a robust extended complex kalman filter and sliding-mode control based shunt active power filter

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A Robust Extended Complex Kalman Filter and Sliding-mode Control Based Shunt Active Power FilterRakhee Panigrahi a , Prafulla Chandra Panda a & Bidyadhar Subudhi aa Center for Industrial Electronics and Robotics, Department of Electrical Engineering,National Institute of Technology , Rourkela , IndiaPublished online: 20 Feb 2014.

To cite this article: Rakhee Panigrahi , Prafulla Chandra Panda & Bidyadhar Subudhi (2014) A Robust Extended ComplexKalman Filter and Sliding-mode Control Based Shunt Active Power Filter, Electric Power Components and Systems, 42:5,520-532, DOI: 10.1080/15325008.2013.871609

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Electric Power Components and Systems, 42(5):520–532, 2014Copyright C© Taylor & Francis Group, LLCISSN: 1532-5008 print / 1532-5016 onlineDOI: 10.1080/15325008.2013.871609

A Robust Extended Complex Kalman Filter andSliding-mode Control Based Shunt Active Power FilterRakhee Panigrahi, Prafulla Chandra Panda, and Bidyadhar SubudhiCenter for Industrial Electronics and Robotics, Department of Electrical Engineering, National Institute of Technology,Rourkela, India

CONTENTS

1. Introduction

2. Description of Proposed SMC-RECKF based SAPF

3. SAPF Model: Sliding Modes and Equivalent Control

4. Reference Current Generation

5. Simulation Results

6. Validation with OPAL-RT Real-time Simulator

7. Conclusions

References

Keywords: power quality, shunt active power filter, Kalman Filter,sliding-mode control

Received 14 June 2013; accepted 28 November 2013

Address correspondence to Prof. Bidyadhar Subudhi, Center for IndustrialElectronics and Robotics, Department of Electrical Engineering, NationalInstitute of Technology, Rourkela-769008, India. E-mail: [email protected] versions of one or more of the figures in the article can be found onlineat www.tandfonline.com/uemp.

Abstract—This article presents the design of a new shunt activepower filter that employs a modified robust extended complex Kalmanfilter approach with an exponential robust term embedded for refer-ence current estimation together with a current controller based on thesliding-mode control concept. The robust extended complex Kalmanfilter exploits a new weighted exponential function to handle thesegrid perturbations to estimate the reference signal in shunt activepower filter system. The current controller in the proposed shuntactive power filter has been designed using a sliding-mode controlstrategy because of its ability to handle parameter uncertainties andease in implementation. To test the effectiveness of the proposedshunt active power filter, extensive simulations were performed usingMATLAB/Simulink (The MathWorks, Natick, Massachusetts, USA),and real-time studies were made using OPAL-RT (Montreal, Quebec,Canada). Results obtained from the above studies using the pro-posed shunt active power filter together with the different variants ofKalman filter (Kalman filter, extended Kalman filter, extended com-plex Kalman filter) are analyzed, and it is observed that the proposedrobust extended complex Kalman filter-sliding-mode control basedshunt active power filter provides accurate and improved harmonicsmitigation and reactive power compensation.

1. INTRODUCTION

With the development of power semiconductor devices, shuntactive power filter (SAPF) has become a valuable alternative tosolve the power quality (PQ) problems of customers and util-ities. Extensive usage of non-linear loads, such as adjustable-speed motor drives, uninterruptible power supplies (UPSs),and diode and thyristor rectifiers, in the power system causesvariation in the characteristics of voltage and current wave-forms. As a result, the voltage and current waveforms differfrom pure sinusoidal waveforms. Under these conditions, ef-fective estimation techniques need to be employed for accurateestimation of such electrical power quantities as voltage andcurrent.

Usually a signal can be constructed by using the estima-tion of its frequency, amplitude, and phase. This idea can beextended to identify the fundamental component from a dis-torted power system signal, which generates a reference signal

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Panigrahi et al.: A Robust Extended Complex Kalman Filter and Sliding-mode Control Based Shunt Active Power Filter 521

for the SAPF. The abstention of a high-quality estimate ofthis component is of particular interest. Most of the proposedmethods to identify the fundamental component of voltage orcurrent are based on the low-pass filter (LPF) method, con-ventional unit vector based method, discrete Fourier transform(DFT) method, S-transform method, and positive sequence cal-culation method. In the LPF method [1], the filter introducesa phase shift in the output, which requires a lead compensatorto compensate this phase shift. Any change in the fundamentalfrequency introduces an error in the compensation network andcauses a residual fundamental component to be added to thereference currents. This causes active power flow through theSAPF even under steady-state conditions. In the conventionalunit vector method [2], the steady-state performance underbalanced and sinusoidal conditions is satisfactory, but it pro-duces inaccurate reference currents when the supply voltagecontains distortions, resulting in incomplete compensation. Inthe DFT method [3], the estimation accuracy is inaccurate be-cause of spectral leakage. This happens because grid frequencydoes not remain constant. The S-transform tool was exploitedin [4] to extract the fundamental component of the non-linearload current to generate a reference current signal [5] for ac-tive filter operation. Although it is found to be satisfactory forvarious non-linear loads, this method fails to provide correctcompensation in variations of grid frequency. In the digital sig-nal processor based SAPF technique [6], the reference currentis calculated by two steps: the first is related to the calcula-tion of the positive-sequence component of unbalanced supplyvoltage and the second to deriving a simple fundamental ex-traction filter to extract the fundamental frequency componentfrom the distorted positive-sequence voltage, hence increasingcomputation time. Here additional measurement noise at thepoint of common coupling (PCC) does not seem to be takeninto consideration in reference current generation.

Several estimation techniques have been reported in theliterature, including the least-square error technique [7], or-thogonal component-filtered algorithm [8], Kalman filter (KF)[9, 12], recursive Newton-type algorithm [13], and variants ofthe extended KF (EKF) [14], but these may suffer poor conver-gence because of the presence of higher-order terms in solvingthe Taylor’s expansion. However, both linear and non-linear KFapproaches have attracted widespread attention as they accu-rately estimate the amplitude, phase, and frequency of a signalburied under noise and harmonics. The extended complex KF(ECKF) [15] suffers from inaccuracies in the estimation dueto a highly distorted signal even if the higher-order termsin Taylor expansion are reduced. Most of the existing estima-tion approaches [7–13] have not considered grid perturbations,such as voltage distortion, measurement noise, harmonics, andfrequency deviation; hence, in view of addressing these afore-

said issues (harmonics, voltage distortion, noise), the focusherein is on the development of a new estimation algorithm,the robust ECKF (RECKF), in which a weighted exponentialfunction e−(y−h(x))2

has been incorporated considering all theabove grid perturbations. When any abnormal condition can betaken into account, the value of innovation vector (y − h(x))will be increased twice due to inclusion of a “square term”in the proposed function; as a result, the influences of abnor-mality can be decreased at a faster rate (approximately twice)compared to the exponential function mentioned in [16, 17],and hence, the proposed RECKF approach provides better im-proved estimations independent of all grid perturbations in theSAPF with fast convergence.

Once the current references have been determined afterestimating the fundamental component described above, theSAPF must be able to track accurately such references even insudden slope variations of the reference. Several current con-troller techniques [18–20] have been reported for tracking cur-rent references in the SAPF. Patidar and Singh [21] proposeda digital signal processor based simplified current controllerfor SAPFs, which needs fewer sensors (two current and onevoltage sensors) for its implementation, reducing complexityof the control circuit. It has the disadvantage that it may beaffected by large load variations, which results in poor currenttracking. An efficient sliding-mode controller without a pro-portional part using the d-q reference frame theory [22], wherecurrent tracking results are satisfactory throughout sharp loadchanges, however, cannot offer a quick response to extremeconditions. Capacitor voltage stabilization is also not perfectdue to the absence of a proportional part. Tsang et al. [23]observed that a modular approach to design of a multi-levelactive power filter provides improved capacitor voltage stabi-lization, and also, the controller provides a quick response tosharp variations of load. However, it cannot be robust to largedisturbances of load. This has motivated researchers in the de-sign of a simple, robust, and fast current controller to track thereferences. The proposed control strategy employs the sliding-mode technique, which differs from the previous sliding-modetechnique in the sense that the sliding surface is based uponboth proportional and integral (PI) action. By introducing aproportional part, the essential property of robustness can beretained and SAPF performance enhanced by reducing the ca-pacitor voltage settling time and increasing reference currenttracking behavior.

The rest of the article is organized as follows. Section 2describes the problem statement and presents the scope ofthe article. Section 3 presents the development of the SAPFwith sliding-mode control (SMC). Section 4 provides theimplementation of the reference current estimation tech-nique. Simulation results and a comparative assessment of the

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522 Electric Power Components and Systems, Vol. 42 (2014), No. 5

performances of the KF, EKF, ECKF, and proposed RECKFemployed in the SAPF are provided and discussed in Section5. In addition, the SAPF is implemented in OPAL-RT LAB(Montreal, Quebec, Canada) to further validate the efficacy ofthe proposed SAPF, and the results are presented in Section 6.Finally, the conclusions are given in Section 7.

2. DESCRIPTION OF PROPOSED SMC-RECKFBASED SAPF

Figure 1 depicts the proposed control structure adopted for theSAPF using SMC and the RECKF. The SAPF is composedby a DC-link and three-phase insulated-gate bipolar transistor(IGBT) inverter followed by an inductive output filter. TheSAPF is designed to inject a current at the PCC to cancel theharmonic content of the load. To achieve the above objective,the SAPF is controlled by both linear and non-linear KFs (KF,EKF, ECKF, and RECKF) to generate the adequate referencesfor the controller.

The control system uses the measurement of the PCC volt-ages (va, vb, vc), and the above four estimation algorithms areused for identification of the in-phase fundamental compo-nent in per unit magnitude of PCC voltages. These are mod-ulated with the output of PI controller ism to generate ref-erences for the current controller. SMC is used as a currentcontroller and generates gate drive signals used for the IGBTinverter.

3. SAPF MODEL: SLIDING MODES ANDEQUIVALENT CONTROL

A single-phase circuit of voltage source inverter is consideredin the design of an active power filter. Figure 2 presents theequivalent circuit for a single-phase voltage source inverterused for development of SMC law. If a switching function uis defined such that u = 1 when either S1 or D1 is conducting,and u = −1 when either S2 or D2 is conducting, then the

FIGURE 1. Proposed RECKF-SMC-based shunt active power filter.

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FIGURE 2. Equivalent circuit for a single-phase of voltagesource inverter.

inductor current is given by

diFx

dt= vxn

L F+ u

vc

2L F, (1)

where x denotes the phase, iF and L F are the compensat-ing current and compensating inductance, respectively, and v

and vc represent the phase-to-neutral and capacitor voltage,respectively.

An expression for capacitor voltage taking into account theripple due to the compensating currents can be written as

dvc

dx= −1

2

[ua

iFa

C+ ub

iFb

C+ uc

iFc

C

], (2)

where ua, ub, and uc are the independent controls for phasesa, b, and c, respectively. The active power filter circuit canbe decomposed into three first-order independent systems thatcan be expressed as

isourcex = iloadx + icompx. (3)

To apply SMC theory for designing an active power filter,the sliding surfaces must be defined such that the source currentisourcex should follow the reference current ire fx . The slidingsurfaces for source currents can be defined as

irefx= ism ∗ Ux , (4)

where U is the in-phase fundamental component with perunit magnitude at the PCC, and its estimation methods aredescribed in Section 4. The sliding surface in a standard formcan be written as

Sx = isourcex − irefx= 0. (5)

To ensure that the active power filter can be maintained onthe sliding surface, it must be shown that there is a natural con-trol that satisfies SS ≤ 0. For the active power filter, expressionfor S can be written as

Sx = iloadx + vxn

L Fx

+ (ux )

(vc

2L Fx

)− ism ∗ Ux . (6)

The equivalent control ueqx can be found out by equating Eq.(6) to zero, and the natural control limits of the circuit are−1 ≤ ueqx ≤ 1. The discontinuous control law can be writtenas follows:

if S < 0, then u = 1;if S > 0, then u = −1.

(7)

To apply this control law to the SAPF, a decision clocksignal of frequency 15 kHz is used. The SAPF line currentsand the reference values are compared at the decision clock in-stants, and switching logic is applied to generate the switchingfunction.

4. REFERENCE CURRENT GENERATION

Usually the performance of the SAPF depends upon the accu-racy of the reference signal generator, and for source referencegeneration, identification of the fundamental component is themost critical item in determining SAPF behavior. This arti-cle presents estimation of the fundamental component of PCCvoltages using four types of KFs: the KF, EKF, ECKF, andproposed RECKF.

4.1. Signal Model and KF Formulation

A linear signal zk of single sinusoid is represented by

zk = a1 sin(kω1Ts + φ1), k = 1, . . . , N ; (8a)

ω1 = 2π f1. (8b)

In Eq. (8a), Ts is the sampling time, parameters a1 and f1 arethe fundamental amplitude and frequency, respectively, withinitial phase φ1. The signal zk+1 can be expressed as

zk+1 = x1k+1 = x1k cos(kω1Ts) + x2k sin(kω1Ts); (9)

further,

x2k+1 = −x1k sin(kω1Ts) + x2k cos(kω1Ts), (10)

where x2k is known as the in-quadrature component and isorthogonal to x1k , and they are represented by

x1k = a1 sin(kω1Ts + φ1), (11a)

x2k = a1 cos(kω1Ts + φ1). (11b)

To model amplitude or phase variations in the signal, a pertur-bation vector [ γ1 γ2 ]T

k in the system states is considered. Thestate space representation of the signal then becomes

xk+1 = �k xk + wk, (12)

yk = Hk xk + vk, (13)

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where wk and vk are the process and measurement noises,respectively, and

�k =[

cos(ω1Ts) sin(ω1Ts)− sin(ω1Ts) cos(ω1Ts)

], (14)

Hk = [1 0]. (15)

Denoting the estimate of xk+1 as xk+1|k , the sequential recursivecomputation steps for fundamental component identificationare

xk+1|k = �k xk|k−1 + Kk(yk − Hk xk|k−1), (16)

Kk = �k Pk|k−1 H Tk

(Hk Pk|k−1 H T

k + Rk

)−1, (17)

Pk+1|k = �k Pk|k−1�Tk − Kk Hk Pk|k−1�

Tk + Qk, (18)

Pk+1|k = E{(xk+1 − xk+1|k)(xk+1 − xk+1|k)T }. (19)

In Eq. (16), the innovation vector yk − Hk xk|k−1 is used torefine a priori estimate xk|k−1, and Kk is the Kalman gain.Equation (17) aims to find the particular Kk that minimizes theindividual terms along the major diagonal of error covariancematrix Pk , because these terms represent the estimation errorvariances for the elements of the state vector being estimated.Equation (18) is a general expression for the updated errorcovariance matrix for any gain Kk , where Pk+1|k and Pk|k−1

represent a posteriori and a priori error covariance matrices,respectively. Qk and Rk are the process and measurement errorcovariance matrix, respectively,

Qk = E{wkw

Tk

}, (20)

Rk = E{vkv

Tk

}. (21)

4.2. Signal Model and EKF Formulation

As per simplicity in formulation, the signal in Eq. (8a) can bereplaced by

zk = a1 cos(kω1Ts + φ1). (22)

It may be noted that the three consecutive samples of this singlesinusoid will satisfy the following relationship:

zk − 2 cos ω1Ts zk−1 + zk−2 = 0. (23)

The state space vector is given by

xk = [2 cos ω1Ts xk−1 xk−2]T , (24)

xk+1 =⎡⎣ 1 0 0

0 2 cos ω1Ts −10 1 0

⎤⎦ xk . (25)

The measurement equation can be expressed as

yk = [0 2 cos ω1Ts −1]xk + vk . (26)

The non-linear state-space equations can be represented as

xk+1 = f (xk), (27)

yk = g(xk) + vk, (28)

where

f (xk) = [2 cos ω1Ts 2 cos ω1Ts .xk−1 − xk−2 xk−1, (29)

g(xk) = 2 cos ω1Ts .xk−1 − xk−2. (30)

Linearizing the above system and applying the EKF theoryto a first-order system, a non-linear recursive filter for estimat-ing a single sinusoid is given as follows:

xk|k = xk|k−1 + Kk(yk − g(xk|k−1)), (31)

xk+1|k = f (xk|k), (32)

Kk = Pk|k−1 H Tk .

