EE 455 Power Systems Dynamics and Protecction
Due Thursday, February 25, 2010 at the start of class
Problems are worth 10 points each except as noted.
Problem Set 6
Solutions Rich Christie, Cesar Silva
1. Problem 6.1, p. 212 of Bergen & Vittal.
cos = 0.8
Power System Dynamics and Stability
Part 2
2015 D. Kirschen & University of Washington
1
Example 1
Pe0 = 1.0pu
E = 1.05pu
V = 1.0pu
j 0.4
G
j 0.2
j 0.1
j 0.4
j 0.4
j 0.2
E = 1.05
2015 D. Kirschen & University of Washington
j 0.1
j 0.4
V = 1.00
2
Step 1:
Fault Calculations in Large Systems
2015 D. Kirschen and the University of Washington
1
Modelling the Network for Faults
Network
ZTH
VTH
Location of fault
Location of fault
From the location of the fault, the entire network
is replaced by its Thevenin e
Power System Dynamics and Stability
Part 1
2015 D. Kirschen & University of Washington
1
What is Power System Dynamics?
The power flow equations represent the steady state
or equilibrium state of a power system
Voltage magnitudes and angles such that t
Symmetrical Components
Daniel Kirschen
2015 D. Kirschen and the University of Washington
1
Principle of Fault Current Calculations
Network
Location of fault
Prior to the fault, currents stay in the intact network
During the fault, currents flow from the
Unsymmetrical Faults
2015 D. Kirschen and the University of Washington
1
Types of Faults
Balanced faults
All three phases affected in the same way
Symmetry unaffected
Can be studied using a single phase model of the
system
Unbalanced faults
Not all
Power System Protection
Part 1
2015 D. Kirschen & University of Washington
1
Purpose of power system protection
Isolate faults as quickly as possible
Goals:
Safety
Avoid damage to the equipment
Stability
2015 D. Kirschen & University of Washington
EE 455: Power System
Dynamics and Protection
Winter 2016
Daniel Kirschen
n
n
n
n
At UW since March 2011
Previously at the University of Manchester
(UK)
Ten years in industry developing software
for electric utility control centers
Research interests:
q
q
Interrupting Faults
2015 D. Kirschen and the University of Washington
1
Circuit Breakers
Faults must be removed quickly:
Safety reasons
Protect equipment
Maintain system stability
Must isolate the faulted component
Must interrupt the fault current
Review of Per Unit System
Text: Chapter 3.3
2016 D. Kirschen & University of Washington
Why use the per unit system?
n
Multiple voltage levels:
q
n
n
n
n
765kV, 345 kV, 132 kV
Makes circuit analysis rather confusing
Impedance of transformers depends on s
Introduction to Faults
Daniel Kirschen
2015 D. Kirschen and the University of Washington
1
Faults
Failure of the insulation around
an electric cable
Creates a short circuit
An easier path for the current
A large fault current flows
through this short ci
EE 455 Power Systems Dynamics and Protection
Due Thursday, February 11, 2010 at the start of class
Problems are worth 10 points each except as noted.
Problem Set 5
SOLUTIONS Cesar Silva, Hamody Hindi 02/10
1. Problem 13.2, p. 526 of Bergen & Vittal
If a S
EE 455 Power Systems Dynamics and Protecction
Due Thursday, March 4, 2010 at the start of class
Problems are worth 10 points each except as noted.
Problem Set 7 Solutions
Rich Christie, Cesar Silva 02/09
1. Problem 14.6, p. 577 of Bergen & Vittal
(Hint: U
EE 455 Power Systems Dynamics and Protection
Due Thursday, January 28, 2010 at the start of class
Problems are worth 10 points each except as noted.
Problem Set 3 Solutions
Rich Christie, Cesar Silva, Hamody Hindi 01/10
1. Problem 12.12, p. 491 of Bergen
EE 455 Power Systems Dynamics and Protecction
Due Thursday, March 11, 2010 at the start of class
Problems are worth 10 points each
Problem Set 8
1. Problem 14.10, p. 578 of Bergen & Vittal
We need to calculate Ea in order to find PG() and be able to check
EE 455 Power Systems Dynamics and Protecction
Due Thursday, February 4, 2010 at the start of class
Problems are worth 10 points each except as noted.
SOLUTIONS
Problem Set 4
1. Show mathematically that the two formulatiuons for computing fault current,
[
EE 455 Power Systems Dynamics and Protecction
Problems are worth 10 points each.
Problem Set 2 Solutions
Rich Christie, Cesar Silva 01/09
1. Problem 12.4, p. 488 of Bergen & Vittal
Positive sequence:
Z
1, 60
a
Z
1, 0
If
g
Negative sequence:
Zero sequence:
Balanced Fault Current Calculations
Daniel Kirschen
2015 D. Kirschen and the University of Washington
1
Steps
Current following closure of an RL circuit
Fault at the terminal of a synchronous generator
Faults in a network
No-load approximation
Effec