PEDS 2007

Neural Identification ofAverage Model ofSTATCOM using DNN and MLP

M. Tavakoli Bina* and S. Rahimzadeh** Faculty of Electrical Engineering, K. N. Toosi University of Technology, P. 0. Box 16315-1355, Tehran 16314, Iran,

E-mail: tavakoligieee.org

Abstract-Modeling of STATCOM is conventionallyperformed in the time-domain. Amongst them, dq-theory iswell-known in which state-space equations are used for theanalysis. Power systems, however, use the frequency-domaininformation in phasor-related studies such as load flowanalysis. Because time-domain models of FACTS controllerscannot be directly applied to the power system analysis, anintelligent model can usefully bridge the time-domaininformation to the corresponding frequency-domain data.This paper proposes two neural network identifiers basedon the existing time-domain average model of STATCOM.Extended resultant bridge presents an average-neuralmodel of STATCOM, which can be analytically applied topower systems. To this extent, design and development oftwo neural network identifiers are performed using thedynamic neural network (DNN) and the multi-layerperceptron (MLP). To verify the developed models, theexact solutions obtained from the average model ofSTATCOM are compared with the outcomes of the DNNand the MLP identifiers. Moreover performance of the twoidentifiers is accordingly compared as well.

Index Terms-- DNN, FACTS controllers, MLP, modeling,neural-averaging, STATCOM.

I. INTRODUCTIONDEREGULATED systems consider transmission

lines as the principal components of theelectricity market for both producers and consumers ofenergy. At the same time, an optimal power flow (OPF)determines the amount of energy to be transferredthrough each transmission line. This further helps themarket to achieve a competitive pricing tool. Therefore,it is necessary to develop accurate models in order toestablish a fair pricing system. In fact, if the operation ofthe modelled equipments is close to that of their exactdevices, the energy pricing will be more accurate. Inparticular, this would be crucial when FACTS devices areengaged in the OPF for mitigation of congestion oftransmission systems (CTS).

Typically, in [1]-[5], FACTS devices are suggested toalleviate and/or regulate the CTS. Additionally, theFACTS devices are modelled as either pure reactiveelements (e.g. inductors and capacitors) or independentvoltage/current sources. However, power losses ofFACTS devices are not included in the analysis by theintroduced models, assuming negligible energyconsumption by the device itself. When the number andcapacity of the employed FACTS devices increases,

considerable energy losses is cancelled in power flowanalysis (i.e. part of the network load is cancelled). Thisundermines the correctness of the process of energypricing management.

Meanwhile, the principal objective is to bridge theinstantaneous models to the power system single-frequency requirement. For example, power flow analysisis widely used in power systems in order to control activeand reactive power as well as protection systems and pre-fault calculations. Moreover, deregulated power systemsand the CTS control are additional applications inelectricity market. This paper develops a bridgingintelligent identifier that includes power losses in theanalysis. Moreover, we assume an existing average modelof STATCOM that is based on the well-known stat-spaceaveraging technique [6]-[8]. The average modelappropriately takes into account the low-frequencyvariations of the DC-link of the converter as well as thepower losses related to the AC-side. It should be notedthat the switches are treated as ideal.

However, one issue concerned with this model is thatfor each switching period a considerable number ofdifferential equations have to be solved. This depends onthe switching frequency, and takes long to process theOPF. To remedy this issue, the neural network modellingtechnique is employed to link the instantaneous outcomesof the STATCOM to the single-frequency power systemanalysis. The developed model produces power losses aswell as angles and magnitudes that are suitable for phasoranalysis in steady-states. Here it is examined twoidentifiers; the dynamic neural network (DNN) and themulti-layer perceptron (MLP). The objective is tocompare the accuracy and reliability of the twoidentifiers. In this paper the developed model is calledaverage-neutral (AN) model of STATCOM.

II. AVERAGE MODELAveraging technique is a common approach to the

modeling of power converters. Switch-mode convertershave a discontinuous behavior, which is very complex inanalysis. Average modeling approximates the behavior ofthe converter from a periodic discontinuous system to aperiodic continuous one, maintaining smooth waveformsby removing high order harmonics. Average model ofSTATCOM is presented in [6], shown here by Fig. l(a).

1-4244-0645-5/07/$20.00©2007 IEEE 1665

pR U.2

g (D(t, Vl) f

Z L R 1. -1:;-0.5 0 1052 10 1.5

(a) (b)

V~~~~~~~~~~~~~

1~~~~ ~ ~~~~~~~~~~~~~~~~~~~~~ ton

C~ON

(c)Figure 1: (a) Average circuit model of STATCOM, (b) typical internal power losses of STATCOM obtained by the average model, and

(c) adaptation of the average model connected to the power system by adding a bus for STATCOM.

In this model, L introduces the equivalent couplinginductance between the converter and the power system.The resistance R is part of the compensator losses relatedto the interconnection of the converter to the powersystem. The other part of the power losses corresponds tothe converter losses that are absorbed by the propermodulation of the converter switches. Fig. l(b) showstypical STATCOM power losses in P.U. against thephase shift between the converter output and the powersystem voltage ( a ) that is obtained by the averagemodel.

