Modeling and Stability Analysis of Converter-Dominated Grids with Dynamic Loads

Pole–zero placement based feed-forward damping control for virtual synchronous generators in power systems with inverter-based resources

An enhanced second-order-consensus-based distributed secondary frequency controller of virtual synchronous generators for isolated AC microgrids

Virtual synchronous generator (VSG) is the concept of controlling the grid-connected inverters to mimic conventional synchronous generators (SGs), and it is considered to be a promising method to enhance the grid inertia and power regulation ability when the renewable energy has a high penetration rate in the grid. In this paper, the power frequency characteristic and the synchronization mechanism of the VSG are analyzed in detail, and a modified pre-synchronization method is proposed. Compared to the existing methods, the proposed method in this paper regulates the VSG frequency by resetting its active power reference according to the local load and eliminates the phase deviation by feedback control of the virtual power, thus the phase angle of the VSG in standalone mode is in accordance with the steady operation point in grid-connected mode and the dynamic power adjustment can be avoided when the VSG connect to the grid. A 30kV A VSG prototype was developed and tested in the laboratory, and the effectiveness of the proposed method is verified with the simulation results based on Matlab/Simulink results based on the VSG prototype.

Traditional microgrid lacks rotational inertia and it needs to operate in the economic state. A dynamic power optimization strategy is proposed for microgrid based on the virtual synchronous generator's frequency regulation characteristics in this paper. Load in microgrid is divided into planned load and unplanned load. The optimization model with the goals of minimizing the generation operation cost and the transmission power of the linking-up road is established to distribute the planned load. The genetic algorithm-simulated annealing algorithm is used to solve the optimization model. Active power generation plans for the VSGs are formulated in the light of calculation results. Central controller estimates the power fluctuation value when unplanned load fluctuations occur in the microgrid. VSG's output power is dynamically adjusted based on the principle of equal marginal cost to achieve dynamic power optimization of microgrid. The effectiveness of the proposed control strategy is verified by simulation.

Designing a central MIMO state feedback controller for a microgrid with multi-parallel VSGs to damp active power oscillations

The cascaded hybrid LCC-MMC inverter is considered as a feasible option to mitigate the commutation failure problem of conventional LCC-HVDC while maintaining bulk power transmission capability. However, the coupling between different types of converters may result in instability when the inverter integrates with weak AC systems. This paper establishes a small-signal model of the cascaded LCC-MMC inverter based hybrid HVDC system and validates the model against PSCAD/EMTDC. Through eigenvalue analysis, the impact of the strength and proximity of receiving AC systems on the small-signal stability is investigated, and the stable zone of the strength of receiving AC systems is identified. Besides, a supplementary coupling mitigation control is proposed to tackle the instability problem under weak AC systems integration. Both analytical results and time-domain simulations demonstrate the validity of the supplementary control.

A hardware testbed platform emulating multiple-area power system scenario dynamics has been established aiming at multiple time-scale real-time emulations. In order to mimic real power flow situations in the utility system, the load emulators have to behave like real ones in both their static and dynamic characteristics. A constant-impedance, constant-current, and constant-power (ZIP) model has been used for static load types, while a three-phase induction motor model has been built to represent dynamic load types. In this paper, ways of modeling ZIP and induction motor loads and the performance of each load emulator are discussed. Comparisons between simulation and experimental results are shown as well for the validation of the emulator behaviors. A real-time composite power load emulator is then demonstrated with desired characteristics and detailed transients for representing a power system PQ bus dynamics.

