# Three Phase AC Systems

#### Paul Scholes

Joined Oct 13, 2004
1
Q1) a balanced 3 phase load has 3 coils, each with resistance of 27ohms & Inductance of 0.02H connected across a 3 phase 400 V, 50 Hz supply.

a) Determine the total Power dissipated iwhen the coils connected in star
B) det. the total pwer dissipated when the coils are connected in Delta.

Q2) 3 impedances each having a resistance of 10ohms and an inductive reactance of 25ohms are connected in star across a 400V 3 phase supple, calculate:
a) the line current
B) the power factor
c) the total power in kW

Q3) a 230V 3 phase voltage is applied to a balanced delta connected in 3 phase load of phase impedance (33-J25)ohms, calculate
a) the current in each phase
B) the active power consumed
c) the total reactive power supplied

#### Perion

Joined Oct 12, 2004
43
First, take a look at this web page. Check out the the star-delta or delta-star equivalent circuit (Fig. 3-15). Read through the article but don't worry if you don't understand everything. Look around the other sections at that web site and just get a feel for the material since it is directly related to your problems.

OK - now that you've seen some potentially useful stuff, you may have realized that the name of the game is to calculate the impedance for one coil. This will allow you to figure the phase current and voltage-current phase angle for a coil. Then you can use that info for each connection type (delta or star) to find the combined 3 phase values that the problems are requesting.

Coil impedance is found by the usual method for caculating a series RL circuit.

1. Figure the inductive reactance: XL = 2*pi*f*L (you were given the freq f and inductance L)

2. The impediance Z for the coil (where R=resistance): Z = sqrt(R^2 + XL^2)

3. voltage-current phase angle A = arctan(XL/R)

BTW - if ya want the power factor, PF = cos(A).

There's a worked out example on this web page which should be very helpful. Notice the phase angle and various power calculations that follow the impedance calculation in the example. These simple calculations could be pretty useful. Anyway, once you know the coil impedance you can easily calculate the phase current and current-voltage phase angle for one coil:

phase current I = E/Z where E is the voltage across the coil and Z is the impedance.

Just don't forget that since you need to use the phase voltage for this calculation the star connection's phase voltage will be V/1.73 (in Q1, phase voltage equals 400/1.73). The phase voltage for the delta connected coils will just be V (in Q1, V = 400 volts).

Now that you have the coil impedance, phase current, and voltage-current phase angle (and more ) go back and look at this info. Look at how the results of this single coil calculation can be used for total power calculations for both star and delta configurations. Getting any ideas about solving Q1? B)

Follow the same kind of analysis for the other questions and you should be good to go. You may need to review what is meant by "active power", "reactive power", "total power", and "power factor". This article describes them in a really clear way that may help you kick Q2 and Q3's butt. Also, I assume you know that an impedance of "33-J25" means that it is composed of a pure resistance R equal to 33 ohms and an inductive reactance XL equal to 25 ohms. If you're not sure about phasors and phasor notation take a look at this easy to understand page

Hope this gets you going.

Perion