ESTIMATION OF PV ARRAY POWER LOSSES DUE TO PARTIAL SHADING

Evagelia PARASKEVADAKI Stavros PAPATHANASSIOU NTUA, Electric Power Division - Greece

evaparas@mail.ntua.gr

ABSTRACT: One of the conditions that can be detrimental for PV system performance is partial shading. Several factors affect PV module and array performance under partial shading conditions. Main PV module electrical characteristics, expressed by equivalent electrical circuit models, have a significant impact on I-V curve formation. Low shunt resistance values can be detrimental to the performance of shaded modules and may cause irreversible cell damage if the module is not electrically protected. In this paper, the effect of various partial shading patterns on a study case PV array of 1 kW is examined. The analysis is performed for several shading levels. In addition, the effect of low shunt resistance combined with partial shading conditions is evaluated via simulation of shading scenarios on modules with various Rsh values.

1 INTRODUCTION

Photovoltaic systems are one of the leading technologies in the field of renewable energy sources. They are currently employed in various applications, from large PV plants to small residential systems, interconnected to the utility grid. PV energy is also utilized in stand - alone systems, combined or not with other energy sources. These systems can be a reliable source of energy, as one comes to understand the nature of their performance.

One of the main considerations when it comes to PV systems is the ability to track the maximum power available, for the given irradiance and temperature conditions. Multiple techniques performing Maximum Power Point Tracking (MPPT) have been developed over the last 20 years, reflecting the fact that the efficiency of a solar system depends greatly on the efficiency of the MPPT. Conditions that deteriorate MPPT efficiency should be avoided in order to extract maximum power at any given operating state.

One of the conditions that can be detrimental for PV system performance is partial shading of a PV module or array. In this case, the irradiance differs between PV cells or modules in the same string, resulting in a mismatch of PV module characteristics. The form of the resulting P-V curves of the string becomes then more complex, presenting multiple peaks, which renders the MPPT process ineffective. The power loss, when a local instead of the global maximum is tracked, can be significant, leading to the deterioration of the overall system performance.

Several factors affect PV module and array performance under partial shading conditions. The main PV module electrical characteristics, expressed by equivalent electrical circuit models, have a significant impact on I-V curve formation. More specifically, low shunt resistance values can be detrimental to the performance of shaded modules and may cause irreversible cell damage if the module is not electrically protected.

In order to improve the performance of a PV system under partial shading, conclusions must be drawn on the impact of shading on the PV array basic curves. In this paper, the effect of various partial shading patterns on a study case PV array of 1 kW is examined. The analysis is performed for several shading levels. In addition, the

effect of low shunt resistance combined with partial shading conditions is evaluated via simulation of shading scenarios on modules with various Rsh values.

2 PV ARRAY MODEL

Various models have been developed and utilized in order to study solar cell behavior. The most widely used are single and double diode models. It is reported that single diode models can not represent precisely the IV characteristic of a PV cell. Thus, in this paper, the behavior of each PV cell is modeled using the two-diode equivalent circuit, with the addition of an expansion term in order to describe solar cell operation at the negative voltage region, as developed in [1]. The conventional two diode model comprises two parallel-connected diodes in order to account for the two main physical phenomena inside the solar cell: diffusion (D1) and recombination (D2). The equivalent electrical circuit of the PV cell is presented in Fig. 1.

Figure 1: Equivalent electrical circuit of a PV cell based on the two–diode model.

Equations (1) – (5) describe the extended two-diode

model. Iph is the photocurrent, depending on the irradiance and temperature of the PV cell as per eq. (2). Saturation currents Is1 and Is2 correspond to the first (D1) and second diode (D2), with Is2 obtaining values larger than Is1. The first diode is assumed to be ideal, setting the ideality factor n1 to 1. The ideality factor n2 of the second diode is set to 2, which is a common value describing recombination effects due to impurity inside the solar cell.

−−−−Ι−=++

)1()1( 2121

TT VnIRsV

sVnIRsV

sph eIeII

n

br

ss

sh

s

VIRVIRVb

RIRV −+

−+−+

− )1)(( (1)

)( 21 TccEI ph += (2)

TVVgap

ss eTcI−

= 311 (3)

TVVgap

ss eTcI 22/522

−

= (4)

qkTVT /= (5)

Rs is the series resistance and Rsh is the shunt

resistance. c1 is the photocurrent coefficient that relates the amount of irradiance on the PV cell to the current generated by the equivalent current source. The dependence of Iph, Is1 and Is2 on cell temperature is accounted for, using coefficients c2, cs1 and cs2. The last term in Eq. (1) is related to the second current source of the equivalent PV cell circuit, accounting for the cell behaviour in reverse bias.

Table I: Datasheet characteristics of the simulated PV module and the corresponding array

Simulated Module Simulated Array

PMAX 165 990

IMPP 4.77 4.77

VMPP 34.6 207.6

Isc 5.31 5.31

Voc 43.1 258.6

Cells 72 72 Bypass Diodes 3 18

The model of a PV cell is implemented in Pspice. An

extended module and array model is created by connecting in series the individual cell circuits. Due to the cell-based array model, a detailed analysis is possible, setting parameter values for each cell independently and allowing for the simulation of various shading scenarios.

