Nikita Belyak | Searcharxiv

arXiv2024

Renewable Energy Expansion under Taxes and Subsidies: A Transmission Operator's Perspective

This paper investigates the role of a transmission system operator within a carbon footprint reduction strategy incorporating carbon taxes and renewable energy generation subsidies in the decentralised energy market. This is achieved via an optimisation bi-level model in which a welfare-maximizing transmission system operator makes investments in transmission lines at the upper level while considering power market dynamics at the lower level. To account for the deregulated energy market structure, this paper assumes that the generation companies at the lower level make capacity investments as price-takers in perfect competition. Considering alternative transmission infrastructure expansion budgets, carbon emission taxes and monetary incentives for renewable energy generation capacity expansion, the impact of alternative compositions of these factors is analysed against three output factors: the share of renewable energy in the generation mix, total generation amount, and social welfare. The proposed modelling assessment is applied to an illustrative three-node instance and a case study considering a simplified representation of the energy system of the Nordic and Baltic countries. The results highlight that, under certain circumstances, renewable energy generation subsidies may lead to an increase of renewable energy in the generation mix followed by a simultaneous fall in the total generation amount. Nevertheless, when applied together, these three measures demonstrated a positive impact on all output factors within Nordics' and Baltics' energy systems. The experiments additionally suggest that considering the high value of the carbon tax does not have an impact on the output factors while the composition of high values of renewable energy generation subsidies and budget for transmission infrastructure expansion has the strongest effect.

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arXiv2023

A novel dual-decomposition method for non-convex two-stage stochastic mixed-integer quadratically constrained quadratic problems

We propose the novel p-branch-and-bound method for solving two-stage stochastic programming problems whose deterministic equivalents are represented by non-convex mixed-integer quadratically constrained quadratic programming (MIQCQP) models. The precision of the solution generated by the p-branch-and-bound method can be arbitrarily adjusted by altering the value of the precision factor p. The proposed method combines two key techniques. The first one, named p-Lagrangian decomposition, generates a mixed-integer relaxation of a dual problem with a separable structure for a primal non-convex MIQCQP problem. The second one is a version of the classical dual decomposition approach that is applied to solve the Lagrangian dual problem and ensures that integrality and non-anticipativity conditions are met once the optimal solution is obtained. This paper also presents a comparative analysis of the p-branch-and-bound method efficiency considering two alternative solution methods for the dual problems as a subroutine. These are the proximal bundle method and Frank-Wolfe progressive hedging. The latter algorithm relies on the interpolation of linearisation steps similar to those taken in the Frank-Wolfe method as an inner loop in the classic progressive hedging. The p-branch-and-bound method's efficiency was tested on randomly generated instances and demonstrated superior performance over commercial solver Gurobi.

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