Proceedings of Intemational Joint Conference on Neural Networks, Montreal, Canada. July 31 - August 4. 2005

System and Method for Determining HarmonicContributions from Non-Linear Loads Using Recurrent

Neural Networks

Joy Mazumdar and Ronald G. HarleySchool of Electrical and Computer Engineering

Georgia Institute of TechnologyAtlanta, GA 30332-0250 USAron.harley@ece.gatech.edu

Abstract - This paper proposes a neural network solutionmethodology for the problem of measuring the actual amount ofharmonic current injected into a power network by a non-linearload. The determination of harmonic currents is complicated bythe fact that the supply voltage waveform is distorted by otherloads and is rarely a pure sinusoid. Harmonics may therefore beclassified as contributions from the load on the one hand andcontributions from the power system or supply harmonics on theother hand. A recurrent neural network architecture basedmethod is used to find a way of distinguishing between the loadcontributed harmonics and supply harmonics, withoutdisconnecting the load from the network. The main advantage ofthis method is that only waveforms of voltages and currents haveto be measured. This method is applicable for both single andthree phase loads. This could be fabricated into a commercialinstrument that could be installed in substations of largecustomer loads, or used as a hand-held clip on instrument.

I. INTRODUCTIONThe objective of the electric utility is to deliver a

sinusoidal voltage at fairly constant magnitude and frequencythroughout its network. However, with the widespreadproliferation of power electronic and other non-linear loads,significant amounts of harmonic currents are being injectedinto the network by these loads. When such loads are suppliedfrom a sinusoidal voltage source, their injected harmoniccurrents are referred to as contributions from the load. Figure1 shows a simple network structure.

i, (1) = (.h)+ ,ih () --w NrLna

L f'0I'(t) Point of common.x() /' Luping (P,Ci

Supply Network---------------------- __ _Other

Loads

Fig. 1. Simple power system network

The harmonic currents cause harmonic volt drops in thesupply network. Any other loads, even linear loads, connectedto the PCC, will have harmonic currents injected into them bythe distorted PCC voltage. Such currents are referred to as

Frank LambertNational Electric Energy Testing Research and

Applications Center (NEETRAC)Forest Park, GA 30297 USA

frank.lambert@neetrac.gatech.edu

contribzutionsfrom thepower system, or supply harmonics.If the sum of the harmonic currents in the network exceeds

a certain limit, it creates problems. Limits of the levels ofharmonic currents injected into the system are specified invarious IEEE as well as IEC standards, guidelines andrecommended practices [ 1, 2].

If several loads are connected to a PCC, it is not possibleto accurately determine the amount of harmonic currentinjected by each load, in order to tell which load(s) isinjecting the excessively high harmonic currents. If individualharmonic current injections were known, then a utility couldpenalize the offending consumer in some appropriate way,including say a special tariff or insist on corrective action bythe consumer. Simply measuring the harmonic currents ateach individual load is not sufficiently accurate since theseharmonic currents may be caused by not only the non-linearload, but also by a non-sinusoidal PCC voltage.

This paper proposes a novel method based on ArtificialNeural Networks (ANN) to distinguish between the twocomponents of harmonic sources (i.e. load or power system).This will enable standards of harmonic pollution to beenforced by utilities and most importantly improve the powerquality. Several methods like DFT/FFT [31, stochastic method[4J and in recent years artificial neural networks (ANN) [5, 6,7, 8, 9] have been proposed to measure the harmonic contentin the load current, or to predict it, but most of them assume aradial feeder supplying a single load through a known feederimpedance, or multiple loads connected to a PCC which has asinusoidal voltage and with zero impedance in the supplyfeeder.

II. RECURRENT NEURAL NETWORKRecurrent neural networks (RNN) are feedback networks

in which the present activation state is a function of theprevious activation state as well as the present inputs. Addingfeedback from the prior activation step introduces a kind ofmemory to the process. Thus adding recurrent connections toa back propagation network enhances its ability to leamtemporal sequences without fundamentally changing thetraining process. Recurrent networks will, in general, perform

0-7803-9048-2/05/$20.00 02005 IEEE 36

better than regular feed forward networks on systems withtransients. They may be trained to identify or approximateany desired continuous vector mapping functionf(.)over aspecified range.

