Forecasting PV power production

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Solar Energy 84 (2010) 1301–1309

Forecasting photovoltaic array power production subject tomismatch losses

D. Picault a,*, B. Raison a, S. Bacha a, J. de la Casa b, J. Aguilera b

a Grenoble Electrical Engineering Laboratory (G2Elab), 961, rue Houille Blanche BP 46, 38402 St Martin d’Heres, Franceb Grupo de Investigacion IDEA, Departamento de Electronica, Escuela Politecnica Superior, Universidad de Jaen, Campus Las Lagunillas, 23071 Jaen, Spain

Received 16 February 2010; received in revised form 9 April 2010; accepted 10 April 2010Available online 12 May 2010

Communicated by: Associate Editor Nicola Romeo

Abstract

The development of photovoltaic (PV) energy throughout the world this last decade has brought to light the presence of module mis-match losses in most PV applications. Such power losses, mainly occasioned by partial shading of arrays and differences in PV modules,can be reduced by changing module interconnections of a solar array. This paper presents a novel method to forecast existing PV arrayproduction in diverse environmental conditions. In this approach, field measurement data is used to identify module parameters once andfor all. The proposed method simulates PV arrays with adaptable module interconnection schemes in order to reduce mismatch losses.The model has been validated by experimental results taken on a 2.2 kWp plant, with three different interconnection schemes, which showreliable power production forecast precision in both partially shaded and normal operating conditions. Field measurements show interestin using alternative plant configurations in PV systems for decreasing module mismatch losses.� 2010 Elsevier Ltd. All rights reserved.

Keywords: Photovoltaic array modelling; Mismatch losses; Interconnection scheme

1. Introduction

The growing number of PV installations throughout theworld these last decades has exposed differences betweenexpected power production forecasts and field experienceof photovoltaic arrays. These power losses, more com-monly referred to as mismatch losses, can be defined asthe difference between the sum of the maximum power ofeach module of an array and the maximum power of theentire plant. In the case of partial shading of an array,the losses are not proportional to the shaded area, butincrease non-linearly (Rauschenbauch, 1971; Nguyenet al., 2008). Prior work on the mismatch effect has shown

0038-092X/$ - see front matter � 2010 Elsevier Ltd. All rights reserved.

doi:10.1016/j.solener.2010.04.009

* Corresponding author.E-mail addresses: [email protected] (D. Picault),

[email protected] (B. Raison), [email protected] (S. Bacha).

to be responsible for losses up to 10% of the total generatedpower (Chouder et al., 2009). A second effect of modulemismatch is the presence of multiple peaks in the power-voltage characteristic of the PV plant. The appearance ofsuch local maximums can mislead some maximum powerpoint tracking (MPPT) algorithms, especially perturb andobserve or incremental conductance methods, which mayfail to extract the most power from a solar array (Patelet al., 2008; Petrone et al., 2007).

Mainly two causes provoke module mismatch: disper-sion of electrical properties and non-uniformity PV cellillumination composing the array (Chouder et al., 2009;Gautam et al., 2002; Kaushika et al., 2003, 2007; Meyeret al., 2004; van der Borg et al., 2003). Indeed, electricalproperties of the solar cells may vary due to manufacturer’stolerances or degradation processes. Anti-reflection coatingdegradation, encapsulating material discoloration, light-induced degradation (also known as the Staebler-Wronski

http://dx.doi.org/10.1016/j.solener.2010.04.009

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Nomenclature

BIPV Building-Integrated photovoltaicsBL bridge-link array configurationTCT total-cross tied array configurationSP series–parallel array configurationIph light-induced currentIo reverse saturation current of the p–n junctionRs series resistanceRsh shunt resistanceVt thermal voltageT module temperaturea diode ideality factorNs number of cells in serieskb Boltzmann constant (1.381e�23 J K�1)

q fundamental electric charge (1.6e�19 C)Isc short-circuit currentVoc open-circuit voltageGi irradiance at environmental condition i

