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Real-Time Implementation of ANFIS Control for Renewable Interfacing Inverter in 3P4W Distribution Network
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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 60, NO. 1, JANUARY 2013 121 Real-Time Implementation of ANFIS Control for Renewable Interfacing Inverter in 3P4W Distribution Network Mukhtiar Singh, Member, IEEE, and Ambrish Chandra, Senior Member, IEEE Abstract—Power electronics plays an important role in con- trolling the grid-connected renewable energy sources. This pa- per presents a novel adaptive neuro-fuzzy control approach for the renewable interfacing inverter. The main objective is to achieve smooth bidirectional power flow and nonlinear unbal- anced load compensation simultaneously, where the conventional proportional-integral controller may fail due to the rapid change in the dynamics of the highly nonlinear system. The combined capability of neuro-fuzzy controller in handling the uncertainties and learning from the processes is proved to be advantageous while controlling the inverter under fluctuating operating condi- tions. The inverter is actively controlled to compensate the har- monics, reactive power, and the current imbalance of a three-phase four-wire (3P4W) nonlinear load with generated renewable power injection into the grid simultaneously. This enables the grid to always supply/absorb a balanced set of fundamental currents at unity power factor even in the presence of the 3P4W nonlinear unbalanced load at the point of common coupling. The proposed system is developed and simulated in MATLAB/SimPowerSystem environment under different operating conditions. The digital signal processing and control engineering-based laboratory exper- imental results are also provided to validate the proposed control approach. Index Terms—Distributed generation, grid interconnection, neuro-fuzzy control, nonlinear load, power quality, renewable energy, unbalanced load. I. I NTRODUCTION T HE increase in global energy demand, air pollution, global warming, and the rapid evaporation of fossil fuel has made it necessary to look toward renewable sources as a future energy solution. However, the higher penetration level of these intermittent renewable energy sources (RESs) poses a great threat to network security. Therefore, the RESs are required to comply with strict technical and regulatory frameworks to ensure the safe, reliable, and efficient operation of the overall network. With the advancement in power electronics and digital Manuscript received September 18, 2009; revised April 27, 2011 and September 14, 2011; accepted November 20, 2011. Date of publication January 26, 2012; date of current version September 6, 2012. M. Singh is with the Department of Electrical Engineering, Deenbandhu Chhotu Ram University of Science and Technology, Murthal, Haryana 131039, India (e-mail: [email protected]). A. Chandra is with the Department of Electrical Engineering, Ecole de technologie superieure, Universite du Quebec, Montreal, QC H3C 1K3, Canada (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIE.2012.2186103 control technology, the RES can now be actively controlled to enhance the system stability with an improved power quality at the point of common coupling (PCC). Recently, a lot of control strategies for renewable interfacing inverter have been introduced [1]–[7]. Some control strategies for grid-connected inverters incorporating power quality so- lution have also been investigated by researchers. In [8], an inverter operates as an active inductor at a certain frequency to absorb the harmonic current. However, the exact calculation of network inductance in real time is very difficult and may deteriorate the control performance. A similar approach in which a shunt active filter acts as an active conductance to damp out the harmonics in distribution network is proposed in [9]. In [10], a control strategy for renewable interfacing inverter based on pq theory is proposed. A similar decoupled current control technique using PI regulator in dq reference frame is presented in [11]. In both of these strategies, the load and inverter current sensing is required to compensate the load current harmonics. The current-regulated voltage source inverters have a very wide range of applications such as the grid synchronization of RES, static reactive power compensation, uninterruptible power supply, active power filters (APF), and adjustable speed drives. However, in the case of the very first application, the installed inverter rating has a very low utilization factor due to the inter- mittent nature of RES. According to [12] and [13], the expected RES output during peak is nearly 60% of the rated output, yet the annual capacity factor may be in the 20%–30% range. Therefore, the authors have incorporated the APF features in the RES interfacing inverter to maximize its utilization without any additional hardware cost. Moreover, the proposed control strategy requires only the grid current sensing, which further reduces the cost and complexity. The grid-interfacing inverter injects the generated active power from renewable as well as compensates the load reactive power, current harmonics, and load imbalance in a three-phase four-wire (3P4W) system. This enables the grid to always supply a balanced set of sinusoidal currents at unity power factor (UPF). Since the inverter works under highly fluctuating operating conditions, it is not possible to set the optimal value of gains for the conventional PI regulator [14]–[16]. This may lead to a false operation of the inverter. To alleviate this problem, an adaptive neuro-fuzzy controller is developed, which has well-known advantages in modeling and control of a highly nonlinear system [17], [18]. An adaptive error backpropagation method is used to update the weights of the system for the fast convergence of control. 0278-0046/$31.00 © 2012 IEEE
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  • IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 60, NO. 1, JANUARY 2013 121

