The smart grid brings electric distribution and consumption into the 21stcentury. It allows for coordination between electricity producers, distributors and consumers, enabling higher reliability and increased efficiency. One advantage of the smart grid is that it allows for a scheme called Demand Response (DR), in which consumers are incentivized to time-shift their electricity consumption from peak to non-peak hours. Ding et al.  developed a Mixed Integer Programming (MIP)-based algorithm for production plants that would allow them to implement time-shifting in their process schedules. Unfortunately, these models are computationally expensive. In other applications the method of Economic Linear Optimal Control (ELOC) has been used to reduce the computational burden of determining a smart grid coordination policy . To apply these techniques to the DR scheduling problem, the MIP model must be transformed to a state-space formulation to make it amenable to the ELOC approach. Subramanian et al.  has shown how to convert optimization models from MIP formulation to state-space, introducing concepts such as the lifting of states. The objective of this research is to apply the method of Subramanian to the DR model proposed by Ding.
 Ding, Y.M.; S.H. Hong; X.H. Li (2014) A demand response energy management scheme for industrial facilities in smart grid, IEEE Trans. Ind. Infor., 10(4), pp 2257-2269
 Mendoza, D.I.; Chmielewski, D.J. (2015) Smart grid coordination in building HVAC systems: Computational efficiency of constrained economic linear optimal control, Sci. Tech. Built Env., 21(6), pp 812-823
 Subramanian, K.; Maravelias, C.T.; Rawlings, J.B. (2012) A state-space model for chemical production scheduling, Comp. Chem. Eng., 47, pp 97-110
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