Differential modelling and simulation of solar power potential: a helio-application of biharmonic model

Modelling and simulation of solar power potential (SPP, Wm −2 ) is dominated by non-differential models, which are prone to truncation errors. However, this work focuses on presenting a more precise SPP model through a biharmonic differential model (BDM). The exact solution of the BDM ensures an accurate prediction of SPP in the study area (Uganda). This is possible by transforming the Mercatorian coordinates into Cartesian coordinates and establishing closed boundary conditions describing the SPP (Wm −2 ). Single- and multiple-order-exact solutions of the BDM are presented. The body validation of the simulated results is carried out using National Aeronautic and Space Administration (NASA) quadrennial SPP satellite data (1984–2019). The study is conducted on Regional and Non-regional basis to identify areas with high SPP values. Validation of the simulated SPP results indicates that multiple-order-exact solution is more accurate than the single-order-exact solution based on the mean square error (RMSE) analysis. The SPP (dense area km 2 , percentage area %) for the Non-regional, Northern Region, Eastern Region, Central Region and Western Region is as follows: 870 (170,817, 7.37), 831.4 (20,250, 23.71), 829.2 (10941.6, 27.71), 823.0 (2677.2, 4.36) and 798.0 (13,600, 0.73), respectively, were investigated. Therefore, it is clear that the BDM could be used to model SPP field data using the multiple-order-exact model solution. Thus, BDM produces a better result than non-differential models by eliminating truncation error in its solution. Therefore, for the purposes of estimating accurate information on the SPP, the BDM and its exact multiple-order solution should be applied.