Ti module temperature at environmental conditioni

a short-circuit current correction factor for tem-perature

b open-circuit voltage correction factor for tem-perature

d open-circuit voltage correction factor for irradi-ance

N length of input voltage vector

1302 D. Picault et al. / Solar Energy 84 (2010) 1301–1309

effect (Meyer et al., 2004), hot-spots, and cell structure deg-radation (such as cracked cells) all participate in the trans-formation of solar cell electrical properties. Regardingheterogeneous cell illumination, there are two main causes:partial shading of the array and diversity of tilt angles.Generally, solar plants are consisted of PV modules whichare at the same tilt angle. Yet in certain Building-IntegratedPV (BIPV) applications Benemann et al., 1996; Omer et al.,2003; Fernadez-Infantes et al., 2006; Drif et al., 2008, forexample modules on roof and wall of a building are con-nected to a same inverter, the variety of tilt angles in a samearray could occasion severe module mismatching. More-over, PV plants can be subject to partial shading occa-sioned by nearby trees, antennas, chimneys, passingclouds, or nearby houses that cover a portion of a BIPVplant during the day. In solar tracking plants, shadows ofone tracker can appear over modules of another duringmorning and evening hours. In utility-sized plants, nearbyoverhead power lines and transmission towers can bringmoving shadows across a portion of the plant during theday. In other words, partial shading of solar arrays affectsa great variety of PV systems.

Many solutions for reducing mismatch losses have beenproposed by modifying array interconnections or addingpower converters. Quasi-random cell organization (Feld-man et al., 1981) and plant oriented irradiance equalization(Velasco et al., 2005), intend to distribute the impact ofshadows as uniformly as possible by reorganizing cell/mod-ule connections in strings. Another proposed method is byusing alternative array interconnection topologies such astotal-crossed tied (TCT) and bridge-link (BL) configura-tions, which use series–paralleling of modules, either stati-cally (Gautam et al., 2002; Kaushika et al., 2003, 2007;Karatepe et al., 2007) or dynamically (Nguyen et al.,2008). Connection schemes of series–parallel (SP), TCTand BL topologies are shown in Fig. 1. Investigations onadding power conversion units have also been studied formodule mismatch reduction such as replacing centralizedinverter topologies by string, multi-string, or AC-module

technologies (Kjaer et al., 2005). Other solutions proposedusing cascaded DC–DC converters in PV plants (Bratcuet al., 2009; Shimizu et al., 2003; Roman et al., 2008) havealso been considered for independently extracting maxi-mum power of modules.

This paper deals with solar array modelling using recentphotovoltaic module modelling techniques applied to crys-talline silicon modules in order to predict power produc-tion in existing PV plants. Furthermore, reduction ofmismatch losses by changing interconnection schemes ofmodules in solar generators is addressed. Finally, thispaper presents results on novel field tests conducted on a2.2 kWp plant with several interconnection schemes con-curring with model predictions.

2. PV module modelling using the Lambert W-function

The one-diode model is commonly used for modellingmodules of crystalline silicon technology. The equivalentelectric circuit comprises a current source, two resistors,and a single-diode, as shown in Fig. 2. The one-diodemodel contains five parameters which describe the PVmodule properties: Iph, Io, Rs (caused by resistances insolder bonds, emitter and base regions, cell metallization,cell-interconnect bus bars and resistances in junction-boxterminals) (Meyer et al., 2004), Rsh (representing the leak-age currents through the solar cell or on cell edges due tocrystal damage or impurities near the junction), and Vt

(depending on module technology and cell organization).The voltage–current relationship that can be deduced usingthe equivalent circuit results in a transcendental equation(Patel et al., 2008; Kaushika et al., 2007; Joyce et al.,2001; Kawamura et al., 2003) presented in Eq. (1) [PVmodule current–voltage relation using one-diode model]:

I ¼ Iph � Io � eVþRs �I

V t � 1� �

� V þ Rs � IRsh

with

V t ¼N s � a � kb � T

qð1Þ

Table 1Calculation time (in seconds) of module current with N voltage values.

