If the system frequency operates at 60.02 Hz for two consecutive hours, what is the resulting positive time error?

To determine the resulting positive time error when the system frequency operates at 60.02 Hz for two consecutive hours, it's crucial to recognize the relationship between frequency and time. The standard frequency for electric power systems is 60 Hz. Operating slightly above this frequency indicates that time is progressing faster than it would at the nominal frequency.

To calculate the time error, first, convert the frequency difference from 60 Hz. The frequency of 60.02 Hz means it operates at an increased rate of 0.02 Hz. This indicates that the system completes more cycles in the same amount of time compared to the standard.

Now, for each cycle at 60 Hz, one complete cycle takes 60 seconds / 60 = 1 second. However, at 60.02 Hz, the time taken for each cycle would be:

1 / 60.02 seconds ≈ 0.01665 seconds per cycle.

In a span of two hours (which is 7200 seconds), the number of cycles completed at 60.02 Hz can be calculated:

Number of cycles = Frequency × Time = 60.02 Hz × 7200 seconds = 432144 cycles.

At the nominal frequency (60 Hz), the expected number of cycles