arXiv subjects

Goran Strbac

Publications and source records attributed to Goran Strbac.

At least 19 recordsLinked to original sources

arXiv2026

Data-Driven Dimension Reduction for Industrial Load Modeling Using Inverse Optimization

The intricate mixed-integer constraints in industrial load models not only pose challenges for their direct integration into economic dispatch or market clearing processes but also render current analytical dimension-reduction methods ineffective. We propose a novel data-driven dimension-reduction approach for industrial load modeling, which uses the optimal energy usage data from industrial loads to train a dimension-reduced model that best fits the original constraints. Our approach, implemented by the adjustable load fleet model, outperformed analytical methods across three industrial load datasets.

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arXiv2026

Towards socio-techno-economic power systems with demand-side flexibility

Harnessing the demand-side flexibility in building and mobility sectors can help to better integrate renewable energy into power systems and reduce global CO2 emissions. Enabling this sector coupling can be achieved with advances in energy management, business models, control technologies, and power grids. The study of demand-side flexibility extends beyond engineering, spanning social science, economics, and power and control systems, which present both challenges and opportunities to researchers and engineers in these fields. This Review outlines recent trends and studies in social, economic, and technological advancements in power systems that leverage demand-side flexibility. We first provide a concept of a socio-techno-economic system with an abstraction of end-users, building and mobility sectors, control systems, electricity markets, and power grids. We discuss the interconnections between these elements, highlighting the importance of bidirectional flows of information and coordinated decision-making. We then emphasize that fully realizing demand-side flexibility necessitates deep integration across stakeholders and systems, moving beyond siloed approaches. Finally, we discuss the future directions in renewable-based power systems and control engineering to address key challenges from both research and practitioners' perspectives. A holistic approach for identifying, measuring, and utilizing demand-side flexibility is key to successfully maximizing its multi-stakeholder benefits but requires further transdisciplinary collaboration and commercially viable solutions for broader implementation.

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arXiv2025

Towards Microgrid Resilience Enhancement via Mobile Power Sources and Repair Crews: A Multi-Agent Reinforcement Learning Approach

Mobile power sources (MPSs) have been gradually deployed in microgrids as critical resources to coordinate with repair crews (RCs) towards resilience enhancement owing to their flexibility and mobility in handling the complex coupled power-transport systems. However, previous work solves the coordinated dispatch problem of MPSs and RCs in a centralized manner with the assumption that the communication network is still fully functioning after the event. However, there is growing evidence that certain extreme events will damage or degrade communication infrastructure, which makes centralized decision making impractical. To fill this gap, this paper formulates the resilience-driven dispatch problem of MPSs and RCs in a decentralized framework. To solve this problem, a hierarchical multi-agent reinforcement learning method featuring a two-level framework is proposed, where the high-level action is used to switch decision-making between power and transport networks, and the low-level action constructed via a hybrid policy is used to compute continuous scheduling and discrete routing decisions in power and transport networks, respectively. The proposed method also uses an embedded function encapsulating system dynamics to enhance learning stability and scalability. Case studies based on IEEE 33-bus and 69-bus power networks are conducted to validate the effectiveness of the proposed method in load restoration.

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arXiv2025

Two-Stage TSO-DSO Services Provision Framework for Electric Vehicle Coordination

High renewable penetration has been witnessed in power systems, resulting in reduced system inertia and increasing requirements for frequency response services. Electric vehicles (EVs), owing to their vehicle-to-grid (V2G) capabilities, can provide cost-effective frequency services for transmission system operators (TSOs). However, EVs that are inherently connected to distribution networks may pose voltage security issues for distribution system operators (DSOs) when supporting TSO frequency. To coordinate both TSO frequency and DSO voltage, this paper proposes a two-stage service provision framework for multi-EVs. At stage one, EVs participate in day-ahead TSO-DSO interactions for frequency reserve schedules; at stage two, EVs make real-time dispatching behaviors in distribution networks for reserve delivery while supporting DSO voltage. Considering the potentially large EV number and environment complexity, a decentralized operation paradigm is introduced for real-time EV dispatches at stage two, while a communication-efficient reinforcement learning (RL) algorithm is proposed to reduce the communication overhead during large-scale multi-agent RL training without compromising policy performance. Case studies are carried out on a 6-bus transmission and 33-bus distribution network as well as a 69-bus distribution network to evaluate the effectiveness and scalability of the proposed method in enabling EVs for frequency service and voltage support.

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arXiv2025

Regional Frequency-Constrained Planning for the Optimal Sizing of Power Systems via Enhanced Input Convex Neural Networks

Large renewable penetration has been witnessed in power systems, resulting in reduced levels of system inertia and increasing requirements for frequency response services. There have been plenty of studies developing frequency-constrained models for power system security. However, most existing literature only considers uniform frequency security, while neglecting frequency spatial differences in different regions. To fill this gap, this paper proposes a novel planning model for the optimal sizing problem of power systems, capturing regional frequency security and inter-area frequency oscillations. Specifically, regional frequency constraints are first extracted via an enhanced input convex neural network (ICNN) and then embedded into the original optimisation for frequency security, where a principled weight initialisation strategy is adopted to deal with the gradient vanishing issues of non-negative weights in traditional ICNNs and enhance its fitting ability. An adaptive genetic algorithm with sparsity calculation and local search is developed to separate the planning model into two stages and effectively solve it iteratively. Case studies have been conducted on three different power systems to verify the effectiveness of the proposed frequency-constrained planning model in ensuring regional system security and obtaining realistic investment decisions.

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arXiv2025

Transient Stability-Driven Planning for the Optimal Sizing of Resilient AC/DC Hybrid Microgrids

This paper proposes a transient stability-driven planning framework for the optimal sizing problem of resilient AC/DC hybrid microgrids (HMGs) under different types of contingencies, capturing frequency and voltage stability requirements as well as the frequency-voltage coupling dynamics of AC/DC interlinking converters (ICs). The planning model is formulated into a defender-attacker-defender (DAD) architecture, which can be further merged into two levels, i.e., upper-level and low-level problems, and then iteratively solved by an enhanced genetic algorithm with sparsity calculation and local search. Regarding the operation stage, a novel transient stability-constrained optimal power flow (TSC-OPF) algorithm is proposed for static and transient operations of HMGs, capturing governor dynamics and automatic voltage regulator of conventional generators as well as the droop control dynamics of inverter-based resources (IBRs) for frequency control and voltage control, respectively. Furthermore, a Lyapunov optimisation approach is developed to capture the time-coupling property of energy storages (ESs) and then allow the TSC-OPF to be solved on an hourly basis with a second-scale resolution, achieving the co-optimisation of static and transient stability requirements. Case studies have been conducted to verify the effectiveness of the proposed planning framework in obtaining cost-effective investment decisions for various resources while respecting transient stability requirements under different contingencies.

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arXiv2025

HMPC-assisted Adversarial Inverse Reinforcement Learning for Smart Home Energy Management

This letter proposes an Adversarial Inverse Reinforcement Learning (AIRL)-based energy management method for a smart home, which incorporates an implicit thermal dynamics model. In the proposed method, historical optimal decisions are first generated using a neural network-assisted Hierarchical Model Predictive Control (HMPC) framework. These decisions are then used as expert demonstrations in the AIRL module, which aims to train a discriminator to distinguish expert demonstrations from transitions generated by a reinforcement learning agent policy, while simultaneously updating the agent policy that can produce transitions to confuse the discriminator. The proposed HMPC-AIRL method eliminates the need for explicit thermal dynamics models, prior or predictive knowledge of uncertain parameters, or manually designed reward functions. Simulation results based on real-world traces demonstrate the effectiveness and data efficiency of the proposed method.