INPUTLAYER

HIDDENLAYER

OUTPUTLAYER

notationa= Wx (1)

where the input column vector x c R"+m, hidden layeractivation column vector a E Rm and input weightmatrix W E Rm" , n is the number ofANN inputs and m is thenumber of neurons in the hidden layer. Each of the hiddennode activations in a is then passed through a sigmoidfunction to determine the hidden-layer decision vector d.

di = i+e' C>le{1,2 .....m}

(a)

X _ PLANT I2A, ARl-)

Training eJI ~~~algorithmi~ ~~~ 'A

i~~~~~Jf'+A'W

(b)Fig. 2. (a) RNN Architecturc (b) Training Schemc ofANN

Figure 2 shows the block diagram of a three layer RNNinterconnected by weight matrices W and V. The objective ofthe training is to modify W and V such that the ANN functiong(., W, V) approximates the desired function f(.), so that theerror e between the desired function output y and the ANNoutput 5 is minimal.

Continual online training (COT) is required wheneverf(.) is a time varying signal and g(., W, V) has to track f(.).The online training cycle has two distinct paths: forwardpropagation and error back-propagation. Forward propagationis the passing of inputs through the ANN structure to itsoutput. Error back-propagation is the passing of the outputerror to the input in order to estimate the individualcontribution of each weight in the network to the final outputerror. The weights are then modified so as to reduce theoutput error. The generalized equations are shown below [10].A. Forward Propagation

Every input in the input column vector x is fed via thecorresponding weight in the input weight matrix W to everynode in the hidden layer. The activation vector a isdetermined as the sum of its weighted inputs. In vector

where the decision column vector d E Rm.The decision vector d is then fed back to the input layer

(this introduces the recurrence) as well as fed to thecorresponding weight in the output weight matrix V. TheANN output y is computed as

For a single output system the output weight matrixV E R'X" and y' is a scalar.

B. Error back-propagationThe output error e is calculated as

e=y-y' (4)The output error is back propagated through the ANN to

determine the errors ed and ea in the decision vector d andactivation vector a respectively, such that

The activation errors e are given as a product of thedecision errors ed, and the derivative of the decisions di withrespect to the activations a , where

ad

ditdji e

The change in input weights AW and output weightsAV are calculated as

AW = YmAW + yg e x

AV =,vmAV +Yg,e, d (7)

where YmYg E[0,1]are the momentum and learning gainconstants respectively. The last step in the training process isthe actual updating of the weights.

W=W+AWV=V+AV (8)

III. ESTIMATION OF HARMONIC CURRENTFigure 3 is a one-line diagram of a three-phase supply

network having a sinusoidal voltage source vi, network

367

(2)

riIIx

A.xI'U,'

I.XU

y = (Vd)T (3)

e e=V e (5)

= d, (l -d, )el,, ie {1,2.----,m} (6)

impedance Ls, Rs and several loads (one of which is non-

linear) connected to a PCC.

Fig. 3. Proposed scheme ( Va,, is the voltage at the PCC)

The nonlinear load injects distorted line current it, intothe network. A neural network is trained to identify the non-linear characteristics of the load. This neural network is calledthe Training neural network (ANN 1). A second neuralnetwork exists and is called the Estimating neural network(ANN2). ANN2 is an exact replica of the trained ANN1.Existence of ANN2 enables the simulation action of isolatingthe load from the network and testing it without physicallydisconnecting the load from the network. The function ofANN2 can very well be carried out by ANN1, however thatwould disrupt the continual online training of ANN1 duringthe brief moments of testing.

A. ANN] TrainingThe proposed method measures the instantaneous values of

the three voltages V,bC at the PCC, as well as the three linecurrents 'abc at the khmoment in time. The voltages Vabccould be line-to-line or line-to-neutral measurements. Theneural network ANN1 is designed to predict one step aheadthe line current i, as a function of the present and delayedvoltage vector values v,, (k),Va, (k -1) and vabi (k - 2).When the k + 1 moment arrives (at the next sampling instant),the actual instantaneous values of iabc are compared with the

previously predicted values of ia, and the difference (orerror e ) is used to train the ANN 1 weights. Initially theweights have random values, but after several sampling steps,the training soon converges and the value of the error ediminishes to an acceptably small value. Proof of this isillustrated by the fact that the waveforms for i,,.and iashould practically lie on top of each other. At this point theANN 1 therefore represents the admittance of the nonlinearload. This process is called identijving the load admittance.Since continual online training is used, it will correctlyrepresent the load admittance from moment to moment. Atany moment in time after the ANN 1 training has converged,

its weights are transferred to ANN2. The training cycle ofANN1 continues and in this way ANN2 always has updatedweights available when needed.