• The paper focuses on optimising Virtual Synchronous Generator (VSG) control in Modular Multilevel Converter (MMC)-based HVDC systems to enhance power system stability and oscillation damping. • It introduces virtual inertia and damping to mimic synchronous generator behaviour, improving frequency and voltage regulation. • The proposed control strategy ensures smooth transitions between grid-connected and islanded modes, suppresses harmonics, and addresses challenges like low inertia and weak grid conditions. • Simulation results validate the effectiveness of the VSG-controlled MMC in maintaining stability during dynamic and transient events, making it suitable for future power systems with high renewable energy integration. This paper discusses the development of a Virtual Synchronous Generator utilizing a Modular Multilevel Converter. The control system employs an internal simulation of the electromechanical swing equation to replicate the inertia and damping characteristics of a synchronous generator, enabling the generation of the necessary frequency and phase angle for MMC control as a VSG. The ac-side management involves cascaded voltage and current controllers operating within a synchronous reference frame defined by the virtual swing equation. Simulation findings validate the performance of the VSG-controlled MMC when connected to an external AC grid and in islanded mode with a resistive load. This paper validates, through experimentation, the effectiveness of controlling a Modular Multilevel Converter (MMC) as a Virtual Synchronous Generator (VSG) designed to deliver virtual inertia and robust frequency stabilization in power systems with low physical inertia. The proposed control structure incorporates a virtual swing equation, cascaded voltage and current regulation loops, reactive power control, and emulated impedance. A 60 kVA MMC model was employed to demonstrate the system’s capabilities. During frequency disturbances such as a drop from 50 Hz to 49.8 Hz, the controller facilitated dynamic power injection up to approximately 35 kW while capping peak currents at 100 A. Frequency deviations were mitigated within 300 milliseconds, and the converter exhibited seamless transitions to islanded operation along with reliable voltage control during load variations. These findings confirm the proposed controller’s effectiveness in maintaining grid stability under diverse operating conditions.

This paper deals with the control of current phase advancing in single-leg voltage source inverters (VSI) and matrix converters with a two-phase output. The phase shift of the current in the auxiliary phase is set with the use of switched capacitors. Two distinctive control methods are used for the current phase advancing, open-loop control and closed-loop control. In addition, a new averaging method is derived for the calculation of the switched capacitance used in the open-loop control. The practical use of the designed control methods with the switched capacitor is shown in simulations and experimental verifications on a single-leg matrix converter with a passive and active load (induction motor).

The increasing penetration of inverter-based renewable energy sources has fundamentally altered the dynamic behavior of modern power systems by displacing conventional synchronous generation. Reduced system inertia, higher rates of change of frequency, modified fault responses, and complex voltage regulation have emerged as critical stability challenges in low-inertia grids. This paper presents a comprehensive study of power system stability under high renewable energy penetration through a structured literature review, a unified methodological framework, and a realistic transmission-level case study. The proposed framework integrates grid characterization, component and control modeling, multi-domain stability assessment, contingency analysis, and coordinated mitigation strategies using both phasor-domain and electromagnetic transient simulations. A three-zone network with varying levels of renewable integration is analyzed to quantify impacts on frequency, voltage, and small-signal stability following severe contingencies. Results demonstrate that stability degradation increases nonlinearly with renewable share in baseline grid-following configurations. The deployment of grid-forming inverter controls, synthetic inertia, and fast frequency response from battery energy storage significantly improves system performance by reducing RoCoF, restoring frequency nadir, and enhancing voltage recovery. Eigenvalue analysis further confirms improved damping of critical interaction modes. The findings highlight the necessity of hybrid control architectures and coordinated mitigation strategies to ensure reliable operation of future power systems with high renewable penetration.

