This paper presents a numerical model for thermal energy storage systems’ design, development, and feasibility. The energy storage was composed of a tank that stores phase change material (AlSi12) and internal pipes with heat transfer fluid (Cerrolow 117), coupled to a power block to dispatch electrical energy on a small scale for off-grid industrial applications. Subsequently, the evolution of the temperature in charge/discharge cycles, temperature degradation, and storage efficiency was determined with the appropriate magnitudes and behavior through the resolution of a numerical model. In addition, for the proposed electric power generation plant for an off-grid pumping system in the mining industry of Chile, a numerical model was developed using the finite volumes method to simulate the thermocline performance. As a result, the temperature history reflects stable thermal behavior, low degradation, and high efficiency of approximately 92%, with a storage time increasing up to 13 [h] and 384.8 [kWh] capacity. Also, implementation was feasible on a small scale due to its compact, modular, and economically competitive characteristics in a concentrated solar power plant. Finally, the proposed design was proven to be an accurate and reliable alternative for small-scale off-grid mining applications.