arXiv subjects

Mohammad Reza Hesamzadeh

Publications and source records attributed to Mohammad Reza Hesamzadeh.

17 recordsLinked to original sources

arXiv2026

Pumped-Storage Hydropower Scheduling: An Event-based Convex-hull Approach

Pumped-storage hydropower scheduling couples discrete operating-mode transitions with continuous dispatch decisions through intertemporal reservoir and ramping constraints. Existing convexification methods do not simultaneously accommodate multiple operating modes, persistent continuous reservoir and ramping states, and interval costs that depend on both incoming and outgoing states of the operating modes. We develop an event-based dynamic programming formulation in which mode transitions define variable-length events and mode-specific linear programs optimize continuous within-event operation. We prove that this formulation is equivalent to the conventional time-indexed mixed-integer linear program. Enumerating the finite set of discrete event paths and scaling their boundary-coupled polyhedra then yields an exact finite-dimensional convex-hull LP without state discretization. For tractability, we develop a finite-grid formulation that discretizes reservoir and ramping states only at event boundaries while retaining continuous within-event trajectories. Its feasible set contains that of the corresponding stagewise discretization. Moreover, the resulting LP provides an exact convex-hull representation of the grid-restricted model and admits an error bound linear in the grid resolutions. An event-based branch-and-bound method provides an independent computational verification of the continuous-state reformulation. Standalone experiments verify the theoretical results, while tests on a modified IEEE 24-bus Reliability Test System show that the finite-grid LP substantially reduces computation time with a negligible increase in system cost.

eess.SY↗

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.

eess.SY↗

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.

eess.SY↗

arXiv2026

A Framework for Eliminating Paradoxical Orders in European Day-Ahead Electricity Markets through Mixed-Integer Linear Programming Strong Duality

The presence of integer variables in the European day-ahead electricity market renders the social welfare maximization problem non-convex and non-differentiable, making classical marginal pricing theoretically inconsistent. Existing pricing mechanisms often struggle to balance revenue adequacy with incentive compatibility, typically relying on discriminatory uplift payments or suffering from weak duality. Leveraging the Augmented Lagrangian Duality (ALD) framework, which establishes strong duality for Mixed-Integer Linear Programming (MILP), this paper proposes a novel ALD pricing mechanism. We analytically prove that this mechanism is inherently incentive-compatible, aligning centralized dispatch with individual incentives without requiring side payments. Notably, we demonstrate that the ALD price signals intrinsically eliminate Paradoxically Rejected Orders (PROs) and Paradoxically Accepted Orders (PAOs) for supply orders. For the demand side, a sufficient condition is introduced to further guarantee revenue adequacy, resulting in a transparent and financially consistent settlement system. To ensure computational tractability, we modify the Surrogate Absolute-Value Lagrangian Relaxation (SAVLR) method to efficiently compute the exact penalty coefficients and optimal Lagrangian multipliers. Numerical experiments on illustrative examples and the Nordic 12-area electricity market model confirm the superior economic properties of the ALD pricing mechanism and the tractability of the modified SAVLR algorithm.

math.OC↗

arXiv2025

The Theory of Storage in a Power System with Stochastic Demand

Electric power systems are increasingly turning to energy storage systems to balance supply and demand. But how much storage is required? What is the optimal volume of storage in a power system and on what does it depend? In addition, what form of hedge contracts do storage facilities require? We answer these questions in the special case in which the uncertainty in the power system involves successive draws of an independent, identically-distributed random variable. We characterize the conditions for the optimal operation of, and investment in, storage and show how these conditions can be understood graphically using price-duration curves. We also characterize the optimal hedge contracts for storage units.

econ.TH↗

arXiv2025

Driver Identification and PCA Augmented Selection Shrinkage Framework for Nordic System Price Forecasting

The System Price (SP) of the Nordic electricity market serves as a key reference for financial hedge contracts such as Electricity Price Area Differentials (EPADs) and other risk management instruments. Therefore, the identification of drivers and the accurate forecasting of SP are essential for market participants to design effective hedging strategies. This paper develops a systematic framework that combines interpretable drivers analysis with robust forecasting methods. It proposes an interpretable feature engineering algorithm to identify the main drivers of the Nordic SP based on a novel combination of K-means clustering, Multiple Seasonal-Trend Decomposition (MSTD), and Seasonal Autoregressive Integrated Moving Average (SARIMA) model. Then, it applies principal component analysis (PCA) to the identified data matrix, which is adapted to the downstream task of price forecasting to mitigate the issue of imperfect multicollinearity in the data. Finally, we propose a multi-forecast selection-shrinkage algorithm for Nordic SP forecasting, which selects a subset of complementary forecast models based on their bias-variance tradeoff at the ensemble level and then computes the optimal weights for the retained forecast models to minimize the error variance of the combined forecast. Using historical data from the Nordic electricity market, we demonstrate that the proposed approach outperforms individual input models uniformly, robustly, and significantly, while maintaining a comparable computational cost. Notably, our systematic framework produces superior results using simple input models, outperforming the state-of-the-art Temporal Fusion Transformer (TFT). Furthermore, we show that our approach also exceeds the performance of several well-established practical forecast combination methods.

