## 1 Introduction  
The generator shafting damage accidents in Mohave Power Plant, which were reported in the 1970s, caused people to pay attention to the Sub-synchronous Oscillation (SSO) issue, which is mainly caused by the unreasonable series compensation capacitance of the transmission lines. In recent years, with the global development of renewable power generation and integration technology, because the support of relevant national policies, the stability issue caused by the grid-connected operation of renewable power station further extends the connotation from Sub-synchronous Oscillation (SSO) to Sub/super-synchronous Oscillation (SSO). The analysis results show that the converter control systems of renewable power generation units and direct current transmission or distribution systems have significant impacts on the oscillation phenomenon [1, 2]. At the same time, the oscillation has no connection with the torsional oscillation of shafting. This kind of SSO phenomenon is called Sub-synchronous Control Interaction (SSCI) [3, 4, 5]. The research directions of the existing journal articles are mainly focused on modeling and monitoring analysis, stability analysis of the renewable power system, and controller design for SSCI research [6; 7; 8]. Frequency and damping are the key parameters from a system stability point of view. Prony, Hankel total least squares, eigen realization, and matrix pencil are four commonly used time-domain parametric methods to determine the modal parameters in online and offline environments [6]. The term \"frequency scan analysis\" has been widely used in the industry to evaluate the risk of SSCI in any system. However, the frequency scan is only suitable for SSCI analysis at the planning stage or during the expansion of generation or transmission projects [7]. The Nyquist and reactance-crossover analysis methods can provide information (e.g., frequency and damping) on the unstable oscillation modes. Nonetheless, these methods are unable to provide critical insight into the interaction phenomenon, such as the origin and path of oscillation, and the participation level of certain system components [7]. Such information is critical to properly assess the risk of SSCI and devise effective risk alleviation or mitigation strategies [9]. Stability analysis based on precise models of impedance networks is also partially studied [10]. The impedance method has obvious advantages in system modeling, which can be identified by external characteristics without the need for internal parameters of equipment. In addition, the impedance model is connected according to a topological structure and has a clear physical explanation, which is conducive to mechanism research. However, the impedance model of the whole power system including both the renewable power base and HVDC transmission system under different operation statuses is still in the research and development stage. The whole-system impedance model under different operation statuses is the foundation for the analysis of the interactions between controllers in a renewable power base (source side) and an HVDC transmission system (grid side) on the studied SSO/SupSO modes. Aiming at the SSCI issue, [11] proposes that the mismatch of controller parameters among different controllers which are located on the power generation side and power grid side may induce SSCI issues, and damping coupling exists among oscillation modes. It is necessary to optimize the controller parameters or establish the parameter stability region (PSR) to evaluate the rationality and match degree of the control parameter set. One the one hand, although parameter optimization [12] can improve system stability, this technique is usually used offline due to its high computational complexity; in particular, a large eigenvalue-calculation-duration parameter optimization.