روستای هاونان در 15کیلومتری جنوب غرب بیرجند و در دامنه شمالی رشته‌کوه باقران واقع شده و تاریخ اولین حرکت اصلی لغزش در منطقه در سال 1364 و تاریخ آخرین حرکت اصلی در سال 1385 است. در این مقاله پهنه‌بندی حساسیت به لغزش و تحلیل پارامترهای فیزیکی- هیدرولوژیکی و تکتونیکی به‌منظور شناسایی بیشتر وضعیت شکل‌گیری توده‌های لغزشی منطقه و تحلیل پایداری دامنه‌ها به کمک مدل فرآیندی SINMAP انجام‌شده است. این مدل نشان می‌دهد بخش اندکی از پهنه لغزشی هاونان در محدوده رطوبتی اشباع قرار می‌گیرد و کمتر از 30 درصد آن دارای حساسیت متوسط تا بالا به لغزش است؛ لذا بایستی در این محدوده به دنبال علل خارجی تأثیرگذار در پدیداری لغزش بود. محدوده هاونان متأثر از سه سری گسل اصلی با روندهای مختلف می‌باشد و در اثر تقاطع این سه سری گسل، واحدهای سنگی (اسپیلیت ها، پریدوتیت ها و گابروها) به‌صورت بلوک‌های گسلی کشیده درآمده و در اثر ادامه فرآیند برش، این بلوک‌ها متحمل تغییر شکل، جابجایی و چرخش شده‌اند. ترکیب سنگ‌شناسی (قرارگیری اسپیلیت بر روی سرپانتینیت) و وجود دو سری شکستگی به‌موازات گسل‌های هاونان و مزار مهم‌ترین عوامل ناپایداری هستند. علاوه بر این برخاستگی رشته‌کوه باقران باعث افزایش تدریجی نشیب دامنه و رخداد زمین‌لرزه‌ای ادواری نیز موجب تشدید لغزش می‌گردد.

In an islanded microgrid supplied by virtual synchronous generator (VSG) based inverter-based resources (IBRs), inter-IBR oscillations pose a serious threat to frequency stability and power-sharing accuracy. While VSG control enables gridforming inverters (GFMs) to emulate inertia and improve frequency dynamics, it also introduces poorly damped modes. This paper proposes a distributed cooperative control strategy that enhances damping of inter-IBR oscillations without compromising key frequency performance metrics such as the rate of change of frequency (RoCoF) and frequency nadir. The proposed control introduces a dynamic state variable that adjusts the auxiliary frequency reference in real-time based on both local frequency error and a distributed feedback term derived from the mismatch in normalized active power among neighboring inverters, thereby enhancing damping and actively suppressing inter-IBR oscillations. In addition, the control incorporates normalized active power mismatch to achieve proportional load sharing, implemented using a sparse communication topology among neighboring IBRs. An eigenvalue analysis based on small-signal model is conducted for appropriate selection of control gains to achieve system stability. Simulation results under various IBR configurations demonstrate that the proposed control method effectively suppresses inter-IBR oscillations, ensures proportional power sharing, and achieves robustness. Accordingly, the applicability of the proposed control design is validated for both homogeneous and heterogeneous VSG systems.

This paper develops the impedance models of grid-connected converters under the virtual synchronous generator (VSG) strategy with a cascaded inner control loop and analyzes the system stability of VSG controlled converters with different kinds of weak grid. Different from existing small-signal models with high dimensions, a single-in-single-out (SISO) impedance model with simple mathematical expression is obtained in this paper, which is applied to identify the influence of the cascaded control loop on impedance characteristics and system stability. It is found that the impedance characteristics of VSG controlled converters can become capacitive below the fundamental frequency, and it is mainly caused by the voltage controller in the cascaded control loop of the VSG strategy. Impedance-based stability analysis shows that the capacitive impedance characteristics can benefit the compatibility of converters operated with the series-compensated weak grid, but may deteriorate the system stability with the inductive weak grid, which can be avoided by increasing the proportional coefficients of the cascaded voltage and current controllers or applying a larger virtual resistor to reduce the negative resistance in the capacitive frequency range. Experiments based on the control-hardware-in-loop (CHIL) platform were carried out to verify the developed analytical models and possible system instable cases.

In the context of high proportion of new energy integration and high proportion of power electronic equipment application, due to the grid connection of new energy generation through inverters with different control characteristics, the power system exhibits a regulatory form with the coexistence of grid-following (GFL) and grid-forming (GFM), thus forming a heterogeneous inverter paralleled system (HIPS). Its multi-time scale characteristics and complex interactions pose severe challenges to the stability of the power system. To address this issue, this paper first constructs a complete linear time-periodic (LTP) model of HIPS, and then analyzes the influence of key stabilizing factors on system stability. It provides a theoretical basis for suppressing oscillations, optimizing control parameters, and ensuring the reliable operation of different types of inverters in the power grid.

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