    Real-Time Implementation of ANFIS Controlfor Renewable Interfacing Inverter in

    3P4W Distribution NetworkMukhtiar Singh, Member, IEEE, and Ambrish Chandra, Senior Member, IEEE

    AbstractPower electronics plays an important role in con-trolling the grid-connected renewable energy sources. This pa-per presents a novel adaptive neuro-fuzzy control approach forthe renewable interfacing inverter. The main objective is toachieve smooth bidirectional power flow and nonlinear unbal-anced load compensation simultaneously, where the conventionalproportional-integral controller may fail due to the rapid changein the dynamics of the highly nonlinear system. The combinedcapability of neuro-fuzzy controller in handling the uncertaintiesand learning from the processes is proved to be advantageouswhile controlling the inverter under fluctuating operating condi-tions. The inverter is actively controlled to compensate the har-monics, reactive power, and the current imbalance of a three-phasefour-wire (3P4W) nonlinear load with generated renewable powerinjection into the grid simultaneously. This enables the grid toalways supply/absorb a balanced set of fundamental currents atunity power factor even in the presence of the 3P4W nonlinearunbalanced load at the point of common coupling. The proposedsystem is developed and simulated in MATLAB/SimPowerSystemenvironment under different operating conditions. The digitalsignal processing and control engineering-based laboratory exper-imental results are also provided to validate the proposed controlapproach.

    Index TermsDistributed generation, grid interconnection,neuro-fuzzy control, nonlinear load, power quality, renewableenergy, unbalanced load.

    I. INTRODUCTION

    THE increase in global energy demand, air pollution, globalwarming, and the rapid evaporation of fossil fuel hasmade it necessary to look toward renewable sources as a futureenergy solution. However, the higher penetration level of theseintermittent renewable energy sources (RESs) poses a greatthreat to network security. Therefore, the RESs are requiredto comply with strict technical and regulatory frameworks toensure the safe, reliable, and efficient operation of the overallnetwork. With the advancement in power electronics and digital

    Manuscript received September 18, 2009; revised April 27, 2011 andSeptember 14, 2011; accepted November 20, 2011. Date of publicationJanuary 26, 2012; date of current version September 6, 2012.

    M. Singh is with the Department of Electrical Engineering, DeenbandhuChhotu Ram University of Science and Technology, Murthal, Haryana 131039,India (e-mail: [email protected]).

    A. Chandra is with the Department of Electrical Engineering, Ecole detechnologie superieure, Universite du Quebec, Montreal, QC H3C 1K3, Canada(e-mail: [email protected]).

    Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

    Digital Object Identifier 10.1109/TIE.2012.2186103

    control technology, the RES can now be actively controlled toenhance the system stability with an improved power quality atthe point of common coupling (PCC).

    Recently, a lot of control strategies for renewable interfacinginverter have been introduced [1][7]. Some control strategiesfor grid-connected inverters incorporating power quality so-lution have also been investigated by researchers. In [8], aninverter operates as an active inductor at a certain frequencyto absorb the harmonic current. However, the exact calculationof network inductance in real time is very difficult and maydeteriorate the control performance. A similar approach inwhich a shunt active filter acts as an active conductance to dampout the harmonics in distribution network is proposed in [9]. In[10], a control strategy for renewable interfacing inverter basedon pq theory is proposed. A similar decoupled current controltechnique using PI regulator in dq reference frame is presentedin [11]. In both of these strategies, the load and inverter currentsensing is required to compensate the load current harmonics.

    The current-regulated voltage source inverters have a verywide range of applications such as the grid synchronization ofRES, static reactive power compensation, uninterruptible powersupply, active power filters (APF), and adjustable speed drives.However, in the case of the very first application, the installedinverter rating has a very low utilization factor due to the inter-mittent nature of RES. According to [12] and [13], the expectedRES output during peak is nearly 60% of the rated output,yet the annual capacity factor may be in the 20%30% range.Therefore, the authors have incorporated the APF features inthe RES interfacing inverter to maximize its utilization withoutany additional hardware cost. Moreover, the proposed controlstrategy requires only the grid current sensing, which furtherreduces the cost and complexity. The grid-interfacing inverterinjects the generated active power from renewable as well ascompensates the load reactive power, current harmonics, andload imbalance in a three-phase four-wire (3P4W) system. Thisenables the grid to always supply a balanced set of sinusoidalcurrents at unity power factor (UPF).

