Pareto competition based evolution strategy for two-objective optimization design of SMES solenoids

The superconducting magnetic energy storage (SMES) system has an attractive potential in power systems. Solenoid coil, one important configuration of SMES, can be simply built and provide highly stored energy per unit of the conductor. This paper suggests a novel two-objective optimization design model of solenoid coil. The objectives include the minimization of the solenoid volume and the uniformity of the magnetic field inside the magnet. Three constraints are considered, i.e., the energy requirement, the stray field in the surrounding region, and the quench condition. To optimize this highly constrained two-objective optimization design problem, Evolution Strategy (ES) has been used. The proposed sorting operator with Pareto competition divides the individuals into four groups: feasible Pareto (FP), infeasible Pareto (IP), feasible dominated (FD), and infeasible dominated (ID). FP solutions have the highest selection priority and ID solutions hold the lowest one. The annealing-like deterministic parameter control method for the acceptable tolerance of the energy error is also suggested to improve the constraints handling ability of ES. Numerical solutions show that the Pareto competition based ES can provide a set of feasible Pareto solutions for the two-objective optimization design model of SMES solenoids, among which the best one is to be extracted according to the designer's experience.