Fig 1.
Five-microgrid network topology.
Each microgrid has PV/WT generation, ESS, and DR-enabled loads. Solid lines show tie-line flows Pij; dashed lines show communication links.
Fig 2.
Methodology flowchart of the proposed RDMPC.
At each MPC step, microgrids (i) perform mode-dependent resilience setup with bounded tie-line mismatch and two-sided reserve tightening, (ii) coordinate via lossy-communication ADMM, and (iii) execute the reciprocal consensus tie-line schedule with a local feasibility-repair solve, ensuring anytime feasibility even when ADMM is truncated.
Table 1.
Execution semantics by method.
Table 2.
Experimental scenarios evaluated in Results.
Table 3.
Nominal (Path A) simulation parameters.
Table 4.
Path B results: Loss-phase execution metrics (per-seed totals over 5 steps, n = 20 seeds).
Table 5.
Burst outage results: Loss-phase metrics (Tfail = 3 on critical edges, n = 20 seeds).
Table 6.
Scenario S7 (DR ablation): loss-phase execution metrics under step-level random loss (n = 20 seeds). Loss phase is steps 3–7 (5 steps) after a 3-step burn-in; values are loss-phase totals per seed, averaged across seeds. B3-noDR disables DR flexibility (shiftable and curtailable fractions set to zero). Cost in $.
Fig 3.
Path B loss-phase mean metrics (n = 20 seeds, loss-phase only).
Grouped bar chart comparing B1 (oracle planning), B2 (naive DMPC), and B3 (RDMPC) for executed ENS, cost (shown in $k), and curtailment. Left: random step-level losses (Gilbert–Elliott; directional mean 15.75%, handshake ). Right: Burst outage (Tfail = 3 on critical edges). B3 outcomes are mixed relative to B2; improvements are seed-dependent rather than uniform.
Fig 4.
Sorted per-seed executed ENS improvement (loss-phase only, n = 20 seeds).
Delta values sorted ascending; each curve sorted independently (x-axis is sorted rank position
, not the random seed index). Negative values indicate B3 outperforms B2. Under random step-level loss (blue), deltas are mixed (5/20 better, 5 ties, 10 worse), indicating no uniform improvement. Under burst outage (red), outcomes remain heterogeneous (7/20 better, 5 ties, 8 worse), with no consistent dominance.
Fig 5.
DR ablation: loss-phase execution metrics (n = 20 seeds, per-seed means).
Two-panel bar chart comparing B1 (oracle planning), B2 (naive DMPC), B3 (RDMPC with DR), and B3-noDR (RDMPC without DR). Left: Executed ENS (kWh). Right: Executed cost ($k). Disabling DR increases ENS by 492% (513 vs 86.6 kWh) and cost by 484% ($514k vs $88k).
Table 7.
Scenario S6 (Topology change): loss-phase execution metrics (n = 20 seeds). Middle tie-line between MG3 and MG4 removed at step 3; loss-phase totals per seed, averaged.
Fig 6.
S6: Topology-change impact on B1/B2/B3 performance.
Loss-phase totals (steps 3–7) under topology change where the MG3–MG4 tie-line is removed at step 3. Error bars show standard error (SE = std/) across 20 seeds. B3 (RDMPC) is comparable to B2 in ENS and cost, while B1 remains lowest on average.
Table 8.
Path A results: Cost parity under packet loss (n = 50 seeds per ploss).
Fig 7.
Path A: Cost excess vs. packet loss rate (n = 50 seeds per point).
Mean cost excess for B2 (naive DMPC) and B3 (RDMPC) across . Shaded regions show
standard deviation across seeds (not confidence intervals). Lines overlap within variability bands at all loss rates, confirming cost parity.
Fig 8.
Path A: Anytime behavior vs. iteration budget.
Mean cost excess versus ADMM iteration budget Mmax (n = 50 seeds, ploss = 0.3). Under packet loss, larger Mmax increases cost excess and then saturates, reflecting a tradeoff between coordination effort and cumulative loss exposure; feasibility remains anytime via the execution/repair policy.