Drawing 3-Phase Voltage Waveforms

[JGrecs]

Homework Statement

Draw and label the 3-phase voltage waveforms where VAN= 347∠0° Vrms, VAB= 600∠30° Vrms, Frequency: 50Hz, Volts/Division 200, Time/Division: 2 ms

2. The attempt at a solution

Im really not sure how to tackle this one. My prof hardly went over this in lecture, but gave this out as an assignment (wtf). Does anyone how to go about starting this?

 

[Mr.Tibbs]

So for starters do you know how to convert from the frequency domain to the time domain? It might help get you in the right direction if you convert your readings.

 

[AugustCrawl]

3 phase systems in the most classical sense are provided by 3 sinusoidal voltage sources with:

(1) the same peak values
(2) which alternate at the same frequency
(3) which are displaced in time by 1/3rd of a cycle or 120 degrees

I would expect that you have three voltages which are out of phase (if you want to do the polar plot with the rotating vectors).

So if you had my three classical voltage waves - let's call them Va Vb Vc
and let's say that they are all oscillating at the same frequency, with a magnitude of 5V, but are out of phase.

then Va = 5<+120
Vb = 5<0
Vc = 5<-120

To convert from frequency to time domains in a really proper way is to move from a Fourier transform to a laplace transform. However I think this may not be needed in your case.

Were you to plot out the three waveforms that I have described you would see the following:
http://commons.wikimedia.org/wiki/File:3-phase-voltage.svg

So what you (probably) need to do is:
1) work out the phase difference (displacement along the time axis of your waves.. which ones lead and lag which other ones)
2) assume they are all operating at the same frequency (which they most likely are)... and understand the relationship between frequency and wavelength.. which can help you draw waveforms on the squares
3) use the voltage and time/division to space out your plot squares.

 

[AugustCrawl]

I think the information you have put up at present only describes 2 phases of your 3 phase plot.

VAN= 347∠0° Vrms, VAB= 600∠30

Unless the third phase is somehow "implied" or assumed to be at 0. Ie that the VAN phase happens at exactly the same time as this phase. Those two phases definitely have different magnitudes.. ie different heights on your plot if it is voltage against time... or different vector lengths on your rotational plot..

What exactly has he asked you to plot voltage against? :)

 

[rezeew]

As a scientist, it is important to approach any problem or assignment with a systematic and logical approach. In this case, the first step would be to understand the given parameters and variables. Here, we are given the three-phase voltage values (VAN and VAB), frequency, and the units for volts and time per division.

Next, we can use this information to plot the voltage waveforms on a graph. The vertical axis will represent voltage (in volts) and the horizontal axis will represent time (in seconds). The scale for the vertical axis will be determined by the given volts per division value, and the scale for the horizontal axis will be determined by the given time per division value.

To plot the three-phase voltage waveforms, we will need to use the given values to calculate the amplitude and phase of each waveform. For example, the amplitude for VAN will be 347 volts, and the phase will be 0 degrees. This means that at time t=0, the waveform for VAN will have an amplitude of 347 volts.

We can then plot the waveform for VAN, using the calculated amplitude and phase values, for one complete cycle (from 0 to 2 ms). Next, we can repeat the same process for VAB, using the given amplitude and phase values. The waveform for VAB will have a different amplitude and phase, which will result in a different waveform on the graph.

Finally, we can repeat this process for the third phase, VBC, which will have a different amplitude and phase than the first two phases. Once we have plotted all three waveforms on the graph, we can label them accordingly (VAN, VAB, VBC) and indicate the frequency (50Hz) on the horizontal axis.

In conclusion, drawing and labeling the 3-phase voltage waveforms requires a good understanding of the given parameters and a systematic approach to plotting the waveforms on a graph. With practice and understanding of the concepts, this task can become easier and more intuitive.