The complex power injected by the source into the  th bus of a power system is
Where  is the voltage at the  th bus with respect to ground and  is the source current injected into the bus.
The load flow problem is handled more conveniently by use of  rather than . Therefore, taking the complex conjugate of Eq. , we have  Substituting for  , we can write
Equating real and imaginary parts
In polar form
Real and reactive power can now be expressed as
- DECOUPLED LOAD FOLW METHODS
An important characteristic of any practical electric power transmission system operating in steady state is the strong interdependence between real power and bus voltage angles and between reactive power and voltage magnitudes. This interesting property of weak coupling between  and  variables gave the necessary motivation in developing the decoupled load flow (DLF) method, in which  and  problems are solved separately.
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