Tutorial (A)
Bus Admittance Matrix
1.
For the power system network in Figure 1, determine the element of tbus admittance
matrix, Ybus.
2
Y=4-j10
P2=1.7
|V2|=1.1249
Y=4-j5
3
1
V1=1∟0o
P3= -2
Q3= -1
Figure 1
2.
Determine the element of bus admittance matrix, Ybus in Figure 2.
V1=1∟0o
1
Y=2-j4
Y=3-j63
3
P3= -2pu
Q3= 1pu
Figure 2
2
P2=1.6 pu
|V2|=1.1 pu
Power Flow Analysis (Newton-Raphson Method)
The figure below shows the one-line diagram of a simple three bus power system with bus 1 as a
reference bus and bus 2 as a generator bus. The voltage at bus 1 is fixed at V1=1.025  0o pu.
Voltage magnitude at bus 2 is fixed at 1.03 pu with a real power generation of 300 MW. A load
consisting of 400 MW and 200 MVar is taken from bus 3 (load bus). Line impedances are marked
in pu on a 100 MVA base and line resistance and line charging susceptances are neglected.
j0.05
P3= 300 MW
1
2
V1=1.025∟0o
j0.025
j0.025
3
PL3+ jQL3 = 400MW + j200MVar
i)
Using Newton-Raphson method and an initial estimate of V20  1.03  j0 and
V3(0)  1.0  j0 , determine phasor values of V2 and V3 and magnitude of V3. Perform
one iteration only.
ii)
If after several iterations the bus voltages converge to
V2  1.031.36851o  1.029706 j0.0246pu
V3(0)  1.001243  2.1o  1.000571 j0.0366898pu
Determine the real and reactive power at the reference bus and reactive power at the
generator bus.
iii)
Determine the line flow and line losses.
iv)
Construct a power flow diagram and show the direction of the line flows.
v)
Check the power flow solution using MATLAB software.
Power Flow Analysis (Fast-decouple method)
Obtain the power flow solution by fast-decouple method for the 3 buses system in the figure below.
The values in this figure are marked in per unit on a 100MVA base and line charging susceptances
are neglected. Determine the magnitude and the phase values of voltage at load buses 3, δ3, V3,
and the phase value of the voltage at bus 2, δ2 (for first iteration only).
Z12=0.02+j0.04
1
2
400 MW
250 MVar
Slack bus
|V1|=1.05∟0o
Z13=0.01+j0.03
Z23=0.0125+j0.025
3
200 MW
|V3|=1.04
Figure 1: One-line diagram for 3 buses power system