    Since the inverter works under highly fluctuating operatingconditions, it is not possible to set the optimal value of gainsfor the conventional PI regulator [14][16]. This may lead toa false operation of the inverter. To alleviate this problem,an adaptive neuro-fuzzy controller is developed, which haswell-known advantages in modeling and control of a highlynonlinear system [17], [18]. An adaptive error backpropagationmethod is used to update the weights of the system for the fastconvergence of control.

    0278-0046/$31.00 2012 IEEE

  • 122 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 60, NO. 1, JANUARY 2013

    Fig. 1. Schematic and control description of proposed renewable-based dis-tributed generation system.

    This paper is organized as follows: Section II presents thesystem description and control algorithm for the inverter. InSection III, the simulation results are discussed, while theexperimental results under different operating conditions arepresented and discussed thoroughly in Section IV. Section Vfinally concludes this paper.

    II. SYSTEM CONFIGURATION AND CONTROL

    The system under consideration with control description isshown in Fig. 1, where a RES is connected on the dc linkof a grid-interfacing four-leg inverter. The fourth leg of theinverter is utilized to compensate the neutral current of 3P4Wnetwork. Here, the inverter is a key element since it deliversthe power from renewable to grid and also solves the power-quality problem arising due to unbalanced nonlinear load atPCC. The duty ratio of inverter switches are varied in a powercycle such that the combination of load and inverter-injectedpower appears as balanced resistive load to the grid, resultinginto the UPF grid operation.

    The renewable source may be a dc source or an ac sourcewith rectifier coupled to a dc link [19]. The regulation of dc-linkvoltage carries the information regarding the exchange of activepower in between renewable source and grid. The error betweenreference dc-link voltage (V dc) and actual dc-link voltage (Vdc)is given to the neuro-fuzzy controller, and the same error is usedto update the weights. The output of neuro-fuzzy controller isfurther modified by subtracting the renewable injected current(iRen). This results into the reference d-axis current (id), whilethe reference q-axis current (iq) is set to zero for UPF gridoperation. The grid-synchronizing angle () obtained fromphase lock loop is used to generate the reference grid currents(ia, ib, and ic). The reference grid neutral current in is set to

    Fig. 2. Optimized ANFIS architecture suggested by MATLAB/anfiseditor.

    Fig. 3. Schematic of the proposed ANFIS-based control architecture.

    zero to achieve balanced grid-current operation. The hysteresiscurrent controller is utilized to force the actual grid currents totrack the reference grid currents accurately. This enables thegrid to supply/absorb only the fundamental active power, whilethe RES-interfacing inverter fulfills the unbalance, reactive, andnonlinear current requirements of 3P4W load at PCC.

    Design of Adaptive Neuro-Fuzzy ControllerAn optimized adaptive-network-based fuzzy inference sys-

    tem (ANFIS) having a 1:3:3:3:1 architecture is generated fromthe initial data using MATLAB/anfiseditor as shown in Fig. 2.

    This Takagi-Sugeno-Kang fuzzy model-based ANFIS archi-tecture has one input and one output, which is further tunedonline using the error backpropagation method as shown inFig. 3. The error between reference dc-link voltage and actualdc-link voltage ( = V dc Vdc) is given to the neuro-fuzzycontroller, and the same error is used to tune the preconditionand consequent parameters. The control of dc-link voltage givesthe active power current component (id ), which is furthermodified to take into account the active current componentinjected from RES (iRen). The node functions of each layer inthe ANFIS architecture are described as follows:

    Layer 1: This layer is also known as the fuzzification layerwhere each node is represented by a square. Here, three

  • SINGH AND CHANDRA: IMPLEMENTATION OF ANFIS CONTROL FOR RENEWABLE INTERFACING INVERTER 123

    Fig. 4. Fuzzy membership functions.

    membership functions are assigned to each input. The trape-zoidal and triangular membership functions are used to reducethe computation burden as shown in Fig. 4, and their corre-sponding node equations are given as follows:

    A1() =

    1 b1a1b1a1 b1a1

    0 a1(1)

    A2() ={

    1 a20.5b2 | a2| 0.5b20 | a2| 0.5b2 (2)

    A3() =

    0 a3a3b3a3 a3b3

    1 b3(3)

    where the value of the parameters {ai, bi} changes with thechange in error and accordingly generates the linguistic value ofeach membership function. Parameters in this layer are referredas premise parameters or precondition parameters.

    Layer 2: Every node in this layer is a circle labeled as which multiplies the incoming signals and forwards it to thenext layer

    i = Ai(1) Bi(2) , i = 1, 2, 3. (4)However, in our case, there is only one input, so this layer

    can be ignored and the output of the first layer will directly passto the third layer.

    Here, the output of each node represents the firing strengthof a rule.

