# 3 Phase Systems Theory and Procedure -- Determining Average Power

• OmniNewton
In summary, the conversation discusses three different scenarios involving three-phase circuits with different configurations of load impedances. Each scenario requires a different procedure for calculating the average power, depending on the specific configuration of the circuit. The first scenario involves a delta-connected load with 2Ω line resistances, while the second scenario involves a star-connected load without any line impedance. The third scenario is a general case where the line voltage and current must be found in order to calculate the power.
OmniNewton

## Homework Statement

Consider the 3 following Scenarios:
1.

2.

rms value of line voltage is 208 V

Three equal impedances, 60 +j30 W each, are delta-connected to a 230-V rms, three-phase circuit. Another three equal impedances, 40 +j10 W are wye-connected across the same circuit at the same points.

## Homework Equations

S = 3|Ia|^2(Zy)
P = Real Component (S)

## The Attempt at a Solution

How come when analyzing circuit one the procedure for determining the average power is to
1. find the line current Ia which is simply 110<0 divided by the impedance (Z(delta)/3 + 2)
2. calculate S = 3|Ia|^2(Zy) where Zy =(Z(delta)/3 + 2)
3. take the real component of S and that is your average power.

But when analyzing circuit 2 the procedure is:
1. Convert Van = 208 to Vp = 208/ root(3)
2. compute S by using S = (3 * Vp^2)/ (Zpcomplex conjugate)
3. take the real component of S and that is your average power.

And when analyzing circuit 3 the procedure is:
1. Find the line current
2. compute S by using S = (3 * Vs * (complex conjugate of line current)
3. take the real component of S and that is your average power.

Essentially I am kind of confused about what this Vp, Zp are that is used in the second consideration. Also why for every one of these scenarios the procedure for getting average power is different and the previous methods do not work. All of these examples seem the exact same is what really confuses me. What makes these 3 analyses different? How do I know what procedure to follow? I am doing self study so any help that can be provided is greatly appreciated.

Last edited:
OmniNewton said:
How come when analyzing circuit one the procedure for determining the average power is to
1. find the line current Ia which is simply 110<0 divided by the impedance (Z(delta)/3 + 2)
2. calculate S = 3|Ia|^2(Zy) where Zy =(Z(delta)/3 + 2)
3. take the real component of S and that is your average power.
In this method, they have first converted the delta impedance into its star equivalent impedance and then Zstar=Zdelta/3 is used. Then of course the 2Ω line resistances come in series with the load impedances in the respective phases, so you see the term Z/3+2 ohm in the equation.
OmniNewton said:
Convert Van = 208 to Vp = 208/ root(3)
Van=Vphase and in star, Vph=Vline/√3. Are you sure the problem says Van=208 V?
OmniNewton said:
But when analyzing circuit 2 the procedure is:
1. Convert Van = 208 to Vp = 208/ root(3)
2. compute S by using S = (3 * Vp^2)/ (Zpcomplex conjugate)
3. take the real component of S and that is your average power.
You can use the procedure in circuit 1 for this circuit too. This is already in star configuration, so you need not divide the load impedance by 3 as you did for circuit 1. But here, you do not have any line impedance and hence, you do not have a "voltage-divider" in the line. So, instead of calculating the line current like in circuit 1, you can directly use the given voltage to find the power.
OmniNewton said:
And when analyzing circuit 3 the procedure is:
1. Find the line current
2. compute S by using S = (3 * Vs * (complex conjugate of line current)
3. take the real component of S and that is your average power.
This is the "general" procedure and can be applied to any balanced three phase network.

Last edited:
OmniNewton
Oh I see thank you very kindly for taking the time to explain this. Yes problem 2 does say that the line voltage is that value.

Last edited:
OmniNewton said:
Yes problem 2 does say that the line voltage is that value.
That means Vab=208V, not Van as you have written.Van=208/root3 V.

## 1. What is the purpose of 3 phase systems theory?

The purpose of 3 phase systems theory is to understand the behavior and characteristics of three-phase power systems. It involves analyzing the relationship between voltage, current, and power in a three-phase system and determining the average power consumption.

## 2. How is average power calculated in a 3 phase system?

In a 3 phase system, the average power is calculated by multiplying the line voltage, line current, and the power factor. The result is then multiplied by the square root of 3, which is the ratio between the line voltage and phase voltage in a three-phase system.

## 3. What is the difference between single phase and three phase power?

The main difference between single phase and three phase power is the number of phases. Single phase power has one phase, while three phase power has three phases. This means that three phase power can deliver three times the power of single phase power at the same voltage, making it more efficient for larger loads.

## 4. How is power factor related to three phase systems?

Power factor is a measure of the efficiency of a three phase system. It represents the ratio between the real power (in kW) and the apparent power (in kVA). A high power factor indicates a more efficient use of power, while a low power factor means there is wasted energy in the system.

## 5. What are some common applications of three phase systems?

Three phase systems are commonly used in industrial and commercial settings due to their higher power efficiency. They are also used in large appliances such as air conditioners, refrigerators, and washing machines. Additionally, three phase power is used in electric motors, which are found in various industrial equipment, pumps, and vehicles.

Replies
2
Views
1K
Replies
4
Views
2K
Replies
2
Views
1K
Replies
2
Views
4K
Replies
2
Views
5K
Replies
3
Views
2K
Replies
11
Views
2K
Replies
5
Views
7K
Replies
11
Views
2K
Replies
4
Views
1K