22.a Single Stage Three Phase PV System With Enhanced MPPT

IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 26, NO. 2, APRIL 2011 1017

A Single-Stage Three-Phase Photovoltaic SystemWith Enhanced Maximum Power Point Tracking

Capability and Increased Power RatingHamidreza Ghoddami, Student Member, IEEE, and Amirnaser Yazdani, Senior Member, IEEE

Abstract—This paper proposes a single-stage three-phase photo-voltaic (PV) system that features enhanced maximum power pointtracking capability, and an improved energy yield under partialshading conditions. Further, the proposed PV system can effec-tively double the maximum permissible dc voltage of a groundedconventional single-stage PV system, with no need for insulators,fuses, disconnects, and switchgear of a higher voltage class, withrespect to safety/insulation standards or common system integra-tion practices exercised for conventional grounded single-stage PVsystems. The proposed PV system is realized through the parallelconnection of an auxiliary half-bridge converter to the dc link of aconventional single-stage PV system and, therefore, is also an op-tion for retrofit applications. This paper presents the mathematicalmodel, principles of operation, and the control loops of the pro-posed single-stage PV system. The performance of the proposedsingle-stage PV system is demonstrated by time-domain simula-tion studies conducted on a detailed switched model in the PSCAD/EMTDC software environment.

Index Terms—Control, maximum power point tracking(MPPT), model, partial shading, photovoltaic (PV) systems, powerelectronics, photovoltaic (PV) array, PV cell, voltage-sourcedconverter (VSC).

I. INTRODUCTION

I N RECENT years, renewable energy systems have attractedremarkable attention and investment due to concerns about

environmental issues, ever-increasing world energy demand,and the outlook of fossil fuel reserves’ depletion. Amongrenewable energy systems, photovoltaic (PV) systems areexpected to play an important role in the future and, as such,a great deal of research effort is dedicated to enhancing theirperformance and efficiency at the component and system levels.As two influential factors in regards to the performance and effi-ciency of a PV system, the impact of characteristic mismatchesamongst PV cells and the phenomenon of maximum-powerdrop due to partial shading have been the subject of intenseresearch.

In a PV system, PV modules are connected in series and inparallel in order to enable power generation and processing atan adequately large voltage level and efficiency. However, when

Manuscript received April 26, 2010; revised June 17, 2010; accepted June 22,2010. Date of publication August 19, 2010; date of current version March 25,2011. This work was supported by the Ontario Centres of Excellence (OCE)-Centre for Energy. Paper no. TPWRD-00300-2010.

The authors are with the University of Western Ontario, London, ON, N6A5B9, Canada (e-mail: [email protected]; [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/TPWRD.2010.2055896

PV cells in a module are shaded, they experience a significantpower output drop and can even act as loads to other (unshaded)cells and modules. This phenomenon can result in hot-spot for-mation in, and potential damage of, the shaded cell(s), in addi-tion to a disproportionate maximum-power drop in the overallarray. To circumvent the aforementioned issue, manufacturerstypically install bypass diodes in antiparallel with each groupof 12–18 cells in a module [1]. Nonetheless, the reduced en-ergy yield remains an issue to be further addressed through moreeffective PV module clustering configurations and maximumpower point tracking (MPPT) algorithms.

Thus far, several power-electronic converter configurations[2], [3] and PV module clustering methods [4]–[7] have beenproposed for mitigation of the maximum-power drop due to par-tial shading. Despite the existence of classes of high-power PVsystems that employ a multitude of small converters, that is, oneconverter per subarray [2], [3], the use of one central high-powersingle-stage electronic converter for the entire PV system is verycommon for economical reasons and the relative simplicity ofthe overall system. For this class of PV systems, the way thatPV modules are clustered plays an important role in the perfor-mance of the PV system under partial shading conditions.

References [4] and [6] compare three common PV array con-figurations (i.e., the series-parallel (SP) configuration, the totalcross-tied (TCT) configuration, and the bridge-linked (BL) con-figuration). Reference [4] has studied the characteristic mis-match phenomenon due to the PV cell aging and shading, andhas concluded that the TCT and BL configurations are superiorto the SP configuration. Reference [6] has adopted a more ac-curate model of a PV module that takes into consideration thedependence of the parameters on the operating condition. Themodel in [6] includes bypass diodes which are assumed to beconnected in antiparallel with every 18 PV cell; the model istested through the exposure of modules and submodules to 30different random profiles of insolation, and indicates the supe-riority of the TCT configuration in the sense that it provideshigher maximum power and exhibits lower variations in themaximum power point (MPP) voltage, compared to the BL andSP configurations. Reference [6] further implies that as far asthe characteristic mismatch issue is concerned, a lower numberof series-connected modules is in favor of a lower array max-imum-power drop. This practice, however, is in conflict withthat of the series connection of many modules for higher voltageand, thus, efficiency.

This paper proposes a single-stage three-phase PV systemthat features an enhanced MPPT capability, and an improved

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1018 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 26, NO. 2, APRIL 2011

energy yield under partial shading conditions. Further, the pro-posed PV system can accommodate a dc voltage as large astwice the maximum permissible dc voltage of a conventionalgrounded single-stage PV system, with no need for insulators,fuses, disconnects, and switchgear of a higher voltage class.Thus, based on the proposed PV system, the power rating of asingle-unit, conventional, grounded, single-stage PV system canbe doubled, without compromising the prevalent standards forsafety/insulation or the common system integration practices;presently, this is commonly achieved by the parallel connec-tion of two independent smaller conventional PV systems. Al-ternatively, for a given power rating, the proposed PV system isexpected to offer comparatively higher efficiency due to its in-creased voltage level and enhanced MPPT capability. The pro-posed PV system is realized through the parallel connection ofan auxiliary half-bridge converter to the dc link of a conven-tional single-stage PV system and, therefore, can also be an op-tion for retrofit applications.

