arXiv subjects

Verena Häberle

Publications and source records attributed to Verena Häberle.

At least 19 recordsLinked to original sources

arXiv2026

Quantifying Grid-Forming Behavior: Bridging Device-level Dynamics and System-Level Strength

Grid-forming (GFM) technology is widely regarded as a promising solution for future power systems dominated by power electronics. However, a universally accepted definition of GFM behavior and precise method for its quantification remain elusive. Moreover, the impact of GFM converter on system stability is not precisely quantified, creating a significant disconnect between device and system levels. To address these gaps from a small-signal perspective, at the device level, the paper introduces a novel metric, the Forming Index (FI) to quantify a converter's response to grid voltage fluctuations. Rather than enumerating various control architectures, the FI provides a metric for the converter's GFM ability by quantifying its sensitivity to grid variations. At the system level, a new quantitative measure of system strength that captures the multi-bus voltage stiffness is proposed, which quantifies the voltage and phase angle responses of multiple buses to current or power disturbances. The paper further extends and defines this concept to grid strength and bus strength to identify weak areas within the system. Finally, the device and system levels are bridged by formally proving that GFM converters enhance system strength. The proposed framework provides a unified benchmark for GFM converter design, optimal placement, and system stability assessment.

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arXiv2026

Mitigating Forced Oscillations in Power Systems via Data-Enabled Predictive Control

Sustained forced oscillations in power systems, driven by large cyclic loads such as data centers, pose a challenge to conventional power system stabilizers (PSSs), which rely on fixed tuned parameters and limited adaptability. This paper investigates the use of Data-Enabled Predictive Control (DeePC) as a data-driven alternative for damping such oscillations. DeePC constructs control actions directly from measured trajectories without requiring an explicit system model, enabling adaptation to changing operating conditions. We evaluate the performance of DeePC on a multi-machine two-area system subject to forced oscillations and compare it against a conventional PSS. The study examines the impact of different input-output configurations and the role of representative historical data in the Hankel matrix construction. Results show that DeePC can achieve superior damping. However, its effectiveness depends critically on the quality and representativeness of the underlying dataset. These findings highlight the potential of data-driven predictive control to complement or outperform conventional stabilizers in modern power systems with evolving and uncertain dynamics.

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arXiv2026

A Coalitional Stable and Fair Reward Allocation for Dynamic Virtual Power Plants

This paper establishes crucial cooperation criteria for the operation of Dynamic Virtual Power Plants (DVPPs). We propose a control design and reward allocation mechanism to enable and incentivize Distributed Energy Resources (DERs) to provide dynamic ancillary services (DAS). Our results illustrate how the cooperative aggregation of heterogeneous DERs leverages technical complementarities to outperform standalone DAS provision. The proposed reward allocation fulfills critical game-theoretic criteria, including individual rationality, coalitional stability, incentive compatibility, optimality, fairness and ex-post consistency. The control design and reward allocation are validated using a case study based on the Finnish power grid.

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arXiv2026

Decentralized Parametric Stability Certificates for Grid-Forming Converter Control

We propose a decentralized framework to analytically guarantee the small-signal stability of future power systems with grid-forming converters. Our approach leverages dynamic loop-shifting techniques to compensate for the lack of passivity in the network dynamics and establishes decentralized parametric stability certificates, depending on the local device-level controls and incorporating the effects of the network. By following practical tuning rules, we are able to ensure plug-and-play operation without centralized coordination. Unlike prior works, our approach accommodates coupled frequency and voltage dynamics, incorporates network dynamics, and does not rely on specific network configurations or operating points, offering a general and scalable solution for the integration of power-electronics-based devices into future power systems. We validate our theoretical stability results through numerical case studies in a high-fidelity simulation model.

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arXiv2026

Quantifying Grid-Forming Behavior: Bridging Device-Level Dynamics and System-Level Strength

Grid-forming (GFM) technology is widely regarded as a promising solution for future power systems dominated by power electronics. However, a precise method for quantifying GFM converter behavior and a universally accepted GFM definition remain elusive. Moreover, the impact of GFM on system stability is not precisely quantified, creating a significant disconnect between device and system levels. To address these gaps from a small-signal perspective, at the device level, we introduce a novel metric, the Forming Index (FI) to quantify a converter's response to grid voltage fluctuations. Rather than enumerating various control architectures, the FI provides a metric for the converter's GFM ability by quantifying its sensitivity to grid variations. At the system level, we propose a new quantitative measure of system strength that captures the multi-bus voltage stiffness, which quantifies the voltage and phase angle responses of multiple buses to current or power disturbances. We further extend and define this concept to grid strength and bus strength to identify weak areas within the system. Finally, we bridge the device and system levels by formally proving that GFM converters enhance system strength. Our proposed framework provides a unified benchmark for GFM converter design, optimal placement, and system stability assessment.

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arXiv2026

Next-Generation Grid Codes: Towards a New Paradigm for Dynamic Ancillary Services

This paper introduces a conceptual foundation for Next Generation Grid Codes (NGGCs) based on stability and performance certificates, enabling the provision of dynamic ancillary services such as fast frequency and voltage regulation through decentralized frequency-domain criteria. The NGGC framework offers two key benefits: (i) rigorous closed-loop stability guarantees, and (ii) explicit performance guarantees for frequency and voltage dynamics in power systems. Regarding (i) stability, we employ loop-shifting and passivity-based techniques to derive local frequency-domain stability certificates for individual device dynamics. These certificates ensure the closed-loop stability of the entire interconnected power system through fully decentralized verification. Concerning (ii) performance, we establish quantitative bounds on critical time-domain indicators of system dynamics, including the average-mode frequency and voltage nadirs, the rate-of-change-of-frequency (RoCoF), steady-state deviations, and oscillation damping capabilities. The bounds are obtained by expressing the performance metrics as frequency-domain conditions on local device behavior. The NGGC framework is non-parametric, model-agnostic, and accommodates arbitrary device dynamics under mild assumptions. It thus provides a unified, decentralized approach to certifying both stability and performance without requiring explicit device-model parameterizations. Moreover, the NGGC framework can be directly used as a set of specifications for control design, offering a principled foundation for future stability- and performance-oriented grid codes in power systems.

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arXiv2025

Dispatchable Current Source Virtual Oscillator Control Achieving Global Stability

This work introduces a novel dispatchable current source virtual oscillator control (dCVOC) scheme for grid-following (GFL) converters, which exhibits duality with dispatchable virtual oscillator control (dVOC) in two ways: a) the current frequency is generated through reactive power control, similar to a PLL ; b) the current magnitude reference is generated through active power control. We formally prove that our proposed control always admits a steady-state equilibrium and ensures global stability under reasonable conditions on grid and converter parameters, even when considering LVRT and current saturation constraints. Our approach avoids low-voltage transients and weak grid instability, which is not the case for conventional GFL control. The effectiveness of our proposed control is verified through high-fidelity electromagnetic transient simulations.

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arXiv2025

Ultrafast Grid Impedance Identification in $dq$-Asymmetric Three-Phase Power Systems

We propose a non-parametric frequency-domain method to identify small-signal $dq$-asymmetric grid impedances, over a wide frequency band, using grid-connected converters. Existing identification methods are faced with significant trade-offs: e.g., passive approaches rely on ambient harmonics and rare grid events and thus can only provide estimates at a few frequencies, while many active approaches that intentionally perturb grid operation require long time series measurement and specialized equipment. Although active time-domain methods reduce the measurement time, they either make crude simplifying assumptions or require laborious model order tuning. Our approach effectively addresses these challenges: it does not require specialized excitation signals or hardware and achieves ultrafast ($<1$ s) identification, drastically reducing measurement time. Being non-parametric, our approach also makes no assumptions on the grid structure. A detailed electromagnetic transient simulation is used to validate the method and demonstrate its clear superiority over existing alternatives.

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arXiv2024

Grid-Forming Control of Modular Dynamic Virtual Power Plants

This article explores a flexible and coordinated control design for an aggregation of heterogeneous distributed energy resources (DERs) in a dynamic virtual power plant (DVPP). The control design aims to provide a desired aggregate grid-forming (GFM) response based on the coordination of power contributions between different DERs. Compared to existing DVPP designs with an AC-coupled AC-output configuration, a more generic modular DVPP design is proposed in this article, which comprises four types of basic DVPP modules, involving AC- or DC-coupling and AC- or DC-output, adequately accommodating diverse DER integration setups, such as AC, DC, AC/DC hybrid microgrids and renewable power plants. The control design is first developed for the four basic modules by the aggregation of DERs and the disaggregation of the control objectives, and then extended to modular DVPPs through a systematic top-down approach. The control performance is comprehensively validated through simulation. The modular DVPP design offers scalable and standardizable advanced grid interfaces (AGIs) for building and operating AC/DC hybrid power grids.

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arXiv2024

Dynamic Ancillary Services: From Grid Codes to Transfer Function-Based Converter Control

Conventional grid-code specifications for dynamic ancillary services provision such as fast frequency and voltage regulation are typically defined by means of piece-wise linear step-response capability curves in the time domain. However, although the specification of such time-domain curves is straightforward, their practical implementation in a converter-based generation system is not immediate, and no customary methods have been developed yet. In this paper, we thus propose a systematic approach for the practical implementation of piece-wise linear time-domain curves to provide dynamic ancillary services by converter-based generation systems, while ensuring grid-code and device-level requirements to be reliably satisfied. Namely, we translate the piece-wise linear time-domain curves for active and reactive power provision in response to a frequency and voltage step change into a desired rational parametric transfer function in the frequency domain, which defines a dynamic response behavior to be realized by the converter. The obtained transfer function can be easily implemented e.g. via a PI-based matching control in the power loop of standard converter control architectures. We demonstrate the performance of our method in numerical grid-code compliance tests, and reveal its superiority over classical droop and virtual inertia schemes which may not satisfy the grid codes due to their structural limitations.

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arXiv2024

Optimal Dynamic Ancillary Services Provision Based on Local Power Grid Perception

In this paper, we propose a systematic closed-loop approach to provide optimal dynamic ancillary services with converter-interfaced generation systems based on local power grid perception. In particular, we structurally encode dynamic ancillary services such as fast frequency and voltage regulation in the form of a parametric transfer function matrix, which includes several parameters to define a set of different feasible response behaviors, among which we aim to find the optimal one to be realized by the converter system. Our approach is based on a so-called "perceive-and-optimize" (P&O) strategy: First, we identify a grid dynamic equivalent at the interconnection terminals of the converter system. Second, we consider the closed-loop interconnection of the identified grid equivalent and the parametric transfer function matrix, which we optimize for the set of transfer function parameters, resulting in a stable and optimal closed-loop performance for ancillary services provision. In the process, we ensure that grid-code and device-level requirements are satisfied. Finally, we demonstrate the effectiveness of our approach in different numerical case studies based on a modified Kundur two-area test system.

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arXiv2024

Dynamic Complex-Frequency Control of Grid-Forming Converters

Complex droop control, alternatively known as dispatchable virtual oscillator control (dVOC), stands out for its unique capabilities in synchronization and voltage stabilization among existing control strategies for grid-forming converters. Complex droop control leverages the novel concept of ``complex frequency'', thereby establishing a coupled connection between active and reactive power inputs and frequency and rate-of-change-of voltage outputs. However, its reliance on static droop gains limits its ability to exhibit crucial dynamic response behaviors required in future power systems. To address this limitation, this paper introduces dynamic complex-frequency control, upgrading static droop gains with dynamic transfer functions to enhance the richness and flexibility in dynamic responses for frequency and voltage control. Unlike existing approaches, the complex-frequency control framework treats frequency and voltage dynamics collectively, ensuring small-signal stability for frequency synchronization and voltage stabilization simultaneously. The control framework is validated through detailed numerical case studies on the IEEE nine-bus system, also showcasing its applicability in multi-converter setups.

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arXiv2024

Complex-Frequency Synchronization of Converter-Based Power Systems

In this paper, we study phase-amplitude multivariable dynamics in converter-based power systems from a complex-frequency perspective. Complex frequency represents the rate of change of voltage amplitude and phase angle by its real and imaginary parts, respectively. This emerging notion is of significance as it accommodates the multivariable characteristics of power networks where active and reactive power are inherently coupled with both voltage amplitude and phase. We propose the notion of complex-frequency synchronization to study the phase-amplitude multivariable stability issue in a power system with dispatchable virtual oscillator-controlled (dVOC) converters. To achieve this, we separate the system into linear fast dynamics and approximately linear slow dynamics. The linearity property makes it tractable to analyze fast complex-frequency synchronization and slower voltage stabilization. From the perspective of complex frequency and complex-frequency synchronization, we provide novel insights into the equivalence of dVOC and complex-power-frequency droop control, stability analysis methods, and stability criteria. Our study offers a practical solution to address challenging stability issues in converter-based power systems.

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arXiv2024

Quantitative Stability Conditions for Grid-Forming Converters With Complex Droop Control

In this paper, we analytically study the transient stability of grid-connected converters with grid-forming complex droop control, also known as dispatchable virtual oscillator control. We prove theoretically that complex droop control, as a state-of-the-art grid-forming control, always possesses steady-state equilibria whereas classical droop control does not. We provide quantitative conditions for complex droop control maintaining transient stability (global asymptotic stability) under grid disturbances, which is beyond the well-established local (non-global) stability for classical droop control. For the transient instability of complex droop control, we reveal that the unstable trajectories are bounded, manifesting as limit cycle oscillations. Moreover, we extend our stability results from second-order grid-forming control dynamics to full-order system dynamics that additionally encompass both circuit electromagnetic transients and inner-loop dynamics. Our theoretical results contribute an insightful understanding of the transient stability and instability of complex droop control and offer practical guidelines for parameter tuning and stability guarantees.

