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LSTN: A Linear Model of Industrial Production Process for Demand Response
Ruike Lyu, Hongye Guo, Yuanjie Zheng, Yunlong Bai, Qixin Chen
TL;DR
Industrial demand response needs production models that preserve operational constraints without making large-scale optimization computationally infeasible. The paper develops LSTN, which uses continuous operating times in a linear production model and applies it to aggregated DR. Numerical tests report 0.17% energy-consumption error and much faster computation than conventional STN approaches.
Problem
Conventional production models use binary variables for discrete equipment operating points, creating computational complexity that can hinder large-scale industrial demand response.
Method
LSTN linearizes industrial production modeling by replacing discrete operating-point variables with continuous task operating times while representing production, material, storage, and energy constraints.
Results
0.17% energy-consumption error is reported for LSTN, while aggregated DR models remain solvable in minutes for 2000 factories.
Takeaways & Limitations
LSTN provides a computationally tractable model for evaluating large-scale industrial DR while maintaining close agreement with an accurate STN reference.
Abstract
from arXiv · showhide
Industrial production modeling provides operational constraints for industrial users participating in demand response (DR) programs. Conventional modeling of the production process introduces binary variables to model the discrete operating points of industrial equipment, which can be computationally infeasible in large-scale DR applications. To reasonably model industrial users' operational constraints while balancing computational complexity and modeling accuracy, we developed a linear model of the industrial production process for evaluating DR applications. Numerical results verify the accuracy of the proposed model and its great improvement in computational efficiency over competing approaches.
I. INTRODUCTION
Industrial demand response offers substantial flexibility, but conventional state-task production models introduce binary variables that make large-scale optimization difficult. LSTN replaces these discrete operating-point variables with continuous operating times to improve scalability while representing hourly energy use.
- Industrial users offer substantial demand-response potential because they consume more energy and have more regular consumption characteristics than other load types.
- Conventional STN and RTN production models use binary variables for discrete equipment states, creating MILPs with rapidly increasing computation time.
- Aggregating many factories can make MILP-based joint energy optimization computationally infeasible because solution complexity increases exponentially with problem size.
- Continuous operating-time modeling can better represent hourly industrial energy consumption because equipment switching is usually rapid relative to DR scheduling intervals.
- LSTN models production, material flows, storage, task energy characteristics, and final-product targets while replacing discrete operating-point variables with continuous operating times.
II. INDUSTRIAL PRODUCTION PROCESS MODELING
LSTN formulates industrial production processes as a linear state-task network centered on continuous task operating times and temporal energy-consumption constraints. The model represents production targets, material flows, buffers, energy use, and device-specific operating characteristics while allowing controlled accuracy trade-offs for slow-switching equipment.
- LSTN models industrial production with a state-task network whose nodes represent production tasks and material states across multiproduct processes.
- The model treats task operating times at discrete operating points as continuous because switching is negligible relative to DR scheduling intervals.
- Task energy consumption is calculated from operating-point power and the continuous duration spent at each point within each time interval.
- Material-state equations track feedstock, intermediate, and final-product buffers over time using task production and consumption rates.
- The linear program uses operating durations as decision variables and energy consumption and material states as dependent variables, with equipment parameters obtained from nameplates or factory inventories.
- LSTN can represent nonadjustable and inherently continuous devices, but slow switching requires either conventional binary variables or a continuous approximation that sacrifices accuracy for efficiency.
III. APPLICATION OF LSTN IN INDUSTRIAL USER DR
LSTN can be embedded directly in demand-response optimization, but centralized access to factory parameters raises privacy concerns. The paper therefore motivates a multilayer control design to reduce computational burden and protect industrial-user privacy.
- Because LSTN expresses factory energy costs and production constraints linearly, its primal or optimality conditions can be embedded in dispatch and DR pricing models.
- Direct embedding requires centralized access to factories’ internal parameters, which may be impractical because of privacy concerns.
A. Aggregation and Control
The framework aggregates factories through an intermediary that reports virtual-battery demand-response capacity and distributes grid control signals to individual factories.
- The aggregator calculates aggregated DR capacity from factory parameters, reports it to the grid operator, and assigns received control signals to individual factories.
- The framework uses a virtual battery model to approximate the external characteristics of aggregated factory resources.
- Virtual-battery charging and discharging power and energy capacities may vary across demand-response time intervals.
- The virtual-battery parameters use factory baseline load and a demand-response event horizon, with a four-hour horizon given as an example.
B. Optimal Dispatch
After receiving grid control signals, the aggregator optimizes factory energy consumption while enforcing signal tracking and considering factory costs and operating constraints.
- The grid operator sends control signals to the aggregator through predefined strategies based on the factories’ reported aggregated DR capacity.
- The grid-computing process is omitted because existing battery-related dispatch strategies can be applied directly to determine aggregator signals.
- Upon receiving control signals, the aggregator solves an optimization problem for factory energy consumption and signal response.
- The objective penalizes energy mismatch to enforce load-reduction tracking while costs and operating constraints are considered over the full time horizon.
- The aggregation and dispatching models are linear programs that can be solved efficiently.
IV. NUMERICAL RESULTS
The numerical experiments used Gurobi, MATLAB, and YALMIP on a workstation with an Intel Core i9-10900X CPU and 128 GB RAM.
- The optimization problems were solved using Gurobi V10.0.0, MATLAB R2021a, and YALMIP.
- Computations ran on a workstation with an Intel Core i9-10900X CPU at 3.7 GHz and 128 GB RAM.
A. Modeling Accuracy
The single-user evaluation compares LSTN with STN models using PJM August 2022 prices and a steel powder manufacturing facility, treating STN-2 min as the accurate reference.
- The modeling-accuracy test used hourly August 2022 PJM electricity prices and site parameters from a steel powder manufacturing facility.
- Figure 3 presents the August 5 load profiles produced by the compared models.
- STN-2 min was treated as the accurate industrial-user model because its two-minute interval represents the assumed equipment switching time.
- 0.59 energy-consumption error, or 0.21% of maximum load, was reported for LSTN versus 15.3, or 5.37%, for STN-60 min.
- The comparison indicates that continuous operating time is reasonable and LSTN is more accurate than STN-60 min while using a longer scheduling interval.
B. Computation Efficiency
Using the August 5 load baseline, the study compares STN-60 min and LSTN for aggregated-factory adjustable capacity, dispatch, and computation time. Their adjustable boundaries are similar, while LSTN remains computationally tractable as the number of factories grows.
- Evaluation setup: The evaluation uses 10 industrial users by default, a 4-hour DR duration, and STN-60 min as the MILP comparison model.Device parameters are uniformly distributed between [0.8, 1.2] times the values in Tab. I.
- Instruction dispatch: The grid dispatches energy-reduction instructions to individual factories according to the aggregated factories’ adjustable boundary.Figure 5 compares instruction dispatch under LSTN and STN.
- Computation time: STN-60 min failed to converge within 2 hours at 20 plants, with more than 10,000 binary variables.This result illustrates the computational burden of the conventional MILP-based model as the number of factories increases.
- Computation time: At 2,000 plants, LSTN still solved in minutes, an acceptable computation time for practical application and economic dispatch.Figure 6 reports computation time against the number of factories for adjustable-capacity calculation and optimal dispatch.
V. CONCLUSION
The paper presents LSTN as a linear industrial production-process model for demand-response applications, treating equipment operation as continuous when switching is faster than the DR scheduling interval. Numerical results indicate low energy-consumption error and substantially improved computational tractability for aggregating multiple factories.
- V. CONCLUSION: LSTN models industrial production processes linearly by replacing discrete operating-point variables with continuous operating times.The continuous-operation assumption is motivated by equipment switching times that are usually much shorter than DR scheduling intervals.
- V. CONCLUSION: LSTN has an energy consumption error of only 0.17% relative to a standard STN model that accurately models device switching time.The paper states this error is smaller than that of the conventional STN model with a one-hour scheduling interval.
- V. CONCLUSION: LSTN greatly accelerates aggregated DR-capacity calculation and grid-instruction decomposition when multiple factories participate.The resulting computational tractability makes the model suitable for large-scale industrial DR.