\section{Discussion}\label{sec:Discussion}

The methodology demonstrated in this paper utilized TCC data, FMECA, Cox PHM, and approximate methods for power system reliability analysis. TCC measurements were utilized to assess the onset of failure mechanisms. They are readily available measurements that can detect faults in an HVCB's electrical and mechanical components. However, the TCC could be combined with other condition monitoring measurements to improve the accuracy of the health indices. Moreover, if additional failure data were obtainable and correlated with how the condition monitoring measurements appear when a failure mode occurs, this would enhance the assessment of the onset of failure mechanisms. 

The FMECA process was utilized to analyze various failure mechanisms and provide a structured approach to justify weighting factors within the health index model. However, it does not consider the potential interactions between the failure mechanisms. If two failure mechanisms introduce moderate risk, it could be possible that the risk is much higher when both occur simultaneously. Unfortunately, this is not captured in the FMECA process since failure mechanisms are assessed separately. 

The Cox PHM is used to determine the baseline failure rate by removing the influence of covariates. The outage database used for this case study did not include information on the time failures occurred.
When outage data is not time-stamped, it results in interval-censored data, making it harder to reach convergence when determining the regression coefficients of the Cox PHM. Time stamps would result in right-censored data, for which it is easier to achieve convergence. 

Approximate methods provided a simplified approach in calculating the basic reliability indices and could also account for common-mode failures. However, approximate methods cannot capture the distribution of the reliability indices due to stochasticity in component failures. Time-sequential Monte Carlo simulation methods are capable of capturing the distribution of the reliability indices, which would result in more information for decision-making.

The case study shows how EENS increases both when \( \lambda^s \) is increased and when \( P^m \) is increased due to deteriorated component condition. The relative increase in EENS is relatively small for this test system, in the order of 1\%. One explanation for this moderate system-level impact is that the reliability indices of this test system are dominated by first-order (single-outage) contingencies, which contribute 96\% of the system EENS. Protection system mis-operations and its impact through \( P^m \) mostly make itself noticeable on the system level for second-order contingencies. The relative negative system-level impact would be greater for power systems that are N-1 secure, which is the case for most real power systems, than for the test system used for this case study.

Using TCC measurements to assess the health of an HVCB causes more variability on the parameter $\lambda^s$ than $P^m$. This is because TCC measurements can quantify up to 92\% of the weight of the failure mechanisms that contribute to the failure mode of the HVCB tripping without a command, whereas TCC measurements can only account for 39\% of the weight of the failure mechanisms that lead to the HVCB failing to trip on command. This results in a maximum variation in the input parameters of 184.07\% for $\lambda^s$ and 47.13\% for $P^m$ in scenario 1 when assessing component health with TCC measurements. However, the reliability indices are more sensitive to $P^m$, as it has a $\beta_1$ value of 827.2 for load point 1 and 657.2 for load point 2, while $\lambda^s$ has a $\beta_1$ value of 195.5 for load point 1 and 146.7 for load point 2.

The reliability indices are most sensitive to \( P^m \) due to the common-mode failures that it induces. Therefore, small uncertainties in the scoring of failure mechanisms connected to \( P^m \) can affect the reliability indices significantly. Consequently, when quantifying the condition of an HVCB, it is the failure mechanisms of Table \ref{tab:FM1} that are most important to quantify precisely. Any maintenance procedures that can diminish the likelihood of these failure mechanisms happening would be a productive allocation of resources.

The range of EENS values between the values for Scenario 1 and Scenario 2 corresponds to the region of potential impact of HVCB technical condition that TCC data does not detect. For the test system, this region of uncertainty for $\lambda^s$ is 0.05\% (from 2239.73 MW to 2240.90 MW) for LP1 and 0.05\% (from 1682.37 MW to 1683.25 MW) for LP2. The region of uncertainty for $P^m$ is 0.94\% (from 2238.73 MW to 2259.87 MW) for LP1 and 1.00\% (from 1681.96 MW to 1698.76 MW) for LP2. This suggests that other types of condition data, such as maintenance and operational records, could be used to detect failure mechanisms contributing to $P^m$ and thus obtain a more accurate estimation of the reliability indices.