Power-intensive processes can lower operating expenses when adjusting production planning according to time-dependent electricity pricing schemes, which exist due to fluctuations in power demand. Different researchers dealt with the operational problem of the so-called demand response for power-intensive processes.
The first line of research proposes a control approach. For the economic optimization of air separation plants, Zhu et al. (2010) developed a model based on heat and mass balances, including nonlinear thermodynamics. Huang (2010) proposed the application of economically-oriented nonlinear model predictive control. While these approaches have the advantage of providing an accurate process representation, they cannot incorporate discrete decisions such as equipment shutdowns and startups and corresponding operational constraints such as enforcing minimum up- or downtimes.
The second line of research comes from the area of planning and scheduling. An initial approach by Daryanian et al. (1989) shows the economic benefit of demand response for air separation plants but does not consider discrete operating decisions such as equipment shutdowns and startups. Ierapetritou et al. (2002) as well as Karwan and Keblis (2007) extend the methodology to incorporate discrete operating decisions. However, their models do not capture the transient behavior between - operating modes. Moreover, some of their logic constraints show room for improvement with respect to the tightness of the linear relaxation. For cement plants, Castro and co-workers (2009, 2011) extend the Resource Task Network (RTN) formulation to incorporate hourly changing electricity prices.
In this work, we describe a deterministic MILP model that allows optimal production planning for continuous power-intensive processes using a discrete time formulation. First, we generalize approaches taken by Ierapetritou et al. (2002) - and Karwan and Keblis (2007). We discuss the concept of transitional modes to allow for a more detailed modeling of transitional behavior that is due to plant dynamics. Further, we enhance the computational efficiency of their formulation by improving the logic constraints. Properties on the tightness of several logic constraints are proved. We successfully apply the model to two different real-world air separation plants that supply to the liquid merchant market, as well as cement plants.
For the time horizon of one week and hourly changing electricity prices, we solve an industrial case study on air separation plants, where transitional modes help us capturing the ramping behavior. The operational optimization model created savings of more than 10% when compared to a simple heuristic. Furthermore, we learned that operational flexibility, in terms of production and storage capacity, is the key to lower operating expenses.
We also solve problem instances on cement plants that are reported in Castro et al. (2011). We observe that the introduction of transitional modes results in a large-scale model. Nevertheless, the model is superior compared to a smaller model that only had single product modes and thus lacked control of occurring transitions as well as could not be solved to optimality. Despite the large size of the MILP model with transitional modes, the required solution times to obtain the optimal solution were small for all test cases. Furthermore, the obtained schedules were practical to implement because we were able to control the occurring transitions.
Castro, P.M.; Harjunkoski I.; Grossmann I.E. (2009) New Continuous-Time Scheduling Formulation for Continuous Plants under Variable Electricity Cost. Ind. Eng. Chem. Res., 48:6701–6714
Castro, P.M.; Harjunkoski I.; Grossmann I.E. (2011) Optimal scheduling of continuous plants with energy constraints. Comp. Chem. Eng., 35:372– 387
Daryanian, B.; Boln, R.E.; Tabors, R.D. (1989) Optimal demand-side response to electricity spot prices for storage-type customers. IEEE Transactions on Power Systems, 4:897-903
Huang, R. Nonlinear Model Predictive Control and Dynamic Real Time Optimization for Large-scale Processes. PhD thesis, Carnegie Mellon University, 2010.
Ierapetritou, M.G.; Wu, D.; Vin, J.; Sweeny P.; Chigirinskiy M. (2002) Cost Minimization in an Energy-Intensive Plant Using Mathematical Programming Approaches. Ing. Eng. Chem. Res., 41:5262–5277
Karwan, K.; Keblis M. (2007) Operations planning with real time pricing of a primary input. Computers & Operations Research, 34:848–867
Zhu, Y.; Legg S.; Laird, C.A Multiperiod Nonlinear Programming Approach for Operation of Air Separation Plants with Variable Power Pricing.AIChE Journal, accepted, 2010.