Tool for Automated Simulation of Solar Arrays Using General-Purpose ...

Tool for Automated Simulation of Solar Arrays Using General-Purpose Simulators

N. Pongratananukuland T. Kasparis University of Central Florida Orlando, FL USA 32816 Email: [email protected]

AbstrrrcC The paper describes a tool developed to automate study of solar array configurations u h g a general-purpose simulntor such PJ Spice. Tbe main advantage of the proposed method b that studies can be done for any solar array configurntion formed from eIementnry models of solar cell units. Hierarchid structure o f solar cell elements with semiconductor d e U allows simulations of electrical properties as well as the

of environmental conditions impact AppHution exnmples such ns the effect of unequal illuminntion on various array interconnections and the mismatch of mlnr cells will be presented to demonstrate the usefulness of the tool. The automated proeess will ease investigation of large syatem and wontcase study for given envfronmentnlscenarios. evaluation

1. MTRODUCI'iON The understanding of solar cell source behavior is necessary to specify the size of solar array system or to study the stability of regulators. Placing the solar panels in an optimal way i s an effective measure to take to maximize the energy yield from a photovoltaic-installation. Any shading of the solar panels will lead to considerable reduction in energy yield, even if just a small fraction of the panels i s shaded. Shading can m I y be completely avoided, certainly not in urban or suburban environments. At higher latitudes the sun is often close to the horizon which makes the shading problem more severe than at low latitudes. Therefore especially for high-latitude locations and tubadsuburban sites, a shadingtolemnt system should be chosen. Furthermore, the direction southhorth (azimuth) and elevation angle should also be considered. The connection of photovoltaic modules with different operating currents andlor voltages characteristic may result in the performance of the anay being less than the s u m of the potential performances of individual modules. When connected in series, the current flowing through the lowest productive cell limits the entire array output. The problem arises when modules have different sizes, which may be a result of individual modules not exposed to the same lighting conditions, such as is the case with differently oriented modules or irregular shading of the array. Mismatch is more likely in large systems than in independent arrays, because individual modules may be oriented differently or they may be subject to varying degrees ofshading and heating.

0-7803-8502-0/04/%20.00(82004 TEEE.

10

Taking into account that real operating conditions of a solar array are difficult to reproduce during tests, simulations to

determine electrical characteristics will allow the researcher to gain more insight for better understanding and design. Performance gain is beneficial and can find applications in numerous areas such as the one described in reference [I]. AS the fine modeling of a cell's behavior is the basis for any solar generator, the solar cell model needs to be properly determined. Methods for simulation of general solar amy configuration have been proposed, however, these implementations are associated with special-purpose simulation tools, and detailed modeling has not been performed [2],[3],[4]. Utilizing circuit-simulator such as PSPICE, one can run many component models. This paper proposes an automated tool to provide simuIation of solar arrays by using individual solar cell models. The content of this paper is organized in the following way. Modeling of solar cells and impact of environmental effects on their characteristics are reviewed in section 11. Practical solar panels structure is discussed in section III. The implementation of the proposed method using a genal-

purpose simulator is discussed in section IV. Application examples are presented in section V, 11.

SOLAR CELL MODELING

Solar cells are essentially a very large area pn junction diode where such a diode is created by forming a junction between the n-type and ptype regions. As sunlight srrikes a solar cell, the incident energy is converted directly into electrical energy. Transmitted light is absorbed within the semiconductor by using the energy to excite fke electrons from a low energy status to an unoccupied higher energy level. When a solar cell is illuminated, excess electron-hold pairs are generated by light throughout the material, hence the p-n junction is electrically shorted and current will flow. The equivalent circuit of a solar cell is represented by four components: a ligh-induced current source, a diode parallel to the source, a series resistor and a shunt resistor. The lightinduced current is due to the separation and drift of the photon-generated electrowhole pairs under the influence of the built-in field.

The two-diode model of solar cell is shown in Fig. 1 along with the corresponding equation. The two-diode model is derived from the physics of the p n junction, especially those of poly crystalline silicon [ 5 ] . Amorphous silicon does not exhibit as sharp knee in the curve, so the single-diode model is more appropriate (1, = 0). The first saturation current, Jsl, is due to dimlsion mechanism of the minority carriers into depletion layer, aod the second is due to recombination in space-charge layer.

