Dear Researchers,
Grid impedance measurements/estimation techniques have been used to find the value of resistance and reactance of a three phase line. I would like to know the technical reason, why the values of R and X of a three phase lines cannot be accurately measured through R=V^2/P and X=V^2/Q considering the power factor unity just for simplicity. Technical reasons would be appreciated. Thank you.
Ali Jafer Mahdi Dear Professor, if you could provide your input in this problem. Please tag your friends if you think they can respond to this.
Hi Shah,
The above equations " R=V^2/P and X=V^2/Q " cannot give the correct values of R and X parameters of the transmission line, sine the P&Q here are the power flow in the transmission line.
If you would like to use the above equations to find the grid impedance components, then you will need to find first the power losses in the transmission line ( ΔP and ΔQ). After that, you can calucate the Rg and Xg based on the following equations:
Rg=V^2/ΔP
Xg=V^2/ΔQ
Hopefully, this answer can help you.
Dear Nabil Mohammed , Your answer completely makes sense. Thank you for clearing it for me. As we understand the fact that total amount of losses are unknown in the three phase line therefore these equations cannot give us the exact resistance and reactance. While the P and Q are the load parameters. Thank you.
Dear Shah Fahad ,
As you mentioned that usually the total amount of losses are unknown, maybe not accessible/ measurable easily. Additionally, the above equations of Rg and Xg give correct results only and only if the three-phase system is balanced and the phases cables/headlines are identical.
Therefore, grid/line impedance identification techniques are used to estimate the Rg and Xg values.
The impedance calculated by R=V^2/P and X=V^2/Q is apparent impedance seen by a bus, and NOT the impedance of line connecting to grid. It has nothing to do with losses... (The concept is same as used by distance relays). Such a calculation would give correct values of impedance if and only if there is a bolted fault at the end of line!!! (Same concept as a short circuit test, which can't be practically performed for grid scale applications!!!).
However, if we have synchronized voltage and current measurements on both ends of line, then we can get line impedance by simply Zline=(Vs-Vr)/(I_line)...
Dear Pankaj Achlerkar , Thank you for your response. Can you please share a reference article or Book for understanding this concept in more detail ?
Thank you.
Dear Shah Fahad, you can see the following document for understanding the meanings of R and X computed from V^2/P and V^2/Q...
https://na.eventscloud.com/file_uploads/121fe1ee46274aad56a3b993da3bc7f4_per_pap.pdf
Hi Fahad,
If you apply voltage V across the terminals of a resistance R, then the power absorbed by the resistance is P given by P=V^2/R (This equation can be derived simply from Ohm's law.). To use the same equation in the context of line, the voltage V should be the voltage drop along the line (not the voltage measured at one point on the line), and P is the power loss along the line (not the total power flow along the line). Therefore, you cannot simply use the measured value (which are total power flow (P) and the voltage (V) at one point in the line V) in the above formula to calculate the resistance of the line.
I hope this helps!
Thank you.
Dear Roshan Sharma This couldn't be any more simpler. Thank you for explaining it in a more simple way.
Hi fahad,
Grnerally, in the transmission lin is composed of both resistance and inductance path. Due to that, in the transmission line both power such as active and reactive power is avialable. As the line contains both parameter resistance and inductance, the total resistantance can not be directly calculated from the avialable power. In transmission line, the total power is equal to 'p' and total impedance 'z'. Z is the composition of R+jx. If we are telling about point-point calculation then you can get directly get resistance by using ohms law R=v^2/p. However. As per your question R+jx=v^2/p.
Hope you will get your answer. Thank you
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