II. SHADING AND THE PROPOSED TWO-MPPT STRATEGY

Fig. 1(a) illustrates a schematic diagram of a sampleSP-configured PV array, which consists of a number of par-allel-connected strings of series-connected PV modules. In aconventional single-stage PV system, the array is interfacedwith the grid, through an electronic power converter [not shownin Fig. 1(a)], from terminals A and B. Thus, the converterenables MPPT by controlling the (dc) array voltage .The SP configuration of Fig. 1(a), although effective under anormal condition, exhibits a remarkable maximum-power dropif the array is exposed to an uneven solar irradiation, due, forexample, to partial shading. To mitigate the effect of partialshading and the consequent maximum-power drop, the config-uration of Fig. 1(a) can be modified to that of Fig. 1(b), knownin the literature as the TCT configuration [4], [6], in whichthe strings are also cross connected; again, in a conventionalsingle-stage PV system, the entire TCT array is interfaced withand undergoes MPPT with one power-electronic converter,from terminals A and B.

This section demonstrates that the maximum-power drop ofthe configuration of Fig. 1(b) can be further mitigated if thearray is divided into two subarrays through the introduction ofa center terminal, that is, terminal G [Fig. 1(b)], so that eachsubarray independently undergoes MPPT through the controlof the voltages and . Once this fact is established, inSection III, a power-electronic converter system is introducedthat enables the proposed two-MPPT strategy.

A. Maximum-Power Drop Ratio

To characterize the performance of a PV array configurationunder partial shading, a number of criteria have been introducedin the technical literature. These include the maximum poweroutput of the shaded array [6], [8], the ratio of the maximumpower output of the shaded array to the maximum power outputunder a normal condition [2], and the ratio of the drop in themaximum power output of the shaded array to the maximumpower output under a normal condition [4]. The aforementionedcriteria, however, depend on the shaded area and number of

Fig. 1. Schematic diagrams of a 64-module PV array based on (a) SP configura-tion and (b) TCT configuration. The dashed line in each configuration indicatesthe connection path for the proposed two-MPPT scheme.

shaded modules and, therefore, may not fully characterize thesusceptibility of the configuration under study to partial shading.Thus, an alternative criterion, referred hereafter to as the “max-imum-power drop ratio (MPDR),” is defined in this paper, as

Maximum-power drop of the arrayMaximum-power drop of the base system

(1)

In (1), the base system is defined as a hypotheticaln-module/n-converter PV system in which each module isindependently controlled by one corresponding converter.To appreciate the usefulness of the MPDR, let us considerthe case in which one module of the base system is shadedand, consequently, exhibits a maximum-power drop. In viewof the independence of the modules in the base system, themaximum-power drop experienced by the overall array is thesame as that experienced by the shaded module, and the MPDRis unity; intuitively, one finds the base system to be the mostsuperior system in terms of the performance under partialshading, but, most likely, not economical or desirable fromthe system integration viewpoint. Alternatively, let us considera general configuration in which the number of converters islower than the number of modules, and that the shaded moduleis connected in series and/or in parallel with a number ofother modules. In this configuration, the shaded module alsoaffects the operating points of the other (unshaded) modulesand, as such, will cause a maximum-power drop in them.Consequently, the array maximum-power drop in the generalsystem is expected to be larger than that experienced by thebase system, and the MPDR is therefor larger than unity. Theforgoing example indicates that the MPDR provides a measureof closeness of a PV system to the base system, in terms of thesusceptibility to characteristic mismatch and partial shading.The MPDR can also be interpreted in the way that a shadedmodule results in an array maximum-power drop that is, ingeneral, several times larger than that of the shaded module onits own.

GHODDAMI AND YAZDANI: SINGLE-STAGE THREE-PHASE PHOTOVOLTAIC SYSTEM 1019

B. Shading Scenarios

For the study reported in this subsection, 1, 2, or 4 PV mod-ules of the arrays of Fig. 1(a) or (b) are assumed to be shaded.Thus, a model of an 8 8 array of 64 PV modules, configuredin the ways shown in Fig. 1(a) and (b), is constructed in thePSCAD/EMTDC software environment [9], and a number ofshading scenarios are judiciously selected, simulated, and com-pared in terms of their maximum-power drops. As detailed inAppendix A, each module is a lumped representation of

54 series-connected identical basic PV cells and assumed to in-clude one antiparallel (bypass) diode for every 18 (series-con-nected) cells. Further, it is assumed that each shaded modulereceives a solar irradiation of 0.2 kW/m , one-fifth of the solarirradiation received by an unshaded module, that is, 1.0 kW/m .

For the one-MPPT scheme, the maximum power of the arrayis measured from terminals A and B, while terminal G is leftuntapped [see Figs. 1(a) and (b)]; for the two-MPPT scheme,however, the maximum powers of both subarrays are measured,from the terminals A-G and G-B, and summed up. The max-imum power, whether it is an array or a subarray, is found bysweeping the corresponding terminal voltage from a small valueto a relatively large value.

For the TCT configuration, the following shading scenariosare simulated.

• Scenario #1: Only one module is shaded.• Scenario #2: Two modules in different subarrays are

shaded.• Scenario #3: Two modules of a subarray, but in two dif-

ferent rows, are shaded.• Scenario #4: Two modules of a row are shaded.• Scenario #5: A 2 2 block of four modules, all in one

subarray, is shaded.• Scenario #6: A 2 2 block of four modules is shaded.

However, unlike Scenario #5, two modules are located inone subarray, whereas the other two lie in the other sub-array.

For the SP configuration, the shading scenarios are as follows.• Scenario #7: Only one module is shaded.• Scenario #8: Two modules of different subarrays and

strings are shaded.• Scenario #9: Two modules of a subarray, but in different

strings, are shaded.• Scenario #10: A 2 2 block of four modules, all in one

subarray, is shaded.• Scenario #11: A 2 2 block of four modules is shaded.

However, unlike Scenario #10, two modules are locatedin one subarray, whereas the other two lie in the othersubarray.

