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Maximum power point tracking algorithms for single-stagephotovoltaic power plants under time-varying reactive power injection

M. Carrasco , F. Mancilla-David

Department of Electrical Engineering, University of Colorado Denver, Denver, CO 80217, USA

Received 2 October 2015; received in revised form 18 February 2016; accepted 12 March 2016Available online 25 March 2016

Communicated by: Associate Editor Bibek Bandyopadhyay

Abstract

The power electronic interface of traditional grid-connected photovoltaic (PV) systems includes a boost dc/dc converter and an inver-ter. In large PV power plants, the boost converter is usually eliminated by connecting an appropriate number of PV panels in series toachieve the desired voltage. This architecture, referred to as single-stage topology, is the subject of this paper. The paper presents a unifieddynamic model which is able to reproduce the behavior of any single-stage PV power plant with an arbitrary PV array configurationthrough a single circuital representation. A methodology based on this unified model is developed to enhance the performance of stan-dard iterative maximum power point tracking (MPPT) algorithms under time-varying reactive power injection. In particular, enhancedversions of the perturb & observe and incremental conductance algorithms are discussed. Furthermore, a predictive MPPT algorithmbased on a neural network is proposed to improve the dynamic of the dc-link voltage. The unified model and MPPT control schemesare validated via detailed PSCAD/EMTDC computer simulations in a 450 kW PV system, designed according to a typical 1000 V dc

architecture. Real solar irradiance and cell temperature data collected in a partially cloudy day are utilized in the simulations, providingcomparative performance under rapidly changing atmospheric conditions. 2016 Elsevier Ltd. All rights reserved.

Keywords: Photovoltaic panels; MPPT; Single-stage PV systems; Grid-connected PV systems

1. Introduction

Photovoltaic (PV) power generation is increasinglyattracting the attention of industry and academia mainlymotivated by the urgent need to depart from fossil fuel-based electricity generation. As the cost of PV panels pro-duction continues to decrease, it is expected that bulk solarpower generation will be competitive with other forms ofrenewable energy, and hence massively deployed.

As illustrated in Fig. 1(a), traditional PV systems areconnected to the ac grid via a power electronic interface

that includes a boost dc/dc converter, a dc-link capacitor,an inverter, and a low-pass filter. The boost converter liftsthe PV array voltage level to a constant voltage across thedc-link which is then converted to ac by the inverter. In thisarchitecture, the maximum power point tracking (MPPT)control is performed by the dc/dc converter. The inverter,in turn, transfers the power collected from the PV arrayto the ac grid with independent control of reactive power.However, in large PV power plants the dc/dc convertercan be eliminated if a number of PV panels are stackedin series so that the dc-link voltage is large enough forproper operation of the inverter, resulting in a single-stagetopology. SeeFig. 1(b). A single-stage architecture is moreefficient and economical than its two-stage counterpart

http://dx.doi.org/10.1016/j.solener.2016.03.023

0038-092X/ 2016 Elsevier Ltd. All rights reserved.

Corresponding author.E-mail address:[email protected](M. Carrasco).

www.elsevier.com/locate/solener

Available online at www.sciencedirect.com

ScienceDirect

Solar Energy 132 (2016) 321331
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(Kadri et al., 2011). In this topology, the inverter performsboth the MPPT function, as well as the power transfer tothe ac grid. Research on the topological realization of theinverter includes: H-bridge multilevel inverters (Cecatiet al., 2010), flyback inverters with center-tapped secondary(Kasa et al., 2005), Z-source inverters (Huang et al., 2006),and current-source converters (Sahan et al., 2008). How-ever, the topology realized through a two-level voltage-source inverter (VSI) is widely adopted as the configurationof choice by most major PV system manufacturers(Yazdani et al., 2011; Figueres et al., 2009). Several workshave studied dynamic models for thesingle-stage VSI-basedPV system. See (Kadri et al., 2011; Figueres et al., 2009;Yazdani and Dash, 2009) and references therein. InNousiainen et al. (2013), a low-frequency model of a PVpanel is presented based on the operating-point-dependentoutput impedance of a single-diode model. This low-fre-quency model is used to study the effect of the PV nonlinearcharacteristic on the operation of dcdc and dcac convert-ers. InMesso et al. (2014), the aforementioned PV modelalong with a linearized model of the three-phase PV inver-ter cascaded with a L-filter is utilized to determine the min-imum value of the dc-link capacitance required for stableoperation. In the present work, a unified dynamic modelfor a single-stage VSI-based PV system cascaded with a

LC-filter making use of a modified PV array model isdescribed.

