24_Velez_Power System Protection, Transient Stability_p38

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Lecture 22

Power System Protection, Transient Stability

Professor Tom Overbye

Department of Electrical and

Computer Engineering

ECE 476

POWER SYSTEM ANALYSIS



1

Announcements

Be reading Chapters 9 and 10

After exam read Chapter 11

HW 9 is 8.4, 8.12, 9.1,9.2 (bus 2), 9.14; do by Nov 10 but

does not need to be turned in.

Start working on Design Project. Firm due date has been

extended to Dec 1 in class

Second exam is on Nov 15 in class. Same format as first

exam, except you can bring two note sheets (e.g., the one

from the first exam and another)

Exam/solution from 2008 will be posted on website shortly

Exam covers through Chapter 10



2

In the News: Boulder municipalization

• Last week Boulder, CO narrowly voted to move

forward with municipalization of their electric grid

• Currently Boulder is in the Xcel Energy electric service

territory (Xcel is a large Investor Owned Utility)• Xcel has recently decided not to continue funding

the Boulder “SmartGridCity” initiative, which has

cost $45 million, triple its original cost.

• Xcel does not wish to sell its electric grid inBoulder, saying it would be extremely expensive

for Boulder to go on their own.Source: NY Times 11/3/11; Thanks to Margaret for pointing out this story



3

Power System Protection

Main idea is to remove faults as quickly as possible

while leaving as much of the system intact as

possible

Fault sequence of events1. Fault occurs somewhere on the system, changing the

system currents and voltages

2. Current transformers (CTs) and potential transformers

(PTs) sensors detect the change in currents/voltages3. Relays use sensor input to determine whether a fault has

occurred

4. If fault occurs relays open circuit breakers to isolate fault



4

Power System Protection

Protection systems must be designed with both

primary protection and backup protection in case

primary protection devices fail

In designing power system protection systemsthere are two main types of systems that need to be

considered:

1. Radial: there is a single source of power, so power

always flows in a single direction; this is the

easiest from a protection point of view

2. Network: power can flow in either direction:

protection is much more involved



5

Radial Power System Protection

Radial systems are primarily used in the lower

voltage distribution systems. Protection actions

usually result in loss of customer load, but the

outages are usually quite local.The figure shows

potential protection

schemes for a

radial system. The

bottom scheme is

preferred since it

results in less lost load



6

Radial Power System Protection

In radial power systems the amount of fault current is

limited by the fault distance from the power source:

faults further done the feeder have less fault current

since the current is limited by feeder impedance Radial power system protection systems usually use

inverse-time overcurrent relays.

Coordination of relay current settings is needed to

open the correct breakers



7

Inverse Time Overcurrent Relays

Inverse time overcurrent relays respond instan-

taneously to a current above their maximum setting

They respond slower to currents below this value

but above the pickup current value



8

Inverse Time Relays, cont'd

The inverse time characteristic provides backup

protection since relays further upstream (closer to

power source) should eventually trip if relays closer

to the fault fail Challenge is to make sure the minimum pickup

current is set low enough to pick up all likely faults,

but high enough not to trip on load current

When outaged feeders are returned to service therecan be a large in-rush current as all the motors try to

simultaneously start; this in-rush current may re-trip

the feeder



9

Inverse Time Overcurrent Relays

Relays have

traditionally been

electromechanical

devices, but are

gradually being

replaced by

digital relays

Current and timesettings are ad-

justed using dials

on the relay



10

Protection of Network Systems

In a networked system there are a number of

difference sources of power. Power flows are

bidirectional

Networked system offer greater reliability, sincethe failure of a single device does not result in a

loss of load

Networked systems are usually used with the

transmission system, and are sometimes used withthe distribution systems, particularly in urban areas



11

Network System Protection

Removing networked elements require the opening

of circuit breakers at both ends of the device

There are several common protection schemes;

multiple overlapping schemes are usually used1. Directional relays with communication between

the device terminals

2. Impedance (distance) relays.

3. Differential protection



12

Directional Relays

Directional relays are commonly used to protect

high voltage transmission lines

Voltage and current measurements are used to

determine direction of current flow (into or out ofline)

Relays on both ends of line communicate and will

only trip the line if excessive current is flowing into

the line from both ends

– line carrier communication is popular in which a high

frequency signal (30 kHz to 300 kHz) is used

– microwave communication is sometimes used



13

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

V V Normally is high; during fault

I I

x Z



14

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 isinstantaneous

– 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



15

Impedance Relay Trip Characteristics

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



16

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



17

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 muchquicker 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)



18

Sequence of Events Recording

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 ofevents

Most utilities now have sequence of events

recording that provide time synchronization of at

least 1 microsecond





20

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) therotors 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



21

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



22

Example of Transient Behavior



23

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 anglechanges according to the mechanical dynamics

'( ) sinT ae

d

V E P X



24

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



25

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



26


s

s s

s

s

( )rotor angle

( )

inertia of machine at synchronous speedConvert 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

d

dt

P P J J

J S

P P J

S S S

2 s



27


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 s s s

B B s

s

B

m e s s

m e

P P J S S S

P P J f

S S f J

S

H H P P M

f f

P P

M



28

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

k x gM Mx Dx



29

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 aninfinite bus) through a transmission line with

impedance jXL



30

SMIB, cont’d

'

'

( ) sin

sin

ae

d L

a M

d L

E P

X X

E M D P X X



31

SMIB Equilibrium Points

'

Equilibrium points are determined by setting theright-hand side to zero

sina M

d L

E D P

X X

'

'th

1

sin 0

Define X

sin

a M

d L

d L

M th

a

E P

X X

X X

P X

E



32

Transient Stability Analysis

For transient stability analysis we need to consider

three systems

1. Prefault - before the fault occurs the system is

assumed to be at an equilibrium point2. Faulted - the fault changes the system equations,

moving the system away from its equilibrium

point

3. Postfault - after fault is cleared the system

hopefully returns to a new operating point



33

Transient Stability Solution Methods

There are two methods for solving the transient

stability problem

1. Numerical integration

this is by far the most common technique, particularlyfor large systems; during the fault and after the fault the

power system differential equations are solved using

numerical methods

2. Direct or energy methods; for a two bus systemthis method is known as the equal area criteria

mostly used to provide an intuitive insight into the

transient stability problem



34

SMIB Example

Assume a generator is supplying power to aninfinite bus through two parallel transmission lines.

Then a balanced three phase fault occurs at the

terminal of one of the lines. The fault is cleared by

the opening of this line’s circuit breakers.



35

SMIB Example, cont’d

Simplified prefault system

1

The prefault system has two

equilibrium points; the left one

is stable, the right one unstable

sin M th

a

P X

E



36

SMIB Example, Faulted System

During the fault the system changes

The equivalent system during the fault is then

During this fault no power can be transferred

from the generator to

the system



37

SMIB Example, Post Fault System

After the fault the system again changes

The equivalent system after the fault is then



SMIB Example, Dynamics

eDuring the disturbance the form of P ( ) changes,altering the power system dynamics:

1sina th

M

h

E V P

M X

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24_Velez_Power System Protection, Transient Stability_p38