arXiv subjects

Lukas Sigrist

Publications and source records attributed to Lukas Sigrist.

At least 19 recordsLinked to original sources

arXiv2026

Revisiting angle stability in power systems with grid-forming power converters

This letter presents a comprehensive analysis of the stability phenomenon related to the ability of generators to remain in synchronism when subjected to small or large disturbances, in power systems with both synchronous machines and grid-forming voltage source converters (GFM-VSC). This phenomenon is associated with two stability classes in the IEEE/PES classification, namely, rotor-angle stability (when involving synchronous machines and slow-interaction converter-driven stability (when involving power converters). However, this work shows that this phenomenon is fully characterised with the slow dynamics of the angle difference between the voltage sources connected to the power system, regardless of whether they are synchronous machines (with rotors) or GFM-VSCs. Therefore, we suggest using the term angle stability to refer to this phenomenon, while slow-interaction converter-driven stability should only include slow interactions of different nature involving power converters.

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arXiv2026

Active-power control strategies in grid-forming power converters to improve transient stability in power systems with 100% converter-based generation

Grid-forming voltage source converters (GFM-VSCs) play a crucial role in the stability of power systems with large amounts of converter-based generation. Transient stability (angle stability under large disturbances) is a critical limiting factor in stressed power systems. Previous studies have proposed control strategies in GFM-VSCs to improve transient stability. These approaches typically rely on suitable current-limiting algorithms, voltage/reactive-power and active-power supplementary control strategies. This paper investigates and compares the effectiveness of three active-power control strategies in GFM-VSCs to enhance transient stability in power systems with 100 % converter-based generation: (i) a wide-area control strategy (TSP-WACS) using the centre of inertia (COI) frequency, (ii) a local transient damping method (TSP-TDM), and (iii) a novel local control strategy (TSP-L) proposed in this work. All strategies were implemented and assessed using short-circuit simulations on Kundur two-area test system with 100 % GFM-VSC generators, demonstrating critical clearing time (CCT) improvement. The TSP-WACS strategy achieves the best performance but requires a communication infrastructure, while TSP-L strategy offers a simple-but-robust alternative using local measurements, only.

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arXiv2025

Enhancing Robust Multi-Market Participation of Renewable-Based VPPs through Flexible Resources

In the transition toward a sustainable power system, renewable-based Virtual Power Plants (RVPPs) have emerged as a promising solution to the challenges of integrating renewable energy sources into electricity markets. Their viability, however, depends on effective market participation strategies and the ability to manage uncertainties while leveraging flexible resources. This paper analyzes the impact of different flexible resources - such as concentrated solar power plants, hydro plants, biomass plants, and flexible demand - on the participation of RVPPs in energy and reserve markets. Multiple sources of uncertainty in generation, consumption, and electricity prices are addressed using a two-stage robust optimization approach. The contribution of different technologies to RVPP profitability is evaluated through a marginal contribution method, ensuring fair allocation of profits among them according to their actual role in energy and reserve provision across markets. Simulations for an RVPP in southern Spain demonstrate how strategic decisions and the availability of flexible resources influence viability, market participation, and unit scheduling.

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arXiv2025

Integration of Concentrated Solar Power Plants in Renewable-Only VPP with Electrical and Thermal Demands: A Two-Stage Robust Bidding Approach

This paper proposes the integration of Concentrated Solar Power Plant (CSP) in the Renewable-only virtual power plant (RVPP) for bidding in the electricity day-ahead and secondary reserve markets, as well as trading thermal energy through a heat purchase agreement. A reformulated two-stage robust optimization approach is introduced to account for multiple uncertainties, including electricity prices, non-dispatchable renewable energy sources electrical production, CSP thermal production, and uncertainties in electrical and thermal demand consumption. The provision of energy and reserve by the thermal storage of CSP is modeled using an adjustable approach, which allocates a share of energy for up and down reserves based on the profitability of the RVPP. Simulations are conducted for several case studies to demonstrate the effectiveness and computational efficiency of the proposed approach under different RVPP operator decisions against uncertain parameters and various trading strategies for electricity and thermal energy. The simulation results show that integrating CSP into RVPP enhances RVPP flexibility for both electrical and thermal trading. Furthermore, the results indicate that the profitability of the RVPP increases when all trading options are considered, across different levels of conservatism adopted by the RVPP operator in response to uncertain parameters.

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arXiv2025

Quasi Steady-State Frequency

Accurate frequency estimation is critical for the control, monitoring and protection of electrical power systems, in particular, of systems with a high penetration of power electronics. This paper introduces the novel concept of Quasi Steady-State (QSS) frequency as a quantity that fills the gap between stationary and instantaneous frequency. QSS frequency coincides with the fundamental frequency of an AC voltage in any stationary conditions, including unbalanced and non-sinusoidal, and is able to capture the time-varying fundamental frequency in transient conditions. The paper also proposes a metric borrowed from fluid dynamics, namely, the time derivative of the circulation, to define the scope of validity of the QSS frequency. Analytical examples as well as a case study based on a fully-fledged EMT model of the IEEE 39-bus system serve to illustrate, respectively, the properties of the QSS frequency and its behavior in transient conditions.

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arXiv2025

Impact on transient stability of self-synchronisation control strategies in grid-forming VSC-based generators

Grid-forming voltage source converters (GFM-VSCs) are emerging as a solution for integrating renewable energy resources (RERs) into power systems. GFM-VSCs need a self-synchronisation strategy to ensure that all converters and generators in the power system are in synchronism and they reach the same frequency in steady state. The self-synchronisation strategy in GFM-VSCs that has received most attention in previous research is virtual synchronous machine (VSM) control. However, no systematic study of the effects on transient stability of different variants of this strategy has been carried out in previous work. This paper analyses and compares transient stability of four self-synchronisation strategies for GFM-VSCs: VSM without phase-locked loop (PLL), VSM with PLL, VSM without PLL using wash-out filter and integral-proportional (IP) controller. The paper also analyses two different methods that can \color{black} be applied to GFM-VSC self-synchronisation strategies to improve transient stability: the concept of virtual unsaturated active-power controller (VAPC), proposed in previous work, and an algorithm for frequency limitation in the GFM-VSC (FLC), which is proposed in this paper.

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arXiv2025

Implementing General-Order Frequency Dynamic Response Model and Frequency Excursion Duration Criterion in Unit Commitment Problem

This paper introduces a novel approach for incorporating frequency dynamics into the unit commitment (UC) problem through a general-order differential equation model, solved using Bernstein polynomial approximation. Traditional frequency-constrained UC (FCUC) models typically rely on simplified first-order assumptions or scalar frequency metrics, such as frequency nadir, to indirectly enforce dynamic behavior. In contrast, our formulation explicitly models time-domain frequency response using second-order dynamics, enabling a more accurate and flexible representation of generator behavior. The resulting differential equations are approximated with high fidelity using Bernstein polynomials, leading to a mixed-integer linear programming (MILP) formulation that remains computationally tractable for small-scale power systems. Additionally, we introduce a new constraint based on the duration of frequency excursions below a critical threshold, motivated by practical concerns such as relay operation and equipment protection. A data-driven method is employed to relate the area under this threshold-computed as the integral of the Bernstein approximation-to the duration of frequency deviation. The proposed framework is validated using real-world data from an island system in Spain, demonstrating enhanced frequency security with a moderate increase in operational cost. These results suggest the method's strong potential for application in low-inertia, small-scale power systems.

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arXiv2025

A Corrective Frequency-Constrained Unit Commitment with Data-driven Estimation of Optimal UFLS in Island Power Systems

This paper presents a novel corrective \gls{fcuc} formulation for island power systems by implementing data-driven constraint learning to estimate the optimal \gls{ufls}. The Tobit model is presented to estimate the optimal amount of \gls{ufls} using the initial rate of change of frequency. The proposed formulation enables co-optimizing operation costs and \gls{ufls}. The aim is to account for optimal \gls{ufls} occurrences during operation planning, without increasing them. This would potentially reduce system operation costs by relaxing the reserve requirement constraint. The performance of the proposed formulation has been analyzed for a Spanish island power system through various simulations. Different daily demand profiles are analyzed to demonstrate the effectiveness of the proposed formulation. Additionally, a sensitivity analysis is conducted to demonstrate the effects of changing the cost associated with \gls{ufls}. The corrective \gls{fcuc} is shown to be capable of reducing system operation costs without jeopardizing the quality of the frequency response in terms of \gls{ufls} occurrence.

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arXiv2025

A Comparative Study on Frequency-Constrained Unit Commitment Approaches in Island Power Systems

The increasing penetration of renewable energy sources reduces rotating inertia and even frequency control capacity, affecting frequency stability. This challenge is significant in \gls{ips} that already suffer from low inertia and frequency control capacity. This paper presents a comparative study on different \gls{fcuc} formulations applied to \gls{ips}. Then, by considering under-frequency load shedding as a significant measure of frequency stability in \gls{ips}, two indices are presented to fully compare the formulations from system benefits and computational burden perspectives. Simulations conducted on a real Spanish island show that the data-driven corrective \gls{fcuc} formulation has the most advantages among other formulations.

