Question

A system has a continuous load requirement of 80 MW. Find the expected load loss and the probability of load loss (loss of load probability) if the generation system is composed of nine 10 MW units each with an unavailability (probability of failure) of 1.5%.

Answer 1

Answer:

Expected load loss = 1.35

P (Load Loss) = 0.127

Step-by-step explanation:

The probability of failure is: q = 0.015

The probability of success is: p = 1 - q = 1 - 0.015 = 0.985

The number of units the generation system is composed of is, n = 9.

The capacity of each unit is 10 MW.

Let X = number of units that failed or are unavailable.

The random variable X follows a Binomial distribution with parameters n and q.

The probability function is:

$P (X=x)={n\choose x}p^{x}(1-p)^{n-x}$; x =0, 1, 2, 3...

• The expected number of failures is:

$E(X)=nq=9\times0.015=0.135$

Then the expected load loss is:

$E (Load\ Loss)=10\times E(X)=10\times 0.135=1.35$

Thus, the expected load loss is 1.35.

• The load loss will be when at least one unit fails.

The probability that at least one unit fails is:

P (X ≥ 1) = 1 - P (X < 1) = 1 - P (X = 0)

             $=1-[{9\choose 0}(0.015)^{0}(1-0.015)^{9-0}]\\=1-0.8728\\=0.12718\\\approx0.127$

Thus, the probability of load loss is 0.127.