This work presents a simplified mathematical model for solving the reactive optimal power flow problem with continuous and discrete control variables. The distributed slack bus modeling was used in the tested electrical systems. The problem is formulated as a nonlinear programming problem with continuous and discrete variables so that its resolution is obtained fundamentally from mathematical modifications by the algorithm proposed in this work, in which discrete variables are treated as continuous by sinusoidal functions added to the original objective function. This work also proposes an effectiveness analysis of the results provided by different commercial solvers for the discretized reactive optimal power flow problem. The proposed modeling was applied on the IEEE 14, 30, 57, 118 and 300-bus test systems. The results presented reveal that the proposed model was effective in the optimization of the objective function and discretization of control variables of the systems.