Unconstrained model and merge sorted serpentine arrangement method for dynamic reconfiguration of large PV arrays

Abstract

• An unconstrained optimization model, and a heuristic method namely, Merge Sorted Serpentine Arrangement, are proposed for modelling and solving the problem of finding the optimal reconfiguration of a photovoltaic array to minimize partial shading losses. • The proposed unconstrained optimization model formulation enables the application of different meta-heuristic and heuristic optimization algorithms for solving the problem of finding the optimal reconfiguration of a photovoltaic array to minimize partial shading losses. • Extensive case studies show that the proposed method reduces average computation time by up to 80 % when compared with other methods. • The proposed method consistently reduces partial shading losses by up to 11 % under dynamic and static partial shading conditions due to its lower computation time as demonstrated by extensive case studies. • The main drawback of the proposed method is that it increases memory requirements by up 100 % when compared with other methods. The problem of finding the optimal interconnection between photovoltaic modules in a dynamic photovoltaic array to minimize partial shading losses is a Non-deterministic Polynomial time-hard (i.e., NP-hard) problem. Therefore, no known deterministic method can solve the problem in polynomial time. However, meta-heuristic and heuristic methods can provide solutions to this problem. In this paper, an unconstrained optimization model and a heuristic method, namely, Merge Sorted Serpentine Arrangement (MSA), are proposed for the first time for modelling and solving the problem. In the proposed method, the irradiance levels of the PV modules are accurately estimated using the double diode model and then sorted according to the merge sorting algorithm. After that, the PV modules are arranged in the PV array according to their sorted irradiance levels in a serpentine way using the proposed switching matrix. The proposed method has consistently resulted in lower computational time and partial shading losses when compared with the other methods in the literature, due to the application of the Merge Sorting Algorithm, which has an average time complexity of O (n log(n)). However, the proposed method has resulted in increased memory, switches, and sensor requirements when compared with some of the other methods in the literature.