SuDoKu Reconfiguration Technique

Categories: Energy Efficiency


Mismatch losses ignore the performance of individual photovoltaic (PV) modules and cut back most of the power from the PV array. These losses mainly due to partial shading condition (PSC), are caused by the reduction of spacing between PV modules, passing clouds, and near buildings, etc.

Several techniques are present in the literature to cut back the partial shading issues. One of the most effective methods is the reconfiguration techniques, namely reconfigure the location of PV modules in PV array so as to distribute partial shading effects and increase the maximum power output.

This paper proposes a SuDoKu reconfiguration pattern for 9X9 Total-Cross-Tied (TCT) PV array to enhance maximum power output under partial shading conditions. The main aim of this approach is to arrange the PV modules in TCT array according to the SuDoKu pattern without altering the electrical connections.

Further, the performance of the proposed pattern is evaluated with different existing PV array configurations by comparing the Global Maximum Power Point (GMPP), Mismatch Losses (ML), Fill Factor (FF) and Efficiency (η).

Based on the results of this paper, it is concluded that the proposed improved SuDoKu PV array arrangement enhances the global maximum power under all shading conditions.


In the recent years, the renewable energy sources (RES) become more popular and broadly replaced conventional energy sources. Examples of RES are the solar, the wind, the biomass and the geothermal energy sources.

Among all, solar energy is the most essential and prerequisite sustainable resource because of its ubiquity and abundance in nature.

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The energy from photovoltaic (PV) arrays, in addition to requiring little Maintenance, is fuel free and pollution free .Also, the PV energy is employed in several scenarios such as residential buildings, street lights, integration of power systems and rural areas.

The efficiency of PV modules is affected by various factors, but one of the most significant issues is partial shadings. Partial shading occurs if the PV modules are shaded in PV array by cause of flying birds, passing clouds and adjacent buildings, etc. Under PSCs, the amount of irradiance received by the shaded module is smaller than that Pruthvi H R [1], Laxmana C [2] received by the unshaded module.

Since the shaded PV module limit the output current of an array, the entire PV system is affected by mismatch losses that might cause the damage to the PV cells or modules. One of the ways to protect the shaded PV modules from the damage is by connecting bypass diodes across the terminals. Insertion of bypass diodes causes multiple steps in I-V and multiple peaks in P-V characteristics of the PV array.

Among the multiple peaks, there is only one global peak (GP) which produces the highest maximum power, which is also known as Global Maximum Power Point (GMPP) and rest of all Local Maximum Power Points (LMPPs).The existence of multiple peaks may mislead the maximum power point tracking (MPPT) technique by tracking the LMPPs instead of GMPP; this would add extra power loss to the PV system.

The power loss as a result of partial shading is dictated by the chosen array configuration, shading pattern and physical location of PV modules in the PV array. However, the effect of PV array configuration shows a severe impact on maximum power output. Therefore, choosing the right configuration is necessary under PSCs.

Literature Survey

The Competence square based PV array reconfiguration technique to reduce the partial shading condition. They considered several types of shading. From the results, it is observed that the proposed method is better compared to DS and TCT’s mismatch power loss and percentage power enhancement. CST has proved its excellence in achieving smoother output characteristics, improving fill factor and improving power and energy [1].The cross diagonal view configuration of a PV system to reduce partial shading condition. They considered several types of shadings. In CDV matrix sum of each rows, each columns and each diagonals are equal.

From the results, it is observed that the proposed method is better with compared to CST method where power loss will be less and efficiency is more comparatively [2]. A simple, sensor less and fixed reconfiguration scheme for maximum power enhancement in PV systems. They used several types of shadings.


An implemented SuDoKu 9×9 puzzle and pattern arrangement is a logic-based number placement puzzle. It consists of nine 3×3 sub-array matrices. The formation of this logic puzzle is based on the Backtracking method. Backtracking is an algorithm for finding solutions to some computational problems ,notably constraints satisfaction problems.

The constraint of this problem is to place the digits 1 to 9 in 9×9 array so that each row, each column, each 3x3sub array and diagonal contains the same number only once. The proposed algorithm works as follows. Chose the partially filled 9×9 array. Try to fill each unsigned cell with the digits from 1to 9. If the assigned digits satisfied the condition, then try to fill each unsigned cell by performing recursive checking until build the solution. Otherwise backtracking algorithm takes place to exchange the assigned cell.

Fill factor (%)=(Power of GMPP)/(Voc*Isc) M L(%)=(MPPuni-GMPPpsc)/(GMPPpsc) Efficiency(%)=(Power at GMPP)/(Pin) CONCLUSION: This paper proposes on SuDoKu arrangement for TCT PV array to increase maximum power output under partial shading condition. Here four important shading conditions are considered.

They are short and wide, long and wide, short and narrow and long and narrow. In each condition, the location of GMPP is calculated and validated by using MATLAB/SIMULINK. From the results obtained, it is clearly observed that the SuDoKu arrangement enhances the global maximum power, reduces the mismatch losses and gives better efficiency and fill factor as compared to CST, CDT, Sensor less and TCT methods. Moreover, the proposed arrangement defeated the multiple peaks under most shading conditions.


  1.  B. Dhanalaksmi, N. Rajasekar. A novel Competence square based PV array reconfiguration technique for solar PV maximum power extraction.
  2. IEEE journal paper, Energy conversion and Management 174(2018)897-912.
  3. M. John Bosco, M.Carolin Mabel. A novel cross diagonal view configuration of a PV system under partial shading condition.
  4. IEEE journal paper, solar Energy 158(2017)760-773.
  5. Dhanup S. Pillai, J. Prasanth Ram, and others. A simple, sensor less and fixed reconfiguration scheme for maximum power enhancement in PV systems.
  6. IEEE journal paper, Energy conversion and Management172 (2018)402-417.

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SuDoKu Reconfiguration Technique. (2021, Oct 31). Retrieved from

SuDoKu Reconfiguration Technique
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