Previous studies regards that the grid-forming (GFM) converter switches from the constant voltage control (CVC) to the current limiting control (CLC) at the point of intersection of the unsaturated and saturated power-angle curves, which might not be held in most situations. This paper firstly derives the switching rule of GFM converter between two controls from the current limiting inequality. Accordingly, the conventional algebraic-variable switched model is transferred to the proposed state-variable switched model. Based on Lyapunov Theory, the stability of equilibrium points (EPs) is studied and the stable regions under two controls are further derived. In addition, one necessary stabilizing condition for the power synchronization loop based GFM (PSL-GFM) converter being locked in CLC is derived. As a result, one global stabilization on CVC is proposed by regulating the angle between the saturated current vector and d-axis . Finally, the maximum system boundary of the first swing can be obtained by placing stable equilibrium points (SEPs) under CLC on the right switching line.

Traditional permanent magnet synchronous generator (PMSG)‐based wind turbine (WT) normally utilises phase lock loop (PLL) for obtaining accurate phase angle of AC grid to make sure of maximum power point tracking (MPPT). However, a weak AC system with a low short circuit ratio (SCR) and high control bandwidth of PLL might have impaired effects on the stability of the system. To overcome these, a novel power synchronous control of PMSG‐based WT with grid forming ability of PMSG for integrating very weak AC system is first proposed in this study. Grid‐side converter (GSC) of PMSG emulates the inertia response of synchronous generator (SG) by artificially coupling the DC‐link voltage with the grid frequency based on the certain droop property, while the converter voltage magnitude is regulated according to DC‐link voltage deviation by controlling the modulation index of GSC. This novel scheme can realise the grid synchronisation without PLL by mimicking the natural characteristic of SG. Small‐signal analysis of the proposed scheme indicates the DC‐link capacitor energy can be exerted for system inertia support during system disturbances, while the system damping can be provided by spontaneously alternating converter voltage magnitude. More importantly, MPPT property of PMSG is not compromised while providing inertia and damping for the system, and the related inertia and damping coefficient of WT with the proposed control can be easily tuned for satisfying the system requirement. Non‐linear simulations of one PMSG connected with one large SG considering a sudden change of active power reference and variable wind speeds have been studied to verify the effectiveness of the proposed grid‐forming control.

Existing wind turbine (WT) control strategies realize damping support mainly by active power modulation, which may affect wind energy harvest. To improve energy efficiency and robustness, this article proposes a two-stage coordinated control of type-4 WT for damping support using the cost-effective WT resources, where the grid-forming control is applied. In the first stage, two reactive power-based dampers are designed using DC voltage synchronization control. The impacts of the dampers on stability are analytically evaluated. In this stage, the reactive power modulation, along with the partial DC capacitor energy, are jointly utilized for damping provision, while the WT is operated at maximum power point tracking (MPPT) mode. The second stage that seeks active power modulation is only activated when the DC voltage exceeds the threshold. An MPPT recovery process is further designed to eliminate the droop errors induced by the damper. The proposed scheme is validated under various contingencies compared with existing controls. Numerical results show it does not require a frequency estimator or the active power modulation for WT synchronization and grid-forming purposes; meanwhile is relatively energy-efficient and robust to provide strong damping support.

Multimodal sub-synchronous resonance (SSR) induced by the interactions between the generator shafts and the fixed series capacitors has become a serious threat for the power system. To overcome this, a voltage source converter (VSC) based controller for multimodal SSR suppression, named sub-synchronous resonance dynamic suppressor (SSRDS), is presented and analyzed in this paper. The controller is placed at the point of common coupling (PCC) of the power plant for multi-generator SSR suppression purpose so that the investment costs can be minimized while making sure the requirements of the SSR damping. To quantify the contribution of SSRDS to the SSR damping, the damping torque analysis is carried out, which can reveal the influences of the operating conditions and the correlated control parameters on the damping performance. Furthermore, to avoid the negative affects between the different TMs in close range as well as maximize the damping ability of SSRDS, the parameters tuning method of the mode filters and the gain and phase shifters are proposed. A detailed nonlinear simulation model is established in PSCAD/EMTDC based on the Jinjie series compensated transmission system located in China. The damping torque analysis, the eigenvalues analysis and the simulation results have fully demonstrated the effectiveness and the robustness of the proposed SSRDS for multi-generator and multimodal SSR suppression under both small and large disturbances in various operating conditions.

The instability issue of the grid-connected Voltage Source Converter (VSC) dominated by phase-lock loop (PLL) is investigated using the electrical torque method in this paper. The system dynamic model and steady-state relationship of variables are first established. Then, a basic two-order model representing the PLL natural oscillation mode is extracted. The impacts of the current control loop and altering current grid (ACG) on the PLL oscillation mode are derived using the electrical torque method. As a result, analytical expressions of the system synchronous and damping coefficients are obtained. Based on the derived synchronous and damping coefficient, qualitative evaluations of the impacts of the system parameters on the oscillation frequency and system stability can be achieved. It is drawn that a small PLL time constant, low infinite source voltage, heavy load, reactive power absorption, and long electrical distance will deteriorate system stability. Moreover, a sufficient analytical stability criterion for the grid-connected VSC is derived from the damping coefficient. The system stability can be directly evaluated through the operation points and system parameters, and the quantitative evaluation of the system stability is achieved. The eigenvalue analysis and electromagnetic transient simulation have verified the reliability and effectiveness of the theoretical analysis.

The loop impedance-based criterion (LIC) is a practical approach for studying the sub-synchronous oscillation (SSO) instability induced by converter-interfaced wind turbine generators (WTGs) via checking whether the resistance is positive or not. However, few existing works have discussed the background mathematical theory of such criterion. In this paper, a theoretical impedance solving method is raised based on a forced oscillation analysis method, which is efficient to obtain accurate impedance and can connects the state-space function, eigenvector and impedance inherently. Therefore, the applicability of LIC can be revealed in different stability regions from the viewpoint of the strict eigen-analysis based method (EBM). The general LIC stability criteria is then derived, and the conditions where LIC may cause misjudgment are discussed. Cases considering different operating scenarios are conducted to verify the proposed impedance calculation method and illustrate the connections and differences between LIC and EBM.