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Journal of ZheJiang University (Engineering Science)  2020, Vol. 54 Issue (4): 678-683    DOI: 10.3785/j.issn.1008-973X.2020.04.006
Mechanical Engineering,Electrical Engineering     
Saddle dynamic based distributed algorithm for economic dispatch problem
Xia-sheng SHI1(),Rong-hao ZHENG1,Zhi-yun LIN1,2,Gang-feng YAN1,*()
1. College of Electrical Engineering, Zhejiang University, Hangzhou 310058, China
2. School of Automation, Hangzhou Dianzi University, Hangzhou 311305, China
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Abstract  

A distributed algorithm based on the first-order continuous-time multi-agent system was proposed for the widely studied economic dispatch problem in the power system inspired by the consensus model and saddle point dynamic method in order to realize the safe, stable, and economical operation of the smart grid. The total demand and generating capacity of each generators during its iteration were considered, in which each agent only knew its own cost function. Three Lagrange multipliers were designed in order to solve above constraints. The control parameters in the above proposed algorithm were constants by adding one variable to balance the difference of the local subgradient. Since the adjoint matrix of the directed network was asymmetrical, one variable was introduced to balance the weight gain of each edge. The output power of each agent was obtained by using the local subgradient and the corresponding Lagrange multipliers. The simulation results show that the proposed algorithm is effective and useful for the economic dispatch problem.



Key wordseconomic dispatch      directed network      distributed algorithm      first-order continuous-time multi-agent system     
Received: 16 January 2019      Published: 05 April 2020
CLC:  TM 73  
Corresponding Authors: Gang-feng YAN     E-mail: shixiasheng@zju.edu.cn;ygf@zju.edu.cn
Cite this article:

Xia-sheng SHI,Rong-hao ZHENG,Zhi-yun LIN,Gang-feng YAN. Saddle dynamic based distributed algorithm for economic dispatch problem. Journal of ZheJiang University (Engineering Science), 2020, 54(4): 678-683.

URL:

http://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2020.04.006     OR     http://www.zjujournals.com/eng/Y2020/V54/I4/678


基于鞍点方程的分布式经济调度算法

为了实现智能电网的安全稳定经济运行,针对电力系统中广泛研究的经济调度问题,受到一致性模型和鞍点动态法的启发,提出基于一阶连续系统的分布式算法. 该算法考虑了迭代过程中节点生产能力和网络总负荷需求的约束,且每个节点只知道自身的代价函数. 为了解决上述约束,该算法设计3种对应的拉格朗日乘子. 为了实现控制参数的常量化,该算法添加了一个变量,用于平衡局部梯度差值. 由于有向网络的权矩阵是非对称的,该算法引入一变量用于平衡各有向边的权增益. 通过节点局部梯度与拉格朗日乘子,获取节点输出功率. 实验结果表明,该算法针对经济调度问题是可行且有效的.


关键词: 经济调度,  有向网络,  分布式算法,  一阶连续系统 
Fig.1 IEEE-14 bus systems
节点编号 ${a_{i,1}}$/(美元·MW?2) ${a_{i,2}}$/(美元·MW?1) xi/MW
1 0.04 2.0 [0,80]
2 0.03 3.0 [0, 70]
3 0.035 4.0 [0, 70]
6 0.03 4.0 [0, 70]
8 0.04 2.5 [0, 80]
Tab.1 Cost function parameters and box constraint
Fig.2 Trajectories of all agents in example
Fig.3 Trajectories of Lagrange multiplier $\lambda $ in example
Fig.4 Trajectories of Lagrange multiplier ${\lambda _m},{\lambda _M}$ in example
Fig.5 Trajectories of balance variable $z_i^i$ in example
Fig.6 Trajectories of auxiliary variable ${y_i}$ in example
Fig.7 Error trajectories of balance variable $z_i^i$ with different initial state
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