econ.EM↗

arXiv2025

Sparse Polynomial Regression under Anomalous Data

This paper starts with the general form of the polynomial regression model. We reformulate the Sparse Polynomial Regression Model (SPRM) with anomalous data filtering as Mixed-Integer Linear Program (MILP). This MILP is then converted to a non-convex Quadratically Constrained Quadratic Program (QCQP). Through a proposed mapping, the derived QCQP is reformulated as a Fractional Program (FP). We theoretically show that the reformulated FP has better computational properties than the original QCQP. We then suggest a conic-relaxation-based algorithm to solve the proposed FP. A Two-Step Convex Relaxation and Recovery (TS-CRR) algorithm is proposed for sparse polynomial regression with anomalous data filtering. Through a series of comprehensive computational experiments (using two different datasets), we have compared the results of our proposed TS-CRR algorithm with the results from several regression and artificial intelligent models. The numerical results show the promising performance of our proposed TS-CRR algorithm as compared to those studied benchmark models.

math.OC↗

arXiv2025

Optimal Trading of a Charging-Station Company in Auction Markets for Electricity

This paper addresses a charging-station company (Chargco) for electric and hydrogen vehicles. The optimal trading of the Chargco in day-ahead and intraday auction markets for electricity is modeled as a stochastic Mixed-Integer Quadratic Program (MIQP). We propose a series of linearization and reformulation techniques to reformulate the stochastic MIQP as a mixed-integer linear program (MILP). To model stochasticity, we utilize generative adversarial networks to cluster electricity market price scenarios. Additionally, a combination of random forests and linear regression is employed to model the relationship between Chargco electricity and hydrogen loads and their selling prices. Finally, we propose an Improved L-Shaped Decomposition (ILSD) algorithm to solve our stochastic MILP. Our ILSD algorithm not only addresses infeasibilities through an innovative approach but also incorporates warm starts, valid inequalities and multiple generation cuts, thereby reducing computational complexity. Numerical experiments illustrate the Chargco trading using our proposed stochastic MILP and its solution algorithm.

cs.DM↗

arXiv2024

A New Computational Approach for Solving Linear Bilevel Programs Based on Parameter-Free Disjunctive Decomposition

Linear bilevel programs (linear BLPs) have been widely used in computational mathematics and optimization in several applications. Single-level reformulation for linear BLPs replaces the lower-level linear program with its Karush-Kuhn-Tucker optimality conditions and linearizes the complementary slackness conditions using the big-M technique. Although the approach is straightforward, it requires finding the big-M whose computation is recently shown to be NP-hard. This paper presents a disjunctive-based decomposition algorithm which does not need finding the big-Ms whereas guaranteeing that obtained solution is optimal. Our experience shows promising performance of our algorithm.

eess.SY↗

arXiv2023

Probabilistic Multi-product Trading in Sequential Intraday and Frequency-Regulation Markets

With the increasing integration of power plants into the frequency-regulation markets, the importance of optimal trading has grown substantially. This paper conducts an in-depth analysis of their optimal trading behavior in sequential day-ahead, intraday, and frequency-regulation markets. We introduce a probabilistic multi-product optimization model, derived through a series of transformation techniques. Additionally, we present two reformulations that re-frame the problem as a mixed-integer linear programming problem with uncertain parameters. Various aspects of the model are thoroughly examined to observe the optimal multi-product trading behavior of hydro power plant assets, along with numerous case studies. Leveraging historical data from Nordic electricity markets, we construct realistic scenarios for the uncertain parameters. Furthermore, we then proposed an algorithm based on the No-U-Turn sampler to provide probability distribution functions of cleared prices in frequency-regulation and day-ahead markets. These distribution functions offer valuable statistical insights into temporal price risks for informed multi-product optimal-trading decisions.

eess.SY↗

arXiv2023

Ancillary Services in Power System Transition Toward a 100% Non-Fossil Future: Market Design Challenges in the United States and Europe

The expansion of variable generation has driven a transition toward a 100\% non-fossil power system. New system needs are challenging system stability and suggesting the need for a redesign of the ancillary service (AS) markets. This paper presents a comprehensive and broad review for industrial practitioners and academic researchers regarding the challenges and potential solutions to accommodate high shares of variable renewable energy (VRE) generation levels. We detail the main drivers enabling the energy transition and facilitating the provision of ASs. A systematic review of the United States and European AS markets is conducted. We clearly organize the main ASs in a standard taxonomy, identifying current practices and initiatives to support the increasing VRE share. Furthermore, we envision the future of modern AS markets, proposing potential solutions for some remaining fundamental technical and market design challenges.

physics.soc-ph↗

arXiv2023

Transmission Investment Coordination using MILP Lagrange Dual Decomposition and Auxiliary Problem Principle

