arXiv subjects

Mads R. Almassalkhi

Publications and source records attributed to Mads R. Almassalkhi.

At least 19 recordsLinked to original sources

arXiv2026

Towards Input-Convex Neural Network Modeling for Battery Optimization in Power Systems

Battery energy storage systems (BESS) play an increasingly vital role in integrating renewable generation into power grids due to their ability to dynamically balance supply. Grid-tied batteries typically employ power converters, where part-load efficiencies vary non-linearly. While this non-linearity can be modeled with high accuracy, it poses challenges for optimization, particularly in ensuring computational tractability. In this paper, we consider a non-linear BESS formulation based on the Energy Reservoir Model (ERM). A data-driven approach is introduced with the input-convex neural network (ICNN) to approximate the nonlinear efficiency with a convex function. The epigraph of the convex function is used to engender a convex program for battery ERM optimization. This relaxed ICNN method is applied to two battery optimization use-cases: PV smoothing and revenue maximization, and it is compared with three other ERM formulations (nonlinear, linear, and mixed-integer). Specifically, ICNN-based methods appear to be promising for future battery optimization with desirable feasibility and optimality outcomes across both use-cases.

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arXiv2026

Making Aggregations Reliable: Realizability Guarantees for Battery Fleets with Heterogeneous Power and Energy Limits

Aggregated battery energy storage systems (BESS) enable large fleets of heterogeneous battery elements to participate in system-level optimization and electricity markets. Scheduling each element independently is computationally impractical at scale. While many aggregate battery models rely on convex relaxations, they often ignore element complementarity constraints, leading to dispatch solutions that may be infeasible when implemented on individual battery elements. This paper develops a realizable composite battery model for parameter-heterogeneous BESS fleets that guarantees feasibility at the element-level while preserving computational tractability. We derive simple linear conditions under which aggregate charging and discharging trajectories can be safely disaggregated while respecting individual power limits, energy limits, and complementarity constraints under a priority-based controller. Numerical experiments in a unit-commitment setting demonstrate that the proposed realizable composite battery formulation produces feasible dispatch solutions. Solve times are effectively independent of system size, unlike micro-model mixed-integer formulations. Solutions obtained from the proposed formulation converge to the optimal benchmark as control granularity is refined. Additional studies illustrate the robustness of the framework to moderate violations of key modeling assumptions, including heterogeneous power-to-energy ratios.

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arXiv2026

Power-Duration Characterization of Aggregated Thermostatically Controlled Loads via Reach and Hold Sets

Aggregations of thermostatically controlled loads (TCLs), such as air conditioners, offer valuable flexibility to the power grid. The aggregate power consumption of a TCL fleet can be controlled by adjusting thermostat setpoints. An \textit{ex-ante} quantification of the flexibility that results from such setpoint change can inform grid operator decisions. This paper develops a rigorous, yet practical method to quantify flexibility in terms of the `reach-and-hold' set of TCL aggregations, which defines how much power can be shifted (reach) and for how long (hold). To quantify the reach-and-hold set, we employ a Markov-chain-based model of the TCL aggregation that captures second-order TCL dynamics, enabling accurate characterization of reach-and-hold sets. A tractable optimization problem is then formulated to numerically compute an inner approximation of these sets. Simulation results validate that our method accurately characterizes the fleet's flexibility and effectively controls its power consumption. Furthermore, a robustness analysis is carried out to investigate the effects of uncertainty in initial conditions and TCL parameters.

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arXiv2026

Cross-Atlantic Research Agenda for Scalable Grid Architectures and Distributed Flexibility

Electric power systems are rapidly evolving into deeply digital, cyber-physical infrastructures in which large fleets of distributed energy resources must be coordinated as system-level flexibility across multiple spatial and temporal scales. Despite growing distributed energy resource deployment, existing grid and market architectures lack scalable, interoperable mechanisms to reliably translate device-level flexibility into grid-aware services, creating risks to reliability, affordability, and resilience at high penetration. We propose that scalable and reliable coordination of distributed energy resource-based flexibility in future power systems is fundamentally an architectural problem that can be addressed through laminar cyber-physical design using minimal, standardized interoperability interfaces that link device autonomy with system-level objectives. To assess this claim, we present and discuss a layered cyber-physical systems architecture and explicate its implementation through standards-based interfaces, Flexibility Functions, hierarchical control, and case studies spanning U.S. and Danish regulatory, market, and operational contexts. Empirical evidence from New York's Grid of the Future proceedings, Danish Smart Energy Operating System pilots, and operational aggregator deployments demonstrates that such architecture enables predictable, grid-aware flexibility while preserving device autonomy, interoperability, reliability, and quality of service. These results support a cross-Atlantic research agenda centered on joint testbeds, harmonized interoperability mechanisms, and coordinated policy experiments to accelerate the deployment of resilient, scalable, and flexible clean energy systems.

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arXiv2026

Data-Driven Power Flow for Radial Distribution Networks with Sparse Real-Time Data

Real-time control of distribution networks requires accurate information about the system state. In practice, however, such information is difficult to obtain because real-time measurements are available only at a limited number of locations. This paper proposes a novel data-driven power flow (DDPF) framework for balanced radial distribution networks. The proposed algorithm combines the behavioral approach with the DistFlow model and leverages offline historical data to solve power flow problems using only a limited set of real-time measurements. To design DDPF under sparse measurement conditions, we develop a sensor placement problem based on optimal network reductions. This allows us to determine sensor locations subject to a predefined sensor budget and to explicitly account for the radial nature of distribution networks. Unlike approaches that rely on full observability, the proposed framework is designed for practical distribution grids with sparse measurement availability. This enables data-driven power flow for real-time operation while reducing the number of required sensors. On several test cases, the proposed DDPF algorithm could demonstrate accurate voltage magnitude predictions, with a maximum error less than 0.001 p.u., with as little as 25% of total locations equipped with sensors.

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arXiv2026

Experimental Multi-site Testbed for Advanced Control and Optimization of Hybrid Energy Systems

This paper presents a hybrid energy system (HES) experimental testbed developed at the University of Vermont, featuring a dual-site architecture that integrates on-campus laboratory facility with an off-campus solar and meteorological station. This supports the prototyping and validation of advanced HES control and optimization strategies. The platform integrates hardware-in-the-loop (HIL) simulations with a reconfigurable set of kVA-scale assets.A unified monitoring and communication architecture supports real-time data acquisition, model validation, and control implementation. The capabilities of the testbed are demonstrated through an HIL experiment in which a battery systems participate in solar PV smoothing.

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arXiv2025

Optimal Bidding and Coordinated Dispatch of Hybrid Energy Systems in Regulation Markets

The increasing integration of renewable energy sources and distributed energy resources (DER) into modern power systems introduces significant uncertainty, posing challenges for maintaining grid flexibility and reliability. Hybrid energy systems (HES), composed of controllable generators, flexible loads, and battery storage, offer a decentralized solution to enhance flexibility compared to single centralized resources. This paper presents a two-level framework to enable HES participation in frequency regulation markets. The upper level performs a chance-constrained optimization to choose capacity bids based on historical regulation signals. At the lower level, a real-time control strategy disaggregates the regulation power among the constituent resources. This real-time control strategy is then benchmarked against an offline optimal dispatch to evaluate flexibility performance. Additionally, the framework evaluates the profitability of overbidding strategies and identifies thresholds beyond which performance degradation may lead to market penalties or disqualification. The proposed framework also compare the impact of imbalance of power capacities on performance and battery state of charge (SoC) through asymmetric HES configurations.

