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CHAPTER 3

PERFORMANCE ANALYSIS OF BASIC SPV ARRAY

CONFIGURATIONS UNDER PARTIAL SHADED

CONDITIONS

3.1 INTRODUCTION

A number of series/parallel connected SPV modules are used to

form a solar array for a desired voltage and current level. The major challenge

in using a SPV source containing a number of cells in series is to deal with its

non-linear internal resistance. The problem gets all the more complex when

the array receives non-uniform irradiance (partially shading). In a solar array

spread over vast area, it is likely that shadow may fall over some of its cells

due to tree leaves falling over it, birds or bird litters on the array, shade of a

neighboring construction etc. In a series connected string of cells, all the cells

carry the same current. Even though a few cells under shade produce less

photon current but these cells are also forced to carry the same current as the

other fully illuminated cells. The shaded cells may get reverse biased, acting

as loads, draining power from fully illuminated cells. If the system is not

appropriately protected, hot-spot problem (Quaschning and Hanitsch 1996)

can arise and in several cases, the system can be irreversibly damaged.

Nowadays there is an increasing trend to integrate the SPV arrays at the

design level in the building itself. In such cases it is difficult to avoid partial

shading of array due to neighboring buildings throughout the day in all the

seasons. In conventional SPV systems, those shadows lower the overall

generation power to a large degree. Hence the SPV installation cost is

increased, because the number of SPV modules must be increased, and as a

45

result, SPV power generation will be less attractive. This makes the study of

partial shading of modules a key issue. Moreover it is very important to

understand the characteristics of SPV under partial shaded conditions to use

SPV installations effectively under all conditions.

In recent years, the impact of partial shading on the SPV array

performance has been widely discussed (Herrmann et al 1997, Kaushika and

Gautam 2003, Klenk et al 2002, Woyte et al 2003). With a physical SPV

module it is difficult to study the effects of partial shading since the field

testing is costly, time consuming and depends heavily on the prevailing

weather condition. Moreover it is difficult to maintain the same shade under

varying numbers of shaded and fully illuminated cells throughout the

experiment. However it is convenient to carryout the simulation study with

the help of a computer model. In most of the studies (Rauschenbach 1971,

Alonso-Garcia et al 2006 b, Alonso-Garcia 2006 c, Karatepe et al 2007), the

effect of partial shading in reducing the output power of the solar PV array

has been discussed. But a little attention has been given as to how the power

dissipated by the shaded cells is affecting the array life and utilization of the

array for the worst shaded case. The work presented in this chapter is mainly

concentrated to study the harmful effects of the shading patterns in basic

configurations, that is, series and parallel connected modules. The comparison

is made between these two connections. For other configuration types, a

generalized MATLAB programs have been developed which are capable of

simulating any number of modules connected in series or parallel and any

type of shading pattern.

3.2 BASIC CONNECTION METHODS OF SPVA AND

ASSOCIATED PROBLEMS

As with the connection of cells to form modules, a number of

modules can be connected in series string to increase the voltage level, in

46

parallel to increase the current level or in a combination of the two. The exact

configuration depends on the current and voltage requirements of the load.

Matching of the interconnected modules in respect of their outputs can

maximize the efficiency of the array. The conventional SPV module is

constructed of several SPV cells (normally 36 cells) connected in series. In

the SPV power generation system, multiple SPV modules are generally

connected in series in order to obtain sufficient dc voltage. If there is one

shaded module in a series connected array, it can then act as a load to the

array. It may cause damage to the module due to the heavy current passing

through it. To prevent this damage, bypass diodes are connected in anti

parallel with each module, and, in case of the module is shaded; the current

may flow through the bypass diode rather than through the module. In series

connected array, even the slightest shadow falling on a SPV module causes a

significant drop in generated power (Shimizu et al 2001).

In parallel connected modules, if one module is severely shaded, or

if there is a short circuit in one of the module, the blocking diode prevents the

other strings from sending current backwards down the shaded or damaged

string. Diodes placed in series with modules can perform the function of

blocking currents from flowing back to the modules thus preventing the

modules from becoming loads. When the non shaded SPV modules and the

shaded SPV modules are connected in parallel, the generation voltage is fixed

for each SPV module and is uniform throughout the entire SPV generation

system, and the current generated from each SPV module flows without

restriction. In other words, the output voltage of the SPV system becomes the

voltage of a single module, and the output current becomes the sum of the

currents in each module. In contrast, when each PV module is connected in

series, the same current flows through each module and the output voltage

becomes the sum of the voltages across each of the modules. However, the

voltage of each module is decided according to the generation current, which

depends on the generation/shaded conditions. Therefore, the optimal

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generation voltages are not always obtained for each SPV module. In

particular, when some of the SPV modules do not have sufficient generation

current, the voltage of the SPV modules is greatly decreased and the resultant

generation power is also greatly decreased. The performance analysis for

series and parallel connected SPV modules is analyzed in the following

sections through consideration of the operating point.

3.3 OPERATION OF PARALLEL CONNECTED SPV

MODULES

The model developed in chapter 2 is used to simulate the parallel

and series connected modules. The simulation is carried out using MATLAB

software (M-file). Parameters like number of cells in series, parallel,

illumination and temperature are set as input to the software model. To

illustrate the performance of parallel connected modules three modules are

connected in parallel as shown in Figure 3.1. Each module consists of 36 cells

in series. The maximum power expected under uniform insolation condition is

111 Watts.

Figure 3.2 shows the characteristics of SPVA consisting of three

parallel connected modules where each module receives different

illumination. For example Module-1 receives 100% illumination, Module-2

receives 75% illumination and Module-3 receives 25% illumination. While

doing experiments, the panels are mounted on a tilting stand. The illumination

is considered as proportional to the short circuit current. A panel is tilted till

its short circuit current becomes the maximum. This panel is considered as

receiving 100% insolation. The panel to receive 25% insolation is tilted till its

short circuit current is equal to 25% of that of the panel receiving 100%

insolation. As the output current of the system increases from zero to short

circuit current, the operating point of each panel moves. The characteristics

reveal that both the shaded and non shaded modules can operate in the area

where each module can contribute power. So, the total output power

characteristics of these modules are obtained as shown in Figure 3.2. The total

output power is given by Equation (3.1).

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out3out2out1total PPPP (3.1)

If the voltage of all the three modules is equal at the maximum

power point, then the total maximum power is given by Equation (3.2)

max3max2max1maxtotal PPPP (3.2)

Figure 3.1 Parallel Connected SPVA with blocking diodes

Figure 3.2 Characteristics of three parallel connected modules under

partial shading

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3.4 OPERATION OF SERIES CONNECTED SPV MODULES

Figure 3.3 shows the connection diagram of three modules

connected in series.

Figure 3.3 Series Connected SPVA with bypass diodes

Figure 3.4 shows the characteristics of SPVA consisting of three

series connected modules where each module receives different illumination.

The same type of shaded condition (100%, 75% and 25%) as in case of

parallel connected modules has been considered. The effect of shading in

series connected modules is explained with the help of Figure 3.3. Diodes Db1,

Db2 and Db3 are bypass diodes.

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3.4.1 Performance without bypass diodes

In the first case let us consider that the bypass diodes are absent.

Let the irradiance on the first module be 100%, on the second module be 75%

and on the third module be 25%. It means Iph1>Iph2>Iph3. Now if the current IPV

through RL is lower than Iph3 then ID3=Iph3-IPV, ID2=Iph2-IPV and ID1=Iph1-IPV.

Now let IPV>Iph3 but IPV<Iph2 and IPV<Iph1 then, ID3 will tend to become IPV-Iph3

in the reverse direction. Reverse biased diode D3 will offer a high resistance

and it will significantly reduce the load current IPV itself. The point M will go

positive with respect to the point L and this voltage will become high, if

difference in irradiance levels is high, the diode D3 may get damaged due to

excessive heating.

3.4.2 Performance with bypass diodes

Now if the bypass diodes are present then the reverse current IPV-

Iph3 will flow through the bypass diode Db3 and the module will be saved from

the damage. A portion of power from highly illuminated modules, instead of

getting wasted in low illuminated modules will be available to the load. Low

illuminated modules however make no contribution to the load power as these

are short circuited by the bypass diodes. Electrical characteristics of the

SPVA having three SPV modules in series with different illumination with

bypass diode are shown in Figure 3.4.

In series connection, array characteristics can be obtained by

adding the voltage of each module at every current. In case the array current

exceed the short circuit current of a particular module, the voltage of that

module will be -0.7 V (the forward cut-in voltage of the bypass diode). I-V

characteristics of the array for three non-uniformly illuminated series

connected modules plotted in this manner is illustrated in Figure 3.4.a. P-V

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characteristic of this array derived from I-V characteristic of Figure 3.4.a is

shown in Figure 3.4.b.

a. I-V characteristics b. P-V characteristics

Figure 3.4 Characteristics of three series connected panels under

partial shading

3.5 COMPARISON OF SERIES AND PARALLEL CONNECTED

MODULES

The SPV array is formed by either series or parallel combination.

To find which configuration is less affected under partial shaded conditions,

the comparative study is required. In this section a comparison is made

between series and parallel connected modules.

Photon current directly depends upon the insolation. Band gap and

therefore the cell voltage vary slightly with change in temperature. Change in

insolation causes drastic change in cell current and has comparatively less

effect on the cell voltage. But temperature affects the voltage. (Reference

Figure 2.16 and Figure 2.17). In case of non-uniformly illuminated series

array, voltage across the modules is different whereas current through each

module is the same. In parallel connected array all the modules have the same

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voltage but the currents are different. This difference between series and

parallel connection has a great bearing on the utilization of series and parallel

arrays under partial shaded conditions. This is illustrated with the help of

Figures from 3.5 to 3.8. Figure 3.5 shows P-I characteristics of series array

consists of six modules receiving 9 different insolation patterns shown in

Table 3.1 (page no. 55) As the current in series array is the same through all

the modules, the current line corresponds to maximum power is taken as

reference for finding the percentage of contribution of individual modules to

produce maximum power and also their utilization for the same. From Figure

3.5, utilization of individual modules in series array is very poor. This is

illustrated in Figure 3.6 for different shading patterns. At every current, the

power produced by the individual modules is added to get the array power.

For low illuminated modules, some intersection points are lying on negative

power axis which indicates the power loss due to shading. If bypass diodes

are used, this is terminated in zero axes, which are preventing power loss.

For comparison purpose the same set of shading patterns (Table

3.1) are considered for parallel array of the six modules. In this case, voltage

line corresponds to maximum power is taken as reference and illustrated in

Figure 3.7. From this figure, it is understood that in parallel array all the

modules are contributing to produce maximum power and utilization of the

individual module is far better than that of series array. This is illustrated in

Figure 3.8. For the same reason, the power produced by parallel array is

higher than the series array. For Figure 3.6 and Figure 3.8, utilization of the

module is defined as a ratio of power delivered by the module in the array to

the maximum power developed by the module when used in isolation.

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Figure 3.5 Characteristics of series connected array with individual

module characteristics for a single shadow pattern ‘A’ in

Table 3.1

Figure 3.6 Utilization of individual modules in series array under

different shading patterns

54

Figure 3.7 Characteristics of parallel connected array with individual

module characteristics for a single shadow pattern ‘A’ in

Table 3.1

Figure 3.8 Utilization of individual modules in parallel array under

different shading patterns

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Table 3.1 Shading patterns

Insolation Levels (W/m2)Shading

Pattern G1 G2 G3 G4 G5 G6

A 1000 800 700 600 500 300

B 1000 1000 1000 800 800 800

C 1000 1000 800 500 300 200

D 1000 1000 1000 500 200 200

E 1000 1000 1000 1000 200 200

F 1000 1000 500 200 200 200

G 1000 800 700 600 500 300

H 1000 1000 800 200 200 200

I 200 200 200 200 200 200

Utilization of the modules for other shading patterns for series and

parallel arrays have been computed and numerically presented in Table 3.2.

Table 3.2 Utilization factor for series and parallel array for the

shading patterns in Table 3.1

Utilization factor

Series array

Module number

Parallel array

Module number

Shading

Pattern

1 2 3 4 5 6 1 2 3 4 5 6

A 0.64 0.78 0.87 0.96 0.93 0 0.99 1 0.99 1 0.99 0.99

B 0.92 0.92 0.92 0.99 0.99 0.99 0.99 0.99 0.99 1 1 1

C 0.93 0.93 0.97 0 0 0 0.99 0.99 0.99 1 0.99 0.99

D 0 0.77 0.77 0.96 0.95 0 0.99 0.99 0.99 1 1 0.99

E 0.87 0.87 0 0.64 0.96 0.93 1 1 0.99 1 1 1

F 0.99 0.99 0.99 0 0 0 1 1 1 1 0.99 0.99

G 0.93 0 0.97 0.93 0 0 0.99 0.99 0.99 0.99 0.99 0.99

H 1 1 0 0 0 0 0.99 0.99 0.99 0.99 0.99 0.99

I 0.26 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99

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The characteristics of series and parallel connected SPVA under

different shaded conditions with MPP are simulated using the MATLAB M-

file (Appendix A1.5) and presented in Figure 3.9 considering Figure 3.1 and

Figure 3.3. Let us take the full illumination condition as G = 1 and G1, G2 and

G3 be illumination levels of module-1, module-2 and module-3 respectively.

Let T1, T2 and T3 be the temperature of module-1, module-2 and module-3

respectively.

Figure 3.9 Characteristics of SPVA under different shading and

different temperature conditions

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From Figure 3.9, it is clear that for different irradiance and

temperature conditions, Parallel connected SPVA produces highest power

under all shaded conditions.

For different irradiance and temperature conditions, the output of

series and parallel configurations are observed using the proposed plotter

(Figure 2.14) in the DSO screen. The shading effect is artificially generated

by tilting the panels at different angles. The readings are used to compare the

practical characteristics with simulation output. A typical snap shot of DSO

screen for a particular shading pattern using this plotter is shown in Figure

3.10 for parallel array and Figure 3.11 for series array.

Figure 3.10 Snap shot of DSO screen for parallel array

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Figure 3.11 Snap shot of DSO screen for series array

3.6 CONCLUSION

Series connection of solar cells in an array is essential to get

practically utilisable voltage. From the results and inferences from Section

3.3, it is concluded that there is a substantial power loss due to non uniform

illumination of a series string. The power generated by highly illuminated

cells is wasted as a heat in the poorly illuminated cells. So care should be

taken to see that all the cells connected in series receive the same illumination

under different patterns of shading. Such a care will give a better protection to

the array and at the same time the total energy output will also be higher. A

number of such strings are connected in parallel to get the requisite power. In

this chapter, the series connected and parallel connected SPVA is compared

under different shaded conditions. Use of bypass diodes/blocking diodes can

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save the poorly illuminated panels from damage and also make this energy

available to the load. It is found that parallel connected SPVA is dominant

under shaded condition. Each strings connected in parallel should have the

same number of cells connected in series and at the same time equally

illuminated cells should be in series. This condition is difficult to realize in

field. Therefore, series-parallel hybrids known as derived configurations have

been considered and presented in the next chapter.