Estimation of magnitude and time duration of temporary overvoltages using ANN in transmission lines...

Simulation Modelling Practice and Theory xxx (2010) xxx–xxx

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Simulation Modelling Practice and Theory

journal homepage: www.elsevier .com/ locate/s impat

Estimation of magnitude and time duration of temporary overvoltagesusing ANN in transmission lines during power system restoration

Seyed Abbas Taher *, Iman SadeghkhaniDepartment of Electrical Engineering, University of Kashan, Kashan 87317-51167, Iran

a r t i c l e i n f o

Article history:Received 1 October 2009Received in revised form 2 December 2009Accepted 21 January 2010Available online xxxx

Keywords:Artificial neural networksSwitching overvoltagesHarmonic resonancePower system restorationTransmission lines energizationNonlinear input–output mapping

1569-190X/$ - see front matter � 2010 Elsevier B.Vdoi:10.1016/j.simpat.2010.01.016

* Corresponding author. Tel.: +98 9131614352; faE-mail address: [email protected] (S.A. Tahe

Please cite this article in press as: S.A. Taher, IANN in transmission lines during power syste

a b s t r a c t

In most countries, the main step in the process of power system restoration, following acomplete/partial blackout, is energization of primary restorative transmission lines. Artifi-cial neural network (ANN) is employed for performing a nonlinear input–output mappingin this work, in order to estimate the temporary overvoltages (TOVs) due to transmissionlines energization. In the proposed methodology, Levenberg–Marquardt second ordermethod is used to train the multilayer perceptron. Proposed ANN is trained with equivalentcircuit parameters of the network as input parameters, trained ANN has therefore satisfac-tory generalization capability. Both single and three-phase line energizations are analyzed.The simulated results for 39-bus New England test system, indicate that the proposed tech-nique can estimate the peak values and duration of switching overvoltages with acceptableaccuracy.

� 2010 Elsevier B.V. All rights reserved.

1. Introduction

During the early stages of restoring high voltage overhead and underground transmission lines, concerns are with threerelated overvoltages: sustained power frequency overvoltages, switching transients (surges), and harmonic resonance. In theearly stages of the restoration, the lines are lightly loaded; resonance therefore is lightly damped, which in turn means theresulting resonance voltages may be very high [1–4].

In recent years, due to economic competition and deregulation, power systems are being operated closer and closer totheir limits. At the same time, power systems have increased in size and complexity. Both factors increase the risk of majorpower outages. After a blackout, power needs to be restored as quickly and reliably as possible and, consequently, detailedrestoration plans are necessary [1,5].

Switching overvoltage is a primary importance in insulation co-ordination for extra high voltage (EHV) lines. The objec-tive of simulating switching overvoltage is to assist a proper insulation co-ordination which would lead to minimize damageand interruption to service as a consequence of steady state, dynamic and transient overvoltage [6–9].

At the beginning of a system restoration, temporary overvoltage is an important issue. During the early stages of the res-toration procedures following a partial or complete blackout, the power system is lightly loaded and resonance conditionsare different from normal operations. The magnitude and shape of the switching overvoltages vary with the system param-eters and network configuration. Even with the same system parameters and network configuration, the switching overvol-tages are highly dependent on the characteristics of the circuit breaker operation and the point-on-wave where theswitching operation takes place.

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. Sadeghkhani, Estimation of magnitude and time duration of temporary overvoltages usingm restoration, Simulat. Modell. Pract. Theory (2010), doi:10.1016/j.simpat.2010.01.016

http://dx.doi.org/10.1016/j.simpat.2010.01.016

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Maximal voltages induced on overhead power lines by a nearby lightning stroke are estimated by Jankov [10]. Cooray in[11], a comparison is made between two coupling models frequently used to estimate the lightning-induced overvoltages inpower lines. Fast transient overvoltage in gas-insulated substation is estimated by Yanabu et al. [12]. Wedepohl and Wilcox[13], introduced a qualitative method of prediction for voltages to the first peak value, which becomes quantitative once the‘universal curve’ (defined in the text) is known. Shafiee et al. [14], used an artificial neural network (ANN) to estimate peakovervoltage generated in presence of back flashover. Also, Thukaram et al. [15] estimated transmission line overvoltage peakusing ANN.

In this paper power system blockset (PSB), a MATLAB/Simulink-based simulation tool [16] is used for computation of bothswitching and temporary overvoltages. This paper presents the ANN application for estimation of peak and duration over-voltages under switching transients during transmission lines energization. A tool such as proposed in this paper that can

0 0.01 0.02 0.03 0.04 0.05-3

-2.5-2

-1.5-1

-0.50

0.51

1.52

2.53

Time [s]

Vol

tage

[p.

u.]

Distributed Model One PI Section Model

(a)

0 0.01 0.02 0.03 0.04 0.05-3

-2.5-2

-1.5

-1-0.5

0

0.51

1.5

22.5

3

Time [s]

Vol

tage

[p.

u.]

Distributed Model 10 PI Section Model

(b)

Fig. 1. Harmonic overvoltage in receiving end of a 250 km transmission line after switching. (a) Distributed model vs. one PI section model, (b) distributedmodel vs. 10 PI section model.

Table 1Comparison between distributed model and PI model.