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arXiv2025

An Iterative Problem-Driven Scenario Reduction Framework for Stochastic Optimization with Conditional Value-at-Risk

Scenario reduction (SR) alleviates the computational complexity of scenario-based stochastic optimization with conditional value-at-risk (SBSO-CVaR) by identifying representative scenarios to depict the underlying uncertainty and tail risks. Existing distribution-driven SR methods emphasize statistical similarity but often exclude extreme scenarios, leading to weak tail-risk awareness and insufficient problem-specific representativeness. Instead, this paper proposes an iterative problem-driven scenario reduction framework. Specifically, we integrate the SBSO-CVaR problem structure into SR process and project the original scenario set from the distribution space onto the problem space. Subsequently, to minimize the SR optimality gap with acceptable computation complexity, we propose a tractable iterative problem-driven scenario reduction (IPDSR) method that selects representative scenarios that best approximate the optimality distribution of the original scenario set while preserving tail risks. Furthermore, the iteration process is rendered as a mixed-integer program to enable scenario partitioning and representative scenarios selection. And ex-post problem-driven evaluation indices are proposed to evaluate the SR performance. Numerical experiments show IPDSR significantly outperforms existing SR methods by achieving an optimality gap of less than 1% within an acceptable computation time.

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arXiv2025

Improved Voltage Regulation with Optimal Design of Decentralized Volt-VAr Control

Integration of distributed energy resources has created a need for autonomous, dynamic voltage regulation. Decentralized Volt-VAr Control (VVC) of grid-connected inverters presents a unique opportunity for voltage management but, if designed poorly, can lead to unstable behavior when in feedback with the grid. We model the grid-VVC closed-loop dynamics with a linearized power flow approach, leveraging historical data, which shows improvement over the commonly used LinDistFlow model. This model is used to design VVC slopes by minimizing steady-state voltage deviation from the nominal value, subject to a non-convex spectral radius stability constraint, which has not been previously implemented within this context. We compare this constraint to existing convex restrictions and demonstrate, through simulations on a realistic feeder, that using the spectral radius results in more effective voltage regulation.

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arXiv2025

Aggregate Modeling of Air-Conditioner Loads Under Packet-based Control with Both On and Off Grid Access Requests

Coordination of distributed energy resources (DERs) can engender flexibility necessary to improve grid reliability. Packetized Energy Management (PEM) is a method for coordinating DERs, such as thermostatically controlled loads (TCLs) and electric vehicles, within customer quality-of-service (QoS) limits. In PEM, a DER uses local information to offer flexibility by sending a request to the DER coordinator to turn-ON or turn-OFF. Much work has focused on modeling and analyzing aggregations of DERs under PEM with fixed packet durations and only turn-ON requests. Different recent efforts to enable variable packet lengths have shown an increase in available flexibility and ramping capability, but have not been modeled in aggregate, which limits systematic analyses. To address this issue, this paper presents a new aggregate bin-based (macro) model of PEM loads that incorporates both turn-ON and turn-OFF request features, enabling the model to accurately characterize the capability of the fleet of DERs to track a power reference signal, population temperature dynamics, aggregate request rates, and variable packet lengths. Simulation-based validation is performed against an agent-based (micro) model to evaluate robustness and quantify model accuracy. Finally, the distribution of variable packet lengths from macro-model simulations are applied to inform past work on PEM with randomized packet lengths

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arXiv2025

Linear Aggregate Model for Realizable Dispatch of Homogeneous Energy Storage

To optimize the dispatch of batteries, a model is required that can predict the state of energy (SOE) trajectory for a chosen open-loop power schedule to ensure admissibility (i.e., that schedule can be realized). However, battery dispatch optimization is inherently challenging when batteries cannot simultaneously charge and discharge, which begets a non-convex complementarity constraint. In this paper, we develop a novel composition of energy storage elements that can charge or discharge independently and provide a sufficient linear energy storage model of the composite battery. This permits convex optimization of the composite battery dispatch while ensuring the admissibility of the resulting (aggregated) power schedule and its disaggregation to the individual elements.