B. ANN2 EstimatingANN2 uses the load admittance identified by ANN 1,

applies a mathematically generated sine wave voltage to it,and calculates an estimated current iahab-distorted 'The

abc - disio,ted therefore represents the current that the nonlinearload would have drawn had it been supplied by a sinusoidalvoltage source. In other words, this gives the sameinformation that could have been obtained by quicklyremoving the distorted PCC voltage (if this were possible)and connecting a pure sinusoidal voltage to supply thenonlinear load, except that it is now not necessary to actuallydo this interruption. Any distortion present in the

lahc-distorfLed waveform can now be attributed to the non-

linearity of the load admittance.

IV. EXPERIMENTAL RESULTSIn most non-linear circuits, some sort of switching power

devices are used as the interface between the supply networkand the actual load. Experiments with different circuits havebeen carried out.

A. Light Dimmer TestThe experimental setup is shown in Fig.4.

supplyNetwork

.1". A<tutoK5_.J7 'Transformer

Signal PowerGenerato Amplifier

Fig. 4. Experimental setup with dimmer circuit

The proposed scheme is implemented with a single phasedimmer feeding a lamp bank (Load-i) and another lamp bank(Load-2), both connected to the PCC. The voltage at the PCCis fixed at 50 Vnns, 60 Hz. Two different cases are evaluatedwith switch S either in position I or 2. Total HarmonicDistortion is measured by a dedicated spectrum analyzerwhich measures up to the 20th harmonic as well as byMATLAB software.

Data acquisition for cases 1 and 2 is carried out with asystem from National Instruments and LABVIEW softwarewhich stores the data on a personal computer. This data is

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then imported to MATLAB and using the powergui block ofSIMULINK, the THD's are recomputed. These recomputedTHD's are then compared with measurements taken directlyby a spectrum analyzer, in order to verify that the LABVIEWand MATLAB computer code are working correctly. Thesampling frequency for data acquisition is 4 kHz whichensures that harmonics up to the 30th can be measured.

Case 1: Switch S in position IThe circuit is supplied from the 120V utility wall socket andstepped down by the auto-transformer to 5OV.THD of voltage at PCC without any loads = 4.25%.(MATLAB computation yielded 3.37%)THD of voltage at PCC with both loads connected = 4.24%THD of current i, = 14.5%. (MATLAB computation yielded13.27%)

Case 2: Switch S in position 2A sine wave voltage generated by a function generator is

the closest approximation to a pure sine wave. The currentsignal from the fumction generator is amplified by a poweramplifier and that is used as the power source.THD of voltage at the PCC without any loads is 1.9%.(MATLAB computation yielded 1.89%)THD of voltage at PCC with both loads connected = 1.9%THD of current it = 16.7%. (MATLAB computation yielded15.68%)

A small discrepancy is seen between the readings of thespectrum analyzer and that obtained from MATLAB. Thiscould probably be attributed to the way the data is acquired.The input channels of the data acquisition system areequipped with elliptic filters and that smoothens out thewaveforms to some extent. However an important result isthat the current THD of the dimmer circuit is higher when it isbeing supplied by the function generator ( less THD in v, )as compared to when it is supplied by the utility (more THDin v, ). When several loads are supplied from the PCC, withits own background THD, the individual currents are due tothe combined effects of the distorted v, and the non-linearities of the loads. This results in some amount of phasecancellation which may reduce the overall harmonic currentin the network [11] and thus benefit some of the non-linearloads. Linear loads do not introduce harmonics into thenetwork, but do get affected by the distorted PCC voltage.Hence, it is essential that the method should be able toanalyze each and every load on its own merit [ 12].

The data obtained from case I is used to train the neuralnetwork ANN 1 until the training error converges to near zero,and the current i, of Load-1 correctly tracks the output ofANN1. Figure 5 indicates how well ANNI has convergedsince its output i1 lies on top of the actual it waveform.

