(400b) Multistage Robust Mixed-Integer Optimization for Industrial Demand Response with Interruptible Load

Industrial electricity consumers often adapt demand response as a strategy to tackle volatile electricity prices and reduce operating costs (Zhang and Grossmann, 2016). Owing to the reliability benefits that such demand-side activities bring to the grid, electricity markets also incentivize electricity consumers to provide operating reserves in the form of interruptible load (Dowling et al., 2017). Interruptible load providers are expected to reduce their power consumption up to an agreed amount when requested by the grid operator. However, commitment to provide interruptible load introduces uncertainty into the production schedule of an industrial process, as one does not know in advance when and how much load reduction will be requested. Disregarding this uncertainty may jeopardize plant safety or lead to situations in which product demand can no longer be satisfied due to excessive load reduction.

Zhang et al. (2015) capture this uncertainty using a tailored uncertainty set and apply robust optimization to the resulting scheduling problem. However, they only model the static case where no recourse is considered, which leads to very conservative solutions. Zhang et al. (2016) address this shortcoming by incorporating continuous recourse decisions using affine decision rules and show significant increases in cost savings enabled by flexible recourse. Yet the proposed approach still cannot realize the full potential of interruptible load since it does not consider discrete recourse and hence does not allow, for example, full plant shutdowns when load reduction is required, which is what is often done in practice.

In this work, we extend the previous framework to also include integer recourse decisions for a general network of power-intensive processes. Piecewise linear decision rules are used to cater mixed-integer recourse (Bertsimas and Georghiou, 2018; Feng et al., 2021), and adjustable robust optimization techniques (Yanıkoğlu et al., 2019) are applied to arrive at a solvable mixed-integer linear programming formulation. The resulting model is applied to a compressor train case study with added storage tanks between compressors for operational flexibility. We find that providing interruptible load results in a substantial reduction in operating costs in exchange for the initial capital investment in the storage tanks. The results also demonstrate the considerable improved cost savings when mixed-integer recourse is considered as compared to the case with only continuous recourse.

References

Bertsimas, D. and Georghiou, A., 2018. Binary decision rules for multistage adaptive mixed-integer optimization. Mathematical Programming, 167(2), pp.395-433.

Dowling, A.W., Kumar, R., and Zavala, V. M. 2017. A multi-scale optimization framework for electricity market participation. Applied Energy, 190, 147-164.

Feng, W., Feng, Y., and Zhang, Q., 2021. Multistage robust mixed-integer optimization under endogenous uncertainty. European Journal of Operational Research, 294(2), pp.460-475.

Yanıkoğlu, İ., Gorissen, B. L., & den Hertog, D., 2019. A survey of adjustable robust optimization. European Journal of Operational Research, 277(3), 799-813.

Zhang, Q. and Grossmann, I.E., 2016. Enterprise-wide optimization for industrial demand side management: Fundamentals, advances, and perspectives. Chemical Engineering Research & Design, 116, 114-131.

Zhang, Q., Grossmann, I.E., Heuberger, C.F., Sundaramoorthy, A. and Pinto, J.M., 2015. Air separation with cryogenic energy storage: optimal scheduling considering electric energy and reserve markets. AIChE Journal, 61(5), pp.1547-1558.

Zhang, Q., Morari, M.F., Grossmann, I.E., Sundaramoorthy, A., and Pinto, J.M., 2016. An adjustable robust optimization approach to scheduling of continuous industrial processes providing interruptible load. Computers & Chemical Engineering, 86, pp.106-119.