While the average model presents a time-dependentcircuit, a PQ or PV model is essential for the power flowanalysis. Hence, here it is performed adaptive analysis toget the supplied active and reactive powers ofSTATCOM ( PCON and QCON). A new bus is added forevery STATCOM as the converter AC voltage, which isconnected to an existing bus n through the commutationreactance (XCON ) and the AC resistance (R ).

III. IDENTIFICATION OF STATCOM MODEL USINGNEURAL NETWORK

Average model of Fig. l(a) describes a state-spacemodel in a circuit format, which solving differentialequations will lead eventually to a steady-state solution.Meanwhile, moving from one steady state to anothertakes time to complete the transient regime that is notsuitable for the OPF. An OPF program seeks among thefeasible region for a desirable solution. Thus, it is

necessary for the OPF to be performed as fast as possible.One approach to achieve a fast OPF is the identificationof the average model of STATCOM using the neuralnetwork. The average model is analyzed as a reference togenerate required training data for the average-neuralmodel (AN).

Training data can be produced in two steps. First, Fig.l(a) is assumed as the exact model suggested in [6].Then, to cover operating range of STATCOM, magnitudeof the terminal voltage is varied within lVt1 E [0.7,1.2]P.U. by small steps (e.g. 0.01 P.U. (see Fig. 1(c))). Also,the phase angle between the converter voltage VCONand the terminal voltage Vt ( Z(VCON,Vt) ) is varied

within a E [-1.5°,1.5°] by small steps (e.g. 0.01° ). Forthe given small steps, total number of operating pointssums up to 15000 set of steady-state training data for theSTATCOM.

Second, for every operating point, the time-domainmodel of Fig. l(a) is solved. Then, the steady-statephasors are obtained from the instantaneous solution.This is used to calculate and store the absorbing active aswell as generating/absorbing reactive powers ofSTATCOM delivered to bus n. Gathering all thecalculated data leads to formation of a database forsingle-frequency operation of STATCOM in powersystem.

The next step will be the study and selection of asuitable neural network identifier for the average model

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of Fig. l(a). Here we identify the average model ofSTATCOM by two well-known neural networkidentifiers, dynamic neural network (DNN) and multi-layer perceptron (MLP). It is noticeable that otheridentifiers should also be investigated that is left forfuture studies. Outcomes of the AN identifiers ofSTATCOM are then correspondingly compared.

A. The DNN neural identifierThere are various structures for the dynamic neural

network. The employed structure for identifying the ANmodel is given by Fig. 2 in which the DNN includes twolayers. The hidden layer has delay blocks taken from theneurons, which take the data history of the network intoaccount for the progressing output. Index e correspondsto the exhibitory positive classes (e.g. positive input

vector Xe ), and index i relates to inhibitory negativeclasses (e.g. negative input vector Xi ). Each neuron fromthe exhibitory class has a delayed input from itscorresponding neuron in inhibitory class and vice versa.Output of each neuron is applied to a non-linear neuronactivation function to be able to model non-linearsystems.

Then, the outcomes of the activation functions are

weighted by a2 for exhibitory classes, and by b2 forinhibitory classes. These weighted productions areeventually applied to the linear activation function of theoutput layer to get the output of the DNN. Theadvantages of the DNN are non-linear modellingcapability as well as the fast network convergence

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Figure 2: The structure of the DNN that is designed to identify the average model of STATCOM.

.C0' Avrage Mode Responses002 ynarmic Neura NetWrk Responses

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0016 0005r

001

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0002 -

0 5100 1000 2 4 6 8 10 14 1b 18 20 U 500U 1UUUU 1!UV

Epochs Train Data

(a) (b)Figure 3: (a) Mean squared error of the trained data, (b) The output (power losses) of the DNN AN together with the exact output of

average model for 15000 trained data.

because of the inherit delays of the structure. The

following relationships describe the designed feedforward state of the network:

X =[XX(x21)Xi =[IX X2 ]

Net1 (t) al Xe (t) + aNet1 (t- 1) -bl Netd (t- 1) (2)

Net1 (t) b1 Xi (t) + bi Neti (t - 1) - al Net1 (t - 1) (3)

1(t) + (4)NetT1 (1) =Net Net.

O (t) = f3(t) =1 -NetT' (t).k

l+e(5)-NetT' (t).k

All parameters of the network are trained using theback propagation method, and the structure is designed

by trial end error. In this research, different structureswere examined in which 25 neurons is considered for thehidden layer alongside with one neuron for the outputlayer.

