Ralf Gollmer

Unit commitment in power generation – a basic model and some extensions

For the unit commitment problem in the hydro-thermal power system of VEAG Vereinigte Energiewerke AG Berlin we present a basic model and discuss possible extensions where both primal and dual solution approaches lead to flexible optimization tools. Extensions include staggered fuel prices, reserve policies involving hydro units, nonlinear start-up costs, and uncertain load profiles.

Validation of nominations in gas network optimization: models, methods, and solutions

In this article, we investigate methods to solve a fundamental task in gas transportation, namely the validation of nomination problem: given a gas transmission network consisting of passive pipelines and active, controllable elements and given an amount of gas at every entry and exit point of the network, find operational settings for all active elements such that there exists a network state meeting all physical, technical, and legal constraints. We describe a two-stage approach to solve the resulting complex and numerically difficult nonconvex mixedinteger nonlinear feasibility problem. The first phase consists of four distinct algorithms applying mixedinteger linear, mixedinteger nonlinear, nonlinear, and methods for complementarity constraints to compute possible settings for the discrete decisions. The second phase employs a precise continuous nonlinear programming model of the gas network. Using this setup, we are able to compute high-quality solutions to real-world industrial instances that are significantly larger than networks that have appeared in the mathematical programming literature before.

Stochastic Programs with First-Order Dominance Constraints Induced by Mixed-Integer Linear Recourse

We propose a new class of stochastic integer programs whose special features are dominance constraints induced by mixed-integer linear recourse. For these models, we establish closedness of the constraint set mapping with the underlying probability measure as a parameter. In the case of finite probability spaces, the models are shown to be equivalent to large-scale, block-structured, mixed-integer linear programs. We propose a decomposition algorithm for the latter and discuss computational results.

A note on second-order stochastic dominance constraints induced by mixed-integer linear recourse

We introduce stochastic integer programs with second-order dominance constraints induced by mixed-integer linear recourse. Closedness of the constraint set mapping with respect to perturbations of the underlying probability measure is derived. For discrete probability measures, large-scale, block-structured, mixed- integer linear programming equivalents to the dominance constrained stochastic programs are identified. For these models, a decomposition algorithm is proposed and tested with instances from power optimization.

Primal and Dual Methods for Unit Commitment in a Hydro-Thermal Power System

The unit commitment prob lem in a power generation system com prising thermal and pumped storage hy dro units is addressed A large scale mixed integer optimization model for unit commitment in a real power system is de veloped and solved by primal and dual ap proaches Both solution methods employ state of the art algorithms and software Results of test runs are reported

Risk Management with Stochastic Dominance Models in Energy Systems with Dispersed Generation

Dispersed power generation is the source of many challenging optimization problems with uncertain data. We review algorithmic approaches to risk aversion with stochastic dominance constraints. Dispersed power generation provides the practical background for illustration and comparison of the methods.