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Figure 1
(Color online) Optimal dispatch of each generator.
Figure 2
(Color online) (a) Structure chart of IEEE 14-bus; (b) topology of IEEE 14-bus.
Figure 3
(Color online) (a) Power output of the distributed generators; (b) load demand of the users.
Figure 4
(Color online) (a) Mismatch of entire grid and (b) the incremental cost of each generation in five time slots.
Figure 5
(Color online) Values of (a) $\mu_{i,h}$ and (b) $\nu_{i,h}$ in five time slots.
Figure 6
(Color online) Consensus values of the Lagrangian multipliers $\theta_i$ (a) and $\gamma_i$ (b) of the power flow constraints.
Figure 7
(Color online) Active power flow of the transmission lines.
| Parameter | Generator number | ||||
| 1 | 3 | 4 | 13 | 14 | |
| $a_i$ | 0.08 | 0.062 | 0.075 | 0.072 | 0.066 |
| $b_i$ | 2.25 | 4.2 | 3.25 | 6.25 | 3.2 |
| $c_i$ | 23 | 12 | 23 | 14 | 19 |
| $P_i^m$ | 20 | 10 | 20 | 9 | 5 |
| $P_i^M$ | 80 | 80 | 95 | 70 | 80 |
| $P_i^R$ | 10 | 10 | 10 | 8 | 7 |
| $\beta_i$ | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 |
| User number | Time 1 | Time 2 | Time 3 | Time 4 | Time 5 |
| 7 | 10 | 15 | 6 | 13 | 6 |
| 8 | 5 | 12 | 5 | 15 | 10 |
| 10 | 4 | 17 | 3 | 12 | 18 |
| 11 | 15 | 32 | 10 | 20 | 13 |
| User number | $\omega_i$ | $\upsilon_i$ | $d_i^m$ | $d_i^M$ |
| 2 | 0.06 | 15.12 | 30 | 60 |
| 5 | 0.082 | 11.984 | 15 | 39 |
| 6 | 0.065 | 12.992 | 15 | 35 |
| 7 | 0.062 | 13.216 | 15 | 37 |
| 8 | 0.066 | 12.04 | 15 | 35 |
| 9 | 0.071 | 15.904 | 20 | 58 |
| 10 | 0.062 | 12.544 | 10 | 25 |
| 11 | 0.075 | 13.3 | 15 | 30 |
| 12 | 0.076 | 12.572 | 18 | 32 |
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | |
| From | 1 | 1 | 2 | 2 | 2 | 3 | 4 | 4 | 4 | 5 | 6 | 6 | 6 | 7 | 7 | 9 | 9 | 10 | 12 | 13 |
| To | 2 | 5 | 3 | 4 | 5 | 4 | 5 | 7 | 9 | 6 | 11 | 12 | 13 | 8 | 9 | 10 | 14 | 11 | 13 | 14 |
| $T_l$ | 54 | 66 | 36 | 42 | 69 | 96 | 28 | 48 | 36 | 36 | 46.8 | 36 | 36 | 36 | 54 | 42 | 54 | 25.2 | 46.8 | 72 |
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