tutorial power flow analysisportal.unimap.edu.my/portal/page/portal30/lecture...

Tutorial Power Flow Analysis

EET 308-Power System Analysis (Semester II – Session 2016/2017)

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



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)



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



Figure 3: Single line diagram of three-bus power system

Solution



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



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



6) From Figure 5, obtain the power flow solution using the fast decoupled algorithm. Perform two

iterations.

tutorial power flow analysisportal.unimap.edu.my/portal/page/portal30/lecture...

Documents