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Three phase delta load problem

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skyline1397

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Hi all,
I have solved the problem attached and my answer isn't the same as the solution manual. Can you please review and advise me if I am wrong or not?

The problem is:
problem.png

The solution manual approach:
solution manual.png

My approach:
my solution.png
 

BradtheRad

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It's a lot to expect, for a student to understand immediately how power factor behaves, how the formulas are derived and how to apply them.

A simulation can further our understanding, now that we have computers. I recommend a simple circuit consisting of an inductor and resistor, powered from 240VAC 60Hz. (Later you can add the correction capacitor.)

Examine voltage and current waveforms.
In particular notice how the Ampere waveform does not coincide with the supply voltage waveform, but is delayed for a fraction of a cycle.

For load impedance your approach agrees with the solution. 6.144 ohmic and some inductive. In series their combined effect produces power factor 0.8.
I guess 6kW is the 'real' power consumed. At 240V this calculates to 25A in 9.6 ohm effective impedance (6.144 + a few ohms 'choke' effect of the inductor).
Notice that power factor=.9 requires less inductor.
Power factor =.7 requires more inductor.

Your third image seems to omit some of your own calculations.
To select pfc capacitor value, the aim is to achieve resonance with the RL load at 60 Hz. Then the Ampere waveform shall coincide with the supply voltage waveform. The real Ampere level can be minimized. It drops to 25A.

It helps to experiment with a capacitive load too. You can observe the advanced timing of the Ampere waveform as compared to the supply voltage waveform. Experiment by trying various RC combinations.

- - - Updated - - -

My above reply has to do with a single phase AC supply. It makes for a simpler learning environment. The exercise specifies a 3-phase supply which creates complications.
 

skyline1397

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Thanks, Mr. Brad. Which software would be easy to simulate such problems i.e. three phase circuits?
 

BradtheRad

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Thanks, Mr. Brad. Which software would be easy to simulate such problems i.e. three phase circuits?
Falstad's animated interactive simulator is easy to draw schematics, add or remove components, change values, create scope traces.
Free to download and use at:

www.falstad.com/circuit

This is a 3-phase 230VAC system. Scope traces tell the story. LED's light to indicate current flow.

3 phase delta 230V AC supplies 6 led's show current direc.png
 

KlausST

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Hi,

Thanks, Mr. Brad. Which software would be easy to simulate such problems i.e. three phase circuits?
Since this is very basic .. I assume almost all analog simulators should do.
Ltspice for sure...

Klaus
 

c_mitra

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Can you please review and advise me
I do not understand how do you get

I_p=31.25/0-acos(0.8)

where I use acos function as the inverse function as you have written.
 

wondrous

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Falstad's animated interactive simulator is easy to draw schematics, add or remove components, change values, create scope traces.
Free to download and use at:

www.falstad.com/circuit

This is a 3-phase 230VAC system. Scope traces tell the story. LED's light to indicate current flow.

View attachment 151111
Thanks mr BradtheRad for the simulator
but how to download it
 

BradtheRad

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how to download it
It took a bit of searching to find his downloadable zip file since there are additional options to package the simulator.

Click the link below, then find the line which says: "Zip archive of this applet. (double-click on circuit.jar to run)" and click that.

http://www.falstad.com/circuit-java/

Or it may be sufficient simply to click this link:

http://www.falstad.com/circuit-java/circuit.zip

You need Java on your computer to run the applet. Java is a popular programming language. There are reports of hacker vulnerabilities in Java but updates are issued with the intent to eliminate these. It's a good idea to so some research to help you decide.
 

wondrous

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Thanks mr BradtheRad
sorry for let you search to me
i will do my effort
thanks again
 

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