slides psbook2006 revised july2007

7/28/2019 Slides PSBook2006 Revised July2007

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Copyright Ned Mohan 2006 1

Ned MohanOscar A. Schott Professor of Power Electronics and SystemsDepartment of Electrical and Computer EngineeringUniversity of MinnesotaMinneapolis, MN 55455USA

First Course on

POWER SYSTEMS


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Bus-1 Bus-3

Bus-2

1m P 1e P

2m P

2e P

P jQ+

200 km

150 km150 km

A 345-kV Example System


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TOPICS IN POWER SYSTEMS

Week Book Chapters Laboratory1 Chapter 1: Overview

Chapter 2: Fundamentals

Lab 1: Visit to a local substation; otherwise avirtual substation

2 Chapter 3: Energy Sources Lab 2: Introduction to PSCAD/EMTDC ; 3- phase circuits, vars, power-factor correction

3 Chapter 4: Transmission Lines Lab 3: Transmission Lines using PSCAD-

EMTDC 4 Chapter 5: Power Flow Lab 4: Power Flow using MATLAB and

PowerWorld

5 Chapter 6: Transformers Lab 5: Including Transformers in Power Flowusing PowerWorld and MATLAB

6 Chapter 7: HVDC, FACTS Lab 6: Power Converters and HVDC using PSCAD-EMTDC, HVDC in PowerWorld

7 Chapter 8: Distribution Systems Lab 7: Power Quality using PSCAD-EMTDC

8 Chapter 9: SynchronousGenerators

Lab 8: Synchronous Generators and AVR using PSCAD-EMTDC .

9 Chapter 10: Voltage Stability Lab 9: Voltage Regulation using PowerWorld

10 Chapter 11: Transient Stability Lab 10: Transient Stability using MATLAB

11 Chapter 12: InterconnectedSystems, Economic Dispatch

Lab 11: AGC using Simulink , and EconomicDispatch using PowerWorld

12 Chapter 13: Short-CircuitFaults, Relays, Circuit Breakers

Lab 12: Transmission Line Faults using PowerWorld and MATLAB

13 Chapter 14: Transient Over-Voltages, Surge Arrestors,Insulation Coordination

Lab 13: Over-voltages and Surge Arrestorsusing PSCAD-EMTDC


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Chapter 1

POWER SYSTEMS: A CHANGINGLANDSCAPE


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Fig. 1-1 Interconnected North American Power Grid [2].

NATURE OF POWER SYSTEMS


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Fig. 1-2 NERC Interconnections [3]. Source: NERC.

Control Areas


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Fig. 1-3 One-line diagram as an example.

13.8 kVTransmissionline

Generator

Load

Feeder

Step upTransformer

One-line Diagram


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CHANGING LANDSCAPE OF POWER SYSTEMS AND UTILITYDEREGULATION

Fig. 1-4 Changing landscape [4]. Source: ABB.( )a ( )b( )a ( )b


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CHAPTER 2

REVIEW OF BASIC

ELECTRIC CIRCUITS ANDELECTROMAGNETICCONCEPTS


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Fig. 2-1 Convention for voltages and currents.

i

av

+

bv

baabv

+

+ i

av

+

bv

baabv

+

+

Symbols andConventions


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Fig. 2-2 Phasor diagram.

Imaginary

Real

I I =

V V 0=

positive

angles

Imagin ary

Real

I I =

V V 0=

positive

angles

Phasors


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Fig. 2-3 A circuit (a) in time-domain and (b) in phasor-domain; (c) impedance triangle.

Im

Z

c jX

R

L jX

Re0

i(t )

L

R

C

+

v( t )

2V cos( t ) =V V 0=

I

L j L j X =

R

C 1

j j X C

=

+

( )a ( )b ( )c

Im

Z

c jX

R

L jX

Re0

Im

Z

c jX

R

L jX

Re0

i(t )

L

R

C

+

v( t )

2V cos( t ) =V V 0=

I

L j L j X =

R

C 1

j j X C

=

+

( )a ( )b ( )c

i(t )

L

R

C

+

v( t )

2V cos( t ) =

i(t )

L

R

C

+

v( t )

2V cos( t ) =V V 0=

I

L j L j X =

R

C 1

j j X C

=

+

V V 0=

I

L j L j X =

R

C 1

j j X C

=

+

( )a ( )b ( )c

Phasor Analysis


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Fig. 2-4 Impedance network of Example 2-1.

5 j

0.1 j

2 5 j

0.1 j

2

Example of ImpedanceCalculation


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Fig. 2-5 Circuit of Example 2-2.

0.3 0.5 j 0.2 j

15 j 7.0

+

1V

1 I

m I 2 I

Example of ImpedanceCalculation


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Figure 2-6 A generic circuit divided into two sub-circuits.

( ) ( ) ( ) p t v t i t =

+

Subcircuit 1 Subcircuit 2( )v t

Power Flow


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Figure 2-7 Instantaneous power with sinusoidal currents and voltages.

( )i t ( )v t

t

( ) p t averagepower

0

( )i t

( )v t

/

t


0

( )a ( )b( )i t ( )v t

t


0

( )i t

( )v t

/

t


0

( )a ( )b

Real and ReactivePower


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Fig. 2-8 (a) Circuit in phasor-domain; (b) phasor diagram; (c) power triangle.

V

I

S P jQ= +

+

Subcircuit 1 Subcircuit 2

vV V =

i I I =

Im

Re

Q

P

S Im

Re

( a )

( b ) ( c )

V

I

S P jQ= +

+

Subcircuit 1 Subcircuit 2

vV V =

i I I =

Im

Re

Q

P

S Im

Re

( a )

( b ) ( c )

P, Q and VA by Phasors


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Fig. 2-9 Power factor correction in Example 2-5.

