Sensorless Control for DFIG Wind Turbines Based on Support Vector Regression

1,2Ahmed G. Abo-Khalil, lHammad Abo-Zied lAssiut University, Assiut, Egypt

lAlmajmaah University, Almajmaah, Saudi Arabia

Abstract - In this paper, a sensorless based doubly-fed

induction generator (DFIG) control in wind power genera­

tion systems is proposed, which is based on the theory of

support vector regression (SVR). The inputs of the SVR wind

speed estimator are chosen as the wind turbine power and

rotational speed. During the offline training, a specified

model which relates the inputs to the output is obtained.

Then, the wind speed is determined online from the instan­

taneous inputs. Meanwhile, the DFIG rotor dq-axis currents

are controlled to optimize the stator active and reactive

power. The stator active power is adjusted in order to extract

the maximum power from the wind power. The output reac­

tive power of the wind power conversion system is controlled

as zero to keep unity power factor of the stator voltage and

current. However, the stator reactive power control is used to

optimize the generator efficiency by sharing the reactive

power between stator and rotor. The experimental results

show the excellent of performance of the power, current and

pitch angle controllers in the steady state and transient res­

ponses for the different modes and wind speed. The experi­

mental results have verified the validity of the proposed es­

timation and control algorithms.

I. INTRODUCTION

A doubly-fed induction generator is most connnonly used in wind power generation. It is a wound rotor type of induction machines with slip rings attached to the rotor and fed by the power converter. With DFIG, generation can be accomplished in variable speed ranging from sub­synchronous speed to super-synchronous speed. The power converter feeding the rotor winding is usually con­trolled in a current-regulated PWM type, thus the stator current can be adjusted in magnitude and phase angle. The rotor-side converter operates at the slip frequency and the power converter processes only the slip power.

Thus if the DFIG is to be varied within ± 30% slip, the rating of the power converter is only about 30% of the rated power of the wind turbine. In this control type of machines the net power out of the machine is a sunnna-

used as the reference value for the DFIG outer control loop. In the inner current control loop, the stator-flux vector position is used to establish a reference frame that allows q-axis components of the rotor current to be con­trolled. The stator reactive power is controlled to the de­sired value by controlling the reference d-axis rotor cur­rent.

In the most of wind energy generation systems, ane­mometers are used to measure the wind speed for the MPPT(maximum power point tracking) control [7]. The anemometer installed on the top of nacelle may be a source of inaccurate measurement of the wind speed. In wind farms, several anemometers are often placed at some locations to measure the average wind speed [8]. Using of anemometers raises a problem of calibration and measurement accuracy as well as increases the initial cost of the wind generation systems. For these reasons, it is desirable to replace the mechanical anemometers by the digital wind speed estimator based on the turbine charac­teristics.

Recently, the wind speed estimation methods have been reported in the literature, which can be categorized into two approaches. The first method is to use a power equation as a function of power coefficient and tip-speed ratio. Since the polynomial order of power coefficient may be higher than the seventh order for accurate estima­tion, the real-time calculation of the roots of the poly­nomial is a time-consuming task. The other one is to use a look-up table of power-mapping [2]. However, this me­thod requires a lot of memory space, and the estimation speed and accuracy depend on the size of the look-up ta­ble.

In this paper, a novel wind speed estimation scheme for the MPPT control of wind power systems is proposed, which is based on the SVR theory. The effectiveness of the proposed algorithm and the proposed control scheme have been verified by the experimental results.

II. SYSTEM DESCRIPTION

tion of the power coming from the stator and the rotor [1], DFIGs allow active and reactive power control through [2]. In the a rotor-side converter, while the stator is directly con-DFIG, the applied rotor voltage controls the real and reac- nected to the grid. The active part is due to the stator tive powers and generator's speed, when its stator termin- power and rotor power when ignoring the stator copper als are connected to a power system and the stator voltage and core losses. The stator power can be determined by is held constant by the grid [3]- [6]. the wind turbine maximum output power corresponding

In this paper, the stator power which results in a to a particular wind speed, however the rotor power may maximum turbine output-power for a measured wind be either drawn from the grid to compensate the rotor

978SJl�€lj�..cM�q�f�mhtoo�fu� mBtWlled so as tQ347tibsses or supplied to the utility depending on the operat­maintain the desired stator power. The stator power is then

+

Vds

+

V qs

Wind turbine P,Qstator --

Fig. I Basic configuration of DFIG wind tnrbine system.