    Layer 3: Every node in this layer is represented by a circle.This layer calculates the normalized firing strength of each ruleas given in the following:

    i =i

    1 + 2 + 3, i = 1, 2, 3. (5)

    Layer 4: Every node in this layer is a square node with a nodefunction

    Oi = i fi = i(ai0 + a

    i1

    ), i = 1, 2, 3 (6)

    where the parameters {ai0, ai1} are tuned as the function ofthe input (). The parameters in this layer are also referred asconsequent parameters.

    Layer 5: This layer is also called the output layer whichcomputes the output as given in the following:

    Y = 1 f1 + 2 f2 + 3 f3. (7)

    The output from this layer is multiplied with the normalizingfactor to obtain the active power current component (id ). Thedetailed algorithm for the training of the ANFIS architecture isgiven in Appendix II.

    III. SIMULATION RESULTS AND DISCUSSION

    An extensive simulation study has been carried out for therenewable interfacing inverter in order to verify the proposedcontrol strategy. The system under consideration is simulatedusing the SimPowerSystem tool box of MATLAB/Simulink. AnIGBT-based four-leg current-controlled voltage source inverteris actively controlled to achieve the balanced sinusoidal gridcurrents at UPF despite the highly unbalanced nonlinear loadat the PCC under varying renewable generating conditions. ARES with variable output power is connected on the dc linkof the grid-interfacing inverter. An unbalanced 3P4W nonlin-ear variable load, whose harmonics, unbalance, and reactivepower are to be compensated, is connected on the PCC. Thewaveforms of grid voltage (Vg), grid current (ig), unbalancedload current (il), injected inverter currents (iinv), and dc-linkvoltage (Vdc) are shown in Fig. 5. In Fig. 6, the traces of phasea grid current (iga), phase a load current (ila), and phase ainverter current (iinva) are shown w.r.t. phase a grid voltage(Vga). In addition, the waveforms of grid neutral current (ign),load neutral current (iln), and inverter neutral current (iinvn)are also shown in the same diagram. Fig. 7 shows the traces ofphase a grid voltage (Vga) and phase a grid current (iga) onthe same plot, phase a load current (ila), and phase a invertercurrent (iinva).

    The main purpose of the proposed control strategy is to injectthe generated renewable active power, load harmonics, and re-active power in such a way that only the injection/absorption ofthe active power takes place in the grid. Initially, the generatedactive power is more than the load active power demand, sothe extra generated power is being injected into the grid. Thisfact can be verified from the traces of different currents, wherethe current supplied from the renewable is more than the loadcurrent, so the difference of these is being injected into the gridas evident from the out-of-phase relation of the grid voltage(Vga) and grid current (iga). In addition, the inverter is alsosupplying the harmonics, neutral current, and reactive currentcomponent of the load current demand. This results into theperfectly balanced sinusoidal grid current even in the presenceof a 3P4W unbalanced nonlinear load at PCC as shown inFig. 5. This fact can also be visualized from Figs. 6 and 7,where the phase a grid current (iga) is purely sinusoidal andin phase opposition with the phase a grid voltage (Vga). Here,it can also be noticed that the load neutral current (iln) is fullysupplied by the inverter neutral current (iinvn). This results intothe zero value of the grid neutral current (in).

    At t = 0.375 s, there is a sudden increase in the load powerdemand, and the generated renewable active power is not suf-ficient enough to meet this enhanced demand. At this instant,the renewable interfacing inverter supplies the generated activepower and total load reactive power demand, while the gridsupplies only the deficient amount of load active power. Thisfact can be verified from Figs. 6 and 7, where the phase a grid

  • 124 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 60, NO. 1, JANUARY 2013

    Fig. 5. Simulation results. (a) Grid voltages. (b) Grid currents. (c) Unbalancedload currents. (d) Inverter currents.

    current, which was in the opposite phase to the grid voltagebefore t = 0.375 s, is now in phase with the grid voltageand the load neutral current is still being supplied from theinverter. Thus, from the simulation results, it is clear that thegrid always works at UPF under fluctuating renewable powergeneration and dynamic load conditions with an unbalancednonlinear load at PCC. It can also be noticed that the dc-linkvoltage is almost constant at 300 V under both steady state anddynamic conditions, except negligible deviation due to a changein injected active power. Here, the dc-link voltage is shown ona very small scale, just to demonstrate the performance of theproposed ANFIS controller in controlling the dc-link voltage.

    IV. EXPERIMENTAL RESULTS AND DISCUSSION

    The proposed adaptive neuro-fuzzy controller is imple-mented in real time on a four-leg IGBT-based inverter us-

    Fig. 6. Simulation results: Phase a grid voltage, grid current, load current,inverter current, load neutral current, and inverter neutral current.