Overvoltage peak (p.u.) Duration of (Vpeak > 1.3 p.u.) (s)

Distributed model 2.7516 0.4892One PI section model 2.4285 0.392710 PI section model 2.3817 0.4594

Please cite this article in press as: S.A. Taher, I. Sadeghkhani, Estimation of magnitude and time duration of temporary overvoltages usingANN in transmission lines during power system restoration, Simulat. Modell. Pract. Theory (2010), doi:10.1016/j.simpat.2010.01.016


S.A. Taher, I. Sadeghkhani / Simulation Modelling Practice and Theory xxx (2010) xxx–xxx 3

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give the maximum switching overvoltage and it’s duration will be helpful to the operator. It can be used as training tool forthe operators. The proposed ANN is expected to learn many scenarios of operation. In order to give the maximum peak over-voltage and it’s duration in a shortest computational time which is the requirement during online operation of power sys-tems, we have considered the most important technical aspects, which influence the transient overvoltages such asequivalent source voltage, resistance, inductance, and capacitance as well as switching angle, line length, line capacitance,and shunt reactor capacity. This information will help the operator to select the proper sequence of transmission lines tobe energized safely with transients appearing safe within the limits. Since ANN is trained with equivalent circuit parameters,thus it could be applied to all studied systems. In fact, proposed ANN is trained just once with a simple circuit that includesequivalent circuit parameters. Therefore, developed ANN can estimate overvoltage peak and duration for every studied

Fig. 2. Simplified transformer magnetization characteristic.

Fig. 3. Study system for transmission line energization. G: generator, Reqv: equivalent resistance, Leqv: equivalent inductance, Ceqv: equivalent capacitance.

0 0.02 0.04 0.06 0.08 0.1-2.4

-2-1.6-1.2-0.8-0.4

00.40.81.21.6

22.42.8

Time [s]

Vol

tage

[p.

u.]

Fig. 4. Harmonic overvoltage at bus 3 after switching of transmission line.




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system. In addition, both single and three-phase transmission line energization is analyzed. Results of the studies are pre-sented for 39-bus New England test system to illustrate the proposed approach.

2. Study system modeling

In this paper the simulations are carried out employing PSB. The simulation tool has been developed using state variableapproach and runs in the MATLAB/Simulink environment. This program has been compared with other popular simulationpackages (EMTP and Pspice) in [16]. The user friendly graphical interfaces of PSB enable faster development for power sys-tem transient analysis.

2.1. Transmission line model

In this paper a distributed model is employed as transmission line model, as it is more accurate than one or multi-PI sec-tion model, as shown in Fig. 1 and Table 1.

2.2. Generator model

In [17], generators have been modeled by the generalized Park’s model in which electrical and mechanical parts are thor-oughly modeled. In this work, generators are represented by a sinusoidal voltage source behind their sub-transient reac-tance, X00d. Phases of voltage sources are determined by the load-flow results.

2.3. Transformer model

The model takes into account the winding resistances (R1, R2), the leakage inductances (L1, L2) as well as the magnetizingcharacteristics of the core, which is modeled by a resistance, Rm, simulating the core active losses and a saturatable induc-tance, Lsat. The saturation characteristic is specified as a piece-wise linear characteristic [18].

0.95 1 1.05 1.12.25

2.35

2.45

2.55

2.65

2.75

Equivalent Source Voltage [p.u.]

Vol

tage

[p.

u.]

CLine

= 1.1875e-8 F/km

CLine

= 1.2865e-8 F/km

(a)

0.95 1 1.05 1.10.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55


Dur

atio

n of

(V

peak

> 1

.3 p

.u.)

[s] C

Line = 1.1875e-8 F/km

CLine

= 1.2865e-8 F/km

(b)

Fig. 5. Overvoltage at bus 3 as equivalent source voltage while equivalent resistance 0.003 p.u., equivalent inductance 0.03 p.u., equivalent capacitance1.2825 p.u., switching angle 54�, line length 300 km, and shunt reactor capacity 10 MVAR. CLine is line capacitance. (a) Peak and (b) duration.




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In order to analyze the saturation of transformer, consider a single-phase transformer having a magnetizing characteristicas given in Fig. 2. If the voltage applied to the shunt branch of transformer is v ¼ V cos xt at time t0 for which xt0 = h, the estab-lished flux linkage will be a function of the applied voltage and the flux linkage offset w0 as given by the following expression:

Fig. 6.switchi

PleaseANN i

w ¼ Vx

sin xt þ w0 ð1Þ

The flux linkage offset is made up of the remnant flux linkage wr and the component –V/x sin h due to the linkage mis-match condition at energization,

w0 ¼ wr �Vx

sin h ð2Þ

Under normal system conditions the transformer core would be driven temporarily into saturation asymmetrically whenthe flux linkage w exceeds the saturation level ws. The expression for the inrush current is:

i ¼ 1Lsatðw� wsÞ ð3Þ

2.4. Load and shunt devices model

All of the loads and shunt devices, such as capacitors and reactors, are modeled as constant impedances.

150 200 250 300 3502.2

2.3

2.4

2.5

2.6

2.7

2.8

2.9

3

3.1

3.2

Line Length [km]

Vol

tage

[p.

u.]

XLeqv

= 0.02 p.u.

XLeqv

= 0.035 p.u.

(a)

150 200 250 300 3500.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

Line Length [km]

Dur

atio

n of

(V pe

ak >

1.3

p.u

.) [

s]

XLeqv

= 0.02 p.u.

XLeqv

= 0.035 p.u.

