Electrical Power and Energy Systems 64 (2015) 212–220

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Electrical Power and Energy Systems

journal homepage: www.elsevier .com/locate / i jepes

Neuro-evolutionary approaches to power system harmonics estimation

http://dx.doi.org/10.1016/j.ijepes.2014.07.0350142-0615/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author.E-mail addresses: rayp@nitrkl.ac.in (P.K. Ray), bidyadhar@nitrkl.ac.in (B. Sub-

udhi).

Pravat Kumar Ray, Bidyadhar Subudhi ⇑Department of Electrical Engineering, National Institute of Technology Rourkela, Rourkela 769008, India

a r t i c l e i n f o a b s t r a c t

Article history:Received 1 July 2013Received in revised form 7 June 2014Accepted 6 July 2014

Keywords:Harmonic estimationBFOAdalineDFTFFTLeast Square (LS)

This paper focuses on exploiting two computational intelligence techniques such as artificial neural net-work and evolutionary computation techniques in estimation of harmonics in power system. Accurateestimation of harmonics in distorted power system current/voltage signal is essential to effectivelydesign filters for eliminating harmonics. No standard design is available for handling of local minimaand training of NN but Evolutionary Computation (EC) techniques are capable of resolving local minima.Neural Network and Evolutionary Computing (Bacterial Foraging Optimization (BFO)) are combined toachieve accurate estimation of different harmonics components of a distorted power system signal. Firstestimation of unknown parameters are carried out using BFO, then optimized output of BFO are taken asinitial values of the unknown parameters for Adaline. Amplitude and phase of fundamental and harmon-ics components are determined from final updated values of unknown parameters using Adaline. ThisAdaline based Bacterial Foraging Optimization (Adaline-BFO) hybrid estimation algorithm addressesthe problems of slow convergence and reduction of time generation of off-springs happening in GeneticAlgorithm (GA), and to avoid local minima in Particle Swarm Optimization (PSO). The proposed Adaline-BFO algorithm has been applied for estimation of harmonics of the voltage obtained across the inverterterminals of a prototype Photovoltaic (PV) system. From the obtained results, it is confirmed that the pro-posed Adaline-BFO algorithm provides superior estimation performance in terms of improvement in %error in estimation, processing time in computation and performance in presence of inter and sub-harmonic components when compared with the Discrete Fourier Transform (DFT), Kalman Filter (KF)and BFO algorithms.

� 2014 Elsevier Ltd. All rights reserved.

Introduction

Voltage and current waveforms in an AC power system areexpected to be sinusoidal with constant amplitude and frequency.However, almost all power plant components possess the undesir-able property of introducing distortion into AC power system caus-ing the voltage and current waveforms to deviate from theirsinusoidal waveforms. As a matter of fact, voltage and currentspossess a set of sinusoidal waveforms of varying amplitudes andphase having frequencies that are integer multiples of fundamentalfrequency. These frequency multiples of the fundamental fre-quency are called harmonic frequencies. Due to the significantgrowth of the solid-state power switching devices in recent years,there is corresponding increase in harmonic levels in power sys-tems. Further, excessive usage of nonlinear loads such as powerelectronics devices introduces significant amounts of harmonicsinto power system. Power converters used in variable-speed

drives, power supplies and uninterruptible power supply (UPS)systems are responsible for a disproportionate amount of harmon-ics troubling power systems now-days. Arc furnace is anothersignificant source of harmonics.

As discussed in the earlier paragraph, power system voltage orcurrent signal deviates from pure sinusoidal waveform and inparticular the distortion of the current waveform becomes morecomplex as shown in Fig. 1.

If suitable filtering is not undertaken then these devices willintroduce inter-harmonics (having frequencies non-integer multi-ple of fundamental but more than fundamental frequency) andsub-harmonic ((having frequencies non-integer multiple of funda-mental but less than fundamental frequency) components into thepower system. Both harmonics and interharmonics have adverseeffects such as increased I2R losses, over voltage, unbalancing andmal-operations of the relays and saturation of transformer core.It is pertinent that accurate estimation of harmonics in distortedpower system current/voltage signal is essential to effectivelydesign filters for eliminating harmonics. Since measurement ofpower system harmonics in presence of noise, dc decaying compo-nent, inter-harmonics, sub-harmonics and dynamic changes in

Non-linear loads such as UPS and

Power Converters etc.

Distorted load current

Transmission Line

Power Generation

Fig.1. Schematic of harmonics estimation problem.

Power System(Plant)

Optimization

Power System(Model)

+

_

Desired Output

Estimated Output

Error

Input

Fig. 2. Power system estimation as an optimization problem.

P.K. Ray, B. Subudhi / Electrical Power and Energy Systems 64 (2015) 212–220 213

signal may give rise to erroneous results estimation techniques areemployed to mitigate harmonics from the distorted signals. Hence,the harmonics estimation problem is intended to develop accurateestimation algorithms for obtaining amplitude and phase of theharmonics of the distorted voltage/current signal.

From the literature [1,2], it is found that several techniqueshave been employed to evaluate the harmonics. Out of which theFast Fourier Transform (FFT) is widely used because of its fastercomputational capability [1,2]. Other algorithms include recursiveDiscrete Fourier Transform (DFT), digital differentiator basedmethod [3], spectral observer and Hartley transform as a meansof harmonic extraction. The most commonly used technique forparameter estimation is Least Square (LS) and Recursive LeastSquare (RLS) algorithms [4,5].RLS is used extensively for estimatingfrequency contents on-line. Kalman filtering technique uses a sim-ple, linear and robust algorithm to estimate the magnitude of theknown harmonics embedded in the signal along with stochasticnoise [6,7]. It gives a better noise rejection and estimation com-pared to FFT algorithms [1]. But the dynamics involved in KF raisesconcern since it exhibits poor performance with respect to suddenchange in amplitude, phase or frequency of signal.

Joorabian et al. [8] decomposed the total harmonics estimationproblem into a linear and non-linear problem. A linear estimator(Least Square (LS)) has been employed for amplitude estimationand an adaptive linear combiner ‘‘Adaline’’ which is very fast andhas been employed for harmonics phase estimation. It is observedthat improvements in convergence and processing time areachieved using this algorithm. This algorithm provide correctestimates for both static, dynamic and fault signal, but estimationof harmonics for inter and sub harmonic components has not beenattempted. Lai et al. [9] combined the Least Square technique withartificial neural networks (NNs) for harmonic extraction in timevarying situations. This method is capable of dealing simulta-neously the measurement of varying frequency, amplitude andany harmonic components present in the power system. There isno restriction about evaluation of the number of harmonic compo-nent excepting increasing complexity of neural network as thenumber of harmonics components is increased. Mori et al. [10]presented a method based on back propagation learning for feed-forward neural network for harmonics estimation. For the effec-tiveness of the proposed method, it has been applied to the voltageharmonics [11] observed through a computer based measurementsystem and its performance has been compared with differentconventional methods. A neural network based algorithm has beendeveloped in [12] to estimate both magnitude and phase up toeleventh harmonics (550 Hz) of a power system. They used amethod for determination of model parameters involving the noiseenvironment. Estimation performance of the neural method is alsocompared with that of a conventional DFT method. This compari-son says that NN approaches yields fast response and high accu-racy compared to DFT and the method is also validated byexperimental results. Discrete Wavelet Transform [13] is also pop-ularly used for detection and classification of power qualitydisturbances.

The contributions of the paper include development of a newAdaline-BFO approach to power system harmonics estimation thatgives improvement in estimation performance. Performance of theproposed hybrid technique is compared with that of DFT, KalmanFilter and BFO algorithm.

The paper is organized as follows. Section 2 brief about theproblem statement of the paper. Section 3 describes the proposedAdaline–BFO hybrid estimation scheme for harmonics estimation.Section 4 presents simulation studies on some existing methodssuch as DFT, KF and BFO together with the proposed Adaline-BFOapproach for harmonics estimation applied to distorted power sig-nals. Section 4 also describes the experimental set-up developed tovalidate the efficacy of the proposed algorithm. Section 5 concludesthe paper.

Problem statement

An estimation problem can be posed as an optimization prob-lem. Consider Fig. 2, which shows the parameter estimation prob-lem for a power system, where the optimization needs to beperformed for example, by using Evolutionary Computation (EC)approaches such as PSO, BFO [17] in view of the global optimumcharacteristics or through a hybrid algorithm involving neuraland EC techniques in view of benefiting their individual character-istics in achieving global parameter estimation.