    Fig. 7. Simulation results. (a) Phase a grid voltage and current. (b) Loadcurrent. (c) Inverter current.

    ing digital signal processing and control engineering DS1104,whereas the RES is emulated with an auxiliary inverter con-nected on a dc link. It takes a sampling time of 75 s torealize the proposed ANFIS controller in real time. The 3P4Wnonlinear load is composed of three-phase nonlinear RL load,one-phase RL nonlinear load connected in between phase a andneutral, and a single-phase RL load in between phase b andneutral.

    An extensive experimental study is carried out to highlightthe performance of the inverter as a multiobjective device.The inverter operation is mainly divided into two parts: activefilter operation and renewable interfacing operation. All theexperimental results are captured with an oscilloscope in realtime as shown in Figs. 810.

    A. Active Filter Operation

    In this mode of operation, only the active filtering capabilitiesof the inverter are demonstrated. In Fig. 8(a), the traces of3P4W grid currents are shown before and after compensation.Initially, the grid supplies an unbalanced nonlinear load currentwith a high neutral current, which is highly undesirable. Inorder to compensate this unbalanced nonlinear current, theinverter currents are injected in such a way that the combinationof load and inverter current appears as a balanced set of fun-damental currents. The traces of the injected inverter currentsare shown in Fig. 8(b), just before and after compensation.Here, it can be easily noticed that the grid currents are perfectlybalanced with a sinusoidal profile. Moreover, the inverter is

  • SINGH AND CHANDRA: IMPLEMENTATION OF ANFIS CONTROL FOR RENEWABLE INTERFACING INVERTER 125

    Fig. 8. Experimental results: (a) Grid currents and (b) inverter currents, justbefore and after compensation.

    successfully able to supply the load neutral current demandlocally, as evident from the zero value of the grid neutral current(ign).

    B. Renewable Interfacing OperationIn this mode of operation, the bidirectional power flow

    capabilities of the renewable interfacing inverter are discussed.Here, the main objective is not only the grid interfacing ofthe renewable but also to compensate the 3P4W nonlinearunbalanced load at PCC simultaneously. The inverter suppliesthe renewable injected current and the nonlinear unbalancedcomponent of load current. This enables the grid to alwayssupply/absorb only the balanced set of currents at UPF. InFig. 9, the traces of grid voltage (Vg), grid current (ig), loadcurrent (il), and inverter injected current (iinv) are shown. InFig. 9(a), initially, the inverter current is supporting the loadcurrent partially and it goes on increasing. At middle stage,the inverter current is almost equal to the load current, and thisforces the grid current to be almost zero. In the last stage, theinverter current is more than the load demand, and at this stage,the grid absorbs this excessive amount of current as evident bythe out-of-phase relationship of the grid voltage and current.Similarly, in Fig. 9(b), the grid current is again shown from

    Fig. 9. Experimental results: Inverter performance under the renewable inter-facing mode of operation.

    Fig. 10. Experimental results: Inverter performance under the renewableinterfacing mode of operation.

    absorption mode to supplying mode with the correspondingchange in the inverter current. Fig. 10 shows the traces ofgrid voltage (Vg) and grid current (ig) on the same axis, dc-link voltage (Vdc), and inverter injected current (iinv), where

  • 126 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 60, NO. 1, JANUARY 2013

    TABLE IINVERTER PERFORMANCE AS A COMPENSATING DEVICE

    it can be noticed that the dc-link voltage is almost constantirrespective of any kind of variation in injected inverter current.

    A comparative table showing the total harmonic distortions(THDs) and unbalance factor (UF) before and after compensa-tion is given in Table I, where the percentage UF is calculatedseparately for each phase using

    %UFabc =|iabc iavg.|

    iavg. 100. (8)

    Here, it can be noticed that the grid current is highly unbalancedwith the UFs of 20.48%, 0.41%, and 21.07% in phase a, phaseb, and phase c, respectively, resulting into the flow of a 1.1-Acurrent in neutral wire. The percent THDs present in phase a,phase b, and phase c currents are 14.7%, 18.2%, and 23.2%,respectively. However, once after the interconnection of therenewable interfacing inverter, the grid currents become almostbalanced and harmonic free with a very low UF of 0.7%, a verylow level of THDs of 2.9%, and an almost zero current in grid-side neutral wire.

