This document contains the answers to questions on a mid-semester exam for a power systems analysis course. The questions cover topics like: - Deriving the power mismatch equation and Jacobian matrix for the Newton Raphson load flow method. - Discussing the steady-state modeling of power system components. - Converting component parameters in a sample power system diagram from real to per unit values. - Constructing the admittance matrix and obtaining the Thevenin equivalent circuit for a part of the sample system. - Calculating line power flows and system losses based on a given load and generator power factors.

1. UJIAN TENGAH SEMESTER GANJIL
UNIVERSITAS BRAWIJAYA MALANG
NAMA : SUPARMAN
NPM :136060300111003
MK : ANALISA SISTEM TENAGA LANJUT
Question 1: (30 marks)
A. What is the Power mismatch? Discuss and derive the involved equation.
Answer:
It is usual to use the power mismatch as an accurate test. The complex power
mismatch at a node i is the difference between the specified power ̅ and the
calculated power ̅ ̅ where ̅ is the voltage evaluated at iteration r
Above equation can be separated into real and imaginary parts and expressed in polar
form or rectangular form as:
It is assumed in the above equations that Vi is the voltage evaluated at iteration r. The
most common convergence criterion used in practice is
B. Derive the following Jacobian matric in Newton Raphson method:

2. Answer:
 Equation 1
∑ ( )
Verification:
∑ ( )
( )
( )
 Equation 2
( )
Verification:
∑ ( )
( ) ( )
( )
 Equation 3
∑ ( )
Verification:
∑ ( )

3. ( ) ( )
( )
 Equation 4
( )
Verification:
∑ ( )
( )
( )
Question 2: (20 marks)
Discuss briefly the steady state (load flow) modeling of each power system component
involved in the power system.
Answer:
steady state (steady / steady) is the normal condition of post-occurring disorders in an
RL circuit with t ≠ 0 and steady state always has the same magnitude but opposite in
sign to declare the value zero from existing flows.
Picture below is an image of power system modeling and graphic images of steady
state conditions:

4. Picture below is an image of power system modeling
Picture below is graphic images of steady state conditions:

5. Question 3: (50 marks)
Figure 1 shows three phase system that are connected to generators A, B, C and D at
11kV level. The five nodes of the system with the specific ID are given in the figure.
The power supplies the load through node 2 at 132kV level. The reactance of the
transmission line and component parameters in per unit are shown in the Figure.
a) Change all components in Figure 1 which are given in real parameters to per unit
system. Note: use 100MVA as reference to determine the per unit system.
Answer:
VBase4 =33 KV
VBase5 =33x(11/33)=11 KV
VBase3 =11x(11/11)=11 KV
VBase2 =33x(11/33)=11 KV
VBase1 =11x(11/11)=11 KV
ZBase gen 1 = (11 KV) 2
/(100 MVA)=1,21 Ω
ZBase 2 = (11 KV) 2
/(100 MVA)=1,21 Ω
ZBase 5 = (11 KV) 2
/(100 MVA)=1,21 Ω
ZBase 4 = (33 KV) 2
/(100 MVA)=10,89 Ω
ZBase 1 = (11 KV) 2
/(100 MVA)=1,21 Ω

6. ZGen / Z5 = 1,21 x (11 ) 2
/(33) x (200/100)=0,26 pu
Z1 = 1,21 x (11 ) 2
/(132) x (200/100)=0,16 pu
Z2 = 1,21 x (11 ) 2
/(11) x (100/100)=1,21 pu
Z3 = 1,21 x (11 ) 2
/(132) x (150/100)=0,012 pu
Z4= 10.89 x (33 ) 2
/(33) x (100/100)=10,89 pu
Z5 = 0
b) Construct the admittance matrix of the system.
Answer:
Y11 Y12 Y13 Y14 Y15 V1 I1
Y21 Y22 Y23 Y24 Y25 V2 I2
Y31 Y32 Y33 Y34 Y35 V3 = I3
Y41 Y42 Y43 Y44 Y45 V4 I4
Y51 Y52 Y53 Y54 Y55 V5 I5
c) Obtain the Thevenin equivalence circuit at bus 2.
Answer:

7. V 1
V 2
V 3
V 4
V 5
I 1
I 2
I 3
I 4
I 5
Y 10
Y 40
Y 12
Y 24
Y 23
Y 20
Y 30
Y 45 a Y 45 b Y 45 c
Y 50
d) Assume that the power load required in the system is about 525 MW and all
gernerators running on pf 0.9, determine the power flow in the Lines: 1-2, 2-3, 2-4
and calculate the system losses.
Answer: