(a) (b) Figure 5.1: (a) TCT and (b) Futoshiki configuration of a PV array.
Using Kirchhoff’s voltage law, the voltage of the array is calculated using the following equation:
V =
5
X
x=1
Vmx (5.2)
whereVmx is the voltage of the xthrow of a PV array.
Figure 5.2:Futoshiki arrangement of a 5×5 grid.
5.2.3 Futoshiki configuration of a PV array
Futoshiki is a logic based puzzle for a n ×n square grid. In this puzzle, the number 1 to n is placed in such a way that, each row and column of a square grid contains the digit 1 to n without repeating any number. During the placement of the digits in the square grid, the digit must respect
5.2 Description of Different PV Array Configuration
Table 5.2: Different configuration of a 5×5 PV array (a) TCT
11 12 13 14 15 21 22 23 24 25 31 32 33 34 35 41 42 43 44 45 51 52 53 54 55
(b) Futoshiki 11 42 33 54 25 21 52 43 34 15 31 22 53 14 45 51 12 23 44 35 41 32 13 24 55
the initially specified inequality constraint between two adjacent numbers, and hence the puzzle has a unique solution. Linear programming approach (LPA) is used to generate the proper logic Futoshiki puzzle, which always contains a unique solution [109]. A Futoshiki puzzle pattern of a 5×5 PV array is shown in Figure 5.2. In this pattern, the row position of a 5×5 PV array is arranged using the digits 1 to 5, as shown in Table 5.2(b), and this arrangement shows that there is no repetition of digits 1 to 5 in each row and each column of a PV array. During PSC, the shaded modules in a PV array will be dispersed in such a way that, for any Futoshiki puzzle patterns, the low current in the row and the output voltage of an array will remain the same. Therefore, the output power, i.e., the product of low current and output voltage, will remain the same. Therefore, in the present analysis, a particular Futoshiki puzzle pattern has been chosen. The modules of a PV array in TCT configuration (Figure 5.1(a)), are rearranged using the Futoshiki configuration technique, without changing the electrical connection of the modules under PSC, as shown in Figure 5.1(b). In this arrangement, the module 42 (fourth row, second column) is physically placed on the first row second column, and the module 15 is physically placed on the second row fifth column of a PV array without changing the electrical connections. The modules of the same row in the TCT configuration are moved to different rows in the proposed configuration of the array without changing the column position. Thus, it enables to decrease the shading effect in the same row and to enhance the current in the same row. Hence, bypass panels are reduced, and the power generated by a PV array is increased under PSC. The voltage and current equations of the proposed configuration remain same as in the TCT configuration, because the electrical connection of a PV array is unchanged.
The shading effect is distributed in both the EAR and the proposed method. However, the practical implementation of reconfiguration method requires a number of sensors, switches, and a control algo- TH-1895_11610232
rithm, because the electrical connection of the modules is changed dynamically according to shading conditions. However, the practical implementation of the proposed method does not require sensors, switches, and a control algorithm, because the electrical connection of the PV modules remains fixed.
For the practical implementation of the Futoshiki configuration for the enhancement of the power generation in shading condition, the modules of a PV array in TCT configuration need to be rear- ranged once only, because of the same configuration holds effective for any shading condition. This rearrangement of the modules is carried out only once by the PV plant installer at the time of instal- lation. As an illustration of the proposed method, a 1 MW, 750 V, 25×160 PV array which can be integrated with the microgrid or the distribution network is constructed by assembling 160 numbers of 6.25 kW, 150 V, 5×5 sub-array arranged using the proposed method. Hence, this large PV system is viewed as a 5× 32 array, as shown in Figure 5.3. At the time of installation, the modules of all sub-array, i.e., 5×5 PV array, are rearranged using the proposed technique. Whenever shading occurs in a 25×160 PV array, the shade is dispersed in the sub-array which ensures the enhancement of the power generation. Therefore, the proposed technique can be applied for large square or rectangular PV array for the enhancement of the power generation compared with the TCT configuration during shading condition.
Table 5.3: Solar irradiation on hourly basis during sunshine hours
Sunshine 5 6 7 8 9 10 11 12 13 14 15 16 17 18
hours
USI (W/m2) 40 150 250 400 560 700 800 900 800 650 450 250 100 10 SSI (W/m2) 16 60 100 160 224 280 320 360 320 260 180 100 40 4
For the validation of power enhancement of a PV array in the proposed configuration with respect to the TCT configuration in a real time scenario, the monthly averaged daily on an hourly basis solar irradiation during the sunshine time in hours (5 to 18 h) in the month of May-2012 of Guwahati city as shown in Table 5.3, is considered. Matlab platform is used for different intensity of shading modules of a PV array, and the effect of power generation of a PV array is demonstrated. Assuming some of the modules of a PV array receive 40% of unshaded solar irradiation (USI) (i.e., shaded solar irradiation (SSI)) in the presence of neighborhood obstacle, the shaded modules for each hour from 9
5.2 Description of Different PV Array Configuration
Figure 5.3:A 1 MW, 750 V 25×160 large PV array assembled by a 6.25 kW, 150 V 5×5 sub-array arranged by the proposed method.
to 15 h is represented by different symbols, as shown in Figure 5.4.
Figure 5.4:PSC occur on a 5×5 PV array an hourly basis during sunshine hours.
TH-1895_11610232
4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 0
10 20 30 40 50
Time (h)
Power (W)
TCT Futoshiki
Figure 5.5:Power versus sunshine hours of a PV array.
From Figure 5.5, it is seen that there is a significant power enhancement in the proposed configu- ration with respect to the TCT configuration of a PV array under different types of shading conditions from 9 to 15 h. Therefore, in this work, four different standard shading conditions, such as SW, LW, SN, and LN [1] are taken for the estimation of power output of a PV array by using the proposed method, as shown in Figure 1.11.