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arXiv2023

Grid-Forming and Spatially Distributed Control Design of Dynamic Virtual Power Plants

We present a novel grid-forming control design approach for dynamic virtual power plants (DVPP). We consider a group of heterogeneous grid-forming distributed energy resources (DER) which collectively provide desired dynamic ancillary services, such as fast frequency and voltage control. To achieve that, we study the nontrivial aggregation of grid-forming DERs to establish the DVPP, and employ an adaptive divide-and-conquer strategy that disaggregates the desired control specifications of the aggregate DVPP via adaptive dynamic participation factors to obtain local desired behaviors of each DER. We then design local controllers at the DER level to realize these local desired behaviors. In the process, physical and engineered limits of each DER are taken into account. We extend the proposed approach to make it also compatible with grid-following DER controls, thereby establishing the concept of so-called hybrid DVPPs. Furthermore, we generalize the DVPP design to spatially dispersed DER locations in power grids with different voltage levels and R/X ratios. Finally, the DVPP control performance is verified via numerical case studies in the IEEE nine-bus transmission grid with an interconnected medium voltage distribution grid.

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arXiv2023

MIMO Grid Impedance Identification of Three-Phase Power Systems: Parametric vs. Nonparametric Approaches

A fast and accurate grid impedance measurement of three-phase power systems is crucial for online assessment of power system stability and adaptive control of grid-connected converters. Existing grid impedance measurement approaches typically rely on pointwise sinusoidal injections or sequential wideband perturbations to identify a nonparametric grid impedance curve via fast Fourier computations in the frequency domain. This is not only time-consuming, but also inaccurate during time-varying grid conditions, while on top of that, the identified nonparametric model cannot be immediately used for stability analysis or control design. To tackle these problems, we propose to use parametric system identification techniques (e.g., prediction error or subspace methods) to obtain a parametric impedance model directly from time-domain current and voltage data. Our approach relies on injecting wideband excitation signals in the converter's controller and allows to accurately identify the grid impedance in closed loop within one injection and measurement cycle. Even though the underlying parametric system identification techniques are well-studied in general, their utilization in a grid impedance identification setup poses specific challenges, is vastly underexplored, and has not gained adequate attention in urgent and timely power systems applications. To this end, we demonstrate in numerical experiments how the proposed parametric approach can accomplish a significant improvement compared to prevalent nonparametric methods.

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arXiv2023

Control Design of Dynamic Virtual Power Plants: An Adaptive Divide-and-Conquer Approach

In this paper, we present a novel control approach for dynamic virtual power plants (DVPPs). In particular, we consider a group of heterogeneous distributed energy resources (DERs) which collectively provide desired dynamic ancillary services such as fast frequency and voltage control. Our control approach relies on an adaptive divide-and-conquer strategy: first, we disaggregate the desired frequency and voltage control specifications of the aggregate DVPP via adaptive dynamic participation matrices (ADPMs) to obtain the desired local behavior for each device. Second, we design local linear parameter-varying (LPV) $\mathcal{H}_\infty$ controllers to optimally match this local behaviors. In the process, the control design also incorporates the physical and engineered limits of each DVPP device. Furthermore, our adaptive control design can properly respond to fluctuating device capacities, and thus include weather-driven DERs into the DVPP setup. Finally, we demonstrate the effectiveness of our control strategy in a case study based on the IEEE nine-bus system.

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arXiv2023

Experimental Validation of a Dynamic Virtual Power Plant Concept Based on Multiple-Converter Power Hardware-In-the-Loop Test Bench

Recently, the concept of dynamic virtual power plants (DVPP) has been proposed to collectively provide desired dynamic ancillary services such as fast frequency and voltage control by a heterogeneous ensemble of distributed energy resources (DER). This paper presents an experimental validation of a recent DVPP control design approach on a multi-converter power hardware-in-the-loop (PHIL) test bed system. More specifically, we consider a DVPP composed of a wind generation system, a photovoltaic (PV) system, and a STATCOM with small storage capacity to collectively provide grid-following fast frequency regulation in the presence of grid-frequency and load variations. The performance of the aggregated DVPP response is evaluated with respect to its ability to match a desired dynamic behavior while taking practical limitations of the individual DVPP units into account.

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