(b)

Overvoltage 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.,ng angle 54�, line capacitance 1.237e�8 F/km, and shunt reactor capacity 10 MVAR. XLeqv is equivalent inductance. (a) Peak and (b) duration.

cite this article in press as: S.A. Taher, I. Sadeghkhani, Estimation of magnitude and time duration of temporary overvoltages usingn transmission lines during power system restoration, Simulat. Modell. Pract. Theory (2010), doi:10.1016/j.simpat.2010.01.016



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3. Transient overvoltages during restoration

One of the major concerns in power system restoration is the occurrence of overvoltages as a result of switchingprocedures. These can be classified as transient overvoltages, sustained overvoltages, harmonic resonance overvoltages,and overvoltages resulting from ferro-resonance. Steady-state overvoltages occur at the receiving end of lightly loaded trans-mission lines as a consequence of line-charging currents (reactive power balance). Excessive sustained overvoltages maylead to transformer damage and other power system equipment. Transient overvoltages are a consequence of switchingoperations on long transmission lines, or the switching of capacitive devices, and may result in arrester failures. Ferro-res-onance is a non-harmonic resonance characterized by overvoltages whose waveforms are highly distorted and can cause cat-astrophic equipment damages [1,19].

The sample system considered for explanation of the proposed methodology is a 400 kV EHV network shown in Fig. 3. Thenormal peak value of any phase voltage is 400

p2/p

3 kV and this value is taken as base for voltage p.u. In the system studies400 kV line-to-line base voltage and 100 MVA as a base power is considered. Fig. 4 shows the switching transient at bus 3when transmission line is energized. In practical system a number of factors affect the overvoltages factors due to energiza-tion or re-closing. In this paper following parameters is considered:

� Equivalent source voltage of the network.� 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.

0 10 20 30 40 50 60 70 80 901.5

1.6

1.7

1.8

1.9

2

Switching Angle [deg.]

Vol

tage

[p.

u.]

Reqv

= 0.003 p.u.

Reqv

= 0.006 p.u.

(a)

0 10 20 30 40 50 60 70 80 900

0.05

0.1

0.15

0.2

0.25


Dur

atio

n of

(V

peak

> 1

.3 p

.u.)

[s] Reqv

= 0.003 p.u.

Reqv

= 0.006 p.u.

(b)

Fig. 7. Overvoltage 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. (a) Peak and (b) duration.




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� Shunt reactor capacity.

Source voltage affects the overvoltage strongly. Fig. 5 shows the effect of equivalent source voltage on overvoltage at dif-ferent line capacitance. Fig. 6 shows the effect of line length on overvoltages at different equivalent inductance. Also, Fig. 7shows the effect of switching angle on overvoltage at different equivalent resistance. Controlled switching of high voltage ACcircuit breakers has become a commonly accepted means of controlling switching transients in power systems. Fig. 8 showsthe effect of shunt reactor capacity on overvoltage at different equivalent capacitance.

As discussed above for an existing system, the main factors which affect the peak and duration values of switching over-voltage are equivalent source voltage, resistance, inductance, and capacitance as well as switching angle, line length, linecapacitance, and shunt reactor capacity. Here, it should be mentioned that a single parameter often cannot be regarded inde-pendently from other important influencing factors. The magnitude and duration of the overvoltages normally does not de-pend directly on any single isolated parameter and a variation of one parameter can often alter the influence of anotherparameter. In other words, there exists an interaction between the various system and breaker parameters. This forbidsthe derivation of precise generalized rule of simple formulae applicable to all cases [20]. So an ANN can help estimatingthe peak and duration values of switching overvoltages generated during transmission line energization. An ANN is pro-grammed by presenting it with training set of input/output patterns from which it then learns the relationship betweenthe inputs and outputs. In the next section, an ANN-based approach is described which can give an acceptable solution ofswitching transients by which an operator can take a quick decision at the time of operation.

4. Artificial neural network

The proposal in this work considers the adoption of feed forward multilayer perceptron (MLP) architecture. A MLP trainedwith the back propagation algorithm may be viewed as a practical vehicle for performing a nonlinear input–output mapping

20 30 40 50 60 70 801.4

1.5

1.6

1.7

1.8

1.9

Shunt Reactor Capacity [MVAR]

Vol

tage

[p.

u.]

Ceqv

= 0.065 p.u.

Ceqv

= 2.5 p.u.

(a)

20 30 40 50 60 70 800.03

0.04

0.05

0.06

0.07

0.08


Dur

atio

n of

(V

pea

k > 1

.3 p

.u.)

[s] C

eqv = 0.065 p.u.

Ceqv

= 2.5 p.u.

(b)

Fig. 8. Overvoltage at bus 3 as shunt reactor capacity while equivalent source voltage 1 p.u., equivalent resistance 0.004 p.u., equivalent inductance0.025 p.u., switching angle 18�, line length 250 km, and line capacitance 1.237e�8 F/km. Ceqv is equivalent capacitance. (a) Peak and (b) duration.



Fig. 9. Proposed MLP-based ANN architecture.

Fig. 10. Supervised learning of ANN.

0 5 10 15 20 25 30 3510

-4

10-3

10-2

10-1

100

101

102

39 Epochs

Tra

inin

g-So

lid L

ine

Goa

l-D

ash

Lin

e

Performance is 0.000998276, Goal is 0.001

Fig. 11. Squared error against epoch curve.


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of a general nature [14,21,22]. Function approximation by feed forward MLP network is proven to be very efficient, consid-ering various learning strategies like simple back propagation or the robust Levenberg–Marquardt. Its ability to perform wellis affected by the chosen training data as well as training scheme. The schematic diagram of the proposed MLP neuralnetworks architecture is shown in Fig. 9. The composition of the input variables for the proposed neural networks has beencarefully selected.



Table 2Some sample testing data and output.

S.V. Reqv XLeqv Ceqv S.A. L.L. CLine S.R. VPSB VANN Errorv TPSB TANN ErrorT

0.925 0.003 0.0225 1.2825 54 175 1.199e�8 10 2.1105 2.0563 2.5669 0.0988 0.0973 1.49180.925 0.003 0.0225 1.2825 54 325 1.199e�8 10 2.2415 2.1486 4.1432 0.1817 0.1862 2.47660.975 0.003 0.0275 1.2825 54 325 1.249e�8 10 2.4057 2.4859 3.3321 0.2814 0.2782 1.13620.975 0.003 0.0375 1.2825 54 275 1.298e�8 10 2.2544 2.2409 0.6039 0.2836 0.2887 1.81571.025 0.003 0.0325 1.2825 54 225 1.274e�8 10 2.3064 2.2696 1.5948 0.2852 0.2784 2.38891.025 0.003 0.0325 1.2825 54 375 1.224e�8 10 3.0053 2.9785 0.8932 0.4356 0.4332 0.54191.075 0.003 0.0275 1.2825 54 375 1.249e�8 10 3.0372 2.9137 4.0674 0.4601 0.4492 2.37861.075 0.003 0.0225 1.2825 54 275 1.298e�8 10 2.3213 2.4127 3.9361 0.2325 0.2358 1.41941.025 0.0035 0.025 0.3694 45 250 1.237e�8 70 1.7102 1.6685 2.4359 0.1022 0.1031 0.92061.025 0.0035 0.025 1.5869 81 250 1.237e�8 30 2.0231 1.9344 4.3861 0.2026 0.1993 1.61481.025 0.0045 0.025 1.5869 27 250 1.237e�8 30 1.9062 1.9324 1.3716 0.0652 0.0663 1.68941.025 0.0045 0.025 2.8044 27 250 1.237e�8 50 1.7478 1.6914 3.2278 0.0632 0.0617 2.41071.025 0.0055 0.025 2.1956 63 250 1.237e�8 10 2.1745 2.1722 0.1074 0.1863 0.1837 1.39561.025 0.0055 0.025 0.9781 9 250 1.237e�8 50 1.5126 1.5481 2.3517 0.0224 0.0226 1.06421.025 0.0065 0.025 2.8044 45 250 1.237e�8 70 1.7745 1.7409 1.8975 0.0628 0.0642 2.27841.025 0.0065 0.025 0.3694 81 250 1.237e�8 10 2.2733 2.2895 0.7159 0.1636 0.1611 1.5136

S.V., equivalent source voltage (p.u.); Reqv, equivalent resistance (p.u.); XLeqv, equivalent inductance (p.u.); Ceqv, equivalent capacitance (p.u.); L.L., line length(km); CLine, line capacitance (F/km), S.A., switching angle (deg.); S.R., shunt reactor capacity (MVAR); errorV, voltage error (%), and errorT, duration time error(%).

0.9 0.95 1 1.05 1.12

2.1

2.2

2.3

2.4

2.5

2.6

2.7

2.8

2.9

3

3.1

3.2


Vol

tage

[p.

u.]

L.L.=175km-PSBL.L.=175km-ANNL.L.=375km-PSBL.L.=375km-ANN

(a)

0.9 0.95 1 1.05 1.10

0.1

0.2

0.3

0.4

0.5

0.6

0.7


Dur

atio

n of

(V

pea

k > 1

.3 p

.u.)

[s]

L.L.=175km-PSBL.L.=175km-ANNL.L.=375km-PSBL.L.=375km-ANN

(b)

Fig. 12. Overvoltage vs. equivalent source voltage at bus 3 simulated by ANN and PSB while equivalent resistance 0.003 p.u., equivalent inductance0.0225 p.u., equivalent capacitance 1.2825 p.u., switching angle 54�, line capacitance 1.274e�8 F/km, and shunt reactor capacity 10 MVAR. L.L. is linelength. (a) Peak and (b) duration.


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Supervised training of ANN is a usual training paradigm for MLP architecture. Fig. 10 shows the supervised learning ofANN for which input is given to PSB to get the peak and duration values of transient overvoltages and the same data is usedto train the ANN. Error is calculated by the difference of PSB output and ANN output. This error is used to adjust the weight ofconnection. Output values of the trained neural networks must be capable of computing the voltages with very good preci-sion. Gradient-based training algorithms, like back propagation, are most commonly used for training procedures. They arenot efficient due to the fact that the gradient vanishes at the solution. Hessian-based algorithms allow the network to learnmore subtle features of a complicated mapping. The training process converges quickly as the solution is approached, be-cause the Hessian does not vanish at the solution. To benefit from the advantages of Hessian-based training, the Leven-berg–Marquardt (LM) algorithm reported in [23,24] were considered.

4.1. Levenberg–Marquardt (LM) algorithm

Suppose that we have a function g(x) which we want to minimize with respect to the parameter vector x, where

Fig. 130.0055angle. (

PleaseANN i

gðxÞ ¼XN

i¼1

e2i ðxÞ ð4Þ

Then the Marquardt–Levenberg modification to the Gauss–Newton method is

D x ¼ ½JTðxÞJðxÞ þ lI��1 JTðxÞeðxÞ ð5Þ

0 10 20 30 40 50 60 70 801.5

1.6

1.7

1.8

1.9

2

2.1

2.2

2.3

2.4

2.5


Vol

tage

[p.

u.]

S.A.=27°-PSBS.A.=27°-ANNS.A.=81°-PSBS.A.=81°-ANN

(a)

0 10 20 30 40 50 60 70 800

0.05

0.1

0.15

0.2

0.25


Dur

atio

n of

(V

peak

> 1

.3 p

.u.)

