Region LOLP

Units:%
Mode:Output Only
Multi-band:False
Default Value:
Validation Rule:
Key Property:No
Description:Loss of load probability (summary type "Average")

NOTE: LOLP is only computed by LT Plan and PASA when their Compute Reliability Indices setting is 'on' respectively.

This algorithm iterates through all units in the system, accumulating the unit outages and calculating their respective probabilities. Each of the outage states and their probabilities are entered into a capacity outage probability table (COPT), which is used to build an LDC curve, from the peak PASA region load. This is known as the "Effective Load Approach". This modified curve is then used to obtain the LOLP per PASA period by using the formula, as given below.

For units defined with multi-band Forced Outage Rate (or Effective Forced Outage Rate ) and Outage Rating , these units are considered as multi-state generators and all the states are convolved into the COPT.

For multi-region connected as a network, the LOLP in each region will be much lower as assistance can be obtained from other regions which have excess capacities.

NOTE: The peak PASA region load is the region's peak load value within each period as defined in the PASA resolution settings. It is comprised of region load + net capacity interchange + any region physical contract load - any region physical contract generation.

Convolution Examples

A simple example of the convolution method is to take a single generator and convolve it with another generation unit. For example, say we have two generators with the same properties, for simplicity, such that their maximum capacity is 100MW and their FOR is 0.1. Given that the generator has a FOR value of 0.1, then the probability that it is on is 0.9 (1 - 0.1 = 0.9).

The outage table for the single generator is given in Table 1. It can be seen that this is a two-state unit, i.e. it is either on, generating 100MW with a probability of 0.9 or it is off, giving a 100 MW outage, with a probability of 0.1.

Table 1: Capacity Outage Table for 1 Unit
Outage (MW) Probability
0 0.9
100 0.1


Convolving this generation unit with another generation unit, which has identical properties, produces an outage table as shown in Table 2.

Table 2 : Capacity Outage Table for 2 Units
Outage (MW) Probability
0 0.81
100 0.18
200 0.01


Table 2 shows that there can be three possible outage states, zero, 100MW and a 200MW outage. Both generating units could produce an outage of 100MW, so the probabilities are lumped together.

Convolving another generator with the same properties as the previous two generators results in the following outage capacity table as shown in Table 3.

Table 3 : Capacity Outage Table for 3 Units
Outage (MW) Probability
0 0.729
100 0.243
200 0.027
300 0.001


Table 3 shows that there can be four possible outage states for these three generation units when convolved together. Thus far we have provided a very simple example, by only convolving generation units that have the same properties. The fact that we have used generators with the same maximum capacity values, means that we are able to lump the probabilities together for the same outages.

Now, the number of outage states and their equivalent would become much larger if we were to convolve generation units that have different capacity values. For example, if we were to now convolve another generation unit with the same FOR of 0.1, but with a different maximum capacity value of 5MW, then we would obtain the capacity outage table as detailed in Table 4.

Table 4 : Capacity Outage Table for 4 Units
Outage (MW) Probability
0 0.656
5 0.0729
100 0.219
105 0.0243
200 0.0243
205 0.0027
300 0.00009
305 0.00001

LOLP Formula

The LOLP formulation is given as:

LOLP = Sum ( fy.Cc.Fd(IC-Cc) ) for c = 1 to c = N

where :

Cc: is the capacity outage MW value, which can be seen in the above tables fy.Cc: is the probability that a capacity outage, Cc, occurs IC: is the installed capacity for the region Fd(IC-Cc): is the value of the built LDC value at demand, IC-Cc

Note:

The reliability indices are calculated on a regional basis and do not consider transmission unreliability. Discrete maintenance is included in reliability indices calculation.

See also: