arXiv subjects

Trine Krogh Boomsma

Publications and source records attributed to Trine Krogh Boomsma.

3 recordsLinked to original sources

arXiv2026

Unit commitment constrained Nash equilibrium in power markets

Equilibrium modeling for power markets usually assumes convexity of each players' optimization problem. Although the importance of accounting for fixed generation costs and start-up costs, minimum generation levels and/or minimum up-time and down-time restrictions in production scheduling is widely acknowledged, such modeling does not allow for discrete decisions. This paper considers unit commitment constrained Nash equilibria. First, we derive novel optimality conditions tailored for the mixed-integer convex programming problem of joint unit commitment and economic dispatch of a self-scheduling profit-maximizing producer. Next, we use these to formulate a Nash equilibrium as a mixed-integer complementarity problem, which facilitates the development of a procedure to obtain multiple equilibria. The approach can be adapted to both perfectly and imperfectly competitive market settings. While an equilibrium may not always exist, we give sufficient conditions under which a Cournot-Nash equilibrium can be obtained by mixed-integer convex programming under the standard assumption of an affine inverse demand curve and convex generating costs, and use this to establish existence. A case study demonstrates the feasibility of using optimisation to obtain a Cournot-Nash equilibrium for unit commitment constrained market clearing. Our results confirm that ignoring unit commitment creates significant welfare losses, although these vary substantially across equilibria.

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arXiv2022

Approximate dynamic programming for profit estimation of connected hydro reservoirs

In this paper, we study the operational problem of connected hydro power reservoirs which involves sequential decision-making in an uncertain and dynamic environment. The problem is traditionally formulated as a stochastic dynamic program accounting for the uncertainty of electricity prices and reservoir inflows. This formulation suffers from the curse of dimensionality, as the state space explodes with the number of reservoirs and the history of prices and inflows. To avoid computing the expectation of future value functions, the proposed model takes advantage of the so-called post-decision state. To further tackle the dimensionality issue, we propose an approximate dynamic programming approach that estimates the future value of water using a linear approximation architecture. When the time series of prices and inflows follow autoregressive processes, our approximation provides an upper bound on the future value function. We use an offline training algorithm based on the historical data of prices and inflows and run both in-sample and out-of-sample simulations. Two realistic test systems of cascade and network connected reservoirs serve to demonstrate the computational tractability of our approach. In particular, we provide numerical evidence of convergence and quality of solutions. For our test systems, our results show that profit estimation is improved by 20% when including inflows in the linear approximation.

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arXiv2014

Impact of Forecast Errors on Expansion Planning of Power Systems with a Renewables Target

This paper analyzes the impact of production forecast errors on the expansion planning of a power system and investigates the influence of market design to facilitate the integration of renewable generation. For this purpose, we propose a stochastic programming modeling framework to determine the expansion plan that minimizes system-wide investment and operating costs, while ensuring a given share of renewable generation in the electricity supply. Unlike existing ones, this framework includes both a day-ahead and a balancing market so as to capture the impact of both production forecasts and the associated prediction errors. Within this framework, we consider two paradigmatic market designs that essentially differ in whether the day-ahead generation schedule and the subsequent balancing re-dispatch are co-optimized or not. The main features and results of the model set-ups are discussed using an illustrative four-node example and a more realistic 24-node case study.

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