It should be noted that Scenarios #5, #6, #10, and #11 enablestudying the impact of a more widespread shadow that simulta-neously covers four modules in a 2 2 block. These scenariostake into account the combined effect of both series- and par-allel-connected shaded modules.

Table I provides a summary of the study results, reporting themaximum power of the arrays, under the one- and two-MPPTschemes, for each aforementioned scenario. For each scenarioand scheme, Table I also reports the corresponding MPDR, with

TABLE IMP AND MPDR FOR DIFFERENT SCENARIOS AND MPPT SCHEMES

Fig. 2. MPDRs under the one- and two-MPPT schemes for the TCTconfiguration.

reference to a 64-module base system, while Figs. 2 and 3 pro-vide a graphical illustration of the study results.

Fig. 2 indicates that, for the TCT configuration, the MPDRunder the two-MPPT scheme is always smaller than, or at mostequal to, the MPDR under the one-MPPT scheme. For example,in Scenario #1, where only one module is shaded, the operatingpoint of the entire array is affected in the one-MPPT scheme;however, when the two-MPPT scheme is employed, the oper-ating point of only half of the array is affected by the shadedmodule, whereas the other subarray produces its normal max-imum power. In Scenario #2 where two modules in differentsubarrays are shaded, the one- and two-MPPT schemes per-form identically. In Scenarios #3 and #4 where the two shadedmodules are located in the same subarray, again, the two-MPPTscheme is superior since only the operating point of one sub-array is affected by the shaded modules. The reason for thelarger maximum-power drop in Scenario #4 compared to Sce-nario #3 is explained by the fact that an increased number ofshaded modules in a row results in a fairly large deviation of


Fig. 3. MPDRs for the SP and TCT configurations, under the two-MPPTscheme.

Fig. 4. Schematic diagram of the conventional single-stage three-phase PVsystem.

the operating point of the row. In Scenarios #5 and #6, to studya more realistic shading condition, a 2 2 block of 4 shadedmodules is moved around within the array, to include parallel-and series-connected modules. In Scenario #5 where all of theshaded modules are located in one subarray, the two-MPPTscheme is more effective, whereas in Scenario #6 in which theshaded block is equally shared by both subarrays, the MPDRsof the one- and two-MPPT schemes are equal.

For the (conventional) one-MPPT scheme, the superiority ofthe TCT configuration over the SP configuration has alreadybeen reported in the literature [4] and [6], and observed by thisstudy (not discussed). Fig. 3 indicates that the advantage is pre-served under the proposed two-MPPT scheme; as Fig. 3 shows,for geographically-identical shading scenarios, the MPDR ofeach shading scenario in the TCT configuration is lower thanits counterpart in the SP configuration.

III. PROPOSED TWO-MPPT SINGLE-STAGE PV SYSTEM

A. Structure and Principles of Operation

Fig. 4 illustrates a simplified schematic diagram of a con-ventional single-stage PV system [10]. The kernel of the PVsystem is a current-controlled voltage-sourced converter (VSC)that interfaces a PV array with the utility grid. The PV array isconnected to the VSC dc side through a series reverse-blockingdiode, while the VSC ac side is connected to the grid, at the pointof common coupling (PCC) through a three-phase LC filter anda coupling transformer. The reverse-blocking diode preventscurrent flow from the VSC to the PV array if the solar irradi-

ation is low. The LC filter prevents the switching voltage andcurrent harmonics generated by the VSC from penetrating intothe grid. The VSC employs the pulsewidth modulation (PWM)switching strategy, and controls the real and reactive power de-livered to the grid. This, in turn, makes the regulation of thePV array (dc) voltage possible and enables MPPT. The dc-linkcapacitor provides a low impedance path for the high-fre-quency components of the VSC dc-side current and, therefore,eliminates the dc-link voltage ripple. As detailed in [10], thecontrol is exercised in a -frame that is synchronized to the gridvoltage vector, for example, through a phase-locked loop (PLL).The two-MPPT single-stage PV system proposed in this paperis realized through modifications made on the conventional PVsystem of Fig. 4 as will be explained.

Fig. 5 illustrates a schematic diagram of the proposed two-MPPT PV system. As Fig. 5 shows, the proposed two-MPPT PVsystem is realized by augmenting the conventional PV systemof Fig. 4 with an auxiliary half-bridge converter. The auxiliaryconverter consists of a half-bridge transistor leg, a reactor, ashunt capacitive voltage divider, and the two reverse blockingdiodes and . The reactor connects the ac-side terminal ofthe half-bridge leg to the center point of the capacitive voltagedivider, which, in turn, is connected to terminal G of the PVarray [see also Figs. 1(a) and (b)]. The two transistors of thehalf-bridge leg are pulsewidth-modulated in a complementarymanner and control the voltage of terminal G of the PV array;this configuration enables independent control of the voltages

and in favor of an enhanced MPPT performance underpartial shading conditions, as discussed in Section II. L and Rrepresent the inductance and resistance of the reactor, respec-tively. The latter also embeds the effect of the on-state resistanceof the half-bridge leg transistors. Fig. 5 indicates that the aux-iliary converter can be viewed as a module that sits in parallelwith the dc link of the conventional PV system, and provides thethird terminal that is required for the two-MPPT scheme. Thisfeature is attractive in retrofit applications.

The other salient feature of the proposed two-MPPT PVsystem of Fig. 5 (i.e., apart from its enhanced MPPT capability),becomes apparent in view of the fact that terminal G of the PVarray is solidly grounded. This, in turn, means that the dc-linkvoltage of the proposed two-MPPT PV system can be chosen astwo times that of a conventional counterpart for the same safetyand insulation requirements. For example, North Americanstandards require that the voltage of a PV array be limited to amaximum of 600 V with reference to the ground [11]. In the PVsystem of Fig. 4, this requirement translates into a maximumdc-link voltage of 600 V for the VSC, and results in large currentsand suboptimum efficiencies for a high-power PV system [11].Although the trend is toward the adoption of higher voltage levels(e.g., 1000 V) at least for “behind the fence” systems, the limitedavailability of fuses, disconnects, etc., in the 1000-V voltageclass has presented the PV industry with a major challengein its attempt to quickly move in that direction. By contrast, amaximum voltage of 600 V for each subarray in the two-MPPTPV system of Fig. 5 corresponds to a maximum dc-link voltageof 1200 V, that is, the rating of the proposed two-MPPT PVsystem can be doubled while the existing safety and insulationrequirements are nonetheless respected.