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arXiv2024

Inclusion of Frequency Nadir constraint in the Unit Commitment Problem of Small Power Systems Using Machine Learning

As the intention is to reduce the amount of thermal generation and to increase the share of clean energy, power systems are increasingly becoming susceptible to frequency instability after outages due to reduced levels of inertia. To address this issue frequency constraints are being included in the scheduling process, which ensure a tolerable frequency deviation in case of any contingencies. In this paper, a method is proposed to integrate the non-linear frequency nadir constraint into the unit commitment problem, using machine learning. First a synthetic training dataset is generated. Then two of the available classic machine learning methods, namely logistic regression and support vector machine, are proposed to predict the frequency nadir. To be able to compare the machine learning methods to traditional frequency constrained unit commitment approaches, simulations on the power system of La Palma island are carried out for both proposed methods as well as an analytical linearized formulation of the frequency nadir. Our results show that the unit commitment problem with a machine learning based frequency nadir constraint is solved considerably faster than with the analytical formulation, while still achieving an acceptable frequency response quality after outages.

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arXiv2024

Impact of current limiters and fast voltage boosters in grid-forming VSC-based generators on transient stability

Transient stability is a complex phenomenon presented in multi-machine and multi-converter systems, and it is still considered a key limiting factor for stressed power systems. The increasing integration of non-synchronous generation further emphasises the need to address the challenges of improving the transient stability faced by these power systems. Several studies have focused on developing control strategies for GFM-VSCs to improve transient stability. These strategies include the use of current limiting algorithms and/or control of active/reactive power injections. This paper investigates the impact of fast voltage boosters (FVBs) and hybrid current limiters (HCLs) on transient stability of power systems with 100% grid-forming VSC-based generators. Short-circuit simulations and critical clearing time analysis are performed to evaluate the effectiveness of HCLs and FVBs in improving transient stability. The simulation results demonstrate the effectiveness of these approaches in avoiding the loss of synchronism. This research contributes to the current studies on transient stability in power systems and provides valuable insights into the potential of HCLs and FVBs as effective approaches to improve system stability.

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arXiv2024

Data-Driven Continuous-Time Framework for Frequency-Constrained Unit Commitment

The conventional approach to solving the unit commitment problem involves discrete intervals at an hourly scale, particularly when integrating frequency dynamics to formulate a frequency-constrained unit commitment. To overcome this limitation, a novel continuous-time frequency-constrained unit commitment framework is proposed in this paper. In this approach, Bernstein polynomials represent continuous variables in the unit commitment problem and enable the calculation of frequency response-related metrics such as the rate of change of frequency, quasi-steady-state frequency, and frequency nadir. Notably, startup and shut-down trajectories are meticulously considered, transforming the formulation into a fully continuous-time model and simplifying constraints related to variable continuity. To address the complexities associated with integrating the obtained non-linear frequency nadir constraint into a mixed-integer linear problem, an alternative data-driven frequency nadir constraint is proposed, which accurately constrains frequency nadir deviations throughout the time interval. To validate the proposed model, it is applied to the real-life network of the Spanish Island of La Palma. The results demonstrate the effectiveness of the proposed formulation, indicating that the model is solved timely while mitigating the impact of intra-hour real-time power fluctuations on system frequency.

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arXiv2024

Data-driven Estimation of Under Frequency Load Shedding after Outages in Small Power Systems

This paper presents a data-driven methodology for estimating Under Frequency Load Shedding (UFLS) in small power systems. UFLS plays a vital role in maintaining system stability by shedding load when the frequency drops below a specified threshold following loss of generation. Using a dynamic System Frequency Response (SFR) model we generate different values of UFLS (i.e., labels) predicated on a set of carefully selected operating conditions (i.e., features). Machine Learning (ML) algorithms are then applied to learn the relationship between chosen features and the UFLS labels. A novel regression tree and the Tobit model are suggested for this purpose and we show how the resulting non-linear model can be directly incorporated into a Mixed Integer Linear Programming (MILP) problem. The trained model can be used to estimate UFLS in security-constrained operational planning problems, improving frequency response, optimizing reserve allocation, and reducing costs. The methodology is applied to the La Palma island power system, demonstrating its accuracy and effectiveness. The results confirm that the amount of UFLS can be estimated with the Mean Absolute Error (MAE) as small as 0.213 MW for the whole process, with a model that is representable as a MILP for use in scheduling problems such as unit commitment among others.