N Lambert-W Newton–Raphson

100 0.001 1.4091000 0.005 79.7122000 0.313 340.001

Fig. 1. Diagram of series–parallel (SP), total-cross tied (TCT) and bridge-link (BL) connection schemes.

Rs

RshIph

I

V

Fig. 2. Equivalent electrical circuit of photovoltaic module.

D. Picault et al. / Solar Energy 84 (2010) 1301–1309 1303

In recent years, interest in using the Lambert W-func-tion, frequently referred to as W(z), for photovoltaic cellmodels (Petrone et al., 2007; Jain et al., 2006; Ding et al.,2008) has proven to be convenient by directly expressingcurrent as an exact analytical expression of voltage, asshown in Eq. (2) [PV module current–voltage relation usingLambert W-function]:

I ¼V t

Rs� Rs �Rsh � ðIphþ IoÞ

V t � ðRsþRshÞ�W

Io

V t� Rs �Rsh

RsþRsh�e

RshðRsþRshÞ

VþRs �ðIphþIoÞV t

� ��

� VRsþRsh

ð2Þ

The previous expression can be simplified by using thecommon approximation that the series resistance is negligi-ble with respect to the shunt resistance value (Rs� Rsh), asshown in Eq. (3) [Current–voltage relation withapproximation]:

I ¼ f ðV Þ

¼ V t

Rs� Rs � ðIphþ IoÞ

V t�W

Io

V t�Rs � e

VþRs �ðIphþIoÞV t

� �� V

Rshð3Þ

This model has two main advantages: expressing modulecurrent as explicit function of module voltage and acceler-ated simulation time. Prior research using this model haslacked to emphasize the rapid simulation time of current–

voltage values compared with the traditional calculationusing the transcendental equation. The Lambert W-func-tion and embedded Newton–Raphson method have beenused in MATLAB for module characterization. Theparameters of a 200 Wp module have been previouslyentered in order to calculate the module current–voltagecharacteristic. The developed programs determine the cur-rent vector corresponding to an input voltage vector andmodule parameters. The proposed model uses the seriesexpansion of the Lambert W-function to calculate thenumerical current values whereas the Newton–Raphsoniteratively determines the corresponding current that veri-fies Eq. (1). Calculation time resulting from both iterativemethod and direct calculation are shown in Table 1.Results show that the Lambert W-method solves much fas-ter (approximately 1000 times) which can considerablyreduce simulation time in complex calculations.

Furthermore, the proposed model has been used toextract the five characteristic parameters of modules byusing the least-square fitting method. Curve-fitting resultsusing the explicit function show high concordance betweenmodel and field measurements, as will be seen afterwards.

3. PV array modelling with alternative interconnection

schemes

PV array production forecasting has brought interestthrough recent years accompanying the expansion of pho-


tovoltaic systems. Previous papers have proposed matrixmodels for simulating PV arrays in series–parallel config-uration with various environmental conditions (Patelet al., 2008; Kaushika et al., 2003; Kawamura et al.,2003). This method has proven to be convenient of usefor implementation and verification of simulations results.The proposed model also uses a matrix approach to solvea PV array problem. The principle is to use either modulevoltages or currents as unknowns (in our case voltages arechosen for better numerical precision) to determine anunknown vector X. Electrical relations describing the PVarray are transcribed into mathematical equations andput in matrix format F. The solution is obtained oncethe residual of the product F � X is sufficiently small. Inthis paper, the modelling of alternative connectionschemes is presented. Custom interconnection schemesmay be simulated by dynamically modifying the PV arrayelectrical model matrix F. The values of module voltageand current can therefore be determined with givenincoming solar irradiance G and module temperature T,DC plant voltage as well as other parameters shown inFig. 3.

3.1. The traditional series–parallel topology

In a PV array composed of M modules per string with N

strings, that is to say an array comprising M � N modules,we can identify (M � 1) � N nodes and (M � 1) � (N � 1)possible interconnections of modules, as shown in Fig. 3.The most common topology for PV arrays is series–paral-lel, where M modules are connected in series, and N stringsof M modules are connected in parallel.

The equations describing the electric behaviour of thePV array can be classified into three groups: current laws,voltage laws and DC bus voltage law.

The current laws describe current flow through the arrayof PV modules using Kirchhoff’s current laws at the nodesof the array. In the case of the SP topology, the currentflowing through two consecutive modules in a same string

Fig. 3. Operational diagram of t

is equal, as shown in Eq. (4) [Expression of current laws forseries–parallel array]:

8 i 2 ½1;M� 1�; 8 j 2 ½1;N�; f ðV i;jÞ � f ðV iþ1;jÞ ¼ 0

ð4ÞThe DC bus voltage law expresses the voltage that the

string is submitted to at the entry point of the inverter,the DC bus voltage. In order to determine the plant currentfor each DC bus voltage value, the operating point of theplant current–voltage characteristic is calculated for a DCbus voltage VDCbus. By choosing to submit the first stringvoltage to DC bus voltage we obtain Eq. (5) [Expressionof DC bus voltage law for series–parallel array]:

XMi¼1

V i;1 � V DCbus ¼ 0 ð5Þ

Finally, the voltage laws describe the voltage equalitiesthat lie between single modules or strings of modules con-nected in parallel. In the case of the SP topology, (N � 1)strings of M modules are connected to the first string inparallel, bringing supplementary Eq. (6) [Expression ofvoltage laws for series–parallel array]:

8 j 2 ½2;N�;XM

i¼1

V i;1 �XMi¼1

V i;j ¼ 0 ð6Þc

By using the previous M � N equations, the M � N ranknon-linear system can be solved. This is done by determin-ing the solution to the matrix equation F � X = 0, where F

is a square matrix of dimension M � N �M � N and X is thevoltage vector of length M � N. The iterative Newton–Raphson method is applied to solve the equation systemusing the F matrix and its associated jacobian matrix.The process is initialized by supposing that each modulein the array have the same voltage value VDCbus/M.

3.2. Alternative module interconnection schemes

Prior research has shown interest in modifying moduleinterconnection schemes for reducing mismatch losses.

he PV array forecast model.


Alternative topologies have been proposed such as theTCT and BL configurations which have improved globalPV array efficiency by reducing mismatch losses. In previ-ous papers (Kaushika et al., 2003, 2007), simulations werecarried out for each topology with a dedicated set of equa-tions in order to forecast PV power production. This paperproposes a simulation model for a PV array where electricequations are automatically modified in order to simulate acustom interconnection scheme, that is to say one singlealgorithm for various configurations.

As stated previously, in an array of M � N modules thereare (M � 1) � (N � 1) possible module interconnections.The interconnection matrix ConMat, describes the inter-connections in an array, by using the null value if theconnection is not established, and one in the correspondingcell if modules are interconnected. For example, in thecase of the SP topology, the corresponding interconnec-tion matrix is a null matrix of dimension (M � 1) �(N � 1).

When a module is interconnected with another, that isto say a parallel connection is established, a current law isreplaced with a voltage law, thus conserving the totalnumber of equations in the system. Indeed, if nodes Ni,j

and Ni,j+1 are connected, as shown in Fig. 3, the two cur-rent laws describing current flow between modules Mi�1,j

and Mi,j and modules Mi�1,j+1 and Mi,j+1 are fused intoa new current law shown in Eq. (7) [Expression of currentlaw fusion equation for ConMati,j connection]:

f ðV i�1;jÞ � f ðV i;jÞ ¼ 0

f ðV i�1;jþ1Þ � f ðV i;jþ1Þ ¼ 0

�

) f ðV i�1;jÞ � f ðV i;jÞ þ f ðV i�1;jþ1Þ � f ðV i;jþ1Þ ¼ 0 ð7Þ

Furthermore, the node connection generates an addi-tional voltage equation, since interconnected modules havethe same voltage. In the previous case, the additional equa-tion ties the sum of voltages of modules in the same stringprior to modules Mi�1,j and Mi�1,j+1, as shown in Eq. (8)[Additional voltage law due to ConMati,j connection]:

Xi�1

k¼1

V k;j �Xi�1

k¼1

V k;jþ1 ¼ 0 ð8Þ

Hence, by using and interpreting the interconnectionmatrix to modify the PV array electrical property matrixF, the user can simulate any PV array interconnectionscheme.

The shade scenario on the solar array is taken intoaccount by applying a shade factor, with values takenbetween 0 (for totally shaded modules) and 1 (for non-shaded modules), to the irradiance received by themodules. This simplified model of the effect of shade doesnot take into account the temperature drop due to shading.Shade factors for each model are grouped into the shadematrix S thus giving the shade scenario for the entire solararray.

4. Module parameter translation method to desired

environmental conditions

Module current–voltage characteristics depend on envi-ronmental conditions such as irradiance and module tem-perature. Current–voltage curve translation is based onthe calculation of the short circuit current (Isc) and open-circuit voltage (Voc) at desired environmental conditions(G2, T2) from a measured I–V curve taken at (G1, T1).Translation equations have been investigated throughoutthe past (Blaesser et al., 1988; Anderson, 1996; Marion,2002; Hermann et al., 1996; Tsuno et al., 2005), demon-strating linear variation of short circuit current withirradiance and variation of open-circuit voltage with tem-perature, as shown in Eq. (9), these translation equationsuse temperature and irradiance correction factors a, band d (Marion, 2002). The translation method can beadapted to other PV module technologies by using suitablecorrection factor values [Translation equation for modulecurrent (I) and voltage (V) from conditions (G1, T1) to(G2, T2)].

IðG2; T 2Þ ¼ IðG1; T 1Þ � G2

G1� 1þ aðT 2 � T 1Þ½ �

V ðG2; T 2Þ ¼ V ðG1; T 1Þ � 1þ bðT 2 � T 1Þ½ � � 1þ d � ln G2

G1

� �h i

ð9Þ

In order to describe the influence of environmentalconditions on the five parameters used in the one-diodemodel, the translation method was applied to Eq. (1) andby parameter identification, translation formulas werededuced, as shown in Fig. 4. The parameter translationequations can be applied to any crystalline silicon or othertechnology that uses the single-diode equivalent circuit as amodel. The novel parameter translation method uses thecorrection factor calculation method proposed by Marion(2002). Module parameters have previously been identifiedfrom a reference curve and then translated using previouslydetermined correction factors for Isofoton I-106 modules(a = �0.009 �C�1, b = �0.0028 �C�1, d = �0.0039), resultsare shown in Fig. 4. The parameter translation methodconserves the precision used by the chosen translationmodel, in our case the Marion method. The translationof I–V curves by parameter extraction has two benefits:flexibility in translation models and observation of param-eter evolution with environmental conditions.

5. Case study: influence of modifying topologies in partial

shaded installations

In order to validate the simulation model, measurementshave been carried out on a 2.2 kWp rooftop installation,consisting of 20 Isofoton I-106 modules, part of the UNI-VER project at Jaen University in Spain (Drif et al., 2007)as can be seen in Fig. 5. Originally, the plant was grid-con-nected and made up of two strings of 10 modules to fitinverter specifications. In order to see the influence of mod-

Fig. 4. I–V curve translation method using measurements taken at environmental conditions (G1, T1) for prediction of I–V characteristic at (G2, T2)conditions.


ule interconnections, the plant has been reconfigured intofour strings of five series-connected modules. Furthermore,modifications on the installation have been made in orderto rapidly change the module interconnection scheme. Todo so, a connection box has been designed to centralizemodule terminals into a unique location, facilitating planttopology changes in a short time span (less than 15 min)

(a) 2.2 kW plant containing 20 Isofoton I-106 modules

(b) PV modules withused for shaded

Fig. 5. PV plant and connection box u

in order to keep similar environmental conditions duringmeasurements.

The experimental procedure consisted in successivelymeasuring the current–voltage characteristic of three topol-ogies (SP, TCT and BL) followed by the I–V characteristicrecording of each module within the array. This procedurewas carried out in both non-shaded and partially shaded

(c) Connection box in SP configuration for 2 strings of 10 modules

plastic film scenario

sed during measurement campaign.