Due to the absence of a dc/dc converter, the MPPTfunction is realized by altering the dc-link voltage includingan additional outer loop in the inverter control scheme. Asa result, the inverter is operated at variable dc-link voltage,where the reference for the voltage is provided by theMPPT algorithm. Once the dc-link voltage reference iscomputed, the inverter is modulated through an inner loopbased on standard current control methods (Yazdani et al.,2011; Yazdani and Iravani, 2010). Variations of this con-trol structure have also appeared in the literature. In

Yazdani and Dash (2009), a feedforward compensation

mechanism is proposed for the dc-link voltage-control loopin order to make the PV system dynamics immune to thePV array nonlinear characteristic. Other approaches forcontrolling single-stage PV systems such as nonlinear con-trol strategies (Bao et al., 2013) and resonant controllers(Mastromauro et al., 2012) have also been investigated.

MPPT plays an important role in increasing the effi-ciency of PV systems and therefore some of the ongoingefforts are focused on developing and improving MPPTalgorithms. Since there are many different MPPT tech-niques, several comparative studies have been reported.While some of these studies were performed without focus-ing on a specific topology (Subudhi and Pradhan, 2013;Esram and Chapman, 2007), most make use of a dcdcconverter (de Brito et al., 2013; Chen et al., 2015). A com-parison of MPPT techniques for single-stage PV systems isreported inJain and Agarwal (2007), but it is limited to sin-gle-phase systems. InAzevedo et al. (2008), a comparisonof the most popular iterative optimization algorithms,namely perturb & observe (P&O) and incremental conduc-tance (IC), applied to single-stage three-phase PV systemswas reported. However, neither the PV array nor VSImodel are properly modeled. As Fig. 2 shows, power vs

Fig. 1. Grid-connected PV power plants. Double-stage (a) and single-stage (b) architectures.

Fig. 2. Typical PV performance curves for different values of G(G1< G2 < G3 < G4 < G5) (top), and T (T1< T2 < T3 < T4 < T5)

(bottom).

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generated by the PV array into the ac grid with the capabil-ity of reactive power injection.

3. Unified dynamic model of a single-stage PV power plant

In this section a unified dynamic model to reproduce the

behavior of a grid-connected single-stage PV power plantwith a PV array of an arbitrary size is proposed. The uni-fied model allows the representation of the overall systemthrough a single equivalent circuit, as shown in Fig. 4.

The circuital model for a single PV cell and its general-ization to a number of cells in series is well established interms of a current source, an anti-parallel diode, a seriesand a shunt resistance (Masters, 2013). However, thispaper makes use of a modified circuit introduced in Tianet al. (2012)that replaces the anti-parallel diode by a con-trolled current source. The controlled current source is gov-erned by a modified diode equation which allows thegeneralization of the model to an arbitrary number of cellsconnected in series, NS, and in parallel, NP. A single cir-cuital representation can therefore be used to reproducethe behavior of an arbitrary PV array including all detailsof each cell. The generalized model is presented in the leftside ofFig. 4and takes the form of

ipv I0irr I

00 exp

qvpvipvR0S

NSnkT

1

vpv ipvR

0S

R0P;

1

where q 1:6021019 C is the electrons electric charge,

k 1:38065031023 J/K is the Boltzmann constant, andn is the ideality factor or the ideal constant of the diode. The

various ``primevalues are related to their cell-specic counter-

parts according to

I0irr : NPIirr; I00 : NPI0; R

0S :

NS

NPRS; R

0P :

NS

NPRP;

where Iirr is the photo current or irradiance currentgenerated when the cell is exposed to sunlight; I0 is thediode saturation current or cell reverse saturation current;andRPand RSrepresent the cell shunt and series resistance,respectively (Masters, 2013). The cell-specific parametersand n depend on G; T, and certain reference parametersmeasured at standard reference condition (SRC), namely