T

26 danC, Irr. (rrtod X )

26.0, 40.0, 76.0, 100

Fig. 2 IV curves for various irradiance I -

Irr. (rated)

r

100%. Tamp (dagC) I

0.00 25.0, 50.0, 75.0

I

I

where,

I

= solar cell output current (A)

= solar cell output voltage (V) = generated photo-current (A) Is,, Id = diodes' reverse saturation currents (A) nl, n2 = diode ideality factors R, = series resistance (n) & = parallel resistance (fl) T = absolute temperature (Kelvin) = elementary charge coastant (1 A02 x 1O-" q k = Boltzmann constant (I ,380 x JK)

V 1,

r-----r

Voltng. (V)

Fig, 3 IV curves for various temperature

C)

Fig. 1 Two-diode solar cell model Series resistance F& is the effect of the path that photo generated electrons have to uaverse a surface semiconductor

region to reach the nearest finger electrode. The value of R, can also further increase for a thin finger electrode. A small fraction of the photo-generated carrier can also flow through the crystal surfaces or through grain boundaries in polycrystalline devices instead of flowing though the external load. This leakage can be represented by an effective internal patallel resistance & [6]. Solar cell model parametem vary with environmental conditions with the two most important effects from temperature and the irradiance. Solar cell open-circuit voltage decreases with increasing tempemture, and the short circuit current is proportional to the amount of irradiance. The photo current is directly proportional to solar irradiance. The current vs. voltage curves (IV curves) for various irradiance and temperature we shown in Fig. 2 and Fig. 3, respectively. The equations showing modeling effects of irradiance and temperature on model parameters [5] are:

T = cell temperature Tref = cell reference temperature Eg = band gap energy of the semiconductor (V) n = diode ideality factors T = absolute temperature(Kelvin) = elementary charge conskut (1.602 x 10" C) q k = Boltzmann constant (1.380 x JK) KO = short-circuit temperature coefficient(A/K) K&= resistance temperature coefficients (lm)

111.

SOLAR ARRAY STRUCTCIRE

Solar cells are often connected together to form strings that produce a desirable voltage. In the string connection, the voltage is the sum of the device voltages and the s ~ n current g i s limited to the current of the least productive device in the string. Multiple strings are connected in parallel to form a panel. In practice, additiod diodes are included for protection, Bypass diodes are depicted with black-filling, whde gray-filled diode symbols represent blocking diodes. Diodes connected in series witb cells perfom a blocking function, preventing backflow of current back into the module string. When diodes are installed in parallel witb cells/modules, they perform a bypass function allowing current to pass around a shaded area of a module. The configuration, including physical layout, will have impact on the system performance [7][8]. Fig. 4 shows various solar cell interconnections. Fig. 4a and b have blocking diode on every string before the positive array terminal. Bypass diode is connected across every cell in Fig. 4% while across every 18 cells in Fig. 4b. Fig. 4c has the same electrical configuration as in Fig. 4b, but each string is arranged as 2 columns with 9 cells per column. When a portion of the panel is shaded, the shaded cells will not be able to produce as much current as the unshaded cells. Since all cells are connected in series, the same amount of current must flow through every cell. The unshaded cells will force the shaded cells to pass more current than their new short circuit current. The shaded cells operate in reverse-bias region and cause a net voltage loss to the system.The product of the current and the negative voltage gives the power dissipated by the shaded cells. In other words, the shaded cells will dissipate power as heat and cause “hot spots” [93. To minimize the shading effect on a single cell in a string, we use bypass diodes in the junction box. Bypass diodes allow current to pass around shaded cells and thereby reduce the voltage losses though the module. When a module becomes shaded its bypass diode becomes “forward biased” and begins to conduct current through itself. All the current greater than the shaded cell’s new short circuit current is “bypassed” through the diode, thus reducing drastically the amount of local heating at the shaded area. Diodes placed in series with cells or modules can perform the function of bloclung reverses current backwards through the modules; thus, preventing modules fiom becoming loads. In battery charging systems, the module potentia1 drops to zero at night, and the battery could discharge backwards through the module. Diodes placed in the circuit between the module and the battery can block any discharge flow. In case that one string becomes severely shaded, or if there is a short circuit in one of the modules, the blocking diode prevents the other strings from loosing current backwards down the shaded or damagsd string.

1 Fig. 4 Various solar cells interconnection a) Bypass diode across every cell, b) Bypass diode across a group of cells, c) Same as b) with different physical layout

Iv.

