<p>This paper presents a unified framework for estimating the parameters of equivalent circuits of solar photovoltaic (PV) cells and induction machines. The framework is based on a novel metaheuristic algorithm that relies on the hybridization of the Simulated Annealing (SA) and Equilibrium Optimizer (EO) algorithms, referred to as SA-EO, proposed in this work, which integrates the advantages of local exploitation and global exploration to enhance convergence and accuracy. According to the available literature, solar PV cells can be represented using single-, double- and, most accurately, triple-diode equivalent circuits. In a similar way, an induction machine (IM) can be modeled using single- and double-cage equivalent circuits. The estimation of parameters for both solar PV cells and IMs can be performed using either the manufacturer’s data or experimentally recorded measurements. In both cases, the parameters are typically extracted using analytical, numerical, or metaheuristic optimization techniques. Based on the analogy between multi-diode models of solar PV cells and multi-cage models of IMs, this paper introduces a unified parameter estimation framework applicable to all solar cell and IM configurations. The proposed hybrid metaheuristic algorithm is tested on several benchmark models reported in the literature and further validated experimentally. The obtained results confirm that the proposed unified framework offers improved accuracy, faster convergence, and greater robustness compared to existing parameter estimation methods for both solar PV cells and IMs.</p>