An industrial demand-response model called LSTN remained solvable at 2,000 plants in minutes. The comparison model, STN-60 min, failed to converge within 2 hours at 20 plants, after its binary-variable count exceeded 10,000. The authors present that contrast as evidence of LSTN's computational tractability for large-scale industrial demand response.
The shortcut is continuous operating time
LSTN is a linear STN model developed for industrial production-process modeling in demand-response applications. Its central simplification is to treat the time a task spends at each operating point as a continuous variable. The resulting formulation is a linear program, or LP, meaning the model keeps the relationships it optimizes in linear form.
The accuracy result comes with a warning
For its accuracy test, the study modeled one industrial user: a steel powder manufacturing facility. The production target was set at 24 times the lowest task production rate, listed as 15 Ton/h, and the starting material was half the buffer limit.
To create a benchmark, the researchers assumed equipment switching took 2 minutes and treated STN-2 min as the accurate reference. A mixed-integer linear program, or MILP, generated the reference load profiles and daily energy costs, which were then used as the true values for calculating errors in the other models.
The comparison covered 31 days and used root mean square error, or RMSE, to measure each model's difference from the reference for the load profile and energy cost. The reported load-profile errors were 15.3 kW (5.37%) for STN-60 min, 3.43 kW (1.21%) for STN-30 min, 0.59 kW (0.21%) for STN-5 min and 0.30 kW (0.17%) for LSTN.
Energy-cost RMSEs were $1.979 for STN-60 min, $0.398 for STN-30 min, $0.034 for STN-5 min and $0.033 for LSTN. On that reported measure, LSTN had the lowest listed error for both load profile and energy cost.
But the reporting is internally inconsistent. Nearby prose says LSTN's energy-consumption error was 0.59, or 0.21% of maximum load, while the reported accuracy values assign 0.59 kW (0.21%) to STN-5 min's load-profile RMSE and give LSTN a load-profile RMSE of 0.30 kW (0.17%). That discrepancy makes the exact accuracy claim harder to interpret, even though the reported results favor LSTN.
Flexibility looked similar despite different baselines
Although LSTN and STN-60 min produced different load baselines, their adjustable-boundary results were very similar. No exact boundary values are given in the text, so this is a qualitative, figure-based comparison.
The test was built for scale
For the computation tests, the default case combined 10 industrial users. Device parameters were varied uniformly from 0.8 to 1.2 times the stated values, and the demand-response duration was 4 hours; STN-60 min was included as a comparison.
The optimization problems were solved with Gurobi 10.0.0, MATLAB R2021a and YALMIP on a workstation using an Intel Core i9-10900X CPU at 3.7 GHz and 128 GB of RAM. The paper's text does not give exact runtime figures or normalized, hardware-independent speed comparisons.
The study's accuracy evidence came from one modeled steel powder facility, while its scalability tests used aggregated industrial users. This means the numerical comparison is tied to the tested model settings.
The main caveat is the continuous-time assumption: for equipment with non-negligible switching times, LSTN may sacrifice accuracy in exchange for computational efficiency, while conventional binary variables remain an alternative.
Within those boundaries, the authors characterize LSTN as suitable for large-scale industrial demand response and attribute that suitability to computational tractability. In their conclusion, they also describe LSTN's reported energy-consumption error as 0.17%, lower than conventional STN with a 1-hour scheduling interval.
The manuscript is an arXiv version 1 preprint dated 26 Aug 2026 and reports support from the Science and Technology Program of State Grid Corporation of China under Grant 5108-202218280A-2-378-XG.
Paper data and sources
Original title: LSTN: A Linear Model of Industrial Production Process for Demand Response
Authors: Ruike Lyu, Hongye Guo, Yuanjie Zheng et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: 10.1109/isgteurope56780.2023.10408608
Original paper · Full text