A.C. Voltage waveforms and harmonics?

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Discussion Overview

The discussion revolves around the calculation of an A.C. voltage waveform that includes harmonics, specifically focusing on the expression for the voltage waveform, the voltage at a specific time (20ms), and the percentage error compared to an ideal voltage. Participants are exploring the mathematical expressions and calculations involved in these aspects.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant presents an expression for the voltage waveform that includes the fundamental frequency and its harmonics, but expresses doubt about the accuracy of their calculations due to a large percentage error.
  • Another participant corrects the phase angle of the 5th harmonic from lagging to leading.
  • A different participant points out that the percentage error could be significant when calculated at a single point in time, questioning the relevance of the error at t=0.
  • One participant recalculates the voltage at 20ms and arrives at a different value, prompting questions about the accuracy of the calculations.
  • Another participant realizes their calculator was not set to radians, which affects their calculations and suggests a revised percentage error.
  • A new participant shares their own calculations for the voltage at 20ms, which differ from previous results, and seeks clarification on potential errors in their approach.

Areas of Agreement / Disagreement

Participants express differing views on the calculations of the voltage at 20ms and the resulting percentage error. There is no consensus on the correct approach or final values, as multiple calculations yield different results.

Contextual Notes

Participants have noted potential issues with phase angles and calculator settings, which may affect the accuracy of their calculations. The discussion highlights the complexity of calculating A.C. voltage waveforms with harmonics.

alex.daciz
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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!?
 
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v = [141.1sin(240πt)] + [28.3sin(720πt] + [14.1sin(1200πt+1.2)]

That 5th harmonic is 1.2 radians leading, not lagging.
 
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?
 
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?
 
alex.daciz said:
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.
 
Last edited:
Sorry my calculator wasn't in radians! Would that then make the error 3.3%?
 
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
 

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