[Hk Pk|k−1 H T

k + Rk

]−1, (33)

Pk|k = Pk|k−1 − Kk Hk Pk|k−1, (34)

Pk|k+1 = Fk Pk|k F Tk , (35)

where

Fk = ∂ f (xk)

∂ xk=

⎡⎣ 1 0 0

x2k x1k −10 1 0

⎤⎦

and

Hk = ∂g(xk)

∂ xk= [

x2k x1k −1].

Since the objective is to find in-phase fundamental componenta1 sin(kω1Ts + φ1) as per Eq. (11a), a 90◦ phase shift of theestimated signal zk is required.

4.3. Signal Model and ECKF Formulation

The signal in Eq. (8a) can be represented in complex form as

zk = (−0.5i)(a1ej(kω1Ts+φ1)

) + (0.5i)(a1e−j(kω1Ts+φ1)

). (36)

The complex type state variable xk can be given as

x1k = eiω1Ts , (37a)

x2k = a1e j(kω1Ts+φ1), (37b)

x3k = a1e− j(kω1Ts+φ1), (37c)

The non-linear state space equations can be represented as

xk = f (xk−1), (38)

yk = g(xk) + vk, (39)

where

f (xk−1) =[

x1(k−1) x1(k−1)x2(k−1)

x3(k−1)

x1(k−1)

]T. (40)

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The recursion process of the ECKF for estimating the signalparameters of sinusoid waves is given below:

xk = f (xk−1), (41)

Mk = Fk Pk−1 F Tk + Qk, (42)

xk = xk + Kk(yk − Hk xk), (43)

Kk = Mk H Tk

[Hk Mk H T

k + Rk

]−1, (44)

Pk = Mk(I − Kk Hk), (45)

where the symbols ∼ and ∧ stand for the predicted and esti-mated values, respectively; Mk and Pk represent the predictedand estimated error covariance, respectively. The values of Fk

and Hk are now given:

Fk = ∂ f (xk−1)

∂ xk−1=

⎡⎢⎣

1 0 0x2(k−1) x1(k−1) 0

−x3(k−1)

/x2

1(k−1)0 1

/x1(k−1)

⎤⎥⎦, (46)

Hk = ∂(g(xk))

∂xk= [0 −0.5i 0.5i] . (47)

The parameters of frequency fk , amplitude ak , and phaseangle φk can be expressed as

f1k = 1

2πTs[Im(ln(x1k ))], (48)

a1k = ∣∣x2k

∣∣, (49)

φ1k = Im

[ln

(x2k∣∣x2k

∣∣ × (x1k )k

)]. (50)

Using the above parameters f1k , a1k , and φ1k , the fundamentalcomponent of PCC voltage can be identified.

4.4. Signal Model and Proposed RECKF Formulation

The signal model and filter formulations in the RECKF aresame as in the ECKF. The only difference is in the measurementerror covariance Rk , which is the inverse of the weighting Wk ,i.e.,

Rk = W −1k , (51)

Wk = Wk−1e−(yk−Hk xk )2, (52)

where the exponential term e−(yk−Hk xk )2is the proposed robust

exponential function, and the variable Rk is replaced in Eq.(44). When any grid disturbances occur at the PCC, the inno-vation vector (yk − Hk xk) increases twice due to the inclusionof a “square term” in the proposed exponential function. Con-sequently, the value of the proposed robust exponential func-tion decreases twice, and finally, a fast reduction of weightingand mitigation of error can be achieved. Thus, estimation usingthe proposed RECKF is more effective compared to the ECKF,where the weightings are the same throughout the estimatedprocess.

