Calculating phase currents practical approach

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1

I have a three phase circuit for my workshop which consists of -

  1. One three phase motor in delta configuration which is of 0.75 kW (power factor -0.9)
  2. One three phase transformer (500 MVA converting 415 V to 24 V)
  3. Two 60 watt bulbs on Red phase (power factor -1)
  4. Two 70 watt fans on Yellow phase (power factor -0.9)
  5. One AC on Blue phase (2400 watt, power factor - 0.8)

The supply voltage (line to line) is 415 V

I want to know how much current is being drawn in each phase.
I am not sure but although the load is unbalanced, however it may be the voltage is balanced. The 415 volt power supply is from electricity company.

2

I find that AI’s are good at this type of thing; here’s what perplexity & claude had to say:

To calculate the current drawn in each phase of your three-phase circuit, we need to consider the various loads connected to each phase and their respective power factors. Let’s break down the calculations for each component and then sum up the currents for each phase.

Calculations

First, some important notes:

  1. For a balanced 415V line-to-line supply, the phase voltage is 415/√3 = 239.6V
  2. We’ll need to distribute the three-phase loads across all phases
  3. We’ll calculate single-phase loads on their respective phases

Let’s calculate each load’s current:

  1. Three Phase Motor (Delta Configuration):
  • Power = 750W
  • Line voltage = 415V
  • Power factor = 0.9
  • Line current = P/(√3 × VL × PF)
  • Line current = 750/(√3 × 415 × 0.9) = 1.16A This current is equal in all phases.
  1. Three Phase Transformer:
  • 500 MVA seems extremely large for a workshop. This might be a typo, but I’ll calculate anyway:
  • Full load current = MVA × 10^6/(√3 × V)
  • = 500 × 10^6/(√3 × 415) = 696.41 kA This seems unrealistic for a workshop. Please verify if this rating is correct.
  1. Red Phase Loads:
  • Two 60W bulbs = 120W total
  • Phase voltage = 239.6V
  • Power factor = 1
  • Current = 120/239.6 = 0.50A
  1. Yellow Phase Loads:
  • Two 70W fans = 140W total
  • Phase voltage = 239.6V
  • Power factor = 0.9
  • Current = 140/(239.6 × 0.9) = 0.65A
  1. Blue Phase Loads:
  • One AC = 2400W
  • Phase voltage = 239.6V
  • Power factor = 0.8
  • Current = 2400/(239.6 × 0.8) = 12.52A

Total current in each phase (excluding transformer):

  • Red phase: Motor (1.16 A) + Bulbs (0.50 A) = 1.66 A
  • Yellow phase: Motor (1.16 A) + Fans (0.65 A) = 1.81 A
  • Blue phase: Motor (1.16 A) + AC (12.52 A) = 13.68 A

These values would represent a more typical unbalanced load scenario for a workshop. The blue phase draws significantly more current due to the AC unit, while the red and yellow phases have relatively lower currents. It’s important to note that in a real electrical system, the voltage would likely become slightly unbalanced due to the unequal loading of the phases.

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3

I’m curious if the bot(s) noticed this, or did you add that comment?

Capture
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Image and caption courtesy of The Ultimate FAQs Guide To 500 MVA Transform

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4

When I first read the original post, I thought “this is a very strange question for a homework assignment.”

So just for giggles, I asked ChatGPT to calculate the wire size required for the 700,000 amps at the specified 24V AC output voltage for the X-former.

Answer: The required cross-sectional area is approximately 326.67 square meters
I’ve seen some impressive Bus Bar, but not a 20meter Diameter conductor.

Ya, I’m thinking we have an issue with some Units in the problem statement :rofl:

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5

I wonder about the nature of the load on the 24V output of the 500 MVA transformer :wink:

6

All of the above! I noticed because I considered buying a 125kV unit a few months ago in an auction (to re-sell) and thus was slightly familiar with common sizes/prices…but both AI pointed out that it there was very likely an error in the # or units :slight_smile: