The study applies the equilibrium optimizer (EO) and the secretary bird optimization algorithm (SBOA) to minimize the total electricity generation fossil fuel costs of thermal power plants (ThPPs) in hybrid power systems with solar photovoltaic power plants (SoPPs) and pumped storage hydropower plants (PuHPs) for one operating day. Two systems are employed: System 1 has two ThPPs and one SoPP, and System 2 is expanded by integrating one more PuHP into System 1. The generation of the SoPP is calculated using solar radiation from a specific location in Vietnam; meanwhile, the generation of ThPPs and the pumping power and generation of the PuHP are optimally determined by EO and SBOA. The pumping power and generation of the PuHP are supposed to be continuous. System 2 is run for two cases: Case 1- no running pumps, and Case 2- running pumps. As a result, EO can reach smaller costs than SBOA for the two systems. System 1 costs the most, $9,155,384, whereas Case 2 of System 2 costs the least, $9,006,450. System 2 can reach a smaller cost than System 1 by $148,934, about 1.63%. For System 2, the total cost of Case 2 is smaller than that of Case 1 by $81,025 per day, about 0.9%. The results indicate that the optimal operation of pumps in PuHPs can contribute to a high-cost reduction for ThPPs in hybrid power systems.