arXiv subjects

Mohammad Reza Karimi Gharigh

Publications and source records attributed to Mohammad Reza Karimi Gharigh.

3 recordsLinked to original sources

arXiv2026

Fast Analytical Method for Resource Adequacy Assessment in Renewable-Rich Power Systems

This paper proposes a novel analytical method for resource adequacy assessment in renewable rich power systems. The approach begins by applying the stress strength method to estimate two key resource adequacy indices: loss of load expectation (LOLE) and expected energy not supplied (EENS). This method requires defining the probability distribution functions (PDFs) for both the generation side and the load side. The load is assumed to follow a normal probability distribution, while the generation side probability distribution is derived from the combined PDFs of conventional, wind, and solar power sources. The approach models the cumulative impact of uncertainties on resource adequacy using the central limit theorem (CLT), and improves accuracy with a cumulant based Gram Charlier expansion when the CLT alone is insufficient. The effectiveness of the proposed method is validated through Monte Carlo simulations conducted on the IEEE single area and multi-area RTS-96 test systems. The results demonstrate that the proposed method achieves a substantial reduction in computational time, which is crucial in the context of operational planning, without sacrificing accuracy. Furthermore, its performance improves as renewable penetration increases, making it particularly suitable for future power systems operation and planning.

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arXiv2026

A Tax-Subsidy Scheme for Efficient Investment in Renewable Generation Capacity

The impact of energy production significantly affects system sustainability, which has enabled a shift towards renewable energy sources. Thus, producer behavior is crucial in electricity markets to achieve sustainability goals. In this paper, we address two key challenges comprising electricity markets and generation investment. Firstly, electricity markets typically are operated with competitive market clearing and merit-order dispatch, which neglects negative externalities from pollution. A Pigouvian tax is proposed in order to investigate the impacts of these externalities on electricity prices and resolve this issue. Secondly, renewable energy sources entail low operational costs, which result in lower system prices and reduced profits for producers. Furthermore, producers face high investment costs when moving into renewable energy resources, which leads to strategic investment decisions. In order to mitigate this strategic behavior, subsidies are proposed equal to producers' contribution to consumer surplus. These subsidies incentivize producers to decrease prices and increase consumer surplus, so, producers would be motivated to invest in socially optimal generation capacity. Finally, we demonstrate that implementing the proposed tax and subsidy does not increase the regulator's information burden.

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arXiv2026

ADMM-based decomposed DNN+RLT Relaxations for Completely Positive Models in Electricity Market Clearing

The day-ahead electricity market clearing with nonconvex order types can be formulated as a mixed-integer linear program (MILP), but its LP relaxation may provide weak bounds, and exact solutions can become computationally intractable in large-scale or extended market settings. We study a welfare-maximizing clearing model with elementary hourly orders, block orders with logical acceptance constraints, and flexible hourly orders. Starting from a compact MILP formulation, we derive an equivalent completely positive programming (CPP) reformulation via matrix lifting and propose relaxed CPP variants that further reduce the modeling burden while maintaining strong bounds. We then develop tractable doubly nonnegative (DNN) relaxations, including decomposed formulations that exploit the problem structure by using smaller positive semidefinite matrices. To further strengthen these bounds, we introduce reformulation-linearization technique (RLT) inequalities tailored to the decomposed structure. To tackle the challenge of large-scale DNNs, we design an alternating direction method of multipliers (ADMM) with adaptive penalty updates and rigorous dual lower bounds, enabling certified early termination. Computational experiments on synthetic instances show that the proposed DNN+RLT relaxations substantially tighten LP bounds, while decomposition and first-order methods significantly reduce computational effort.

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