Power transformers #2
1.0 Introduction
In the first set of notes on transformers, we
developed a basic model. Today we will see
how to use that model to identify the values
of its parameters. In addit
Power Flow Algorithm
1.0 Introduction
In these notes we articulate the basic steps
taken by a standard power flow algorithm.
2.0 The algorithm
The NR algorithm, for application to the
power flow probl
PowerFlow2
1.0 Introduction
We derive two forms of the power flow
equations in these notes. We also provide an
example of using these equations.
2.0 Derivation of power flow equations
Our goal here is
PowerFlow1
1.0 Introduction
The power flow problem may be stated
roughly as follows. Given knowledge of the
real and reactive demands, the real power
generation, and the generator terminal
voltages, t
Power Flow Examples
1.0 Introduction
We will solve the same problem in three
different ways:
- Full Newton
- Fast decoupled
- DC
This problem and the solution by full
Newton and the solution by decoup
Course Design Project
1.0 Design project overview
The goal of this project is to develop design
plans to modify an existing transmission
system so as to serve new needs.
The existing transmission syst
Admittance Matrix
1.0 Introduction (Section 9.1)
Current injections at a bus are analogous to
power injections. The student may have
already been introduced to them in the form
of current sources at a
Use of Tables
1.0 Introduction
We have now the ability to compute
inductive
reactance
and
capacitive
susceptance of a transmission line given its
geometry. To remind you, the most general
form of the
Synchronous Machine Modeling
1.0 Introduction
Our motivation at this point is to put you in
a position to understand synchronous
machine modeling for power system
dynamic analysis.
If you take EE 457,
Problem 3.1: Suppose that a 60-Hz single phase power line and an open-wire telephone
line are parallel to each other and in the same horizontal plane. The power line spacing is
5 ft; the telephone wir
Line Models and SIL
1.0 Introduction
In these notes, I present different line
models that are used, and I also make some
comments on Examples 4.2 and 4.3 leading
to discussion of surge impedance loadi
Fast Power Flow Methods
1.0 Introduction
What we have learned so far is the so-called
full-Newton power flow algorithm. The
full-Newton is perhaps the most robust
algorithm in the sense that it is mos
Effect of Bundling and Transposition on
Series Inductance of Overhead Lines
1.0 Bundling
The text, pp 64-65, considers a four
conductor bundle in an equilateral
configuration. We will consider a twoco
LU Decomposition
1. Introduction
We have seen how to construct the Y-bus
used in the matrix equation
(1)
If we are given the bus voltages, we can
construct Y and then very easily find I.
Unfortunately
Transmission Matrix
Comments on Example 1, and
Lumped Circuit Equivalent
1.0 Introduction
In these notes, I want to write the equations
from last time in a matrix form. Then I will
say a few words abo
Power transformers #3
1.0 Introduction
In the first set of notes on transformers, we
developed a basic model. The second set of
notes dealt with the two issues of (a)
measuring parameters for that mod
Problem 3.2: Repeat problem 3.1 but assume that the telephone line has been displaced
vertically by 10 ft, i.e., the nearest conductors of the two lines are now (20 2+102)1/2 ft
apart.
From problem 3.
Example 3.2: Compute inductance per meter of each phase of a 3-phase transmission line
with equilateral spacing. Assume
1. The conductors are equally spaced, D, and have equal radii r.
2. The currents
Admittance Matrix#2
1.0 Introduction
We have seen how to model a network using
the admittance matrix (Y-bus). Our interest
in these notes is to see how to deal with the
network if it contains off-nomi
Power transformers #1
1.0 Introduction
You have been introduced to transformers in
EE 303. In these notes, I will review some
of the main ideas related to transformers, but
I do expect that you have c
Obtaining the Jacobian
1.0 Introduction
We have seen that the Jacobian matrix is
essential for solving a set of nonlinear
algebraic equations using the NewtonRaphson method.
In the last set of notes,
Problem 3.5: Find the round-trip inductance of a single-phase line made up of round
wires of radius r separated by a distance D between centers.
Solution: Lets draw the situation below.
Recall that in
Newton Raphson
1.0 Introduction
The Newton-Raphson algorithm is an
iterative method for solving nonlinear
algebraic equations.
We provide a couple of simple numerical
examples to begin.
2.0 Scalar cas
EE 456 Exam 2, October 13, 2006, NAME:_
Closed notes, Closed book, no calculators allowed, no computers, no cell phones, 50 minutes
1. (18 pts) To maintain a safe margin of stability, the power angle
PowerFlow3
1.0 Introduction
We define and discuss some terminology
necessary for understanding the power flow
problem and solution procedure.
2.0 Classification of buses
Although it is physically appe
Terminal Relations
1.0 Introduction
Our work in Chapter 3 resulted in ability to
compute two parameters:
z in /m
y in mhos/m
We can use these parameters to compute the
series impedance and shunt adm
Name (1 pt): _
EE 456 Exam 1, September 15, 2006: Closed notes, closed book, no calculator, 50 minutes
1.
(30 pts) For the circuit shown below, the waveforms for voltage v(t), current i 2(t) into Z2,
Autotransformers (Section 5.10)
1.0 Introduction
Autotransformers are heavily used in
transmission level voltage transformation,
e.g., between different combinations of
500kV, 345kV, 230kV, 161kV, 138
Tap Changers
1.0 Introduction (Section 5.9)
Section 5.9 discusses voltage regulators, tap
changers, and phase shifters. Of these, tap
changers are the most common at the
transmission level, and that i
Synchronous Machine Modeling Notes2
1.0 Inductances
Recall the relation between flux linkages
and currents developed in the previous
notes.
a La
L
b ab
c Lac
=
F LaF
D LaD
Q LaQ
Lab
Lb
Lac
Lb