# Dynamic forecasting and optimal scheduling of by-product gases in integrated iron and steel works

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## Abstract

The by-product gases, which are generated in ironmaking, coking and steelmaking processes, can be used as fuel for the metallurgical processes and on-site power plants. However, if the supply and demand of by-product gases are imbalanced, gas flaring may occur, leading to energy wastage and environmental pollution. Therefore, optimal scheduling of by-product gases is important in iron and steel works. A BP_LSSVM model, which combines back-propagation (BP) neural network and least squares support vector machine (LSSVM), and an improved mixed integer linear programming model were proposed to forecast the surplus gases and allocate them optimally. To maximize energy utilization, the stability of gas holders and boilers was considered and a concise heuristic procedure was proposed to assign penalties for boilers and gas holders. Moreover, the optimal level of gas holder was studied to enhance the stability of the gas system. Compared to the manual operation, the optimal results showed that the electricity generated by the power plant increased by 2.93% in normal condition and by 22.2% in overhaul condition. The proposed model minimizes the total cost by optimizing the boiler load with less adjustment frequency and the stability of gas holders and can be used as a guidance in dynamic forecasting and optimal scheduling of by-product gases in integrated iron and steel works.

## Keywords

Iron and steel works Back-propagation neural network Least squares support vector machine Mixed integer linear programming Dynamic forecasting Optimal scheduling## List of symbols

*B*{

*b*| Boilers}*G*{

*g*| Gases}*GH*{

*k*| Gas holders}*P*{

*t*| Periods}*TB*{

*tb*| Turbines}- \(a_{tb}\)
First regression parameter from steam production of turbine

*tb*- \(b_{tb}\)
Second regression parameter from steam production of turbine

*tb*- \(C_{\text{c}}\)
Unit price for coal (RMB/t)

- \(C_{\text{e}}\)
Unit price for electricity (RMB/kWh)

- \(C_{g}\)
Economic benefit of gas

*g*by generating electricity (RMB/m^{3})- \(C_{\text{w}}\)
Unit price for water (RMB/t)

- \(C_{{1\,{\text{kJ}}}}\)
Economic benefit of 1 kJ thermal energy by generating electricity (RMB/kJ)

- \(D_{st}^{\text{pro}}\)
Amount of steam supplied to steelmaking process (m

^{3}/h)- \(D_{st}\)
Steam demand in steelmaking process (m

^{3}/h)*E*_{tb, t}Electricity generated by turbine

*tb*in period*t*(RMB/kWh)- \(f_{b}^{ \hbox{min} }\)
Minimum heat value of boiler

*b*combustion in period*t*(kJ/m^{3})- \(f_{b}^{ \hbox{max} }\)
Maximum heat value of boiler

*b*combustion in period*t*(kJ/m^{3})- \(f_{t,b}\)
Heat value of mixed fuel used by boiler

*b*in period*t*(kJ/m^{3})- \(F\)
Total energy consumption released by fuel combustion (kJ)

- \(F_{{{b}},{t}}^{\text{v}}\)
Heat supplied by fuel to boiler

*b*in period*t*(kJ/h)- \(F_{t}^{g}\)
Surplus of gas

*g*in period*t*(m^{3}/h)- \(h_{k}^{ \hbox{min} }\)
Lowest level of gas holder

*k*(m^{3})- \(h_{k}^{ \hbox{max} }\)
Highest level of gas holder

*k*(m^{3})- \(h_{t,k}\)
Level of gas holder

*k*in period*t*(m^{3})- \(H_{g}\)
Heat value of gas

*g*(kJ/m^{3})- \(H_{st}\)
Enthalpy of steam (kJ/t)

- \(H_{\text{w}}\)
Enthalpy of water (kJ/t)

- \(I\)
Binary variables that indicate boiler load fluctuation

- \(T_{b}^{ \hbox{min} }\)
Minimum load of boiler

*b*in period*t*(m^{3}/h)- \(T_{b}^{ \hbox{max} }\)
Maximum load of boiler

*b*in period*t*(m^{3}/h)- \(T_{t,tb}\)
Steam get into steam turbine

*tb*in period*t*(t/h)- \(T_{t,tb}^{tb}\)
Steam consumed by turbine

*tb*in period*t*(t/h)- \(T_{{i,t,tb}}^{\text{dem}}\)
Sum of steam

*i*consumed in steelmaking process (t/h)- \(T_{t,b}\)
Production of steam in boiler

*b*in period*t*(t/h)- \(v_{b,t}^{{{\text{c}},{ \hbox{min} }}}\)
Minimum coal consumption of boiler

*b*in period*t*(t/h)- \(v_{b,t}^{{{\text{c}},{ \hbox{max} }}}\)
Maximum coal consumption of boiler

*b*in period*t*(t/h)- \(v_{b,t}^{\text{c}}\)
Coal consumption of boiler

*b*in period*t*(t/h)- \(v_{b,t}^{\text{w}}\)
Water consumption of boiler

*b*in period*t*(t/h)- \(v_{k}\)
Maximum running speed of piston in gas holder

*k*(m^{3}/h)- \(v_{t}^{{{\text{w}},{\text{cnd}}}}\)
Condensate water recovered from steam turbine in period

*t*(m^{3}/h)- \(W_{b}\)
Load fluctuation penalty factor for boiler

*b*(RMB/times)- \(W_{g}\)
Penalty factor of gas flaring for gas

*g*(RMB/h)- \(W_{\text{h}}\)
Penalty factor for gas holder above optimal level but in stable level (RMB/m

^{3})- \(W_{\text{hh}}\)
Penalty factor for gas holder in high level (RMB/m

^{3})- \(W_{\text{l}}\)
Penalty factor for gas holder below optimal level but in stable level (RMB/m

^{3})- \(W_{\text{ll}}\)
Penalty factor for gas holder in low level (RMB/m

^{3})- \(W_{t,b}\)
Total water flowing into boiler

*b*in period*t*(m^{3}/h)- \(\Delta B_{t}^{g}\)
Gas consumption of boiler

*b*in period*t*(m^{3}/h)- \(\Delta D_{t}^{{g}}\)
Gas flaring of by-product gas

*g*(m^{3}/h)- \(\Delta D_{t}^{{{g}},{ \hbox{max} }}\)
Maximum gas flaring of gas

*g*in period*t*(m^{3}/h)- \(\Delta L_{t}^{g}\)
Amount of gas

*g*entering gas tank within period*t*(m^{3}/h)- \(\Delta V_{\text{h}}\)
Amounts of by-product gases above optimal levels (m

^{3}/h)- \(\Delta V_{\text{hh}}\)
Amounts of by-product gases that deviate from high level (m

^{3}/h)- \(\Delta V_{\text{l}}\)
Amounts of by-product gases below optimal levels (m

^{3}/h)- \(\Delta V_{\text{ll}}\)
Amounts of by-product gases that deviate from low level (m

^{3}/h)- \(\Delta V_{t,k}\)
Level variation of gas holder

*k*during period*t*(m^{3})- \(\Delta t\)
Duration of a period (h)

- \(\eta_{b}\)
Efficiency of boiler

*b*

## Notes

### Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 51874095) and by the National Key Research and Development Program (Project Nos. 2016YFB0601305 and 2016YFB0601301). The authors gratefully acknowledge the reviewers and editors for their fruitful comments.

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