Table 2Maximum power values of experimental and simulation results in non-shaded scenario.

SP TCT BL

Experimental (Wp) 1087.5 1089.9 1090.2Simulation (Wp) 1103.4 1103.8 1104.2Simulation error (%) 1.46 1.28 1.28


scenarios in order to forecast the plant power productionusing the proposed method. Static partial shade was per-formed by covering two modules with bubble wrap film,as shown in Fig. 5b, which decreased incoming irradianceby 40 percent. All of the experimental work was carriedon the rooftop installation using a calibrated solar cell, amodule temperature sensor and a PVPM 2540C curve tra-cer. In addition, environmental conditions varied slightlyduring the measurement campaign with values of incomingsolar irradiance ranging between 600 and 660 W m�2 andmodule temperatures from 32 �C to 35 �C. Module param-eters were extracted separately from the measured I–V

characteristics and translated to the experimental environ-mental conditions. Finally, plant production forecast wascarried out using the proposed method and compared toexperimental data.

5.1. Normally operating PV array results

In normal operating conditions, photovoltaic plants arenot subject to partial shade and therefore have a power-voltage characteristic containing only one maximum peak.Experimental results, presented in Fig. 6, show that inhomogeneous irradiance conditions all three topologieshave similar power-voltage characteristics. Furthermore,TCT and BL topologies have slightly higher maximumpower ratings than the series–parallel topology at sameenvironmental conditions. However, in such conditionsthe power gain remains negligible: +0.2% maximum powerincrease with respect to the SP topology, considering themeasurement apparatus error.

The production forecast method was then applied usingthe earlier mentioned steps: parameter extraction of indi-vidual modules, parameter translation to plant measure-ment conditions, and plant I–V curve construction.Maximum power points of the predicted and experimentalcurves are presented Table 2. Simulation results fit closely

0 10 20 30 40 50 60 70 80 90 1000

10

20

Voltage [V]

Cur

rent

[A]

0

1000

Pow

er [W

]

SP 1087.5 Wp, 633 W/m², 33.2 °CTCT 1089.9 Wp, 633 W/m², 33.3 °CBL 1090.2 Wp, 631 W/m², 33 °C

Fig. 6. Experimental values of non-shaded 2.2 kWp plant.

to experimental results throughout the curve, yet some dis-persion in maximum power remains due to errors in mod-ule I–V curve parameters extraction and environmentalcondition translations. It should be noticed that simulationresults always over-estimate maximum power. However,simulation errors are satisfactory remaining between 1%and 2% of experimental maximum power.

5.2. Partially shaded PV array results

In partially shaded conditions photovoltaic plants, I–V

curves present two main properties: maximum powerreduction and appearance of multiple power peaks. Thefirst effect is a consequence of lower incoming solar poweronto the array. The appearance of multiple peaks is due tomodule mismatch, which may be accentuated by bypassdiode operation. The multi-peak effect is visible on theexperimental results, presented in Fig. 7, in case of partialshading of an array. Although all three topologies showinflexion points on their current–voltage characteristics,both TCT and BL arrays have smoother curves conse-quently lessening the multi-peak effect. Furthermore, mea-surements show an increase of roughly 4% and 2.5% inmaximum power for the TCT and BL interconnectionschemes. In other words, the PV array is able to produce4% more power than the SP topology by simply modifyingthe array interconnections of the plant into a TCT config-uration. PV plant owners can therefore expect higher

0 10 20 30 40 50 60 70 80 90 1000

10

20

Voltage [V]

Cur

rent

[A]

0

1000Po

wer

[W]

SP 1001.2 Wp, 650 W/m², 35.5 °CTCT 1039.7 Wp, 651 W/m², 35.4 °CBL 1025 Wp, 650 W/m², 36 °C

Fig. 7. Experimental values of partially shaded 2.2 kWp plant.

Table 3Maximum power values of experimental and simulation results in shadedscenario.

