Research on Distributed Power Market Trading Model Based on Grid Line Transmission Security
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摘要: 电力市场分布式交易模型可有效缓解传统集中模型下市场主体的隐私安全等问题, 但难以在保障市场主体收益和电力系统安全稳定运行的同时, 实现社会福利最大化. 因此, 基于电网线路传输安全, 首先以社会福利最大化为目标, 构建集中式交易模型, 并采用拉格朗日乘子法和对偶定理, 将其等价分解为各市场主体自身利益最大化的分布式交易模型. 在此基础上, 设计2种适用于不同情形的分布式交易方法及其求解算法, 并构造电网安全成本影响市场主体的决策, 从而保证电网线路传输安全. 最后, 基于算例分析, 验证了2种交易方法的有效性.Abstract: The distributed power market trading model can effectively alleviate the problems among market entities such as privacy problem in the traditional centralized trading model. However, there is still a lack of distributed trading models that can maximize social welfare while ensuring the benefits of market entities and the safe and stable operation of the power system. Therefore, a centralized trading model with the objective of maximizing social welfare is constructed, which considers the power grid line transmission security. Then, it is equivalently decomposed into a distributed trading model that maximizes the interests of each market agent using the Lagrange multiplier method and dual duality theorem. On this basis, two distributed trading methods and the corresponding solution algorithms suitable for different scenarios are designed, and the grid security cost is used to influence the decision-making of market entities, thereby ensuring grid line transmission security. Finally, the effectiveness of the two trading methods are verified based on simulation analysis.
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图 4 2种交易方法求得的社会福利对比
Fig. 4 Comparison of social welfare obtained by the 2 trading methods
图 7 情形1下, 2种算法求得的各发电商的出力
Fig. 7 Power generation of each generator obtained by the 2 algorithms in scenario 1
图 8 情形2下, 2种算法求得各发电商的出力
Fig. 8 Power generation of each generator obtained by the 2 algorithms in scenario 2
图 10 在IEEE 33节点电力系统中, 2种交易方法求解结果的残差
Fig. 10 Residuals of the solution results of the 2 trading models in IEEE 33 bus power system
图 11 情形1下, 2种算法求得的各发电商的出力
Fig. 11 Power generation of each generator obtained by the 2 algorithms in scenario 1
图 12 情形2下, 2种算法求得的各发电商的出力
Fig. 12 Power generation of each generator obtained by the 2 algorithms in scenario 2
图 13 情形1下, 3种算法的迭代求解结果
Fig. 13 The iterative solution results of the 3 algorithms in scenario 1
图 14 情形2下, 3种算法的迭代求解结果
Fig. 14 The iterative solution results of the 3 algorithms in scenario 2
表 1 2种分布式交易情形下, IEEE 9节点电力系统的发电商出力上限和下限(MW)
Table 1 Upper and lower limits on generator output for IEEE 9 bus power system in 2 distributed trading scenarios (MW)
发电商 $G_1$ $G_2$ $G_3$ 情形1 $p_{G,i}^{\max }$ 350 290 400 $p_{G,i}^{\min }$ 10 20 15 情形2 $p_{G,i}^{\max }$ 120 100 140 $p_{G,i}^{\min }$ 10 20 15 
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表 2 2种分布式交易情形下, IEEE 9节点电力系统的柔性负荷商需求上限和下限(MW)
Table 2 Upper and lower limits on flexible loaders＇demand for IEEE 9 bus power system in 2 distributed trading scenarios (MW)
