Recently, the photovoltaic (PV) parameter extraction using the fitting process between the measured current-voltage (I-V) curve and the single-diode-model (SDM) is recognised as a non-convex optimization problem with multiple local minima. Due to this nature, the direct use of the deterministic methods is not found suitable for the global optimum solution. However, the global optimum solution is only possible when the SDM is used with reduced-dimensions search. Standing opposite to this concept, the present work claims to have global optimum solution without reduced-dimensions search in the SDM. In order to prove this claim, a per-unit-single-diode-model parameter extraction algorithm (PUSDM-PEA) is developed which establishes a nonlinear least-squared-fitting between the measured I-V curve and the PUSDM. Through multiple tests on various cells and modules, commonly employed in the PV literature, the findings show that the convergence to the global optimum is always guaranteed if initial ideality factor n e [0.5, 2.5]. In addition, the computation cost is highly influenced by the initial n selection, and there exists a single or a couple of initial n values with the minimum computation cost. Only I-V curve as an input without any additional PV module information, the high-quality PV solution is obtained for the full and partial I-V curves with the minimum computation cost.