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Plant-wide byproduct gas distribution under uncertainty in iron and steel industry via quantile forecasting and robust optimization

Sheng-Long Jiang, Meihong Wang, I. David L. Bogle

Abstract

In the modern iron and steel industry, the efficient distribution of byproduct gases faces significant challenges due to quantity- and quality-related uncertainties of gases. This study presents an optimal approach to gas distribution that addresses this issue by incorporating the energy flow network and the uncertain surplus gases from the manufacturing system. The uncertain optimization problem is formulated as a two-stage robust optimization (TSRO) model, including "here-and-now" decisions aimed at minimizing the start-stop cost of energy conversion units, as well as "wait-and-see" decisions aimed at minimizing the operating cost of gasholders and the penalties resulting from energy excess or shortage. To facilitate practical implementation, we propose a "first quantify, then optimize" approach: (1) quantifying the uncertainty of surplus gases via a conditional quantile regression (CDQ)-based T-step time series model, and (2)finding the optimal solution through a column-and-constraint generation algorithm. Furthermore, a case study is conducted on an industrial energy system to validate the proposed methodology. Computational results, using evaluation indicators, such as MAPE, RMSE, PICP, and PINAW, confirm the effectiveness of the data-driven time series model in accurately quantifying uncertainties in each period. Sensitivity analysis demonstrates that the proposed TSRO model achieves a favorable balance between robustness and flexibility by selecting the combination of "budget and quantile" and the parameters of storage and conversion units. Consequently, TSRO can efficiently find a robust gas distribution solution with the desired level of conservativeness for integrated iron and steel plants.

Plant-wide byproduct gas distribution under uncertainty in iron and steel industry via quantile forecasting and robust optimization

Abstract

In the modern iron and steel industry, the efficient distribution of byproduct gases faces significant challenges due to quantity- and quality-related uncertainties of gases. This study presents an optimal approach to gas distribution that addresses this issue by incorporating the energy flow network and the uncertain surplus gases from the manufacturing system. The uncertain optimization problem is formulated as a two-stage robust optimization (TSRO) model, including "here-and-now" decisions aimed at minimizing the start-stop cost of energy conversion units, as well as "wait-and-see" decisions aimed at minimizing the operating cost of gasholders and the penalties resulting from energy excess or shortage. To facilitate practical implementation, we propose a "first quantify, then optimize" approach: (1) quantifying the uncertainty of surplus gases via a conditional quantile regression (CDQ)-based T-step time series model, and (2)finding the optimal solution through a column-and-constraint generation algorithm. Furthermore, a case study is conducted on an industrial energy system to validate the proposed methodology. Computational results, using evaluation indicators, such as MAPE, RMSE, PICP, and PINAW, confirm the effectiveness of the data-driven time series model in accurately quantifying uncertainties in each period. Sensitivity analysis demonstrates that the proposed TSRO model achieves a favorable balance between robustness and flexibility by selecting the combination of "budget and quantile" and the parameters of storage and conversion units. Consequently, TSRO can efficiently find a robust gas distribution solution with the desired level of conservativeness for integrated iron and steel plants.
Paper Structure (16 sections, 18 equations, 13 figures, 1 algorithm)

This paper contains 16 sections, 18 equations, 13 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Literature review
  3. Optimal distribution under supply uncertainty
  4. Network of byproduct gas system
  5. Deterministic optimization model
  6. TSRO model
  7. DDRO formulation and solving
  8. Uncertainty quantification via machine learning
  9. Reformulation for TSRO
  10. Column-and-constraint generation algorithm
  11. Case study
  12. Uncertainty quantification
  13. Budget vs. Robustness
  14. Flexibility vs. Robustness
  15. Solutions of the proposed approach
  16. ...and 1 more sections

Figures (13)

  • Figure 1: Byproduct gas system in a integrated iron and steel plant.
  • Figure 2: Network flow of byproduct gas system.
  • Figure 3: Flowchart of the proposed DD-TSRO framework.
  • Figure 4: The violin plot of gas type and supply on dataset.
  • Figure 5: MAPE metric of the test set.
  • ...and 8 more figures