Designed structure of Fig. 2 is simulated withMATLAB, where Fig. 3(a) shows the reduction in meansquared error of the training data, Fig. 3(b) depicts theoutput of the DNN as well as the power losses analysedby the average model, and details of zooming Fig. 3(b)

for various terminal voltages over a E [-1.5 ,1.5° ] willbe presented in the full paper. Simulation results indicatethat the AN model of STATCOM, developed by theDNN, introduces the mean squared error of 0.12% andmean error of 0.3775% for the trained data. This situationconfirms that the DNN is unable to develop successfullythe AN model of STATCOM because the DNN uses thehistory of the response to identify the progressing output.

B. The AN model using the MLPThe MLP neural network is a global estimator, which

an initial processing on training data is taken place

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Hidden Layers Output Layer

Input First Layer Second Layer Third Layer

f ____________la a

Sl X; g2S SIw|u

a-f, (Xp±b ) an-f X +b') a=tf x) f3as = f 3 (Wt3f (WXp+I1)+h +b3)

Figure 4: (a) The structure of the designed MLP neural network to identify the average model of STATCOM.

Performance is 3.79562e-008X Na&eural Netork Responses

-0-005

-0-015V.~~~~I

lo-'~~~~~~~~~~~~~~~~HH-0.025

~~~~~~~- -00 '' iItI Ii

-0.03O 51) 10 150 200 250 300 350 400 450 500 b 500C 10000 15000

600 Epochs Train Deta

(a) (b)Figure 5: (a) Mean squared error of the trained data, (b) The output (power losses) of the MLP AN together with the exact output of

average model for 15000 trained data

followed by designing its structure for the AN model.Structure of this design is shown by Fig. 4, where threehidden layers are proposed for the MLP neural network.By examining and performing various tests, eight neuronsare considered for the first and the second layers and oneneuron for the third layer. Neuron functions of the firstand the second layers are considered identical as follows:

n -nf (n)= f (n)= e (6)

Also, weighting matrices of the three layers areW,

W2 and W3, and the 2 x I input vector P includes theterminal voltage and injected reactive power ofSTATCOM to bus n as shown by Fig. 1(c). Threevectors bI, b2 and b3 are the threshold values of theneurons, and three outputs of the three layers are ala2 and a3.To train this network, again 15000 operating states are

used. Figure 9(a) demonstrates the reduction of the meansquared error during the training process, and Fig. 5(b)gives the response of the MLP AN model to these traineddata alongside with the exact power losses of the averagemodel. Simulation results show that when the AN modelof STATCOM is identified by the MLP, then the errorbetween the average and the AN models is considerablylow. The mean error is equal to 0.0147%, and the meansquared error is 0.000003795%. Hence, the MLPidentifies the average model with an acceptable error,much lower compared to the DNN.

IV. CONCLUSIONAverage model of STATCOM describe its exact

operation, while high frequency ripples are ignored. Thismodel can be used for steady state analysis of powersystems such as load flow program. However, anidentifier is needed to bridge the time domain averagemodel to the frequency domain power system analysis.

This paper aims at doing this objective by designing twoneural network identifiers; the dynamic neural network(DNN) and the multi-layer perceptron (MLP). Theseneural networks are trained using up to 15000 steadystate operating data that are obtained by simulating theaverage model of STATCOM. Outcomes of the twoidentifiers are compared with the exact solutions of theaverage model. The results show that the MLP providesmuch more accurate outcomes compared to the DNN.Therefore, the MLP identifier can be applied to the powersystem planning and analysis purposes.

ACKNOWLEDGEMENT

The authors would like to thank the support of theResearch Laboratory of power quality and reactive powercontrol in K. N. Toosi University of Technology.

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FACTS Devices", IEEE Transactions on Power Systems,vol. 20, no. 3, August 2005, pp. 1597-1605.

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[3] G. M. Huang and P. yan, "Establishing Pricing Schemes forFACTS Device in Congestion Management", IEEE PES GeneralMeeting 2003, vol. 2, Issue 13-14, July 2003, pp. 1025-1030.

[4] s. C. Srivastava and P.Kumar, "Optimal Power Dispatch inDeregulated Market Considering Congestion Management",IEEE, International Conf on Electric Utility Deregulation andRestructuring and Power Technologies Proceedings, DRPT 2000,vol. 1, pp. 53-59.

[5] s. Verma et al, "FACTS Devices Location for Enhancement ofTotal Transfer Capability", IEEE PES Winter Meeting 2001, vol.2, 2001, pp. 522-527.

[6] M. Tavakoli Bina and D. C. Hamil, "Average Circuit Model forAngle-Controlled STATCOM", IEE Proceedings.-Electric PowerApplications, vol. 152, no.3, May 2005, pp. 653-659.

[7] P. T. Krien and et al, "On the use of averaging for the analysis ofthe power electronic systems", IEEE Transactions on PowerElectronics, vol. 5, no. 2, pp. 182-190, April 1990.

[8] M. Tavakoli Bina and M. Panahlou, "Application of AveragingTechnique to the Power System Optimum Placement and sizingof Static Compensators" International Power EngineeringConference, 2005, IPEC 2005, 29 Nov.-2 Dec. 2005, pp. 1-6.

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