Modelling of OHL and UG.pdf

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Journal of Electrical and Control Engineering (JECE)

JECE Vol. 2 Iss. 3, 2012 PP. 24-29 C 2011-2012 World Academic Publishing24

Modelling of Overhead Lines and Underground Cables Components for Harmonic Analysis Using

Artificial Neural Network Abderrazak Gacemi, Mohamed Boudour, Tayeb Kermezli, Hamza Houassin

Industrial & Electrical Systems Laboratory (LSEI)University of Sciences & Technology Houari Boumediene, USTHB

El Alia, BP.32, Bab Ezzouar 16111, Algiers, [email protected]

Abstract -A practical method is developed using ANN to selectoptimal number of segment constituting a model to represent apower cable at required frequencies for different levels of accuracy. As the model for distributed parameters of a powercable is considered as a reference, the present approach is basedon a mathematical analysis to improve recursive formula whichdepends on infinite cascade cells, yielding the gain response. Bycomparing the distributed parameter model to the recursiveformula, identification of the appropriate number of cellsrepresenting the cable at defined frequencies has been determined;this procedure enables to build a sufficient computed database forlearning ANN. The simulated results in ANN parametervariations of the environment compared to numerical methodsand validated experiments showed the same efficiency androbustness of our method.

Keywords - Harmonic; Power Cable; Segmented Model; Lumped Parameter; ANN

I. INTRODUCTIONElectric power transmission lines are critical network

component of electric power system. For large scale power system studies, transmission lines are traditionally modeled viaa uniformly distributed parameter or a lumped parameter configuration.

These line models have been historically developed for studies at fundamental frequency and under nominal operatingconditions. Several assumptions are often made whenmodelling transmission lines, which includes uniform currentdensity, constant material characteristics, constant externalconditions and temperature.

However, especially in recent years the high demand inelectric power and renewable energy resources with

corresponding enabling technologies (e.g. power electronicdevices) has an impact on electric power system. For example,with the augmented use of power electronic devices, anincrease in non-fundamental frequency components in the

power system can be expected.

An emerging characteristic of modern power systems is theincreased level of non-fundamental frequency components

presented in the network and it is attributed to the augmented use of power electronic switches. In addition, approximatelyup to the 15th, harmonic component is introduced in thenetwork in a capacitor-switching scenario, while common

power electronic devices introduce up to the 39th harmonic [1][2]. Under increasing presence of non-fundamental frequencycomponents, trasmission line models are investigated in thiswork.

There is a consensus that lines and cables can be modeled with a multiphase-coupled equivalent pi-circuit. For balanced harmonic analysis, the model can be further simplified into asingle-phase pi-circuit determined by positive sequenceimpedance data of component. It is important to include theshunt element. Its associated length becomes quite significantat higher frequencies. This effect can be easily represented using the exact or equivalent pi-circuit model [3].

Thus far research work on frequency-dependenttransmission line models has been performed with a focus ontransient analysis [4]-[5]. These studies consider models withfrequencydependent parameters, but not frequency-dependentstructures. Limited research has been performed on therelationship between line model segmentation and modelaccuracy [6]-[7]. In general, the previous work on the subjecthas revolved around switching studies. The exact number of gamma or pi-forms segments that are used to model the power lines is rarely addressed and is either determined arbitrarily or

by trial. Indeed, none of the published works has demonstrated the accuracy of such a modelling technique. In [6] it has beenconcluded that the model is completely inaccurate above thecut-off frequency which is the natural frequency of asegment. Even at frequencies below the cut-off frequency, thefrequency performance of the line may be inaccurate.

Several purely numerical methods have been developed tosimulate the finitely segmented Cadence Pspice softwaremodel like [8] who proposed a tool for electric power linemodelling to determine the adequate structure of power linemodel. The approach consists of a step-by-step computation toachieve correspondingly finite segmentation. However, this

tool has larger computational time because it uses an iterative process.

The main purpose of this paper is to develop a new ANN- based technique that allows users to determine the appropriatesegmentation of the line model for studies under non-fundamental frequencies. This technique will give appropriateline modelling without any iterative computation in short time.

