Question

Explanation of the system: G1 G2 G3 Transmission Lines Load Generators: Three generators are supplying a load as shown in the Figure above. For generators G1, G2, and G3 each either has a full capacity of 75 MW or 0 MW when failed. The failure rate of each generator is 0.1/day, and the mean repair time is 12 hours. Transmission Lines: The failure rate of each transmission line is assumed to be 10 /year. The mean down-time is 8 hours. The capacity of each line is 100MW. Load: Load fluctuates between two different values 105 MW with a mean time of 16 hours and 205 MW with a mean time of 8 hours. 1. For the described system, using an analytical method, please find the exact values of loss of load probability and frequency of load loss. (6 Points) 2. For the described system, using Monte Carlo Simulation (Random sampling), please find the loss of load probability. (7 Points)

          Explanation of the system:
G1
G2
G3
Transmission Lines
Load
Generators: Three generators are supplying a load as shown in the Figure above. For
generators G1, G2, and G3 each either has a full capacity of 75 MW or 0 MW when
failed. The failure rate of each generator is 0.1/day, and the mean repair time is 12
hours.
Transmission Lines: The failure rate of each transmission line is assumed to be 10
/year. The mean down-time is 8 hours. The capacity of each line is 100MW.
Load: Load fluctuates between two different values 105 MW with a mean time of 16
hours and 205 MW with a mean time of 8 hours.
1. For the described system, using an analytical method, please find the exact
values of loss of load probability and frequency of load loss.
(6
Points)
2. For the described system, using Monte Carlo Simulation (Random sampling),
please find the loss of load probability.
(7 Points)

Explanation of the system:
G1
G2
G3
Transmission Lines
Load
Generators: Three generators are supplying a load as shown in the Figure above. For
generators G1, G2, and G3 each either has a full capacity of 75 MW or 0 MW when
failed. The failure rate of each generator is 0.1/day, and the mean repair time is 12
hours.
Transmission Lines: The failure rate of each transmission line is assumed to be 10
/year. The mean down-time is 8 hours. The capacity of each line is 100MW.
Load: Load fluctuates between two different values 105 MW with a mean time of 16
hours and 205 MW with a mean time of 8 hours.
1. For the described system, using an analytical method, please find the exact
values of loss of load probability and frequency of load loss.
(6
Points)
2. For the described system, using Monte Carlo Simulation (Random sampling),
please find the loss of load probability.
(7 Points)

Added by David M.

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