Fig. 5. Schematic diagram of the proposed two-MPPT, single-stage, three-phase PV system.

B. Mathematical Model

This subsection formulates a mathematical model for the two-MPPT PV system of Fig. 5. The model describes the dynamicsof the array voltages and , and will be employed inSection III-C for designing the control loops that regulateand . In the subsequent developments, all node voltages areexpressed with reference to the dc-link virtual midpoint, that is,node “0” in Fig. 5.

Dynamics of the reactor current are governed by

(2)

(3)

where represents the ac-side terminal voltage of the half-bridge leg. Adding both sides of (2) and (3), and dividing theresultant by 2, one deduces

(4)

For a pulsewidth modulated half-bridge leg, is formulated as

(5)

where is the PWM modulating signal of thehalf-bridge leg, normalized to the amplitude of a symmetrical,high-frequency, triangular carrier waveform [12]. Thus, (4) canbe rewritten as

(6)

where is the difference between the subarrayvoltages, and is the net dc-link voltage.

With reference to Fig. 5, the application of KCL to terminalsA and B yields

(7)

(8)

Subtracting (8) from (7), one finds

(9)

The application of KCL to the node where meets the pos-itive rail of the VSC dc link requires that

(10)

Similarly, KCL for the node where meets the negative railof the VSC dc link requires that

(11)

Adding both sides of (10) and (11), one obtains

(12)

On the other hand, adding both sides of (7) and (8) results in

(13)

Substituting for in (12), from (13), one deduces

(14)

The currents through the upper and lower transistors of the half-bridge leg are formulated as [12]

(15)

(16)


Fig. 6. Block diagram of the system representing the dynamics of � and� .

Therefore, based on (15) and (16), and (14) canbe rewritten as

(17)

where is hereafter referred to as the effectivedc-link capacitance. The VSC dc-side current can, in turn,be expressed in terms of the real power that leaves the VSC acside, that is, [Fig. 5]. Thus, , and (17)can be rewritten as

(18)

and are expressed in terms of and , asand , which can be rewritten

in the following matrix form:

(19)

Equations (6), (9), (18), and (19) constitute a state-spacemodel for a nonlinear control plant for which and are theinputs, and are the outputs, and , and are thestate variables; the control objective for this plant is to regulate

and at their respective reference values, and, which are, in turn, determined by the MPPT schemes of

Subarray #1 and Subarray #2, respectively. The control strategyand loops required to fulfill this objective are presented in thefollowing subsection. Fig. 6 illustrates a block representationof the described control plant.

C. Net and Differential DC-Link Voltage Controller

The control plant represented by (6), (9), (18), and (19) isa multi-input-multi-output (MIMO), nonlinear system and, assuch, inherently difficult to control. Therefore, as discussed inthe subsequent subsections, a combination of feedforward anddecoupling compensation techniques is employed to overcomethe complications. The overall control task is managed by threedistinct control loops: The first control loop is a current-con-trol loop, based on (6), that regulates the reactor current at itsreference value . The second control loop regulates the differ-ence between the subarray voltages , based

Fig. 7. Block diagram of the reactor current-control loop.

on (9) and in view of the fact that is controlled by the firstloop. The third control loop regulates the dc-link net voltage(i.e., ), through the control of , thatis, the power that leaves the VSC ac-side terminals; this controlloop is based on (18). The overall control system will have tworeference commands and , which are determined basedon (19) from the reference commands and ; these, inturn, are received from the MPPT schemes of Subarray #1 andSubarray #2, respectively. The assumption here is that, in ad-dition to , the Subarray currents ( and ) and voltages( and ) are measured. The measurements are required,not only for the control, but also for independent MPPT of thetwo subarrays.

1) Reactor Current-Control Loop: The first control loop, il-lustrated in Fig. 7, is the reactor current-control loop whosefunction is to regulate at its reference value . The regulatedcurrent, in turn, will appear as an input to the control loop thatregulates the voltage difference between the two subarrays. As(6) suggests, can be controlled by the modulating signal ,while and are considered undesirable inputs. Let bedetermined based on the control law

(20)

where is a dummy control signal. Then, substituting forfrom (20) into (6), one finds

(21)

Equation (21) represents a first-order system for which andare the input and the output, respectively. Let be provided bya proportional-integral (PI) compensator

(22)

for which and are the proportional and integral gains, re-spectively. Then, if and are chosen as

(23)

and

(24)

one finds the following closed-loop transfer function:

(25)

in which the time constant is chosen to be a small value, sub-ject to the limitations imposed by the inductance of the reactorand the switching frequency of the half-bridge leg.


Fig. 8. Block diagram of the differential dc-link voltage-control loop.

Fig. 9. Block diagram of the net dc-link voltage-control loop.

2) Differential DC-Link Voltage Controller: The second con-trol loop is based on (9), receives as the control input, andregulates as the output; for this control loop,the subarrays current difference is the disturbanceinput. Fig. 8 illustrates a block diagram of the second controlloop, in which a measure of is included as a feedfor-ward signal to improve the transient response of the closed-loopsystem. Thus, is calculated as

(26)

where is the output of a compensator . If a fast currentcontrol is assumed, can be approximated by in (26), and (9)is rewritten as

(27)

which represents an integrator. To stabilize and control thisplant, is sufficient to be a PI compensator, say

(28)

in which and are the proportional and integral gains, re-spectively; the gains can be calculated for an adequately largephase margin and closed-loop bandwidth based on the assump-tion that or . As Fig. 8 shows, is lim-ited by a saturation block to ensure protection of the half-bridgetransistor leg against dc-side ground faults as well as normaltransient excursions; the upper and lower limits should be sym-metrically set to, for example, 1.2 times the maximum short-cir-cuit current level of a subarray. However, the output ofis symmetrically limited to a small value in order to prevent anintegrator wind up.

