## 1 Introduction  
The ability of a power system to maintain the continuity of power supply to its customers mainly depends on the implementation of operating decisions, provided that the system is adequately planned. Determining the optimum number, type, and capacity of generating units that must be operated and deciding how these units should be dispatched to meet the projected load are two key questions that must be prudently answered by the system operator before making operating decisions on these two tasks, commonly known as unit commitment and load dispatch, respectively. The power generated by the operating or \"committed\" units at a given time must be equal to the load at the same instant. The balance between supply and demand of power can be disturbed by random and sudden changes in load or generation due to incidents, such as an outage of a committed unit. The ability of the system to respond quickly to these disturbances to regain the balance and maintain the continuity of power supply will depend on the load dispatch decision taken prior to the disturbances, which in turn will depend on the unit commitment decision that was taken prior to the load dispatch. The continuity of the power supply or the reliability of the operating system condition will therefore depend on both the unit commitment and load dispatch decisions. Both of these tasks should therefore be considered in the operating system reliability evaluation. Many power system operators have conventionally used a deterministic criterion, such as the N-1 [1], to assess the operating reserve required during unit commitment. Many utilities operating within the North American Reliability Corporation (NERC) guidelines use this criterion to determine their minimum operating reserve requirements. As deterministic methods do not consider the stochastic nature of the unit failures and load variations, these methods can result in high operational cost or poor operating reliability due to over scheduling or under scheduling of the generators, respectively. The committed generating units must be able to provide sufficient response capacity in a short time of several minutes, referred to as the response time, to regain power balance and provide necessary frequency control [2] after a disturbance occurs. This response capacity, or regulating margin (RM), that can be obtained within the response time is generally estimated deterministically based on operator experience. With the use of these deterministic methods, the inconsistency in system operating risk will further increase as uncertainty in power systems increases due to ongoing system changes, such as the rapid growth of wind power. Most system operators use the economic load dispatch (ELD) method to make decisions on dispatching the committed units to serve the load. This deterministic method minimizes the operating cost. As reliability and economics often compete with each other, the dispatch decisions based on this method can result in unacceptable reliability. The above concerns have led to research and development of probabilistic methods that can incorporate the uncertainties in system operation and provide proper evaluation of system operating risks. The Pennsylvania-New Jersey-Maryland (PJM) method [3] provided pioneer work in applying probabilistic methods in operating reserve evaluation. A probability distribution of committed generation is created in this method as a function of the lead time. It is the exposure time of the operating components to random failures in a given operating condition, within which time additional capacity assistance will not be available. The unit commitment risk (UCR) index quantifies the operating risk associated with the unit commitment decision, which is the probability of the committed generation just meeting or failing to meet the load requirement [1]. The PJM method was extended to incorporate rapid start units in [4] and import/export constraints in [5].