Faults, Relaying, & Circuit Breakers - mty.itesm.mxe9tricas/Faults_Relays_C… · Faults, Relaying,...

Faults, Relaying, & Circuit

Breakers

ONR/NSF/EPRI/AEP Faculty Workshop-

First Course in Power Systems

June 18-22, 2007

Richard Wies ([email protected])- University of Alaska-Fairbanks

Dave Young- University of Deleware

2

Power Systems Curriculum at UAF

Undergraduate Courses

•EE 303 – Electric Machinery

•EE 471 – Automatic Control Systems

•EE 404 – Electric Power Systems

•EE 406 – Electric Power Engineering

•EE 408 – Power Electronics

3

EE 303: Electric Machinery (3 lec + 1 lab)

Text: Electric Machinery Fundamentals, by S. J. Chapman, McGraw-Hill, 4th ed., 2005.

Prerequisites: EE 204 (Electrical Engineering Fundamentals II)

Course Description:

Introduction to electromechanical energy conversion principles, characteristics

and applications of transformers, synchronous machines, induction machines,

and DC machines, single-phase and special purpose motors.


4


EE 404: Electric Power Systems (3 lec + 1 lab)

Text: Power Systems Analysis by J. J. Grainger and W. D. Stevenson, Jr., McGraw-Hill, 1994.

Prerequisites: EE 303 (Electrical Machinery)

Course Description:

Electrical power transmission and distribution systems, power flow,

symmetrical faults, and economic dispatch with computer-aided analysis.

5


EE 406: Electric Power Engr. (3 lec + 1 lab)

Text: Power System Analysis and Design by J. D. Glover and M. Sarma, 3rd ed., Brooks/Cole, the Wadsworth Group, a division of Thomson Learning, 2002.

Prerequisites: EE 404 (Electrical Power Systems)

Course Description:

Economic operation of power systems, symmetrical and unsymmetrical faults,

power system protection, dynamic power system stability, and computer-aided

fault and transient stability analysis.

6


EE 408: Power Electronics (3 lec.)

Text: Mohan, Undeland, and Robbins, Power Electronics: Converters, Applications, and Design, 3rd ed., Wiley, 2003.

Prerequisites: EE 303 (Electric Machinery) and EE 333 (Electronics)

Course Description:

Study current technology used in power conversion and control equipment.

Topics will include the theory and application of thyristors, rectifiers, DC-DC

converters, inverters, resonant converters, AC and DC switches and

regulators, power supplies, DC drives, and adjustable-speed drives including

variable-frequency drives.

© Copyright Ned Mohan 2006 7

CHAPTER 13

TRANSMISSION LINE

FAULTS, RELAYING AND

CIRCUIT BREAKERS


Chapter 13 Topics

Symmetrical Components

Sequence Networks

Three-Phase and Unbalanced

Fault Analysis

Sequence Impedance of Devices

Power System Protection

Relays

Circuit Breakers


Fig. 13-1 Fault in power system.

a

b

c

g

ai

f

bi

ci

a

b

c

g

aI

f

bI

cI

( )a ( )b

Fault (Symmetric or Unsymmetric) on a Balanced Network


Fig. 13-2 Sequence components.

2cI

1aI

1bI

1cI

2aI2bI

aI

bI

cI0cI

0aI0bI

Symmetrical Components

• 1-Positive

• 2-Negative

• 0-Zero


Transformation to and from Phase Variables

1201

24012Īa = Īa1+Īa2+Īa0

Īb = Īb1+Īb2+Īb0

Īc = Īc1+Īc2+Īc0

c

b

a

a

a

a

I

I

I

I

I

I

111

1

1

3

1 2

2

0

2

1

0

2

1

2

2

1

1

111

a

a

a

c

b

a

I

I

I

I

I

I

Īb1 = 2Īa1; Īc1 =

Īa1

Īb2 = Īa1; Īc2 = 2Īa1

(13-1)(13-2)

(13-3)

(13-5) (13-6)


Example Calculation of Symmetrical Components

694913847060

85715660340

63192620272

..

