Solving large-scale unit-commitment problems using dual dynamic programming and open-source solvers

The astonishing dimensions and complexity of power systems render them impossible to be managed without the help of cutting-edge software. Due to a lack of scalable, reliable and well documented free and open-source solutions, system operators, regulators, and government agencies often rely on proprietary software to provide them information that ultimately will be used to … Read more

Parallel Dual Dynamic Integer Programming for Large-Scale Hydrothermal Unit-Commitment

Unit commitment has been at the center of power system operation for well over 50 years. Yet, this problem cannot be considered solved due to its size and complexity. Today, operators rely on off-the-shelf optimization solvers to tackle this challenging problem, and often resort to simplifications to make the problem more tractable and solvable in … Read more

Exponential Decay of Sensitivity in Graph-Structured Nonlinear Programs

We study solution sensitivity for nonlinear programs (NLPs) whose structure is induced by a graph $\mathcal{G}=(\mathcal{V},\mathcal{E})$. These graph-structured NLPs arise in many applications such as dynamic optimization, stochastic optimization, optimization with partial differential equations, and network optimization. We show that the sensitivity of the primal-dual solution at node $i\in \mathcal{V}$ against a data perturbation at … Read more

Scalable Preconditioning of Block-Structured Linear Algebra Systems using ADMM

We study the solution of block-structured linear algebra systems arising in optimization by using iterative solution techniques. These systems are the core computational bottleneck of many problems of interest such as parameter estimation, optimal control, network optimization, and stochastic programming. Our approach uses a Krylov solver (GMRES) that is preconditioned with an alternating method of … Read more

Mixed-Integer PDE-Constrained Optimal Control of Gas Networks

We develop a mixed-integer optimal control model with partial differential equation (PDE) constraints for gas transport networks, designed for controlling extreme state transitions, such as flow reversals. Our model shows how to combine binary compressor controls with PDE flow models. We model the flow of gas using a variant of the Euler equations, which we … Read more

A Sigmoidal Approximation for Chance-constrained Nonlinear Programs

We propose a sigmoidal approximation (SigVaR) for the value-at-risk (VaR) and we use this approximation to tackle nonlinear programming problems (NLPs) with chance constraints. We prove that the approximation is conservative and that the level of conservatism can be made arbitrarily small for limiting parameter values. The SigVar approximation brings computational benefits over exact mixed-integer … Read more

A Scalable Global Optimization Algorithm for Stochastic Nonlinear Programs

We propose a global optimization algorithm for stochastic nonlinear programs that uses a specialized spatial branch and bound (BB) strategy to exploit the nearly decomposable structure of the problem. In particular, at each node in the BB scheme, a lower bound is constructed by relaxing the so-called non-anticipativity constraints and an upper bound is constructed … Read more

A Stochastic MPC Framework for Stationary Battery Systems

We present a stochastic model predictive control (MPC) framework to determine real-time commitments in energy and frequency regulation markets for a stationary battery system while simultaneously mitigating long-term demand charges for an attached load. The framework solves a two-stage stochastic program over a receding horizon that maximizes the expected profit and that factors in uncertainty … Read more

MPC as a DVI: Implications on Sampling Rates and Accuracy

We show that the evolution of a dynamical system driven by controls obtained by the solution of an embedded optimization problem (as done in MPC) can be cast as a differential variational inequality (DVI). The DVI abstraction reveals that standard sampled-data MPC implementations (in which the control law is computed using states that are sampled … Read more

An Augmented Lagrangian Filter Method for Real-Time Embedded Optimization

We present a filter line-search algorithm for nonconvex continuous optimization that combines an augmented Lagrangian function and a constraint violation metric to accept and reject steps. The approach is motivated by real-time optimization applications that need to be executed on embedded computing platforms with limited memory and processor speeds. In particular, the proposed method enables … Read more