+

1V

L P P =

C jQ

L L P jQ+13.963 j

Example of Power Factor Correction


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Fig. 2-10 One-line diagram of a three-phase transmission and distribution system.

Feeder

Step upTransformer

Generator

Transmissionline

13.8 kV

Load

One-line Diagram


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Fig. 2-11 Three-phase voltages in time and phasor domain.

( )bnv t

t 0

23

( )cnv t ( )anv t

23

120

a b c

positivesequence

bnV

cnV

anV 120

120

( )a

( )b

Three-Phase Voltages


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Fig. 2-12 Balanced wye-connected, three-phase circuit.

a I

bnV cnV +

c I

L Z

b I c b

a

n N

anV +

+

a I

bnV cnV

+

c I

L Z

b I c b

a

n N

anV

+

+

n I

( a ) (b)

a I

bnV cnV +

c I

L Z

b I c b

a

n N

anV +

+

a I

bnV cnV +

c I

L Z

b I c b

a

n N

anV +

+

a I

bnV cnV

+

c I

L Z

b I c b

a

n N

anV

+

+

n I

( a ) (b)

Balanced Three-PhaseCircuit Analysis


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Fig. 2-14 Balanced three-phase network with mutual couplings.

a AaA Z

(Hypothetical)

self Z

self Z

self Z

mutual Z

mutual Z

mutual Z

a

b

c

A

B

C

a I

b I

c I

( )a ( )b

Balanced MutualCoupling


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Fig. 2-15 Line-to-line voltages in a three-phase circuit.

o30

anV

bV abV

cnV

caV

bcV

bnV

Line-Line Voltages


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Fig. 2-16 Delta-wye transformation.

a I

Z

cb

a

Z

a I

bc I ca I

ab I

Z Z c b

a

( b )( a )

Z

Z

a I

Z

cb

a

Z

a I

bc I ca I

ab I

Z Z c b

a

( b )( a )

Z

Z

Wye-DeltaTransformation


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Fig. 2-17 Power transfer between two ac systems.

sV RV

+

+

I

jX

RV

sV

I

( )a

( )b

jXI

Power Flow in ACSystems


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Fig. 2-18 Power as a function of .

max/ P P

0

0.5

090 0180

1.0

Power-Angle Diagram


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Per Unit Quantities, , basebase base base

base

V R X Z

I = (in ) (2-48)

, , basebase base basebase

I G B Y

V = (in ) (2-49)

( ), ,base base base basebase P Q VA V I = (in Watt, VAR, or VA) (2-50)

In terms of these base quantities, the per-unit quantities can be specified as

actual valuePer-UnitValue =

base value(2-51)


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Fig. 2-19 Energy Efficiency /o in P P = .

in P o P

loss P

Power SystemApparatus

Energy Efficiency of Apparatus


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Fig. 2-20 Amperes Law.

3i

2i

1i H

dl

(a) (b) (c)

3i

2i

1i H

dl

3i

2i

1i H

dl

(a) (b) (c)

Electro-MagneticConcepts: Amperes Law


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Fig. 2-22 B-H characteristic of ferromagnetic materials.

m B

m H

sat B

o

o

m

m B

m H

(a) (b)

m B

m H

m B

m H

sat B

o

o

m

m B

m H

sat B

o

o

m

m B

m H

(a) (b)

B-H Curves inFerromagnetic Materials


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Fig. 2-23 Toroid with flux m .

m A

m

m A

m

Flux and Flux-Density


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Inductance

Fig. 2-24 Coil inductance.

2

mm

m m

N L

A

=A

m ( ) N

m ( )m A( )m

m Bm H m

N A

i

2

mm

m m

N L

A

=A

m ( ) N

m ( )m A( )m

m Bm H m

N A

i

(a) (b)

m

m m A

i

N

m

m m A

i

N


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Fig. 2-25 Rectangular toroid.

h

w r

h

w r

Example of a Toroid


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Fig. 2-27 Example 2-11.

( )t ( )e t

t 0

( )t ( )e t

t 0

Plot of time-varying Fluxand Voltage


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Fig. 2-28 Including leakage flux.

(a) (b)

i

+

e

i

+

e

i

+

e

m

l

i

+

e

m

l

Leakage Flux


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Fig. 2-29 Analysis including the leakage flux.

( )v t +

R

m

l L( )i t

( )me t ( )e t +

+

( )v t +

R

m

l L( )i t

( )me t ( )e t +

+

l di

Ldt

( )me t ( )e t

+

+

+ ( )i t

m L

l L

l di

Ldt

( )me t ( )e t

+

+

+ ( )i t

m L

l L

(a) (b)

Representation of LeakageFlux by LeakageInductance


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CHAPTER 3

ELECTRIC ENERGY ANDTHE ENVIRONMENT


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Fig. 3-2 Electric power generation by various fuel types in the U.S. in 2005 [1].

Power Generation byVarious Fuel Types in theU.S.


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Fig. 3-3 Hydro power (Source: www.bpa.gov ).

H Generator

Penstock

Turbine

Water

Hydro Power Generation


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Fig. 3-4 Rankine thermodynamic cycle in coal-fired power plants.

Steam at High pressure

Pump

Heat in

Heat out

TurbineBoiler

Condenser

Gen

Rankine ThermodynamicCycle in Coal Plants

Visit the following website for Power Plant Animations:http://www.cf.missouri.edu/energy/?fun=1&flash=ppmap


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Fig. 3-5 Brayton thermodynamic cycle in natural-gas power plants.

