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
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
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
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 |
Unit | $\alpha_i$ | $\beta_i$ | $\gamma_i$ | $P_{Gi}(0)$ |
$i$ | [100,~500] | [7.5,~8] | [0.001,~0.004] | [175,~225] |
Unit | $P_i^m$ | $P_i^M$ | $P_{Gi}(0)$ |
1 | 250 | 300 | 260 |
2 | 200 | 300 | 220 |
3 | 150 | 200 | 170 |
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 |