Complex Power Flow in a Single Phase Load:

Here we are going to discuss about complex power flow in a single phase load. Consider a single phase load fed from a source as in Fig. 4.9. Let

Complex Power Flow in a Single Phase Load

 

When θ  is positive, the current lags behind voltage. This is a convenient choice of sign of θ in power systems where loads have mostly lagging power factors.

Complex Power Flow in a Single Phase Load

Complex power flow in the direction of current indicated is given by

or

 

Here

It immediately follows from Eq. (4.17) that Q, the reactive power, is positive for lagging current (lagging power factor load) and negative for leading current (leading power factor load). With the direction of current indicated in Fig. 4.9, S = P + jQ is supplied by the source and is absorbed by the load.

Phasor Diagram of Complex Power

Equation (4.17) can be represented by the phasor diagram of Fig. 4.10 where

Complex Power Flow in a Single Phase Load

 

 

If two (or more) loads are in parallel as in Fig. 4.11

 

As per Eq. (4.19), Kirchhoff’s current law applies to complex power flow (also applies separately to real and reactive powers).

Complex Power Flow in a Single Phase Load

In a series RL load carrying current I,

 

In case of a series RC load carrying current I,

Complex Power Flow in a Single Phase Load

 

Consider now a balanced three-phase load represented in the form of an equivalent star as shown in Fig. 4.12.

Complex Power Fed to Three Phase Load

The three phase complex power flow fed into load is given by

If

Then

Here

Complex Power Flow in a Single Phase Load

where

 

 

 

If VL, the line voltage, is expressed in kV; and IL, the line current in amperes, S is in kVA; and if the line current is in kiloamperes, S is in MVA.

In terms of load impedance Z,

Complex Power Flow in a Single Phase Load

 

Substituting for IL in Eq. (4.20)

Complex Power Flow in a Single Phase Load

 

If VL is in kV, S is now given in MVA. Load impedance Z if required can be calculated from

Complex Power Flow in a Single Phase Load