[s]

S.A.=27°-PSBS.A.=27°-ANNS.A.=81°-PSBS.A.=81°-ANN

(b)

. Overvoltage vs. shunt reactor capacity at bus 3 simulated by ANN and PSB while equivalent source voltage 1.025 p.u., equivalent resistancep.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 switchinga) Peak and (b) duration.



Fig. 15. Studied system for case 1.

0.02 0.025 0.03 0.035 0.042.1

2.2

2.3

2.4

2.5

2.6

2.7

2.8

Equivalent Inductance [p.u.]

Vol

tage

[p.

u.]

CLine

=1.2246e-8F/km-PSB

CLine

=1.2246e-8F/km-ANN

CLine

=1.2989e-8F/km-PSB

CLine

=1.2989e-8F/km-ANN

(a)

0.02 0.025 0.03 0.035 0.040.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

Equivalent Inductance [p.u.]

Dur

atio

n of

(V

peak

> 1

.3 p

.u.)

[s]

CLine

=1.2246e-8F/km-PSB

CLine

=1.2246e-8F/km-ANN

CLine

=1.2989e-8F/km-PSB

CLine

=1.2989e-8F/km-ANN

(b)

Fig. 14. Overvoltage vs. equivalent inductance at bus 3 simulated by ANN and PSB while equivalent source voltage 1.075 p.u., equivalent resistance0.003 p.u., equivalent capacitance 1.2825 p.u., switching angle 54�, line length 325 km, and shunt reactor capacity 10 MVAR. CLine is line capacitance. (a)Peak and (b) duration.


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The parameter l is multiplied by some factor b whenever a step would result in an increased gðxÞ. When a step reduces gðxÞ,l is divided by b. Notice that when l is large the algorithm becomes steepest descent; while for small l the algorithm be-comes Gauss–Newton. The LM algorithm is very efficient when training networks have up to a few hundred weights.Although the computational requirements are much higher for iterations of the LM algorithm, this is more than made upfor by the increased efficiency. This is especially true when high precision is required.

4.2. Training artificial neural network

One of the most critical problems in constructing the ANN is the choice of the number of hidden layers and the number ofneurons. In this study, a MLP with two hidden layers and 10 hidden units per layer is found to yield sufficient accuracy and



Table 4Some sample testing data and output of case 2.

S.V. S.A. L.L. S.R. VPSB VANN ErrorV TPSB TANN ErrorT

0.925 75 410 26 2.2194 2.2384 0.8562 0.2509 0.2518 0.34950.925 75 262 26 2.0927 2.0387 2.5781 0.2153 0.2047 4.90360.975 15 175 40 1.9835 2.0167 1.6724 0.1864 0.1928 3.42790.975 90 175 7 2.6173 2.5691 1.8405 0.4311 0.4365 1.26131.025 30 315 35 2.5441 2.4291 4.5197 0.3697 0.3748 1.37591.025 14 227 76 2.3428 2.4052 2.6631 0.2718 0.2704 0.51641.075 25 160 16 2.5892 2.6818 3.5749 0.4276 0.4162 2.65921.075 81 344 55 2.4367 2.4739 1.5284 0.3924 0.4017 2.3581

S.V., equivalent source voltage (p.u.); S.A., switching angle (deg.); L.L., line length (km), S.R., shunt reactor capacity (MVAR), errorV, voltage error (%), anderrorT, duration time error (%).

Fig. 16. Studied system for case 2.

0 0.02 0.04 0.06 0.08 0.1-3

-2.5

-2

-1.5

-1-0.5

0

0.5

11.5

2

2.5

33.5

Time [s]

Vol

tage

[p.

u.]

vA

vB

vC

Fig. 17. Harmonic overvoltage at bus 3 after switching of three-phase transmission line.

Table 3Some sample testing data and output of case 1.

S.V. S.A. L.L. S.R. VPSB VANN ErrorV TPSB TANN ErrorT

0.925 30 180 15 2.0164 1.9825 1.6825 0.1651 0.1638 0.81670.925 60 180 15 2.1375 2.1082 1.3716 0.1944 0.1982 1.93510.975 60 245 65 2.1571 2.1454 0.5426 0.2301 0.2248 2.31940.975 45 290 23 2.3409 2.4376 4.1305 0.2618 0.2584 1.29851.025 90 150 5 2.8534 2.9314 2.7328 0.5359 0.5219 2.61011.025 23 400 87 2.3795 2.4071 1.1583 0.3241 0.3259 0.56291.075 75 210 50 2.5172 2.4345 3.2849 0.3746 0.3785 1.03921.075 38 210 33 2.7716 2.7352 1.3148 0.4783 0.4867 1.7546

S.V., equivalent source voltage (p.u.); S.A., switching angle (deg.); L.L., line length (km); S.R., shunt reactor capacity (MVAR); errorV, voltage error (%), anderrorT, duration time error (%).


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generalization for the proposed scheme. 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 thesystem on the data not used in learning. The testing data samples have been generated employing PSB program by placingthe parameter values not used in learning, and applying different parameters.

A large number of testing data have been used to check the proposed solution in the most objective way at practically allpossible parameters variation. Percentage errors are calculated as:

Fig. 18.line len

PleaseANN i

errorð%Þ ¼ jANN� PSBjPSB

� 100 ð6Þ

Neural network is trained with the goal of mean square error (MSE) 1e�3. Fig. 11 shows the training of neural network.Results for a sample test data are presented in Table 2 and Figs. 12–14. Table 2 contains a few sample results of test data.Data in column VPSB (column 9) show the absolute values of peak voltage at bus 3, calculated by PSB program, while VANN

column shows the values (column 10) simulated by the trained network. Also, values in column TPSB (column 12) corre-sponds to the values of overvoltage duration calculated by PSB program and TANN indicate the values (column 13) simulatedby the trained network. These data suggest that the maximum voltage error ‘‘errorV” and maximum duration time error‘‘errorT” are 4.3861% (column 11) and 2.4766% (column 14), respectively. Figs. 12–14 show the overvoltage peak and dura-tion at bus 3 against the equivalent source voltage at different line length, the shunt reactor capacity at different switchingangle, and also the equivalent inductance at different line capacitance.

