# Electrical power systems mathmatetics Essay Example

Power
system
protection

Feeder 1: Load = 14MVA; PF= 0.7 lagging.

Load is delta connected with impedance per phase = Z1

Taking line voltage, VLL = 11KV

1. Calculate Z1 per phase

Power (S) = VLL* ILL =

1. Phase currents

Source line to line voltages is equal to load line to line voltages.

Load line to line voltages is same as phase voltages for delta connection

= 1273.15A

=1273.15A

=1273.15A

1. Phasor diagram

d). using Kirchoff’s current law

Ia = IAB – ICA

= 1273.15 — 1273.15

=1273.15
A

Ib = IBC – IAB

=1273.15 — 1273.15
A

=1273.15
A

Ic = ICA — IBC

=1273.15 — 1273.15

=2205.16
A

circuit diagram

feeder 2:

S = 11 MVA, 0.8 PF lagging

VL = 11000V

Line voltage =
* Phase voltage

= 6350.85V

Van = 6350.85V

Vbn = 6350.85V

Vcn = 6350.85V

impedances Z for each phase.

For a star connection,

h). line currents into the load

=1730.48A

=1730.48A

=1730.48 A

I = Ia + Ib + Ic

=1273.15
A + =1273.15
A +=1273.15
A

j). feeder 1 currents when two feeders are paralled.

k). feeder 2 currents when two feeders are paralled.

l). residual current for feeder 1

m). residual current for feeder 2

paralleling the feeders without disabling the sensitive earth fault protection can cause the feeders to trip since the currents may be unbalanced as a result of the residual currents.