3) Net DC-Link Voltage Controller: The third control loop,shown in Fig. 9, is the one that regulates the net dc-link voltage

based on (18) and through the control of . Thus, for thisloop, is the input, is the output, and and

are the undesirable inputs. On the other hand, in a three-phaseVSC, the control of the real and reactive power is commonly

accomplished by -frame control of the VSC ac current, sothat

(29)

and

(30)

where is the magnitude of the voltage , and andare the direct and quadrature components of the VSC ac current

[12]. As extensively discussed in [12, Ch. 8], proper tuningof the VSC controllers ensures that

(31)

where and are the reference values for and , respec-tively; is the time constant of the closed-loop step response,and is a design choice [12]. Thus, as Fig. 9 illustrates, the errorbetween and its reference value is processed by the compen-sator and forms the control signal . The control signalis, in turn, augmented with measures of the disturbance inputs

, and , so that is de-termined as

(32)

can be obtained from the synchronization scheme of the PVsystem.

If, assuming a fast real-power control response, is replacedby in (32), then, combining (18), (29), and (32), one finds theeffective control plant in the compact form

(33)

which represents an integrator and can be readily controlled bya PI compensator, such as

(34)

for which the proportional and integral gains and can becalculated for a reasonably large phase margin and closed-loopbandwidth, based on the assumption that . As Fig. 9shows, is limited by a saturation block to ensure protectionof the VSC against overcurrents, for example, due to ac externalfaults. The saturation limits are typically set to 1.1–1.2 times therated ac current of the PV system.

Equation (30) indicates that is proportional to and,thus, to in a steady state. The reactive power that the PVsystem delivers to the grid is the sum of and the reactivepower supplied by the filter capacitor . Typically, is setto a positive value so that is negative and equal in absolutevalue to the reactive power supplied by in order to ensurethat the PV system exhibits unity power factor to the grid.

IV. SIMULATION RESULTS

To evaluate the effectiveness of the PV system of Fig. 5and its control strategy, a detailed switched model of a 1-MWsystem is constructed and simulated in the PSCAD/EMTDC


software environment. The grid is represented by a balancedthree-phase voltage source where each phase is connectedin series with a corresponding series RL branch; the sourcevoltage, the per-phase inductance, and the per-phase resistanceare 4.16 kV (line-to-line, rms), 0.63 mH, and 0.4 , respec-tively. Each subarray is modeled as a lumped representationof 144 parallel-connected strings of 18 se-ries-connected PV modules; each module is, in turn, assumed tobe composed of 54 identical basic PV cells. The modeland parameters of the modules are introduced in Appendix A.The MPPT schemes employ the incremental conductance (IC)algorithm [13], and are updated once every 50 ms. Parametersof the PV system and its controllers are given in Appendix B.

The simulation results demonstrate the PV system perfor-mance under the startup process, normal operating conditions,and dc- and ac-side faults. In the first two cases, the two MPPTschemes are disabled in order to allow a more clear evaluation ofthe proposed control strategy, free of periodic disturbances asso-ciated with the MPPT process. However, in the subsequent fivecases, the system response is also demonstrated under a morepractical scenario in which the MPPT schemes are in effect.

A. Case 1: PV System Response Under the Startup Processand Normal Operation

This case demonstrates the PV system overall response to astartup process and normal operation. In this case, the two PVsubarrays are exposed to a solar irradiation of 1.0 kW/m , andthe reference commands and are imposed externally(i.e., no MPPT is exercised). Thus, is assigned the valueof 400 V, from 0 s to 0.6 s, is stepped down to 300V at 0.6 s, and is stepped up to 450 V at 0.7 s. Sim-ilarly, is assigned the value of 400 V until 0.55 s, isstepped up to 500 V at 0.55 s, and is stepped down to 350V at 0.65 s. Until 0.5 s, all controllers are disabledand the switching pulses of the VSC and those of the auxiliaryhalf-bridge converter are blocked. However, the dc-link capac-itors are precharged by the PV subarrays, up to the sum of theopen-circuit voltages of the two subarrays, since the solar irra-diation is adequately large. Otherwise, if the PV subarrays weresubjected to low solar irradiation, the antiparallel diodes of theVSC would precharge the capacitors up to a net dc-link voltageabout the peak value of the ac-side line-to-line voltage throughthe preinsertion resistors of the breaker Br (not shown in Fig. 5).

Fig. 10(a) and (b) illustrates the responses of the subarrayvoltages to their respective reference commands. The figures in-dicate that the responses are almost decoupled from one anotherand settle at their steady-state values in about 10 ms; perfectdecoupling of and is not possible due to the limitedspeed of response of the reactor current-control scheme and thefact that the net dc-link voltage is fairly robust to changes dueto the large dc-link (effective) capacitance. Fig. 10(c) illustratesthe waveform of the net dc-link voltage, which is a response to

. Fig. 10(d) and (e) illustrates the waveformsof the two subarray powers and , respectively, andconfirms that the power delivered by each subarray is a functionof the subarray voltage, which, in turn, tracks its respective ref-erence command.

Fig. 10. PV system overall response to stepwise changes in the subarrayvoltage setpoints, from the startup instant to a steady state, without MPPT.

B. Case 2: PV System Response to Unequal Solar Irradiationsof Subarrays

This case study demonstrates the PV system response to un-equal subarray solar irradiations, while no MPPT process is ex-ercised. Initially, the PV system is in a steady state and the twosubarrays are subjected to a solar irradiation of 1.0 kW/m , and

and are both set to 400 V. Subsequently, the solar irra-diations of Subarray #1 and Subarray #2 assume the values (1.0,0.5) from 1.0 s to 1.05 s, (0.5, 0.5) from 1.05 s to1.1 s, (0.5, 1.0) from 1.1 s to 1.15 s, and (0.8, 1.0) from

1.15 s onward (the solar irradiation values are in kW/m ).Fig. 11 illustrates the current and voltage waveforms of the twoPV subarrays and the current waveform of the reactor.

