Although the expression for steady state load flow equation contain trigonometric functions still they are called as algebraic nonlinear equations instead of transcendental nonlinear equations. Why is it so?
Dear Rajanarayan,
Bejo is right. The power flow equations are obviously non-linear and therefore superposition doesn't hold.
I think the reason is that the trigonometric terms only occur if you state the power flow equations on polar coordinates. in Cartesian coordinates they result in polynomials which in turn are algebraic.
But when thinking about the power flow equations one should not forget that they are actually complex valued. I personally prefer analysing them in Cartesian coordinates anyway, rather than polar, because they a) stay somewhat simpler and b) there analysis based on computers is much faster (trigonometric function take a real long time to determine).
For further reading, you might want to have a look at work by Thomas J. Overbye, who is an authority when it comes to analysis of these equations. And he's even kind enough to also make his lecture notes publicly available. A good introduction are the lecture notes about power flow in his course ECE476, available here: https://courses.engr.illinois.edu/ece476/
Furthermore you might want to consider that another feature of the complex-valued power flow equations is that they are not differentiable. Since they are complex-valued, they would need to be complex differentiable and therefore have to fulfil the Cauchy-Riemann equations - which they don't (you might want to try yourself to see that they don't. I really recommend doing this in Cartesian coordinates, though).
But in short: I think calling them algebraic refers to their formulation in Cartesian coordinates.
I hope this helps.
best regards,
Olav
The nature of the steady state load flow equations are nonlinear algebraic one. Both the above answers are correct.
Even the load flow equation can be written in rectangular form which never have any trigonometric function.
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