BE 45'? Homework #2 Solution
1. Consider the twobus system shown in Fig. l l. The two generators and
transformers are assumed of equal rating  soc MVA  which is the 3
phase base power for all pu u
Protection 5
1.0 Introduction
Recall there are five basic classes of relays:
Magnitude relays
Directional relays
Ratio (impedance) relays
Differential relays
Pilot relays
We provide only a very b
Protection 4
1.0 Introduction
Recall there are five basic classes of relays:
Magnitude relays
Directional relays
Ratio (impedance) relays
Differential relays
Pilot relays
We study the impedance r
Stability 3
1.0 Introduction
In our last set of notes (Stability 2), we
described in great detail the behavior of a
synchronous machine following a faulted
condition that is cleared by protective rela
Stability 2
1.0 Introduction
We ended our last set of notes, concluding that
the following equation characterizes the
electromechanical dynamics of a synchronous
machine.
(t ) P0 Ea V sin
M
M
(1)
Xd
Stability 1
1.0 Introduction
We now begin Chapter 14.1 in your text.
Our previous work in this course has focused on
analysis of currents during faulted conditions in
order to design protective system
AGC 4
1.0 Problem 11.2
For the isolated generating station with local
load shown in Fig. 1 below, it is observed that
PL=0.1pu brings about =0.2rad/sec in the
steadystate.
1
R
PL

PC +

1
s 1
+
10
AGC 3
1.0 Introduction
The primary controller response to a
load/generation imbalance results in generation
adjustment so as to maintain load/generation
balance. However, due to droop, it also results
AGC 2
1.0 Introduction
In the last set of notes, we developed a model of
the speed governing mechanism, which is given
below:
xE
KG
1
(PC )
1 TG s
R
(1)
In these notes, we want to extend this model s
February 18, 2016
NAME fOLqu Ford
1. (4 pts) For a line to line fault analysis using symmetrical components( choose the
right answer) :
a) The positive. negative and zero sequence networks at the faul
Protection 1
(read section 13.0 of text)
1.0 Introduction
Faults do not occur that frequently 1/year/100
miles of transmission is typical. Distribution
systems may see more than this.
However, when th
Protection 2
1.0 Introduction
There are five basic classes of protective relays:
Magnitude relays
Directional relays
Ratio (impedance) relays
Differential relays
Pilot relays
We will study each o
Protection 3
1.0 Introduction
Recall there are five basic classes of relays:
Magnitude relays
Directional relays
Ratio (impedance) relays
Differential relays
Pilot relays
We study the directional
Examples
I will do 2 of your assigned problems
Problem 12.3
The problem requires us to find the three
currents Ia, Ib, and Ic, and also Vng, given that
Ea=1, Eb=1, and Ec=j1.
Ia
j1
Ec=j
Eb=1
j1
Ea
E
Examples
Example 1: Compute sequence components
of the following balanced abc sequence
linetoneutral voltages.
Van 2770
V abc Vbn 277 120
Vcn 277120
Solution:
1 Van
1 1
1
1
V S A V abc 1 2
Symmetrical Components 2
Sequence impedances
Although the following focuses on loads, the
results apply equally well to lines, or lines
and loads. Read these notes together with
sections 12.6 and 12.9
Fault Analysis Using Zbus
1.0 Introduction
The previous notes on Zbus resulted in
some useful knowledge: diagonal element
Zkk of the Zbus is the Thevenin impedance
seen looking into the network fro
LU Decomposition
1.0 Introduction
We have seen how to construct the Ybus
used in the matrix equation
I YV
(1)
If we are given the bus voltages, we can
construct Y and then very easily find I.
Unfortu
Symmetrical Fault Analysis
1.0 Definition
A symmetrical fault is a fault where all
phases are affected so that the system
remains balanced. A threephase fault is a
symmetrical fault. The other three
EDC3
1.0 Introduction
In the last set of notes (EDC2), we saw how
to use penalty factors in solving the EDC
problem with losses. In this set of notes, we
want to address two closely related issues.
W
EDC2
1.0 Introduction
In the previous set of note (EDC1), we
developed the EDC problem with losses
included and provided the corresponding
KKT conditions which lead to its solution
procedure. However,
EE 457, Exam 2, Spring 2015, Dr. McCalley, Time: 75 minutes,
Calculator allowed; closed book, closed notes, communication devices not allowed
1.
(25 pts) Consider the 138 kV transmission system.
Bus 1
Homework #9 Solution
Assignment: 11.8  11.12 and 11.16 11.18 Bergen & Vittal
Solutions:
11.8
IC1 8.0 .003P 1
G
IC2 8.0 .001PG 2
IC3 7.5 .002PG 3
It helps to estimate the common IC graphically and the
Homework #6 Solution
Assignment: 14.1, 14.4, 14.5, 14.8, 14.9, and 14.10 Bergen & Vittal
Solutions:
14.1
Part A:
Wkinetic
3
H 3 Wkinetic H * Sb 5 *100M 500Megajoules
SB
Part B:
To find the kinetic ene
Homework #5 Solution
Assignment: 13.1, 13.2, 13.3 ,13.4, and 13.5 Bergen & Vittal
Solutions:
13.1
Assuming a fault at bus 4.
Deriving the Thevenin equivalent circuits:
Z ag j5 j10 j10 j10 j35
Z ag j5
EE457 Assignment 1 Due Tuesday, Feb. 2 2016
1. Problem 12.2 from the textbook
Find the symmetrical components of Ea = 110°, Eb : 14—90", EC 2 21135°
Convert to balanced. Find 1;, If, L9. See Eq. 12.5
EE 457
Problem Set #3 Solution
Due by March 10, 2106
1. Consider the transmission system shown below
The relay parameters are:
Line to neutral voltage =79.7kV
Current transformer ratio = 500:5
Voltage
EE457 Assignment 1 Due January 24th 2017
1. Problem 12.2 from the textbook
Find the symmetrical components of = 10, = 1 90, = 2135,
Convert balanced. Find + , , 0 . See Eq. 12.5 and 12.6, page. 447.
2
Summary of fault currents for various types of faults
LG fault at kth Node
Iak Iak Iak 0
VKfprefault
Zkk Zkk Zkk 0 3Z f
or
Iak1 Iak2 Iak0
VKfprefault
Zkk1 Zkk2 Zkk0 3Z f
1 1 1
A 1 a 2 a
1 a a 2
February 18, 2016
l. (4 pts) For a line to line fault analysis using symmetrical components( choose the
right answer) :
a) The positive, negative and zero sequence networks at the fault point are conn
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