(OJe-{Or)Aqr R )......-'In'"'"""--r-,....---....ra>>'-� r

L m R

I

({Oe-{Or)Adr �

L m

Fig. 2. Equivalent circuit of DFIG.

Vdr

V qr

ing modes. For sub synchronous mode when rotor angular speed is less than the grid angular frequency, the power flows from the grid to the rotor; othelWise the rotor power is supplied to the grid. Hence the net DFIG generated power is the summation of the stator and rotor power. The reactive power is determined by the machine excitation requirement and the desired grid power factor [9]- [12]. A back-to-back converter provides a bidirectional power­flow control thereby enabling the DFIG to operate in ei­ther sub synchronous or supersynchronous modes. Confi­guration of the overall wind generation system is shown in Fig. 1. The stator of DFIG is directly connected to the grid and the rotor is connected through back-to-back PWM converters. The DFIG is controlled in a rotating d-q reference frame, with the d-axis aligned with the stator flux vector. The stator active and reactive powers of DFIG are controlled by regulating the current and voltage of the rotor. Therefore the current and voltage of the rotor needs to be decomposed into the components related to stator active and reactive power.

A. DFIGmodel Figure 2 shows the d-q equivalent circuit of DFIG. Under stator flux-oriented control, the fluxes, currents and vol­tages can be expressed as [13]

. dAds ] Vds = Rids +---OJ.,/Cqs dt (1)

where

,

dA v =Ri +�-m A dr r dr dt sf qr

,

e qr � \

, ,

\ \ \ \ \ \

'. \ '. \

'" '" {Or'\ de _� r --

'.\ s "'-'==--L..-_L..-___ d,

Fig. 3. Vector diagram for stator flux-oriented control.

dAqr v =Ri +--+Ws1A"r qr r qr dt U

Lm: Magnetizing inductance; Ls : Stator self-inductance; Lr : Rotor self-inductance; Adqs : Stator d-q axis flux linkage; Ad : Rotor d-q axis flux linkage; . qr . I dqs' I dqr: Stator and rotor d-q axis currents.

Ads = L)ds + Lmidr Aqs = L)qs + Lmiqr Adr = Lmids + Lridr

(3)

(4)

(5)

(6)

(7) Aqr = Lmiqs + Lriqr (8)

The aim of the generator's control is to achieve optimal power tracking of the wind turbine power curves. By set­ting the stator flux vector aligned with d-axis as shown in Fig. 3, then

Ads = As' Aqs = o. The stator flux angle is calculated as follows

�s = J (V�s -R)'as)dt �s = J (v;s -Rsi;s )dt

(9)

(10) (11)

AS () = tan -) --.!l!.... (12) s

A�s By neglecting stator resistance, equation (2) can be used to determine the d-axis stator flux as:

(13)

The rotor flux equations are calculated from stator flux and currents

L2 Adr = ---.!!2...ims + C5Lridr

Ls Aqr = (JLri dr

L2 0" = 1 - __ m_

LrLs

(14)

(15)

(16)

dAs V =Ri +-q-+m A qs s qs dt e ds (2) where ims = Vqs /(OJeLm) 3476

The stator voltage vector is consequently in quadrature advance in comparison with the stator flux vector. Then

Vqr Synchronization mode ,---_=..L----"'--'-----_--,

Fig. 4. Active and reactive power control for synchronization mode and running mode.

the q-axis voltage is given as

v =V qs s (17)

And the stator currents are determined from the flux and voltage equations as:

. Lm· lqs = --y;:lqr

ids = (Ads - Lmidr) / Ls Substituting (17) into (19)

(18)

(19)

ids = (Vqs / We - Lmidr) / Ls (20)

Adjustment of the q-axis component of the rotor current controls either the generator developed-torque or the sta­tor-side active power of the DFIG.

active power is controlled to the desired value to produce the reference d-axis rotor voltage. It can be seen how the outer stator power feedback loop provides a reference

.* . value, 1 dr' to the mner current feedback control loop. The

rotor d-axis current is then determined and controlled to produce the reference q-axis rotor voltage. The overall control system for both synchronization mode and mn­ning mode is shown in Fig. 4 [14].

