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The paper introduces the concept of complex frequency. The imaginary part of the complex frequency is the variation with respect of a synchronous reference of the local bus frequency as commonly defined in power system studies. The real…

Systems and Control · Electrical Eng. & Systems 2026-03-24 Federico Milano

This paper proposes a taxonomy of power converter control schemes based on the recently proposed concept of complex frequency. This quantity captures local frequency variations due to the change of both the phase angle and amplitude of bus…

Systems and Control · Electrical Eng. & Systems 2023-04-18 Dionysios Moutevelis , Javier Roldan-Perez , Milan Prodanovic , Federico Milano

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…

Systems and Control · Electrical Eng. & Systems 2024-07-03 Xiuqiang He , Verena Häberle , Florian Dörfler

The increasing penetration of renewable energy leads to a continuous reduction in system inertia, for which conventional synchronization criteria based solely on frequency consistency can no longer accurately capture the coupled dynamics of…

Systems and Control · Electrical Eng. & Systems 2025-11-24 Yusen Wei , Lan Tang , Peidong Li

This paper proposes a novel control for Inverter-based Resources (IBRs) based on the Complex Frequency (CF) concept. The controller's objective is to maintain a constant CF of the voltage at the terminals of the IBR by adjusting its current…

Systems and Control · Electrical Eng. & Systems 2025-01-06 R. Bernal , F. Milano

In this article, we investigate small-signal frequency and DC voltage stability of hybrid AC/DC power systems that combine AC and DC transmission, conventional machine- based generation, and converter-interfaced generation. The main…

Systems and Control · Electrical Eng. & Systems 2025-09-26 Dahlia Saba , Dominic Groß

This paper analyzes how power injections affect frequency quality in power systems. We first derive a general expression linking active and reactive power injections at buses to the system's frequency. This formulation explicitly considers…

Systems and Control · Electrical Eng. & Systems 2025-05-20 Angel Vaca , Federico Milano

As the concern about climate change and energy shortage grow stronger, the incorporation of renewable energy in the power system in the future is foreseeable. In a hybrid power system with a large penetration of PV generation, PV panel is…

Systems and Control · Electrical Eng. & Systems 2021-08-10 Songyao Jiang , Takeyoshi Kato

Advantages of operating portions of a power system at frequencies different from the standard 50 or 60 Hz have been demonstrated in the low frequency AC (LFAC) and high voltage DC (HVDC) literature. Branches constrained by stability or…

Systems and Control · Electrical Eng. & Systems 2021-01-28 David Sehloff , Line Roald

The increasing integration of renewable energy sources has introduced complex dynamic behavior in power systems that challenge the adequacy of traditional continuous-time modeling approaches. These developments call for modeling frameworks…

Systems and Control · Electrical Eng. & Systems 2026-01-19 B. G. Odunlami , M. Netto , Y. Susuki

One of the fundamental concerns in the operation of modern power systems is the assessment of their frequency stability in case of inertia-reduction induced by the large share of power electronic interfaced resources. Within this context,…

Systems and Control · Electrical Eng. & Systems 2022-01-03 Francesco Conte , Stefano Massucco , Mario Paolone , Giacomo-Piero Schiapparelli , Federico Silvestro , Yihui Zuo

Low-order frequency response models for power systems have a decades-long history in optimization and control problems such as unit commitment, economic dispatch, and wide-area control. With a few exceptions, these models are built upon the…

Systems and Control · Electrical Eng. & Systems 2025-11-10 Marena Trujillo , Amir Sajadi , Bri-Mathias Hodge

Power system coherency refers to the phenomenon that machines in a power network exhibit similar frequency responses after disturbances, and is foundational for model reduction and control design. Despite abundant empirical observations,…

Systems and Control · Electrical Eng. & Systems 2025-11-11 Yixuan Liu , Yingzhu Liu , Pengcheng You

Due to the energy transition, today's electrical networks include synchronous machines and inverter-based resources interfacing renewable energies such as wind turbines, solar panels, and Battery Energy Storage Systems to the grid. In such…

Systems and Control · Electrical Eng. & Systems 2024-02-08 Pamela Zoghby , Bogdan Marinescu , Antoine Rosse , Gregoire Prime

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.…

Systems and Control · Electrical Eng. & Systems 2024-08-23 Roger Domingo-Enrich , Xiuqiang He , Verena Häberle , Florian Dörfler

This paper proposes a generic and unified model of the power flow (PF) problem for multiterminal hybrid AC/DC networks. The proposed model is an extension of the standard AC-PF. The DC network is treated as an AC one and, in addition to the…

Systems and Control · Electrical Eng. & Systems 2023-10-02 Willem Lambrichts , Mario Paolone

In this paper, we extend a circuit-based, current-voltage power flow formulation to include frequency deviations and implicitly model generator primary and secondary control actions as a function of their temporal dependence. This includes…

Systems and Control · Electrical Eng. & Systems 2019-09-02 Aayushya Agarwal , Amritanshu Pandey , Marko Jereminov , Larry Pileggi

This paper shows that the concept of complex frequency, originally introduced to characterize the dynamics of signals with complex values, constitutes a generalization of eigenvalues when applied to the states of linear time-invariant (LTI)…

Systems and Control · Electrical Eng. & Systems 2026-05-22 Nikolas Sofos , Federico Milano

This letter proposes a simple and inexpensive technique to improve the frequency control of distributed energy resources. The proposed control consists in modifying the conventional estimated bus frequency signal with an additional feedback…

Systems and Control · Electrical Eng. & Systems 2023-09-01 Federico Milano , Bibi Alhanjari , Georgios Tzounas

This paper proposes an electronic circuit simulator-based method to accelerate the power system transient simulation, where the modeling of a generic HVDC (High Voltage Direct Current) system is focused. The electronic circuit simulation…

Systems and Control · Electrical Eng. & Systems 2023-05-17 Yongli Zhu , Xiang Zhang , Renchang Dai
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