5. SIMULATION RESULTS

The designed control strategy, the structure of which is shownin Figure 1, has been tested using MATLAB/Simulink (TheMathWorks, Natick, Massachusetts, USA). A balanced three-phase voltage supply has been applied to a typical non-linearload composed of a three-phase diode rectifier bridge feedingan RL load. Table 1 summarizes the simulation parameters,where Ls and Rs correspond to the source impedance, L f andR f correspond to the filter impedance, Vs is the source voltage,C is the capacitance of the DC bus, v∗

dc is the reference DCbus voltage, K p and Ki are the PI controller constants, f isthe system frequency, fsw is the power converter switchingfrequency, and Td is the maximum simulation time interval.

Four identification algorithms, namely the KF, EKF, ECKF,and RECKF, were tested and analyzed using the following sim-ulation results. For convenience, the initial state variables x0

were chosen to be 0.0, and the filtered error covariance matrixP0 was selected to be diagonal with the value of 10 p.u.2.Themeasurement error covariance matrix R0 was selected to be1.0 p.u.2 to represent an inaccurate measurement and the pro-cess error covariance matrix Q0 is fixed to be 0.001 p.u.2.The covariance matrices P0 and R0 will be updated during theestimation process.

Figure 3 shows the PCC voltage at phase A and its fun-damental component estimated with the help of the KF, EKF,ECKF, and RECKF. It can be seen from Figure 3(a) that the KFtakes about 0.012 sec for estimation of the fundamental com-ponent to remain same and in-phase with the distorted PCCvoltage. But in case of the EKF, as shown in Figure 3(b), thefundamental is initially not in-phase with the PCC, and it takesabout 0.05 sec to be in-phase with PCC. The fundamental com-ponents are exactly matched with the PCC voltages throughoutthe process, as seen from Figures 3(c) and 3(d). From thesefigures, it is obvious that better estimation is achieved in theECKF and RECKF cases.

Figure 4 depicts the behavior of the reference currents forthree phases in the SAPF. Figure 4(a) shows the transient be-havior of the initial reference current in the KF case, but itbecomes steady at about 0.1 sec. In the EFK case, depictedin Figure 4(b), the transient behavior of the reference current

Vs 100 V f 50 HzLs 0.1 mH Rs 1 �

L f 2.7 mH R f 1 �

v∗dc 250 V C 1000 μF

K p 0.248 Ki 4.19fsw 10.5 kHz Td 2/fsw sec

TABLE 1. Simulation parameters.

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FIGURE 3. PCC voltage with its fundamental estimated with:(a) KF, (b) EKF, (c) ECKF, and (d) RECKF.

is still present, showing poor performance of the system. Thesteady-state behavior of the sinusoidal reference current, givenby Figures 4(c) and 4(d), exhibits the outperformance of theECKF and RECKF as compared to the KF and EKF.

Before the compensating capabilities of the SAPF aretested, the capacitor in the DC link has to be charged. Thus,adequate effort will be used by the sliding-mode controllerto charge vdc to the desired level, and then harmonics com-pensation is performed. The capacitor voltage waveforms are

FIGURE 4. Reference currents generated by: (a) KF, (b) EKF,(c) ECKF, and (d) RECKF.

displayed in Figure 5 and compared on the basis of above fourfilter algorithms. Generally, the harmonic compensating per-formance will be spoiled when large fluctuation of the voltageoccurs across the DC capacitor. As can be seen in Figure 5,the fluctuation is more in the EKF case as compared to theother three. Further comparison among the KF, ECKF and

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FIGURE 5. Waveform of DC-link capacitor voltage: (a) KF,(b) EKF, (c) ECKF, and (d) RECKF.

RECKF shows that the RECKF method enables suppressionof the voltage fluctuations across the DC capacitor, showinggood harmonic compensating performance.

