A.C. Voltage waveforms and harmonics?

[alex.daciz]

Hi, I have the following question:

An A.C. voltage, V comprises of a fundamental voltage of 100V rms at a frequency of 120Hz, a 3rd harmonic which is 20% of the fundamental, a 5th harmonic which is 10% of the fundamental and at a phase angle of 1.2 radians lagging.

(1) Write down an expression for the voltage waveform

(2) The voltage at 20ms (milliseconds)

(3) Given an ideal V = 100V rms, what is the percentage error at 20ms

I have an idea for the first and second parts but I get a huge percentage error in (3) which makes me doubt whether the first 2 parts were correct, can anyone help please?

(1) Since V = Vrms x sqrt2 = 141.4V at 120Hz

3rd harmonic = 20% of 141.4 = 28.3V at 360Hz

5th harmonic = 10% of 141.4 = 14.1V at 600Hz

v = [141.1sin(240πt)] + [28.3sin(720πt] + [14.1sin(1200πt+1.2)] π=pi


(2) V at 20ms = 36.8 + 20.1 + 13.7 = 70.6V


(3) Error is [(100-70.6)/100]X100 = 29.4% !? That seems like a massive error, where has my equation gone wrong?

Help anyone!?

 

[uart]

v = [141.1sin(240πt)] + [28.3sin(720πt] + [14.1sin(1200πt+1.2)]

That 5th harmonic is 1.2 radians leading, not lagging.

 

[uart]

BTW. You calculated the error incorrectly, however there is no reason why the percentage error could not be huge when calculated at a single point.

For example, what would the percentage error by at t=0?

 

[alex.daciz]

Well spotted, it should be -1.2 but re-calculating V at 20ms it's still 70.5V. How have I calculated the error incorrectly?

 

[uart]

Well spotted, it should be -1.2 but re-calculating V at 20ms it's still 70.5V. How have I calculated the error incorrectly?

Using your equations I get (2) V at 20ms = 82.9 + 26.9 - 13.1.

 

[alex.daciz]

Sorry my calculator wasn't in radians! Would that then make the error 3.3%?

 

[jitznerd]

Hi
Im stuck on the same question. I've been using 141.4sin(2pi x f(120) x 0.02), which gives me 9.41v
28.3Sin(2pi x 360 x 0.02) = 21.45v
14.1sin(2pi x 600 x .02 - 1.2) = 18.08v

Then added these up to give combined voltage at 20ms of 48.93v
This is obviously a diffenrent answer to answers above, could someone please point out if I am doing something wrong.
Many thanks