The proposed model is tested with portions of 39-bus New England test system. Various cases of line energization aretaken into account and corresponding peak and duration values estimated from trained model.

5. Simulation results

In this section simulations are performed on single and three-phase transmission line energization.

0.95 1 1.05 1.11.1

1.3

1.5

1.7

1.9

2.1

2.3

2.5

2.7

Equivalent source Voltage [p.u.]

Vol

tage

[p.

u.]

XLeqv

=0.025p.u.-A

XLeqv

=0.025p.u.-B

XLeqv

=0.025p.u.-C

XLeqv

=0.035p.u.-A

XLeqv

=0.035p.u.-B

XLeqv

=0.035p.u.-C

0.95 1 1.05 1.10

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45


Dur

atio

n of

(V

pea

k >

1.3

p.u

.) [

s]

XLeqv

=0.025p.u.-A

XLeqv

=0.025p.u.-B

XLeqv

=0.025p.u.-C

XLeqv

=0.035p.u.-A

XLeqv

=0.035p.u.-B

XLeqv

=0.035p.u.-C

(b)

(a)

Overvoltage at bus 3 as equivalent source voltage while equivalent resistance 0.005 p.u., equivalent capacitance 1.8912 p.u., switching angle 36�,gth 250 km, line capacitance 1.2121 F/km, and shunt reactor capacity 15 MVAR. XLeqv is equivalent inductance. (a) Peak and (b) duration.



0 18 36 54 72 901.2

1.4

1.6

1.8

2

2.2

2.4

2.6


Vol

tage

[p.

u.]

Ceqv

=0.065p.u.-A

Ceqv

=0.065p.u.-B

Ceqv

=0.065p.u.-C

Ceqv

=1.8912p.u.-A

Ceqv

=1.8912p.u.-B

Ceqv

=1.8912p.u.-C

(a)

0 18 36 54 72 900

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45


Dur

atio

n of

(V

pea

k >

1.3

p.u

.) [

s]

Ceqv

=0.065p.u.-A

Ceqv

=0.065p.u.-B

Ceqv

=0.065p.u.-C

Ceqv

=1.8912p.u.-A

Ceqv

=1.8912p.u.-B

Ceqv

=1.8912p.u.-C

(b)

Fig. 20. Overvoltage at bus 3 as switching angle while equivalent source voltage 1 p.u., equivalent resistance 0.004 p.u., equivalent inductance 0.025 p.u.,line length 300 km, line capacitance 1.237e�8 F/km, and shunt reactor capacity 20 MVAR. Ceqv is equivalent capacitance. (a) Peak and (b) duration.

150 200 250 300 3501.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

Line Length [km]

Vol

tage

[p.

u.]

CLine

=1.1875e-8F/km-A

CLine

=1.1875e-8F/km-B

CLine

=1.1875e-8F/km-C

CLine

=1.2617e-8F/km-A

CLine

=1.2617e-8F/km-B

CLine

=1.2617e-8F/km-C

(a)

150 200 250 300 3500

0.05

0.1

0.15

0.2

0.25

Line Length [km]

Dur

atio

n of

(V

peak

> 1

.3 p

.u.)

[s]

CLine

=1.1875e-8F/km-A

CLine

=1.1875e-8F/km-B

CLine

=1.1875e-8F/km-C

CLine

=1.2617e-8F/km-A

CLine

=1.2617e-8F/km-B

CLine

=1.2617e-8F/km-C

(b)

Fig. 19. Overvoltage at bus 3 as line length while equivalent source voltage 1.05 p.u., equivalent resistance 0.005 p.u., equivalent inductance 0.02 p.u.,equivalent capacitance 1.8912 p.u., switching angle 36�, and shunt reactor capacity 15 MVAR. CLine is line capacitance. (a) Peak and (b) duration.


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20 40 60 801.6

1.7

1.8

1.9

2

2.1

2.2


Vol

tage

[p.

u.]

Reqv

=0.003p.u.-A

Reqv

=0.003p.u.-B

Reqv

=0.003p.u.-C

Reqv

=0.006p.u.-A

Reqv

=0.006p.u.-B

Reqv

=0.006p.u.-C

(a)

20 40 60 800

0.05

0.1

0.15

0.2

0.25


Dur

atio

n of

Vp

eak >

1.3

p.u

.) [

s]

Reqv

=0.003p.u.-A

Reqv

=0.003p.u.-B

Reqv

=0.003p.u.-C

Reqv

=0.006p.u.-A

Reqv

=0.006p.u.-B

Reqv

=0.006p.u.-C

(b)

Fig. 21. Overvoltage at bus 3 as shunt reactor capacity while equivalent source voltage 1 p.u., equivalent inductance 0.025 p.u., equivalent capacitance1.2825 p.u., switching angle 90�, line length 300 km, and line capacitance 1.237e�8 F/km. Reqv is equivalent resistance. (a) Peak and (b) duration.

Fig. 22. Proposed MLP-based ANN architecture to estimate overvoltage peak and duration in three-phase transmission line.


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Table 5Some sample testing data and output of three-phase transmission line energization.