Air in

Compressor Turbine

Exhaust

Fuel in

CombustionChamber

Brayton Cycle in GasTurbines


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Fig. 3-6 (a) BWR and (b) PWR reactors [5].( )a ( )b

Nuclear Power PlantTypes

Visit the following websites for Nuclear Power Plant Animations:PWR: http://www.nrc.gov/reading-rm/basic-ref/students/animated-pwr.htmlBWR: http://www.nrc.gov/reading-rm/basic-ref/students/animated-bwr.html


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Fig. 3-7 Wind-resource map of the United States [6].

Wind Resources in theU.S.


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Fig. 3-8 pc as a function of [7]; these would vary based on the turbine design.

Coefficient of Performance

Wind Generation using an


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Fig. 3-9 Induction generator directly connected to the grid [8].

Utility

InductionGenerator

WindTurbine

Wind Generation using an

Induction Generator Connected Directly to the AC Grid


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Fig. 3-11 Power Electronics connected generator [10].

Gen

Utility

Power Electronics Interface

1Conv 2Conv

Wind Generation using an ACGenerator Connected through Power Electronics


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Fig. 3-12 PV cell characteristics [11].

Photovoltaics


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Fig. 3-13 Photovoltaic systems.

IsolatedDC-DC

Converter

PWMConverter

Max. Power- point Tracker

Utility1

IsolatedDC-DC

Converter

PWMConverter

Max. Power- point Tracker

Utility1

Interfacing PV with ACGrid


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Fig. 3-14 Fuel cell v-i relationship and cell power [12].

1.4 -

1.2 -

1 -

0.8 -

0.6 -

0.4 -

0.2 -

0 - - 0

- 200

- 400

- 600

- 800

- 1000

- 1200

|

0|

500|

1000|

1500|

2000

Maximum Theoretical Voltage

Current Density ( iin mA/cm2 )

ActivationLoss es

O h m i c Lo s s e s

MassTr anspor t

Losse s

OpenCircuitVoltage

C e l

l P o w e r

( P

C i n m

W )

C e l

l V o

l t a g e

( V

C i n

V o

l t s

)

- gE =2 F

Cell Power P C = V C x i

1.4 -

1.2 -

1 -

0.8 -

0.6 -

0.4 -

0.2 -

0 -

1.4 -

1.2 -

1 -

0.8 -

0.6 -

0.4 -

0.2 -

0 - - 0

- 200

- 400

- 600

- 800

- 1000

- 1200

- 0

- 200

- 400

- 600

- 800

- 1000

- 1200

|

0|

500|

1000|

1500|

2000|

0|

500|

1000|

1500|

2000

Maximum Theoretical Voltage

Current Density ( iin mA/cm2 )

ActivationLoss es

O h m i c Lo s s e s

MassTr anspor t

Losse s

OpenCircuitVoltage

C e l

l P o w e r

( P

C i n m

W )

C e l

l V o

l t a g e

( V

C i n

V o

l t s

)

- gE =2 F - gE =2 F

Cell Power P C = V C x i

Fuel Cells


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Fig. 3-15 Greenhouse effect [13].

Greenhouse Effect


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Fig. 3-16 Resource mix at XcelEnergy [14].

1

12

2

3

3445

5

6

6

1

12

2

3

3445

5

6

6

Resource mixXcelEnergy


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Fig. 3-17 Electric power industry fuel costs in the U.S. in 2005 [1].

Fuel Costs in the U.S. in2005


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CHAPTER 4

AC TRANSMISSION LINES

AND UNDERGROUNDCABLES


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Copyright Ned Mohan 2006 59Fig. 4-1 500-kV transmission line (Source: University of Minnesota EMTP course).( )a ( )c

( )b

( )a ( )c

( )b

Transmission Tower,Conductor and Bundling


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Fig. 4-2 Transposition of transmission lines.

1 D2 D

3 D

1 cycle

( )a ( )b

a

b

c

Transposition


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Fig. 4-3 Distributed parameter representation on a per-phase basis.

line

neutral (zeroimpedance)

line R L

C

Distributed Parameters

Calculation of


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Fig. 4-4 (a) Cross-section of ACSR conductors, (b) skin-effect in a solid conductor.

D

T J

towards center surface( )a ( )b

Calculation of Transmission LineResistance: Skin Effect

Calculation of


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Fig. 4-5 Flux linkage with conductor-a.

( )a ( )b ( )c

Dr ai bi

ci

r ai x dx

a b

c

a b

c

D

D

bidx

xa

b

c

Calculation of Transmission LineInductance


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Fig. 4-6 Electric field due to a charge.

x

q1 21 x

2 x

Electric Field Due toTransmission Line Voltage

Calculation of Transmission Line


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Fig. 4-7 Shunt capacitances.

aq bq

cq

a b

c

D

aq bq

cq

a b

c

D a b

c

a b

c

( )a ( )b

C C

C

n

hypotheticalneutral

Calculation of Transmission LineCapacitance

Typical Parameters for various


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Table 4-1

Transmission Line Parameters with Bundled Conductors (except at 230 kV)at 60 Hz [2, 6]

Nominal Voltage ( / ) R km ( / ) L km ( / )C km

230 kV 0.055 0.489 3.373

345 kV 0.037 0.376 4.518500 kV 0.029 0.326 5.220

765 kV 0.013 0.339 4.988

ypVoltage Transmission Lines

Calculating Transmission


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Fig. 4-8 A 345-kV, single-conductor per phase, transmission system.

Calculating TransmissionLine Parameters usingEMTDC


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Fig. 4-9 Distributed per-phase transmission line ( G not shown).

+

( ) RV s

+

( )S V s

+

( ) xV s

0 x

( ) R I s( )S I s R sL

1 sC

( ) x I s

Distributed-Parameter Representation


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Fig. 4-10 Per-phase transmission line terminated with a resistance equal to c Z .

