In this paper, a novel framework for optimal sizing of a grid-connected photovoltaic (PV)/battery system is presented to minimize the total net present cost using a novel optimization algorithm based on the teaching and learning process, namely Teaching-Learning-Based Optimization (TLBO). The TLBO algorithm is an efficient optimization method based on the teacher's influence on the learners' output in a class. This article shows how backup PV/battery systems can reduce electricity bills, even in countries where their electricity is cheap and subsidized. In comparison to the non-renewable case, the net present cost (NPC) and the cost of energy (COE) of the on-grid PV/battery system are 15.6% and 16.8% more efficient, respectively. The NPC and COE factors were calculated and compared with two other popular optimization algorithms, particle swarm optimization, and genetic algorithm to validate the proposed approach and to ascertain the strength and accuracy of the TLBO algorithm. To compare the results, different cities were examined and the similarity of the results showed that the system is efficient regardless of the surrounding climate. Also, sensitivity analyses on different cities' climatic data, different load demands and PV prices outlined the economic optimal size of the system.