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arXiv2024

Flexible Robust Optimal Bidding of Renewable Virtual Power Plants in Sequential Markets

In this paper, a novel approach to define the optimal bidding of renewable-only virtual power plants (RVPPs) in the day-ahead, secondary reserve, and intra-day markets is proposed. To this aim, a robust optimization algorithm is developed to account for the asymmetric nature of the uncertainties that characterize the market prices, as well as the energy production of the RVPP stochastic sources and flexible demand consumption. Simulation results show increased RVPP benefits compared to other existing solutions and demonstrate the potential of renewable sources to further increase their economic competitiveness. The simplicity of the implementation, the computational efficiency, and the flexible robustness are also verified.

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arXiv2023

Unit commitment with analytical underfrequency load-shedding constraints for island power systems

This letter presents a corrective frequency-constrained UC (C-FCUC) for island power systems implementing analytical constraints on underfrequency load shedding (UFLS). Since UFLS is inevitable for sufficiently large disturbances, one can argue that less spinning reserve could be held back since UFLS takes place anyway. Congruently, the reserve criterion should consider UFLS likely to occur under disturbances. The C-FCUC can be converted into a preventive frequency-constrained UC (P-FCUC) or the standard unit commitment (UC) and the C-FCUC is thus a generalization. The proposed formulation is successfully applied to a Spanish island power system.

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arXiv2022

Coordinated control in multi-terminal VSC-HVDC systems to improve transient stability: Impact on electromechanical-oscillation damping

Multi-terminal high-voltage Direct Current technology based on Voltage-Source Converter stations (VSC-MTDC) is expected to be one of the most important contributors to the future of electric power systems. In fact, among other features, it has already been shown how this technology can contribute to improve transient stability in power systems by the use of supplementary controllers. Along this line, this paper will investigate in detail how these supplementary controllers may affect electromechanical oscillations, by means of small-signal stability analysis. The paper analyses two control strategies based on the modulation of active-power injections (P-WAF) and reactive-power injections (Q-WAF) in the VSC stations. Both control strategies use global signals of the frequencies of the VSC-MTDC system and they presented significant improvements on transient stability. The paper will provide guidelines for the design of these type of controllers to improve both, large- and small-disturbance angle stability. Small-signal stability techniques (in Matlab) will be used to assess electromechanical-oscillation damping, while non-linear time domain simulation (in PSS/E) will be used to confirm the results. Results will be illustrated in Nordic32A test system with an embedded VSC-MTDC system. The paper analyses the impact of the controller gains and communication latency on electromechanical-oscillation damping. The main conclusion of the paper is that transient-stability-tailored supplementary controllers in VSC-MTDC systems can be tuned to damp inter-area oscillations too, maintaining their effectiveness for transient-stability improvement.

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arXiv2022

Robust Frequency Constrained UC Using Data Driven Logistic Regression for Island Power Systems

In the current practice of short-term power scheduling, online power reserves are used to address generation mismatches and contingencies. Neither online inertia nor the speed of the committed units is considered in the scheduling process. With the increasing injection of uncertain renewable energy sources, this practice is starting to fall short especially in island power systems, where the primary frequency response is already scarce, and any contingency leads to potentially poor frequency response. This paper introduces a data driven linear constraint to improve the post-fault frequency quality in island power systems. A coherent initial data-set is obtained by simulating the system frequency response of single outages. Then logistic regression is employed as a predictive analytic procedure to differentiate the acceptable and unacceptable incidents. To compare the conventional methods with the proposed approach and also to handle the uncertain nature of renewable energy generation, an adaptive robust unit commitment formulation is utilized. Results for the island power system of La Palma show that depending on the chosen cut-point on the logistic regression estimation the proposed method can improve the frequency response quality of the system while reducing the operation costs.

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arXiv2021

Optimal Participation of Heterogeneous, RES-based Virtual Power Plants in Energy Markets

In this work, we present a detailed model of a Renewable Energy Source (RES)-based Virtual Power Plant (VPP) that participates in Day-Ahead Market (DAM) and Intra-Day Market (IDM) with dispatchable and non-dispatchable RESs and flexible demand assets. We propose a demand model with bi-level flexibility which are associated with the market sessions plus an improved solar thermal plant model with piece-wise linear formulation of efficiency. A network-constrained unit commitment model is used by the VPP to submit DAM auctions and consequently participates in IDM to correct for deviations. Finally, we validate our model by assessing its operation on different weather conditions of uncertainty.

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