## Mathematical current to be supplied by DG

Mathematical equations arepresented here to determine optimal DG rating at unity and lagging power factorto minimise total power losses. Place these DG sizes at each bus except source busand 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 correspondingDG size.

= total active power loss =total reactive power loss=branchcurrent=branchresistance=activecomponent of branch current=reactivecomponent of branch current                                                                  =lossassociated with active component of branch current=loss associated with reactive component of branch current                                                                                                         (1)                                                                                    (2)                                                                                                  (3)(a)  DG atunity power factor placed at bus ‘k'(Novel Method)=active component of current supplied by DGat node ‘k’                                         (4)Subtract Eqn. (2) from Eqn. (4)               or For maximum loss savingrequired current to be supplied by DG is given by  = is the voltage magnitude of DG at node ‘k’Optimal size of DG at unitypower factor is given as                                                                                                    (5)(b)   DGat lagging power factor placed at bus ‘k’ (Modified Novel Method) 43                                                                                                                                            (6)Subtract Eqn.(2) from Eqn.(6) (7)Forminimum loss, the following conditions are applied.

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(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 losssavings as:                                                                                                                  (15)                                                                                                                 (16)Solving eqns. (15) and (16), we get components of currents as:                                                                                                     (17)                                                                                                      (18)=activecomponent 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 savingat node ‘k’                                                                                      (19)                                                                                      (20)=optimalreal power supplied by DG at power factor   at bus ‘k’=optimalreactive power supplied by DG at power factor   at bus ‘k’                                                                                        (21)                                                                                       (22)                                                                                                    (23)Using eqns.

(21) and (22), optimal DG sizescan be obtained at lagging power factor respectively.

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