Short Notes: Load Flow Study | Short Notes for Electrical Engineering - Electrical Engineering (EE) PDF Download

 Page 1


 
 
 
 
 
         
                   
Power System Matrices 
? 
BUS 
Y matrix 
 
10 12 12
BUS 12 20 12 23 23
23 23 30
y y y 0
Y y y y y y
0 y y y
????
??
? ? ? ? ?
??
?? ? ? ?
??
 
OBSERVATIONS 
1) The diagonal elements are sum of all admittance connected to that particular bus. 
2) The off-diagonal elements are negative of admittance connected between two buses. 
3) If two buses are not connected to each other than that elements is zero. 
4) 
BUS
Y Matrix is a symmetrical matrix. 
5) Most of the elements are zero & hence it is a sparse matrix. 
Total number of zero elements
% sparsity = 
Total number of elements
 
 
? 
BUS
Z matrix 
       ? ?
1
BUS BUS
ZY
?
? 
? 
BUS
Z matrix used in fault analysis. 
? Suppose a 3 – phase SC fault occurs on bus ‘k’ then fault current 
 
pre fault
f
kk f
V ,k
I
ZZ
?
?
?
 
pre fault
k Pr e fault voltage at bus 'k' V,
?
?? 
kk
Z = elements of 
BUS
Z matrix. 
f
Z = fault impedance 
? Due to fault voltage at other buses are also affected. 
Page 2


 
 
 
 
 
         
                   
Power System Matrices 
? 
BUS 
Y matrix 
 
10 12 12
BUS 12 20 12 23 23
23 23 30
y y y 0
Y y y y y y
0 y y y
????
??
? ? ? ? ?
??
?? ? ? ?
??
 
OBSERVATIONS 
1) The diagonal elements are sum of all admittance connected to that particular bus. 
2) The off-diagonal elements are negative of admittance connected between two buses. 
3) If two buses are not connected to each other than that elements is zero. 
4) 
BUS
Y Matrix is a symmetrical matrix. 
5) Most of the elements are zero & hence it is a sparse matrix. 
Total number of zero elements
% sparsity = 
Total number of elements
 
 
? 
BUS
Z matrix 
       ? ?
1
BUS BUS
ZY
?
? 
? 
BUS
Z matrix used in fault analysis. 
? Suppose a 3 – phase SC fault occurs on bus ‘k’ then fault current 
 
pre fault
f
kk f
V ,k
I
ZZ
?
?
?
 
pre fault
k Pr e fault voltage at bus 'k' V,
?
?? 
kk
Z = elements of 
BUS
Z matrix. 
f
Z = fault impedance 
? Due to fault voltage at other buses are also affected. 
 
 
 
 
 
11
kk
BUS BUS
BUS
f
nn
VI
0
..
0
..
.
VI
.
. Z .     V Z
I
..
.
VI
.
0
? ? ? ? ??
?? ? ? ? ?
?? ? ? ? ?
?? ? ? ? ?
?? ? ? ? ?
??
?? ? ? ? ?
?? ? ? ? ?
? ? ? ? ? ? ? ? ?
? ? ? ? ? ??? ? ? ? ?
?
?? ? ? ? ?
?? ? ? ? ?
??
?? ? ? ? ?
?? ? ? ? ?
?? ? ? ? ?
??
? ? ? ?
? ? ? ?
 
 
k f kk
V I Z ? ? ? 
? ?
f
ff
kk
V
I Z 0
Z
?? 
? ?
"
j jk f
V Z I ? ? ? 
jk
jf
kk
Z
VV
Z
?
?? 
 
? Post – fault voltage at bus j 
                
jk
j jf f
kk
Z
V V V
Z
?? 
If there is generator connected to bus ‘ j ’ then current supplied by generator. 
                  
g jf
"
d
EV
I
jX
?
? 
Classification of buses 
At each bus, there are 4 parameter: V , ,P,Q ? . 
At any bus, out of these 4 quantities any 2 are specified. 
1) Slack Bus / Swing Bus/Reference Bus 
       V, ? are know quantities. 
         P, Q are unknown quantities. 
Any extra power needed by the system is supplied by slack bus. 
2) Generator Bus / PV Bus 
         P, V is specified 
         Q,  are unspecified ? 
Page 3


 
 
 
 
 
         
                   
Power System Matrices 
? 
BUS 
Y matrix 
 
10 12 12
BUS 12 20 12 23 23
23 23 30
y y y 0
Y y y y y y
0 y y y
????
??
? ? ? ? ?
??
?? ? ? ?
??
 
OBSERVATIONS 
1) The diagonal elements are sum of all admittance connected to that particular bus. 
2) The off-diagonal elements are negative of admittance connected between two buses. 
3) If two buses are not connected to each other than that elements is zero. 
4) 
BUS
Y Matrix is a symmetrical matrix. 
5) Most of the elements are zero & hence it is a sparse matrix. 
Total number of zero elements
% sparsity = 
Total number of elements
 
 
? 
BUS
Z matrix 
       ? ?
1
BUS BUS
ZY
?
? 
? 
BUS
Z matrix used in fault analysis. 
? Suppose a 3 – phase SC fault occurs on bus ‘k’ then fault current 
 
pre fault
f
kk f
V ,k
I
ZZ
?
?
?
 
pre fault
k Pr e fault voltage at bus 'k' V,
?
?? 
kk
Z = elements of 
BUS
Z matrix. 
f
Z = fault impedance 
? Due to fault voltage at other buses are also affected. 
 
 
 
 
 
11
kk
BUS BUS
BUS
f
nn
VI
0
..
0
..
.
VI
.
. Z .     V Z
I
..
.
VI
.
0
? ? ? ? ??
?? ? ? ? ?
?? ? ? ? ?
?? ? ? ? ?
?? ? ? ? ?
??
?? ? ? ? ?
?? ? ? ? ?
? ? ? ? ? ? ? ? ?
? ? ? ? ? ??? ? ? ? ?
?
?? ? ? ? ?
?? ? ? ? ?
??
?? ? ? ? ?
?? ? ? ? ?
?? ? ? ? ?
??
? ? ? ?
? ? ? ?
 
 
k f kk
V I Z ? ? ? 
? ?
f
ff
kk
V
I Z 0
Z
?? 
? ?
"
j jk f
V Z I ? ? ? 
jk
jf
kk
Z
VV
Z
?
?? 
 
? Post – fault voltage at bus j 
                
jk
j jf f
kk
Z
V V V
Z
?? 
If there is generator connected to bus ‘ j ’ then current supplied by generator. 
                  
g jf
"
d
EV
I
jX
?
? 
Classification of buses 
At each bus, there are 4 parameter: V , ,P,Q ? . 
At any bus, out of these 4 quantities any 2 are specified. 
1) Slack Bus / Swing Bus/Reference Bus 
       V, ? are know quantities. 
         P, Q are unknown quantities. 
Any extra power needed by the system is supplied by slack bus. 
2) Generator Bus / PV Bus 
         P, V is specified 
         Q,  are unspecified ? 
 
 
20 
 
 
 
3) Load Bus / PQ Bus 
       P & Q are constant as specified  
       V & are unknown ? 
       Generally, newton – Raphson method is used for load flow solution and we form Jacobian 
matrix, & the order of Jacobian matrix is 
? ? ? ?
2n m 2 2n m 2 ? ? ? ? ? 
N = no. of total buses 
M = no. of pv buses 
Economic Power Generation 
? Incremental cost 
If is cost required to generate an additional unit of energy. 
? ?
i
IC = Incremental cost of 
th
i generator 
? ?
i
i
Gi
C
IC
P
?
?
?
 
Gi
P = Power generated by 
th
i generator 
i
C = cost of 
th
i generator 
 
? Transmission Loss 
                   
mm
L i j ij
i 1 j 1
P PPB
??
?
??
 
ij
P , P : Real power injection at 
th th
i & j buses 
ij
B = loss coefficient 
m : no. of generator units 
 
Penalty Factor 
              
i
L
Gi
L
1
P
1
P
??
??
??
??
?
?
?
?
 
For economic power sharing 
             ? ?
i
i
IC L constant ? 
? Constant is called as incremental cost of system. 
? ? ?
i
IC = incremental cost 
th
i unit 
? 
i
L = penalty factor of 
th
i unit