Distributed stochastic model predictive control for energy dispatch with distributionally robust optimization

doi:10.1007/s10483-025-3215-6

Abstract

Abstract:

A chance-constrained energy dispatch model based on the distributed stochastic model predictive control (DSMPC) approach for an islanded multi-microgrid system is proposed. An ambiguity set considering the inherent uncertainties of renewable energy sources (RESs) is constructed without requiring the full distribution knowledge of the uncertainties. The power balance chance constraint is reformulated within the framework of the distributionally robust optimization (DRO) approach. With the exchange of information and energy flow, each microgrid can achieve its local supply-demand balance. Furthermore, the closed-loop stability and recursive feasibility of the proposed algorithm are proved. The comparative results with other DSMPC methods show that a trade-off between robustness and economy can be achieved.

Key words: distributed stochastic model predictive control (DSMPC), distributionally robust optimization (DRO), islanded multi-microgrid, energy dispatch strategy

2010 MSC Number:

TM73

Mengting LIN, Bin LI, C. CECATI. Distributed stochastic model predictive control for energy dispatch with distributionally robust optimization. Applied Mathematics and Mechanics (English Edition), 2025, 46(2): 323-340.

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Figures/Tables 15

Fig. 1

Fig. 2

Table 1

Parameters of ESSs"

Unit	$E i min$ /kWh	$E i max$ /kWh	$P i chrg,max$ /kW	$P i dcrg,max$ /kW	$η i chrg$	$η i dcrg$
ESS1	40	320	100	100	0.65	0.7
ESS2	40	320	100	100	0.85	0.8
ESS3	40	320	100	100	0.95	0.9

Table 1

Table 2

Parameters of DGs[17]"

Unit	$P i DG,min$ /kW	$P i DG,max$ /kW	$P i DG,down$ /kW	$P i DG,up$ /kW
DG1	10	150	30	30
DG2	8	135	25	25
DG3	15	280	40	40

Table 2

Fig. 3

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Table 3

Comparison of over-all system cost with different ε"

Method	$ε$
Method	0.01	0.05	0.1	0.15	0.2
Proposed DDR-MPC	$1.625 × 106$	$1.497 × 106$	$1.439 × 106$	$1.403 × 106$	$1.476 × 106$
Approach in Ref. [13]	$1.521 × 106$	$1.446 × 106$	$1.354 × 106$	$1.314 × 106$	$1.290 × 106$

Table 3

Table 4

Comparison of constraint violations with different ε"

Method	$ε$
Method	0.01	0.05	0.1	0.15	0.2
Proposed DDR-MPC	0/1 000	16/1 000	25/1 000	42/1 000	83/1 000
Approach in Ref. [13]	0/1 000	21/1 000	32/1 000	80/1 000	121/1 000

Table 4

References 17

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