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How to Convert Cycle to millisecond
For System Protection Application


Assume voltage or current waveform frequency = 60 cycles/sec or 60 Hz

Related topic: Explain the difference between 240 samples / second versus 4 samples / cycle

cycle = millisecond


° degree = milliseconds


° degree = cycle


Assume voltage or current waveform frequency = 50 cycles/sec or 50 Hz

cycle = millisecond


° degree = millisecond


° degree = cycle


Assume voltage or current waveform frequency = 100,000 cycles/sec or 100 kHz

This visualization is useful in analyzing transient recovery overvoltage (TRV) due to restrike voltage in SF6 Gas in Extra High Voltage Power Circuit Breakers.

The normal operating frequency of EHV Power Circuit Breaker in the U.S. is 60 Hz. If the breaker is calibrated to trip at 2 cycles out of 60 Hz , it means the operating speed of the breakers is 33.33 millisecond not including the time delay for relay operation. TRV is very fast in 20 nanosecond up to 10 microsecond.

ASSUME FREQUENCY IS 100,000 Hz or 100 kHz

cycle = microsecond
10 microsecond = 10µsec = 10 x 10-6 second =10 e-6 second = 0.000010 sec


ASSUME FREQUENCY IS 50,000,000 Hz or 50 MHz

cycle = nanosecond
20 nanosecond = 20 nsec = 20 x 10-9 second =20 e-9 second = 0.000000020 sec


For 60 Hz

1 cycle * sec /60 cycles = 0.0166667 seconds = 16.667 milliseconds


360 electrical degree = 1 cycle

1 ° degree = 1/360 cycle = 0.002778 cycle


For 50 Hz

1 cycle * sec /50 cycles = 0.02 seconds = 20 milliseconds


Angular Degree to Radian Calculator

radian = degree

Memory recall : 2π radian = 360 ° 1 radian = 360 ° / 2π = 360 ° / 6.2832 = 57.296 °

2π = 2 * 3.1416 = 6.2832







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