+

S V

S I j L

1 j

C

c Z

+

0 R RV V =

0 x

S V RV

( )a ( )b

R I

Voltage Profile under SIL


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Table 4-3

Loadability of Transmission Lines [6]

Line Length (km) Limiting Factor Multiple of SIL

0 - 80 Thermal > 3

80 - 240 5% Voltage Drop 1.5 - 3240 - 480 Stability 1.0 1.5

Loadability of Transmission Lines


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Fig. 4-11 Long line representation.

+

( )S V s

( )S I s+

( ) RV s

( ) R I s series Z

2 shunt Y

2 shunt Y

Long-LineRepresentation

Transmission Line


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Fig. 4-12 Per-phase transmission line representation based on length.

+

S V

S I

+

RV

R I series Z

2 shunt Y

2 shunt Y

+

S V

S I

+

RV

R I line j L

2

line

jC

2line

jC

line R

( )a ( )b ( )c

+

S V

S I

+

RV

R I line j L line R

Representations


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Fig. 4-13 Underground cable.

Underground Cables


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CHAPTER 5

POWER FLOW IN

POWER SYSTEMNETWORKS


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Table 5-1 Per-Unit Values in the Example System

Line Series Impedance Z in (pu) Total Susceptance B in (pu)

1-2 12 (5.55 56.4) Z j= + = (0.0047 0.0474) j+ pu 675Total B = = (0.8034) pu

1-3 13 (7.40 75.2) Z j= + = (0.0062 0.0632) j+ pu 900Total B = = (1.0712) pu

2-3 23 (5.55 56.4) Z j= + = (0.0047 0.0474) j+ pu 675Total B = = (0.8034) pu

Transmission Lines inExample Power System


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Fig. 5-2 Example system of Fig. 5-1 for assembling Y-bus matrix.

Bus 1 Bus 3

Bus 2

1 I

2 I

3 I

13 Z

12 Z 23 Z 1V 3V

2V

Calculating Y-Bus in theExample Power System


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Fig. 5-4 Power-Flow results of Example 5-4.

01 1 0V pu=

02 1.05 -2.07V pu=

03 0.978 -8.79V pu=

( )0.69 - 1.11 j pu

( )2.39 0.29 j pu+

( )2.68 1.48 j pu+

( )5.0 1.0 j pu+1 1 (3.08 - 0.82) P jQ j pu+ =

2 2 ( 2.0 2.67) P jQ j pu+ = +

Power Flow Results in theExample Power System


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CHAPTER 6

TRANSFORMERS IN POWER SYSTEMS


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Fig. 6-1 Principle of transformers, beginning with just one coil.

+

1e1 N

m +

1e1 N

m mi+

1em L

mi+

1em L

(a) (b)

Transformer Principle:Generation of Flux


83/243


Fig. 6-2 B-H characteristics of ferromagnetic materials.

m B

m H

m B

m H

sat B

o

o

m

m B

m H

sat B

o

o

m

m B

m H

(a) (b)

Core in Transformers


84/243


Fig. 6-3 Transformer with the open-circuited second coil.

+

mi+

1e m L

IdealTransformer

1 N 2 N

2e

+

mi+

1e m L

IdealTransformer

1 N 2 N

2e

+

1e1 N

m

2e

2 N

+

+

1e1 N

m

2e

2 N

+

(a) (b)

Flux Coupling

Transformer with Load


85/243


Fig. 6-4 Transformer with load connected to the secondary winding.

+

1e1 N

m

2e

2 N

+

( )1i t

( )2i t

+

1e1 N

m

2e

2 N

+

( )1i t

( )2i t

( )2i t ( )1i t

+

mi+

1e m L

Ideal

Transformer

1 N 2 N

2e

( )2i t ( )2i t ( )1i t

+

mi+

1e m L

Ideal

Transformer

1 N 2 N

2e

( )2i t

(a) (b)

Connected to theSecondary


86/243


Fig. 6-5 Transformer equivalent circuit including leakage impedances and core losses.

'

2 I 1 I

+

mi+

1 E m jX

Ideal Transformer

1 N 2 N

2 E

2 I 1

Rl1 jX 2 Rl2 jX

2V

+

1V

+

Real Transformer

he R

'

2 I 1 I

+

mi+

1 E m jX

Ideal Transformer

1 N 2 N

2 E

2 I 1

Rl1 jX 2 Rl2 jX

2V

+

1V

+

Real Transformer

he R

Transformer Model


87/243


Fig. 6-6 Eddy currents in the transformer core.

m

circulatingcurrents

im

circulatingcurrents

i

m

circulatingcurrents

m

circulatingcurrents

(a) (b)

Eddy Current andHysteresis Losses


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Fig. 6-7 Simplified transformer model.

+

pV

+

sV

p I s I p Z s Z

1: n

pn sn

+

sV

Transformer SimplifiedModel

Transferring Leakage


89/243

Copyright Ned Mohan 2006 89Fig. 6-8 Transferring leakage impedances across the ideal transformer of the model.

+

pV +

sV

p I s I ps Z

1: n

pn sn

+

pV

+

sV

p I s I sp Z 1: n

pn sn

( )a

( )b

Impedances from One Sideto Another


90/243


Fig. 6-9 Transformer equivalent circuit in per unit (pu).

+

(pu) pV +

(pu) sV

(pu) I (pu) I (pu)tr Z

Transformer EquivalentCircuit in Per Unit

Connection of Transformer d


91/243


Fig. 6-10 Winding connections in a three-phase system.( )a ( )b

Windings

Including Nominal Turns-R i T f i


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Fig. 6-11 Including nominal-voltage transformers in per-unit.

345/500 kV 500/345 kV

500 kV Bus 3Bus 1

Ratio Transformer inPower Flow Studies

A T f


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Fig. 6-12 Auto-transformer.

