Power System

In the normal operation of the power system, the frequency should be limited to the normal band. It has been defined by the IEGC that the frequency should be limited to 49.5 to 50.3.

Let

p = proportion of all cases which fall into normal band

From the data it shows that p = 0.987.

With the confidence interval analysis we can say that with 95% confidence that the power frequency of the Karnataka state board satisfies the regulations for 97.5% to 0.99.9% cases.

Case 2

The average frequency of the sample(the whole data) is 49..With the observed variance it can be concluded that the average frequency lie between 49.74 and 49.71 for 95% of the cases. This shows that the system is quite stable and there is very little fluctuation. The system frequency can be expected to lie within 49.74 and 49.71 for most of the cases in the long run.

Case 3

From the data for the power frequencies of the system, the Karnataka state Power Corporation can make a claim that it maintains the frequency with the regulatory limits for 98.7% of cases. Now, in order to prove the fact, we take the data for two consecutive days.

It is found that it abides by the regulatory limit for 97.9% of the cases. We can check the truth of the claim by hypothesis testing. The level of significance is considered as 5%.

From the testing of hypothesis we find that, we can get a sample proportion of 0.979 for 29.6% (p-value) of the cases with the given variance and population proportion. So, at 5% level of acceptance the null hypothesis, i.e. Karnataka state Power Corporation maintains the frequency with the regulatory limits for 98.7% of cases, cannot be rejected.