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浙江大学学报(工学版)
浙江大学学报(工学版)  2020, Vol. 54 Issue (4): 678-683    DOI: 10.3785/j.issn.1008-973X.2020.04.006
机械工程、电气工程     
基于鞍点方程的分布式经济调度算法
时侠圣1(),郑荣濠1,林志赟1,2,颜钢锋1,*()
1. 浙江大学 电气工程学院，浙江 杭州 310058
2. 杭州电子科技大学 自动化学院，浙江 杭州 311305
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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摘要：

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    
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 words: economic dispatch    directed network    distributed algorithm    first-order continuous-time multi-agent system
收稿日期: 2019-01-16 出版日期: 2020-04-05
CLC:  TM 73  
基金资助: 国家自然科学基金资助项目（61873235，61673344）；2019年度广东省重点领域研发计划重点专项项目（2019B111109002）
通讯作者: 颜钢锋     E-mail: shixiasheng@zju.edu.cn;ygf@zju.edu.cn
作者简介: 时侠圣（1992—），男，博士生，从事分布式资源分配研究. orcid.org/0000-0001-9079-5705. E-mail： shixiasheng@zju.edu.cn
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引用本文:

时侠圣,郑荣濠,林志赟,颜钢锋. 基于鞍点方程的分布式经济调度算法[J]. 浙江大学学报(工学版), 2020, 54(4): 678-683.

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.

链接本文:

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

图 1  IEEE-14测试系统
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]
表 1  代价函数参数及生产能力约束范围
图 2  案例中各节点状态轨迹图
图 3  案例中拉格朗日乘子 $\lambda $轨迹图
图 4  案例中拉格朗日乘子 ${\lambda _m},{\lambda _M}$轨迹图
图 5  案例中各节点平衡变量 $z_i^i$的状态轨迹图
图 6  案例中的辅助变量 ${y_i}$的轨迹图
图 7   $z_i^i$不同初始值对应的误差轨迹图
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