Gref; Tref; Iirr;ref; I0;ref; RP;ref; RS;ref, and nref, as describedby(2)(6),

Iirr G

GrefIirr;ref aTTTref; 2

I0 I0;refT

Tref

3

exp Eg;ref

kTrefEg

kT ; 3

RP RP;refGref

G

; 4

RS RS;ref; 5

n nref: 6

In (2), aT is the absolute temperature coefficient of theshort-circuit current, which represents the rate of changeof the short-circuit current with respect to T. In(3), Eg isthe bandgap energy for silicon in eV. Analytical expres-sions for Eg are obtained through curve fitting from exper-imental measurements and varies from author to author.

Herein the expression fromKim et al. (2009)is used,

Eg 1:174:73104

T2

T636: 7

TheIVcurves described by(1) plus the breakdown of thevarious constituent parameters described by (2)(7) pro-vide a detailed representation for the performance of aPV array. The reference parameters at SRC are PV cell-specific and may be obtained from information availableon manufacturerss datasheets following the methodologyintroduced inTian et al. (2012). A PV power plant containsa large number of cells in series and in parallel in order to

match particular levels of voltage and power. For instance,if 0.5 V/2 W PV cells are used as a building block to realizea 450 kW power plant,NS and NP would be in the order of1300 and 180, respectively. The key advantage of thismodel is that an arbitrary number of cells connected inseries and/or paralleland therefore a PV array with anarbitrary configurationcan be modeled through a singlecircuital representation including the details of each cell.

The cascaded connection of the dc capacitor, VSI,LC-filter and ac grid is modeled in the dqreference frameusing dynamic phasors. The right side ofFig. 4illustratesthe dynamic equivalent circuit in terms of controlledsources (Yang et al., 2003; Yazdani and Iravani, 2010).

Fig. 4. Unified dynamic equivalent circuit schematic of a grid-connected single-stage PV power plant.


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The equations which describe the states evolution aregiven by(8)(11),

d

dtvpv

1

C ipv

3

4~m~i

; 8

d

dt

~i jx~i1

L

~mvpv

2

RRf ~iRf~ig~vf ; 9d

dt~vf jx~vf

1

Cf~i~ig

; 10

d

dt~ig jx~ig

1

Lg~vf Rg Rf

~igRf~i~vg

: 11

In(8)(11), the vector quantities relate to their abccounter-parts considering a generic vector quantity ~x xd jxq,

with

xd xq T

Tdqabc xa xb xc T;

where Tdqabc is the Park transformation,

Tdqabc

2

3

cosh cos h 2p3

cos h 4p

3

sinh sin h 2p

3

sin h 4p

3

!

:

In(8), the operator denotes the dot product betweentwo vectors, yielding a dc value. In (8) and (9), ~m is theVSIs modulating function. Furthermore, x and h are thesynchronizing frequency and phase angle, respectively.The synchronizing quantities are measured at the LC-fil-ters output and are synthesized through a phase-locked-loop (PLL) which is explained in Section 4. In (11), LgandRgrepresent the grid inductance and resistance, respec-tively, as seen from the LC-filters output. These values cor-respond to lumping the coupling transformers impedanceand the (uncertain) Thevenin impedance of the ac grid seenfrom the point of common coupling (PCC). Finally, in(11)~vgis the Thevenin voltage of the ac grid. Refer toFig. 3forthe interpretation of the remaining parameters.

The state space model readily follows from (8)plus thesix equations which result from separating(9), (9)(11)intoreal and imaginary parts, yielding a seven-order state spacemodel. Moreover, the nonlinear relationship between vpvandipv established by(1) plus(2)(7)leads to a differentialalgebraic equations (DAEs) formulation. Thus, (1)(11)provide a unified dynamic model of a grid-connected sin-

gle-stage PV power plant. The DAE formulation can beutilized to develop more rigorous feedback control algo-rithms. Furthermore, the equivalent single circuit showninFig. 4may be utilized to study PV power plants in ac sys-tems by incorporating the circuit into power flow, optimalpower flow and dynamic simulation programs. In this work

the presented unified model is used to develop a methodol-ogy to enhance iterative MPPT algorithms for single-stagearchitectures.