柔性负荷商 ${{D}_{4}}$ ${{D}_{5}}$ ${{D}_{6}}$ ${{D}_{7}}$ ${{D}_{8}}$ ${{D}_{9}}$ 情形1 $p_{D,j}^{\max }$ 150 100 145 140 150 170 $p_{D,j}^{\min }$ 60 50 90 60 50 70 情形2 $p_{D,j}^{\max }$ 150 90 100 140 150 150 $p_{D,j}^{\min }$ 20 15 30 30 15 20
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表 3 IEEE 9节点电力系统线路潮流上限(MW)
Table 3 Upper limit of grid line power flow for IEEE 9 bus power system (MW)
线路 1-4 4-6 6-9 3-9 9-8 8-7 7-2 7-5 5-4 $P_{l}^{PF\max}$ 160 100 100 150 100 100 120 100 100
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表 4 2种交易方法下, 各市场主体交易量对比 (MW)
Table 4 Comparison of the trading volume of market entities obtained by the 2 trading methods (MW)
交易量 集中式 分布式 ${{G}_{1}}$ 155.374 155.376 ${{G}_{2}}$ 97.747 97.747 ${{G}_{3}}$ 126.912 126.918 ${{D}_{4}}$ 59.998 60.002 ${{D}_{5}}$ 50.010 50.007 ${{D}_{6}}$ 90.007 90.007 ${{D}_{7}}$ 60.006 60.006 ${{D}_{8}}$ 50.009 50.006 ${{D}_{9}}$ 70.012 70.006
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表 5 IEEE 9节点电力系统下, 2种算法的迭代次数和 计算时间对比
Table 5 Comparison of iterations and computation time of the 2 algorithms in IEEE 9 bus system
情形 算法1 算法2 迭代次数 计算时间(s) 迭代次数 计算时间(s) 情形1 248 71.5 265 79.8 情形2 216 60.2 52 15.7
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表 6 IEEE 33节点电力系统中, 2个案例的 潮流对比(MW)
Table 6 Comparison of the power flow in the 2 cases of the IEEE 33 bus power system (MW)
线路 $P_{l}^{PF,\;{\rm{case} }\;1}$ $P_{l}^{PF,\;{\rm{case} }\;2}$ $P_{l}^{PF\max}$ 1-2 189.22 190.36 250 2-3 145.40 78.52 250 3-4 136.56 98.60 150 4-5 58.56 56.30 250 5-6 258.55 168.56 200 6-7 59.87 43.69 250 7-8 25.21 8.96 250 8-9 62.17 56.18 250 9-10 32.74 32.80 250 10-11 62.15 57.71 150 11-12 16.12 15.23 150 12-13 30.06 34.89 200 13-14 51.10 40.55 250 14-15 218.53 188.37 200 15-16 39.89 22.97 150 16-17 101.01 59.95 150 17-18 165.36 137.69 150 2-19 74.80 60.84 150 19-20 95.37 87.90 250 20-21 212.80 183.99 200 21-22 61.00 68.73 150 3-23 58.97 60.04 150 23-24 45.51 37.73 200 24-25 75.72 43.37 250 6-26 145.70 155.01 250 26-27 169.74 125.79 150 27-28 243.25 188.26 200 28-29 135.98 97.89 150 29-30 14.31 32.59 150 30-31 34.64 44.72 250 31-32 43.94 44.88 150 32-33 140.00 122.20 150 21-8 122.87 99.63 150 9-15 87.32 65.97 150 12-22 120.66 156.98 200 18-33 35.62 40.33 200 25-29 158.77 142.65 200
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表 7 IEEE 33节点系统下, 2种算法迭代次数和 计算时间对比
Table 7 Comparison of iterations and computation time of the 2 algorithms in IEEE 33 bus system
情形 算法1 算法2 迭代次数 计算时间(s) 迭代次数 计算时间(s) 情形1 402 158.3 433 165.9 情形2 374 143.3 86 32.6
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表 8 情形1下, 3种算法的迭代次数和计算时间对比
Table 8 Comparison of iterations and computation time of the 3 algorithms in scenario 1
算法名称 迭代次数 计算时间(s) 原始对偶法 458 162.2 F-ADMM 262 96.5 算法1 402 158.3
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表 9 情形2下, 3种算法的迭代次数和计算时间对比
Table 9 Comparison of iterations and computation time of the 3 algorithms in scenario 2
算法名称 迭代次数 计算时间(s) 原始对偶法 395 149.8 F-ADMM 218 80.4 算法2 86 32.6
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