00483421 - Neural Network Based Estimation of Power Electronic Waves

7/28/2019 00483421 - Neural Network Based Estimation of Power Electronic Waves

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NEURAL NETWORK BASED ESTIMATION OFPOWER ELECTRONIC WAVESMin-Huei Kim*, M . Godoy Sim8es** and Bimal K . Bose

Department of Electrical EngineeringThe University of TennesseeKnoxville, TN 37996

Abstract - Artificial neural network techniques are recentlyindicating a lot of promise for application in power electronicsystems. So far, these applications are mainly confined in thecontrol, identification and diagnostic problems, but the applicationin estimation is fairly new. The paper explores the application ofneural network for estimation of power electronic waveforms. Thedistorted line current waves in single-phase thyristor ac controllerand three-phase diode rectifier that feeds an inverter-machine loadhave been taken into consideration and neural networks have beentrained to estimate the total rms current, fundamental rms current,displacement factor and power factor. The performance of theneural network based estimators has been compared with the actualvalues, and indicate excellent performance. Neural network basedestimation has the usual advantages of very fast and simultaneousresponse of all the outputs, noise and fault-tolerant performance,and can be easily implemented in dedicated analog or digitalhardware chips which can coexist with DSP and/or ASIC chips.The estimation techniques can be extended to more complexwaveforms in power electronics.

I. INTRODUCTIONPower electronic circuits generate complex voltage andcurrent waves due to their switching mode operation. For control,monitoring and diagnostic purposes, it is frequently necessary toprocess these waves and generate the outputs, such as rms current,fundamental rms current, active power, reactive power,

displacement factor, distortion factor, power factor, etc. It ispossible to make estimation from basic closed form mathematicalmodel of the system, if such a model can be obtained. The modelequations are often nonlinear, complex and distributed in naturemaking this approroach difficult. The topological form of thesystem canbe simulated on computer with the known parameters,and then analytical calculations can be made on the resultingwaveforms. Sometimes, the mathematical model and parametersmay be totally unknown making such estimation approachimpossible. For a prototype operating system, electronicinstrumentation (both hardware and software) techniques areextensively used for such measurements. For example, thewaveforms may be captured and then analyzed by FFT in realtime to derive the estimated outputs. Similar techmque can beused for estimation from the waveforms recorded on oscilloscope*Dr K m s currently in leave of absence from Yeungnam J m o r College of Korea and isbeing supported by Academic Research and Promotion Division ofKorean Government

or chart recorder. One difficulty in all the above estimationmethods is that the response tends to be slow because of theprocessing involved.To avoid the complexity of estimation, it maybepossible to get the solution by one or multi-dimensional look-up tables in microcomputer memory. However, for improvementof accuracy, the size of the look-up table should be large, orinterpolation calculation is required.Recently, fuzzy lo ac was applied [11 to solve some of theproblems in the estimation of power electronic waveforms.Because of large number of manual iterations necessary fordesigning the membership functions, fuzzy estimation algorithmdevelopment is tedious and time consuming. Besides, sequentialcomputation is generally necessary in DS P to implement thecomplex steps of the algorithm.In this paper, feedforward neural network techniques havebeen systematically explored for estimation of power electronicwaveforms. Single-phase hyristor ac controller and three-phasediode rectifier line current waves have been taken intoconsideration and neural networks have been trained to estimatethe total rms current, fundamental rms current, displacementfactor and power factor. Neuralworks Professional IIPLUS [2]simulator program that uses back propagation training algorithmwas used for training the networks. In the beginning, neuralnetwork was trained to function as a calculator for estimation ofthe outputs with the input variables, such as firing angle,impedancemagnitude and angle for the thyristor controller. Then,for both the circuits, the patterns of the waveforms characterizedby the width and height were used to train the estimator networks.The performance of the neural network based estimators wasfound to be excellent.

11. NEURAL NETWORK PRINCIPLESSince the neural network technology is somewhat new to thepower electronics community, it is appropriate here to brieflyreview its salient features 131-[7]. Neural network or artificialneural network (ANN) is the interconnection of artlficial neuronsthat tends to emulate the nervous system of human brain. Themodel of an artificial neuron that closely matches a biologcal

**Prof Sunzes is currently in leave of absence from University of SHo Paulo, Bradl and iski upported by National Council forScientific and Technological Development(CN Pq).

