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Under partially shaded conditions (PSC), a photovoltaic (PV) array takes on more complex characteristics. It is very difficult and utterly necessary for PV system designers to understand and predict them. Other than the prevailing methodology of solving a set of non-linear equations, the proposed methodology focuses on three key points of short circuit, MPP and open circuit. Besides, its V-I curve is split into three regions and replaced by three asymptote lines. From this viewpoint, this paper presents a novel Psim-based piece-wise linear macro-model whose circuit parameter values are determined based on the foregoing three key points. The novel model, compared with the other published models, is characterised by short running time, relative high accuracy, and reliable unique solution. This model avoids the computational complexity and convergence issue. Furthermore, based on the novel model, an optimising configuration-simulation model is presented for PV system designers to optimise PV array configurations under several given shaded patterns. Two new concepts of power and voltage reducing rate shall be introduced to estimate the PSC effect. The novel model and formulas, therefore, shall provide a good solution for studying the behavior of a large-scale PV array in a complex scenario.