S.V. Reqv XLeqv Ceqv S.A. L.L. CLine S.R. VPSB VANN ErrorV TPSB TANN ErrorT Phase

0.925 0.003 0.0275 1.8912 36 325 1.298e�8 15 2.4199 2.4626 1.7629 0.3512 0.3564 1.4925 B0.925 0.003 0.0275 1.8912 36 175 1.298e�8 15 2.0966 2.0319 3.0849 0.1573 0.1591 1.1538 B0.975 0.003 0.0325 1.8912 36 175 1.249e�8 15 2.2215 2.1938 1.2462 0.2697 0.2741 1.6134 C0.975 0.003 0.0375 1.8912 36 275 1.249e�8 15 2.4739 2.5283 2.1975 0.4027 0.3886 3.4968 B1.025 0.003 0.0225 1.8912 36 375 1.199e�8 15 2.6932 2.6735 0.7304 0.4945 0.4806 2.8029 B1.025 0.003 0.0325 1.8912 36 225 1.224e�8 15 1.9621 1.9241 1.9346 0.0937 0.0962 2.6719 B1.075 0.003 0.0275 1.8912 36 225 1.274e�8 15 2.1225 2.1306 0.3794 0.1975 0.1958 0.8462 B1.075 0.003 0.0225 1.8912 36 325 1.249e�8 15 2.6028 2.6434 1.5584 0.4493 0.4386 2.3794 C1.05 0.0035 0.025 0.9781 45 300 1.237e�8 50 2.4215 2.5274 4.3726 0.3817 0.3764 1.3951 B1.05 0.0035 0.025 0.9781 45 300 1.237e�8 10 2.5375 2.4915 1.8129 0.4306 0.4281 0.5731 C1.05 0.0045 0.025 0.3694 81 300 1.237e�8 30 2.2905 2.3548 2.8067 0.3184 0.3259 2.3649 C1.05 0.0045 0.025 1.5869 27 300 1.237e�8 30 2.2429 2.2108 1.4295 0.2917 0.2945 0.9503 B1.05 0.0055 0.025 2.1956 9 300 1.237e�8 70 2.2981 2.3837 3.7258 0.3156 0.3252 3.0427 B1.05 0.0055 0.025 2.8044 63 300 1.237e�8 50 2.3612 2.3775 0.6904 0.3742 0.3695 1.2519 B1.05 0.0065 0.025 2.8044 63 300 1.237e�8 10 2.4688 2.5027 1.3721 0.4195 0.4268 1.7348 C1.05 0.0065 0.025 1.5869 81 300 1.237e�8 30 2.2473 2.2832 1.5971 0.3082 0.3004 2.5173 B

S.V., equivalent source voltage (p.u.); Reqv, equivalent resistance (p.u.); XLeqv, equivalent inductance (p.u.); Ceqv, equivalent capacitance (p.u.); L.L., line length(km), CLine, line capacitance (F/km), S.A., switching angle (deg.); S.R., shunt reactor capacity (MVAR), errorV, voltage error (%), and errorT, duration time error(%).

0 10 20 30 40 50 60 70 8010

-4

10-3

10-2

10-1

100

101

84 Epochs

Tra

inin

g-So

lid L

ine

Goa

l-D

ash

Lin

e

Performance is 0.00098387, Goal is 0.001

Fig. 23. Squared error against epoch curve for three-phase transmission line energization study.


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5.1. Study of single-phase transmission line energization

In this section, the proposed algorithm is demonstrated for two case studies that are a portion of 39-bus New England testsystem, the parameters of which are listed in [25]. The simulations are undertaken on a single-phase representation.

In the proposed method, first, studied system must be converted to equivalent circuit of Fig. 3, i.e., values of equivalentsource voltage, resistance, inductance, and capacitance are calculated by using equivalent circuit theory. These values areused in trained ANN to estimate overvoltages peak and duration.

5.1.1. Case 1: energization of line 16_19Fig. 15 shows a one-line diagram of a portion of 39-bus New England test system which is in restorative state. The gen-

erator at bus 35 is a black-start unit. In this case, line 16_19 must be energized. Shunt reactor installed at the receiving end oftransmission line, reduces the maximum overvoltage. First, equivalent circuit of this system, seen behind bus 16, is deter-mined and values of equivalent source voltage, resistance, inductance, and capacitance are then calculated. In other words,this system is converted to equivalent system of Fig. 3. For testing trained ANN, values of equivalent source voltage, switch-ing angle, line length, and shunt reactor capacity are varied and in each state, overvoltage peak and duration values are cal-culated from trained ANN and actual system (no equivalent). Table 3 contains the some sample result of test data of case 1. Itcan be observed from this Table, the maximum percentage errors are less than 4.13%, therefore, ANN is able to learn the pat-tern and present results with an acceptable accuracy.



10 30 50 701.5

1.7

1.9

2.1

2.3

2.5

2.7


Vol

tage

[p.

u.]

VA-PSB

VA-ANN

VB-PSB

VB-ANN

VC-PSB

VC-ANN

(a)

10 30 50 700

0.1

0.2

0.3

0.4

0.5


Dur

atio

n of

(V

pea

k >

1.3

p.u

.) [

s]

tA-PSB

tA-ANN

tB-PSB

tB-ANN

tC-PSB

tC-ANN

(b)

Fig. 25. Overvoltage vs. shunt reactor capacity at bus 3 simulated by ANN and PSB while equivalent source voltage 1.05 p.u., equivalent resistance0.0045 p.u., equivalent inductance 0.025 p.u., equivalent capacitance 1.5869 p.u., switching angle 45�, line length 300 km, and line capacitance 1.237e�8 F/km. (a) Peak and (b) duration.