..

..

I

I

I

c

b

a

Given:

Find: Īa1, Īa2, and Īa0

4550

30750

1501

111

1

1

3

1 2

2

0

2

1

.

.

.

I

I

I

I

I

I

c

b

a

a

a

a

Solution: using 13-6


Fig. 13-3 Sequence networks.

1aE

1Z

1aV2aV 0aV

1aI 2aI 0aI

2Z 0Z

Sequence Networks: Per-Phase Representation of a Balanced Three-phase Representation


Fig. 13-4 Three-phase symmetrical fault.

a

b

c

g

aI

f

bI

cI

( )a

1aE

1Z

1 0aV

1aI

( )b

Three-Phase Symmetrical Fault (ground may or may no be involved)


Fig. 13-5 Single line to ground fault.

( )a

( )b

1aE

2aV

0aV

a

b

c

g

aI

f

fZ

1Z

2Z

0Z

1aI

2aI

0aI

3 fZ

1aV

Single-Line to Ground (SLF) Fault through a Fault Impedance

3021

aaaa

IIII

f

aaaa

ZZZZ

EIII

3021

1021

0cb II

0aV

Applying 13-6 for currents

Means all sequence

circuits are in series

at fault point.

(13-7)

1021 3 afafaaaa IZIZVVVV

(13-8)

(13-9 &

10)

(13-11

&12)

(13-13)


Fig. 13-6 Double line to ground fault.

( )a ( )b

1aE

a

bc

g

bI

f

1Z

1aI

1aVcI

2Z

2aI

2aV0Z

0aI

0aV

Double-Line to Ground Fault

02

021

02

02

1021

ZZ

ZZZ

ZZ

ZZ

EVVV aaaa

02

012

ZZ

ZII aa

3021

aaaa

VVVV

0aI

0cb VV

Applying 13-6 for voltages

Means all sequence

circuits are in parallel

at fault point.

(13-14)

(13-15)

(13-16)02

02

11

ZZ

ZZ

VI a

a

If Zg is present then

add 3Zg to all Z0.210 aaa III

0021 aaa III


Fig. 13-7 Double line fault (ground not involved).

( )a

a

bc

g

bI

f

cI

( )b

1aE1Z

1aI

1aV2Z

2aI

2aV

1f aZ I

Double-Line Fault (ground not involved)

12

22

1 )()( aaacb IIIII

12

22

1212 )( afaaaa IZVVVV

bfcb IZVV

0aI

cb II

Īa0 = 0 with no ground;

Va0 = 0 and no zero

sequence circuit.

(13-17)

(13-18)

(13-19)

21 aa II (13-22)

Applying 13-5, 13-18, & 13-22 for currents

(13-23)

Applying 13-5, 13-19, & 13-23 for voltages

(13-24)

121 afaa IZVV (13-25)


Positive:

Round rotor (sub-transient, transient, or steady

state):

Approximation:

Negative:

Produces air gap flux rotating in opposite direction of rotor at 2X synchronous speed.

Use damper circuits of d- and q-axes as dominant elements.

Approximation:

Zero:

Air gap flux is zero for sinusoidal mmf distribution in each phase

Use per-phase leakage reactance:

Also include 3Zn if neutral is grounded through Zn.

Sequence Impedance for Synchronous Generators

d'd

"d XXXXXX 111 ;;

120.X "d

1202

2 .XX

X"d

"d

20 50 X.XX l

(13-26)


Fig. 13-8 Path for zero-sequence currents in transformers.

( )a ( )b ( )c

Path for Zero-Sequence Currents in Transformers

Scanned from A. Bergen & V. Vittal, Power

Systems Analysis, 2nd ed., Prentice-Hall, New

Jersey, 2000.

• Use per phase leakage reactance for all

sequence impedances.


Fig. 13-9 Neutral grounded through an impedance. ( )a

nZ

( )b

0aV

0Z

0aI

3 nZ

Neutral Grounded through a Neutral Impedance)

0000222111 3)()()( acbacbacbacban IIIIIIIIIIIIII

0 0

nannng ZIZIV 03

000 )3( ana IZZV


Fig. 13-10 (a) One-line diagram of a simple power system and bus voltages.

