## 2 Proposed Operating Reliability Assessment Model  
A power system is operated to respond to the stochastic nature of system component failures and/or load variations to continuously match the supply of power to the system demand in real time. Large variations that pose a risk of load curtailment are termed as disturbances in this paper. Forced outages of committed units can lead to load curtailment situations, and are therefore considered as the major disturbance events in this paper. The operational reliability methodology presented in this paper is scoped to the bulk system operator's jurisdiction where utilities are required to meet the N-1 transmission planning criteria, such that a single order line contingency does not curtail the ability of the system to serve the bulk-load points. The probability of multiple transmission contingencies in a short operational exposure time is very small. The transmission lines are therefore not considered in this study. Similarly, the load variations are neglected in this study since the load uncertainty in the short time from the known initial condition is insignificant. For any kind of disturbance, such as a generating unit outage, the healthy operating units must respond and fulfill the lost power within a specified response time to avoid load curtailment situations. The probability of such load curtailment situation depends on the probability and magnitude of power disturbances, the amount of operating reserve in the system, ramp rates and responding capacity of the units carrying the reserve, and the lead time after which the system will receive further capacity assistance. All of these parameters are therefore considered in developing an operating system reliability model to evaluate the comprehensive operating risk, designated as the CGRR in this paper. Figure 1 portrays the underlying concepts in the evaluation of the CGRR index. An operating condition has \(m\) number of generating units committed for a lead time \(T_{L}\). It is shown in Figure 1 that \(D_{i}\) is the disturbance at time \(T_{i}\) associated with the \(i^{\text{th}}\) event out of the total 2\({}^{\text{m}}\) contingencies, and \(T_{R}\) is the response time within which the healthy generating units must respond with sufficient capacity to avoid a load curtailment situation. The outage probability of a single committed unit is given by (1), and is known as the outage replacement rate (ORR) [1]:  
\[ORR_{i}=P(D_{i,i\in F})=1-e^{-\lambda_{i}T_{L}} \tag{1}\]  
where, \(i\in F\) includes all first order contingencies of unit outages, and \(\lambda_{i}\) is the failure rate of unit \(i\). A discrete cumulative distribution function \(F(Z)=P(Z_{k\,=\,1\,to\,s})\) of \(s\) capacity outage states within the lead time \(T_{L}\) can be obtained using (2) to recursively calculate the cumulative probability of \(Z_{k}\) MW outage in committed capacity [1]. \[P(Z_{k})=\left(1-ORR_{j}\right)\star P^{\prime}(Z_{k})+ORR_{j}\star P^{\prime }\left(Z_{k}-C_{j}\right) \tag{2}\]  
where \(C_{j}\) and ORR\({}_{j}\) are the capacity and ORR for \(T_{L}\) lead time respectively of unit \(j\) added recursively to modify \(F(Z)\); \(P^{\prime}(Z_{k})\) and \(P(Z_{k})\) are the cumulative probabilities of \(Z_{k}\) capacity outage before and after adding the \(j^{th}\) unit. Equation (2) is initialized by setting \(P^{\prime}(Z_{k})=1\) for \(Z_{k}\leq 0\) and \(P^{\prime}(Z_{k})=0\) otherwise [1]. Figure 1: Conceptual illustration of CGRR evaluation of an operating condition. A capacity outage \(Z_{k}\) due a major disturbance \(D_{i}\) results in a reduction in operating capacity \(X_{k}\) given by (3), where \(m\) is the number of committed units, \(N\) is the total number of healthy operating units after the disturbance and \(c_{Lj}\) is the loading capacity of unit \(j\) prior to the disturbance.