IMPLEMENTAITON

The implementation of the proposed tool is broadly consisted of four components. The first is an electrical configuration representing the interconnection of the elementary solar cells and protective diodes. Various models of photovoltaic devices and that of diodes can be applied to accommodate. different types of solar cells. The second component is the environmental condition that account for climatic-variation. These environmental conditions, such as short circuit curcent and temperature, can be incorporated into netlist as passing parameters to the solar cell elements via subcircuit parameterization. Circuit simuiator solves the array circuit network, then a script file finally extracts data. A pictorial representation of the automated process is shown in Fig. 5.

12

a selected electrical configuration composing of solar cell PSPICE's sub-circuit. Node name is automatically updated to represent the electrical connections between solar cells for such structure. One of the advantage for this implementation is the ability to create batches of simulations,so for example, the performance of the solar m y can be simulated with varying illumination as it varies throughout 8 day. An important aspect of this batch mode is that the resulting IV curves are automatically collected and analyzed, allowing large quantities of data to be handled with ease.

Cofiguration

v.

APPLICATION EXAMPLES

To demonstrate the proposed method, some applications examples are presented. Comparison of shading effect on Fig. 5 Implementation flow chart different panel configurationsare considered, namely 1) panel with bypass diode across every solar cells, and 2) with bypass PSPlCE's sub-circuit [IO] is used to model the individual diode across every Nb cells with the same physical layout. cell and allow variable input parameters to fine-tune the The physical layout considered is strings of vertically-aligned model. With the sub-circuit of a singlediode model solar cell solar cells wirh blocking diode at the output terminal of the shown in Fig. 6, short circuit current, saturation current and panel and top most cells as shown in Fig. 4.a and b with 54 ideality factor of the body diode, and equivalent series and rows by 72 columns dimension. Variation of various parallel resistances are variables. A call to the sub-circuit is parmeters can be represented by two-dimensional matrix, also shown. such as an image file. The dimension of the image N rows x R M columns corresponds to the physical layout of a s o h panel NIC 411 +" 68with NxM solar cells. Illumination of each image pixel provides a mapping to the amount of short circuit current, i.e. white area corresponds to full short circuit current, while darker area has less. For an 8-bit grayscale image, a pixel value of 255 can corresponds to irradiance that produces the full short circuit current. By anfogy, mapping of solar cells' I 1 K temperature by a two-dimension image is also possible. For example, a high pixel value can correspond to high temperature. For a partially shaded cell, the parameter value * * * * * Single diode solar cell model is assumed constant and is equal to the corresponding .SUBCKT CELLlD N+ N- PAWLMS: averaged value [12]. For instance, cell illumination is set to + Isc-4 Is-Dbodyl-le-14 N-Dbodyl-1 Rs-lu Rp-1G the average solar irradiance over the entire cell. In Fig. 7.a ISC NNIC DClIsCl and by a gradual shadow is casted across the diagonal and Dbodyl NIC NDbodyl .MODEL -Dbodyl D fs-{ls-Dbodyll N-iN-Db~dylJ along the vertical of the panel as represented with intensity RS NIC N+ IRs) levels shown. For simplicity, other parameters are kept RP NNIC (Rp) constant in this case. A variable load across each solar array .ENDS CELLlD configuration obtains I vs. V characteristic, and Power vs. Voltage is calculated and displayed. As it can be noticed, * Examplc of call to subcircuir X-sOl-cO1 N-sO1-cOOdO1 N-sol-col-02 CELLlD certain shading patterns produce local maxima in rhe power + PAw\NS: SSC-7.059E-001 I ~ - D b ~ d y l ~ l , O 0 0 E - 0 1 0 curve, and the proposed method provides a too1 to study the + N-DbOdyl*l.000E+O00 Rs-1.000E-003 Rp-5.000E+O03 severity of such shading effects. Fig. 6 PSPICE subcircuit model and schematic equivalent Even though, it is possible to assume that each celf in a The proposed method has been implemented using two module has the same semiconductor characteristic, another general-purpose soffware: a simulator to obtain electrical potential feature of the proposed method is that it allows measurements given varying environmental condition andor distribution of the parameters statistically to account for electrid structure, and a scriptor to update the netlist file manufacturing tolerances. As B result, all solar cells can be FIIJZ.CIR., start the simulator, read simulation results f" simulated together as a module, allowing the effects of cell the output file BILE.oUT, and perform data analysis. mismatching to be evaluated. MATLAB script file is developed to create PSPlCE netlist of ~

*I*+*

*t****t****tC**ft*l

13

Conference Record of the Twenty-Fifth IEEE, 13-17 May, pp.1287-

VI.

