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Tutorial Power Flow Analysis
EET 308-Power System Analysis (Semester II – Session 2016/2017) Page 1
1) A power system network is shown in Figure 1. The values marked are impedances in per unit on
a base of 100 MVA. Convert network impedances to admittances and determine the bus
admittance matrix.
Figure 1: Single line diagram with network impedances
Solution
Tutorial Power Flow Analysis
EET 308-Power System Analysis (Semester II – Session 2016/2017) Page 2
2) In the power system network shown in Figure 2 below, bus 1 is a slack bus with V1 = 1.00 per
unit and bus 2 is a load bus with S2 = 280 MW + j60 Mvar. The line impedance on a base of 100
MVA is Z = 0.02+j0.04 per unit.
a) Using Gauss-Seidel method, determine V2. Use an initial estimate of V2(0)
= 1.0+j0.0 and
perform three iterations.
b) If after several iterations voltage at bus 2 converges to V2 = 0.90-j0.10, determine S1 and
the real and reactive power loss in the line.
Figure 2: Single line diagram of two-bus power system
Solution
a)
Tutorial Power Flow Analysis
EET 308-Power System Analysis (Semester II – Session 2016/2017) Page 3
3) Figure 3 shows the single-line diagram of a simple three-bus power system with generation at
buses 1 and 3. The voltage at bus 1 is V1 = 1.0250 per unit. Voltage magnitude at bus 3 is fixed
at 1.03 per unit with a real power generation of 300 MW. A load consisting of 400 MW and 200
Mvar is taken from bus 2. Line impedances are marked in per unit on a 100 MVA base. Line
resistances and line charging susceptances are neglected.
a) Using Gauss-Seidel method and initial estimates of V2(0)
=1.0+j0 and V3(0)
=1.03+j0 and
keeping V3 = 1.03 pu, determine the phasor values of V2 and V3. Perform two iterations.
b) If after several iterations the bus voltages converge to
Determine the line flows and the line losses and the slack bus real and reactive power
c) Construct a power flow diagram and show the direction of the line flows
pujV
pujV
0246.0029706.136851.103.1
0366898.0000571.11.2001243.1
3
2
Tutorial Power Flow Analysis
EET 308-Power System Analysis (Semester II – Session 2016/2017) Page 4
Figure 3: Single line diagram of three-bus power system
Solution
Tutorial Power Flow Analysis
EET 308-Power System Analysis (Semester II – Session 2016/2017) Page 5
Tutorial Power Flow Analysis
EET 308-Power System Analysis (Semester II – Session 2016/2017) Page 6
Tutorial Power Flow Analysis
EET 308-Power System Analysis (Semester II – Session 2016/2017) Page 7
4) In the two-bus system shown in Figure 4, bus 1 is a slack bus with V1 =1.00 pu. A load of 150
MW and 50 Mvar is taken from bus 2. The line admittance is y12 = 10-73.74 pu on a base of
100 MVA. The expression for real and reactive power at bus 2 is given by
Using Newton-Raphson method, obtain the voltage magnitude and phase angle of bus 2. Start
with an initial estimate of V2(0)
= 1.0 pu and 2(0)
= 0. Perform two iterations.
Figure 4: Single line diagram of two-bus system
Solution
)74.73sin(10)26.106sin(10
)74.73cos(10)26.106cos(10
2
212122
2
212122
VVVQ
VVVP
Tutorial Power Flow Analysis
EET 308-Power System Analysis (Semester II – Session 2016/2017) Page 8
Tutorial Power Flow Analysis
EET 308-Power System Analysis (Semester II – Session 2016/2017) Page 9
5) Figure 5 shows the single-line diagram of a simple three-bus power system with generation at
buses 1 and 2. The voltage at bus 1 is V =1.00 per unit. Voltage magnitude at bus 2 is fixed at
1.05 pu with a real power generation of 400 MW. A load consisting of 500 MW and 400 Mvar is
taken from bus 3. Line admittances are marked in per unit on a 100 MVA base. Line resistances
and line charging susceptances are neglected.
a) Show that the expression for the real power at bus 2 and real and reactive power at bus 3
are:-
b) Using Newton-Raphson method, start with the initial estimates of V2(0)
=1.0+j0 and V3(0)
=1.0+j0 and keeping V2 = 1.05 pu, determine the phasor values of V2 and V3. Perform
two iterations.
Figure 5: Single line diagram of three-bus power system
Solution
2
3232313133
233213133
323212122
40)90sin(20)90sin(20
)90cos(20)90cos(20
)90cos(20)90cos(40
VVVVVQ
VVVVP
VVVVP
Tutorial Power Flow Analysis
EET 308-Power System Analysis (Semester II – Session 2016/2017) Page 10
Tutorial Power Flow Analysis
EET 308-Power System Analysis (Semester II – Session 2016/2017) Page 11
6) From Figure 5, obtain the power flow solution using the fast decoupled algorithm. Perform two
iterations.
Tutorial Power Flow Analysis
EET 308-Power System Analysis (Semester II – Session 2016/2017) Page 12