Zone LOLP

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

The Loss of Load Probability (LOLP) is calculated by using a convolution method.

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

Basically it iterates through all units in the system, accumulating the unit outages and calculating their respective probabilities. Each of the outage states and the probabilities are then entered into an outage capacity table, which is used to build a LDC curve, from the peak PASA Zone load (plus the net capacity interchange minus any fixed capacity). 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.

The formula for calculating the new probabilities when convolving generators is:

f(X_p) = (1 - FOR_c).f_prev(X_p) + (FOR_c).f_prev(X_p-C_c)

where :

f_prev(X_p): is the probability of X capacity outage occurs prior to convolving the current generation unit FOR_c: is the forced outage rate for the current generation unit C_c: is the capacity of the current generation unit

This is for the c^th generation unit. This formula is repeated for all generators, with FOR's, in the Zone.

NOTE:

Discrete maintenance is included in reliability indices calculation.

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.

Outage (MW)	Probability
0	0.9
100	0.1

Table 1 : Capacity Outage Table for 1 Unit

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

Outage (MW)	Probability
0	0.81
100	0.18
200	0.01

Table 2 : Capacity Outage Table for 2 Units

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 produces the following outage capacity table as shown in Table 3.

Outage (MW)	Probability
0	0.729
100	0.243
200	0.027
300	0.001

Table 3 : Capacity Outage Table for 3 Units

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.

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

Table 4 : Capacity Outage Table for 4 Units

The LOLP formulation is given as:

LOLP = Sum ( f_y.C_c.F_d(IC-C_c) ) for c = 1 to c = N

where :

C_c: is the capacity outage MW value, which can be seen in the above tables f_y.C_c: is the probability that a capacity outage, C_c, occurs IC: is the installed capacity for the Zone F_d(IC-C_c): is the value of the built LDC value at demand, IC-C_c

Note:

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

Zone LOLP

Convolution Formula

Convolution Examples

LOLP Formula