(26e) Demand Side Management of a Steel Plant Incorporating the Maintenance of Eafs with Alternative Operating Modes

The scheduling of production and maintenance is a critical decision process for the profitable management of any process plant [1]. Maintenance makes sure that the plant assets are available, and in a condition required to perform the production tasks. Maintenance can reset the status of a unit to full health [1,2] or just partially improve its residual life. These two alternatives, in the form of offline and online washing, were considered in [3] when scheduling a network of compressors. One interesting aspect of the model is that the decrease in health is associated to a decrease in efficiency, which is translated into extra power consumption, modelled as a linear function of cumulative operational time. In contrast, most works assume that the health of a unit does not affect its performance.

We consider electrode degradation in the electric arc furnaces (EAFs) of a steel plant. As described in [1], the way the energy is provided over time to melt the metal can follow different power profiles, called melting curves. These can be viewed as alternative operating modes for the EAF, allowing for a more flexible operation [4]. The selection of the melting curve effects the duration of melting and the lifetime of the electrodes, with higher power peaks shortening the duration of the tasks while wearing the furnace electrodes faster. In the real-life system considered, the electrodes of an EAF need to be replaced every day and have a cost that is of the same order of magnitude of electricity consumption. Together with hourly changing electricity prices, all these features lead to a challenging industrial demand-side management problem.

In this work, we extend the mixed-integer linear programming (MILP) discrete-time scheduling formulation in [5] to consider alternative operating modes for the EAFs and electrode replacement tasks. Electrode replacement tasks reset the mass of electrode to the condition of new, the challenging being deciding how much remaining mass to consume, a value that depends on the assignment of batches to each EAF and on the operating modes selected, decisions to be made by the optimization. We take full advantage of the Resource-Task Network (RTN) process representation [6] to address the challenge of defining replacement tasks that consume an unknow value of electrode mass. It is an alternative to the constraints proposed in [1] that rely on a State-Task Network based formulation [7], which involve one non-linear constraint with a bilinear term (product of a binary and a continuous variable) that is linearized into three sets of constraints.

Discrete-time formulations are known to be very tight, ensuring a good computational performance for problems with tens of thousands of variables and constraints. However, this is no longer the case when including electrode replacement tasks, since the LP relaxation can buy a fraction of the full electrode, the minimum mass required to execute the remaining processing tasks. To overcome this issue, we propose a simple 2-stage decomposition procedure to first determine the minimum number of replacement tasks. The results show that 1-day problems with 24 batches and three operating modes for each EAF can be solved to less than 0.5% optimality gap in a couple of minutes of computational time.

Acknowledgments: Financial support from Fundação para a Ciência e Tecnologia (FCT) through projects CEECIND/00730/2017andUID/MAT/04561/2019 as well as from the Marie Curie Horizon 2020 EID-ITN Project “PROcess NeTwork Optimization for efficient and sustainable operations of Europe’s process industries taking machinery condition and process performance into account – PRONTO”, Grant agreement No. 675215.

References:

[1] Biondi, M., Sand, G., Harjunkoski, I., 2017. Optimization of multipurpose process plant operations: A multi-time-scale maintenance and production scheduling approach. Comp. Chem. Eng. 99, 325-339.

[2] Castro, P.M., Grossmann, I.E., Veldhuizen, P., Esplin, D., 2014. Optimal maintenance scheduling of a gas engine power plant using generalized disjunctive programming. AIChE J. 60, 2083–2097.

[3] Xenos, D.P., Kopanos, G.M., Cicciotti, M., Thornhill, N.F., 2016. Operational optimization of networks of compressors considering condition-based maintenance. Comp. Chem. Eng. 84, 117-131.

[4] Zhang, X., Hug, G., Harjunkoski, I., 2017. Cost-effective scheduling of steel plants with flexible eafs. IEEE Transactions on Smart Grid, 8(1), 239-249.

[5] Castro, P.M., Sun, L., Harjunkoski, I., 2103. Resource-Task Network Formulations for Industrial Demand Side Management of a Steel Plant. Ind. Eng. Chem. Res. 52, 13046-13058.

[6] Pantelides, C., 1994. Unified frameworks for the optimal process planning and scheduling. In Proceedings of the Second Conference on Foundations of Computer Aided Operations.

[7] Shah, N., Pantelides, C.C., Sargent, W.H., 1993. A general algorithm for short-term scheduling of batch operations-II. Computational issues. Comp. Chem. Eng. 2, 229-244.