(180d) An Adjustable Robust Optimization Approach to Provision of Interruptible Load By Continuous Processes

A power grid is designed to reliably match electricity supply and demand. When real-time electricity supply falls below the demand, e.g. due to generator failures or sudden load changes, backup capacities are called upon to eliminate this supply-demand gap. One kind of such backup capacities is called operating reserve, which has to be ready upon request within minutes. Operating reserve can be provided by generators that are able to quickly increase electricity supply. Alternatively, operating reserve can be provided by electricity consumers by reducing their load and therefore reducing electricity demand; this operating reserve provided on the demand side is also referred to as interruptible load.

Providing interruptible load is attractive because one is rewarded even when no actual load reduction is required. This market incentive reflects the value of flexible loads that can react quickly to unexpected changes in the power grid. However, there is a lack of systematic methods for determining the optimal amount of interruptible load to provide. The main challenge lies in the uncertainty which stems from the fact that one does not know in advance when load reduction will actually be requested.
Recently, robust optimization has been applied to scheduling considering provision of operating reserve under uncertainty (Vujanic, et al., 2012; Zhang, et al., 2015). The applied traditional robust optimization approach guarantees feasibility for every possible realization of the uncertainty, but does not consider recourse, which makes the solution highly conservative. However, when interruptible load is provided by complex chemical processes, accounting for recourse decisions is crucial.

In this work, we use a detailed scheduling model to capture all critical operational constraints of a continuous power-intensive process, and propose an adjustable robust optimization approach (Ben-Tal, et al., 2009) that uses affine decision rules to account for recourse decisions with respect to uncertainty in load reduction demand. This results in a large-scale MILP model, to which additional redundant constraints are added to make the formulation computationally more efficient. The proposed model is applied to an industrial air separation case provided by Praxair, and the results show significant benefit from providing interruptible load. Compared to a traditional robust formulation, the adjustable robust model provides much better and more realistic solutions while guaranteeing the same level of robustness.

References
Ben-Tal, A., El Ghaoui, L. & Nemirovski, A., 2009. Robust Optimization. New Jersey: Princeton University Press.
Vujanic, R., Mariéthos, S., Goulart, P. & Morari, M., 2012. Robust Integer Optimization and Scheduling Problems for Large Electricity Consumers. 2012 American Control Conference, pp. 3108-3113.
Zhang, Q., Heuberger, C.F., Grossmann, I.E., Sundaramoorthy, A. & Pinto, J.M., 2015. Air Separation with Cryogenic Energy Storage: Optimal Scheduling Considering Electric Energy and Reserve Markets. AIChE Journal.