II. PROPOSED MODELLING APPROACHThe proposed approach tends to determine the frequency

characteristics of distributed line model to compare themthrough a set of parameters for a required loading condition.We take into account some assumptions such as temperature

and current density constant since line parameters aredistributed along the line. The model parameters uniformly and


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mathematically distributed represent the power line model to be taken as the reference.

To assess the accuracy of the line model, the study is based on the features and performance of wave propagation; in

particular the attenuation and phase shift of the voltage. Thenthe model is compared to the reference one. Hence sensitive

parameters are selected to compare appropriate models

representing the line at the desired frequency, and then therequired characteristics are expressed as follows:

a. Validity of the model after the terminal behaviour i . e.at the sending and receiving ends.

b. Insensitivity to load changes in fact, this characteristicis crucial for nodal analysis in power system studies.

The selection of parameters and insensitivity to load variations of the finitely segmented model is well validated bythe present work. The model performance is characterized by areproduction of wave propagation including wave attenuationand phase shift. For this reason, quantification of the accuracyof the model is based on the analysis of loading voltage interms of difference in magnitude and phase shift betweendistributed and finitely segmented models developed from therecursive formula:

1) = -Difference in loading voltage magnitude

2) = - Difference in loading voltage phase

5TThe desired level of accuracy of the model is expressed interms of threshold values for attenuation of loading voltageand phase shift. 5T7TThese thresholds are expressed by:

5TVThreshold: Threshold value on difference in loadingvoltage magnitude

5TThreshold: Threshold value on difference in loadingvoltage phase

These threshold values representing the desired accuracydepend on the application of the resulting model. Users willselect according to this application, regardless that the mostimportant role is due to the attenuation of voltage or to the

phase shift. The frequency characteristics of the line modelwith distributed parameters can be determined analytically or through simulation software. A differential section of thedistributed line model (per-phase analysis) is shown in Figure

1 for a section of length dx. The behaviou r of the or gammamodel finitely segmented is simulated by recursive formulawith the same frequency, and then compared to the referencemodel through a set of defined parameters.

+ + + +

x dxl

Vs V+dV

Zdx

dV Is I+dI I I R

dI

ydx V RV

- - - -

Fig.1 Representation of the distributed parameter model

The equations for the distributed line model conduct are todetermine steady-state voltages and currents at any point alongthe line.

However, the relationship between terminal voltages and terminal currents at sending and receiving ends is oftensufficient in power system studies since nodal analysis isconducted:

= cosh ( ) + sinh( ) (1)= cosh ( ) + sinh( ) (2)2TBy replacing: = We obtain:

= 1

( )+ ( ) (3)With is the lin e length and = : is the propagationconstant

= is the characteristic impedance Z RR RisLoad charge

A. Mathematical Analysis 5TThe K -segments models in Fig 2 are obtained by dividingevenly the basic -model in a number K

5T(K = 1, 2, 3 ... n). When n = , we obtain the distributed parameter model.

VS Vn-1 V2 V1 VR R

Zn Zn- 1 Z 2 Z 1 ZR

12K-1K

Fig. 2 Lumped sections with K identical section terminated with ZRR

Consider the lumped sections consisting of K identical two- port sections, each of these sections is composed of impedanceZ Ra R in series and impedance Z R b R in parallel. Z Rn R and Z RR R arerespectively the input and terminals i.e. load impedances of thelumped sections. In the cascade segments these admittancesare: Z Ra R = R + jL and 1/ Y R b R = jC+G = Z R b R.

The gain response can be calculated by the followingrecursive formula:

1 = + +;

1=

//

1= 1 1

2 = +1

+ 1; 1

2= // 1

2= 1

2

. .= + 1+ 1 ;

1 =// 1 = 1 (4)

The gain response is written as follows:

=1

. 12

1 = (1 =1 ) (5)Where: = + ( // 1 )

= +

= +

B. Modeling with Neural NetworksThe artificial neural networks (ANN) are taking part of

modern techniques for modelling. They offer an alternative tomathematical modelling where system models are non- parametric statistics and non-linear. Their main advantage 3T lies


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in their 3Tcapacity of generalization. ANN has attracted muchattention due to their computational speed and robustness.Learning and architecture design of the ANN are based on acomparative approach of the line governed by the distributed model as a reference and the finitely segmented models under various predefined frequencies and accuracy 3T.

