Mathematical equations are

presented here to determine optimal DG rating at unity and lagging power factor

to minimise total power losses. Place these DG sizes at each bus except source bus

and run the load flow to plot the total real power loss variation with DG size.

Then select the node at which loss saving is maximum and obtain the corresponding

DG size.

= total active power loss

=total reactive power loss

=branch

current

=branch

resistance

=active

component of branch current

=reactive

component of branch current

=loss

associated with active component of branch current

=

loss associated with reactive component of branch current

(1)

(2)

(3)

(a)

DG at

unity power factor placed at bus ‘k'(Novel Method)

=active component of current supplied by DG

at node ‘k’

(4)

Subtract Eqn. (2) from Eqn. (4)

or

For maximum loss saving

required current to be supplied by DG is given by

= is the voltage magnitude of DG at node ‘k’

Optimal size of DG at unity

power factor is given as

(5)

(b) DG

at lagging power factor placed at bus ‘k’ (Modified Novel Method) 43

(6)

Subtract Eqn.(2) from Eqn.(6)

(7)

For

minimum loss, the following conditions are applied.

(8)

(9)

From eqn. (7)

(10)

(11)

, (12)

(13)

Equation (13) can be written as:

(14)

From eqn. (14), the equations can be derived for maximum loss

savings as:

(15)

(16)

Solving eqns. (15) and (16), we get components of currents as:

(17)

(18)

=active

component of the current to be supplied by DG for maximum loss saving at node

‘k’

=

reactive component of the current to be supplied by DG for maximum loss saving

at node ‘k’

(19)

(20)

=optimal

real power supplied by DG at power factor

at bus ‘k’

=optimal

reactive power supplied by DG at power factor

at bus ‘k’

(21)

(22)

(23)

Using eqns. (21) and (22), optimal DG sizes

can be obtained at lagging power factor respectively.