Re: Where do we use the 1.73 when calculating 3 phase
Ronald, I agree.
Three phase power calculations, and in particular, when to use that "magic number", the square root of 3 (1.73) seemed to be the most difficult concept for my apprentice classes.
And it was for me too, back when I was trying to learn it.
Some how, each of us has to "get-a-hold" of where this constant comes from, and why it shows up in three phase power calculations.
Just in case there are folks here that are interested, I?d like to try to explain this in "electrician?s language"
The simplest formula for three phase power in a balanced load, if the phase voltage and phase current (the voltage and current values for
each phase) are known, is ?
E phase x I phase x 3
Example ? Three single phase heaters, each rated 120 volt, 10 amp, 1200 watt, are wye-connected to a 208 volt three phase supply. Calculate the total power used.
The simplest way, when the watts rating of each heater is known is ? 1200 x 3 = 3600 watts.
If the watts rating of each heater is not known ?
Watts = E phase x I phase x 3
Watts = 120 x 10 x 3
Watts = 3600
However, in the real world, the
phase values of voltage and current are usually not known, so standard procedure is to use the
line values of voltage and current.
For instance, you can?t measure the individual phase currents in a motor without pulling apart the terminal connections. What you measure in the wires supplying a three phase load is the line voltage and current. Let?s call them E line and I line.
How do the line values of voltage and current compare with the phase values? That depends on whether the system is wye connected or delta connected.
Let?s look at that, in case it isn?t well understood.
In a wye connection -
- E line = E phase x 1.73
- I line = I phase
In a delta connection -
- E line = E phase
- I line = I phase x 1.73
So, if you?re calculating the wye connected example above using the line voltage - 208 v, you can?t multiply E x I x 3 this time, because the voltage you are now using has already been multiplied by 1.73 once. (208 = 120 x 1.73) So in the formula, you multiply it by 1.73 again, which is the equivalent of using the phase voltage and multiplying by 3.
Watts = E line x I line x 1.73
Watts = 208 x 10 x 1.73
Watts = 3600 (3598.4)
For delta connected loads, it is the
line current that is equal to the phase current times 1.73, so again the power formula has to be Watts = E line x I line x 1.73
In most cases we do not even know whether the loads are wye or delta connected, but it does not matter, as 1.73 must be used in the power calculation if the line voltage and current values are used.
The sketch below can be used for practice, but it is
not the same example as the one above.
Ed
[ February 19, 2005, 06:10 PM: Message edited by: Ed MacLaren ]
