How Do You Derive the Equation for a Medium-Distance Power Transmission Line?

[MissP.25_5]

Hello.
I need to derive this equation (attached), can you help me please?

That's the equation for a two-pair terminal medium-distance power transmission line (20~100km).
I have no idea how to start it. Can someone guide me, please?

 

[NascentOxygen]

Hi MissP.25_5. Perhaps a clue lies in that bottom line.

Try a Pi network, with the two vertical limbs each a capacitor, and the horizontal part R + L.

So this leaves the Earth as a straight-through link common to both ports.

Note, I haven't examined this further.

 

[MissP.25_5]

Hi MissP.25_5. Perhaps a clue lies in that bottom line.

Try a Pi network, with the two vertical limbs each a capacitor, and the horizontal part R + L.

So this leaves the Earth as a straight-through link common to both ports.

Note, I haven't examined this further.

Oh, yes! That's right, the Pi network is the solution! I just solved it, thanks to you!

 

[NascentOxygen]

Oh, yes! That's right, the Pi network is the solution! I just solved it ...

Glad it worked! http://imageshack.com/a/img593/2259/girlpower.gif

 

[rezeew]

Hello there,

I am happy to assist you with deriving the equation for a two-pair terminal medium-distance power transmission line. To start, let's break down the equation and understand each component.

The first part of the equation, Vt, represents the voltage at the transmitter end of the power line. This can be calculated using Ohm's law, which states that voltage is equal to current multiplied by resistance (V=IR). In this case, the resistance is the total resistance of the power line, which includes both the resistance of the conductors and any additional resistance from components such as transformers or switches.

The second part of the equation, Vr, represents the voltage at the receiver end of the power line. This can also be calculated using Ohm's law, with the resistance being the same as the transmitter end.

The third part of the equation, Zt and Zr, represent the impedance at the transmitter and receiver ends, respectively. Impedance is the total opposition to current flow in the circuit, and it takes into account both resistance and reactance (the opposition to current flow caused by inductive and capacitive elements in the circuit).

The fourth part of the equation, It and Ir, represent the current at the transmitter and receiver ends, respectively. These can be calculated using Ohm's law, with the voltage being the same as the transmitter and receiver ends.

Finally, the term e^(-αL) represents the attenuation of the power line, which takes into account the loss of energy due to resistance and reactance as the power travels through the line.

To derive this equation, you will need to use a combination of Ohm's law and other electrical principles such as Kirchhoff's laws and the power formula (P=IV). It may also be helpful to draw a circuit diagram to visualize the different components and their relationships.

I hope this helps guide you in deriving the equation for a two-pair terminal medium-distance power transmission line. If you have any further questions, please don't hesitate to ask. Best of luck with your calculations!