Reliability Equivalence and Sensitivity Analysis to UHVDC Systems Based on the Matrix Description of the F&D Method

For reliability analysis to ultra HVDC transmission (UHVDC) systems, the transition rates after multi-step equivalence are not explicit expressions of the reliability parameters. Thus, the sensitivity of the reliability indices to the parameters cannot be analytically expressed. A new sensitivity model after equivalence is proposed. The state space considering the winding of converter transformers is derived, two half-capacity levels are differentiated, and the passive reserve shutdown is considered. The derivatives of the state probabilities to reliability parameters are given by the transition rates. The transition frequencies before and after state aggregation are given by matrix form to facilitate the frequency and duration (F&D) method, thus yielding sensitivities after reliability equivalence. Numerical results validate accuracy of the sensitivity and the resulting reliability indices, and quantify the dependency of the sensitivity on the parametric change and spare schemes. The proposed model helps determine the vulnerable parameter and component of UHVDC systems, find countermeasures, or estimate error due to the uncertainty of reliability parameters.