Penalty alternating direction methods for mixed-integer optimal control with combinatorial constraints

We consider mixed-integer optimal control problems with combinatorial constraints that couple over time such as minimum dwell times. We analyze a lifting and decom- position approach into a mixed-integer optimal control problem without combinatorial constraints and a mixed-integer problem for the combinatorial constraints in the control space. Both problems can be solved very efficiently with existing methods such as outer convexification with sum-up-rounding strategies and mixed-integer linear programming techniques. The coupling is handled using a penalty-approach. We provide an exactness result for the penalty which yields a solution approach that convergences to partial minima. We compare the quality of these dedicated points with those of other heuristics amongst an academic example and also for the optimization of electric transmission lines with switching of the network topology for flow reallocation in order to satisfy demands

Mathematical properties of formulations of the gas transmission problem

The paper presents the mathematical properties of several formulations for the gas transmission problem that account for the nonlinear flow pressure relations. The form of the nonlinear flow pressure relations is such that the model is in general nonconvex. However, we show here that under a restrictive condition (gas inlet or gas pressure fixed at every entry/outgoing node) the problem becomes convex. This result is obtained by use of the variational inequality theory. We also give a computational method to find a feasible solution to the problem and give a physical interpretation to this feasible solution

Heuristics for Lagrangian Relaxation Formulations for the Unit Commitment Problem

The expansion of distributed energy resources (DER), demand response (DR), and virtual bidding in many power systems and energy markets are creating new challenges for unit commitment (UC) and economic dispatch (ED) techniques. Instead of a small number of traditionally large generators, the power system resource mix is moving to one with a high percentage of a large number of small units. These can increase the number of similar or identical units, leading to chattering (switching back and forth among committed units between iterations). This research investigates alternative and scalable ways of increasing the high penetration of these resources. First, the mathematical formulations for UC and ED models are reviewed. Then a new heuristic is proposed that takes advantage of the incremental nature of Lagrangian relaxation (LR). The heuristic linearizes and distributes the network transmission losses to appropriately penalize line flow and mitigate losses. Second, a mixed integer programming (MIP) is used as a benchmark for the proposed LR formulation. The impact of similar and identical units on the solution quality and simulation run time of UC and ED was investigated using the proposed formulation. Third, a system flexibility study is done using DR and a load demand pattern with a high penetration of renewables, creating a high daily ramp rate requirement. This work investigates the impact of available DR on spikes in locational marginal pricing (LMP). Fourth, two studies are done on improving LR computational efficiency. The first proposes a heuristic that focuses on trade-offs between solution quality and simulation run time. The heuristic iterates over lambda and energy marginal price while the convergence issue is handled using Augmented LR (ALR). The second study proposes a heuristic that penalizes transmission lines with binding line limits. The proposed method can reduce power flow in the transmission lines of interest, and considerably reduce the simulation time in optimization problems with a high number of transmission constraints. Finally, the effect of a large number of similar and identical units on simulation run time is considered. The proposed formulation scales linearly with the increase in system size

Open-Source, Open-Architecture SoftwarePlatform for Plug-InElectric Vehicle SmartCharging in California

This interdisciplinary eXtensible Building Operating System–Vehicles project focuses on controlling plug-in electric vehicle charging at residential and small commercial settings using a novel and flexible open-source, open-architecture charge communication and control platform. The platform provides smart charging functionalities and benefits to the utility, homes, and businesses.This project investigates four important areas of vehicle-grid integration research, integrating technical as well as social and behavioral dimensions: smart charging user needs assessment, advanced load control platform development and testing, smart charging impacts, benefits to the power grid, and smart charging ratepayer benefits

Global optimization with piecewise linear approximation

textGlobal optimization deals with the development of solution methodologies for nonlinear nonconvex optimization problems. These problems, which could arise in diverse situations ranging from optimizing hydro-power generation schedules to estimating coefficients of non-linear regression models, are difficult for traditional nonlinear solvers that iteratively search the neighborhood around a starting point. The Piecewise Linear Approximation (PLA) method that we study in this dissertation seeks to generate ‘good’ starting points, hopefully ones that lie in the basin of attraction of the globally optimal solution. In this approach, we approximate the non-linear functions in the optimization problem by piecewise linear functions defined over the vertices of a grid that partitions the domain of each nonlinear function into cells. Based on this approximation, we convert the original nonlinear program into a mixed integer program (MIP) and use the solution to this MIP as a starting point for a local nonlinear solver. In this dissertation, we validate the effectiveness of the PLA approach as a global optimization approach by applying it to a diverse set of continuous and discrete nonlinear optimization problems. Further, we develop various modeling and algorithmic strategies for enhancing the basic approach. Our computational results demonstrate that the PLA approach works well on non-convex problems and can, in some cases, provide better solutions than those provided by existing nonlinear solvers.Information, Risk, and Operations Management (IROM