To achieve the full control of the grid-side current, the dc-link voltage must be boosted to a level higher than the amplitude of the line-line voltage. The power flow of the grid-side converter is controlled so as to keep the dc-link voltage constant. To maintain the dc-link voltage constant and to ensure the reactive power flowing into the grid at null, the grid-side converter currents are controlled using the d-q vector control approach. The dc-link voltage is controlled to the desired value by using an IP controller and the change in the dc-link voltage represents a change in the q-axis current. A current feed-forward control loop is also used here to improve the dc-link voltage response to load disturbance. For unity power factor, the demand for the d-axis current is zero.

III. SUPPORT VECTOR REGRESSION

A regression method is an algorithm to estimate a re­lationship between the system input and output from the samples or training data. It is known that the estimation with the SVR is very effective for power system applica­tions [10]. In this section, the principle of the SVR is de­scribed briefly.

Let us consider a set of training samples

{(Yl'x1)' ...... (Yn'xn)}' where Xi and Yi denote the in­

put and output spaces, respectively, and n is the dimen­

sion of training data, The idea of the regression problem is to determine a function that can identify unknown pa­rameters accurately [1 0], [1 1 ],

The general SVR function for estimation takes the form [14]:

f(x) = (w· <I> (x)) + b (23) 3 3 L P =-(v i +v i )=--·----':!!...·v i s 2 qs qs ds ds 2 L qs qr

s (21) where w is a weighting matrix, b is a bias term, <I>

denotes a nonlinear transformation from an n-dimensional On the other hand, regulating the rotor d-axis current component controls directly the stator-side reactive power.

Q 3 ( . . ) 3 Lm (. . ) (22) s ="2 V qsl ds -V ds1 qs ="2' L . v qs 1 ms -1 dr

space to a higher dimensional feature space as shown in Fig. 3, and the dot represents the inner vector product. To calculate w , the following cost function should be mini­mized [15], [16]:

s It is noticeable that the stator active and reactive power components are proportional to the iqr, and idr, respec-

1 n

Min -1IwI12 + rI/(f(xJ-yJ (24) 2 i�l

tively. Provided the magnitude of ims is kept constant, which is subject to

both power components can be controlled linearly by ad- IY i -w· <I>(xJ - bl:::; £: +';i justing the relative rotor current components. The control *

(25)

procedure is explained in details in the following section. i = 1,2, . . . . . . . . . . . . . n ';O';i � 0

By calculating the stator active power as (21), the outer where £ is the permissible error and r is a pre-specified

stator power feedback loop provides a reference val- value that controls the cost incurred by training errors. The

ue, i;r ' to the inner current feedback control loop. The ro- slack variables, c;i and ( , are introduced to accommo­

tor q-axis current is then determined and controlled tQ date the error on the input training set . produce the reference q-axis rotor voltage. The stator re:J477

Training •• ' '" (off-line)

.... : �: : ::: ...... ... �:..."".lf.¥lf.,/ v

Testing (on-line)

Running data (testing)

Fig. 6. Flowchart of wind speed estimation.

The constraints include [; which specifies a permiss­ible estimation error. The value of [; influences the number of support vectors used to obtain the regression function. As [; is lager, the support vectors selected are fewer. With a reasonable choice of r, a trade-off between

minimizing training errors and minimizing the model complexity term 11�12 is accomplished.

The key idea to satisfy these constraints is to determine a Lagrange function from the objective function in (24) and the corresponding constraints in (25) using Lagrange multipliers ai and ai' associated to each sample as

1 n

L = -11wII2 + yI r(f(xJ - yJ 2 i=l + I ai(Yi -w· <I>(xJ - b -E -;i)

+ I ai' ( -Yi + W· <I>(xJ + b -E -;i')

(26)

which is subjected to ai' ai' , C;, C;. > O. Now (24) has to

be minimized with regard to the primal variables

( w, b, ';i ' and ;i*) and maximized with regard to the

Lagrange multipliers � and ai'. Therefore, by setting

the gradient of L with respect to the primal variables to zero [17],

dL " . -=;- = 0 ---t w = L. (ai -ai )<I>(xJ oW i dL " •

db =O-t L.(ai-ai)=O

dL �. d( = 0---7 r=� i dL d';i = 0 ---7 r=';i

(27)

(28)

(29)

If the constraints in (27)-(29) are included in Lagrange function in (26), an optimization problem is then obtained as

30001---�-D;;;;:::::::::;:;:;::::::::::::--1 � t2000 � o 0.. Q) � 1000

500 1000 Turbine speed [rpm] Fig. 5. Power-speed characteristics for 3[kW] wind turbine.

subject to n

'" , L.,(ai -ai) = O. ai.ai E [0. rl i=l where K represents the kernel matrix [16], which is de­fined as

K(xi' x) = <I>(x)·<I>(xJ (31)

The optimization problem in (19) can be transformed into the final form as

n

f(x) = I (ai -ai')· K(Xi' x) + b (32) i= l

which is subject to 0< < 0< ' < _ai-r, _ai -r

and the bias term, b, in (32) is expressed as a function of Lagrange multipliers and kernel,

b = mean ( t {Yi -(ai -ai')K(Xi,X)}) ' (33)

Only the training samples whose corresponding Lagrange multipliers are nonzero are involved in the solution, which are called as support vectors.

Several choices for the kernel are possible to reflect

special properties of approximating functions [1 7], [1 8]: CD Polynomial kernel function

K(Xi'X) =[(xi,x)+lF where q is the polynomial degree.

(2) Radial basis function (RBF)

Ixi,xl2 K(xox) = exp{ ---2-} (J

where (j is the Gaussian width.

IV. WIND SPEED ESTIMATION BASED ON SVR

For the application of the SVR to estimate the wind speed, the training samples for input and output, kernel function, and parameters of C and [; should be firstly de­cided. Thereafter, training samples are obtained from the turbine power equation with pre-specified rotor speed

OJm and wind speed V samples as [1 9]

(34)

1 P, = -pffR2v3C (A) 2 p

where p is the specific density of air and R is the radius

of the turbine blade. Max (30) For each sample, the rotor speed and the correspond-n n

+ �>J a, - a,')- E�) a, + a,') i=l i=l ing turbine power are combined as a pair for the inputs of

347fue SVR estimator. It is well known that for the fixed

3-Phase

Host Computer

Wind Turbine Modeling

Wind sp. General

DFIG Generator Part

� � � ] � �t * � � � 8� r' � � � � � � � . � � �

- .. . ..,."...,. ..-

Grid

] -c:c-� ]

� ---

Fig. 7 System c, 1 I \ I I -............ l/ Rotor power [W] X

f'\ MC!1SlU"cd \!UC 1\

11\ firm/ <I r ,n A 'If " \ "" If - 3

II V\ II 1\ no \11\ A IA II 1\1/ \ \1/ 18 \U 'f ,. � I [m!sl/div -

Fig. 8. Experimental result for wind speed estimation

� A J:.enerator spel ed [rp�]

� '\ \ \ I \ 1800 [rpm] 1 \ 11 l

If \ r , V L/ "-Rotor current [A] 0.5 [s]/div

Fig. 9 Rotor current variation due to speed transition.

pitch turbine the power-speed characteristics are fixed for each wind speed without intersection as shown in Fig. 5 [6]. Hence, if the turbine power and the rotor speed are

known for any operating condition, the wind speed can be

calculated. The RBF as a kernel with £ =0.005, (J = 23, and C =500 is used, which are usually selected based on a

priori knowledge and/or user expertise. Thereafter, La­grange multipliers (ai - ai*) are decided by using Matlab,

and the wind speed is calculated online as depicted in Fig.

6. During on-line operation, the turbine power is calcu­

lated as

� ",. "- I .A" � r---

o 1600 [rpm]

A 1\

Generator speed [rpm] 100 [rpm]/div, 100 [w]/div

T 5 [s]/dIV Fig. 10 Rotor power variation due to speed transition.

r n --J

� ./ D

� _ .. -.r ",.

O[W]

100 [rpm]/div, 750 [w]/div I 01 T I I r I

Generator sp eed [rpm]

1500 [rpm]

Fig. 11 Stator power variation due to speed transition.

the AID inputs of the gate-driver. In order to calculate reference torque, the control program reads wind velocity.

Fig. 8 shows the estimated wind speed which matches the measured one with a slight delay. This delay occurs not only because the system dynamic characteristic is not in­cluded in training process but also because the generator speed control response is not instantaneous.

Figure 9 shows the transition through synchronous � = JOJm dOJm + BtOJ� + Pg

dt (35) speed, the speed changes from sub synchronous to super synchronous smoothly when a back-to-back converter is used. As a result of increasing rotor speed, the rotor pow­er decreases up to zero and the increase in the reverse di-

where Pg is the generator power, J is the system moment of inertia, and Bt is the friction coefficient.

V. EXPERIMENTAL RESULTS rection. Theoretically, the zero crossing point occurs at synchronous speed. However, in Fig. 10 the zero crossing

Figure 7 shows the proposed configuration of the con- occurs at 1875 rpm due to the different sources of loss trol system with the laboratory 3kW system. The charac- such as rotor and converter losses. teristics of the wind turbine are simulated using a tor- On the other hand, the stator power is optimized to ex-que-controlled induction motor drive. Torque reference is tract the maximum power for different wind speed. Re­calculated using torque equations by a control program gion AB in Fig. 11 shows the power optimization during running in a DSP TMS320C33 control board. Reference the wind speed increasing. If the rotor speed reaches the torque is passed to the gate-drivers as a voltage signal b}j4 7

gnaximum value, the rotor speed is controlled to this value using one of the D/A outputs of the control board and one' while the stator power increase as the region BC depicts

in Fig. 11. During high speed operation, pitch angle con­troller is activated to protect the rotating system. In this case, the power is controlled to the rated value as de­scribed by the region DE.

VI. CONCLUSIONS

This paper addresses the dynamic modelling and con­trol system of the Doubly-fed induction generator in the wind power generation system. The dynamic model of the DFIG is complete with its active power and reactive power control. The stator active power is adjusted in order to ex­tract the maximum power from the wind power. Normally, the output reactive power of the wind power conversion system is controlled as zero to keep unity power factor of the stator voltage and current. However, the stator reactive power control is used to optimize the generator efficiency by sharing the reactive power between stator and rotor. The steady state and transient responses of the power, current and pitch angle controllers show excellent per­formance for the different modes and wind speed.

VII. CONCLUSIONS

A novel wind speed estimator using the SVR algorithm has been proposed for wind power generation systems, which is based on off-line training of the input-output samples. The main advantages of the proposed estimation algorithm are the high accuracy and the fast transient performance since a relevant function between system input and output is deduced by off-line training and the output can be calculated directly with the inputs.

REFERENCES

[1] L. M. Craig, M. Davidson, and N. Jenkins, A. Vaudin, "Integration of wind turbines on weak rural networks," Opportunities and Advances in International Power Generation, Conference Publication no. 419, pp 164-167, 1996.

[2] H. De Battista, P.F. Puleston, RJ. Mantz, and c.F. Christiansen, "Sliding mode control of wind energy systems with DFIG-power efficiency and torsional dynamics optimization," IEEE Trans. on Power systems, vol. 15, pp. 728 - 734, May 2000.

[3] S. Foster, L. Xu, and B. Fox, "Coordinated reactive power control for facilitating fault ride through of doubly fed induction generator­and fixed speed induction generator based wind farms," lET Renewable Power Generation, vol. 4, no. 2, pp. 128-138, March 2010.

[4] D. Zhi, L. Xu, and BW. Williams, " Model-based predictive direct power control of doubly-fed induction generators," IEEE Trans.on Power Elec.,vol. 25, no. 2, pp. 341-351, Feb. 2010.

[5] L. Chien-Hung , and H. Yuan-Yih, " Effect of rotor excitation voltage on steady-state stability and maximum output power of a doubly-fed induction generator." IEEE Trans. on Industrial Electronics, vol. 58, no. 4, pp. 1096 - l l09, , Apri1 201l .

[6] M. Rahimi, and M. Parniani, " Transient performance improvement of wind turbines with doubly-fed induction generators using nonlinear control strategy," Trans. on Energy Conv., vol. 25, no. 2, pp. 514- 525, June 2010.

[7] A. Luna, et aI., "Simplified modeling of a DFIG for transient studies in wind power applications," IEEE Trans. on Industrial Electronics, vol. 58, no. 1, pp.9 - 20" Jan. 201l .

