SCIENTIA SINICA Informationis, Volume 48, Issue 10: 1395-1408(2018) https://doi.org/10.1360/N112018-00020

Event-triggered-based consensus approach for economic dispatch problem in a microgrid

More info
  • ReceivedApr 1, 2018
  • AcceptedApr 17, 2018
  • PublishedOct 12, 2018


This study aims to propose an event-trigger consensus approach for the economic dispatch problem (EDP) that is encountered in microgrids. The proposed scheme was based on the consensus algorithm, wherein each agent participated in neighborhood information exchange and local computation. Then, the scheme was converged to an optimal dispatch after iteration. Each agent must sense only its local cost parameters, local load, and neighborhood communication. Furthermore, event-triggered feedback was considered to reduce the frequency of the computation and communication of agents with their neighbors. Communication bandwidth and energy can be saved to meet the goal of the EDP. Several simulation cases were presented to illustrate the effectiveness of the proposed scheme.

Funded by





[1] Lasseter R H. Microgrids. In: Proceedings of Power Engineering Society Winter Meeting, New York, 2002. 305--308. Google Scholar

[2] Lasseter R H, Paigi P. Microgrid: aconceptual solution. In: Proceedings of the 35th Annual Power Electronics Specialists Conference, Aachen, 2004. 4285--4290. Google Scholar

[3] Katiraei F, Iravani R, Hatziargyriou N. Microgrids management. IEEE Power Energy Mag, 2008, 6: 54-65 CrossRef Google Scholar

[4] Liu D, Cai Y. Taguchi Method for Solving the Economic Dispatch Problem With Nonsmooth Cost Functions. IEEE Trans Power Syst, 2005, 20: 2006-2014 CrossRef ADS Google Scholar

[5] Yang S, Tan S, Xu J X. Consensus Based Approach for Economic Dispatch Problem in a Smart Grid. IEEE Trans Power Syst, 2013, 28: 4416-4426 CrossRef ADS Google Scholar

[6] Zhang Z, Chow M Y. Convergence Analysis of the Incremental Cost Consensus Algorithm Under Different Communication Network Topologies in a Smart Grid. IEEE Trans Power Syst, 2012, 27: 1761-1768 CrossRef ADS Google Scholar

[7] Zhang Z, Chow M Y. Incremental cost consensus algorithm in a smart grid environmen. In: Proceedings of Power and Energy Society General Meeting, San Diego, 2011. Google Scholar

[8] Zhang Z, Ying X C, Chow M Y. Decentralizing the economic dispatch problem using a two-level incremental cost consensus algorithm in a smart grid environment. In: Proceedings of North American Power Symposium, Boston, 2011. Google Scholar

[9] Xing H, Mou Y, Fu M. Distributed Bisection Method for Economic Power Dispatch in Smart Grid. IEEE Trans Power Syst, 2015, 30: 3024-3035 CrossRef ADS Google Scholar

[10] Kim B Y, Oh K K, Ahn H S. Coordination and control for energy distribution in distributed grid networks: Theory and application to power dispatch problem. Control Eng Practice, 2015, 43: 21-38 CrossRef Google Scholar

[11] Binetti G, Davoudi A, Lewis F L. Distributed Consensus-Based Economic Dispatch With Transmission Losses. IEEE Trans Power Syst, 2014, 29: 1711-1720 CrossRef ADS Google Scholar

[12] Yang Z Q, Xiang J, Li Y J. Distributed virtual incremental cost consensus algorithm for economic dispatch in a microgrid. In: Proceedings of the 12th IEEE International Conference on Control and Automation, Kathmandu, 2016. 383--388. Google Scholar

[13] Xie J, Chen K X, Yue D, et al. Distributed economic dispatch based on consensus algorithm of multi agent system for power system. Electric Power Autom Eq, 2016, 36: 112--117. Google Scholar

[14] Hu J, Ma H. Multi-agent system based optimal power dispatch algorithm for microgrid. Power Syst Technol, 2017, 41: 2657--2665. Google Scholar

[15] Astrom K J, Bernhardsson B M. Comparison of Riemann and Lebesgue sampling for first order stochastic systems. In: Proceedings of the 41st Conference on Decision and Control, Las Vegas, 2002. 2011--2016. Google Scholar

[16] Tabuada P. Event-Triggered Real-Time Scheduling of Stabilizing Control Tasks. IEEE Trans Automat Contr, 2007, 52: 1680-1685 CrossRef Google Scholar

[17] Seyboth G S, Dimarogonas D V, Johansson K H. Event-based broadcasting for multi-agent average consensus. Automatica, 2013, 49: 245-252 CrossRef Google Scholar

