For a fixed value of complex power flow in a transmissi

For a fixed value of complex power flow in a transmissi on line having a sending end voltage V, the real powerloss will be proportional to

S = P + jQ = VI (cosφ + j sinφ) = VIe^jφ

P = I²R =		S		²	R =		S²R		×	1
		Ve^jφ					Ve^2jφ			V²

Alternately
Complex power,
VI* = P + jQ (taking V reference).

∴ I* =	P + jQ
	V

I* =	P - jQ
	V

I =	√P² + Q²
	V

∴ Real power loss = I²R

I =	P² + Q²	R
	V²

But (P² + Q² × R) = constant

∴ Power loss ∝	1
	V²