We study a continuous-time pump scheduling problem for a flow transmission task. A finite table of empirical operating points of pump combinations is given, each point specifying a flow rate and power consumption. Electricity prices follow a time-of-use tariff, and combination changes are penalized or limited by per-shift switch caps. We prove a structural theorem: … Read more
Electric power infrastructure faces increasing risk of damage and disruption due to wildfire. Operators of power grids in wildfire-prone regions must consider the potential impacts of unpredictable fires. However, traditional wildfire models do not effectively describe worst-case, or even high-impact, fire behavior. To address this issue, we propose a mixed-integer conic program to characterize an … Read more
We study linear complementarity problems (LCPs) under uncertainty, which we model using chance constraints. Since the complementarity condition of the LCP is an equality constraint, it is required to consider relaxations, which naturally leads to optimization problems in which the relaxation parameters are minimized for given probability levels. We focus on these optimization problems and … Read more
Potential-based flows provide an algebraic way to model static physical flows in networks, for example, in gas, water, and lossless DC power networks. The flow on an arc in the network depends on the difference of the potentials at its end-nodes, possibly in a nonlinear way. Potential-based flows have several nice properties like uniqueness and … Read more
This paper presents a Marginal Reliability Impact (MRI) based resource accreditation framework for capacity market design. Under this framework, a resource is accredited based on its marginal impact on system reliability, thus aligning the resource’s accreditation value with its reliability contribution. A key feature of the MRI-based accreditation is that the accredited capacities supplied by … Read more
Capacity Planning problems are a class of optimization problems used in diverse industries to improve resource allocation and make investment decisions. Solving real-world instances of these problems typically requires significant computational effort. To tackle this, we propose machine-learning-aided column generation methods for solving large-scale capacity planning problems. Our goal is to accelerate column generation by … Read more
Power systems modeling and planning has long leveraged mathematical programming for its ability to provide optimality and feasibility guarantees. One feature that has been recognized in the optimization literature since the 1970s is the existence and meaning of multiple exact optimal and near-optimal solutions, which we call alternative solutions. In power systems modeling, the use … Read more
The Stochastic Unit Commitment (SUC) problem models the scheduling of power generation units under uncertainty, typically using a two-stage stochastic program with integer first-stage and continuous second-stage variables. We propose a new Benders decomposition approach that leverages an extended formulation based on interval variables, enabling decomposition by both unit and time interval under mild technical … Read more
The interdiction defense (ID) problem solves a defender-attacker-defender model where the defender and attacker share the same set of components to harden and target. We build upon the best response intersection (BRI) algorithm by developing the BRI with suboptimal solutions (BRI-SS) algorithm to solve the ID problem. The BRI-SS algorithm utilizes off-the-shelf optimization solvers that … Read more
Traditional end-to-end contextual robust optimization models are trained for specific contextual data, requiring complete retraining whenever new contextual information arrives. This limitation hampers their use in online decision-making problems such as energy scheduling, where multiperiod optimization must be solved every few minutes. In this paper, we propose a novel Data-Driven Contextual Uncertainty Set, which gives … Read more