[18] Chen G, Zhao Z. Delay Effects on Consensus-Based Distributed Economic Dispatch Algorithm in Microgrid. IEEE Trans Power Syst, 2018, 33: 602-612 CrossRef ADS Google Scholar

[19] Godsil C, Royle G. Algebraic graph theory. In: Graduate Texts in Mathematics. Berlin: Springer, 2001. Google Scholar

[20] Dimarogonas D V, Frazzoli E, Johansson K H. Distributed Event-Triggered Control for Multi-Agent Systems. IEEE Trans Automat Contr, 2012, 57: 1291-1297 CrossRef Google Scholar

[21] Chen G, Ren J, Feng E N. Distributed Finite-Time Economic Dispatch of a Network of Energy Resources. IEEE Trans Smart Grid, 2017, 8: 822-832 CrossRef Google Scholar

  • Figure 1

    Topology 1

  • Figure 2

    (Color online) General consensus algorithm. (a) $\lambda_i$; (b) $P_{G_i}$

  • Figure 3

    (Color online) Event-triggered algorithm. (a) $\lambda$ and event-trigged instants; (b) state error $e(t)$

  • Figure 4

    (Color online) $\mu$. (a) $\mu$ and event-trigged instants; (b) state error $e(t)$

  • Figure 5

    (Color online) $\phi$. (a) $\phi$ and event-trigged instants; (b) state error $e(t)$

  • Figure 6

    (Color online) The evolution before and after capacity constraints are imposed. (a) $\lambda$; (b) $P_{G_i}$

  • Figure 7

    Topology 2

  • Figure 8

    (Color online) Event-triggered algorithm with another given topology. (a) $\lambda$ and event-trigged instants;protect łinebreak (b) $P_{G_i}$

  • Table 1   Generator parameters
    Agent $a_i$ (/MW$^2$) $b_i$ (/MW) $P_{{G_i}{\rm~max}}$ (MW)
    1 0.04 2.0 70
    2 0.035 1.3 80
    3 0.02 2.8 50
    4 0.03 3.0 90
    5 0.05 3.5 80

    Algorithm 1 算法流程

    Require:${\lambda}(0)$, $P_{L_{ik}}$, $P_{G_i}(0)$;

    Output:$\dot{\xi}_i(t)=\hat{\lambda}_i(t)$, $~\,~\frac{1}{2a_i}\dot{\lambda}_i(t)=\frac{1}{2}\sum\nolimits_{i=1}^{n}a_{ij}(\hat{\lambda}_j(t)~-\hat{\lambda}_i(t))+\frac{1}{2}\dot{P}_{G_i}(t)$,



    如果 $P_{G_i}^*~<0$, 那么$P_{G_i}^*=0$; 如果 $P_{G_i}^*>P_{{G_i}{\rm~max}}$, 那么 $P_{G_i}^*=P_{{G_i}{\rm~max}}$. 从而确定 $\Theta$, $\bar{\Theta}$;

    $\mu_i(0)~\Leftarrow~\left\{\begin{aligned} &\frac{\lambda^*}{2a_i}-\frac{b_i}{2a_i}-\bar{P}_{G_i},~~~~i\in~\bar{\Theta},\\ &0,~~~~~~~~i\in~\Theta; \end{aligned}\right.$

    $\phi_i(0)~\Leftarrow~\left\{\begin{aligned} &\frac{1}{2a_i},~~~i\in~\Theta,\\ &0,~~~~i\in~\bar{\Theta}. \end{aligned}\right.$

    Require:$\mu_i(0)$, $\phi_i(0)$;

    Output:$\dot{\mu}_i(t)=\sum\nolimits_{i=1}^{n}a_{ij}(\hat{\mu}_j(t)-\hat{\mu}_i(t))$; $~\,~\dot{\phi}_i(t)=\sum\nolimits_{i=1}^{n}a_{ij}(\hat{\phi}_j(t)-\hat{\phi}_i(t))$;


    $\bar{P}_{G_i}~\Leftarrow~\left\{\begin{aligned} &~\frac~{\bar{\lambda}_i(t)-b_i}{2a_i},~~~0<~\frac~{\lambda^*_i(t)-b_i}{2a_i}<~P_{{G_i}{\rm~max}};\\ &~P_{{G_i}{\rm~max}},~~~\,~\frac~{\lambda^*_i(t)-b_i}{2a_i}\geq~P_{{G_i}{\rm~max}};\\ &~0,~~~~~\,~\frac~{\lambda^*_i(t)-b_i}{2a_i}\leq0. \end{aligned}\right.$结果: $\lambda^*$, $P_{G_i}^*$ 或者 $\bar{\lambda}$, $\bar{P}_{G_i}$.

Copyright 2020 Science China Press Co., Ltd. 《中国科学》杂志社有限责任公司 版权所有

京ICP备18024590号-1       京公网安备11010102003388号