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Sched
Gen
Sched
Load
P
+ jQ
Li
Li
P
+ jQ
Gi
Gi
P
+ jQ
Ti
Ti
Bus N
Bus 1
Bus 2
Bus i
REF
NETWORK AS
DEFINED BY
LINES, XFMRS,
SHUNT CAPS, REACTORS
Y
BUS
V
i
~
+

I
i
~
NEWTONRAPHSON LOAD FLOW FORMULATION
Dr. Bruce Mork
EE 5200  Fall 2009
At a given bus
i
in the system, there can exist
:
Fixed P and Q injection consisting of
:
<
Scheduled generation that injects P
G i
into the bus.
<
A fixed load of P
L i
+ jQ
L i
(an injection of  P
L i
 jQ
L i
)
P and Q flowing into bus from the network
(all part of [Y
BUS
]):
<
Transmission lines  short, medium, long; singlecircuit, doublecircuit where
mutual coupling is neglected, or doublecircuit with mutual coupling effects.
<
Transformers  2winding or 3winding; fixed ratio, LTC, or PhaseShifting.
<
Shunt reactors:
Y = 1/(j
ω
L) =  jB
REACT
<
Shunt capacitor banks:
Y = j
ω
C = jB
CAP
<
A voltagedependent load represented as a shunt admittance: Y
LOAD
= G + jB.
Important things to note
:
<
The scheduled generation P
G i
is dictated by the system dispatch center via
SCADA.
The generator’s governor is given a “set point” and holds P
G i
constant
within a close tolerance.
Also, the generator’s exciter holds the bus voltage
V
i
at a constant magnitude (its angle
δ
i
is not directly controlled and is an
unknown).
<
The fixed load P
L i
+ jQ
L i
represents the aggregate load supplied to local
consumers.
In planning studies, this is usually a worstcase projection of what
planners think the load will be 5 or 10 or more years into the future.
<
P
T i
and Q
T i
are the total P and Q flowing
INTO
the transmission grid defined
by [Y
BUS
].
This includes the effects of shunt capacitor banks and reactors.
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View Full Document PP
P
P
INTO BUS i
Gi
Li
Ti
∑
=−−=
0
QQ
Q
Q
INTO BUS i
Li
∑
0
When forming equations, it is extremely important to establish a reference direction
for the flow of P, Q, and current.
This is clearly labeled on the sketch on the
preceding page.
Recall that the current
is the net current injected
into
the
~
I
i
network at bus i by the generator and load (this is the same injected current that
occurs in the equation [Y
BUS
][V] = [I] ).
Bus voltages are measured with respect to the
same reference that [Y
BUS
] is referred to.
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This note was uploaded on 10/20/2010 for the course ECE 5200 taught by Professor Bonk during the Fall '10 term at Michigan Technological University.
 Fall '10
 Bonk

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