4. Control scheme

The VSIs control scheme utilized herein corresponds toa conventional current control (Yazdani and Iravani, 2010)plus a variety of three proposed MPPT algorithms specifi-cally tailored to perform in concert with a single-stagearchitecture. The overall scheme is presented in Fig. 5.As observed in the figure, the control is broken down into

four blocks: (i) a PLL utilized for synchronization with theac grid; (ii) a dc voltage control to track the PV arraysMPP; (iii) a power-to-current transformation; and (iv) aconventional current control.

4.1. Synchronization and control of power & current

The current control is synchronized with the ac grid bymeans of a simple PI-based PLL. The grid voltage is mea-sured, transformed into the dq reference frame, and its qcomponent is forced to zero through a PI controller. ThePLL block also provides a measure ofvdand the grid phaseangle. Further information about the PLL design andgains tuning is readily available in the literature (Chung,2000).

The grid current is controlled according to active andreactive power references. The active power reference isgenerated by the dc-link voltage control, whereas the reac-tive power reference may be supplied directly. In steady-state, the power-to-current transformation reduces toPref 3=2vdId ref and Qref 3=2vdIq ref. Accordingto the computed current references, a conventional currentcontrol loop generates a modulating signal through two de-coupled compensators (Yazdani and Iravani, 2010).Finally, the modulating signal in the abc domain is com-

Fig. 5. Block diagram for the VSI control.

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pared against a triangular carrier signal at FSusing double-edge pulse width modulation (PWM) in order to generatethe IGBTs pulses.

4.2. Control of dc-link voltage

A main feature of the single-stage architecture describedin this paper is the operation at a variable dc-link voltage.

This may be explainedand justifiedconsideringFig. 6.The figure illustrates that within most values of G and Tthe MPP voltage remains within a relatively narrow range.Only when G falls considerably (below 200 W/m2), theMPP voltage becomes too low and thus unacceptable forthe operation of the inverter. The inverter can only buckthe voltage, hence there is a minimum voltage atwhich the inverter can operate when connected to the acgrid. In practice, inverters manufacturers design the con-trol system specifying a range vpv 6 vpv 6 vpv for whichthe VSI will perform MPPT.

The dc-link voltage has to follow the PV arrays MPP,

which is controlled by the MPPT algorithm through chang-ing the dc-link voltage reference. As Fig. 5 suggests, oncethe dc-link voltage reference,V pv ref, is computed, the valueis processed through a voltage limiter and fed to a PI con-troller yielding a power command. Alternatively, the dc-link voltage control may be performed by regulating theenergy flow in and out of the capacitor controlling thesquare of voltages. Energy-based controllers are reportedto feature faster dynamics than those of their voltage-basedcounterparts (Yazdani and Iravani, 2010). However, bothcontrollers are fast enough within the MPPT timescale,and hence the voltage-based approach is selected here forthe sake of simplicity.

5. MPPT under time-varying reactive power

The aim of a MPPT algorithm is to keep the PV arrayoperating at the MPP as the atmospheric conditionschange with time. AsFig. 2suggests, the atmospheric con-ditions which have an effect on the MPP are Gand T. TheMPP (vmpp; impp) can be found numerically ifGand Taremeasured (Zhao et al., 2015). It follows from solving (1)plus(2)(7), and (12)which holds at the MPP:

dppv

dvpv

0; 12

where ppv vpvipv is the PV arrays output power. As

observed inFig. 2, if the PV array is not under partial shad-ing (Daz-Dorado et al., 2014; Liu et al., 2014; Boukenouiet al., 2016), the concave shape of the PV curve guaran-tees a unique voltage (for a given Gand T) at which theoutput power is maximum. However, Gand Tare usually

unavailable for measurement, and MPPT algorithms thusrely on iterative optimization and/or predictionapproaches.

This paper proposes a methodology to enhance iterativeoptimization algorithms for single-stage architectures.These algorithms solve an optimization problem iterativelyin real time. They are able to detect a change in the MPPdue to a variation inGor Twithout actually sensing them.The operation of these heuristics relies solely on the con-cave shape of the PVcurve, which is common to all PVcells. Therefore, they are able to track the MPP withoutbeing trained for a specific PV cell.