+

1V

+

2V

1 I

1n2n

( )a

2 I

+

1V

( )1 2V V +

1 I

1n

2n2 I

( )1 2 I I +

+

2

V

( )b

+

Auto-Transformer

Phase-Shift Due to Wye-D l T f


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Fig. 6-13 Phase-shift in -Y connected transformers.

( )c

+

AV

+

aV

03012:

3 jn e n

( )a

a

bc

A

B

C ( )b

aV AV

1n

2n

Delta Transformers

Phase-Shift Control byT f


95/243


Fig. 6-14 Transformer for phase-angle control.

a

bc

a

b

c

( )a ( )b

aV

bV cV

abV

bcV

caV

( )c

aV

bV

cV

a bV

b cV

c aV

aV

a

bc

a

b

c

a

bc

a

b

c

( )a ( )b

aV

bV cV

abV

bcV

caV

( )c

aV

bV

cV

a bV

b cV

c aV

aV

Transformers

Three-Winding Auto-T f


96/243


Fig. 6-15 Three-winding auto-transformer.

H

L T H

L

T

( ) H Z

( ) L Z

( )T Z

1n

2n

3n

( )a( )b

a

bc

A

B

C

a a

a

A

C

H

L T H

L

T

( ) H Z

( ) L Z

( )T Z

1n

2n

3n

( )a( )b

a

bc

A

B

C

a a

a

A

C

Transformers

General Representation of A t d Ph Shift


97/243


Fig. 6-16 General representation of an auto-transformer and a phase-shifter.

+

1V

1: t

1 I 2 I

+

2V

+

2V t

1/Y Z =A A

Auto- and Phase-ShiftTransformers

PU Representation of Off-Nominal T rns Ratio


98/243


Fig. 6-17 Transformer with an off-nominal turns-ratio or taps in per unit; t is real.

+

1V

1/Y Z =A A

1: t

1 I 2 I

+

2V

( )a ( )b

11 Y

t

A

2

1 1Y

t t

A

/Y t A+

1V

+

2V

1 I 2 I

11 Y

t

A

2

1 1Y

t t

A

/Y t A+

1V

+

2V

1 I 2 I

Nominal Turns-RatioTransformers

Example of Off-Nominal Turns-Ratio

Transformers


99/243


Fig. 6-18 Transformer of Example 6-3.

+

1V

0.1 j pu

1: t

1 I 2 I

+

2V

( )a ( )b

1 0.909Y j pu=

2 0.826Y j pu=

0.11 s Z j pu=

+

1V

+

2V

1 I 2 I

Transformers

CHAPTER 7


100/243


HIGH VOLTAGE DC (HVDC)

TRANSMISSION SYSTEMS

Symbols and Capabilitiesof Power SemiconductorD i


101/243


Fig. 7-1 Power semiconductor devices.

Thyristor IGBT MOSFETIGCT(a)

101 102 103 104

102

104

106

108

T h y r i s

t o r

IGBT

MOSFET

P o w e r

( V A )

Switching Frequency (Hz)

IGCT

(b)



101 102 103 104

102

104

106

108

T h y r i s

t o r

IGBT

MOSFET

P o w e r

( V A )


IGCT

(b)

101 102 103 104

102

104

106

108

T h y r i s

t o r

IGBT

MOSFET

P o w e r

( V A )


IGCT

101 102 103 104

102

104

106

108

T h y r i s

t o r

IGBT

MOSFET

P o w e r

( V A )


IGCT

(b)

of Power Semiconductor Devices

Power Semiconductor Devices and Applications


102/243


Figure 7-2 Power semiconductor devices: (a) ratings (source: Siemens), (b) variousapplications (source: ABB).

( )a

Device blocking voltage [V]

D e v

i c e c u r r e n

t [ A ]

10 410 310 210 1

10 4

10 3

10 2

10 1

10 0

HVDCTraction

Motor Drive

Power Supply

Auto-motive

Lighting

FACTS


D e v

i c e c u r r e n

t [ A ]

10 410 310 210 1

10 4

10 3

10 2

10 1

10 0


D e v

i c e c u r r e n

t [ A ]

10 410 310 210 1

10 4

10 3

10 2

10 1

10 0

HVDCTraction

Motor Drive

Power Supply

Auto-motive

Lighting

FACTS

( )b( )a


D e v

i c e c u r r e n

t [ A ]

10 410 310 210 1

10 4

10 3

10 2

10 1

10 0

HVDCTraction

Motor Drive

Power Supply

Auto-motive

Lighting

FACTS


D e v

i c e c u r r e n

t [ A ]

10 410 310 210 1

10 4

10 3

10 2

10 1

10 0


D e v

i c e c u r r e n

t [ A ]

10 410 310 210 1

10 4

10 3

10 2

10 1

10 0

HVDCTraction

Motor Drive

Power Supply

Auto-motive

Lighting

FACTS

( )b

Devices and Applications

HVDC System


103/243


Fig. 7-3 HVDC system one-line diagram.1 AC 2 AC

HVDC Line

HVDC System

HVDC Systems: Voltage-Link and Current Link


104/243


Fig. 7-4 HVDC systems: (a) Current-Link, and (b) Voltage-Link.

AC1 AC2

+

AC1 AC2AC1 AC2AC1 AC2

+

AC1 AC2AC1 AC2AC1 AC2AC1 AC2

( )a ( )b

Link and Current-Link

HVDC Projects in NorthAmerica


105/243


Fig. 7-5 HVDC projects, mostly current-link systems, in North America [source: ABB]

3100MW

1920MW

200MW

200MW

200MW

200MW

200MW

210MW

150MW

200MW

600MW

1000MW500MW

1000MW

36MW

312MW

370MW

320MW

100MW

200MW

350MW

330MW

1620MW

2000MW

2000MW

690MW

2250MW

2138MW

3100MW

1920MW

200MW

200MW

200MW

200MW

200MW

210MW

150MW

200MW

600MW

1000MW500MW

1000MW

36MW

312MW

370MW

320MW

100MW

200MW

350MW

330MW

1620MW

2000MW

2000MW

690MW

2250MW

2138MW

America

Current-Link HVDCSystem


106/243


Fig. 7-6 Block diagram of a current-link HVDC system.