Fig. 11(a) and (b) indicates that the steady-state values ofand are proportional to the corresponding subarray

solar irradiations. However, as Fig. 11(c) and (d) shows,and remain regulated at 400 V, due to the actions of thenet and differential dc-link voltage controllers, except at theinstants when the solar irradiation of a subarray changes andresults in short-term excursions in and . It is furtherobserved that the transient excursions of and are ap-proximately mirror images of each other. The reason is that thenet dc-link voltage does not change significantly in response toa short-term disturbance due to the large effective dc-link ca-pacitance. The magnitudes of the excursions can be reduced if


Fig. 11. PV system response to unequal exposures of the subarrays to solarirradiation, without MPPT.

the partial dc-link capacitors are made larger and the reactorcurrent-control loop is made faster; practical and cost consid-erations, however, limit both options. Fig. 11(e) confirms thatthe difference between the subarray currents flows through thereactor.

It is worth explaining the spikes observed on the currentwaveform of a subarray at the instants when the solar irra-diation of the other subarray changes (for example, note thespike on in Fig. 11(a) at 1.0 s). These spikes arenot due to changes in the photocurrent component of the hostsubarray; rather, they are caused by the transient excursions ofthe subarray voltage and the consequent momentary shift in thesubarray operating point.

C. Case 3: PV System Response to the Step Change in SolarIrradiation of One Subarray

In this test, the PV system response to a step change in thesolar irradiation of one subarray is demonstrated in Fig. 12,while the MPPT process is in effect. The PV system is sub-jected to the same startup process as those explained in Case#1, with both subarrays exposed to a solar irradiation of 1.0kW/m . During the startup period, each subarray voltage set-point is assigned by its respective MPPT scheme a constantvalue, for example, equal to 0.78 times a measure of the sub-array open-circuit voltage, sampled at about 0.3 s. Once the

Fig. 12. PV system response to a step change in the solar irradiation of onesubarray, with the MPPT process in place.

PV system startup process is complete, the MPPT schemes startto dynamically issue the voltage setpoints and basedon the incremental-conductance (IC) algorithm. At 1.3 s, thesolar irradiation of Subarray #1 assumes a stepwise decrease to0.5 kW/m , which is reversed by a stepwise increase from 0.5kW/m to 1.0 kW/m , at s; all along, the solar irradia-tion of Subarray #2 remains unchanged at 1.0 kW/m .

Fig. 12(a) and (c) indicates that despite the significant differ-ence in the solar irradiations of the two subarrays over the periodfrom 1.3 s to 2.0 s, the two subarray voltages are more orless the same, corresponding to their MPPs, except at 1.3 sand 2.0 s where they exhibit antiphasal transient excursionsof almost equal magnitudes. Hence, the stepwise decrease in thesolar irradiation of Subarray #1 results in a proportional drop in

as Fig. 12(b) shows, whereas remains fairly undis-turbed, as Fig. 12(d) illustrates. The reason is that a reductionin the solar irradiation has an insignificant impact on the arrayopen-circuit and MPP voltages (unless the solar irradiation isexcessively low), but proportionally reduces the array short-cir-cuit and MPP currents.

D. Case 4: PV System Response to Partial Shading of OneSubarray

This test demonstrates the PV system response to an abruptpartial shading of Subarray #1, while Subarray #2 and the un-shaded modules of Subarray #1 receive a solar irradiation of1.0 kW/m . It is understood that under a partial shading con-dition, the current of a subarray remains more or less constant,whereas its voltage drops drastically. In this paper, the afore-mentioned scenario is simulated by stepping down the number


Fig. 13. PV system response to partial shading of one subarray, when the MPPTprocess is in place.

of rows in Subarray #1, that is, , from 18 to 15, at 1.5 s.This downsizing emulates the effect that the antiparallel bypassdiodes of the shaded modules clamp down to zero the voltages of3 rows (out of 18 rows) of the subarray. Thus, unlike Case #3 inwhich unequal solar irradiations resulted in a significant currentmismatch between the two subarrays, in this case, a significantvoltage difference between the two subarrays manifests itself.Fig. 13(a) and (b) shows that, in response to the disturbance, theMPPT scheme of Subarray #1 finds the new MPP in less than0.35 s. Compared to Subarray #2, the steady-state MPP of Sub-array #1 corresponds to a lower voltage (of about 380 V) andpower (of about 420 kW). Fig. 13(c) and (d) indicates that thedisturbance makes transient impressions on the operating pointof Subarray #2, but has no steady-state impact on it.

E. Case 5: PV System Response to a Symmetrical AC Fault

This case demonstrates the robustness of the PV systemto a symmetrical ac-side fault. Thus, the PV system is in asteady state while both subarrays receive a solar irradiation of1.0 kW/m . Then, each high-voltage phase of the transformerTr is temporarily shorted to the ground, through a 0.4-mHinductance; the fault is incepted at 2.0 s and lasts for 0.1 s.Fig. 14 illustrates the PV system response to the fault.

Fig. 14(a) shows that subsequent to the fault inception, thethree-phase voltage drops to about 26% of its predisturbancevalue. Consequently, as Fig. 14(b) shows, the PV system in-creases (the amplitude of) its ac-side current in order to maintainthe predisturbance power output. However, the current magni-tude is limited due to the reference power saturation block (seeFig. 9) and, therefore, is insufficient to compensate for the severe

Fig. 14. PV system response to the three-phase-to-ground fault.

voltage drop. Consequently, the power output drops as Fig. 14(c)indicates. Since the PV subarrays keep energizing the dc linkof the PV system, the power-output drop results in a net dc-linkvoltage increase, up to the sum of the subarray open-circuit volt-ages, as shown in Fig. 14(d). Once the fault is cleared, the MPPTschemes bring back the PV system to its predisturbance MPP,in about 0.1 s, as Fig. 14(c) and (d) shows.