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arXiv2024

A Review of Hydrogen-Enabled Resilience Enhancement for Multi-Energy Systems

Ensuring resilience in multi-energy systems (MESs) has become increasingly urgent and challenging due to the growing frequency and severity of extreme events, such as natural disasters, extreme weather, and cyber-physical attacks. Among the various approaches to enhancing MES resilience, hydrogen integration offers significant potential in cross-temporal, cross-spatial, and cross-sector flexibility, as well as black-start capability. Although considerable efforts have been devoted to this area, a systematic review of resilience enhancement in hydrogen-enabled MESs is still lacking. To address this gap, this paper presents a comprehensive review of hydrogen-enabled MES resilience enhancement. First, advantages, vulnerabilities, and challenges related to hydrogen-enabled MES resilience enhancement are summarized. Next, a resilience enhancement framework for hydrogen-enabled MESs is proposed, based on which existing resilience metrics and event-oriented contingency models are reviewed and discussed. Planning measures are then classified according to the types of hydrogen-related facilities, together with uncertainty handling methods, scenario generation methods, and planning problem formulation frameworks. In addition, operational enhancement measures are categorized into three response stages: prevention, emergency response, and restoration. Finally, research gaps are identified and future directions are discussed, including comprehensive resilience metric design, advanced extreme-event scenario generation, spatiotemporal cyber-physical contingency modeling under compound extreme events, coordinated planning and operation across multiple networks and timescales, low-carbon resilient planning and operation, and large language model-assisted whole-process resilience enhancement.

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arXiv2024

Strategic Bidding in the Frequency-Containment Ancillary Services Market

The vast integration of non-synchronous renewable energy sources compromises power system stability, increasing vulnerability to frequency deviations due to the lack of inertia. Current efforts to decarbonise electricity grids while maintaining frequency security still rely on Ancillary Services (AS) provision, such as inertia and frequency response, from flexible synchronous generators, placing these type of units in an advantageous position in the AS market. However, in the ongoing transition to decarbonisation, not enough attention has been given to analysing market power in the frequency-containment AS market. This work presents a strategic bidding model designed to analyse market power in the coupled energy and frequency-containment AS market. Through a non-convex primal-dual bi-level formulation, we determine the interaction of a strategic market player with the rest of the market that behaves competitively. The case study is based on Great Britain in 2030, demonstrating the capacity of the strategic player to influence prices. While this impact is perceived in the energy market, it is particularly pronounced in the AS market.

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arXiv2023

Who should pay for frequency-containment ancillary services? Making responsible units bear the cost to shape investment in generation and loads

While the operating cost of electricity grids based on thermal generation was largely driven by the cost of fuel, as renewable penetration increases, ancillary services represent an increasingly large proportion of the running costs. Electric frequency is an important magnitude in highly renewable grids, as it becomes more volatile and therefore the cost related to maintaining it within safe bounds has significantly increased. So far, costs for frequency-containment ancillary services have been socialised in most countries, but it has become relevant to rethink this regulatory arrangement. In this paper, we discuss the issue of cost allocation for these services, highlighting the need to evolve towards a causation-based regulatory framework. We argue that parties responsible for creating the need for ancillary services should bear these costs. However, this would imply an important change in electricity market policy, therefore it is necessary to understand the impact on current and future investments on generation, as well as on electricity tariffs. Here we provide a mostly qualitative analysis of this issue, defining guidelines for practical implementation and further study.

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arXiv2023

Cost Allocation for Inertia and Frequency Response Ancillary Services

The reduction in system inertia is creating an important market for frequency-containment Ancillary Services (AS) such as enhanced frequency response (e.g.,~provided by battery storage), traditional primary frequency response and inertia itself. This market presents an important difference with the energy-only market: while the need for energy production is driven by the demand from consumers, frequency-containment AS are procured because of the need to deal with the largest generation/demand loss in the system (or smaller losses that could potentially compromise frequency stability). Thus, a question that arises is: who should pay for frequency-containment AS? In this work, we propose a cost-allocation methodology based on the nucleolus concept, in order to distribute the total payments for frequency-containment AS among all generators or loads that create the need for these services. It is shown that this method complies with necessary properties for the AS market, such as avoidance of cross-subsidies and maintaining players in this cooperative game. Finally, we demonstrate its practical applicability through a case study for the Great Britain power system, while comparing its performance with two alternative mechanisms, namely proportional and Shapley value cost allocation.