System

Thyristors


107/243


Fig. 7-7 Thyristors.

K

A

G

P

N

P

N

A

G

pn1

pn2

pn3

K

(a) (b)

K

A

GK

A

G

P

N

P

N

A

G

pn1

pn2

pn3

K

P

N

P

N

A

G

pn1

pn2

pn3

K

(a) (b)

Thyristors

Primitive Thyristor Circuits


108/243


Fig. 7-8 Thyristor circuit with a resistive load and a series inductance.

( )b

t

t

t

0

0

0

d vd V

sv si

Gi

0t =

( )a

si

s L+

+

d v sv R

( )b

t

t

t

0

0

0

d vd V

sv si

Gi

0t =

( )b

t

t

t

0

0

0

d vd V

sv si

Gi

0t =

( )a

si

s L+

+

d v sv R( )a

si

s L+

+

d v sv R

Circuits

Three-Phase Thyristor Converter


109/243


Fig. 7-9 Three-phase Full-Bridge thyristor converter.

(a)

d i

6

5

4 2

1 3

cnv +

+

+anv

bnv s L

ai

+

+anv ai

d I +

d v

N

P

1

3

5

46

2

(b)

n n

(a)

d i

6

5

4 2

1 3

cnv +

+

+anv

bnv s L

ai

+

+anv ai

d I +

d v

N

P

1

3

5

46

2

(b)

n n

+

d v

(a)

d i

6

5

4 2

1 3

cnv +

+

+anv

bnv s L

ai

+

+anv ai

d I +

d v

N

P

1

3

5

46

2

(b)

n n

(a)

d i

6

5

4 2

1 3

cnv +

+

+anv

bnv s L

ai

+

+anv ai

d I +

d v

N

P

1

3

5

46

2

(b)

n n

+

d v

Converter

Three-Phase DiodeRectifier Waveforms


110/243


Fig. 7-10 Waveforms in a three-phase rectifier with 0 s

L = and 0 = .

t 0

cvbvav

(a)

ai

0o120

o60t

bi

0

ci

0

N v

P v

(c)t

doV

LL2V d v

0(b)

t

t

t 0

cvbvav

(a)

ai

0o120

o60t

bi

0

ci

0

N v

P v

(c)t

doV

LL2V d v

0(b)

t

t

Rectifier Waveforms

Three-Phase Thyristor Converter Waveforms withzero AC-Side Inductance


111/243

Copyright Ned Mohan 2006 111Fig. 7-11 Waveforms with 0 s L = .

0

0

0

0

t

t

t

t

anv bnv cnv Pnv

Nnv

A

ai

bi

ci

1

4

3

66

1

5 5

2

4

0

0

0

0

t

t

t

t

anv bnv cnv Pnv

Nnv

A

ai

bi

ci

1

4

3

66

1

5 5

2

4

Converter Waveforms withzero AC-Side Inductance

Three-Phase Inverter Waveforms


112/243

Copyright Ned Mohan 2006 112Fig. 7-12 Waveforms in the inverter mode.

0

0

0

0

t

t

t

t

anv bnv cnv

Pnv

Nnv

ai

bi

ci

1

4

3

6

1

5

2

4

3

2

0

0

0

0

t

t

t

t

anv bnv cnv

Pnv

Nnv

ai

bi

ci

1

4

3

6

1

5

2

4

3

2

Waveforms

DC-Side Voltage as aFunction of Delay Angle


113/243


Fig. 7-13 Average dc-side voltage as a function of .( )b( )a

00

d V

090 0160

0180

d V

d I

Rectifier

d d P V I = = +

Inverter d d P V I = =

Function of Delay Angle

Thyristor Converter Waveforms in thePresence of AC-SideI d


114/243


Fig. 7-14 Waveforms with s L .

0

0

t

t

anv bnv cnv Pnv

Nnv

u A

ai 1

4

1

4

u

0

0

t

t

anv bnv cnv Pnv

Nnv

u A

ai 1

4

1

4

u

Inductance


115/243


116/243

( )ai Y Y 12-Pulse Waveforms


117/243


Fig. 7-17 Six-pulse and 12-pulse current and voltage waveforms [2].

( )a ( )b

( )ai Y

HVDC SystemRepresentation for Control


118/243


Fig. 7-18 A pole of an HVDC system.

d i

+

1d v

+

2d vAC 1 AC 2AC 1 AC 2

d R d L

d i

+

1d v

+

2d vAC 1 AC 2AC 1 AC 2

d R d L

p


119/243

A Voltage-Link HVDC

System in NortheasternU.S.


120/243

Copyright Ned Mohan 2006 120Fig. 7-20 Voltage-link HVDC transmission system [source: ABB].

y

Voltage-Link HVDCSystem Block Diagram


121/243


Fig. 7-21 Block diagram of voltage-link HVDC system.

AC1 AC2

+

AC1 AC2AC1 AC2AC1 AC2

+

1 1, P Q 2 2, P Q

Phasor Diagram on the Ac-

Side of the Voltage-LinkConverter


122/243


Fig. 7-22 Block diagram of a voltage-link converter and the phasor diagram.

