for educational purpose only

1. 1. The parameters of a 4 bus system are as under:
Bus Code Line Impedance Charging Admittance (p.u)
𝑦𝑝𝑞
2
1-2 0.2 + j 0.8 j 0.02
2-3 0.3 + j 0.9 j 0.03
2-4 0.25 + j 1 j 0.04
3-4 0.2 + j 0.8 j 0.02
1-3 0.1 + j0.4 j 0.01
Draw the network and find bus admittance matrix.
Ans: check your answer Y11 = 0.882 – j3.498, Y12 = -0.294 + j1.176, Y13 = - 0.588+ j 2.352, Y22
= 0.862-j 3.026, Y33 = 1.215-j 4.468, Y34 = - 0.294 + j 1.176 , Y41 = 0, Y44 = 0.529-j2.056
2. Perform power flow of one iteration for the system as shown in figure using Gauss –
Seidel method. Determine slack bus power, line flows and line losses for the fig shown.
Take base MVA as 100. (α=1.1).
The load connected in Bus 1 is 90 + j 20 .
Ans: S1 = 0.3556 + j0.0388 p.u , 0.97MW MW , -7.63 MVAR

2. 3. Using Gauss –Seidel method, determine bus voltages, slack bus power, line flows and
line losses for the fig shown. Take base MVA as 100. (α=1.1)
Ans: V1= 1.05∠ 0 ̊, V2= 1.02∠ 18.24 ̊, S1 = - 0.607 - j0.18 p.u , 3.3 MW , 6.33 MVAR
4. Using Gauss –Seidal method, determine bus voltages, for the figure shown in question
no . 2. The reactive power limit for generator 2 in this case is 10 < Q2 < 100 MVAR. Take
base MVA as 100. (α=1.1).
Ans: V1= 1.05∠ 0 ̊, V2= 1.254∠ 15.26 ̊
5. For the system shown in figure below, find the voltage at receiving bus at the end of first
iteration using Gauss-Seidal method, voltage at sending end is 1.02∠ 0 ̊p.u. Line
admittance is 1.0-j4 p.u. transformer reactance is j0.4 p.u and off nominal turns ratio is
1.04. Assume VR = 1 ∠ 0 ̊. Determine slack bus power.
Ans: S1 = - 0.0026 + j 0.0294 p.u

3. 6. Use Newton Raphson Method to find the unknown quantities in the given 3 bus system.
Ans: At the end of first iteration , V2= 0.91 ∠ -8.63 ̊, V3= 0.85 ∠ -12.135 ̊
7. The load flow data for the sample power system are given below. The voltage magnitude
at bus 2 is to be maintained at 1.04 p.u. The maximum and minimum reactive power limits
of the generator at bus 2 are 0.35 and 0 p.u. respectively. Determine the set of load flow
equations at the end of first iteration by using Newton Raphson method.
In case the reactive power constraint at bus 2 in the previous problem is - 0.3 ≤ Q2 ≤
0.3. Determine the equations at the end of first iteration.

4. 8. Calculate voltages and angles after one iteration by using fast decoupled load flow for
the system as shown in figure . The line parameters are given in per unit on a 100 MVA
base.
Ans: V2= 0.951∠-10.2 ̊, V3= 0.969∠ -7.39 ̊
9. Obtain the power flow solution (one iteration) for the system shown in figure. The line
admittances are in per unit on a 100 MVA base. Use fast decoupled load flow method.
Ans: V2= 1.026∠2.14 ̊, V3= 1.088∠ 10.48 ̊
10. Write down an algorithm and draw the flowchart for Fast decoupled and Newton Rapson
method of load flow studies.