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arXiv2025

Capacity Credit Evaluation of Generalized Energy Storage Considering Strategic Capacity Withholding and Decision-Dependent Uncertainty

This paper proposes a novel capacity credit evaluation framework to accurately quantify the contribution of generalized energy storage (GES) to resource adequacy, considering both strategic capacity withholding and decision-dependent uncertainty (DDU). To this end, we establish a market-oriented risk-averse coordinated dispatch method to capture the cross-market reliable operation of GES. The proposed method is sequentially implemented along with the Monte Carlo simulation process, coordinating the pre-dispatched price arbitrage and capacity withholding in the energy market with adequacy-oriented re-dispatch during capacity market calls. In addition to decision-independent uncertainties in operational states and baseline behavior, we explicitly address the inherent DDU of GES (i.e., the uncertainty of available discharge capacity affected by the incentives and accumulated discomfort) during the re-dispatch stage using the proposed data-driven distributional robust chance-constrained approach. Furthermore, a capacity credit metric called equivalent storage capacity substitution is introduced to quantify the equivalent deterministic storage capacity of uncertain GES. Simulations on the modified IEEE RTS-79 benchmark system with 20 years real-world data from Elia demonstrate that the proposed method yields accurate capacity credit and improved economic performance. We show that the capacity credit of GES increases with more strategic capacity withholding but decreases with more DDU levels. Key factors, such as capacity withholding and DDU structure impacting GES's capacity credit are analyzed with insights into capacity market decision-making.

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arXiv2025

AC-aware Optimization Framework for Under-Frequency Load Shedding

Under-frequency load shedding (UFLS) prevents system collapse during large disturbances. Increased penetration of distributed energy resources (DERs) and reduced system inertia makes it challenging to design a static UFLS scheme, which relies on preset frequency thresholds and load shed fractions to meet design criteria across all possible operating conditions. Due to non-linearity and traceability issues, previous adaptive UFLS schemes use simplified tractable frequency models that overlook AC network effects such as voltage-dependent load/generation. This paper leverages model order reduction techniques to obtain a higher fidelity low-order model of system frequency dynamics that captures AC network effects while incorporating turbine governor action and their associated limits. The model is then used in a new AC-aware predictive optimization framework to adapt UFLS setpoints periodically based on current operating conditions while minimizing load shed. Validated on a 1,648-bus system with PSS/E simulations, the proposed method meets design criteria under various operating conditions and disturbance scenarios. Furthermore, the framework outperforms conventional static UFLS schemes and adaptive UFLS schemes based on simplified dynamic models.

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arXiv2024

Problem-Driven Scenario Reduction Framework for Power System Stochastic Operation

Scenario reduction (SR) aims to identify a small yet representative scenario set to depict the underlying uncertainty, which is critical to scenario-based stochastic optimization (SBSO) of power systems. Existing SR techniques commonly aim to achieve statistical approximation to the original scenario set. However, SR and SBSO are commonly considered as two distinct and decoupled processes, which cannot guarantee a superior approximation of the original optimality. Instead, this paper incorporates the SBSO problem structure into the SR process and introduces a novel problem-driven scenario reduction (PDSR) framework. Specifically, we project the original scenario set in distribution space onto the mutual decision applicability between scenarios in problem space. Subsequently, the SR process, embedded by a distinctive problem-driven distance metric, is rendered as a mixed-integer linear programming formulation to obtain the representative scenario set while minimizing the optimality gap. Furthermore, ex-ante and ex-post problem-driven evaluation indices are proposed to evaluate the SR performance. Numerical experiments on two two-stage stochastic economic dispatch problems validate the effectiveness of PDSR, and demonstrate that PDSR significantly outperforms existing SR methods by identifying salient (e.g., worst-case) scenarios, and achieving an optimality gap of less than 0.1% within acceptable computation time.

