GRG-Based Optimization of an Off-Grid PV/BESS/DGU Hybrid Power System for Remote Sites in Kazakhstan

Hybrid renewable energy systems are regarded as one of the most promising solutions for the autonomous power supply of remote and weakly electrified sites, where diesel generation remains a costly and carbon-intensive energy source. This study presents the optimization of an off-grid PV/BESS/DGU microgrid for three representative regions of Kazakhstan—North, Central/East, and South/South-West—under different environmental scenarios. The aim of the study was to determine the optimal installed photovoltaic capacity, battery storage capacity, diesel generator rated power, and annual load coverage balance using the Generalized Reduced Gradient (GRG) method. The optimization was carried out using two objective functions: the conventional levelized cost of electricity, LCOE, and the environmentally adjusted cost of electricity, LCOEenv, which includes the monetized cost of emissions associated with diesel generator operation. The model was formulated as a constrained nonlinear programming problem incorporating hourly energy balance, battery state-of-charge constraints, diesel generator operating constraints, and carbon price scenarios of 0, 25, 50, and 100 USD/tCO2. The results show that an increase in the carbon price systematically shifts the optimum toward a higher share of photovoltaic generation and reduced diesel generator use in all regions. The strongest response is observed in the South/South-West region, followed by Central/East, whereas the North exhibits the lowest sensitivity due to the more pronounced seasonality of solar generation. Under the considered scenarios, the optimal PV capacity increases by approximately 24–28%, while the share of diesel generation in annual load coverage decreases by approximately 28% in the North, 44% in Central/East, and 61% in the South/South-West. At the same time, the rated diesel generator capacity remains unchanged in most scenarios, indicating the persistence of its backup function. The results confirm that the PV/BESS/DGU configuration constitutes a technically and economically justified baseline architecture for autonomous power supply under Kazakhstan’s conditions, while the inclusion of environmental costs supports the cost-effective displacement of diesel generation. The GRG method proved to be suitable for the transparent and efficient optimization of hybrid microgrid parameters.