On the other hand, the prediction approach proposedherein makes use of a NN architecture whose parametersdepend on the PVcurves of a PV array. The NN has tobe trained for a specific PV array in order to accomplishthe MPPT function. In this case the optimization processtakes place offline in the training of the NN. The NN-basedalgorithm needs T to be either measured through a dedi-cated sensor or estimated by means of other measurements.

5.1. Iterative optimization algorithms: P&O and IC

Tracking heuristics can be described as iterative opti-mization algorithms that, starting from an initial feasible

solution, progressively improve the solution by applyinga series of local modifications. At each iteration, the searchmoves to an improved solution that differs only slightlyfrom the current one. Following the methodologyproposed in this section, P&O- and IC-based heuristicsare modified to improve their MPPT capabilities whenoperating in concert with single-stage architectures. Bothalgorithms stem from a straightforward manipulation of(12), leading to the following equivalent incrementalexpressions,

vpv~ipv

~vpvipv; 13

~ipv

~vpvipv

vpv; 14

which are equal to zero at the MPP. Throughout the rest ofthe paper, all incremental variables are defined as~x xxk, where k denotes the current sampling period,x is a generic time-varying variable evaluated at the endof the k sampling period, and xk is the value of x at thebeginning of theksampling period. The P&O and IC algo-rithms are based on the evaluation of the quantities definedby(13) and (14), respectively. When the operating point onthePVplane is placed to the right (left) of the MPP, these

quantities are negative (positive). Therefore, based on the

Fig. 6. Operation at variable dc voltage.


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sign of these quantities, the iterative algorithms can pro-vide a new voltage reference as a corrective action toapproach the MPP. In the case of the P&O algorithm,(13)corresponds to~ppv=~vpv, i.e. the ratio between the incre-ment in PV arrays power and voltage. For the IC algo-rithm, the sign of (14) is evaluated by comparing the

incremental conductance with the instantaneousconductance.The error introduced by using the incremental quantities

defined in (13) and (14) depends on the voltage step sizeand the operating point. The closer to the MPP, the morenonlinear the PV curve is, and therefore the worse thisapproximation is. In order to decrease the error introducedby this approximation, a variable step approach is consid-ered in which the voltage step size decreases as the operat-ing point approaches the MPP. Furthermore, thisapproach reduces the oscillations around the MPP, whichin turn increases efficiency. Finally, it allows a quickerresponse when the operating point is far from the MPP

(Lee et al., 2006).Under abrupt changes in G these algorithms perform

slowly and may even fail, which translates into a reduced

efficiency (Masters, 2013). Changes in ~ipv can be tracked

to ~G; ~T, and ~vpv. These algorithms become confused if ~G

or ~T are significant enough to change the sign of the quan-tities defined in (13) and (14). This represents the maindrawback of the standard P&O and IC algorithms andresults in a reduced extracted power under rapidly chang-ing atmospheric conditions. InKadri et al. (2011), a mod-ified version of the standard P&O algorithm was proposedto overcome this issue. The algorithm was improved by

taking advantage of the characteristics of a single-stagearchitecture. Specifically, by using the signal error of thedc voltage control loop to compute the change in powerdue to changing atmospheric conditions. Following thisidea, a generalization of this approach is proposed in thispaper. A small-signal model based on the linearization ofthe unified dynamic model for the single-stage PV systempresented in Section 3 is used to find an expression forthe error of the dc voltage control loop. This approachallows the development of a methodology to (i) improveboth P&O and IC; and (ii) consider a variable reactivepower injection, which would enable voltage regulation.

