Page 69 - Power Quality in Electrical Systems

52 Chapter Four

i(t)

I ∆i PP

Figure 4.12 Pulsating waveform
with duty cycle D and peak-peak
ripple ∆i pp .
t
DT T

Pulsating waveform with ripple
The rms value of a pulsating waveform (Figure 4.12) with duty cycle D
and peak-peak ripple ∆i pp is

1 i pp 2
I rms 5 I 2D 1 1 a ba b
Å 3 2I

Triangular waveform
The rms value of a triangular pulsating waveform (Figure 4-13) with
peak value I pk and duty cycle D is

D
I rms 5 I pk
Å 3
Piecewise Calculation
Let’s assume we have a periodic waveform i(t) that can be broken up
into different frequency components I , I , I , . . . etc. The rms value of
1
3
2
I is I , The rms value of the total waveform made up of the sum of
1 RMS.
1
i(t)

I pk

Figure 4.13 A triangular waveform.
t
DT T