C. Database Set

The selection of the lumped segmented model in gammaconfiguration and the test application are stated in [9]. Further models to localized parameter such as the -form configurationcould be selected.

The cable in delta configuration has the followingcharacteristics defined at a 60 Hz frequency:

R R R=0.0612 / mi; X R R= 0.6081 / mi; X Rc R=0.1423 M/mi .The inductance L and shunt capacitance C for -Model arethen computed with the following expressions:

= .= 2 . (6)=

1.

=

1

2.

(7)

WhereR R R is line resistance per unit length; X R R is the line reactance

per unit length; X Rc R is the reactance of the shunt element per unit length; is the length of the line in kilometers and Z RLaod R isa constant load that is kept the same for every model.

The models are simulated within a desired frequency range.|V Rload R| and Rload R are recorded to evaluate the wave attenuationand phase shift with the desired accuracy.

The whole model is simulated and shown in Figure 5 and 6 , using the variations of distributed model as a reference and finitely segmented models.

III. SIMULATION

RESULTSIn order to assess accuracy of a line model, its performance

is characterized via the wave propagation, specifically voltageattenuation and phase shift, and then it is compared to thedistributed parameter line model. The metrics of differences involtage attenuation and phase shift are chosen according totheir characteristics of representing line terminal behaviour and of being relatively insensitive to load variations.

These features are significant for nodal analysis in power system studies.

A. Comparison between Finitely Segmented Line and the Distributed Line Models

In order to quantify the difference that is qualitatively shownin Figure 3, a comparison of absolute difference in load voltage as a function of frequency is made between each of thesegmented line models (the 1- segment, the 5-segment,, and the 25-segment) and the distributed line model.

Results of this comparison are shown in Figure.4 for avariation of the load resistance from 100 to 1 k (for aline length of 170 mi).

From these simulation results, it can be seen that the behaviour of the finitely segmented line models differs fromthe distributed line model in the fact that, the line attenuation

becomes much greater and keeps increasing after a certainfrequency which is defined as cut-off frequency, f Rc R, on theother hand the cut-off frequency increases as the number of segments increases, then the difference in attenuation between

the finitely segmented line models and the distributed linemodel varies with the number of segments of the segmented models.

Fig.3. Absolute difference in voltage attenuation between the distributed linemodel and finitely segmented models, Z RR R =1K

Fig. 4 Absolute difference in voltage attenuation between the distributed linemodel and finitely 5- segment model with variation of load charge Z RR R()

The distributed line model is compared to lumped, finitelysegmented line model at different frequencies, which varied from 0 Hz to 20 kHz, and at different load resistances, from100 to 1 k. The line model performance is observed under different loading conditions and is characterized through waveattenuation. The line model performance is shown under different loading conditions and is characterized through waveattenuation.

From the simulation results, it can be seen that theobserved behaviour follows the voltage equation for finitetransmission lines for all frequencies as we consider thedistributed model, and up to the cut-off frequency for thefinitely segmented models. These cut-off frequencies increaseas the number of segments increases. It is also noted that as thesegmentation increases, the line model seems to behavequalitatively and quantitatively closer to the distributed linemodel for all frequencies and for all load levels. The overall

performance of the segmented models as compared to thedistributed model is not greatly altered by the variation in load.This demonstrates that voltage attenuation and phase shift areappropriate metrics for the suggested line modelling approach.

Fig.5 Absolute Difference in voltage attenuation between the distributed linemodel and 5-segment m odel for length


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The behaviour of the two different-length lines against thedistributed parameter model is shown to be qualitatively thesame, but quantitatively different:

For a longer-length line, the same model segmentation as ashorter line maintains a certain level of accuracy for a smaller frequency range in comparison to a shorter line i.e. the cut-offoccurs at lower frequencies in a longer line than in shorter one.

In order to study the harmonics in the power lines, thefrequency is scanned in the considered range under the samesupply voltage and with the same loading. The simulation iscarried out for cable lengths with different models segmented in gamma configuration.

The differences :

VLoadDistributed VLoadSegmented andLoadDistributed LoadSegmented

5Tare computed and the segmented model of the appropriate precision level has been identified.

