Parameter design method of magnetic compression power supply based on genetic algorithm
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摘要: 磁压缩电源主要用于为压缩磁体供电，以形成压缩场反等离子体所需的磁场位形，是磁压缩系统中的重要组成部分。压缩磁体线圈数量众多，线圈之间耦合关系复杂，导致求解形成目标磁场所需的电源参数非常困难，对电源设计带来一定挑战。提出了一种基于遗传算法的磁压缩电源参数设计方法，以提高参数设计效率。根据磁压缩电源工作电路拓扑及线圈之间的耦合关系，推导了磁压缩电源系统的物理模型。在物理模型的基础上，提出了基于遗传算法的磁压缩电源参数设计方法，并阐明了该方法的基本原理。编写了算法代码并建立了MATLAB仿真模型，在理想情况及实际工程两种设计情况下对HFRC磁压缩系统电源参数进行了优化设计，得到了优化磁场与目标磁场位形基本一致的结果。同时建立了MAXWELL仿真模型对比分析，两种模型的输出结果吻合度很高，验证了该方法在电源设计时的有效性和准确性。Abstract: The magnetic compression power supply, which is an important part of the magnetic compression system, is mainly used to supply power to the compressed magnet to form the magnetic field shape required for the field reversed configuration (FRC) plasma compression. The large number of compressed magnet coils and the complex coupling relationship between the coils make it difficult to solve the power supply parameters required to form the target magnetic field. A method is proposed for designing the parameters of the magnetic compression power supply based on genetic algorithm with high efficiency. According to the topology of the magnetic compression power supply and the coupling relationship between the coils, the physical model of the power supply system is derived. On the basis of the physical model, the design method of compressed power supply parameters based on genetic algorithm is proposed, and the basic principle of the method is clarified. The algorithm code and the MATLAB simulation model are established. Under the ideal situation and practical engineering design conditions, the power supply parameters of the HFRC magnetic compression system were optimized, the results of the optimized magnetic field are basically consistent with the target magnetic field shape. Meanwhile, a MAXWELL simulation model is established for comparative analysis, the results of these two modes fits well, which verifies the effectiveness and accuracy of the method in power supply design.
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图 5 单个磁压缩线圈示意图及其单匝线圈截面图
Figure 5. Schematic diagram of a single magnetic compression coil and cross-section of a single-turn coil
图 11 线圈中轴线上磁场分布随时间演化图(MATLAB)及50 μs、150 μs、250 μs时两者磁场位形对比
Figure 11. Evolution of the magnetic field distribution on the central axis of the coil (MATLAB) and magnetic field comparison at 50 μs, 150 μs and 250 μs
图 12 目标磁场、优化磁场与初始磁场位形对比
Figure 12. Comparison of target magnetic field, optimized magnetic field and initial magnetic field configuration
图 14 目标磁场、优化磁场(统一电容、不统一电容)与初始磁场位形对比
Figure 14. Comparison of target magnetic field, optimized magnetic field (uniform and unique capacitance) and initial magnetic field configuration
表 1 初始电源参数
Table 1. Initial power supply parameters
coil capacitance/mF voltage/kV C1 3.4 23.5 C2 3.4 23.5 C3 3.5 23.2 C4 3.5 23 C5 3.5 22.9 C6 3.6 22.5 C7 3.7 21.8 C8 4.0 20.1 C9 7.8 9.1 C10 7.8 9.1 C11 9.2 7.7 
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表 2 电源参数寻优域
Table 2. Power parameter optimization domain
coil maximum
capacitance/mFminimum
capacitance/mFmaximum
voltage/kVminimum
voltage/kVC1 3.54 3.26 25.3 21.7 C2 3.54 3.26 25.3 21.7 C3 3.64 3.36 25 21.4 C4 3.64 3.36 24.8 21.2 C5 3.64 3.36 24.7 21.1 C6 3.75 3.45 24.2 20.8 C7 3.85 3.55 23.5 20.1 C8 4.16 3.84 21.7 18.5 C9 8.43 7.17 10.1 8.1 C10 8.43 7.17 10.1 8.1 C11 9.94 8.46 8.5 6.9
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表 3 电源参数优化结果
Table 3. Power supply parameter optimization results
coil capacitance/mF voltage/kV C1 3.44 23.3 C2 3.41 23.5 C3 3.53 22.8 C4 3.67 22.6 C5 3.58 22.4 C6 3.49 23.1 C7 3.81 23.4 C8 3.97 20.9 C9 7.48 9.3 C10 7.91 9.5 C11 9.63 8.5
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表 4 电源参数优化结果(电容值统一)
Table 4. Power supply parameter optimization results (uniform capacitance values)
coil capacitance/mF voltage/kV C1 3.72 22.4 C2 3.72 22.6 C3 3.72 22.3 C4 3.72 22.6 C5 3.72 22.1 C6 3.72 23.6 C7 3.72 23.1 C8 3.72 21.6 C9 8.15 9.4 C10 8.15 9.2 C11 8.15 8.1
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