Optimal Charging Control of No-Insulation HTS Magnets using Pontryagin’s Principle and Advanced Nizar Optimization Technique

High-Temperature Superconducting (HTS) magnets employing No-Insulation (NI) and Controlled-Insulation (CI) winding techniques are widely used in particle accelerators and industrial applications due to their enhanced stability and self-protection features. However, these magnets suffer from extended charging times, excessive heat generation, and inefficient energy utilization, limiting their practical performance. Traditional optimization approaches, struggle with long convergence times, overshooting effects, and computational inefficiencies. To address these limitations, this work integrates Pontryagin’s Minimum Principle with the Nizar Optimization Algorithm (PMP-NOA) to optimize the charging process of NI and CI HTS magnets. The system is modeled using a lumped-element circuit approach, capturing azimuthal and radial currents, operative current, voltage drop, and heat generation dynamics. The optimization framework is formulated using a cost function that minimizes charging time and heat dissipation, incorporating constraints on current, temperature, voltage, and cryocooler power. To efficiently solve the problem, Hamiltonian-based optimal control is applied, and the metaheuristic NOA method enhances search efficiency using effective mixing and transformation mappings. The PMP-NOA framework significantly outperforms existing methods, achieving the fastest charging time (220s, 15-29% improvement), lowest temperature rise (3.2K, 28-75% reduction), minimal current overshoot (6%), and highest steady-state accuracy (1.2%). Additionally, it reduces power dissipation (75W, 13-40% improvement) while requiring fewer iterations (10³), making it the most computationally efficient approach. This work establishes PMP-NOA as an optimal control strategy for improving the efficiency, stability, and practicality of HTS magnet applications in high-performance environments.