Electrical Power Systems

152 Electrical Power Systems
ig. 7.4: i-th bus of a power system.
Net injected current I i into the bus i can be written as:
I i = y i0V i + y i1 (V i – V 1) + y i2 (V i – V 2) + ... + y in (V i – V n)
\ I i = ( y i0 + y i1 + y i2 ... y in ) V i – y i1V 1 – y i2 V 2 ... y inV n ...(7.7)
Let us define
Y ii = y i0 + y i1 + y i2 + ... + y in
Y i1 = –y i1
Y i2 = –y i2
M
Y in = –y in
\ I i = Y iiV i + Y i1 V 1 + Y i2 V 2 + ... + Y inV n ...(7.8)
n
å ik k
k = 1
k ¹ i
or I i = Y ii V i + Y V
The real and reactive power injected at bus i is
Pi – jQi = Vi * Ii \ I i =
P - jQ
*
V
rom eqns (7.9) and (7.10) we get
P - jQ
*
V
i i
\ Y iiV i =
i
i i
i
n
å ik k
k = 1
k ¹ i
= Y iiV i + Y V
P - jQ
*
V
i i
i
n
å ik k
k = 1
k ¹ i
– Y V
...(7.9)
...(7.10)
...(7.11)