If the sampling period is sufficiently short, the followingassumptions can be made: (A1) the dynamics of the dc-linkvoltage can be approximated through the linearization ofEqs. (8), (1), plus (2)(7), around the operating point atthe beginning of the sampling period, defined asipv k; vpv k;Gk; Tk;md k;mq k; vd k; (A2) T remains con-

stant; (A3) Gvaries linearly at a constant rate of change,aG; (A4) Qref varies linearly at a constant rate of change,aQ; and (A5) vd remains constant. As a consequence of

(A1) and (A2),~ipv can be computed according to

~ipv ~ipvG~ipvV KG

~GKV~vpv; 15

where~ipvG and~ipvV are the changes in PV arrays current

due to ~G and ~vpv, respectively; KG @ipv@G

k; KV

@ipv@V

k

;

and ipv is defined by(1), plus(2)(7).Fig. 7shows the block diagram representing the small-

signal dynamics of the dc-link voltage including the voltage

and the current control loops. The incremental error can beexpressed as

~es ~V pv refs ~vpvs

As~V pv refs Bs~Gs Cs~Qrefs Ds~mds

Es~mqs;

where ~V pv refs ~V pv ref=s, since the voltage referenceremains constant during the sampling period. As a conse-

quence of (A3) and (A4), ~Gs aG=s2, and

~Qrefs aQ=s2, respectively. On the other hand, the cur-

rent loop is designed to be faster than the voltage loop.

Therefore, the current loop transfer functions can be con-sidered as Fid s Fiq s 1, and ~mds;~mqs can be

approximated to steps, ~mds ~md=s; ~mqs ~mq=s. Thetransfer functionsAsto Escan be readily obtained fromFig. 7. The steady state error at the end of one samplingperiod, ~ef, can be expressed using the final value theoremfor Laplace transforms:

~eflims!0

s~es aipvmd k2vd k

Kimq kaQ

md kKi; 16

where Ki is the gain used for the integral action of thevoltage control loop; and aipv is the rate of change of the

Fig. 7. Block diagram representing the small-signal dynamics of the dc-link voltage during a sampling period. Note: the block diagram is based on

assumptions (A1), (A2) and (A5).

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PV arrays current caused only by the irradiation variation,expressed as aipv KGaG. As it can be seen, only the pertur-

bations ~Gs, and ~Qrefs contribute to steady state error.The zero-input component of ~es is zero when thesteady-state is reached. Therefore, ~efV pv ref vpv, whereV pv refandvpvare evaluated at the end of the sampling per-

iod. Because ~efcan be measured,(16)can be solved for a ipv ,and~ipvG can be computed as

~ipvG a ipv~tmd kKi~ef mq kaQ

2vd k~t;

where ~tis the sampling period. According to(15), once ~ipvGis determined, quantities (13) and (14) can be evaluated

considering only~ipvV ,

vpv~ipv ~ipvG

~vpvipv; 17

~ipv

~ipvG

~vpv ipvvpv

; 18

and the algorithms can determine the right direction of thenext corrective action.Fig. 8shows a generalized flowchartof the P&O and IC iterative algorithms.

5.2. Prediction algorithm: neural network

A different approach is to consider the MPPT as a pre-diction problem. The prediction problem consists inapproximating the unknown real mapping between theinputsT; vpv and ipv, and the outputvmpp, which is consid-

ered to be V pv ref inFig. 5. In this section a NN-based pre-diction algorithm is proposed. In this approach, the MPPTand the reactive power control are two decoupled prob-lems, and therefore a time-varying reactive power injectiondoes not compromise the efficiency of the MPPT function.NNs may be classified as traditional NNs and locally recur-rent NNs (LRNNs). Traditional NNs have no memory ofthe past inputs: the output is strictly a function of theinstantaneous input to the network (Dounis et al., 2015).In contrast, in a LRNN the output may also be a function

of delayed inputs and delayed outputs. This allows for thecreation of richer and more complex decision surfaces.LRNNs have been successfully applied, for example, tothe electrical load forecasting problem (Khotanzad et al.,1997). In the MPP tracking problem, the voltage at theMPP is only a function of the instantaneous inputs, and

therefore a traditional multi-layer feed-forward networkis well suited. The optimization problem appears in thedesign of the NN which relies on choosing the number oflayers, the number of neurons in the hidden layers, andthe appropriate interconnections. The objective functionto be minimized is the error on a test data set, reached aftera number of iterations or training epochs. In the generalcase, all these parameterssome of which are discrete innatureshould be considered in the optimization problem,leading to a mixed integer programming problem. Meta-heuristics such as simulated annealing, genetic algorithmsand tabu search have been proposed to solve thisoptimization problem (Glover and Marti, 2006). In the

case of a traditional multi-layer feed-forward network,the optimization problem can be simplified. Architectureswith a single hidden layer have been proved to be wellsuited for the MPP tracking problem (Liu et al., 2013).Furthermore, the number of neurons can be determinedby a trial and error process. Therefore, the only variablesleft to be determined are all of continuous nature, andthe process through which are determined is called thetraining process.

