A day-ahead scheduling study in the Journal of Energy Storage reports daily operating cost cuts of 31 percent on a 33 bus microgrid and 48 percent on a 69 bus microgrid, from 8,343.83 to 5,742.26 USD and from 8,742.93 to 4,573.68 USD. The savings hold inside the model, which uses a fixed electricity price of 0.1390 USD per kWh and a battery that has no charging or discharging losses, and the authors state both limits.
What was modelled
The paper schedules photovoltaic generation, battery energy storage and D-STATCOM reactive power devices in two radial AC microgrids at 12.66 kV, one with 33 buses and 32 lines and one with 69 buses and 68 lines. The horizon is 24 hours in 48 intervals of 30 minutes. Each system has three PV generators, three batteries and three D-STATCOMs, so a schedule is a vector of 432 values, nine devices over 48 periods. Constraints cover AC power flow feasibility, device limits, battery state of charge, voltage, line loading and, in islanded mode, diesel generator minimum and maximum output. Battery state of charge starts and ends each day at 50 percent.
A master and slave structure does the search. Black Widow Optimization proposes schedules, and a successive approximation power flow checks that each one is physically feasible. The method is compared with particle swarm optimization (PSO), multiverse optimization (MVO) and a population based genetic algorithm (PGA) over 100 independent runs. Penalty factors for constraint violations are all set to 1,000, which the authors describe as heuristic.
| Case | Unscheduled base, USD per day | Best schedule, USD per day | Saving |
|---|---|---|---|
| 33 bus, grid connected | 8,343.83 | 5,742.26 | 31.2 percent |
| 69 bus, grid connected | 8,742.93 | 4,573.68 | 47.7 percent |
| 33 bus, islanded | Not given in the abstract | 12,263.05 | Not stated |
| 69 bus, islanded | Not given in the abstract | 11,850.64 | Not stated |
Where the saving comes from
Because the grid connected runs use one price for all 48 periods, the study says the saving is not time of use arbitrage. It attributes the saving to coordinated dispatch of the distributed resources and network feasible redistribution of energy, but the abstract does not split it among PV, storage and reactive support, and does not define the unscheduled base case beyond that label. The same price is applied to imports and exports, so there is no separate sale tariff either.
In islanded mode the batteries charge when the diesel unit approaches its minimum loading region and discharge in higher demand intervals, while PV curtailment and reactive support help keep voltage and line loading within limits. All reported best schedules meet the voltage, line loading, diesel and state of charge constraints. The islanded best costs are about 114 percent and 159 percent higher than the grid connected best costs for the two systems, in a setup where the diesel generator replaces the grid as the balancing source.
The battery model and the comparison
The state of charge equation is an ideal efficiency model, so charging and discharging losses are not represented. The authors write that this can overestimate usable storage flexibility and that reported costs should be read within that scope. Cycling enters only as a throughput cost coefficient, not a degradation model, and they cite earlier work showing that degradation aware scheduling can materially change dispatch and cost.
On the algorithm comparison, Black Widow Optimization obtains the lowest average cost in all four cases, but its advantage over the genetic algorithm is small in several cases and comes with higher computing time. The tuning also limits what the ranking means. Each algorithm’s settings were tuned separately, with a PSO using 600 particles and 3,000 iterations, and the tuned population sizes differ, for example 48 against 66 individuals for BWO and PGA in grid connected mode. The paper says the comparison is therefore not an equal budget benchmark, and that a matched evaluation would require rerunning all methods with a common number of fitness evaluations or time limit.
The checks the paper leaves to later work are the ones that decide whether the numbers transfer: time of use or market prices, a loss and degradation aware battery, and an equal budget comparison of the solvers. None has a date. For a market where storage economics are tested on real tenders, see the SECI 3.2 GWh storage tender. Source: Núñez-Cervela, Grisales-Noreña and Sanin-Villa, Battery energy storage driven cost oriented energy management of microgrids using black widow optimization, Journal of Energy Storage 182 (2026) 124997, open access.
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