+

d V

convv

L

busv Li

+

d V

convv

L

busv Li

+

convV

L I

+

busV

+ L L jX I

( )a ( )b ( )c

L I

L I

L L jX I

convV

busV

Representation of Voltage-

Link Converter with IdealTransformers


123/243


Fig. 7-23 Synthesis of sinusoidal voltages.

+

d V

abc

1: ad 1: bd 1: cd 1: ad

ai

d V

dai

+

aN v

( )a ( )b

Synthesis of AverageSinusoidal Voltages


124/243


Fig. 7-24 Sinusoidal variation of turns-ratio ad .

1

0.5

0

d V

0.5 d V

0

t

t

ad

aN v

ad

aV

Converter Output Voltages

and Voltages across theLoad


125/243


Fig. 7-25 Three-phase synthesis.

a

bc

N

2d V

2d

V 2

d V

av bv cvac-side

( )a

d V

0.5 d V

0

av

t

( )a

aN v bN v cN v

Buck Boost

Switching Power-Pole of Voltage-Link Converters


126/243


Fig. 7-26 Realization of the ideal transformer functionality.

aq

+

d V

daiai

a

N

+

aN v

(a) (b)

+

d V

aq

Buck Boost

aq

ai+

aN v

Switching in Sinusoidal

Average VoltageWaveform


127/243


Fig. 7-27 PWM to synthesize sinusoidal waveform.

aN v

0 t

d V

aN v

aN v

aN v

0

0 sT

( )a

( )b

hV

1 f s f 2 s f 3 s f


128/243


CHAPTER 8

Distribution System, Loads

and Power Quality


129/243


130/243

Lighting 19%

Lighting 19%

Lighting 19%

Utility Load Distribution


131/243


Fig. 8-3 Utility loads.

Motors 51%HVAC 16%

IT14%

Lighting 19%

Motors 51%HVAC 16%

IT14%

Lighting 19%

Motors 51%HVAC 16%

IT14%

Lighting 19%

36%Residential35%

Commercial

29%Industrial

36%Resident ial35%

Commercial

29%Industrial

( )a ( )b

Power Factor and Voltage

Sensitivity of Power Systems Load


132/243


Table 8-1 Power Factor and Voltage Sensitivity of Power Systems Load

Type of Load Power Factor /a P V = /b Q V = Electric Heating 1.0 2.0 0

Incandescent Lighting 1.0 1.5 0Fluorescent Lighting 0.9 1.0 1.0

Motor Loads 0.8 0.9 0.05 0.5 1.0 3.0Modern Power-

Electronics basedLoads

1.0 0 0

Voltage-Link System used

in Power ElectronicsBased Loads


133/243


Fig. 8-4 Voltage-link-system for modern and future power-electronics based loads.

d V

+

Utility

Load

'ra I a I

Induction Motor Per-PhaseDiagram


134/243


Fig. 8-5 Per-phase, steady state equivalent circuit of a three-phase induction motor.

+

(at ) aV

+

ls j L

ma I ma E

raa s R

'

lr j L

' synr slip

R

m j L

emT

Torque-SpeedCharacteristics


135/243


Fig. 8-6 Torque-speed characteristic of induction motor at various applied frequencies.

1 f LoadTorque

0

2 f 3 f 4 f 5 f

m 1 syn 1 slip 3 syn 3 slip

input dc to HF acinput dc to HF ac

Switch-Mode DC Power Supplies


136/243


Fig. 8-7 Switch-mode dc power supply.

60Hzac

rectifier

topology to convertdc to dc with isolation

Feedback controller

HF transformer

OutputinV

+

*oV

oV 60Hzac

rectifier

topology to convertdc to dc with isolation

Feedback controller

HF transformer

OutputinV

+

*oV

oV

lll

Uninterruptible Power Supplies (UPS)


137/243


Fig. 8-8 Uninterruptible power supply.

Rectifier Inverter Filter CriticalLoad

EnergyStorage


EnergyStorage


EnergyStorage

Feeder 1Feeder 1

Static Power-Transfer Switch


138/243


Fig. 8-9 Alternate feeder.

Load

Feeder 1

Feeder 2

Load

Feeder 1

Feeder 2

CBEMA Curve Showing

Acceptable Voltage-TimeRegion


139/243


Fig. 8-10 CBEMA curve.

+injv +injv

Dynamic VoltageRestorers (DVR)


140/243


Fig. 8-11 Dynamic Voltage Restorer (DVR).

Power ElectronicInterface

Load sv

+

injv

Power ElectronicInterface

LoadPower ElectronicInterface

Load sv

+

injv

Voltage RegulatingTransformers


141/243


Fig. 8-12 Three-Phase Voltage Regulator (Courtesy of Siemens) [5].

STATCOM


142/243


Fig. 8-13 STATCOM [4].

Utility

STATCOM

jX

Utility

STATCOM

jX

i si si sLinear Load


143/243


Figure 8-14 Voltage and current phasors in simple R-L circuit.

s I

sV

v s

+

( )a( )b

s I

sV

v s

+

v s

+

( )a( )b

vv

Waveforms Associated

with Power Electronics-Based Load


144/243


Figure 8-15 Current drawn by power electronics equipment without PFC.

t

( )distortion s s1i i i=

t 0/1

s1ii s

v s

1T

0

( )a

( )b

t

( )distortion s s1i i i=

t 0/1

s1ii s

v s

1T

0

( )a

( )b

si I si

I

si I si

I

Example of DistortedCurrent


145/243


1T

t I 0

s1i

t 0

I

I

/4I

t

distortioni

0

Figure 5-4 Example 5-1.

