SCIENCE CHINA Information Sciences, Volume 61 , Issue 1 : 012204(2018) https://doi.org/10.1007/s11432-016-9114-y

Economic power dispatch in smart grids: a framework for distributed optimization and consensus dynamics

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  • ReceivedDec 31, 2016
  • AcceptedApr 20, 2017
  • PublishedAug 29, 2017



This work was supported by National Key Research and Development Program of China (Grant No. 2016YFB0800401), National Natural Science Foundation of China (Grant Nos. 61673107, 61673104, 61621003, 61532020), National Ten Thousand Talent Program for Young Top-notch Talents, Cheung Kong Scholars Programme of China for Young Scholars, Six Talent Peaks of Jiangsu Province of China (Grant No. 2014-DZXX-004), and Fundamental Research Funds for the Central Universities of China (Grant No. 2242016K41058).


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  • Figure 1

    Illustration of networks with pinning control.

  • Figure 2

    (Color online) (a) The incremental cost of all three generation units as well as (b) their corresponding output powers in Table tab1.

  • Figure 3

    (Color online) (a) The incremental cost of all three generation units as well as (b) their corresponding output powers at power demands 650 MWh and 850 MWh.

  • Figure 4

    (Color online) (a) The incremental cost of all generation units as well as (b) their corresponding output powers in a scale-free network structure.

  • Figure 5

    (Color online) (a) The modified incremental cost of all three generation units with capacity limitations as well as (b) their corresponding output powers in Table 3.

  • Figure 6

    The diagram of IEEE 30-bus.

  • Figure 7

    The communication topology of IEEE 30-bus.

  • Figure 8

    (Color online) (a) The states for the modified incremental cost of all generation units with capacity limitations and (b) their corresponding output powers in Table 4for IEEE 30-bus test system.

  • Table 1   Parameters of three-unit system
    Unit $\alpha_i$ $\beta_i$ $\gamma_i$ $P_{Gi}(0)$
    1 561 7.92 0.001562 300
    2 310 7.85 0.00194 250
    3 78 7.8 0.00482 100
  • Table 2   Parameters of 100-unit system in a scale-free network
    Unit $\alpha_i$ $\beta_i$ $\gamma_i$ $P_{Gi}(0)$
    $i$ [100,~500] [7.5,~8] [0.001,~0.004] [175,~225]
  • Table 3   Parameters of three-unit system
    Unit $P_i^m$ $P_i^M$ $P_{Gi}(0)$
    1 250 300 260
    2 200 300 220
    3 150 200 170
  • Table 4   Parameters of generations in IEEE 30-bus
    Unit (Generator No.) $\alpha_i$ $\beta_i$ $\gamma_i$ $P_{\min}$ $P_{\max}$
    1 (1) 0 2.00 0.00375 50 200
    2 (2) 0 1.75 0.01750 20 80
    3 (5) 0 1.00 0.06250 15 50
    4 (8) 0 3.25 0.00834 10 35
    5 (11) 0 3.00 0.02500 10 30
    6 (13) 0 3.00 0.02500 12 40