## 5 Conclusions  
Aiming at the prevention and control of the SSO issue in renewable power grids and rapid online assessment of the matching of controller parameters between power generation side and grid side under the current operation mode, a novel method to construct controller PSR is proposed. Based on GDT, the eigenvalue distribution range of the system state matrix containing controller parameter variables is rapidly estimated, instead of the time-consuming direct calculation of eigenvalues, and then the PSR is deduced according to the small signal stability criterion and corresponding stability constraints on the obtained eigenvalue distribution range. On the basis of PSR, the stability margin evaluation index is proposed to rapidly evaluate the distance between the controller parameter set and the boundary of the PSR, providing guidance for the reasonable selection and online refreshing of the controller parameters under the current operation mode for the prevention and control of SSO, so as to secure the safe and stable operation of the high-proportion renewable power grid. Specifically, the preconditions of the application of the GDT on the PSR construction are discussed in detail, and a construction method of transition matrix is proposed based on a system state matrix. The transition matrix is used for the PSR construction instead of applying the system state matrix directly to overcome its limitations. Furthermore, to reduce the conservativeness of the PSR, a method for extension of the PSR is also given. The validity and correctness of the proposed methods are verified via a DPMSG-HVDC benchmark. The efficiency of the proposed method is highlighted by comparing the proposed method and the point-wise eigenvalue calculation of the state matrix from a time-consuming perspective, which demonstrates its potential for online application. This paper mainly focuses on the PSR construction method and its application procedure; the further research directions are in following:  
1. The method of rapid PSR construction's application to the impedance model;
2. The application of the proposed PSR method in a practical large-scale renewable power system;
3. The mechanism for the constructed PSR, which is more robust to the unknown control parameters and uncertainties;
4. Detailed investigations into whether and how wind-farm output fluctuates affect the PSR of different benchmarks are currently taking place. The progress is expected to be reported is a separate submission. Conceptualization, T.L. and S.K. ; methodology, Y.S., R.C. and B.C. ; validation, T.L. and S.K. ; investigation, Q.L., S.L. ; resources, H.D. ; data curation, S.K. ; writing--original draft preparation, S.K. and T.L. ; writing--review and editing, T.L. and S.K. ; visualization, S.K. ; supervision, T.L. ; project administration, T.L. ; funding acquisition, T.L. All authors have read and agreed to the published version of the manuscript. This work is supported by the National Key R&D Program of China (2017 YFB0902000) and State Grid Corporation Headquarters Science and Technology Project (SGXJ0000 KXJS1700841). Not applicable. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Method** & **Method 1** & **Method 2** \\ \hline time-consuming(s) & 2119.2 & 2.2411 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Time-consuming comparison under 0.001 parameter interval. * [PERSON] and [PERSON] (2011) [PERSON]; [PERSON] Distributed control of a class of interconnected systems in a string. _IET Control Theory Appl._**2011**, \(5\), 963-975. [CrossRef]
* [PERSON] et al. (2013) [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Guaranteed stability of recursive multi-input-single-output time series models. In Proceedings of the 2013 American Control Conference, Washington, DC, USA, 17-19 June 2013; pp. 77-82. * [PERSON] (1995) [PERSON] D-stability of continuous time-delay systems subjected to a class of highly structured perturbations. _IEEE Trans. Autom. Control_**1995**, _40_, 1803-1807. * [PERSON] et al.