In this study, a multicrystalline silicon based PV module is assumed with main electrical characteristics as presented in Table I. Each module comprises three bypass diodes, forming corresponding cell groups,

defined as the number of cells protected by the same anti-parallel diode. Parameter values for the simulation model of each PV cell are shown in Table II.

3 EFFECT OF PARTIAL SHADING ON PV ARRAY OUTPUT POWER

The effects of partial shading on PV array maximum

power (PMAX) are examined by shading an increasing number of cell groups, gradually covering PV modules. Cell temperature is maintained at a constant value (25 oC). The shading case is homogeneous, meaning that all shaded cells are under the same illumination conditions. Irradiance on shaded cells (IRsh) is set to 30% and 70% of the irradiance incident on the non shaded module area, which is assumed to be 1000 W/m2.

The selected values of IRsh represent realistic conditions. As indicated in [2], if the shadow casting object is situated close to the PV array, the PV module is hit by the core shadow which reduces energy incident by approximately 60-80%. Hence, core shadow effect implies irradiance values in the range of 200-400 W/m2 for STC un-shaded irradiance. Partial shade is brighter than core shadow and develops when greater distances exist between the shadow casting object and the PV module. The reduction of energy incident on the PV module is about 30-40%. An irradiance value of 700 W/m2 for illumination of PV cells under partial shade is thus selected for the simulation.

Figure 2: Shading patterns examined, for various PV array configurations (a) Portrait and (b) Landscape

The first shading scenario refers to portrait module

arrangement. Simulations have been implemented for 1, 2 and 3 shaded rows of cells, counting from the bottom of the PV string, as shown in Fig. 2(a). The most significant impact on array output is caused by the irradiance on shaded cells. An increase in shaded area from 8% to 25%, causes only a slight decrease of 3% in output power (IRsh = 700W/m2), as illustrated in Fig.

PV cell c1 c2 cs1 cs2 n1 n2 Rs Rsh b Ubr n model

parameters (1) (2) (3) (4) - - mΩ Ω mS (V) -

Module A 2.24 1.85 210.4 18.1 1 2 13.5 20 2 -18 1.5 1. mV-1m2 2. μV-1K-1m2 3. AK-3 4. mAK-5/2

Table II: Selected PV cell model parameters

(a)

(b)

3(a). Results of partial shading on a landscape array configuration (Fig. 2(a)), with shading evolution discretized in cell group steps are presented in Fig. 3(b). Similar conclusions are drawn: doubling the shaded area from 1 to 2 cell groups (CGs), a decrease of only 4% in the second peak (P2 on the diagram) is detected (IRsh = 700W/m2). Ongoing, shading of one cell and of one module is analyzed (Fig. 4). When only one cell of the PV array is shaded (shaded area of 0,23%), a decrease of 6% in array output is observed. Detailed numerical results of P-V curve maxima, for the examined shading scenarios, are presented in Table III.

0 50 100 150 200 2500

200

400

600

800

1000

1200

1400

Voltage (V)

Pow

er (W

)

700W/m2, 1 shaded cell300W/m2, 1 shaded cell700W/m2, 1 shaded module300W/m2, 1 shaded module1000W/m2

150 200 250 300200

300

400

500

600

700

800

900

1000

Voltage (V)

Pow

er (W

)

1 shaded row2 shaded rows3 shaded rows

300 W/m2

700 W/m2

1000 W/m2

Figure 4: P-V curve for the shading cases of one cell and one module under shade.

4 SHUNT RESISTANCE EFFECT In cell based simulation models, it is assumed that the

current flow is homogeneous across the whole area of a PV cell. The shunt resistance, Rsh, represents parallel high-conductivity paths across the solar cell p-n junction or on the cell edges. Currents that are developed due to shunts have a detrimental effect on module performance, which is more obvious at low irradiance levels.

(a)

0 50 100 150 200 2500

200

400

600

800

1000

1200

1400

Voltage (V)

Pow

er (W

)

300W/m2, 2 shaded CGs700W/m2, 2 shaded CGs300W/m2, 1 shaded CG700W/m2, 1 shaded CG1000W/m2

P2

P1

0 50 100 150 200 2500

1

2

3

4

5

Voltage (V)

Cur

rent

(A)

Rsh=0.5 OhmRsh=2 OhmRsh=5 OhmRsh=10 OhmRsh=20 OhmRsh=40 OhmRsh=60 Ohm

(b)

(a) Figure 3: P-V curves for the case of partial shading on PV array with (a) portrait and (b) landscape arrangement

0 50 100 150 200 250 3000

100

200

300

400

500

600

700

800

900

1000

1100

Voltage (V)

Pow

er (W

)

Rsh=0.5OhmRsh=2OhmRsh=5OhmRsh=10OhmRsh=40OhmRsh=60OhmRsh=20Ohm

1000 W/m2

Several conclusions can be drawn from this analysis.

