Calculating Three Phase Power Load: Help & Homework Statement

[Tomas_89]

Homework Statement

I have an exam coming up and one of the practice questions is as follows
A 415V 50Hz three phase supply energises a balanced star-connected load through a three phase feeder with a per-phase series impedance of Zline = ( 0.165 + j0.413 ). A power meter at the source end of the feeder measures the power delivered to the feeder-load combination as 23.3kW at a lagging power factor of 0.9.

1. Calculate the magnitude of the supply line current in the feeder.

2. Calculate the real and reactive power delivered to the load, and hence determine the line to line voltage that is developed at the load end of the feeder. A delta-connected capacitor bank is connected across the supply at the source end of the feeder, so as to improve the power factor of the feeder-load combination.

3. Determine the capacitor value required to ensure that the power factor as seen by the

4. Calculate the overall power factor of the feeder-load combination if the capacitor bank supply is unity is accidentally connected in star rather than delta.[/B]

Homework Equations

The Attempt at a Solution

I have done the following

1. Power = 23.3kw
Reactive Power = 11.3 KVAR
Apparent Power = 25.9 KVA

Current = 36.03 amps

2. Load, by working out the power loss through the three-phase feeder
Ploss = 36.03^2 x 0.165 = 214.2 watts
Power = 23300 -214 = 23086 watts

Reactive Power loss = 36.03^2 x .413 = 536.14 VAR
Reactive Power = 11300 - 536.14 = 10764 VAR

Apparent Power at the load end of the feeder = 25472 VA

Voltage at the load end
V = 25472/sqrt(3)*36.03 = 412.49 volts

3. Capacitor value
Xc = 3*415^2/11300 = 45.72 ohms
C = 69.62 uF

4. Overall power factor if accidentally connected as a star instead of delta
Zy = 45.72/3 = 15.24 ohms

Q = 3*415^2/15.24 = 33902 VAR

pf = 23300/33902 = .68 power factor

Any help or guidance would be most appreciated. If any more working out is required let me know and I'll post the rest up.

Cheers

 

[gneill]

Homework Statement

I have an exam coming up and one of the practice questions is as follows
A 415V 50Hz three phase supply energises a balanced star-connected load through a three phase feeder with a per-phase series impedance of Zline = ( 0.165 + j0.413 ). A power meter at the source end of the feeder measures the power delivered to the feeder-load combination as 23.3kW at a lagging power factor of 0.9.

1. Calculate the magnitude of the supply line current in the feeder.

2. Calculate the real and reactive power delivered to the load, and hence determine the line to line voltage that is developed at the load end of the feeder.


A delta-connected capacitor bank is connected across the supply at the source end of the feeder, so as to improve the power factor of the feeder-load combination.

3. Determine the capacitor value required to ensure that the power factor as seen by the

4. Calculate the overall power factor of the feeder-load combination if the capacitor bank supply is unity is accidentally connected in star rather than delta.[/B]

Homework Equations

The Attempt at a Solution

I have done the following

1. Power = 23.3kw
Reactive Power = 11.3 KVAR
Apparent Power = 25.9 KVA

Current = 36.03 amps

2. Load, by working out the power loss through the three-phase feeder
Ploss = 36.03^2 x 0.165 = 214.2 watts
Power = 23300 -214 = 23086 watts

Reactive Power loss = 36.03^2 x .413 = 536.14 VAR
Reactive Power = 11300 - 536.14 = 10764 VAR

Apparent Power at the load end of the feeder = 25472 VA

Voltage at the load end
V = 25472/sqrt(3)*36.03 = 412.49 volts

3. Capacitor value
Xc = 3*415^2/11300 = 45.72 ohms
C = 69.62 uF

4. Overall power factor if accidentally connected as a star instead of delta
Zy = 45.72/3 = 15.24 ohms

Q = 3*415^2/15.24 = 33902 VAR

pf = 23300/33902 = .68 power factor

Any help or guidance would be most appreciated. If any more working out is required let me know and I'll post the rest up.

Cheers

Hi Tomas_89, Welcome to Physics Forums.

Where the question statement says: "A power meter at the source end of the feeder measures the power delivered to the feeder-load combination as 23.3kW at a lagging power factor of 0.9", does that refer to the per-phase power delivered, or is it to be interpreted as a total delivered by all phases to the feeder-load? I realize that the interpretation may depend upon conventions or assumptions made by the given text or course content.

Some of your values you provide without showing your calculation method, so it's hard to tell what might have gone wrong if the values look a bit "off" to someone checking (particularly if the question interpretation is not certain for the checker). For example, can you show the details of how you arrived at your current magnitude value of 36.03 amps?

 

[Tomas_89]

Hey thanks for that, it's been taught per phase in this course so that's the assumption.

Power is equal to 23.3KW as stated.

The reactive power was calculated as:
Q = ( 23.3x10^3/0.9 (power factor) ) x sin(inverse cos (0.9)
Q = 11.3 KVARS

Apparent power :
S = P + jQ = √23.3^2 + 11.3 ^2
S = 25.9 KVA
For the current I used the apparent power formula (S = VI) and rearranged as
I = 25900VA/√3x 415V
I = 36.03 A