Commitment and dispatch of heat and power units via affinely adjustable robust optimization

In this paper, we study the performance of affine policies for a two-stage, adjustable, robust optimization problem with a fixed recourse and an uncertain right-hand side belonging to a budgeted uncertainty set. This is an important class of uncertainty sets, widely used in practice, in which we can specify a budget on the adversarial deviations of the uncertain parameters from the nominal values to adjust the level of conservatism. The two-stage adjustable robust optimization problem is hard to approximate within a factor better than [Formula: see text] even for budget of uncertainty sets in which [Formula: see text] is the number of decision variables. Affine policies, in which the second-stage decisions are constrained to be an affine function of the uncertain parameters provide a tractable approximation for the problem and have been observed to exhibit good empirical performance. We show that affine policies give an [Formula: see text]-approximation for the two-stage, adjustable, robust problem with fixed nonnegative recourse for budgeted uncertainty sets. This matches the hardness of approximation, and therefore, surprisingly, affine policies provide an optimal approximation for the problem (up to a constant factor). We also show strong theoretical performance bounds for affine policy for a significantly more general class of intersection of budgeted sets, including disjoint constrained budgeted sets, permutation invariant sets, and general intersection of budgeted sets. Our analysis relies on showing the existence of a near-optimal, feasible affine policy that satisfies certain nice structural properties. Based on these structural properties, we also present an alternate algorithm to compute a near-optimal affine solution that is significantly faster than computing the optimal affine policy by solving a large linear program.

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A survey of adjustable robust optimization

European Journal of Operational Research ◽

10.1016/j.ejor.2018.08.031 ◽

2019 ◽

Vol 277 (3) ◽

pp. 799-813 ◽

Cited By ~ 37

Author(s):

İhsan Yanıkoğlu ◽

Bram L. Gorissen ◽

Dick den Hertog

Keyword(s):

Robust Optimization ◽

Adjustable Robust Optimization

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Comparative Analysis of Adjustable Robust Optimization Alternatives for the Participation of Aggregated Residential Prosumers in Electricity Markets

Energies ◽

10.3390/en12061019 ◽

2019 ◽

Vol 12 (6) ◽

pp. 1019 ◽

Cited By ~ 4

Author(s):

Carlos Correa-Florez ◽

Andrea Michiorri ◽

Georges Kariniotakis

Keyword(s):

Comparative Analysis ◽

Robust Optimization ◽

Electricity Markets ◽

Optimization Model ◽

Energy Transition ◽

Point Of View ◽

Alternative Formulation ◽

Energy Prices ◽

Water Heaters ◽

Adjustable Robust Optimization

Active participation of end users in energy markets is identified as one of the major challenges in the energy transition context. One option to bridge the gap between customers and the market is aggregators of smart homes or buildings. This paper presents an optimization model from the standpoint of an aggregator of residential prosumers who have PV panels, electric water heaters, and batteries installed at home level. This aggregator participates in the day-ahead energy market to minimize operation costs by controlling the settings of flexible devices. Given that energy prices, PV production, and demand have uncertain behavior, appropriate models should be used to include these effects. In the present work, Adjustable Robust Optimization (ARO) is used to include uncertainty in the optimization model, and a comparative study of modifications to this formulation is carried out to determine its potential and limitations. The comparative analysis is performed from the point of view of average cost and risk, after performing Monte Carlo simulation. Simulations show the advantages of using an ARO framework when compared to deterministic approaches and also allow us to conclude about the advantages of using the proposed alternative formulation to find more attractive solutions for an aggregator.

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