B. Implementation of ANN The proposed neural network is a multilayer perceptron

(MLP) type with a supervised learning from a given data baseformed by simulation of different cable lengths and differentlevels of precision. For the ANN outputs illustrated in Figure 6,the finitely segmented model is defined as the number of segments appropriate for a given line, whereas the inputs of theANN include cable type i.e. parameters per-length unit, thefrequencies of interest with the desired accuracy 3Tof the modelexpressed in terms of threshold values selected for the voltage

attenuation: V RThreshold R and phase RThreshold R. 3T Another input parameter is reserved for users in order to select among thevoltage attenuation or phase shift according to his or her requirement. 5TThe first layer of the neural network contains four neurons. One neuron (the eighth) is selected depending on themodel objective either V RThreshold Ror RThreshold R.

5TThe application of network strategy for modelling the line

for harmonic frequencies is given by the ANN model witharchitecture (Figure 6) whose structure is shown in Table 1.

Numbre of K_Segment

Selectiveinput

Desired accuracy( V Threshold , Threshold )

Cable Type

i=2

i=1

i=3

i=4

i=5

J=1 /f

2 /f

J /f

16 /f

k=1 /h

2 /h

k /h

21 /h

1 /g

bf1

bf2

bfj

b10

bs1

bs1

bsj

bs12

bt1

Line length

Frequencyof interest

7TFig. 6 Architecture of the neural network

TABLE I STRUCTURE OF OPTIMIZED ANN

T YPENETWORK

INPUT L AYER 1ST HIDDEN L AYER 2ND HIDDEN L AYER O UTPUT L AYER T RAINING

ALGORITHM Nb. of neurons

Nb. of neurons

ActivationFunction

Nb. of neurons

ActivationFunction

Nb. of neurons

ActivationFunction

MLP 5 16 TANSIG 21 TANSIG 1 PURLING TRINLM

The obtained ANN is trained by a database matrix of dimension (640, 10) with normalized values. Once the learning

phase achieved, the ANN is tested with a new set of input/output that forms the basis of generalization. This stepverifies the behavior of ANN on cases not learned. Theoptimization results after 1200 iterations with an error

performance are presented in table 2.

TABLE 2 7T ERROR OF THE ANN MODE 7T7TL

ANN AARE (%) AARE (%)

G ENERALIZATION MAE (%) T EST CASE

Output 0,12 0,09 0,087

C. Results and DiscussionThe desired outputs and those predicted by ANN which

lead to a very satisfactory correlation that demonstrateseffectiveness of the developed neural model and that ischaracterized by an optimal capacity of prediction for segmentnumber. The parameters form the finitely segmented modelwhich covers the harmonic and inter-harmonic frequencies of

the power cable.

Test results are carried out from a new base including datanot used in the learning phase.

The validation test is yielded from Figure 7 and 8representing the segment number changes ( = 1deg and V=1db ) against the Upper Bounds frequencies,which show good agreement between simulated and predicted values. Figure 9 and 10 representing the segment number changes against the RThreshold R and V RThreshold R show good agreement between simulated and predicted values whichconfirms the performance of our proposed ANN.

In Figure 7 and 8, graphics of upper bounds on frequencyas a function as the number of segments K is shown for accuracies set to:

Threshold = 1 deg in terms of voltage phase shift.VThreshold 1 dBthe simulation results, it can be seen that accuracy level againstthe voltage magnitude, where V 1 dB, a discrete step

behavior is observed. The behavior for accuracy level as afunction of the voltage phase, where

1 degree (deg), a more linear behavior is noted.