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neuron is gwen by an op-amp-like summer. The input signals X,,X X, X are normally continuous signals which flow throughsynaptic weights and then accumulate in the summing node. Theweights can be positive or negative, and correspondingly,accelerate or inhibit the respective signals coming to the summingnode. The summed signal then flows to the output through atransfer hc tion which is usually nonlinear. The transfer functioncan be threshold type, signum type or linear threshold type, or itcan be nonlinear continuously varying type, such as sigmoid,inverse-tan, hyperbolic or Gaussian type. The sigmoidal transferfunction is most commonly used, and is given by the equation

where a is the gain that adjusts the slope of the function. At highgain, f(x) approaches a step function. The sigmoidal function isnonlinear, monotonic, differentiable, and has the largestincremental gain at zero signal, and these properties are ofpacular interest in the application of neural network. Note thatthe nonlinearity of the transfer function gives the networkcapability to emulate nonlinear mapping property. A neuralnetwork can be classified as feedforward or feedback typedepending on the interconnection of the neurons. At present, byfar the majority of applications (including that in this project),uses feedforward architecture and this type will be discussed inthe paper. Fig. 1shows the structure of a feedforward multilayernetwork whch consistsofthree ayers: the input layer , he hiddenlayer, and the output the layer. The circles represent neurons andthe dots in the connections indicate the weights. The input andoutput layers have neurons equal to the respective number ofsignals.O U T P u rIDDENLAVER

x ,

LwlDP F

PF

Fig.1 Structureof a three-layer freedforward neural network showingback parpagation training.For example, in Fig.1, the input signals may be current wavepatterns characterized by the width (W) and height (H),and thecorresponding output signals may be total rms current (Is),

fundamental rms current (13, displacement factor (DPF) andpower factor (PF). The particular network shown with 4 hiddenlayer neurons can be defined as 2-4-4 network. The input layerneurons do not have transfer function, but there are scale factorsto normalize the input signals, as shown. Similarly, there can bescale factors at the output for denormalization. There can be morethan one hdden layer. The number of hidden layers and thenumber ofneurons in each layer depend on the complexity of theproblem being solved and the desired accuracy. Note that neuralnetwork computes very fast in parallel and distributed mannercompared to slow sequential computation in a conventional VonNeumann computer that takeshelp of centralized CPU and centralmemoq. Besides, the network has fault-tolerant property andprovides noise-immune computation [SI. If a few weights areerroneousor several connections are destroyed in a large network,the output remains practically unaffected because of distnbutedknowledge throughout the network. The computation of neuralnetwork basically relates to nonlinear mapping or patternrecognition function. This means that if an input set of datacorresponds to a definite signal pattern, the network can be"trained" to give a correspondinglydesired pattern at the output.The network has the capability to "learn" because of thedistributed intelligence or "associative memory" propertycontributed by the weights. The input-output pattern matching ispossible if the network is trained, i.e ., appropriate weights areselected. With the network initially untrained, i.e., with theweights selected at random, the output signal pattern will totallymismatch the desired pattern for a given input pattern. The actualoutput pattern can be compared with the desired output patternand the weights can be adjusted by an algorithm until the patternmatching occurs, i.e., the error becomes acceptively small. Backpropagation training algorithm is most commonly used forfeedfoward neural network. The training is usually automatedwith off-line computer simulation program that uses a largenumber of input-output example patterns. The example patternscan be derived ffom analysis, simulation or by experiment ifthemodel is totally unknown. At completion of the training, theweights are downloaded to the prototype network. A trainednetwork should be able not only to recall all the example input-output patterns (look-up table function) but also to interpolate theexample patterns.

III.ESTIMATION FOR THYRISTOR ACCONTROLLER LINE CURRENT

Fig.2 shows the simple circuit of a single-phase anti-parallelthyristor ac controller with passive R-L load. The fving angle ofthe thyristorscanbe controlled symmetrically to control the powerto the load and the minimum firing angle is restricted to theimpedance angle when the conduction becomes continuous. Apopular application of the circuit is incandescent light dimmerwhere the load is resistive, and in this case, the thyristors can be

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replaced by a triac. With purely inductive load, on the other hand,the phase angle control can emulate variable inductance andtherefore the circuit is defined as thyristor-controlled reactor(TCR). A TCR in parallel with fixed capacitor is popularly usedas static VAR compensator. The line current waveform inthyristor ac controller is highly nonsinusoidal and depends onfiring angle, load impedance and the impedance angle [9].Feedforward neural networks will be trained to estimate the totalm line current, hndamental rms line current, line displacementfactor and power factor. The supply voltage will alwavs beassumed as sinusoidal and constant.

Fig. 2 Single-phase thyristor ac controller with R-L loadA. Estimation for R-L Load

The instantaneous line current in Fig.2 can be expressed as[101:

where a=fr ing angle, V,=peak value of supply voltage (4 2 Vsj,R=load resistance, X=load reactance, IZ =impedance amplitude,o=angular frequency, @=impedance ngle (tan-'(X/R)).Assuming the supply voltage and frequency as constants, i.e.,220 V and 60 Hz, espectively, the eqn.(2) shows that the linecurrent is a hction of firing angle (a), impedance maptude( 1 Zl ) and impedance angle(@). Derivation of mathematicalexpression forrmcurrent, fundamental rms current, displacementfactor and power factor &om eqn.(2) tends to be very complex [ 9 ] .In the present project, the circuit of Fig.2 was simulated bySIMNON to derive the line current wave. Then, the current wavewas analyzed by FFT program in the MATLAB and the correctvalues of Is,I , DP F andPF were derived. This data table relatingthe input variables and the correspondingly calculated values wasthenused to trai nthe neural network which will be described next.1) Variable Firing Angle (a)In the beginning, it was decided to test the feasibility ofestimation of I,, I , DPF and PF with the help of a neural networkfor variable firing angle only, i.e., the load parameters remain

constant.The inng angle is varied in the range of 30 O -180 wherethe waveform becomes continuous at the minimum firing angle.The training data table was prepared for peak current 1 OA (i.e.,Vm=220d2V and -220d2 Q with 16steps of firing angle anda neural network of structure 1-4-4 was trained with the help ofNeuralworks Professional IIPLUS simulator program. Afterlarge number of training steps (1.5 million), the neural networkbased estimator error was found to be below 0.1%. Fig.3 givesthe estimator performance for variable firing angle. While theDPF and PF show the actual values, the I,(pu) and IXpu) can bedenormalized after multiplying by the scale factor 1Z, /I Z .Notethat supply voltage variation has a similar scaling effect (seeeqn(1 ). An attempt to reduce the hidden layer neurons or lessnumber of training steps gave larger estimation error. Althoughsixteen a angle steps were used for the training, Fig.3 indicatesprecision estimation in the interpolateda values

Fig.3 Neural network estimator performance with variable firing angle2) Variable Load Impedance (I Zl )Nest, estimation was continued for variable load impedance(magnitude only) maintaining the firing angle and impedanceangle constant. With IZ, //Z as input variable, Fig.4 shows theperformance of a 1-4-4 neural network estimator. Again, theestimation error after large number of training steps converges tobe less than 0.1%. As indicated before, DPF and PF wereinsensitive to impedance variation, but I, (pu) and If pu) showlinear variation.

1.0 I I II

Fig.4 Neural network estimator performance with variable impedance

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B. Estimation from Wave Patterns3) Variable Impedance Angle (4)Next, neural network estimation was considered with vanableimpedance angle only Note that the current wale is alwavsdiscontinuous except when a{$ Fig 5 shows the estimatorperformance where the accuracy was comparable with Figs 3 and4

Fig.5 Neural network estimator performancewith variable impedanceangle4) Variable Firing Angle, Impedance and Impedance AngleOnce the feasibility of estimation was proved and highaccuracy was demonstrated for individuala, ZI and 4 inputs, itwas decided to train a network where all the three input variablescan change. After a number of trials, it was found that the networkrequires twohidden layers with 16 neurons in each for reasonableaccuracy.Any combination of inputs that results continuous currentwave was excluded.For example, any as@ will cause continuousconduction. Large number of 1Z, /I Z values are not desirablebecause DPF and PF outputs will not be affected by it and I,(pu)and IXpu) will have only linear scaling effect by impedancevariation.As mentioned before, I,(pu) and Ikpu) can be convertedto actual values by multiplying with the scale factor ~Z,!I Z forthe input condition IZ,,l/IZI=l.O. Very large number of trainingsteps (14.3 million) were used to train the complex network andthe error was found to converge below 0.2%. Figs.6;7,8,9 showthe estimator performance for I,(pu), I, (pu), DPF and PF;respectively, where$4indicates resistive load. Note that in allthe figures, the estimation curve for constant 4 terminates at a=@ so that conduction is always discontinuous. Because ofcrowding, the estimation curves for Figs. 6 and 7 are shown foronly a few values of 4.