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arXiv2023

A Machine Learning-Enhanced Benders Decomposition Approach to Solve the Transmission Expansion Planning Problem under Uncertainty

The necessary decarbonization efforts in energy sectors entail the integration of flexibility assets, as well as increased levels of uncertainty for the planning and operation of power systems. To cope with this in a cost-effective manner, transmission expansion planning (TEP) models need to incorporate progressively more details to represent potential long-term system developments and the operation of power grids with intermittent renewable generation. However, the increased modeling complexities of TEP exercises can easily lead to computationally intractable optimization problems. Currently, most techniques that address computational intractability alter the original problem, thus neglecting critical modeling aspects or affecting the structure of the optimal solution. In this paper, we propose an alternative approach to significantly alleviate the computational burden of large-scale TEP problems. Our approach integrates machine learning (ML) with the well-established Benders decomposition to manage the problem size while preserving solution quality. The proposed ML-enhanced Multicut Benders Decomposition algorithm improves computational efficiency by identifying effective and ineffective optimality cuts via supervised learning techniques. We illustrate the benefits of the proposed methodology by solving a number of multi-stage TEP problems of different sizes, based on the IEEE24 and IEEE118 test systems, while also considering energy storage investment options.

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arXiv2023

Regularised Learning with Selected Physics for Power System Dynamics

Due to the increasing system stability issues caused by the technological revolutions of power system equipment, the assessment of the dynamic security of the systems for changing operating conditions (OCs) is nowadays crucial. To address the computational time problem of conventional dynamic security assessment tools, many machine learning (ML) approaches have been proposed and well-studied in this context. However, these learned models only rely on data, and thus miss resourceful information offered by the physical system. To this end, this paper focuses on combining the power system dynamical model together with the conventional ML. Going beyond the classic Physics Informed Neural Networks (PINNs), this paper proposes Selected Physics Informed Neural Networks (SPINNs) to predict the system dynamics for varying OCs. A two-level structure of feed-forward NNs is proposed, where the first NN predicts the generator bus rotor angles (system states) and the second NN learns to adapt to varying OCs. We show a case study on an IEEE-9 bus system that considering selected physics in model training reduces the amount of needed training data. Moreover, the trained model effectively predicted long-term dynamics that were beyond the time scale of the collected training dataset (extrapolation).

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arXiv2022

Reinforcement Learning and Mixed-Integer Programming for Power Plant Scheduling in Low Carbon Systems: Comparison and Hybridisation

Decarbonisation is driving dramatic growth in renewable power generation. This increases uncertainty in the load to be served by power plants and makes their efficient scheduling, known as the unit commitment (UC) problem, more difficult. UC is solved in practice by mixed-integer programming (MIP) methods; however, there is growing interest in emerging data-driven methods including reinforcement learning (RL). In this paper, we extensively test two MIP (deterministic and stochastic) and two RL (model-free and with lookahead) scheduling methods over a large set of test days and problem sizes, for the first time comparing the state-of-the-art of these two approaches on a level playing field. We find that deterministic and stochastic MIP consistently produce lower-cost UC schedules than RL, exhibiting better reliability and scalability with problem size. Average operating costs of RL are more than 2 times larger than stochastic MIP for a 50-generator test case, while the cost is 13 times larger in the worst instance. However, the key strength of RL is the ability to produce solutions practically instantly, irrespective of problem size. We leverage this advantage to produce various initial solutions for warm starting concurrent stochastic MIP solves. By producing several near-optimal solutions simultaneously and then evaluating them using Monte Carlo methods, the differences between the true cost function and the discrete approximation required to formulate the MIP are exploited. The resulting hybrid technique outperforms both the RL and MIP methods individually, reducing total operating costs by 0.3% on average.