[8] K. Tan and S. Islam, "Optimal control strategies in energy conver­sion of PMSG wind turbine system without mechanical sensors," IEEE Trans. on Energy Con v., vol. 19, no. 2, pp. 392-399, June

[9] R. Pena, et aI., "Doubly-fed induction generator using back-to-back PWM converter and iIts application to variable-speed wind-energy generation", IEE Proc. B, vol. 143, No.3, pp.231-241, 1996.

[10] S. Muller, M. Deicke, and R.W. De Doncker, "Doubly fed induction generator systems for wind turbines," IEEE Ind. Applicat. Mag., pp. 26-33, May/June 2002.

[ l l ] L. Xu and C. Wei, " Torque and reactive power control of a doubly fed induction machine by position sensorless scheme," IEEE Trans. Ind. Applicat., vol. 31, no. 3, pp. 636-642, May/June 1995.

[12] R. Pena, 1. C. Clare, and G. M. Asher, "A doubly fed induction generator using back-to-back PWM converters supplying an isolated load from a variable speed wind turbine," IEE proc. on Electric Power Appl., vol. 143, no. 5, pp. 331-338, Sep. 1996.

[13] S. Bhowmik, R. Spee, and 1. H. R. Enslin, "Performance optimization for doubly fed wind power generation systems,"

IEEE Trans. on Ind. Appl. , vol. 35, no. 4, pp. 949-958, Jul.!Aug. 1999.

[14] A. G. Abo-Khalil, D-C. Lee, and S-H. Lee, "Grid connection of doubly-fed induction generators in wind energy conversion system," IPEMC, Shanghai, vol. 3, 2006, pp. 1487-149l .

[15] Y. Li and H. Yu, "Three-phase induction motor operation trend prediction using support vector regression for condition-based maintenance," World Congress on Intelligent Control and Automation WCICA, vol. 2, June 2006, pp. 7878-7881.

[16] K. R. Nuller, A. Smola, G. Ratrch, B. Scholkopf , 1. Kohlmargen, and V. Vapnik ,"Predicting time series with support vector machine," in Pm/CA, Springer LNCS 1327, 1997, pp. 999-1004.

[ l7] V. Cherkas sky, and F. Miller, Learning from data concepts, theory and methods, Wiley, 1998.

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2004. 3480

(a) Total Inductance (LTpu) (b) Filter Capacitance (C f pu) (c) Resonant Frequency (f res)

Fig. 3: Total inductance, capacitance and resonant frequency as functions of 'a' and 'r/ with design constraints.

�-

�15 ! � 20 '015 t :'10 •

Time(s) Fundumenlul (50Hz) =225, THD= 66.26%

600 Harmonic ordlr

(a) Output phase voltage of inverter (vd.

r��.· •••. · ••••. · ••••••• ·· · ... · ••............ · •• ·· •.....•••..••••..••••..••.......••.. .... . ....

.• : .... ...•.••..••••..•••••.•..

r l • � -20 - - - - - - - - � - - - - - , - - - - - - - - - - - , - - - - - : - - - - - - - - - - - - � 0.1

Time{s) Funciemenlel (50Hz) = 23.95, THD= 14.91%

(b) Inverter-side inductor current (I LJ.

r Jr\Z\ZX] ; ::[\l\l\J 0.06 0.01 0.08 0.09 0.1 0 .1 1 Time(s) Time(s)

Fundamental (9JHz) _22.3& , THD. 0.24'% Fundamental (50Hz) '" 178.9, 'T1-D= 1.35% 0.18

0,16

::=- 0.14 � � 0.12 1 01

'00,08 i-DO 0.06 ,; 0.04 0.2

002 0 .1

Harmonic order Harmonicorcler

(c) Grid-side inductor current (1£g). (d) Filter Capacitor Voltage (Vc f)'

Fig. 5: Performance of the designed filter with ARS PWM based three-phase two level inverter.

with different modulation schemes. The cancelation of har­monics due to three-phase topology, specifically the carrier band harmonics, are considered in the paper, resulting in the

optimized design. The paper also discusses exhaustively the design constraints one has to consider while designing filter for grid-interactive converters. The effect of choice of active or passive damping on selection of resonant frequency has also been discussed and it is shown that the selection of resonatl92 frequency is independent of the choice of damping method.

Moreover, the presented design approach in p.u. system allows the comparison of filters designed for converters of different ratings and topologies. The complete analysis and performance of the designed filter are validated by simulation studies on

5kVA, 220V, three-phase LCL filter based grid-interactive converter.