(715d) Novel Formulation for Optimal Schedule with Demand Side Management in Multi-Product Air Separation Processes
In this work, we focus on the optimal scheduling of air separation in industrial gases processes with electricity purchased from spot market. We consider the electricity price forecast in the scheduling horizon as a model input, based on fixed time intervals. As for the continuous process, the variable production levels are achieved by properly adjusting the units to meet various production constraints, such as different product demands. This could be interpreted as the transition of operation states of the production system. In this work, the continuous space of plant operation is discretized into several operation states. Therefore, the main goal of the scheduling problem is to minimize the total production costs by selecting the optimal operation state for each unit in the production system for each time period. Besides the energy consumption, we also consider the setup costs and other related cost item.
To represent the production states and the transition between them, an advanced process state transition network (APSTN) is proposed. The formulation relies on a basic concept of previous work , where states with minimum processing time are disaggregated into sub states. However, the APSTN representation is more compact, especially when dealing with more complex production systems. Specifically, for multi-product air separation processes, a discrete-time mixed integer linear (MILP) model is developed based on the APSTN, which has proven to provide a tighter LP relaxation to handling industrial-scale instances.
Three main features characterize the air separation process: 1) minimum consecutive operating time for specific states; 2) setup costs of transition of states and finally, 3) pre-defined direction for some transitions. The proposed MILP model involves the constraints with the previously mentioned features, as well as other considerations, such as inventory level and product demand. The computational efficiency of the model is demonstrated with data provided by the company. Numerical experiments are performed in order to make comparisons between our model and previous ones [1-3]. The response of the scheduling and production level is also tested regarding to various intervalâs length for the electricity pricing and the time horizon for the scheduling.
 BasÃ¡n, N.P., Grossmann, I.E., Gopalakrishnan, A., Lotero, I., Mendez, C.A., 2018. Novel MILP Scheduling Model for Power-Intensive Processes under Time-Sensitive Electricity Prices. Ind. Eng. Chem. Res., 57 (5), 1581â1592.
 Mitra, S., Grossmann, I.E., Pinto, J.M., Arora, N., 2012. Optimal production planning under time-sensitive electricity prices for continuous power-intensive processes. Comput. Chem. Eng. 38, 171â184.
 Mitra, S.; Sun, L.; Grossmann, I. E. Optimal Scheduling of Industrial Combined Heat and Power Plants Under Time-sensitive Electricity Prices. Energy 2013, 54, 194.