F. Case 6: PV System Response to an Asymmetrical AC Fault

This case is similar to Case #5 except that the PV systemis subjected to a single-phase-to-ground fault, through 0.4-mHinductance. Thus, the ac-side voltage becomes severely unbal-anced, as Fig. 15(a) shows. The fault results in a limited in-crease in the PV system current, as Fig. 15(b) shows; the cur-rent, nonetheless, retains its predisturbance, balanced sinusoidalform. The imbalance and the positive-sequence amplitude dropof the ac-side voltage result in power-output double-frequencypulsations and an average value drop, respectively, as Fig. 15(c)shows. Consequently, as Fig. 15(d) illustrates, the net dc-linkvoltage also fluctuates while its average value increases rela-tive to the predisturbance condition. The PV system resumes itsnormal operation as soon as the fault is cleared at 2.1 s, andthe MPPT schemes rapidly reclaim the predisturbance MPP.

G. Case 7: PV System Response to a DC-Side-to-Ground Fault

This case demonstrates the robustness of the PV system to adc-side ground fault. Initially, the PV system is in a steady state,while the subarrays receive a solar irradiation of 1.0 kW/m .Then, at 1.5 s, terminal A of Subarray #1 (see Fig. 5) isshorted to the ground. Consequently, the diode becomesreverse-biased and isolates Subarray #1 from the rest of thePV system. This, in turn, results in about a 50% drop in the


Fig. 15. PV system response to a single-phase-to-ground fault.

Fig. 16. PV system response to a dc-side terminal to ground fault.

PV system power output, as Fig. 16(a) shows. Moreover, asFig. 16(b) shows, the MPPT scheme of Subarray #1 reduces

to a low voltage at 1.55 s, that is, the first time thatit is updated after the disturbance incident; this voltage is afraction of an estimate of the subarray open-circuit voltage andis enforced by the MPPT scheme whenever the subarray cur-rent is sensed to be zero. This mechanism is particularly usefulif a shadow suddenly extends over a large area of a subarrayand drops the subarray open-circuit voltage inasmuch as it fallsbelow the subarray terminal voltage, which, in turn, would resultin a negative or zero subarray current (depending on whether aseries diode is provided for the subarray); this is the trap wheremany MPPT algorithms fall into and consequently lose the en-tire power output. Fig. 16(c) shows that the fault has no steady-state impact on the voltage of Subarray #2. Hence, Subarray #2retains its predisturbance power output. Fig. 16(c) also showsthe transient excursions of when changes. As ex-plained earlier, the transient excursions are due to the resilienceof the net dc-link voltage to voltage variations. Fig. 16(d) indi-cates that the reactor current shoots up to about 1115 A, whichis equal to the current delivered by Subarray #2 and transferredby the auxiliary half-bridge converter to the VSC; it should benoted that during the fault presence, the current of Subarray #1is the same as the subarray short-circuit current and circulates inthe fault path. Fig. 16(e) illustrates the waveforms of the threeac-side currents prior and subsequent to the fault occurrence.

V. CONCLUSION

In this paper, a single-stage three-phase PV system wasproposed that features enhanced MPPT capability, and animproved energy yield under partial shading conditions. Inaddition, the proposed PV system can effectively double themaximum permissible dc voltage of a grounded conventionalsingle-stage PV system, with no need for insulators, fuses,disconnects, and switchgear of a higher voltage class, withrespect to safety/insulation standards or common system inte-gration practices exercised for the grounded conventional PVsystems. The proposed PV system is realized by the parallelconnection of an auxiliary half-bridge converter to the dc linkof a conventional single-stage PV system and, therefore, mayalso be attractive for retrofit applications.

Compared to a single-unit, conventional, grounded, single-stage PV system of the same power rating, the proposed PVsystem:

• offers superior energy yield due to its enhanced MPPT ca-pability;

• runs at lower current levels and, therefore, lower conduc-tion power losses. Even though the power losses associatedwith the dc reactor and the two additional semiconductorswitches of the proposed PV system compromise the men-tioned reduction in the system power loss, the overall effi-ciency of the proposed PV system is expected to be higherthan that of a conventional counterpart, as the conductionpower losses are proportional to the square of current;

• however, requires semiconductor switches of a highervoltage class, two more semiconductor switches, acenter-tapped dc capacitor bank, and a dc reactor.

In many installations, high-power PV systems are realizedthrough the parallel connection of two half-rated, conventional,grounded, single-stage PV systems. Compared to this two-unit


Fig. 17. Circuit diagram of the PV array model employed for simulations.

PV system of the same overall power rating, the proposed PVsystem:

• requires four fewer semiconductor switches, which runat the same current levels as those of the conventionalsystem, and is thus expected to offer higher efficiency de-spite power losses of the dc reactor and the center-tappedcapacitor bank;

• effectively integrates two half-rated PV systems into onecubicle; further, it avoids the interphase transformer thatis required for parallelling the two half-rated PV systems;therefore, the proposed PV system is expected to econo-mize on the manufacturing costs and on the footprint;

• however, requires semiconductor switches of a highervoltage class, a center-tapped dc capacitor bank, and a dcreactor.

This paper presented the mathematical model, principlesof operation, and control loops of the proposed single-stagePV system. The performance and robustness of the proposedsingle-stage PV system were demonstrated for faulted as wellas normal operating conditions by time-domain simulationstudies conducted on a detailed switched model.

APPENDIX APV MODULE MODEL AND PARAMETERS

Fig. 17 illustrates a schematic diagram of the model employedin this paper for simulating a PV array (subarray). The modelrepresents the aggregate effect of parallel-connected stringsof series-connected identical PV modules; hereafter, eachmodule in the set is referred to as “the PV module” and is as-sumed to consist of series-connected basic PV cells.

