.4581 = shunt reactor capacity, and error V =

Table 3. Case 2 Some Sample Testing Data and Output V [p.u.]

S.A. [deg.]

L.L. [km]

0.9068 0.9347 0.9558 0.9558 1.0048 1.0057 1.0538 1.0738

75 75 15 90 30 14 25 81

410 262 175 175 315 227 160 344

R [MVAR]

VPSB [p.u.]

VRBF [p.u.]

errorV [%]

26 26 40 7 35 76 16 55

2.2194 2.0927 1.9835 2.6173 2.5441 2.3428 2.5892 2.4367

2.2034 2.0732 2.0246 2.6565 2.4745 2.3697 2.6003 2.4809

0.7216 0.9304 2.0697 1.4961 2.7359 1.1502 0.4275 1.8134

V = voltage at sending bus of transmission line before switching, S.A. = switching angle, L.L. = line length, R = shunt reactor capacity, and error V = voltage error. [7]

6. Conclusion In this paper transmission lines switching overvoltages are studied. Radial basis function neural network has been used to estimate these overvoltages during power system restoration. Since equivalent circuit parameters of the network are employed, developed ANN is applicable for every studied system The results from this scheme are close to results from the conventional method and helpful in predicting the overvoltage of the other case studies within the range of training set. Therefore, the ANN application is recommended as an operator-training tool for estimation of temporary overvoltages during power system restoration.

[8]

[9]

[10]

[11]

[12]

7. References [1]

[2] [3]

[4]

[5]

[6]

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