SP TCT BL

Experimental (Wp) 1001.2 1039.7 1025Simulation (Wp) 1026.5 1064.2 1041.4Simulation error (%) 2.53 2.36 1.60

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

SP TCT BL

Mis

mat

ch L

osse

s [%

]

Non-shaded Partially shaded

Fig. 8. Calculated mismatch losses of SP, TCT, BL topologies in bothnon-shaded and partially shaded conditions.


energy production yields leading to higher return on invest-ment rates.

Simulation results confirm the plant’s I–V curve evolu-tion, with maximum power brought by the TCT topologyfollowed by the BL topology, as can be seen in Table 3.Simulation errors are slightly higher than previous simula-tions but remain well under the 5% threshold. In the partialshading case, additional errors in the bypass diode modelcan explain higher error levels. Another phenomenon vali-dating the simulation model is the reduction of the multi-peak phenomena which is more pronounced in the simula-tion model than in experimental measurements.

The use of alternative module interconnection schemeshave shown increase in power production during shadedconditions by using simulation tools validated experimen-tally. The experimental power increase in alternativeschemes is directly linked to mismatch losses consideringthat the use of the connection box reduces significantlythe additional cable losses.

5.3. Analysis of mismatch losses

The proposed PV array forecasting algorithm has beenused to determine mismatches in the experimental results.To do so, the module I–V characteristics have been trans-lated to the I–V plant curve conditions environmental con-ditions for each topology SP, TCT and BL. Then, themaximum power of each module has been calculated andsummed in order to determine the maximal available arraypower at given environmental conditions. The differencebetween the maximal available power and the maximummeasured power for each topology in both non-shadedand partially shaded conditions was then calculated.Results shown in Fig. 8, present the mismatch losses,expressed in percent with reference to the maximal avail-able power of the array.

The TCT configuration shows the least mismatch lossesin partially shaded conditions, whereas the BL configura-tion has the least mismatch losses in non-shaded condi-tions. It should be noticed that in traditionally configuredarrays, the calculated mismatch losses for the 20 moduleplant represent a 19 W loss, that is to say a 1.71% powerloss in this case. Whereas in the BL configuration, mis-match losses in non-shaded conditions add up to 11 W.Module connection modifications are expected to bringhigher power increase ratios in more severe mismatch casessuch as different shade scenarios with higher solar irradi-ance values.

6. Conclusion

A method for forecasting existing photovoltaic plants’power production has been proposed and validated byexperimental measurements in both shaded and non-shaded conditions. The PV module model uses the Lam-bert W-function enabling a direct tie between current andvoltage of modules which significantly reduces calculationtime. Furthermore, various interconnection schemes ofmodules can be simulated thanks to the automatically gen-erated electrical relations which describe solar array opera-tion. This paper also addresses PV module parameteridentification and novel parameter translation to desiredenvironmental conditions, which are necessary for compar-ing expected power production with changing irradianceand temperature levels. Moreover, new experimental workon alternative array configurations shows that modifyingthe module interconnection scheme inside a PV plant canraise maximum power output by up to 4%, especially inpartially shaded conditions, with respect to traditionalmodule interconnection schemes. Further simulationresults should be carried out to see if TCT and BL topolo-gies can have a greater impact in different scenarios.Control strategies for dynamically modifying array inter-connections, thanks to automated DC switches inside aconnection box, could help optimize PV array power out-put in degraded mode operation. Such control strategiescould consist in real-time control of PV plants given therapid simulation times using the Lambert W-functionmodel when applicable. The PV forecast method could alsobe used for determining the optimal interconnectionschemes with given shade scenarios for maximizing powerproduction of PV plants submitted to recurrent partialshading as can be found in previously discussed PVapplications.

Acknowledgements

This work was funded by the Solution PV project by theMINEFI (French Ministry of Industry), the Rhone-Alpes


Region (France), the CG 38, the Metro, and the Competi-tiveness Pole TENNERDIS. The authors would like tothank the University of Jaen’s Solar Energy Laboratoryfor its collaboration which also made this work possible.

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Forecasting PV power production

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