(534f) Operator-Triggered Advisory System for Electric Arc Furnace Process Optimization

Electric arc furnaces (EAFs) are widely used in the steel industry worldwide for production of steel by melting scrap steel collected from different sources. Approximately 25% of the world’s steel is produced using EAFs [1]. EAFs are huge consumers of electricity and approximately 400 kilowatt-hours is used per tonne of steel produced [2]. EAFs are currently operated with a low level of process automation and control, and decisions related to input amounts and timings are determined by the operators. Due to large fluctuations during the process, harsh operating conditions and the limited availability of measurements, real-time process optimization is very challenging [3]. The desired product quality is achieved by altering the chemistry of scrap by addition of fluxes. EAF operating decisions are taken by the operators based on what has worked in the past. Although operator’s experience is important for safe process operation, complex interacting relationships are difficult to take into account. Given the high operating cost due to the level of electricity consumption, considerable savings may accrue through the development and deployment of model-based optimization strategies to support EAF operators’ decision making. A real-time advisory system which computes economically optimal input trajectories based on a first-principles model is proposed in this work.

Optimization and control strategies developed in the past focused only on a sub-system of the EAF, such as electrode movement [4], rather than the entire process dynamics. It is only recently, Swartz and MacRosty studied dynamic optimization based on a detailed first principles EAF model [5]. However, a single optimization at the start of the process is not sufficient to counter various uncertainties such as initial condition discrepancy, process disturbances, plant-model mismatch and measurement noise. The effect of these uncertainties can be tackled by input trajectory manipulation during the batch process at various triggered time points [6]. The re-optimizations need the current knowledge of the plant states for accurate initialization. In this work, we introduce an operator-triggered advisory system for EAF operation that uses a multi-tiered optimization strategy coupled with multi-rate Moving Horizon Estimation (MHE) to provide decision support to the plant operators. MHE is particularly attractive due to its direct handling of nonlinear system model, easy incorporation of constraints and straightforward handling of multi-rate measurements [7, 8]. MHE runs in parallel with the plant so that the advisory system is aware of the current state of the process. The advisory system uses a multi-tiered initialization scheme in combination with state-of-the-art NLP solvers to obtain fast solutions to the optimal control problems at each sampling time. The state estimates are subsequently provided to multi-tiered optimizer to calculate the optimal input sequence to maximize the economics. However, the optimizer is called upon only when the operator triggers the advisory system. The tiered-optimization coupled with MHE has a novel mechanism to handle potential infeasibilities due to end-point constraints.

The real-time economics-based dynamic optimization problem with end-point constraints is handled through multi-tiered optimization. The multi-tiered strategy incorporates three sequential dynamic optimization tiers where the last 2 tiers come into effect if the previous tier fails to give a solution. In the first tier, Direct optimization, we attempt to solve the original end-point constrained dynamic optimization problem. If we detect an infeasible problem or a maximum number of specified optimization iterations is reached then we proceed to the second tier. In tier 2, Feasibility restoration through horizon extension, we reformulate the original dynamic optimization by extending the time horizon in integral steps to find the minimum integral extension required to yield a feasible solution. If feasibility cannot be achieved, then we move to the third tier. In the third tier, End-point relaxation, we remove the end-point constraint and instead minimize the state variable deviation from the upper and lower bounds at the extended end-point. Further, we propose a Sub-tier: Extended implementation which gets activated only at the end-time if the estimated state is not within the specified upper and lower bounds.

The advisory system is applied to a multi-part EAF case study to demonstrate its performance. The energy required to melt the scarp steel is provided in form of electrical and chemical energy. A detailed first-principles DAE model is employed that takes the complex physical phenomena into account [9, 3]. The model considers four zones for the furnace (gas, slag-metal, slag-metal, solid scrap) with material movement between the zones limited by mass transfer. Chemical equilibrium in the slag-metal and gas zones is modeled by embedding equations for Gibbs free energy minimization. The DAE model is discretized and a simultaneous approach employed for solving the dynamic optimization problems. The case studies demonstrate a significant economic benefit if the advisory system is used. We show that the advisory system is capable of providing decision support to the operators in real-time without significant delays. As a future work, we intend to investigate alternate objective function formulations where environmental effects such as emissions are also considered.

References

[1]	"Steel Statistical Yearbook of World Steel Association," [Online]. Available: 1. Steel Statistical Yearbook of World Steel Association, http://www.worldsteel.org/steel- by-topic/statistics/steel-statistical-yearbook-.html. 2016.
[2]	R. J. Fruehan, The Making, Shaping, and Treating of Steel: Ironmaking volume, vol. 2, AISE Steel Foundation, 1999.
[3]	R. D. M. MacRosty and C. L. E. Swartz, "Dynamic modeling of an industrial electric arc furnace," Ind.Eng.Chem.Res., vol. 44, pp. 8067-8083, 2005.
[4]	R. Nadira and P. Usoro, "Self-adjusting model algorithmic control of a three-phase electric arc furnace," Journal of dynamic systems, measurement, and control, vol. 110, no. 4, pp. 361-366, 1988.
[5]	R. D. M. MacRosty and C. L. E. Swartz, "Dynamic optimization of electric arc furnace operation," AIChE journal, vol. 53, no. 3, pp. 640-653, 2007.
[6]	J. Flores-Cerrillo and J. F. MacGregor, "Control of batch product quality by trajectory manipulation using latent variable models," Journal of Process Control, vol. 14, no. 5, pp. 539-553, 2004.
[7]	F. Allgöwer, T. A. Badgwell, J. S. Qin, J. B. Rawlings and S. J. Wright, "Nonlinear predictive control and moving horizon estimation—an introductory overview," Advances in control, pp. 391-449, 1999.
[8]	R. López-Negrete and L. T. Biegler, "A moving horizon estimator for processes with multi-rate measurements: A nonlinear programming sensitivity approach," Journal of Process Control, vol. 22, no. 4, pp. 677-688, 2012.
[9]	S. Shyamal and C. L. E. Swartz, "Real-Time Energy Management for Electric Arc Furnace Operation," in Journal of Process Control, 2018 (in press).