In Fig. 2, power system is treated as a plant, when input is fedto the plant, then the output obtained is the desired output. Whensame input is fed to a model, then output obtained is the estimatedoutput. These desired and estimated output are compared, theerror so obtained is minimized through hybrid optimizationalgorithm.

The optimization task in Fig. 2 can be accomplished by employ-ing any classical optimization techniques but to achieve globaloptimization, it is intended to develop a hybrid algorithm involvingNeural Network (NN) and EC techniques. It may be noted that ECtechniques such as GA [16], BFO and PSO are suitable candidatesfor updatation of NN using global optimum features.

BFO rests on a simple principle of the foraging (food searching)behavior of E.Coli bacteria in human intestine. BFO also outper-forms many powerful optimization algorithms in terms of conver-gence speed and accuracy. Adaline network [14,15] is used toupdate the weights of NNs adaptively so that the estimated valueconverges to the desired value (generated synthetic signal/experi-mental signal).

The instrumentation of the distorted power signal is accom-plished through an experimental set-up involving a DC–DC con-verter, an inverter and a FPGA with Data acquisition system. Theimprovements in estimation performances are achievement in

)(ky

+

Input

W1

W

X1

X ∧

Power System (Plant)

214 P.K. Ray, B. Subudhi / Electrical Power and Energy Systems 64 (2015) 212–220

terms of reduced estimation error, reduced processing time incomputation and achieving improved performance in presence ofinter and sub-harmonic components. The output voltage of theinverter of a PV system has been considered as the distorted volt-age source. It is intended to estimate different harmonic compo-nents of this distorted voltage by employing the proposedAdaline-BFO estimation algorithm.

BFO Optimization

NN (Adaline)Identifier

_

)(ke

∑

2

W3

Wn

2

X3

.

.Xn

)(ky

Fig. 3. Structure of Adaline-BFO estimation scheme.

A new Adaline-BFO hybrid estimation scheme

In this section, we describe how an Adaline based Bacterial For-aging Optimization (Adaline-BFO) hybrid estimation algorithm isdeveloped for addressing the problems of slow convergence andreduction of time generation of off- springs occurring in GA, andto avoid local minima in PSO. This combined approach to powersystem parameter estimation exploits with a view of achievingimprovement in estimation by reducing estimation error, reducingprocessing time for computation and improvement of performancein presence of inter and sub-harmonic components.

Further, we present the application of the Adaline-BFOtechnique for estimating the unknown parameters from whichfundamental and harmonics components of signal are to be deter-mined. The sum of the square error of a signal is considered as aFitness Function as given in the following expression.

Jði;n;m; lÞ ¼XNs

t¼1

e2ðtÞ ¼XNs

t¼1

½yðtÞ � yðtÞ�2 ð1Þ

y(t) – Actual signal, yðtÞ – estimated signal, e(t) – error in signal.The sum of squared error of the signals as defined above is cho-

sen as the fitness function. The optimized output values of theunknown parameters of BFO are used to initialize the unknownparameter for Adaline for more accuracy in estimation. Then theseparameters are updated using Widrow–Hoff delta rule. Amplitudeand phase of the fundamental and harmonic components areestimated from the updated weights of Adaline.

The discrete time version of (1) can be represented as

yðkTÞ ¼XN

n¼1

An sinðxnkT þ /nÞ þ Adc expð�adckTÞ þ gðkÞ ð2Þ

where T is sampling period. Due to the presence of the decayingterm, Adc exp (�adckT) in (2) it is a nonlinear expression. In orderto exploit the simplicity of applying Widrow–Hoff rule we are inter-ested for a linear expression of (2). Hence, performing a Taylor’sseries expansion of (2) and considering the first two terms (givenin eq. (3)) being significant and neglecting the higher terms as theyare very small quantities we obtain eq(4).

ydc ¼ Adc � AdcadckT ð3Þ

yðkTÞ ¼XN

n¼1

An sinðxnkT þ /nÞ þ Adc � AdcadckT þ gðkÞ ð4Þ

It may be noted here that one can still consider the nonlineareq. (2) directly for estimation of harmonics directly by employinga modified line search algorithm but the resulting algorithm willsuffer from slow convergence. While estimating multiple fre-quency components, because of existence of so many parameters,multiple combinations of final convergence may exist [7]. All theabove problems arises due to non-linearity in harmonics estima-tion. By linearizing dc components, convergence of EC (BFO) algo-rithm becomes faster and as the optimized output of EC (BFO) istaken as initial weights of NN (Adaline), it gives more accurateresults with less computational time. As a whole by linearizingdc components as well as combining EC and NN techniques, a more

accurate, faster convergence to many parameters can be obtained.From the discrete signal of eq. (4), we will estimate the amplitudesand phases of the fundamental and all the harmonics components.

Fig. 3 shows the proposed estimation scheme of employingAdaline-BFO combined algorithm. First input signal is fed to BFOalgorithm. Unknown parameters (weight vectors before initializa-tion) are optimized using BFO algorithm. Optimized output of BFOis taken as the initial values of weights for Adaline. Then weights ofAdaline are updated using Widrow–Hoff delta rule. Fundamentalas well as harmonic components are estimated from final updatedweights of Adaline. For estimation of amplitudes and phases,Eq. (4) can be rewritten as

yðkTÞ ¼XN

n¼1

½An sinðxnkTÞ cos /n þ An cosðxnkTÞ sin /n� þ Adc

� AdcadckT þ gðkÞ ð5Þ

NN (Adaline) identifier block in Fig. 3 shows the Adalinestructure of implementation for the estimation of power systemharmonics. X1, X2, X3. . .Xn are the inputs to Adaline. After multipli-cation of the input with the weight vector gives the estimatedoutput yðkÞ.

Reference output y(k) is compared with the estimated outputyðkÞ and the error so obtained is minimized by updating theweights of the Adaline using Widrow–Hoff delta rule [12].

The input to the Adaline is given by

XðkÞ ¼ ½sinðx1kTÞ cosðx1kTÞ . . . sinðxNTÞ cosðxNTÞ1� kT�T

ð6Þ

The weight vector W(k) of the Adaline is given by

WðkÞ ¼ ½W1ðkÞW2ðkÞ . . . W2N�1ðkÞW2NðkÞW2Nþ1ðkÞW2Nþ2ðkÞ�T

ð7Þ

where

WðkÞ ¼ ½A1 cosð/1Þ A1 sinð/1Þ . . . An cosð/nÞ An sinð/nÞ Adc adc�T

The optimized output of the unknown parameter using BFOalgorithm is taken as the initial values of the weight vector of Adalineand is updated using a modified Widrow–Hoff delta rule as

Wðkþ 1Þ ¼WðkÞ þ aeðkÞSðkÞkþ XTðkÞSðkÞ

ð8Þ

P.K. Ray, B. Subudhi / Electrical Power and Energy Systems 64 (2015) 212–220 215

For the weight adaptation of the Adaline, instead of using Wid-row–Hoff delta rule, modified Widrow–Hoff delta rule is used byintroducing a non-linearity using SGN function having its efficacyin accurately estimating the amplitudes and phases of the harmon-ics in noisy signals.

where SðkÞ ¼ SGNðXðkÞÞ ð9Þ

SGNðXiÞ ¼þ1;Xi > 0�1;Xi < 0

8><>: ð10Þ

i = 1, 2, . . ., 2N + 2 (total number of parameters of X(k))0 < a < 1The learning parameter a can be adapted using the following

expression [11]:

aðkÞ ¼ a0

ð1þ kbÞ

ð11Þ

where a0 is the initial learning rate and b is decaying rate constant.k Is a small quantity and is usually chosen to ensure kþ XT X–0, k istaken as 0.01. After updating of weight vector W(k), amplitudes (An),phases (/n) of the fundamental and nth harmonic parameters anddc decaying parameters ðAdc; adcÞ can be obtained from updatedweight W(k) as [7]

An ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

W22n þW2

2n�1

� �rð12Þ

/n ¼ tan�1 W2n

W2n�1b

� �ð13Þ

Adc ¼W2nþ1 ð14Þ

adc ¼W2nþ2

W2nþ1

� �ð15Þ

Algorithm 1. Adaline-BFO algorithm for power systemharmonics estimation

1. Initialization of BFO Parameters2. Elimination-dispersal loop: l = l + 13. Reproduction loop: m = m + 14. Chemo taxis loop: n = n + 1

(a) For i = 1, 2...S (total sample no.)Compute value of cost function J(i, n, m, l)

Jði;n;m; lÞ ¼PNs

t¼1e2ðtÞ ¼PNs

t¼1½yðtÞ � yðtÞ�2

(i.e., add on the cell-to-cell attractant effect).End of for loop

(b) For i = 1, 2. . .S take tumbling/swimming� Tumble

Generate a random vector D(i), on [�1, 1](i) Update parameter(ii) Compute: J(i, n + 1, m, l)� Swim

Compute new J(i, n + 1, m, l) using new positionElse exit swim step

(c) Go to the next sample (i + 1) if i – S [i.e. go to b] toprocess the next sample.(d) If min (J) < tolerance limit, break all loops.

