ECE 476 Power System Analysis Lecture 22: System Protection, Transient Stability Prof. Tom Overbye Dept. of Electrical and Computer Engineering University.

ECE 476 Power System Analysis

Lecture 22: System Protection, Transient Stability

Prof. Tom Overbye

Dept. of Electrical and Computer Engineering

University of Illinois at Urbana-Champaign

[email protected]

Announcements

• Read Chapters 10 and 11• Homework 10 is 9.1,9.2 (bus 3), 9.14, 9.16, 11.7. It

should be turned in on Dec 3 (no quiz)• Design project due date has been extended to Tuesday,

December 8– A useful paper associated with the design project is

T. J. Overbye, "Fostering intuitive minds for power system design," IEEE Power and Energy Magazine, pp. 42-49, July-August 2003.

– You can download it from campus computers at http://ieeexplore.ieee.org/xpl/abstractAuthors.jsp?arnumber=1213526

2

In the News: UI Solar Farm

• The UI 21 acre "solar farm" has its official ribbon cutting today

• It is suppose to produce a maximum of 5.87 MW, with 7.86 thousand MWhs per year (about 2% of the campus total); capacity factor of 15.3%

• UI buys powerfor ten yearsthen owns it,total of $15.5 million

• Cost per MWh (20 year life) is about $99Source: www.news-gazette.com/news/local/2015-11-19/ribbon-cutting-uis-solar-farm-set-morning.html

Impedance Relays

• Impedance (distance) relays measure ratio of voltage to current to determine if a fault exists on a particular line

1 1

12 12

Assume Z is the line impedance and x is the

normalized fault location (x 0 at bus 1, x 1 at bus 2)

V VNormally is high; during fault

I IxZ

4

Impedance Relays Protection Zones

• To avoid inadvertent tripping for faults on other transmission lines, impedance relays usually have several zones of protection:– zone 1 may be 80% of line for a 3f fault; trip is

instantaneous– zone 2 may cover 120% of line but with a delay to prevent

tripping for faults on adjacent lines– zone 3 went further; most removed due to 8/14/03 events

• The key problem is that different fault types will present the relays with different apparent impedances; adequate protection for a 3f fault gives very limited protection for LL faults

5

Impedance Relay Trip Characteristics

Source: August 14th 2003 Blackout Final Report, p. 78 6

Differential Relays

• Main idea behind differential protection is that during normal operation the net current into a device should sum to zero for each phase– transformer turns ratios must, of course, be considered

• Differential protection is used with geographically local devices– buses– transformers– generators

1 2 3 0 for each phase

except during a fault

I I I

7

Other Types of Relays

• In addition to providing fault protection, relays are used to protect the system against operational problems as well

• Being automatic devices, relays can respond much quicker than a human operator and therefore have an advantage when time is of the essence

• Other common types of relays include– under-frequency for load: e.g., 10% of system load must

be shed if system frequency falls to 59.3 Hz– over-frequency on generators– under-voltage on loads (less common)

8

Digital Fault Recorders (DFRs)

• During major system disturbances numerous relays at a number of substations may operate

• Event reconstruction requires time synchronization between substations to figure out the sequence of events

• Most utilities now have digital fault recorders (DFRs) to provide a detailed recording of system events with time resolution of at least 1 microsecond

• Some of this functionality is now included in digital relays

9

Use of GPS for Fault Location

• Since power system lines may span hundreds of miles, a key difficulty in power system restoration is determining the location of the fault

• One newer technique is the use of the global positioning system (GPS).

• GPS can provide time synchronization of about 1 microsecond

• Since the traveling electromagnetic waves propagate at about the speed of light (300m per microsecond), the fault location can be found by comparing arrival times of the waves at each substation

10

Power System Time Scales and Transient Stability

Image source: P.W. Sauer, M.A. Pai, Power System Dynamics and Stability, 1997, Fig 1.2, modified11

Example of Frequency Variation

• Figure shows Eastern Interconnect frequency variation after loss of 2600 MWs

12

Example of Transient Behavior

13Source: August 14th 2003 Blackout Final Report

Power Grid Disturbance Example

Time in Seconds

Figures show the frequency change as a result of the sudden loss of a large amount of generation in the Southern WECC

Frequency Contour

20191817161514131211109876543210

60

59.9959.98

59.97

59.96

59.9559.94

59.93

59.9259.91

59.9

59.8959.88

59.87

59.86

59.8559.84

59.83

59.8259.81

59.8

59.79

59.7859.77

59.76

59.7559.74

59.73

Power System Transient Stability

• In order to operate as an interconnected system all of the generators (and other synchronous machines) must remain in synchronism with one another– synchronism requires that (for two pole machines) the

rotors turn at exactly the same speed

• Loss of synchronism results in a condition in which no net power can be transferred between the machines

• A system is said to be transiently unstable if following a disturbance one or more of the generators lose synchronism

15

Generator Transient Stability Models

• In order to study the transient response of a power system we need to develop models for the generator valid during the transient time frame of several seconds following a system disturbance

• We need to develop both electrical and mechanical models for the generators

16

Generator Electrical Model

• The simplest generator model, known as the classical model, treats the generator as a voltage source behind the direct-axis transient reactance; the voltage magnitude is fixed, but its angle changes according to the mechanical dynamics

'( ) sinT ae

d

V EP

X

17

Generator Mechanical Model

Generator Mechanical Block Diagram

m

D

e

( )

mechanical input torque (N-m)

J moment of inertia of turbine & rotor

angular acceleration of turbine & rotor

T damping torque

T ( ) equivalent electrical torque

m m D e

m

T J T T

T

18

Generator Mechanical Model, cont’d

s

s s

s s

In general power = torque angular speed

Hence when a generator is spinning at speed

( )

( ( ))

( )

Initially we'll assume no damping (i.e., 0)

Then

m m D e

m m D e m

m m D e

D

m e

T J T T

T J T T P

P J T P

T

P P

s( )

is the mechanical power input, which is assumed

to be constant throughout the study time period

m

m

J

P

19

Generator Mechanical Model, cont’d

s

s s

s

s

( )

rotor angle

( )

inertia of machine at synchronous speed

Convert to per unit by dividing by MVA rating, ,

( ) 2

m e m

m s

mm m s

m m

m e m

B

m e s

B B B

P P J

t

ddt

P P J J

J

S

P P JS S S

2 s20

Generator Mechanical Model, cont’d

s

2

2

( ) 22

( ) 1(since 2 )

2

Define H per unit inertia constant (sec)2

All values are now converted to per unit

( ) Define

Then ( )

m e s

B B B s

m e ss s

B B s

s

B

m es s

m e

P P JS S S

P P Jf

S S f

JS

H HP P M

f f

P P

M 21

Generator Swing Equation

This equation is known as the generator swing equation

( )

Adding damping we get

( )

This equation is analogous to a mass suspended by

a spring

m e

m e

P P M

P P M D

kx gM Mx Dx

22

Single Machine Infinite Bus (SMIB)

• To understand the transient stability problem we’ll first consider the case of a single machine (generator) connected to a power system bus with a fixed voltage magnitude and angle (known as an infinite bus) through a transmission line with impedance jXL

23

SMIB, cont’d

'

'

( ) sin

sin

ae

d L

aM

d L

EP

X X

EM D P

X X

24

SMIB Equilibrium Points

'

Equilibrium points are determined by setting the

right-hand side to zero

sinaM

d L

EM D P

X X

'

'th

1

sin 0

Define X

sin

aM

d L

d L

M th

a

EP

X X

X X

P XE

25