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arXiv2024

Transformer Temperature Management and Voltage Control in Electric Distribution Systems with High Solar PV Penetration

The increasing penetration of photovoltaic (PV) systems in distribution grids can lead to overvoltage and transformer overloading issues. While voltage regulation has been extensively studied and some research has addressed transformer temperature control, there is limited work on simultaneously managing both challenges. This paper addresses this gap by proposing an optimization-based strategy that efficiently manages voltage regulation and transformer temperature while minimizing the curtailment of PV generation. In order to make this problem convex, a relaxation is applied to the transformer temperature dynamics constraint. We also provide analysis to determine under which conditions this relaxation remains tight. The proposed approach is validated through simulations, demonstrating its effectiveness in achieving the desired control objectives.

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arXiv2024

Predictive Optimization of Hybrid Energy Systems with Temperature Dependency

Hybrid Energy Systems (HES), amalgamating renewable sources, energy storage, and conventional generation, have emerged as a responsive resource for providing valuable grid services. Subsequently, modeling and analysis of HES has become critical, and the quality of grid services hedges on it. Currently, most HES models are temperature-agnostic. However, the temperature-dependent factors can significantly impact HES performance, necessitating advanced modeling and optimization techniques. With the inclusion of temperature-dependent models, the challenges and complexity of solving optimization problem increases. In this paper, the electro-thermal modeling of HES is discussed. Based on this model, a nonlinear predictive optimization framework is formulated. A simplified model is developed to address the challenges associated with solving nonlinear problems. Further, projection and homotopy approaches are proposed. In the homotopy method, the NLP is solved by incrementally changing the C-rating of the battery. Simulation-based analysis of the algorithms highlights the effects of different battery ratings, ambient temperatures, and energy price variations. Finally, comparative assessments with a temperature-agnostic approach illustrates the effectiveness of electro-thermal methods in optimizing HES.

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arXiv2024

Optimization-based Framework for Selecting Under-frequency Load Shedding Parameters

High penetration of renewable resources results in a power system with lower inertia and higher frequency sensitivity to power imbalances. Such systems are becoming increasingly susceptible to frequency collapse during extreme disturbances. Under-Frequency Load Shedding (UFLS) is a last-resort protection scheme and acts as an emergency brake by shedding load to arrest frequency decline. Current and emerging efforts to optimize UFLS settings and frequency thresholds are mostly network agnostic, ignoring network spatial information. With the prevalence of Distributed Energy Resources (DERs) in the high-renewable paradigm, the power grid is becoming more bidirectional, making some locations in the network less effective for UFLS action than others. This work proposes a Mixed Integer Linear Program that optimizes the UFLS setpoints (prioritizing one location over another) to minimize frequency deviation and load-shed for a given disturbance. The formulation considers system information and DER generation mix at different network locations, increasing model fidelity. The formulation also captures the discrete nature and practical time delays and deadbands associated with UFLS using a minimal set of binary variables, reducing problem complexity. We empirically validate the optimization approach on the dynamic IEEE 39-bus system for performance metrics, including frequency nadir, steady-state frequency and total load shed.

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arXiv2023

Improving frequency response with synthetic damping available from fleets of distributed energy resources

With the increasing use of renewable generation in power systems, responsive resources will be necessary to support primary frequency control in future low-inertia/under-damped power systems. Flexible loads can provide fast-frequency response services if coordinated effectively. However, practical implementations of such synthetic damping services require both effective local sensing and control at the device level and an ability to accurately estimate online and predict the available synthetic damping from a fleet. In addition, the inherent trade-off between a fleet being available for fast frequency response while providing other ancillary services needs to be characterized. In this context, the manuscript presents a novel, fully decentralized, packet-based controller for diverse flexible loads that dynamically prioritizes and interrupts loads to engender synthetic damping suitable for primary frequency control. Moreover, the packet-based control methodology is shown to accurately characterize the available synthetic damping in real-time, which is useful to aggregators and system operators. Furthermore, spectral analysis of historical frequency regulation data is used to produce a probabilistic bound on the expected available synthetic damping for primary frequency control from a fleet and the trade-off from concurrently providing secondary frequency control services. Finally, numerical simulation on IEEE test networks demonstrates the effectiveness of the proposed methodology.

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