1LoadP pu

0LoadQ

Bus-1

Bus-2

Bus-31 0.12genX pu

2 0.12genX pu

0 0.06genX pu1 0.10trX pu

2 0.10trX pu

00.10

trX pu

1 0.10LineX pu

2 0.10LineX pu

0 0.20LineX pu

1 1.0 0V pu0

3 0.98 11.79V pu

One-Line Diagram of a Simple System

• Calculate pre-fault voltage at bus-3 using

MATLAB Power Flow (CH.5) or PowerWorld

Simulator


• Use positive sequence impedances for all elements, and

use X” for generator under sub-transient conditions.

• Fault current is:

Fig. 13-11 Positive-sequence circuit for calculating a 3-phase fault on bus-2.

0.12j pu

1 1.0 0V pu

LoadI

faultI

0.10j pu 0.10j pu

E0.9604LoadR pu

Three-phase Fault on Bus-2 in the Simple System

loadload

P

VR

2

3

6760321120001 ..I.j.E load

pu3283694220

6760321

100120fault

...j

..

.j.j

EI

7911020417911980

01

3

....

pu.

V

SI loadload


Fig. 13-12 Sequence networks for calculating fault current due to SLG fault on bus-2.

1 1.0 0V pu

0.10j pu

E0.9604LoadR pu

0.12j pu 0.10j pu

0.9604LoadR pu

0.9604LoadR pu

1aV

2aV

0aV

0.10j pu0.12j pu 0.10j pu

0.10j pu0.06j pu 0.20j pu

1aV

1aI

2aI

0aI

0aV

Single-Line to Ground (SLG) Fault in the Simple System

3

785715

3

fault1a

..II


Fig. 13-13 A SLG fault in the example 3-bus power system.

1mP 1eP

2eP

Bus-1Bus-3

Bus-2

2mP

An SLG Fault in the Example 3-Bus System

• Use Y-Bus sequence components for calculating

voltages and currents in large systems.

1poswhere YZIZV

VYI

pospospospos

pospospos


Fig. 13-14 Protection equipment.

CB

R

CT

PT

Protection in Power System


Fig. 13-15 Current Transformer (CT) [5].

(a)

(b)

CT

Burden

Current Transformers (CT)


Fig. 13-16 Capacitor-Coupled Voltage Transformer (CCVT) [5].

(a) (b)

Capacitor-Coupled Voltage Transformers (CCVT)


Fig. 13-17 Differential relay.

CT

CT

CT

Relay

Differential Relays


Fig. 13-18 Directional over-current Relay.

CB

R

CT

PT

Directional Over-Current Relays


Fig. 13-19 Ground directional over-current Relay.

Time

instantaneous

Ground Directional Over-Current Relays for Ground Faults


Fig. 13-20 Impedance (distance) relay.

X

R

Impedance (Distance) Relays


Fig. 13-21 Microwave terminal [5].

Microwave Terminal for Pilot Relays


Fig. 13-22 Zones of protection.

Time

A B C

Zone 1: instantaneous

Zone 2: 20-25 cycles

Zone 3: 1-1.5 sec

Zones of Protection


Fig. 13-23 Protection of generator and the step-up transformer.

Gen

Relay RelayRelay

CT CT CTTransformer F1 F2

Protection of Generator and its Step-up Transformer


Fig. 13-24 Relying in the example 3-bus power system.

AB

P jQ

Zone1

Zone2

Zone2

Relaying in the 3-Bus Example Power System


Fig. 13-25 6SF circuit breaker [5].

Circuit Breakers


Fig. 13-26 Current in an RL circuit.

0 0 . 0 5 0 . 1 0 . 1 5 0 . 2- 1

- 0 . 5

0

0 . 5

1

1 . 5

2

asymmetricsymmetric offset

( )sv t ( )v t

( )i t

R L

( )a ( )b

0

Illustration of Current Offset in R-L Circuits

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