The compensating currents are compared in Figure 6. It canbe seen that the KF, ECKF, and RECKF provide almost equalcompensation with a fast response, while the EKF exhibits avery slow response. Figure 7 shows the instantaneous source

After compensationOrder of Before

harmonics compensation KF EKF ECKF RECKF

5th 4.2 0.44 0.45 0.44 0.437th 3.1 0.45 0.48 0.45 0.4411th 2.5 0.48 0.50 0.47 0.4613th 2.5 0.38 0.45 0.38 0.3817th 2.3 0.43 0.44 0.43 0.4319th 1.9 0.40 0.45 0.39 0.3823rd 1.5 0.45 0.50 0.45 0.4425th 1.1 0.38 0.48 0.37 0.30THD (%) 27.8 4.81 5.21 4.78 4.63

TABLE 2. Measurement of harmonics content in supply current.

current for phase A before compensation, which containsfundamental as well as harmonic components. The harmonicscompensation is achieved by the compensating current,which contains equal and opposite harmonic components,already shown in Figure 6. Figure 8 displays the sourcecurrents after compensation and indicates that they aresinusoidal and in-phase with the respective voltages. But theyare compared on the basis of their amplitudes of differentharmonic contents measured with the help of an Fast FourierTransform (FFT) analysis tool. Table 2 summarizes variousharmonics in the supply current for the cases before and aftercompensation using four Kalman algorithm variants. It isobserved that the amplitudes of different harmonic contentsin the source current are quite high, and the source currenthas a Total Harmonics Distortion (THD) of 27.8% beforecompensation; however, it reduces to 4.81, 5.21, 4.78, and4.63% after compensation with the KF, EKF, ECKF, andRECKF, respectively. A comparative reduction in amplitudesof harmonic contents envisages the superiority of the RECKFin harmonic compensation of the SAPF.

The active and reactive power block using MAT-LAB/Simulink measures the active power P and reactive powerQ associated with a supply voltage current pair that comprisesharmonics. From the active and reactive power measurementspecified in Table 3, it is indicated that the reactive powerdrawn from the supply side is significantly reduced in case ofthe RECKF as compared to the other three, achieving a movetoward unity power factor correction at the supply side.

After compensationBefore

compensation KF EKF ECKF RECKF

P = 1.44 kW P = 2.30 kW P = 2.12 kW P = 2.36 kW P = 2.48 kWQ = 89 VAR Q = 10 VAR Q = 19 VAR Q = 8 VAR Q = 2 VAR

TABLE 3. Measurement of real (P) and reactive (Q) power.

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FIGURE 6. Waveform of compensating current: (a) KF, (b)EKF, (c) ECKF, and (d) RECKF

6. VALIDATION WITH OPAL-RT REAL-TIMESIMULATOR

This section presents the real-time results obtained from theimplementation of the proposed SAPF algorithm on OPAL-RT. Figure 9(a) shows the real-time simulation machinealong with a console monitor and digital storage oscilloscope

FIGURE 7. Waveform of source voltage and source currentbefore compensation.

FIGURE 8. Waveform of source voltage and source currentafter compensation: (a) KF, (b) EKF, (c) ECKF, and (d) RECKF.

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FIGURE 9. (a) RT-LAB real-time simulator and (b) layout of OP5142.

interface. The platform provides parallel computing hardwarecapability and accompanying transient solvers and componentlibraries. The optimal model construction for the real-timesimulation needs to take the simulation hardware architectureinto consideration. In addition, the model structures should besimplified to reduce the computational burden. OPAL-RT is anideal tool for the design and testing of power system protectionand control schemes. With a large capacity for both digitaland analog signal exchange (through numerous dedicated,

high-speed input-output [I/O] ports), physical protection andcontrol devices are connected to the simulator to interact withthe simulated power system. The OP5142 shown in Figure9(b) is one of the key building blocks in the modular OP5000I/O system from OPAL-RT Technologies [24]. It allowsthe incorporation of field programmable gate array (FPGA)technologies in RT-LAB simulation clusters for distributed ex-ecution of hardware description language (HDL) functions andhigh-speed, high-density, digital I/O in real-time models.

FIGURE 10. OPAL-RT results for compensating current: (a) KF, (b) EKF, (c) ECKF, and (d) proposed RECKF.

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FIGURE 11. OPAL-RT results for capacitor voltage: (a) KF, (b) EKF, (c) ECKF, and (d) proposed RECKF.

