EEL303: Power Engineering I - Tutorial 6
1. Figure 1 shows the one-line diagram of a four-bus system.
Table 1 gives the line
Figure 1: Sample system for 1Q
impedances identified by the buses on which these terminate. The shunt admittance
at all the buses is assumed to be negligible.
Table 1:
Line, Bus to bus
1–2
1–3
2–3
2–4
3–4
R (p.u)
0.05
0.10
0.15
0.10
0.05
X (p.u)
0.15
0.30
0.45
0.30
0.15
(a) Find YBus , assuming that the line shown dotted is not connected.
(b) What modifications need to be carried out in YBus if the line shown dotted is
connected.
[Ans: (a)

YBus
(b)
0
−1 + j3
0
3 − j9
−2 + j6
−1 + j3
0



 0
1.666 − j5 −0.666 + j2 −1 + j3



=
−1 + j3 −0.666 + j2 3.666 − j11 −2 + j6




0
−1 + j3
−2 + j6
3 − j9

YBus
1 − j3



−2 + j6 3.666 − j11 −0.666 + j2 −1 + j3



=
−1 + j3 −0.666 + j2 3.666 − j11 −2 + j6




0
−1 + j3
−2 + j6
3 − j9
]
Electrical Engineering Dept - IIT Delhi
EEL303: Power Engineering I - Tutorial 6
2. The following is the system data for a load flow solution.
The line admittances are given in Table 2.
The scheduled active and reactive powers are given in Table 3. Determine the voltages
Table 2: The line admittances
Line
1–2
1–3
2–3
2–4
3–4
Admittance
2-j8.0
1-j4.0
0.666-j2.664
1-j4.0
2-j8.0
Table 3: Scheduled active and reactive powers
Bus No.
1
2
3
4
P Q
V
— — 1.06
0.5 0.2 —
0.4 0.3 —
0.3 0.1 —
Remarks
Slack
PQ
PQ
PQ
at the end of first iteration using Gauss-Seidal method. Take acceleration factor (α) as
1.6.
1
1
1
[Ans: V2,acc
= 1.01899-j0.046208; V3,acc
= 0.99059-j0.0467968; V4,acc
= 0.954565-j0.1034944]
3. If in above problem, bus 2 is taken as a generator bus with |V2 |=1.04 and reactive power
constraint is
0.1 ≤ Q2 ≤ 1.0
Determine the voltages starting with a flat voltage profile and assuming acceleration
factor as 1.0. Assume that bus 2 has generator connected on it and injects P2 = 0.5 p.u.
1
1
1
[Ans: V2,acc
= 1.0395985+j0.02891158; V3,acc
= 0.9978866-j0.015607057; V4,acc
= 0.998065j0.022336]
4. For the sample system of Figure 2, the generators are connected at all the four buses,
while the loads are at buses 2, 3 and 4. The values of real and reactive powers are listed
in Table 4. All buses other than slack are of PQ-type. Line data are given in Table
5. Find the voltages and the bus angles at the three buses using the Newton-Raphson
method. [Ans: δ2 = -0.09696 rad; δ3 = -0.11217 rad; δ4 = -0.06928 rad; V2 = 0.94496
p.u.; V3 = 0.92451 p.u.; V4 = 0.95715 p.u.]
Electrical Engineering Dept - IIT Delhi
EEL303: Power Engineering I - Tutorial 6
Figure 2: Sample system
Table 4:
Bus
1
2
3
4
Pi (p.u.) Qi (p.u.)
—
—
-0.45
-0.15
-0.51
-0.25
-0.60
-0.30
Vi (p.u.)
1.05 ̸ 0
—
—
—
Type of bus
Slack
PQ
PQ
PQ
Table 5:
Line No.
1
2
3
4
Line (i-j)
1–2
1–4
2–3
3–4
Line impedance
0.08+j0.20
0.05+j0.10
0.04+j0.12
0.04+j0.14
5. For the sample system of Figure 2, the generators are connected at all the four buses,
while the loads are at buses 2, 3 and 4. The values of real and reactive powers are listed
in Table 6 along with the type of buses. Line data are given in Table 5. Find the voltages
Table 6:
Bus
1
2
3
4
Pi (p.u.) Qi (p.u.)
—
—
-0.45
-0.15
-0.51
-0.25
-0.60
-0.30
Vi (p.u.)
1.05 ̸ 0
1.00 ̸ 0
—
—
Type of bus
Slack
PV
PQ
PQ
and the bus angles at the three buses using the Newton-Raphson method. [Ans: δ2 =
-0.11664 rad; δ3 = -0.12567 rad; δ4 = -0.07658 rad; V3 = 0.96146 p.u.; V4 = 0.973 p.u.]
Electrical Engineering Dept - IIT Delhi