In the model of Fig. 17, the Norton current source and resis-tance are formulated as

(35)

(36)

where the resistances and embed the aggregate effects ofseveral structural resistances of the PV module, and the impactof the leakage current of the - junctions constituting the PVmodule. The model, referred in the literature to as the single-diode model, is governed by the following equations [14]. isformulated as

(37)

TABLE IIPARAMETERS OF THE PV MODULE

where denotes the exponential function; and are,respectively, the terminal current and voltage of the PV module;

is a light-dependent current component; is the diode idealityfactor, and of a value typically in the range from 1 to 1.5; isthe (temperature-dependent) reverse saturation current of a -junction; and is the so-called inverse thermal voltage, whichis defined as

(38)

where is Boltzmann’s constant ,is the electron charge is the

number of series-connected PV cells, and is the - junctiontemperature in .

is a linear function of the solar irradiation and dependson as

(39)

where is the temperature coefficient of the PV moduleshort-circuit current, and , and , respectively, denotethe nominal values of the short-circuit current, solar irradiation,and junction temperature of the PV module. Similarly, the PVmodule open-circuit voltage is formulated as

(40)

where signifies the nominal value of the open-circuitvoltage of the PV module, and is the temperature coeffi-cient of the PV module open-circuit voltage.

Equation (37) must hold for all operating points, includingthe open-circuit operating point at the nominal solar irradiation,represented by , and . Thus, basedon (39) and (40), one deduces

(41)

Table II provides the numerical values of the PV moduleparameters.

APPENDIX BPV SYSTEM PARAMETERS

The PV system parameters are introduced in Table III.


TABLE IIIPV SYSTEM PARAMETERS

ACKNOWLEDGMENT

The authors would like to thank Prof. M. Russo andA. R. Di Fazio from the University of Cassino, Italy, for gener-ously sharing their PV module model.

REFERENCES

[1] S. Silvestre, A. Boronat, and A. Chouder, “Study of bypass diodesconfiguration on PV modules,” Appl. Energy, vol. 86, pp. 1632–1640,2009.

[2] A. Woyte, J. Nijs, and R. Belmans, “Partial shadowing of photovoltaicarrays with different system configurations: Literature review and fieldtest results,” Solar Energy, vol. 74, pp. 217–233, 2003.

[3] M. Garcia, J. M. Maruri, L. Marroyo, E. Lorenzo, and M. Perez, “Partialshadowing, MPPT performance and inverter configurations: Observa-tions at tracking PV plants,” Progr. Photovolt.: Res. Appl., vol. 16, no.6, pp. 529–536, 2008.

[4] N. D. Kaushika and N. K. Gautam, “Energy yield simulation of inter-connected solar PV arrays,” IEEE Trans. Energy Convers., vol. 18, no.1, pp. 127–134, Mar. 2003.

[5] N. D. Kaushika and A. K. Rai, “An investigation of mismatch losses insolar photovoltaic cell networks,” Energy, vol. 32, pp. 755–759, 2007.

[6] E. Karatepe, M. Boztepe, and M. Çolak, “Development of a suitablemodel for characterizing photovoltaic arrays with shaded solar cells,”Solar Energy, vol. 81, pp. 977–992, 2007.

[7] R. Ramabadran and B. Mathur, “Effects of series and parallel con-nected solar PV modules,” Modern Appl. Sci., vol. 3, no. 10, pp. 32–41,Oct. 2009.

[8] A. Ubisse and A. Sebitosi, “A new topology to mitigate the effectof shading for small photovoltaic installations in rural sub-saharanAfrica,” Energy Convers. Manage., vol. 50, pp. 1797–1801, 2009.

[9] PSCAD/EMTDC. ver. 4.2, Manitoba HVDC Res. Ctr., Winnipeg, MB,Canada.

[10] A. Yazdani and P. P. Dash, “A control methodology and character-ization of dynamics for a photovoltaic (PV) system interfaced witha distribution network,” IEEE Trans. Power Del., vol. 23, no. 3, pp.1538–1551, Jul. 2009.

[11] B. Brooks, “Challenges and benefits of 1000 VDC,” SOLARPROAug./Sep. 2009, pp. 24–26.

[12] A. Yazdani and R. Iravani, Voltage-Sourced Converters in Power Sys-tems. Piscataway, NJ: IEEE/Wiley, Feb. 2010.

[13] T. Esram and P. L. Chapman, “Comparison of photovoltaic array max-imum power point tracking techniques,” IEEE Trans. Energy Convers.,vol. 22, no. 2, pp. 434–449, Jun. 2007.

[14] J. A. Duffie and W. A. Beckman, Solar Engineering of Thermal Pro-cesses, 2nd ed. New York: Wiley, 1991.

Hamidreza Ghoddami (S’10) received the B.S. degree in electrical engineeringfrom the Iran University of Science and Technology in 1995, the M.S. degree inelectrical engineering from Urmia University in 1998, and is currently pursuingthe Ph.D. degree at the University of Western Ontario (UWO), London, ON,Canada.

His research interests include design, modeling, and control of photovoltaicenergy conversion systems. From 2001 to 2008, he was a Lecturer with BonabTechnical Faculty at the University of Tabriz, Tabriz, Iran.

Amirnaser Yazdani (M’05–SM’09) received the Ph.D. degree in electrical en-gineering from the University of Toronto, Toronto, ON, Canada, in 2005.

He was with Digital Predictive Systems, Inc., Mississauga, ON. Currently,he is an Assistant Professor with the University of Western Ontario, London,ON, Canada. His research interests include modeling and control of electronicpower converters, renewable electric power systems, distributed generation andstorage, and microgrids.

Dr. Yazdani is a Professional Engineer in the Province of Ontario.

22.a Single Stage Three Phase PV System With Enhanced MPPT

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enhanced mppt

requires semiconductor

normal operating

pv system

renewable

phase pv system

rated pv systems

partial shading