FIGURE 12. OPAL-RT results for source current and its spectrum after compensation: (a) KF, (b) EKF, (c) ECKF, and (d) proposedRECKF.

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Figures 10 to 12 show the waveforms obtained from theRT-LAB real-time simulator. Figures 10, 11, and 12 give thedetails of compensating current, DC-link voltage, and sourcecurrent with its spectrum after compensation, respectively, inthe SMC-based SAPF system using the four KF algorithmsvariants. It is shown in Figure 12 that THDs of the source cur-rent are 4.95, 5.38, 4.89, and 4.70% for the KF, EKF, ECKF,and proposed RECKF-SMC-based SAPF, respectively. As canbe seen, these results are similar to results obtained from MAT-LAB.

7. CONCLUSIONS

In this article, a sliding-mode controller based shunt activepower filter implemented with a new current reference es-timation scheme has been presented. This scheme exploitsthe estimation of the fundamental components of the distortedPCC voltages using the KF, EKF, ECKF, and proposed RECKFalgorithms. The performance of the SAPF is analyzed with acomparative assessment of the above four algorithms. The pro-posed RECKF algorithm is based on applying a new weightedexponential function as a factor to limit the variation of in-novation vector to restrain the unusual measured value and toenhance the estimation accuracy.

Generally, grid perturbations, such as harmonics, frequencydeviations, measurement noise, distorted voltage, and phaseangle jump, degrade the reliability and efficiency of the SAPFsystem. However, under the influence of the above perturba-tions, the different approaches, such as S-transform [4], posi-tive sequence [6], DSP-based controller [19], integral slidingmode [21], and modular approach [24], are unable to providesatisfactory quality of compensation in SAPF, particularly insettling DC capacitor voltage, tracking the reference current,and synchronizing the supply current with a supply voltagethat annihilates reactive power. Hence, the objective to quicklyand accurately estimate the reference current is achieved, andthe developed current controller follows that reference ade-quately in the face of grid perturbations. From the simulationand real-time results, it is observed that the proposed RECKF-SMC approach to design a shunt active power filter is found tobe quite effective and responds faster to the grid perturbationsarising at the PCC, more effectively yielding PQ improvementin terms of efficient harmonics mitigation and reactive powercompensation.

REFERENCES

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BIOGRAPHIES

Rakhee Panigrahi received the B.E. degree in ElectricalEngineering from University College of Engineering, Burla,Odisha, India, in 2002, and the M.Tech degree in Electri-cal Engineering from National Institute of Technology (NIT),Rourkela, India, in 2009. Currently she is pursuing the Ph.D.degree in the Department of Electrical Engineering, NationalInstitute of Technology (NIT), Rourkela, India. Her researchis focused on estimation techniques with application to powerquality.

Prafulla Chandra Panda received the B.Sc., M.Sc., and Ph.D.degrees, all in Electrical Engineering from Sambalpur Uni-versity, Odisha, India, in the year 1971, 1974 and 1990 re-spectively. Since 1977, he has been with National Institute ofTechnology (NIT), Rourkela, India, where he is currently aProfessor in the Department of Electrical Engineering. He isa senior member of the IEEE. At present, his research inter-ests include power system dynamic stability analysis, powerquality and high voltage dc transmission.

Bidyadhar Subudhi received Bachelor Degree in Electri-cal Engineering from National Institute of Technology (NIT),Rourkela, India, Master of Technology in Control & Instru-mentation from Indian Institute of Technology, Delhi in 1988and 1994 respectively and PhD degree in Control System En-gineering from Univ. of Sheffield in 2003. He was as a post-doctoral research fellow in the Dept. of Electrical & ComputerEngg., NUS, Singapore during May-Nov 2005. Currently heis a professor in the Department of Electrical Engineering atNIT Rourkela and coordinator, centre of excellence on renew-able energy systems. He is a Senior Member of the IEEE andFellow IET. His research interests include system identifica-tion & adaptive control, networked control system, control offlexible and under water robots, estimation and filtering withapplication to power system and control of renewable energysystems.

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a robust extended complex kalman filter and sliding-mode control based shunt active power filter

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