    V. CONCLUSION

    This paper has presented a novel adaptive neuro-fuzzycontrol algorithm for the renewable interfacing inverter. Thecontroller works satisfactorily under the dynamic operatingconditions. It has also been shown that the inverter is ableto perform all the duties of the shunt APF while maintain-ing the smooth bidirectional power flow simultaneously. Thesimulation results supported by the experimental results areprovided to validate the fact that the renewable interfacinginverter can act as a multioperation device in order to utilizeits maximum rating. The current unbalance, current harmonics,and load reactive power demand of an unbalanced nonlinearload at PCC are compensated effectively such that the grid-side currents are always maintained as a balanced set (0% UF)of sinusoidal current (2.7% THD) at UPF. Moreover, the loadneutral current is restricted to flow toward the grid side (almostzero) by supporting it locally from the fourth leg of the inverter.When the power generated from the renewable is more thanthe total load power demand, the grid-interfacing inverter withthe proposed control approach successfully fulfills the totalload demand (active, reactive, and harmonics) and delivers theremaining active power to the main grid at UPF operation.

    APPENDIX ISYSTEM PARAMETERS

    Three-phase supply (rms) : Vg = 30 V, 60 HzThree-phase nonlinear load : R = 26.66 , L = 10 mHOne-phase linear load(AN) : R = 26.66 , L = 10 mHOne-phase nonlinear load(BN) : R = 56 , L = 10 mHDC-link capacitance and voltage : Cdc = 3000 F, Vdc = 75 VCoupling inductance : Lsh = 2.0 mHSource impedance ratio : X/R = 7

    APPENDIX II

    A. Online Training of the ANFIS ArchitectureThe ANFIS structure is tuned with a gradient descent tech-

    nique to reduce the error (usually a cost function given by thesquared error), where the weights are iterated by propagatingthe error from output layer to input layer. This backward tripof such a calculation is termed as backpropagation [20].The training algorithm is completed in two stages, known asthe precondition parameter tuning and the consequent para-meter tuning, where the objective function to be minimized isdefined as

    2 = (V dc Vdc)2 . (A1)Precondition Parameter Tuning: The precondition parame-

    ters are required to update the fuzzy membership functions asdiscussed in the previous section for Layer1. To minimize theerror function 2 by the gradient descent method, the change ineach precondition parameter must be proportional to the rate ofchange of the error function w.r.t. that particular preconditionparameter, i.e.,

    aAi = 2

    aAi= 1, 2, 3 (A2)

    where is the constant of proportionality defined as the learn-ing rate. Therefore, the new value of the consequent parameteris given as

    aAi(n + 1) = aAi(n) + aAi , i = 1, 2, 3 (A3)or

    aAi(n + 1) = aAi(n) 2

    aAi, i = 1, 2, 3. (A4)

    Now the partial derivative term in (A4) can be found by thechain rule of differentiation as follows:

    2

    aA1=

    2

    Vdc Vdc

    id i

    d

    1 1A1

    A1aA1

    (A5)

    where

    2

    Vdc=2 (V dc Vdc)=2 (A5a)

    Vdcid

    =J (A5b)

  • SINGH AND CHANDRA: IMPLEMENTATION OF ANFIS CONTROL FOR RENEWABLE INTERFACING INVERTER 127

    id1

    =

    1(1 f1 + 2 f2 + 3 f)=f1 (A5c)

    1A1

    =

    A1

    (A1

    A1 + A2 + A3

    )=

    A2 + A3(A1 + A2 + A3)

    2

    =1

    (A1 + A2 + A3)

    (A2

    (A1 + A2 + A3)

    +A3

    (A1 + A2 + A3)

    )

    =2 + 3

    A1 + A2 + A3(A5d)

    A1aA1

    =

    aA1

    ( aA1

    bA1 aA1

    )=

    bA1(bA1 aA1)2

    = bA1 + aA1 aA1

    (bA1 aA1)2

    =1

    (bA1 aA1)(

    aA1(bA1 aA1)

    bA1 aA1(bA1 aA1)

    )

    =A1 1

    bA1 aA1(A5e)

    where J is Jacobian matrix, which can be taken as constant,being a single-inputsingle-output ANFIS architecture, and canbe included in the learning rate. In computing all the terms of(A5) and putting in (A4), we can find the updated value of theparameter aA1 as follows:

    aA1(n + 1) = aA1(n) + 2 (n) f1(n) 2(n) + 3(n)A1(n) + A2(n) + A3(n)

    A1(n) 1bA1(n) aA1(n)

    . (A6)

    Similarly

    bA1(n + 1) = bA1(n) 2 (n) f1(n)

    2(n) + 3(n)A1(n) + A2(n) + A3(n)

    A1(n)bA1(n) aA1(n)

    . (A7)

    In the same manner, the precondition parameters for the re-maining fuzzy membership functions can be derived as follows:

    bA2(n + 1) = bA2(n) + 2 (n) f2(n)

