Question

A sample system consists of three generation units. Table 1 shows the corresponding generation system data, while Table 2 describes the demand within the system. Generator Table 1. Generation unit data Capacity (MW) Failure rate (day) 0.02 30 0.02 40 0.02 30 Repair rate (day) 0.48 0.48 0.48 2 3 Daily peak load (MW) Days of occurrences (Days) Table 2. Demand data 80 67 5642135 15 T 80 105 117 1 48 a) For a system consisting of the generation units described in Table 1, Generate the Capacity Outage Probability (COP) table including: • Individual Probabilities • Cumulative Probabilities b) With the COP table from question a) and an assumed constant demand of 65MW, determine: • Loss of Load Expectation (LOLE) • Expected Energy Not Supplied (EENS) c) With the COP table from question a) and the demand data of Table 2, determine: • Loss of Load Expectation (LOLE) • Expected Energy Not Supplied (EENS)

Answer 1

Solution:

Capacity Outage Probability Table a. Given that the probability of unit failure is assumed to be 0.02 i:e U-0.02 Therefore P(availability) P(A)-0.98 Assuming the constant demand of 65MW Indicative Generator Capacity Capacity Binomial (out) (in) Cumulative DistributionProbability (Pi) Load loss (Li) Li*Pi Probability units (а) 30MW 1 0 30 0.98 1.00 0 0 U 2 30 0 0.02 0.02 65 1.3 (b) 40MW 0.9604 1 0 40 A*A 1 0 0 0.0396 2 20 20 2AU 0.0392 0 0 U*U 0.0004 0.026 3 40 0 0.0004 65 b. ELL for the first 1.3MW 1300KW _ ELL for the second 0.026MW = 26KW _ LOLP 0.02 LOLE 0.02 365 = 7.3 d/yr LOLP-0.0004 LOLE 0.0004*365 = 0.146 d/yr

Here I done solution by taking the average of all quantities it is not mentioned that to be done for individual or average. C. ie it is 56MW Indicative Cumulative Probability probability Binomial Generator Capacity Capacity Load loss (Li) Li* (out) (in) Distribution units (Pi) (a) 30MW 30 0.98 1 A 1.00 0 30 0 0.02 0.02 56 1.12 2 (b) 40MW 40 A*A 0.9604 1 20 20 2 2AU 0.0392 0.0396 40 3 0 U*U 0.0004 0.0004 56 0.0224 O O

ELL for 1 1.12MW = 1120 kW ELL for 2 0.0224MW = 22.4 kW LOLP-0.02 LOLE 0.02 365 = 7.3d/yr LOLP 0.0004 LOLE 0.0004*365=0.146d/yr. The total no of days is 365(sum) Note: If you want to calculate the individually just change the value of load loss and multiply with respective no of days in spite of 365