Analytical solution of optimized energy consumption of Double Star Induction Motor operating in transient regime using a Hamilton-Jacobi-Bellman equation

The problem of energy optimization of a DSIM (Double Stator Induction Motor) using the concept of a RFOC (Rotor Field Oriented Control) can be treated by an OCS (Optimal Control Strategy). Using OCS, a cost-to-go function can be minimized and subjected to the motor dynamic equations and boundary constraints in order to find rotor flux optimal trajectories. This cost-to go function consists of a linear combination of magnetic power, copper loss, and mechanical power. The dynamic equations are represented by using a reduced Blondel Park model of the DSIM. From the HJB (Hamilton-Jacobi-Bellman) equation, a system of nonlinear differential equations is obtained, and analytical solutions of these equations are achieved so as to obtain a time-varying expression of a minimum-energy rotor flux. This analytical solution of rotor flux achieved maximum DSIM's efficiency and was implemented in the ORFOC (optimal rotor flux oriented control) and compared to the conventional RFOC at different dynamic regime of the DSIM. Simulation results are given and improved the effectiveness of the proposed strategy.