In this paper, a step-by-step solution procedure used to estimate the single-diode model parameters is proposed. The procedure is a combination of least-squares, Newtonian, and quasi- Newtonian numerical methods. Current and voltage measurements are acquired from a conventional 36-cell photovoltaic (PV) module manufactured by AMERESCO Solar. The single-diode equation was then fit to the acquired data in the least-squares sense. The developed least-squares equation is solved by two different numerical methods, the Newton-Raphson (NR) method, and Broyden’s method. Since there are five different parameters to be determined, a system of five nonlinear equations was developed and solved. The main distinction between the NR and Broyden’s algorithms is the way they handle the Jacobian matrix. The NR algorithm requires the computation of a new Jacobian matrix at every iteration. Broyden’s algorithm only requires an initial Jacobian, and then the Jacobian is updated iteratively by means of a correction formula. The functionality of the two algorithms is compared, and the five parameters extracted from each algorithm are used to simulate a 36-cell PV module. The simulation results are compared to experimental data to provide validation and to determine how accurate each procedure was in estimating the model parameters.