Electrical Engineering, power system, transmission line

[louisnach]

Homework Statement

A 400 kV transmission line has a length of 500 km and a reactance of 0,4 Ω/km. How much power can you transmit, if the power angle (the angle between the voltages of the beginning and the end) is limited to 25 degrees? What would then be the line’s boundary power limit for static stability ?

The Attempt at a Solution

Hi, in the lecture we have a formula that give P =(Vs*Vend)*sin(power angle)/Z
where Z is the impedance of the line so i guess it is 500*0.4 reactance, Vs i=400kV (source voltage) but in the problem i don't have Vend voltage at the end of the line, how can i solve the probleme without knowing that ?

 

[donpacino]

Vs and Vend are the magnitude of voltage. So what is the voltage drop across the line?

Hint, look at the given impedance of the line. V=IZ

 

[cnh1995]

Vs and Vend are the magnitude of voltage. So what is the voltage drop across the line?

Hint, look at the given impedance of the line. V=IZ

This problem can't be solved without knowing the sending end voltage. The given 400kV is the receiving end voltage.

However, I believe OP can assume both the voltages to be equal in magnitude (which is mostly the case in practice, thanks to VAR compensation).

 

[donpacino]

The end voltage CAN be solved for with the given material.

Here is a hint.
Given the impedance of the transmission line, what is the voltage drop across the line (in magnitude).

 

[donpacino]

However, I believe OP can assume both the voltages to be equal in magnitude

another hint, you don't need to assume

 

[cnh1995]

what is the voltage drop across the line (in magnitude).

How can we determine it without knowing the current? There is no information about the load that is connected to the receiving end.

 

[donpacino]

How can we determine it without knowing the current? There is no information about the load that is connected to the receiving end.

the magnitude of the voltage loss will not change because there is no resistive element. therefore the voltage drop will always be zero

 

[cnh1995]

the magnitude of the voltage loss will not change because there is no resistive element. therefore the voltage drop will always be zero

No.
What about the I*X_L drop across inductive reactance of the line? This is why you need series compensation in the line.

Absence of resistance means no power loss in the line. But that doesn't mean both the voltages are equal in magnitude. Without knowing anything about the load (pf and MVA) or the sending end voltage, this problem can't be solved. Or OP can simply assume a flat voltage profile (as a result of compensation, which is not mentioned).

 

[donpacino]

No.
What about the I*X_L drop across inductive reactance of the line? This is why you need series compensation in the line.

Absence of resistance means no power loss in the line. But that doesn't mean both the voltages are equal in magnitude. Without knowing anything about the load (pf and MVA) or the sending end voltage, this problem can't be solved. Or OP can simply assume a flat voltage profile (as a result of compensation, which is not mentioned).

Im talking about the absolute magnitude, not instantaneous magnitude, which are the voltages listed in the equation. I should have clarified.

 

[cnh1995]

Im talking about the absolute magnitude, not instantaneous magnitude.

I am talking about rms voltage drop. That can never be zero unless you provide some compensation.
Read:
https://www.physicsforums.com/threads/ac-power-analysis-part-2-network-analysis-comments.864530/.

 

[louisnach]

Thanks for your replies of both of you, i think indeed we have to consider same magnitude so by using the formula it is just (Vs*Vs)/(500*0.4)*sin(25 degrees),