In this paper, a NN-based algorithm is proposed with atwo-fold objective: (i) to provide a continuous step-freevoltage reference to feed the inverters voltage control loop

therefore improving the dynamic across the dc capacitor,and (ii) to track the MPP under changing Gand T whileoperating at a variable dc-link voltage. As illustrated inFig. 9, the considered NN features a three-layer structure:3 input neurons; 8 neurons for the hidden layer; and 1 out-put neuron. The methodology makes use of the modifiedPV array model described by (1) and (2)(7), for findinga suitable matrix of synaptic weights. The backpropagation(BP) method is an effective algorithm based on the steepestdescent direction and it is the most widely used optimiza-tion method for accomplishing the training of the NN(Glover and Marti, 2006). The NN has to be trained topredict vmpp for each characteristic curve of the PV arrayat particular G and T. In this work, the training processwas executed using the LevenbergMarquardt BP

Fig. 8. Generalized iterative MPPT algorithm flowchart. k is defined bythe quantities (17) and (18) for the enhanced P&O and IC iterativealgorithms, respectively. The variable voltage step size is accomplished by

multiplying the quantityk by a proportionality constant K. Fig. 9. Structure of the considered NN.


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algorithm (Glover and Marti, 2006), and the goal for meansquare error (MSE) on the training set was fixed equal to

107.Fig. 10shows the MSE during the NN training. After33 epochs the training process is stopped.

6. Simulation results

In order to validate the control scheme proposed in Sec-tion 4 and evaluate the performance of the three MPPTalgorithms explained in Section5, a detailed computer sim-ulation in PSCAD/EMTDC of a single-stage 450 kW grid-connected PV system was implemented. The system isdesigned according to a typical 1000 V dc architecture.The unified dynamic model of Section3along with the con-trol scheme of Section4 were simulated considering real Gand Tdata collected on PV panels in the city of Denver,Colorado, USA. The collected data is presented in thetop and middle plots ofFig. 11. Measurements were col-

lected every 800 ms over 40 s on a partially cloudy day,which helps evaluate the performance of the MPPT controlschemes under shading conditions. The PV array is realizedusing 40 panels in series and 150 in parallel. The simulatedpanel corresponds to the model KC85TS manufactured byKyocera, with datasheet MPP at 17.4 V/87 W at SRC. Thepanel was characterized and tested in the laboratory usingthe procedure fromTian et al. (2012)and the actual MPPat STC was found to be 16.67 V/75.93 W. The panel fea-tures two parallel strings of 36 cells in series. Therefore,in the simulation the total number of cells in series, NS, is

1440 and the total number of cells in parallel, NP, is 300.The utility grid is rated at 12.47 kV/60 Hz, with a short cir-cuit power of 100 MVA and a unity R/X ratio. The cou-pling transformer is rated at 600 kVA with atransformation ratio of 270 V/12.47 kV and an impedanceof 6%. The filter inductor, capacitor and damping resis-

tance were selected to be L 38:675lH, Cf363:87lFand Rf64:2 mX respectively. The VSIs switching fre-quency is FS 6 kHz, and the dc-link capacitor wasselected 5000lF. Finally, the fixed sampling period forthe iterative MPPT algorithms was set to 0.2 s. In the sim-ulation, a time-varying reactive power injection was consid-ered, following a ramp starting with unity power factor andreaching 100 kVAr after 40 s, as shown in the bottom plotofFig. 11. According toFigs. 3 and 5, the reactive powerreference for the two-layer control can be computed asQrefQinjQc, where Qinj is the desired reactive power

injection before the coupling transformer, and Qc is thereactive power injected by the filter capacitors. The latter

can be calculated as Qc 1:5v2dxCf, assuming that the

PLL forces vq 0.The overall performance of the MPPT algorithms is

illustrated inFig. 12. The voltage plots show: (i) the voltagereference dictated by the algorithms; (ii) actual dc-link volt-age; and (iii) the trajectory of the theoretical voltage toextract the maximum power. The difference between thetheoretical MPP voltage and the actual dc-link voltage isclearly lower in the case of the enhanced algorithms, whilethe NN-based algorithm outperforms the iterative algo-rithms. It is noteworthy that the NN performs the MPPTfunction using only one measurement and in one computa-

tion step. The response time is determined solely by the fre-quency at which vpv; ipv and T are sensed, and hence inpractice the NN will track the MPP in a continuous man-ner. This is in contrast to the P&O and IC algorithms,which require a number of measurements and computa-tional steps to iteratively approach the voltage at theMPP, never settling on the MPP voltage. Each measure-ment-computational step pair generates a dc voltage whichtranslates into a step-like reference that is applied to thevoltage control loop. The VSI dynamic response to changeson the voltage reference dictated by the MPPT algorithmsis illustrated in the zoomed areas of the voltage trajectories.

From the figure it can be seen that the NN algorithm pro-vides a smooth reference to the dc-link voltage control loopand the actual dc-link voltage is able to follow the referencewith an improved dynamic response. In the case of theP&O and IC algorithms, the dc-link voltage is forced to fol-low a step-like reference. Fig. 12 also shows the actualpower being extracted from the array along with the theo-retical maximum power available in the PV array. The dif-ference between the theoretical and the actual power islower in the case of the enhanced iterative algorithms,showing the NN algorithm the best performance. This isreflected in the corresponding tracking factors (TF),defined as the ratio between the actual amount of energy

Fig. 10. MSE during the NN training.

Fig. 11. ActualGand Tprofiles, and reactive power reference used during

the simulation.

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extracted from the PV panel, and the theoretically availablepower. SeeFig. 12.

7. Conclusions

A unified dynamic model for single-stage PV power

plants including a modified PV array model was presented.The unified model is able to reproduce the behavior of anysingle-stage PV power plant with an arbitrary PV arrayconfiguration through a single circuital representation. Amethodology based on this unified model was developedto enhance iterative MPPT algorithms for single-stagearchitectures. The methodology increases the MPPT effi-ciency under rapidly changing atmospheric conditionswhile considering time-varying reactive power injections.This, in turn, would enable voltage regulation withoutcompromising the MPPT performance. Following thismethodology, improved P&O- and IC-based heuristicswere presented. Furthermore, a NN-based predictionMPPT algorithm was proposed to improve the dynamicof the dc-link voltage. Finally, a performance evaluationof the three MPPT strategies was carried out based ondetailed computer simulations. Although the NN-basedalgorithm outperforms the iterative algorithms in trackingthe theoretical voltage at the MPP, all of them feature avery similar performance in terms of extracted power. Itcan be therefore concluded that, if properly designed andparameterized, any of the three aforementioned algorithmscan be utilized for the MPPT operation of single-stagethree-phase PV systems under time-varying reactive powerinjection. The authors are currently working on augment-

ing the proposed control strategies for operation under

abnormal grid operating conditionssuch as sustainedvoltage unbalance or flickerwhich may reveal further dif-ferences among the proposed MPPT strategies. Results willbe reported as they become available.

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Fig. 12. Simulation results showing the performance of the enhanced P&O, standard P&O, enhanced IC, standard IC, and the NN-based predictivealgorithm (from left to right). The interpretation of the legend is as follows. Vpv ref: voltage reference dictated by the algorithm; vpv: actual dc-link voltage;vmpp: theoretical voltage at the MPP; Pdc: actual extracted power; Pmpp: theoretical power at the MPP. Diffis the normalized difference between thetheoretical voltage (power) at the MPP and the actual dc-link voltage (extracted power). The TF values for the enhanced and standard P&O are 99.74%and 99.29%, respectively. The TF values for the enhanced and standard IC are 99.77% and 99.31%, respectively. Finally, the NN-based predictivealgorithm features a TF value of 99.99%.

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