Reactive Power Flow Equation

[smokinfiddler]

In the NCEES Handbook there is a formula for real power flow, but it does not refer to reactive power flow. In the study guide I am using, the equation for reactive power flow is shown as the image below. I'm trying to understand how this equation is derived, since I won't have access to it during the exam.

Thank you in advance for any guidance you can provide!

 

[Zach Stone P.E.]

I'm actually hosting a free webinar next Friday showing how to derive and use this formula for reactive power flow.

It's a continuing education webinar for professional engineers but it is still applicable to the PE exam if you'd like to attend.

I'll be deriving both the real power transfer formula (Pe) and the reactive power transfer formula in your post.

There will also be a couple of example problems using these formulas to solve PE style problems, and I'll also be using a model during the webinar that shows how each of these relationships change in real-time with respect to other changes such as voltage magnitude, electrical torque angle, etc based on phasor digrams.

You can sign up to join the free webinar at www.ohmgurus.com.

Look for the "Power Flow Calculations: Real and Reactive Power Transfer Between Buses by Zach Stone, P.E." webinar scheduled for Friday, July 19th, 2024 at 12:00 PM and click add to calendar.

It looks like this on the page:

 

[xnuke]

The study guide equation in the original post is incorrect as the cosine term is not outside the fraction. See the derivation of equations for both active and reactive power flow from the sending end in the attached pdf. (Corrected per Zach's comment below)

 

[Zach Stone P.E.]

The study guide equation in the original post is incorrect as the cosine term is not outside the fraction. See the derivation of equations for both active and reactive power flow in the attached pdf - I think it is right.

The final formula in this PDF is actually incorrect because it refers to it as "the reactive power delivered from the sending end to the receiving end."

Instead, the formula in the PDF is the complex receiving power sent by the sending bus.

It includes the reactive power absorbed in the line.

The reactive power that gets absorbed in the line does not make it to the receiving end.

It's a common error that I see just about anytime reactive power transfer is discussed.

I should have the videos from the seminar mentioned above available on my YouTube channel in the next week or so, they explain this error and also derive the correct formula for reactive power transfer

 

[xnuke]

I understand. The sending end reactive power is larger than the receiving end reactive power by I^2X. I fixed the pdf to reflect that.