5. If n < Nc (No. of Chemotactic iterations) go to 4, In this casecontinue chemotaxis since the life of bacteria is not over.

6. Reproduction(a) For the given m and l, and for each i = 1, 2, 3. . .S,Compute Jhealth

Sort parameter in ascending Jhealth

(b) Sr = S/2 no. of set parameters with highest will be

removed and other Sr no. of set of parameters with the bestvalue split

7. If m < Nre (maximum no. of reproduction steps) go to 3, inthis case, specified reproduction steps is not reached, sostart next generation in the chemo tactic loop.

8. Elimination-dispersalFor i = 1, 2. . .S, with probability Ped (probability ofelimination and dispersal), eliminate and disperse each setof parameters

9. Obtain optimized values for Weights (parameters)10. Employ Adaline structure and use modified Widrow Hoff

delta rule for final updating of Weights11. Estimate Amplitudes and phases from updated Weights

Algorithm1 describes the proposed Adaline-BFO estimationscheme. This algorithm has two distinct parts, in first part BFO isapplied to optimize the unknown parameters and in second partoptimized output of BFO is again updated using modified Wid-row–hoff delta rule in Adaline structure. As a result the errorbetween the desired and the estimated output is minimized.

Results and discussion

Static signal corrupted with random noise and decaying DCcomponent

The power system signal corrupted with random noise anddecaying DC component is considered. The signal used for the esti-mation, besides the fundamental frequency, contains higher har-monics of the 3rd, 5th, 7th, 11th and a slowly decaying DCcomponent. This kind of signal is mathematically represented by

yðtÞ ¼ 1:5 sinðxt þ 80�Þ þ 0:5 sinð3xt þ 60�Þ þ 0:2 sinð5xt þ 45�Þþ 0:15 sinð7xt þ 36�Þ þ 0:1 sinð11xt þ 30�Þ þ 0:5 expð�5tÞ þ lðtÞ

ð17Þ

The signal is corrupted by random noise g(t) = 0.01rand(t) havingnormal distribution with zero mean and unity variance. The param-eter values used for both simulation and experiment are given inTable 1. The parameter values for different algorithms are tunedon performing many experiments to get the optimal values. Initialchoices of unknown parameters are taken by generating randomnumbers within a prescribed maximum and minimum value.

Figs. 4–6 show comparison of actual vs. estimated signals usingBFO as well as hybrid Adaline-BFO algorithm with SNR values of40 dB, 20 dB and 10 dB respectively. It is seen that at 40 dB SNRvalue, the estimated value closely matches with the actual valuebut as SNR value of signal decreases, there is more deviations ofestimated value from actual value. Figs. 7 and 8 estimate ampli-tudes and phases of fundamental as well as harmonics componentscontained in the signal using Adaline-BFO algorithm respectively.Figs. 9 and 10 show a comparative estimation of amplitudes of fun-damental and 3rd harmonics components of signal respectivelyusing both BFO and Adaline-BFO algorithms. From these figures,it is verified that Adaline-BFO estimates more accurately as com-pared to BFO. The simulations for higher order harmonics showsimilar results and thus are not shown due to space limitations.Figs. 11 and 12 show a comparison of estimation of phases of fun-damental and 3rd harmonics components signal respectively usingboth BFO as well as hybrid Adaline-BFO algorithms. Adaline-BFOgives more correct estimation compared to BFO in these figures.The simulations for higher order harmonics show similar resultsand thus are not shown. Fig. 13 shows a comparison of robustnessof estimation of 3rd harmonics component of signal at differentvalues of SNR. It is found from this Fig. 13 that at SNR of 40 dB,

Table 1Parameters used for simulation and experimental work (BFO and Adaline-BFO).

a0 b k S p Ns Nc Nre Ned Ped C(i) dattract xattract hrepellant xrepellant

0.01 100 0.01 100 12, 18 3 5 10 10 0.1 0.001 0.05 0.3 0.05 10

10 20 30 40 50

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

Sample number

Am

plit

ud

e in

p.u

.

actualBFOAdaline-BFO

Fig. 4. Comparison of actual vs. estimated output of signal using BFO & Adaline-BFOalgorithm (SNR 40 dB).

0 10 20 30 40 50-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

Sample number

Am

plit

ud

e in

p.u

.

actualest(BFO)est(Adaline-BFO)

Fig. 5. Comparison of actual vs. estimated output of signal using BFO & Adaline-BFOalgorithm ((SNR 20 dB).

0 10 20 30 40 50

-2

-1

0

1

2

3

Sample number

Am

plit

ud

e in

p.u

.

actualest(BFO)est(Adaline-BFO)

Fig. 6. Comparison of actual vs. estimated output of signal using BFO & Adaline-BFOalgorithm (SNR 10 dB).

0 20 40 60 80 1000

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Sample number

Am

plit

ud

e in

p.u

.

funda3rd5th7th11th

Fig. 7. Estimation of amplitude of fundamental and harmonics components ofsignal using Adaline-BFO.

0 20 40 60 80 10020

30

40

50

60

70

80

90

Sample number

Ph

ase

in d

eg.

funda3rd5th7th11th

Fig. 8. Estimation of phase of fundamental and harmonics components of signalusing Adaline-BFO.

0 20 40 60 80 1001.35

1.4

1.45

1.5

1.55

1.6

1.65

1.7

Sample number

Am

plit

ud

e in

p.u

.

BFOAdaline-BFO

Fig. 9. Comparison of estimation of amplitude of fundamental component of signal.

216 P.K. Ray, B. Subudhi / Electrical Power and Energy Systems 64 (2015) 212–220

estimation accuracy is more and the accuracy decreases as SNRvalue decreases. Adaline-BFO estimation performance varies lesswith change in SNR value as compared to BFO, it means Adaline-BFO is more robust as compared to BFO. Fig. 14 shows the compar-ative estimation of Mean Square Error (MSE) of signal using the

two considered algorithms. From the figure, it is found that, MSEperformance in case of Adaline-BFO is comparatively better thanBFO algorithm.

Table 2 gives a comparative assessment of the simulationresults obtained by using DFT, Kalman Filter, BFO and the proposed

0 20 40 60 80 1000.46

0.48

0.5

0.52

0.54

0.56

Sample number

Am

plit

ud

e in

p.u

.

BFOAdaline-BFO

Fig. 10. Comparison of estimation of amplitude of 3rd harmonics of signal.

0 20 40 60 80 10078

78.5

79

79.5

80

80.5

81

81.5

Sample number

Ph

ase

in d

eg.

BFOAdaline-BFO

Fig. 11. Comparison of estimation of phase of fundamental component of signal.

0 20 40 60 80 10056

57

58

59

60

61

62

63

64

Sample number

Ph

ase

in d

eg.

BFOAdaline-BFO

Fig. 12. Comparison of estimation of phase of 3rd harmonics component of signal.

0.485

0.49

0.495

0.5

0.505

0.51

0.515

0.52

0.525

0.53

10 20 30 40SNR (dB)

Am

plitu

de in

p.u

.

BFOAdaline-BFO

Fig. 13. Comparison of robustness of estimation of 3rd harmonic amplitude ofsignal.

0 20 40 60 80 1000

1

2

3

x 10-4

Sample number

MS

E

BFOAdaline-BFO

Fig. 14. Comparison of MSE of signal.

Table 2Comparison of DFT, Kalman Filter, BFO and Adaline-BFO.

Methods Param- Fund- 3rd 5th 7th 11th

Actual(syntheticsignal)

f (Hz) 50 150 250 350 550A (V) 1.5 0.5 0.2 0.15 0.1u (�) 80 60 45 36 30

DFT A (V) 1.484 0.4852 0.1706 0.1535 0.0937Deviation(%)

1.040 2.9507 14.682 2.3597 6.2761

u (�) 80.57 60.30 47.098 34.354 25.300Deviation(�)

0.570 0.3002 2.0985 1.646 4.6993

Kalman Filter A (V) 1.506 0.503 0.225 0.158 0.095Deviation(%)

0.453 0.681 12.69 5.717 4.922

u (�) 80.25 59.839 46.827 34.464 34.994Deviation(�)

0.253 0.161 1.827 1.535 4.994

BFO A (V) 1.4878 0.5108 0.1945 0.1556 0.1034Deviation(%)

0.8147 2.1631 2.7267 3.7389 3.4202

u (�) 80.4732 57.900 45.823 34 560 29.127Deviation(�)

0.4732 2.0995 0.8235 1.4394 0.873

Adaline-BFO A (V) 1.5042 0.4986 0.2019 0.1507 0.0977Deviation(%)

0.2777 0.2857 0.9607 0.4369 1.7460

u (�) 80.2338 59.348 45.132 36.851 29.9361Deviation(�)

0.2338 0.6513 0.1327 0.8516 0.0639

P.K. Ray, B. Subudhi / Electrical Power and Energy Systems 64 (2015) 212–220 217

Adaline-BFO algorithm. Referring to Figs. 7–14 and also taking intoaccount the other harmonic estimation results, Table 2 presentedfor clear analysis of the results. The final harmonics parametersobtained with the proposed approach exhibit the best estimationprecision where the largest amplitude deviation is 1.746% occurredat the 11th harmonics estimation and the largest phase angle devi-ation is 0.8516� occurred at the 7th harmonics estimation using theAdaline-BFO algorithm.

Harmonics estimation of signal in presence of inter and sub-harmonics

We then set the frequency of sub-harmonic as 20 Hz, the ampli-tude 0.505 p.u. and the phase is equal to 75�. The frequency,

amplitude and phase of one of the inter-harmonic are 130 Hz,0.25 p.u. and 65� respectively. The frequency, amplitude and phaseof the other inter-harmonic are 180 Hz, 0.35 p.u. and 20� respec-tively. Figs. 15 and 16 show the estimation of amplitude and phase

0 20 40 60 80 1000.44

0.46

0.48

0.5

0.52

0.54

0.56

Sample number

Am

plit

ud

e in

p.u

.

BFOAdaline-BFO

Fig. 15. Estimation of sub-harmonics having amplitude 0.505 p.u.

0 20 40 60 80 10061

62

63

64

65

66

67

68

69

Sample number

Ph

ase

in d

eg.

BFOAdaline-BFO

Fig. 16. Estimation of inter-harmonics having phase 65�.

0.49

0.5

0.51

0.52

0.53

0.54

0.55

10 20 30 40SNR (dB)

Am

plitu

de in

p.u

.

BFOAda-BFO

Fig. 17. Comparison of robustness of estimation of sub-harmonic component ofsignal.

Table 3Comparison of DFT, Kalman Filter, BFO and Adaline-BFO with inter and sub-harmonics.

Methods Param- Sub Inter1 Inter2

Actual (synthetic signal) f (Hz) 20 180 230A (V) 0.505 0.25 0.35u (�) 75 65 20

DFT A (V) 0.5102 0.2401 0.3434Deviation (%) 5.1297 3.9713 1.8814u (�) 72.027 62.410 11.149Deviation (�) 2.9723 2.5895 1.1495

Kalman Filter A (V) 0.492 0.254 0.358Deviation (%) 1.508 1.859 2.322u (�) 75.353 64.218 8.680Deviation (�) 0.353 0.782 1.319

BFO A (V) 0.5252 0.2664 0.3729Deviation (%) 3.9957 6.5574 6.5295u (�) 74.486 63.9910 19.6887Deviation (�) 0.514 1.0090 0.3113

Adaline-BFO A (V) 0.5075 0.2495 0.3399Deviation (%) 0.4943 0.2044 2.8750u (�) 75.2204 65.4904 19.7231Deviation (�) 0.2204 0.4904 0.2769

DSO

FPGA Board Boost Converter

V & I Sensors

LoadData Acquisition

System

Temperature Sensor

Inverter

Fig. 18. Photo of PV system prototype.

