# Mathematical as (5) (b) DG at lagging power factor

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

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=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.