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摘要: 提出了一种全新的迁移蜂群优化算法，并应用到电力系统无功优化问题.利用Q学习的试错与奖励机制构造蜂群的学习模式，并采用强化学习的行为迁移技术实现蜂群的迁移学习.为解决算法求解多变量优化问题遇到的维数灾难，提出了状态-组合动作链的方式将状态-动作空间分解成若干低维空间，明显降低算法的计算难度.仿真结果表明：本文所提算法可以保证最优解质量的同时，寻优速度能提高到传统启发式智能算法的4～67倍左右，非常适用于大规模复杂系统非线性规划问题的快速求解.Abstract: This paper proposes a novel transfer bees optimizer (TBO), which is implemented to solve the reactive power optimization of power systems. The trial-and-error and the reward mechanism of Q-learning is adopted to construct the learning mode of the bees, and the technology of behavior transfer from reinforcement learning is used for transfer learning. Moreover, a space-action chain is proposed to decompose the solution space into several lower-dimensional spaces, thus it can solve the curse of dimension resulted from the multiple variables optimization problem. Simulation results show that TBO can obtain a high-quality optimal solution, while its convergence speed can be accelerated as many as 4 to 67 times faster than that of the conventional heuristic artificial algorithm (AI) algorithm, which is very suitable for fast optimization of nonlinear programming in a large-scale complex system.
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表 1 算例控制变量规模
Table 1 Control variable scale of the simulation case
仿真系统 控制变量个数 总计 无功补偿 变压器分接头 发电机端电压 IEEE 118 节点 3 5 17 25 IEEE 300 节点 11 44 56 111 
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表 2 TBO 算法参数设置
Table 2 TBO parameter setting
参数 取值范围 IEEE 118 节点 IEEE 300 节点 样本学习 迁移学习 样本学习 迁移学习 $n$ - 14 6 30 10 $\alpha $ 0＜$\alpha$＜1 0.99 0.99 0.99 0.99 $\gamma $ 0＜$\gamma$＜1 0.9 0.9 0.9 0.9 $\varepsilon $ 0＜$\varepsilon$ ＜1 0.9 0.98 0.95 0.98 $\beta $ 0＜$\beta$＜1 0.99 0.99 0.99 0.99
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表 3 对比算法主要参数设置
Table 3 Parameter setting of comparative algorithms
算法 参数 取值 IEEE 118 节点 IEEE 300 节点 ABC 蜂群总数 14 40 采蜜蜂 7 20 侦查蜂 2 5 观察蜂 5 15 限制次数 5 5 GSO 群体规模 100 500 游荡者比例 20% 20% 最大搜索角 $\pi/4$ $\pi/4$ 最大搜索转角 $\pi/8$ $\pi/8$ ACO 蚁群总数 50 100 信息素挥发系数 0.8 0.8 启发式值权重 1 1 搜索权重 0.8 0.8 PSO 粒子群总数 50 100 最小旋转速度 -5 -5 最大旋转速度 5 5 加速系数~$c1$/$c2$ 0.5/0.5 1/1 最小惯性系数 0.4 0.4 最大惯性系数 0.9 0.9 GA 种群规模 50 100 变异概率 0.05 0.10 交叉概率 0.80 0.80 遗传代沟 0.8 0.8 进化代数 50 100 CCGA 种群个体数 5 5 种群数 3 10 变异概率 0.90 0.90 交叉概率 0.95 0.95 最大进化代数 80 80 QGA 种群规模 50 100 量子旋转门 0.01$\pi $ 0.01$\pi $ 进化代数 50 100 Ant-Q 蚁群总数 50 80 折扣系数 0.05 0.1 学习因子 0.5 0.1 搜索权重因子 0.8 0.8
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表 4 典型日96 个断面各算法运行10次平均结果统计表
Table 4 Average results of 96 load sections by each algorithm in 10 runs
算法 IEEE 118 节点算例 IEEE 300 节点算例 计算时间(s) 收敛时间(s) $P_{\rm loss}$ (MW) $U_{\rm d}$ (%) 目标函数值 计算时间(s) 收敛时间(s) $P_{\rm loss}$ (MW) $U_{\rm d}$ (%) 目标函数值 ABC 1440 15.00 11105.12 1507.13 6306.13 6941.98 72.31 38182.69 8340.91 23261.80 ACO 2968.27 30.92 11062.35 1437.88 6250.12 21896.02 228.08 38265.31 7359.69 22812.50 Ant-Q 399.61 4.16 11110.67 1501.25 6305.96 11055.19 115.16 37427.55 7143.07 22285.31 GSO 3404.48 35.46 11121.77 1486.45 6304.11 6087.55 63.41 38644.40 8867.76 23756.08 PSO 2792.88 29.09 11103.69 1477.86 6290.77 9822.03 102.31 38098.85 8074.54 23086.70 GA 1032.95 10.76 11120.38 1504.56 6312.47 4631.66 48.25 37735.38 7779.54 22757.46 QGA 301.91 3.99 11093.48 1505.05 6299.27 4588.92 47.80 37631.03 7557.90 22594.46 CCGA 559.20 5.83 11011.74 1482.24 6246.99 2939.77 30.62 37474.88 7507.44 22491.16 TBO 89.91 0.94 11007.69 1482.84 6245.27 323.35 3.37 37513.53 6942.86 22228.19
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表 5 典型日96个断面各算法运行10次目标函数值收敛性能统计表
Table 5 Convergence performance of 96 load sections by each algorithm in 10 runs
算法 IEEE 118 节点算例 IEEE 300 节点算例 最小值 最大值 方差 标准差 相对标准偏差 最小值 最大值 方差 标准差 相对标准偏差 ABC 6308.20 6302.70 3.62 1.90 3.02E-04 23286.90 23230.48 380.55 19.51 8.39E-04 ACO 6253.35 6244.85 5.79 2.41 3.85E-04 22824.96 22784.28 227.72 15.09 6.61E-04 Ant-Q 6310.36 6301.19 7.71 2.78 4.40E-04 22310.62 22263.10 220.97 14.86 6.67E-04 GSO 6312.36 6298.30 17.35 4.17 6.61E-04 23810.08 23711.90 1293.47 35.96 1.51E-03 PSO 6296.83 6284.23 14.64 3.83 6.08E-04 23193.06 23020.09 2371.10 48.69 2.11E-03 GA 6318.80 6308.79 10.80 3.29 5.21E-04 22777.53 22742.54 178.17 13.35 5.87E-04 QGA 6303.66 6295.88 5.73 2.39 3.80E-04 22613.61 22575.91 193.87 13.92 6.16E-04 CCGA 6242.94 6254.14 9.56 3.09 4.95E-04 22460.90 22509.55 286.29 16.92 7.52E-04 TBO 6241.93 6247.39 3.15 1.77 2.84E-04 22217.39 22244.14 84.56 9.20 4.06E-04
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