This paper considers the investment coordination problem for the long term transmission capacity expansion in a situation where there are multiple regional Transmission Planners (TPs), each acting in order to maximize the utility in only its own region. In such a setting, any particular TP does not normally have any incentive to cooperate with the neighboring TP(s), although the optimal investment decision of each TP is contingent upon those of the neighboring TPs. A game-theoretic interaction among the TPs does not necessarily lead to this overall social optimum. We, therefore, introduce a social planner and call it the Transmission Planning Coordinator (TPC) whose goal is to attain the optimal possible social welfare for the bigger geographical region. In order to achieve this goal, this paper introduces a new incentive mechanism, based on distributed optimization theory. This incentive mechanism can be viewed as a set of rules of the transmission expansion investment coordination game, set by the social planner TPC, such that, even if the individual TPs act selfishly, it will still lead to the TPC's goal of attaining overall social optimum. Finally, the effectiveness of our approach is demonstrated through several simulation studies.

eess.SY↗

arXiv2023

A Pricing Mechanism to Jointly Mitigate Market Power and Environmental Externalities in Electricity Markets

The electricity industry has been one of the first to face technological changes motivated by sustainability concerns. Whilst efficiency aspects of market design have tended to focus upon market power concerns, the new policy challenges emphasise sustainability. We argue that market designs need to develop remedies for market conduct integrated with regard to environmental externalities. Accordingly, we develop an incentive-based market clearing mechanism using a power network representation with a distinctive feature of incomplete information regarding generation costs. The shortcomings of price caps to mitigate market power, in this context, are overcome with the proposed mechanism.

econ.TH↗

arXiv2022

A Machine Learning Approach for Prosumer Management in Intraday Electricity Markets

Prosumer operators are dealing with extensive challenges to participate in short-term electricity markets while taking uncertainties into account. Challenges such as variation in demand, solar energy, wind power, and electricity prices as well as faster response time in intraday electricity markets. Machine learning approaches could resolve these challenges due to their ability to continuous learning of complex relations and providing a real-time response. Such approaches are applicable with presence of the high performance computing and big data. To tackle these challenges, a Markov decision process is proposed and solved with a reinforcement learning algorithm with proper observations and actions employing tabular Q-learning. Trained agent converges to a policy which is similar to the global optimal solution. It increases the prosumer's profit by 13.39% compared to the well-known stochastic optimization approach.

cs.LG↗

arXiv2022

Econometric Modeling of Intraday Electricity Market Price with Inadequate Historical Data

The intraday (ID) electricity market has received an increasing attention in the recent EU electricity-market discussions. This is partly because the uncertainty in the underlying power system is growing and the ID market provides an adjustment platform to deal with such uncertainties. Hence, market participants need a proper ID market price model to optimally adjust their positions by trading in the market. Inadequate historical data for ID market price makes it more challenging to model. This paper proposes long short-term memory, deep convolutional generative adversarial networks, and No-U-Turn sampler algorithms to model ID market prices. Our proposed econometric ID market price models are applied to the Nordic ID price data and their promising performance are illustrated.

eess.SY↗

arXiv2021

Stochastic Optimal Operation of the VSC-MTDC System with FACTS Devices to Integrate Wind Power

This paper proposes to use stochastic conic programming to address the challenge of large-scale wind power integration to the power system. Multiple wind farms are connected through the voltage source converter (VSC) based multi-terminal DC (VSC-MTDC) system to the power network supported by the Flexible AC Transmission System (FACTS). The optimal operation of the power network incorporating the VSC-MTDC system and FACTS devices is formulated in a stochastic conic programming framework accounting the uncertainties of the wind power generation. A methodology to generate representative scenarios of power generations from the wind farms is proposed using wind speed measurements and wind turbine models. The nonconvex transmission network constraints including the VSC-MTDC system and FACTS devices are convexified through the proposed second-order cone AC optimal power flow model (SOC-ACOPF) that can be solved to the global optimality using interior point method. In order to tackle the computational challenge due to the large number of wind power scenarios, a modified Benders decomposition algorithm (M-BDA) accelerated by parallel computation is proposed. The energy dispatch of conventional power generators is formulated as the master problem of M-BDA. Numerical results for up to 50000 wind power scenarios show that the proposed M-BDA approach to solve stochastic SOC-ACOPF outperforms the traditional single-stage (without decomposition) solution approach in both convergence capability and computational efficiency. The feasibility performance of the proposed stochastic SOC-ACOPF model is also demonstrated.

eess.SY↗

arXiv2021

A bottom-up quantification of flexibility potential from the thermal energy storage in electric space heating

Non-generating resources such as thermostatically controlled loads (TCLs) can arbitrage energy prices and provide balancing reserves when aggregated due to their thermal energy storage capacity. Based on a performed survey of Swedish single- and two-family dwellings with electric heating, this paper quantifies the potential of TCLs to provide reserves to the power system in Sweden. To this end, dwellings with heat pumps and direct electric heaters are modeled as thermal energy storage equivalents that can be included in a linear two-stage problem formulation. We approach the operational flexibility of the TCLs by modeling a risk-averse aggregator that controls decentralized TCLs and aims to maximize its own profit. The results show a potential of 2 GW/0.1Hz averaged over a year, and up to 6.4 GW/0.1Hz peak capacity. Based on a sensitivity analysis we derive policy implications regarding market timing and activation signal.

eess.SY↗