Normally, the capacity of the transmission path is a  function of the availability of transmission lines and the status of the reactive power compensation devices。 The deterministic reliability assessment normally identifies the transmission upgrade based on a de-rated capacity instead of the full capacity of wind farm。 The target capacity of transmission upgrade that is often used in current practice is the average MW value on hourly wind profile during the peak-load or off- peak load hours, depending on which scenario is selected for the deterministic study。 In some wind resource areas, the average wind capacity during summer peak-load hours may be 60% of the wind farm capacity and even lower; during the off- peak hours it can be as high as 80% [3]。 It is important to select the target capacity appropriately so that both the system reliability and the utilization of green energy will be economically optimized。

Probabilistic reliability models can permit the selection of the optimal target capacity of transmission upgrade。  In this section, a probabilistic reliability model of the composite system of wind generation and transmission lines is developed based on reliability mathematics [12]。 A typical wind generation interconnection is shown in Fig。 1, where a wind

The  capacity  state  pair  (x, Px  )  of  the  wind  farm  can    be

obtained by the method discussed in Sub-section II。B。 The derivation of capacity states of transmission lines, denoted by y, is discussed in the following section。

Fig。 2。  A series connection system

If the forced outages of transmission lines are ignored, the transmission path has two capacity states, path rating and 0。 The probabilities of these two capacity states are 1 and 0, respectively。 Considering line forced outages, each transmission line still has two capacity states, but the probability of capacity states need to be revised according to the outage rate of the line。 For the transmission path with two parallel lines as shown in Fig。 1, its capacity states can be obtained by convoluting the capacity states of two lines。 The algorithm is the same as for calculating the capacity states of generation system with multiple units, which is not repeated here instead the reader is referred to [6]。

The transmission capacity of the transmission path is also affected by the status of the reactive power devices, such as shunt capacitors or series compensators。 If some reactive power devices are out of service, the transmission capacity may need to be de-rated。 The capacity states considering the outages of reactive power devices can be calculated using the series connection system model as shown in Fig。 2。 For simplicity, only the line outage is considered in this paper。 Note that the available capacity of the transmission path between the wind generation and the main grid is determined separately, normally by deterministic reliability assessment method。

The forced outage rate of a two-terminal transmission line can be calculated by (6) [13]:

demonstrate the reliability modeling of wind  energy integration using the proposed models and methods。 In this sub-section, a wind farm as given in [10] is added into the system。 The wind capacity availability of this wind farm is shown in Table I。 The wind capacity factor is 83%。 The capacity of the wind farm is adjusted so that the consumed wind energy is 6% of the total consumed energy。 This reflects the 6% RPS target。 Assume that each wind turbine generator has 2 MW capacity and 10% FOR。 The base case scenario has 2400 MW of peak load and 0 MW of wind generation。 The EENS of this base case scenario is used as the reliability criterion of the system。 For any other studied scenarios, if the EENS is less than the EENS of the base case  scenario, then the studied scenario is deemed reliable; otherwise is not reliable。