logo

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

Abstract


Funded by

北京市自然科学基金(4122075)

国家自然科学基金(61573138)

中央高校基础研究基金


References

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

    $~\,~P_{G_i}(t)=\sum\nolimits_{i=1}^{n}a_{ij}(\xi_j(t)-\xi_i(t))~+\sum\nolimits_{k=1}^{r}d_{ik}P_{L_{ik}}$;

    $P_{G_i}^*~\Leftarrow~\frac~{\lambda_i^*-b_i}{2a_i}$;

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

    $\bar{\lambda}~\Leftarrow~\lambda^*+\frac{\mu_i}{\phi_i}$;

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