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arXiv2022

Chance-constrained allocation of UFLS candidate feeders under high penetration of distributed generation

Under-Frequency Load Shedding (UFLS) schemes are the last resort to contain a frequency drop in the grid by disconnecting part of the demand. The allocation methods for selecting feeders that would contribute to the UFLS scheme have traditionally relied on the fact that electric demand followed fairly regular patterns, and could be forecast with high accuracy. However, recent integration of Distributed Generation (DG) increases the uncertainty in net consumption of feeders which, in turn, requires a reformulation of UFLS-allocation methods to account for this uncertainty. In this paper, a chance-constrained methodology for selecting feeders is proposed, with mathematical guarantees for the disconnection of the required amount of load with a certain pre-defined probability. The correlation in net-load forecasts among feeders is explicitly considered, given that uncertainty in DG power output is driven by meteorological conditions with high correlation across the network. Furthermore, this method is applicable either to systems with conventional UFLS schemes (where relays measure local frequency and trip if this magnitude falls below a certain threshold), or adaptive UFLS schemes (where relays are triggered by control signals sent in the few instants following a contingency). Relevant case studies demonstrate the applicability of the proposed method, and the need for explicit consideration of uncertainty in the UFLS-allocation process.

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arXiv2022

Convergent Economic Model Predictive Control through parameter-varying storage functions for dissipativity

This paper presents a new concept of controlled dissipativity as an extension of the standard dissipativity property to systems with parameter-varying storage functions under the framework of economic model predictive control (EMPC). Based on this concept, two EMPC controllers, integrated with the dissipation inequality constraints rendering the storage function parameters as decision variables, are formulated and the associated recursive feasibility is ensured. Then, the asymptotic convergence to an optimal equilibrium in closed-loop, without requiring the standard dissipativity assumption, is enforced by trading it off with asymptotic performance. The upper bound of asymptotic average closed-loop performance is also evaluated. Finally, an illustrative example by using the EMPC controllers with terminal equilibrium or terminal region conditions is provided to show the effectiveness of our methods.

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arXiv2022

Assigning Shadow Prices to Synthetic Inertia and Frequency Response Reserves from Renewable Energy Sources

Modern electricity grids throughout the world, particularly in islands such as Great Britain, face a major problem on the road to decarbonisation: the significantly reduced level of system inertia due to integration of Renewable Energy Sources (RES). Given that most RES such as wind and solar are decoupled from the grid through power electronics converters, they do not naturally contribute to system inertia. However, RES could support grid stability through appropriately controlling the converters, but currently no market incentives exist for RES to provide this support. In this paper we develop a methodology to optimally clear a market of ancillary services for frequency control, while explicitly considering the participation of grid-forming and grid-following inverter-based technologies. We propose a mathematical framework that allows to compute shadow prices for ancillary services offered by a pool of diverse providers: synchronous and synthetic inertia, enhanced frequency response (e.g. from curtailed RES) and traditional primary frequency response (e.g. by thermal generators). Several case studies are run on a simplified Great Britain system, to illustrate the applicability and benefits of this pricing scheme.

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arXiv2022

A framework for receding-horizon control in infinite-horizon aggregative games

A novel modelling framework is proposed for the analysis of aggregative games on an infinite-time horizon, assuming that players are subject to heterogeneous periodic constraints. A new aggregative equilibrium notion is presented and the strategic behaviour of the agents is analysed under a receding horizon paradigm. The evolution of the strategies predicted and implemented by the players over time is modelled through a discrete-time multi-valued dynamical system. By considering Lyapunov stability notions and applying limit and invariance results for set-valued correspondences, necessary conditions are derived for convergence of a receding horizon map to a periodic equilibrium of the aggregative game. This result is achieved for any (feasible) initial condition, thus ensuring implicit adaptivity of the proposed control framework to real-time variations in the number and parameters of players. Design and implementation of the proposed control strategy are discussed and an example of distributed control for data routing is presented, evaluating its performance in simulation.

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