218 P.K. Ray, B. Subudhi / Electrical Power and Energy Systems 64 (2015) 212–220

of a sub-harmonic and an inter-harmonic. Using Adaline-BFO, theestimation is very much perfect with most of the sample convergetowards the reference value in each case of estimation. Fig. 17shows a comparison of robustness of estimation of sub harmonicscomponent of signal at different values of SNR. It is found from thisFig. 17 that Adaline-BFO estimation performance varies less withchange in SNR value as compared to BFO, it means Adaline-BFOis more robust as compared to BFO in estimation of sub harmonics.The comparative assessment of estimation performance of DFT, KF,BFO and the proposed Adaline-BFO scheme for the case of signalcontaining sub-harmonics and inter-harmonics are given inTable 3. It can be seen from this table that Adaline-BFO achievesa significant improvement in terms of reducing error for harmonicsestimation in comparison to other three algorithms such as DFT,Kalman Filter and BFO.

Experimental results

In this section, the application of the Adaline-BFO for the assess-ment of voltage distortions at a PV system prototype is presented.Fig. 18 shows the photograph of the prototype experimental set-upof the PV system and Fig. 19 depicts the block diagram of the abovesystem. The details of the components are shown in Table 4. Thecomponents of the set-up are connected as follows. The PV panelhas five PV modules connected in series. The positive and negativeterminals of PV panel are connected to the positive and negativeterminals of a DC–DC boost converter. The boost converter doesboth the MPPT as well as boosting up of voltage operations. Boostconverter is next connected to a 1-/ DC–AC inverter. A load is con-nected at the output ends of inverter. The required switchingpulses for boost converter and inverter are generated externallyby an FPGA board. The FPGA board generates pulses from the volt-age and current signals of PV panel, DC–DC converter and inverter.The distorted voltage signal considered for estimation of harmon-ics is an AC voltage which is acquired from the output terminals ofthe inverter of the PV system (Fig. 18) at different time instants.

FPGA operates at voltage and current within 12V and 5A. But, inthe above PV system the voltage ranges of PV panel, DC–DC con-verter and inverter are more than the FPGA range. Hence, the volt-ages and currents of PV panel, DC–DC converter and inverter areconditioned to FPGA usable limits by a signal conditioner and thensupplied to the FPGA.

PVPanel

DC-DCBoost

Converter

FPGABoard

1-phaseInverter

SignalConditioner

Rectifier Load

v1 i1 v2 i2 i3v3

Pulse Pulse

Conditioned signals(6-no.)

Data and CommandFlow Personal Computer

Fig. 19. Complete block diagram of the above PV system prototype.

Table 4Components of PV system prototype.

Components Specifications

DC–DC boost converter Input: 50 V DC–90 V DC and 1–2.5 A,Output: 300 V DC and 0.5 A

1-ph Inverter Input: 300 V DC, Output: 210–240 V ACand 0.5 A

0

2

4

6

810

12

1416

18

1 2 3 4 5 6Harmonics Order

bfo adaline-bfo

Am

plitu

de in

Vol

t

Fig. 20. Comparison of estimation performance of harmonics components of PVsystem data.

P.K. Ray, B. Subudhi / Electrical Power and Energy Systems 64 (2015) 212–220 219

As per IEC 61000-4-30 [18], for computing the power qualityparameters, 10 cycles in a 50-Hz system which is 200-ms window-ing at a sampling time of 0.4 ms has been used. Measurementuncertainties, such as errors introduced due to transducer fre-quency response and errors in the presence of noise and harmoniccan be attributed to model error. Fig. 20 shows the comparativeassessment of harmonics estimation performances studied for aPV system. From this Figure, it can be observed on referring Har-monic Analyzer that the proposed Adaline-BFO algorithm providesimproved estimation performance than BFO.

Conclusion

The paper presents a new estimation algorithm for estimatingharmonic contents in a power system signal contaminated with

noise. In the estimation process, the BFO is used to estimate theunknown parameters to be used for determining amplitudes andphases. Then final amplitudes and phases of fundamental and har-monics components are estimated from the weights of the Adaline.The weights of the Adaline are updated using Widrow–Hoff deltarule and the resultant outputs of BFO are taken as the initialweights of the Adaline. On comparing this new algorithm (Ada-line-BFO) with BFO, it is seen that the former outperforms BFO ineach case of estimation. After estimation of the harmonic contentof the power system signal using the proposed algorithm, this isessential for designing filters for eliminating and reducing theeffects of harmonics in a power system. The proposed estimationalgorithm in its present form or with modifications can also beapplied to other engineering areas such as estimation of channelparameters with noise in communication channels, telephonesand other encrypted signals.

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