This paper proposes an Elastic Energy Equivalent System (EEES) for analyzing the sub-synchronous control interaction (SSCI) in the power system integrated with power electronic converters. The EEES can analyze the energy interaction between the series compensation and the converters' controller, and quantitatively assess the impact on SSCI induced by the converters' controller from the view of elastic energy. First, inspired by the vibration process of a spring-damper system, we establish the EEES to imitate the electromagnetic oscillation, so as to explore the SSCI phenomenon in power systems by analyzing the energy composition of EEES. Then, an equivalent damper of EEES is used to model the controllable dissipated energy of the converters' controller, so a criterion can be developed to evaluate the damping effect for stabilizing the system. Finally, the effectiveness of the proposed EEES is validated on a power system integrated with the doubly-fed induction generator controlled by the virtual synchronous generator. The results demonstrate that the virtual synchronous generator can provide positive damping to the SSCI under specific sub-synchronous frequencies. However, this positive damping is limited due to the noticeable negative damping effect on SSCI induced by the rotor-side converter controller.

Doubly fed induction generator (DFIG) may suffer from huge disturbance owing to the uncertainty of generator parameters and load fluctuation during operation process. Hence, in the context of virtual synchronous generator (VSG) technology and its power-frequency control characteristics, this paper presents a VSG-based nonlinear adaptive robust controller (NARC), aiming to enhance the comprehensive regulation performance of DFIG. Firstly, a nonlinear robust adaptive controller with disturbance rejection and uncertainty adaptive learning ability is designed by establishing an improved dynamic model of the rotor motion equation in VSG, so as to achieve the optimal regulation of DFIG with robustness and adaptability. Secondly, in order to realize the fast dynamic response and autonomous synchronization ability in DFIG, a modified control strategy of the grid side converter (GSC) in DFIG is constructed by voltage and current dual-loop control (DLC) and VSG, which not only retains the significant dynamic response ability of the current inner-loop in DLC, but also improves the inertia and damping of the system. Finally, simulation results indicate that the modified control strategy exhibits satisfied dynamic performance and reliability, and reveals the robustness and adaptability of the control strategy in response to external random interferences and internal uncertain parameters.

This paper proposes a dynamic-tracking damping controller (DTDC) and designs an implementation scheme to alleviate the sub-synchronous control interactions (SSCI) in series-compensated networks integrated with doubly-fed induction generator (DFIG)-based wind farms. The DTDC can track sub-synchronous oscillatory current components under various operating conditions, providing high damping performance for DFIG wind turbines at a broader range of sub-synchronous frequencies. This is accomplished by designing an extra extended state observer (ESO)-based compensated loop for the rotor-side converter of DFIG, which enables the extraction and compensation of oscillatory current components at the sub-synchronous frequencies. In addition, the implementation scheme for the damping controller is designed based on the dissipated energy criterion, which can identify the weak damping wind farm and determine the number of wind turbines required to be installed. The proposed DTDC's effectiveness and implementation scheme are validated using the modified IEEE first benchmark model and a wind farm model in North China, respectively. The control hardware-in-loop (CHIL) experiments results demonstrate that the DTDC outperforms traditional approaches with superior damping and robustness under varying wind speeds, compensation levels, and the number of online wind turbines.

Shunt converter-based damping schemes have been developed to mitigate the unstable subsynchronous control interaction (SSCI) between renewable energy power plants and power grids. However, varying system conditions can alter the dynamic interaction between shunt converters and power systems, making it challenging for these shunt converter-based damping schemes to provide consistently positive damping effects. To address the above-mentioned problem, this article proposes a coupled impedance model and an adaptive coupling reshaping controller (ACRC). First, a coupled impedance model, which considers the implicit coupling relationship between the shunt converter and the power system, is constructed to reveal the dynamic interactions between the shunt converter and the power system. Based on the coupled impedance model, an ACRC is proposed to adaptively reshape the coupling relationship. This online adjustment adaptive for various system conditions, equivalent to reshaping the dynamic interaction between the shunt converter and the power system, increases the grid resistance at the resonant frequency and hence effectively mitigates the SSCI. Finally, impedance-based analysis and controller-hardware-in-loop tests verify the effectiveness and adaptivity of the proposed method.