175 225 275 325 3751

1.21.41.61.8

22.22.42.62.8

33.2

Line Length [km]

Vol

tage

[p.

u.] V

A-PSB

VA-ANN

VB-PSB

VB-ANN

VC-PSB

VC-ANN

(a)

175 225 275 325 3750

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Line Length [km]

Dur

atio

n of

(V

pea

k > 1

.3 p

.u.)

[s]

tA-PSB

tA-ANN

tB-PSB

tB-ANN

tC-PSB

tC-ANN

(b)

Fig. 24. Overvoltage vs. line length at bus 3 simulated by ANN and PSB while equivalent source voltage 1.025 p.u., equivalent resistance 0.003 p.u.,equivalent inductance 0.0275 p.u., equivalent capacitance 1.8912 p.u., switching angle 36�, line capacitance 1.274e�8 F/km, and shunt reactor capacity15 MVAR. (a) Peak and (b) duration.


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Fig. 26. Studied system for testing trained ANN.

Table 6Some sample testing data and output of study system (shown in Fig. 26).

S.V. S.A. L.L. S.R. VPSB VANN ErrorV TPSB TANN ErrorT Phase

0.925 30 375 40 2.3508 2.4024 2.1962 0.3652 0.3704 1.4328 B0.925 30 240 40 2.2769 2.2328 1.9381 0.3107 0.3159 1.6649 C0.975 60 240 55 2.3016 2.3849 3.6172 0.3496 0.3458 1.0793 B0.975 75 195 12 2.3882 2.4523 2.6835 0.4073 0.4034 0.9458 B1.025 15 315 23 2.4195 2.4071 0.5124 0.4217 0.4257 0.9426 C1.025 5 282 45 2.3725 2.3413 1.3157 0.3846 0.3948 2.6419 B1.075 45 137 63 2.3596 2.3902 1.2984 0.3378 0.3424 1.3674 B1.075 53 346 10 2.8537 2.7944 2.0791 0.5449 0.5543 1.7204 B

S.V., equivalent source voltage (p.u.); S.A., switching angle (deg.); L.L., line length (km); S.R., shunt reactor capacity (MVAR), errorV, voltage error (%), anderrorT, duration time error (%).


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5.1.2. Case 2: energization of line 5_6As another case study, the system in Fig. 16 is examined. In the next step of the restoration, line 5_6 must be energized.

After converting this system to equivalent circuit of Fig. 3, i.e., after calculating equivalent circuit seen from bus 5, variouscases of transmission line energization are taken into account and their corresponding peak and duration overvoltages arecomputed from PSB program and trained ANN. Summery of a few results are presented in Table 4. It can be observed fromthis Table that the maximum percentage errors are less than 4.9%, therefore, ANN is able to learn the pattern and provideresults with an acceptable accuracy.

5.2. Study of three-phase transmission line energization

In this section, three-phase transmission line overvoltages are analyzed. Like single-phase analysis, first a sample systemof Fig. 3 is analyzed. Fig. 17 shows the harmonic overvoltages at bus 3 when three-phase transmission line is energized.

The effect of equivalent source voltage on overvoltage at different equivalent inductance as well as the effect of linelength on overvoltages at different line capacitance are presented in Figs. 18 and 19, respectively. The effect of switchingangle on overvoltage at different equivalent capacitance, and that of shunt reactor capacity on overvoltage at different equiv-alent resistance are also given in Figs. 20 and 21, respectively.

5.2.1. Training artificial neural networkIn this study, like single-phase study, a MLP with two hidden layer and 10 hidden units per layer is found to yield suffi-

cient accuracy and generalization for the proposed scheme. Fig. 22 shows the proposed MLP neural network architecture.Neural network is trained with the goal of mean square error (MSE) 1e�3. Fig. 23 shows the training of neural network.

Results for a sample test data are presented in Table 5 and Figs. 24 and 25. Table 5 contains a few sample results of test data.Column VPSB show the absolute values of peak voltage at bus 3, calculated by PSB program, while VANN column shows thevalues simulated by the trained network. Also data in column TPSB corresponds to the values of overvoltage duration calcu-lated by PSB program and TANN indicate the values simulated by the trained network. In addition, values in column phaserelate to phases that have the maximum overvoltages.

5.2.2. Energization of line 26_29For testing trained ANN, the system in Fig. 26 is examined which that is again another portion of 39-bus New England test

system. In the next step of the restoration, line 26_29 must be restarted. As mentioned before, first this system is converted




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to equivalent circuit of Fig. 3. In other words, equivalent circuit parameters seen from bus 26 are calculated. For testingdeveloped ANN, various cases of transmission line energization are taken into account and their corresponding peak andduration overvoltages are computed from PSB program and trained ANN. Summery of a few result are presented in Table6. It can be seen from the results that the developed ANN for three-phase lines energization is able to estimate overvoltagepeak and duration with good accuracy.

6. Conclusions

This paper describes a neural network approach to estimate the peak and duration overvoltages due to transmission lineenergization. Also both single and three-phase transmission lines energization are analyzed. The Levenberg–Marquardt sec-ond order training method has been adopted for obtaining small mean square error (MSE) without losing generalizationcapability of ANN. Since equivalent circuit parameters of the network are employed, developed ANNs (for single andthree-phase transmission lines) could be applied to every studied system. The results from this scheme are close to the onesfrom the conventional method and helpful in predicting the overvoltage of the other case studies within the range of trainingset. Therefore, the ANN application is recommended as an operator-training tool for estimating temporary overvoltages dur-ing power system restoration.

References

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Estimation of magnitude and time duration of temporary overvoltages using ANN in transmission lines...

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