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100200300400500600700800900

1000110012001300140015001600

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32

ANN PredictionSimulation

# of Segments,K

U p p e r

B o u n d o n

f r e q u e n c y

( H z )

1 deg

Fig.7 Upper bounds on frequency vs. segments for selected accuracies(1deg)

0

1000

2000

3000

4000

5000

6000

7000

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34

SimulationANN Prediction

# of Segments,K

U p p e r

B o u n d o n

f r e q u e n c y

( H z )

V 1 dB

Fig. 8 Upper bounds on f requency vs. segments for selected accuracies(V1deg)

0 2 4 6 8 10 12 14 16 18 20 22

02468

1012141618202224262830323436

f=60 Hz: Simulation ANN predectionf=180 Hz: Simulation ANN predectionf=300 Hz: Simulation ANN predectionf=500 Hz: Simulation ANN predectionf=900 Hz: Simulation ANN predectionf=1500Hz: Simulation ANN predectionf=2340 Hz: Simulation ANN predection

N u m

b r e o f

S e g m e n

t k

#of (deg)

Fig. 9 Segment number variation vs Threshold for harmonics frequencies

0 2 4 6 8 10 12 14 16 18 20 22

02468

10121416

1820222426283032

f=60Hz: Simulation ANN predectionf=180Hz: Simulation ANN predectionf=300Hz: Simulation ANN predectionf=500Hz: Simulation ANN predectionf=900Hz: Simulation ANN predectionf=1500Hz: Simulation ANN predectionf=2340Hz: Simulation ANN predection

N u m

b r e o f

S e g m e n

t k

#of V (dB)

Fig. 10 Segment number variation v s. V threshold for harmonics frequencies

Therefore, a single lumped equivalent circuit is sufficient

for line studies at the fundamental frequency and does notconcern the line at higher frequencies. On the other hand, thedifferences of phase and voltage attenuation V betweenthe distributed and the finitely segmented models varyinversely with the number of segments.

IV. CONCLUSIONSThis paper presents a practical method of neural network

modeling for power line to predict an appropriate finitelysegmented model to obtain steady-state analysis of non-fundamental frequencies with a predefined accuracy level.

The optimized architecture ANN- MLP enables us to predict the number of segments with a high performance error.

The simulation was tested on a real line confirming therobustness and the predictive ability of our model which isonly based on the characteristics data of the line.

For future works it would be worth to develop neuralnetwork model by including parameters per-length unit as afunction of frequency and temperature along the line. This willcertainly have an impact on the obtained finitely segmented model.

R EFERENCES [1] G.T.Heydt, Electric Power Quality , 2nd Edition: Stars in a Circle

Publication, 1994.[2] M. Undeland and Robbins, Power Electronics- Converters Applications

and Design , 3rd Edition: John Wiley & Sons: 2003.[3] Vazquez, J., Salmeron, P., Active power filter control sing neural

network technologies ," IEE Procedings-Electric Power Applications, vol.150, pp. 139- 145, 2003.

[4] A. Monticelli, State Estimation in Electric Power Systems, a Generalized Approach (Power Electronics and Power Systems), 1st Edition:Springer, 1999.

[5] J.R. Marti, Accurate Modeling of Frequency-Dependent Transmission Lines in Electromagnetic Transient Simulations , IEEE Transactions onPower Apparatus and Systems, Vol. PAS-101, No. 1, January 1982.

[6] G.L. Wilson, R.F. Challen, D.J. Bosack, Transmission Line Models for Switching Studies: Design Criteria, I. Effects of Non transposition and Frequency , submitted to IEEE, September 1973.

[7] L. M. Wedepohl, H. V. Nguyen, and G. D. Irwin, Frequency-dependent transformation matrices for untransposed transmission lines using

Newton-Raphson method , IEEE Transactions on Power Systems, Vol. 11,Issue 3, August 1996. Page(s): 1538-1546.


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[8] G.L. Wilson and K.A. Schmidt Transmission Line Models for SwitchingStudies: Design Criteria II. Selection of Section Length, Model Designand Tests IEEE Transactions on Power Apparatus and Systems, Vol.PAS-98, January/February 1974. Page: 389-395.

[9] C.Valentina , A. Leger, K. Miu., Modeling Approach for Transmission Lines in the Presence of Non-Fundamental Frequencies IEEE,VOL.24,NO,OCT,2009.

[10] Transactions on Power Ddelivery, Vol. 24, No. 4, October 2009.[11] S. P. Carullo, C. O. Nwankpa, and R. Fischl, Instrumentation of Drexel

Universitys Interconnected Power Systems Laboratory , Proceeding of the 28th Annual North American Power Symposium, Cambridge MA,October 1996, pp. 367-376.

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Modelling of OHL and UG.pdf