    1(n) + 3(n)A1(n) + A2(n) + A3(n)

    1 A2(n)bA2(n)

    (A8)

    aA3(n + 1) = aA3(n) + 2 (n) f3(n)

    1(n) + 2(n)A1(n) + A2(n) + A3(n)

    A3(n) 1bA3(n) aA3(n)

    (A9)

    bA3(n + 1) = bA3(n) 2 (n) f3(n)

    1(n) + 1(n)A1(n) + A2(n) + A3(n)

    A3(n)bA3(n) aA3(n)

    . (A10)

    Consequent Parameter Tuning: To tune the consequent pa-rameters as discussed in Layer 4, the following updated lawsare developed:

    a0i(n + 1) = a0i(n) c 2

    a0i, i = 1, 2, 3 (A11)

    a1i(n + 1) = a1i(n) c 2

    a1i, i = 1, 2, 3 (A12)

    where c is the learning rate for the consequent parameters. Thederivative terms in (A11) and (A12), can be found by the chainrule as already discussed in the case of precondition parametersas follows:

    2

    a0i=

    2

    Vdc Vdc

    id i

    d

    fi fia0i

    , i = 1, 2, 3 (A13)2

    a1i=

    2

    Vdc Vdc

    id i

    d

    fi fia1i

    , i = 1, 2, 3. (A14)

    In the aforementioned (A13) and (A14), the first two termson the right-hand side are already known and the last two termscan be derived as

    idfi

    =i

    A1 + A2 + A3, i = 1, 2, 3 (A15)

    fia0i

    =1, i = 1, 2, 3 (A16)fia1i

    = , i = 1, 2, 3. (A17)

    In substituting the terms derived in (A15)(A17) into (A13)and (A14), the updated value of the consequent parameters canbe derived as follows:

    a0i(n + 1) = a0i(n) + 2 c iA1 + A2 + A3

    , i = 1, 2, 3 (A18)a1i(n + 1) = a1i(n) + 2 c

    ia1 + a2 + a3

    , i = 1, 2, 3. (A19)

    REFERENCES[1] M. Singh and A. Chandra, Power maximization and voltage sag/swell

    ride-through capability of PMSG based variable speed wind energy con-version system, in Proc. 34th IEEE IECON/IECON, Orlando, FL, 2008.

    [2] F. Blaabjerg, R. Teodorescu, M. Liserre, and A. V. Timbus, Overviewof control and grid synchronization for distributed power generationsystems, IEEE Trans. Ind. Electron., vol. 53, no. 5, pp. 13981409,Oct. 2006.

    [3] X. Guo, W. Wu, and Z. Chen, Multiple-complex coefficient-filter-basedphase-locked loop and synchronization technique for three-phase grid-interfaced converters in distributed utility networks, IEEE Trans. Ind.Electron., vol. 58, no. 4, pp. 11941204, Apr. 2011.

    [4] P. Jintakosonwit, H. Akagi, H. Fujita, and S. Ogasawara, Implementationand performance of automatic gain adjustment in a shunt-active filter forharmonic damping throughout a power distribution system, IEEE Trans.Power Electron., vol. 17, no. 3, pp. 438447, May 2002.

    [5] J. M. Carrasco, L. G. Franquelo, J. T. Bialasiewicz, E. Galvn,R. C. P. Guisado, M. . M. Prats, J. I. Len, and N. Moreno-Alfonso,Power-electronic systems for the grid integration of renewable energysources: A survey, IEEE Trans. Ind. Electron., vol. 53, no. 4, pp. 10021016, Jun. 2006.

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    [6] J. H. R. Enslin and P. J. M. Heskes, Harmonic interaction between a largenumber of distributed power inverters and the distribution network, IEEETrans. Power Electron., vol. 19, no. 6, pp. 15861593, Nov. 2004.

    [7] M. Singh, V. Khadkikar, and A. Chandra, Grid synchronization withharmonics and reactive power compensation capability of PMSG basedvariable speed wind energy conversion system, IET Trans. Power Elec-tron., vol. 4, no. 1, pp. 122130, Jan. 2011.

    [8] U. Borup, F. Blaabjerg, and P. N. Enjeti, Sharing of nonlinear loadin parallel-connected three-phase converters, IEEE Trans. Ind. Appl.,vol. 37, no. 6, pp. 18171823, Nov./Dec. 2001.

    [9] P. Jintakosonwit, H. Fujita, H. Akagi, and S. Ogasawara, Implementationand performance of cooperative control of shunt active filters for harmonicdamping throughout a power distribution system, IEEE Trans. Ind. Appl.,vol. 39, no. 2, pp. 556564, Mar./Apr. 2003.

