Solve Underground Cable Reactive Power: 127MVAr

[Lunat1c]

Hello,

I just got a small question.

If a 50Hz grid line is carried underground for a distance of 10km. And it is also known that the capacitance is 400nF per phase per km. What is the total reactive power generated in the 10km length?

Then I could say that we have a total of 400nF * 10 = 4000nF per phase.

$$Power = \frac{V^2}{X_c} = \frac{400k^2}{\frac{1}{2 * \pi * 50 * 4000nF}} = 127MVAr.$$

1. However, this is the power per phase isn't it? From my lecture notes it is the total reactive power however I can't figure out why.

2. Also, I'm trying to find the charging current in each phase of the line.

According to my lecturer power in each phase is the power I got earlier divided by 3, but the same capacitance is used if the formula I^2Xc is used.

Please help, this is really confusing me!

 

[Lunat1c]

Anyone please?

 

[berkeman]

Hello,

I just got a small question.

If a 50Hz grid line is carried underground for a distance of 10km. And it is also known that the capacitance is 400nF per phase per km. What is the total reactive power generated in the 10km length?

Then I could say that we have a total of 400nF * 10 = 4000nF per phase.

$$Power = \frac{V^2}{X_c} = \frac{400k^2}{\frac{1}{2 * \pi * 50 * 4000nF}} = 127MVAr.$$

1. However, this is the power per phase isn't it? From my lecture notes it is the total reactive power however I can't figure out why.

2. Also, I'm trying to find the charging current in each phase of the line.

According to my lecturer power in each phase is the power I got earlier divided by 3, but the same capacitance is used if the formula I^2Xc is used.

Please help, this is really confusing me!

What are you using for the "voltage"? The voltage that is listed for a 3-phase line does not show up across each wire pair...

 

[Lunat1c]

Sorry, my mistake. The question says it's a "400kV grid line"

 

[berkeman]

Sorry, my mistake. The question says it's a "400kV grid line"

So for a 400kV 3-phase transmission line, what is the voltage difference between each pair? See if the answer makes more sense now.

 

[Lunat1c]

I'm not sure I follow. I think I misunderstood the question to be honest. When you're told that a cable is a 400kV cable, what's the meaning of that exactly? I know that when it comes to 3 phase systems for example, when you're told that you have a 415V supply, that means that the line to line voltage is 415. However I'm unsure about this.