Aftervahdation of neural network estimation with control andload parameta variables, it was decided to train the network Lviththe wave pattern input characterized by its width (W ) and height(H), and only resistive load was taken into consideration Theexpressions of DPF, PF, I,(pu) and $(pu) in terms of W and Hparameters are given as follows [1]

0

Fig.6Neural network estimator performance of rms current whenfiring angle and impedance angle are varying

-- I I

bFig.7Neural network estimator performanceof fundamental rm s

current when firing angle an d impedanceangle are varying

DPF

Fig.8Neural network estimator performanceof displacement factorwhen firing angle and impedanceangle are varying

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(9)PF = A - B . W1PF = DPF - 2IS

Where V,=dc link voltage, =peak value of supply phasevoltage, I,,=per phase source inductance, w e=supply frequencyand AO=angular interval of current from peak value to zero. Thepower circuit with the machine load was simulated and the lineside waveforms were derived with the load variation. Obviously,both I, and If are very sensitive to W and H variation ,but DPFand PF are somewhat insensitive to these parameters. For eachsimulated wave pattern characterized by W and H, MATLABanalysis was performed to derive I,, I , , DPF and PF , and thecon-ebpndmgdata table was used to train a 2-8-4 neural network.Fig.12shows the estimator performance with increasing machineload where the error was found to be below 0.25% after a verylarge number (1 3 million) of training exercises.

1 - --- -5 10 15Increasing Mac hine Load (Exp. I )

Fig.12 Neural network based estimator performancefor supply currentwave pattems described by pu lse0 and h e i g h t 0

V. CONCLUSIONThe paper successfully demonstrates the validity offeedfonvard neural network for the estimation of distortedwaveforms in power electronics. Two circuit configurations have

been consideredin the present project: a single-phase anti-parallelthynstor ac controller and a three-phase diode rectzier feeding toan nvmer-inductionmotor load. In both the circuits, the line-sidetotal rms current, fundamental r m s current, displacement factorand power factor were estimated with the help of trained neural

networks. In the beginning, the thyristor controller waveformswere estimated by considering the control and/or load variables asthe input to the neural network. In this function, the neuralnetwork basically acts as a calculator. Then, for both the circuits,the neural network estimates the output from the known wavepattems characterized by their width and height. In this case: thenetwork basically acts like a pattern recognizer. In all cases ofestimation, the training data tables were generated by simulation.After large number of training steps, the estimator accuracy \\'asfound io be excellent. The estimation principle can be extendedto more complex waveforms. The estimator neural network chipscan easily be integrated with DSP andor ASIC chips in a pon.erelectronic ?stem to relieve their computational burden.

VI. REFERENCES[11 M.G.Sim&s and B.K.Bose, "Application of fuzzy logic in theestimation of power electronic waveforms", LEEE-IASAnnual Meeting, 1993. pp.853-861.[2 ] Using Neuralworks Professional IIPlus, NeuralwareReference Manual, 1992 .[3] D.E.Rumelhart and J.L.Mcclelland, Parallel DistnbutedProcessing, The MIT Press, 986.[4] T.Ful\uda, T.Shibata, "Theory and application of neuralnetworks for industrial control systems", IEEE Trans.Industrial Electronics, Vo1.39, 1992, pp.472-489[SI J.G.Kuschewski etc., "Applicationof feedfonvard neuralnetworks to dynamical system identification and control",

IEEE Trans. Control Systems Technology, Vol. 1, No. 1March 1993, pp.37-49.[6] B.K.Bose, "Expert system,fuzzy logic and neural network

applications in power electronics and motion control",Proceedings of the JEEE, pp. 1303-1323, August 1994[7] J.Lawence, S.Luedeking, "Intrcduction o Neural Networks"California Scientific Software, 199 1.[8] M.G.Sim6es and B.K.Bose, "Neural network basedestimation of feedback signals for a vector controlledinduction motor drive", IEEE-IAS Annual Meeting, pp. 47 1-479,1994.91 A.W.Kelley and W.F.Yadusky, "Rectifier design forminimum ine current harmonics and maximum powerpactor", IEEE Trans. Power Electronics, Vo1.7, No.2, April101 W.Shepherd and L.N.Hully, Power Electronics and Motor1992, pp. 332-341.

Control, CambridgeUniv. Press, 1987.

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00483421 - Neural Network Based Estimation of Power Electronic Waves