ANN1 Output Supenmposed on Actual Current

! ,,0.8 - 7 I .

I*

0.6 --

0.4 IX

0.2 -j_ -

-0.2c 0, I : :

-0.2 - -

-0.4 ---.I1

-0.6

-0.8I --- -

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18Time (s)

Fig. 5. il and i1 supenmposed

The convergence of the training can also be verified bylooking at the tracking error ( i, - i, ). Once the tracking error isbelow a pre-defined level, it can be concluded that ANN I hasleamed the admittance of Load-I to an acceptable level ofaccuracy. The weights of ANNI are now passed to ANN2which ideally should be supplied by a sine wave voltage withzero distortion. However such a sine wave source is difficultto obtain in reality. Hence ANN2 is tested with the voltagedata captured from case 2.

c

Output ofANN2

0.8-- 1 I

0.6 .. - - - -

0.4-

0.2 - - - - - - - -- - -

i0,-0.4 I- - - - i- :

0.6 _ r_ a

( :I

4.8L - ---a--- - --g--i- - -g

0 0.02 0.04 0.06 0.08 0.1 0.12Time (s)

- tI t

- -_

0.14 0.16 0.18

Fig. 6. iltdisI waveform (THD=15.23%)

The output ofANN2 is itd,5, and it appears in Fig. 6 whichshows what Fig. 5 would have looked like if the voltage at thePCC had a THD of 1.9% of case 2. The THD of itdjSl in Fig.6 is 15.23% which is very close to the THD of the actualcurrent (15.68%) measured in case 2.ANN2 is now tested with a mathematically generated sine

wave. Figure 7 shows the output of ANN2. This is the currentwaveform we would expect to see from the dimmer circuit ifit were supplied by a pure sine wave voltage.

369

A

I

.I

L

III

7 -

I

- I

I

Output of ANN2 with pure sine wave

0.8

0.6

0.4.-

0.2_ -

0

-0.2 -~ --

:1 :: i1

-0.4 --.

. 0 f 4 f 0 S / E-0.6 - -I.- -m- - I - - - - - --- --- --

-0.8 _I :

-1 +.fi L

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18Time (s)

(a)

0.1

0

0.0

m 0.0

0.0

0.0

Fundamental (60Hz) =0.9674 .THD= 1985%

2-

I

8

4

A -- -- -- I r

U 200 400 600Frequency (Hz)

1000

(b)

Fig. 7. (a) i4,*js, waveform when supplied by mathematically generatedsine wave. (b) FFT Spectrum (THD=19.85%)

The true current THD of i1.d,s, in Fig. 7 tums out to be19.85% instead of 14.5%.

B. Diode Bridge Rectifier Load

A second experiment has been performed with diodebridge rectifiers. The experimental setup is shown in Fig.8.

V'i-F -m i_

linear R-L load (Load-2), both connected to the PCC.The operating voltage at the PCC is 5VR,,S 60Hz which isobtained by using an auto transformer. This reduced voltageallows low voltage diodes to be used. Each individual load israted at lamp, and the THD of i, is 7.8% (measured byspectrum analyzer), but some of this is due to the non-linearity of Load-I and some is due to the distortion in thePCC voltage. Without any load connected, the backgroundTHD at vpccis 3.4%. With both loads connected, this THD

rises to 6.2%. As before, vp-, and i, are acquired intoMATLAB. The online training result of ANNI in MATLABis shown in Fig. 9.

ANN1 Output Superimposed on Actual Current

1 .- 7I S. .E 1N f; 0' 1E I.:

0.8 -I---- - -- - --

0.2~~~~~~~~~~~~~~~~~~~I0.6 _ -..____ i--- -------g..--

iI' I

040.2 - II

T' I

IF 'I

10.4 j

-0.6 - -

o. - -- - -0 -h- : --r- - : -!.018K: :

0 0.02 00 0.06406 008 01 0120-14 0-16 0.18Time (s)

Fig. 9. it and i4 superimposed

The weights of ANN I are now transferred to ANN2 (stillin MATLAB), and ANN2 is tested with a mathematicallygenerated sine wave voltage with zero distortion. The Fourierspectrum of the output l_-55, from ANN2 is plotted in Fig.10and shows what the Fourier spectrum of i, in Fig. 9 wouldhave looked like if the voltage vpcc had no distortion.