    [10] J. P. Pinto, R. Pregitzer, L. F. C. Monteiro, and J. L. Afonso, 3-phase4-wire shunt active power filter with renewable energy interface, in Proc.IEEE ICREPQ Conf., Seville, Spain, 2007.

    [11] S. Rahmani, A. Hamadi, N. Mendalek, and K. Al-Haddad, A new controltechnique for three-phase shunt hybrid power filter, IEEE Trans. Ind.Electron., vol. 56, no. 8, pp. 29042915, Aug. 2009.

    [12] N. Boccard, Capacity factor of wind power realized values vs. estimates,Elsevier Trans. Energy Policy, vol. 37, no. 7, pp. 26792688, Jul. 2009.

    [13] Capacity Factors at Kansas Wind Farms Compared With Total StateElectrical Demand, July 2007 to June 2008. [Online]. Available: http://www.kcc.state.ks.us/energy/charts/Wind_CapacityFactorsatKansasWindFarmsComparedwithTotalStateElectricalDemand.pdf

    [14] L. Yacoubi, K. Al-Haddad, L. A. Dessaint, and F. Fnaiech, Linear andnonlinear control techniques for a three-phase three-level NPC boostrectifier, IEEE Trans. Ind. Electron., vol. 53, no. 6, pp. 19081918,Dec. 2006.

    [15] S. Yang, Q. Lei, F. Z. Peng, and Z. Qian, A robust control schemefor grid-connected voltage-source inverters, IEEE Trans. Ind. Electron.,vol. 58, no. 1, pp. 202212, Jan. 2011.

    [16] J. M. Esp, J. Castell, R. Garca-Gil, G. Garcer, and E. Figueres, Anadaptive robust predictive current control for three-phase grid-connectedinverters, IEEE Trans. Ind. Electron., vol. 58, no. 8, pp. 35373546,Aug. 2011.

    [17] H. Li, K. L. Shi, and P. G. McLaren, Neural-network-based sensorlessmaximum wind energy capture with compensated power coefficient,IEEE Trans. Ind. Appl., vol. 41, no. 6, pp. 15481556, Nov./Dec. 2005.

    [18] J.-S. R. Jang, ANFIS: Adaptive-network-based fuzzy inference sys-tem, IEEE Trans. Syst. Man, Cybern., vol. 23, no. 3, pp. 665685,May/Jun. 1993.

    [19] E. C. dos Santos, Jr., C. B. Jacobina, G. A. de Almeida Carlos, andI. S. de Freitas, Component minimized ACDCAC single-phase tothree-phase four-wire converters, IEEE Trans. Ind. Electron., vol. 58,no. 10, pp. 46244635, Oct. 2011.

    [20] B. K. Bose, Modern Power Electronics and AC Drives. Upper SaddleRiver, NJ: Prentice Hall, 2002.

    Mukhtiar Singh (M11) received the B.Tech. andM.Tech. degrees in electrical engineering from theNational Institute of Technology, Kurukshetra (for-merly known as Regional Engineering College,Kurukshetra), Haryana, India, in 1999 and 2001, re-spectively, and the Ph.D. degree from Ecole de tech-nologie superieure, Universite du Quebec, Montreal,QC, Canada, under the National Overseas Scholar-ship funded by the Government of India in 2010.

    He was a Faculty Member with BhagwanMahaveer Institute Engineering and Technology,

    Sonepat, and the Krishna Institute of Engineering and Technology, Ghaziabad,India, in 20002002. Since 2002, he has been an Assistant Professor with theDepartment of Electrical Engineering, Deenbandhu Chhotu Ram University ofScience and Technology, Murthal, Haryana. His research interests include therenewable energy sources, smart grid, power quality, energy storage systems,electric vehicles, and power electronics and drives.

    Ambrish Chandra (SM99) was born in India in1955. He received the B.E. degree from the Uni-versity of Roorkee [currently, Indian Institute ofTechnology (IIT)], Roorkee, India, in 1977, theM.Tech. degree from IIT, New Delhi, India, in 1980,and the Ph.D. degree from the University of Calgary,Calgary, AB, Canada, in 1987.

    He was a Lecturer and later a Reader with theUniversity of Roorkee. Since 1994, he has been aProfessor with the Department of Electrical Engi-neering, cole de technologie suprieure, Universit

    du Qubec, Montreal, QC, Canada. His main research interests are power qual-ity, active filters, static reactive power compensation, flexible ac transmissionsystems, and renewable energy resources.

    Dr. Chandra is a member of the Ordre des Ingnieurs du Qubec, Montreal.


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