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 重庆大学学报  2018, Vol. 41 Issue (12): 73-82  DOI: 10.11835/j.issn.1000-582X.2018.12.009 RIS（文献管理工具） 0

### 引用本文

XU Ruilin, YANG Yun, LI Junjie, LIAO Yuexi, XIA Haibo, CHEN Minyou. Distributed economic dispatch method for microgrids based on the equal incremental cost criterion[J]. Journal of Chongqing University, 2018, 41(12): 73-82. DOI: 10.11835/j.issn.1000-582X.2018.12.009.

### 文章历史

1. 国网重庆市电力公司 电力科学研究院, 重庆 400021;
2. 国网重庆市电力公司, 重庆 400014;
3. 重庆大学 输配电装备及系统安全与新技术国家重点实验室, 重庆 400044;
4. 国网重庆市电力公司 南岸供电分公司, 重庆 401336

Distributed economic dispatch method for microgrids based on the equal incremental cost criterion
XU Ruilin1 , YANG Yun2 , LI Junjie1 , LIAO Yuexi3 , XIA Haibo3,4 , CHEN Minyou3
1. State Grid Chongqing Electric Power Research Institute, Chongqing 400021, P. R. China;
2. State Grid Chongqing Electrical Power Company, Chongqing 400014, P. R. China;
3. State Key Laboratory of Power Transmission Equipment & System Security and New Technology, Chongqing University, Chongqing 400044, P. R. China;
4. State Grid Chongqing Nan'an Power Supply Company, Chongqing 401336, P. R. China
Supported by the Science and Technology Project of State Grid Corporation of China(5220001600V6)
Abstract: To achieve the minimal operation cost of microgrids(MGs), a distributed economic dispatch method was proposed, in which a two-layer model was used. The upper layer is a communication network for information transmission, while the lower layer is a MG for power transmission. The communication network consists of two sub-networks, one of which is composed of all agents while the other is only composed of controllable agents. Then construction rules of communication network was established, and a general method was systematically given to derive distributed control laws from any communication networks. The distributed control laws derived from the first sub-network ensure the supply-demand balance, while the distributed control laws derived from the second sub-network minimize the cost of power generation, thus realizing the consensus of incremental cost of all the controllable DGs via the iteration of controllable agents. Based on equal incremental principle, the minimal operation cost of all controllable DGs was obtained. Finally, two simulation cases were designed to evaluate the performance of the method. The simulation results show that the proposed method can realize the minimal operation cost of MGs when the loads and renewable resources fluctuate widely.
Keywords: distributed control    economic dispatch    incremental cost    microgrid

1 经济调度模型

 ${\rm{Min}}F = \sum\nolimits_{i = 1}^n {{F_{\rm{i}}}\left( {{p_{\rm{i}}}} \right)} ,$ (1)
 ${\rm{s}}.{\rm{t}}.\sum\nolimits_{i = 1}^n {{p_{\rm{i}}}} = {P_{{\rm{load}}}},$ (2)
 $p_i^{\min } \le {p_i} \le p_i^{\max },$ (3)

 ${F_i}\left( {{p_i}} \right) = {a_i}p_i^2 + {b_i}{p_i} + {c_i},$ (4)

 ${F_i}\left( {{p_i}} \right) = \frac{{{{\left( {{p_i} + {\rho _i}} \right)}^2}}}{{2{\theta _i}}} + {\psi _i}。$ (5)

 $\lambda = \frac{{\partial {F_i}\left( {{p_i}} \right)}}{{\partial {p_i}}} = \frac{{{p_i} + {\rho _i}}}{{{\theta _i}}}。$ (6)

 $U = \sum\nolimits_{i = 1}^n {{F_i}\left( {{p_i}} \right)} + \lambda \left( {\sum\nolimits_i^n {{p_i}} - {P_{{\rm{load}}}}} \right)。$ (7)

 ${\lambda ^ * } = \frac{{\partial U}}{{\partial {p_i}}} = \frac{{p_i^ * + {\rho _i}}}{{{\theta _i}}},$ (8)

 ${\lambda ^ * } = \frac{{{P_{{\rm{load}}}} + \sum\nolimits_{i = 1}^n {{\rho _i}} }}{{\sum\nolimits_{i = 1}^n {{\theta _i}} }}。$ (9)

 $p_i^ * = {\theta _i}{\lambda ^ * } - {\rho _i}。$ (10)
2 微电网分布式调度模型

 图 1 微电网双层经济调度模型 Figure 1 The two-layer economic dispatch model for MGs

3 分布式控制律的设计

 ${w_{ij}} = \frac{1}{{{g_i}}},$ (11)

 $\sum\nolimits_{i = 1}^n {{w_{ij}}} = 1。$ (12)

 $\left. \begin{array}{l} E \cdot P\left( {t + 1} \right) = E \cdot P\left( t \right) + {W^T} \cdot \left[ {{L^p}\left( t \right) - P\left( t \right)} \right],\\ E \cdot Q\left( {t + 1} \right) = E \cdot Q\left( t \right) + {W^T} \cdot \left[ {{L^q}\left( t \right) - Q\left( t \right)} \right], \end{array} \right\}$ (13)

 ${v_{ij}} = \frac{1}{{{d_i}}} - \frac{1}{{{d_i}}} \cdot \frac{{{\theta _i}/{d_i}}}{{{\theta _i}/{d_i} + {\theta _j}/{d_j}}}\left( {j \in {N_i},j \ne i} \right),$ (14)

 ${v_{ii}} = 1 - \frac{1}{{{d_i}}} \cdot \sum {\frac{{{\theta _i}/{d_i}}}{{{\theta _i}/{d_i} + {\theta _j}/{d_j}}}\left( {j \in {N_i}} \right)} 。$ (15)

 $\tilde P'\left( {t + 1} \right) = {V^{\rm{T}}} \cdot \left[ {\tilde P\left( {t + 1} \right) + \rho } \right] - \rho ,$ (16)

 ${{\tilde P'}^\rho }\left( {t + 1} \right) = {V^{\rm{T}}} \cdot \tilde P_i^\rho \left( {t + 1} \right)。$ (17)

4 仿真平台及参数设置

 图 2 放射型微电网结构 Figure 2 Topology of a radial MG

 图 3 所有风机、光伏的输出 Figure 3 Outputs of all PVs and WTs

5 仿真算例

5.1 分布式经济调度的有效性(算例1)

 图 4 在环境和负载同时变化下，不考虑DG容量限制的经济调度仿真结果 Figure 4 Simulation results of economic dispatch without constraints of DG capacities, when fluctuations of load demand and environmental conditions are considered

5.2 不同网络结构对算法的影响(算例2)

 图 5 网络2和网络3的双层网络模型 Figure 5 Different topologies of communication networks: Network 2 and Network 3

 图 6 在环境和负载同时变化下，算法在网络2中的仿真结果 Figure 6 Simulation results on Network 2, when fluctuations of load demand and environmental conditions are considered
 图 7 在环境和负载同时变化下，算法在网络3中的仿真结果 Figure 7 Simulation results on Network 3, when fluctuations of load demand and environmental conditions are considered
6 结语

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