Revisiting Augmented Lagrangian Duals

For nonconvex optimization problems, possibly having mixed-integer variables, a convergent primal-dual solution algorithm is proposed. The approach applies a proximal bundle method to certain augmented Lagrangian dual that arises in the context of the so-called generalized augmented Lagrangians. We recast these Lagrangians into the framework of a classical Lagrangian, by means of a special reformulation … Read more

A counterexample to an exact extended formulation for the single-unit commitment problem

Recently, Guan, Pan, and Zohu presented a MIP model for the thermal single- unit commitment claiming that provides an integer feasible solution for any convex cost function. In this note we provide a counterexample to this statement and we produce evidence that the perspective function is needed for this aim. Citation Research Report 19-03, Istituto … Read more

Operations Planning Experiments for Power Systems with High Renewable Resources

Driven by ambitious renewable portfolio standards, variable energy resources (such as wind and solar) are expected to impose unprecedented levels of uncertainty to power system operations. The current practice of planning operations with deterministic optimization tools may be ill-suited for a future where uncertainty is abundant. To overcome the reliability challenges associated with the large-scale … Read more

A Computationally Efficient Algorithm for Computing Convex Hull Prices

Electricity markets worldwide allow participants to bid non-convex production offers. While non-convex offers can more accurately reflect a resource’s capabilities, they create challenges for market clearing processes. For example, system operators may be required to execute side payments to participants whose costs are not covered through energy sales as determined via traditional locational marginal pricing … Read more

The Value of Multi-stage Stochastic Programming in Risk-averse Unit Commitment under Uncertainty

Day-ahead scheduling of electricity generation or unit commitment is an important and challenging optimization problem in power systems. Variability in net load arising from the increasing penetration of renewable technologies have motivated study of various classes of stochastic unit commitment models. In two-stage models, the generation schedule for the entire day is fixed while the … Read more

A Novel Matching Formulation for Startup Costs in Unit Commitment

We present a novel formulation for startup cost computation in the unit commitment problem (UC). Both the proposed formulation and existing formulations in the literature are placed in a formal, theoretical dominance hierarchy based on their respective linear programming relaxations. The proposed formulation is tested empirically against existing formulations on large-scale unit commitment instances drawn … Read more

Global Solution Strategies for the Network-Constrained Unit Commitment Problem With AC Transmission Constraints

We propose a novel global solution algorithm for the network-constrained unit commitment problem that incorporates a nonlinear alternating current model of the transmission network, which is a nonconvex mixed-integer nonlinear programming (MINLP) problem. Our algorithm is based on the multi-tree global optimization methodology, which iterates between a mixed-integer lower-bounding problem and a nonlinear upper-bounding problem. … Read more

Data-Driven Risk-Averse Stochastic Program And Renewable Energy Integration

With increasing penetration of renewable energy into the power grid and its intermittent nature, it is crucial and challenging for system operators to provide reliable and cost effective daily electricity generation scheduling. In this dissertation, we present our recently developed innovative modeling and solution approaches to address this challenging problem. We start with developing several … Read more

Strengthened MILP Formulation for Combined-Cycle Units

Due to the increased utilization of gas-fired combined-cycle units for power generation in the U.S., accurate and computationally efficient models are more and more needed. The recently proposed edge-based formulation for combined-cycle units helps accurately describe the operations of combined-cycle units including capturing the transition processes and physical constraints for each turbine. In this paper, … Read more