Fundamental (60Hz) = 0.95, THD= 10,26%

iD

EI

2

Fig. 8. Single-phase diode bridge rectifier setup

The proposed scheme is implemented with a single phasediode bridge rectifier feeding an R-L load (Load-1) and a

U 2[1. 400 6b0Frequency (Hz)

.uL

Fig. tO. FFT spectrum of 1i-d,, .THD=10.26%

The THD of iS, is now 10.26% instead of 7.8%. Thismeans that the true current THD of Load-I is higher thanwhat was measured when it was a part of the power networkand supplied by a distorted vp" .

370

I,

8

6

4

2Ii

-T -

-1. -

C. DC motor-converter loadA final experiment was conducted with a controlled

thyristor rectifier driving a DC motor on no-load. Theoperating voltage at the PCC is 1 20VRMs, 60 Hz, takendirectly from the laboratory supply network. The speedreference of the motor is set at about 70%. vpsc and i, arerecorded with both the loads operating. Without any loadconnected, the background THD at vp.c. is 3.76%. The inputcurrent i, of the drive has a current THD of 36.01% and theTHD of vp.c is 3.97%. As before once convergence in trainingof ANN1 is obtained, the next step is to transfer the weightsto ANN2 and test it with a mathematically generated sinewave (in MATLAB). The output of ANN2 is il_, and has aTHD of 26.79% as shown in Fig. 1 1.

F udamentl (601-) = 0.6529. THD= 26.79%

15

10

1I., , 1 ,|0 200 400 600 800Fmquency (Ft)

100U

Fig. 11. FFT spectrum of ii-dist wavefonn. THD=26.79%

A. Summary ofresultsThe salient results from the three tests above are

summarized in Table 1.

TABLE 1: TABULATION OF RESULTS

Load THDJ THDS ( THD d )

Dimmer 14.5% 19.85% 26.95%

Rectifier 7.68% 10.26% 25.15%

DC motor 36.0 1% 26.79% -34.42%

where THDd is iTD from distorted vp and THDs is ifrom pure sine wave.

For the light dimmer and diode bridge rectifiers, the THDin the nonlinear load's current increased when calculated for asine wave vp,c. However for the dc motor-converter, itdecreased. This important finding means that it is erroneousto think intuitively that the current THD, when supplied froma distorted vp.c should always be higher than if the vpC hadno distortion. The neural network is implemented with 20neurons in the hidden layer and the learning gain of 0.05.

V. CONCLUSIONSNon-linear loads exhibit customer contributed harmonics.

Linear loads draw distorted currents because of a distorted

vp, caused by non-linear loads. However in an actualnetwork, loads cannot be isolated. Therefore it is impossibleto say which load is causing the pollution and which load isgetting penalized. The novel method described in this paperavoids disconnecting any loads from the system and estimatesthe actual harmonic current injected by each load. Thisinformation could be used to penalize the offending load.

The biggest advantage of this method is that onlywaveforms of voltages and currents have to be measured. Ona practical system the neural network computations can becarried out on a DSP, together with a suitable A-D interface.Such a system could be installed permanently or be portablefrom one customer to another in order to simply monitorpollution levels at a particular PCC in the network.

ACKNOWLEDGEMENT

Financial support by the National Electric Energy TestingResearch and Applications Center (NEETRAC), USA for thisresearch is greatly acknowledged.

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[8] W.W.L Keerthipala, Low Tah Chong and Tham Chong Leong,"Artificial neural network model for analysis of power systemharmonics", IEEE International Conference on Neural Networks,1995, 27 Nov.-l Dec. 1995, Vol.2, pp. 905 - 910.

[9] N. Pecharanin, H. Mitsui, and M. Sone, "Harmonic detection by usingneural network", IEEE International Conference on Neural Networks,1995, 27 Nov.-l Dec. 1995, Vol.2, pp. 923 - 926.

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[11] W.M. Grady, A. Mansoor, E.F. Fuchs, P. Verde and M. Doyle,"Estimating the net harmonic currents produced by selected distributedsingle-phase loads: computers, televisions, and incandescent lightdimmers", IEEE Power Engineering Society Winter Meeting, 2002,Vol. 2, 27-31 Jan. 2002, pp. 1090 - 1094.

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