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Partial shading of a photovoltaic array is the condition under which different modules in the array experience different irradiance levels due to shading. This difference causes mismatch between the modules, leading to undesirable effects such as reduction in generated power and hot spots. The severity of these effects can be considerably reduced by photovoltaic array reconfiguration. This paper proposes a novel mathematical formulation for the optimal reconfiguration of photovoltaic arrays to minimize partial shading losses. The paper formulates the reconfiguration problem as a mixed integer quadratic programming problem and finds the optimal solution using a branch and bound algorithm. The proposed formulation can be used for an equal or nonequal number of modules per row. Moreover, it can be used for fully reconfigurable or partially reconfigurable arrays. The improvement resulting from the reconfiguration with respect to the existing photovoltaic interconnections is demonstrated by extensive simulation results.