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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

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

Abstract

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

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


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  • 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) $P_{G_i}$

  •   

    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 $\bar{\lambda}$, $\bar{P}_{G_i}$.

  • 1   Table 1Generator 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

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