CONCLUSION Circuit model of a solar m y configuration is discussed in this paper, building up from model of individual solar cell. The proposed tool can be used to enhance a better understanding of the theory of operation of such non-linear device. Two general-purpose simulation programs are used for model analysis. MATLAB creaks script file consisting of the detailed circuit-model netlist correspond to axray structure, and passes it to PSPICE for simulation. Finally, MATLAB collects the result for analysis and visualization. The main advantage of the proposed method is that current-voltage characteristics can be generated efficiently for various array configurations from any solar cell model complexity, including semiconductor detail supported by the circuit simulator (PSPICE). Application examples show effect of array structure, namely the interconnection of solar cells and bypass diodes connection, on its operating characteristics. The proposed tool will be valuable to system integrator and scientist to investigate performance under environmental conditions, to plan the physical layout of array of solar panel, and to develop new design for solar module.

[I]

[2]

1290. lmnap [ Y R

I(

72CI

Iva. v

-”O

10

5

JI

2!i

15 Pw.V

35

I

REFERENCES N.D. Kaushiks and N.K. Gauwq “Energy yidd simulations of interconnected solar PV arrays,” IEEE Transactionr on Energy Conversion, Vol. 18, No. 1, Mar 2003,pp. 127- 134.

-1

0

5

1

0

1

5

2

0

2

5

3

3

3

5

A. Abetc, “Analysis of photovoltaic modules with protection diodes in presence of mismatching,” in Photovoltaic Specialists Conference, 1990, Conference Record of the Twenty F h t IEEE,21-25 May 1990, V01.2,

pp.1005 -1010. of the output characteristics 131 Slonim, M.A.; Shavit, D.S.,“Lin&on of a solar cell and its application for thc design and analysis o f solar cell arrays;’ Enasy Conversion Engmcering Conference, 1997. IECEC-97. Pmxedings of the 32nd Intcrsociety, v01.3,27 Jul-1 Aug 1997, pp.1934 -1938. [4]

V. Quasehning, R Hanitsch, ”Numerical simulation of currcnt voltage

charamriatics of photovoltaic systms with shaded solar celk.,‘‘ S o h Energy, V01.56,No.6, 1996, pp. 513-520. LA. Gow and C.D. Manning, "Development of a photovoltaic m y model for use in power+lmtronics simulation studies,” IEE Proceedings ojEIectric Power Appliatwns, Vol. 146, No. 2, March 1999, pp. 193 200. 161 E h q , S.O.Gpioelectronics and Phoronics, principles and Proctiees. htice-Hall, 2001. [7l V. Qua.sFhning R Piske, and R Hanitsch, “Cost Effedveness of

In. V

:

[5]

.......... ;......... ..........

i

.........

.........................................

SWow T o l m t Photovoltaic Sys!ms,”Euroslm’%,pp.819-824.

[SI V. Quaschning and R Hanitsch, "increased e n q y yield o f 500? at flat

?n.V

roof and field instaIlations with opdmized module structures,”’ 2nd Wodd Confcrcnce and Exhibition on Photovoltaic Solar Energy Conversion, Vienna, AuSeia, 6-10 July W E , pp. 1993- 1996. [9] W.Hrmnann, W. Wicmer, andW. Vassscn, “Hot spot investigationson PV modules-new concepts for a test standard and consequences for module design with respect to bypass diodes,” in Photovoltaic Spcialisu Conference, 1997, Conference Record of the Twenty-Sixth IEEE. 29 S+pt.-3 Oct. 1997,~p.1129-1 132. [lo] orcad PSPICE A I D - R e f ~ e n aGuide, 1999. 1111 A.K. Sbanna, R Jhivedi, S.K Srivamva, “Performance Analysis of a Solar h a y Under Shadow Condition:’ IEE Proceeding.-G, Vol 138, No. 3, June 1991. 1121 V. Quascbnmg and R Hanit&, “Muence of shading on electrical parameters of solar cclls,” in Photovoltaic S p i a l i s Conference, ~ 1996,

I

i i

I

d

35

Fig. 7 IV and PV curve of pattially shaded panel a) Diagonal shade b) Vdcal shade

14