First, the effect of partial shading on PV array power output is not linearly related to shaded area or irradiance and in order to study it, all these factors should be taken into account. Second, open circuit voltage in all studied cases seems to decrease as partial shading becomes more severe, in terms of either the shaded surface or the irradiance level. Maximum power voltage on the other hand, presents an increase in the case of small shaded areas, which diminishes as shaded area increases. Last, the peak marked as P2 in Fig. 3(b) is most likely to be tracked by MPPT algorithms, as discussed in [3]. The case of only one shaded cell across the array does not cause the formation of a second local or global maximum.

700 W/m2

300 W/m2

(b)

Figure 5: (a) I-V and (b) P-V curves of the simulated array for various Rsh values

Module Configuration Shaded Area IRsh = 700 W/m2 IRsh = 300 W/m2

P1 P2 P1 P2 Rows (%) (W) (%) (W) (%) (W) (%) (W) (%)

1 8% 814,2 82,3% 376,7 38,1%

2 17% 795,5 80,4% 366,2 37,0%

Portrait

3 25% 786,2 79,5% 359,1 36,3%

Cell Groups % 1 33% 634,2 64,1% 775,4 78,4% 634,2 64,1% 351,4 35,5% Landscape

2 67% 276,3 27,9% 737,7 74,6% 276,3 27,9% 324,4 32,8%

One cell 0,23% 930,1 94,0% 930,1 94,0% Portrait / Landscape One module 17% 811,3 82,0% 794,3 80,3% 811,3 82,0% 364,3 36,8%

Table III: Numerical results for partial shading scenarios and corresponding array output

Rsh (Ohm) 1000 W/m2 700 W/m2 300 W/m2

0,5 810,2 -18,1% 521 -26,3% 131,9 -56,2%

2 948,4 -4,2% 663,9 -6,1% 258 -14,4%

5 975,7 -1,4% 692,6 -2,0% 286,8 -4,8%

10 984,9 -0,5% 702,2 -0,7% 296,4 -1,6%

20 989,5 0,0% 707 0,0% 301,3 0,0%

40 991,8 0,2% 709,2 0,3% 303,7 0,8%

60 992,8 0,3% 710,2 0,5% 304,5 1,1%

Table IV: Effect of Rsh deterioration on PV array performance

0 50 100 150 200 250 3000

100

200

300

400

500

600

700

800

Voltage (V)

Pow

er (W

)

700 W/m2

300 W/m2

Rsh = 0.5 Ω

Rsh = 60 Ω

0 50 100 150 200 250 3000

200

400

600

800

Vol

tage

(V)

700 W/m2

300 W/m2

0 50 100 150 200 250 3000

200

400

600

800

1000

Voltage (V)

Rsh = 60 Ω

Rsh = 0.5 Ω

Rsh = 0.5 Ω

Rsh = 60 Ω

Figure 6: P-V curves depicting the effect of Rsh on partially shaded PV array (a) PV module with integrated bypass diodes and shaded area of 33.3%, (b) PV module without bypass diodes and shaded area equal to 3%.

In Fig. 5, I-V and P-V curves of the same module are illustrated, varying only the value of shunt resistance from 0.5 to 60 Ω. Rsh values are equal for all cells. Numerical results, presented in Table IV, show that the performance deterioration with decreasing resistance values is more severe in the case of 300 W/m2, where a decrease up to 56% is detected with respect to power output for Rsh = 20 Ω. However, in absolute terms (W), the decrease in maximum power is the practically same, reg

d form hot spots which ma

ardless of the irradiance conditions. In partial shading conditions, the photogenerated

current of the shaded cells is reduced or eliminated. Depending on the severity of the shadow and array configuration, these cells can be reverse biased, thus forced to operate in the negative voltage range. Reverse characteristics of cells are strongly depended on the value of Rsh. It has been shown [4] that lower values of Rsh lead to higher slopes of the I-V curve in the negative voltage region, thus increasing power dissipation. Therefore, high currents flow through the shaded cells, that increase cell temperature an

(a)

y severely damage the cells. P-V curves for the case of landscape module

arrangement and shading of one cell group per module are presented in Fig. 6 (a) for various Rsh values. Irradiance on shaded cells acquires values of 300 W/m2 and 700 W/m2. The effect of decreased Rsh values on the slope of the second peak area is evident. For the case of 300 W/m2 on shaded cells and Rsh=0.5 Ω, a second peak is entirely missing. For partial shading of a PV array without bypass diodes, assuming the same irradiance but smaller shaded surface ratio, the P-V curves of Fig. 6(b) are derived. Reduced shunt resistance values seem to increase power output, with the effect being more marked at low irradiance levels. However, the fact

(b)

remains that in these cases the shaded cells are reverse biased and high currents flow through the shaded cells.

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pean PV-Hybrid and Mini-

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