( )c

( )b

( )a

1T

t I 0

s1i

t 0

I

I

/4I

t

distortioni

0


( )c

( )b

( )a


1T

t I 0

s1i

t 0

I

I

/4I

t

distortioni

0


( )c

( )b

( )a

1T

t I 0

s1i

t 0

I

I

/4I

t

distortioni

0


( )c

( )b

( )a



146/243


147/243

sc I Z s Z s sc I Z s Z s Z s

Short-Circuit Current


148/243


+

V s

+

V s

(a) (b)

Figure 5-6 (a) Utility supply; (b) short circuit current.

+

V s

+

V s

+

V s

(a) (b)

Figure 5-6 (a) Utility supply; (b) short circuit current.Figure 8-18 (a) Utility Supply, (b) Short-Circuit Current.

Retail Price of Electricity inthe U.S.


149/243


Fig. 8-19 Average retail price of electricity to ultimate customers [4].


150/243


CHAPTER 9

SYNCHRONOUS

GENERATORS

Steam at High pressure

Application of Synchronous Generators


151/243


Fig. 9-1 Synchronous generators driven by (a) steam turbines, and (b) hydraulic turbines.

H Generator

Penstock

Turbine

Water

Pump

Heat in

Heat out

TurbineBoiler

Condenser

Gen

( )a ( )b

StatorStator

Cross-section of Synchronous Generators


152/243


Fig. 9-2 Machine cross-section.(a) (b)

Air gap

Stator

Air gap

Stator

S S

N N

Synchronous Generator Structure


153/243


Fig. 9-3 Machine structure.

(a) (b) (c)

S N S N

S

N N

S

N N S

N

S S

N

S

axisb ax

isb

Sinusoidally-DistributedWindings


154/243


Fig. 9-4 Three phase windings on the stator.

axisa

axisb

axisc

2 / 3

2 / 3

2 / 3

bi

ai

ci

axisa

axisb

axisc

2 / 3

2 / 3

2 / 3

bi

ai

ci 1

234

56

7

1'

2 '

3 ' 4 ' 5 '

6 ' ai

ai

7 '

1

234

56

7

1'

2 '

3 ' 4 ' 5 '

6 ' ai

ai

7 '

(a) (b)


155/243

Synchronous Generator Rotor Field


156/243


Fig. 9-6 Field winding on the rotor that is supplied by a dc current f I .

a-axis

N

S

syn

+

Voltage induced in the

Stator Phase due toRotating Rotor Field


157/243


Fig. 9-7 Current direction and voltage polarities; the rotor position shown inducesmaximum ae .

a-axis

N

S syn

ae

+(at 0) f B t =

G Im

Representation of Induced

Stator Voltage due toRotor Field


158/243


Fig. 9-8 Induced emf af e due to rotating rotor field with the rotor.

a-axis

N

S syn

af e

( )a ( )b ( )c

N

S

a-axisaf E

Re

syn

axisb

bi

axi

sb

bi

23

je

Im

Armature Reaction Due toThree Stator Currents


159/243


Fig. 9-9 Armature reaction due to phase currents.

axisa

axisc

2 / 3

2 / 3

2 / 3 ai

ci

axisa

axisc

2 / 3

2 / 3

2 / 3 ai

ci

( )a ( )b ( )c

0 je

43

je

a I

Re

(at 0) AR B t =G

a-axis

,a AR E

090


160/243

generator d

P stability limit

steady state

a I

Power Out as a function of rotor Angle


161/243


Fig. 9-11 Power output and synchronism.

stability limitsteady state

mode

motoringmode

0o90

o90

+

oV V 0 = af af E E =

T jX +

( )a

( )b

e P e P

,maxe P

Steady State StabilityLimit


162/243


Fig. 9-12 Steady state stability limit.

0 o90

( )a

1 2

e1 P e2 P

m1 P m2 P

( )b

0 o90

o90 s a jX I

s a jX I s a jX I

af E af E af E

o90 s a jX I

s a jX I s a jX I

af E af E af E

Reactive Power Control byField Excitation


163/243


Fig. 9-13 Excitation control to supply reactive power.

{aq I

aq I

o90

a I a I

a I aV

aV

aV

( )a ( )b ( )c

{aq I

aq I

o90

a I a I

a I aV

aV

aV

( )a ( )b ( )c

SynchronousCondenser


164/243


Fig. 9-14 Synchronous Condenser.

Synchronous

Condenser

phase-controlledrectifier field winding

Automatic VoltageRegulation (AVR)


165/243


Fig. 9-15 Field exciter for automatic voltage regulation (AVR).

acinput

slip rings

Generator

ac regulator

output

Armature Reaction Flux inSteady State Leading toSynchronous Reactance


166/243


Fig. 9-16 Armature reaction flux in steady state.

Simulation of a Short-Circuit Assuming aConstant-Flux Model


167/243


Fig. 9-17 Armature (a) and field current (b), after a sudden short circuit [source: 4].

( )a ( )b

++

' s a jX I +

a I

Im

af E

s a jX I 'af E

Representation for Steady State,Transient Stability and Fault Analysis


168/243


Fig. 9-18 Synchronous generator modeling for transient and sub-transient conditions.

( )b( )a

'

''

af

af

af

E

E

E

'' s a

s a

jX I jX I

a E

Re

a I

a E

' s a jX I

'' s a jX I

''af E

CHAPTER 10


169/243


VOLTAGE REGULATION

AND STABILITY IN

POWER SYSTEMS

R R P jQ+S V RV

L jX S S P jQ+ S S P jQ

+ R R P jQ+ L jX

+ +

A Radial System


170/243


Fig. 10-1 A radial system.

Load

(a) (b)

S V RV

I

L jX I S V S S

P jQ+

+

L jX I

+

Voltages and CurrentPhasors with Both-SideVoltages at 1 PU


171/243


Fig. 10-2 Phasor diagram and the equivalent circuit with 1puS RV V = = .(a)

I

RV

/ 2

(b)

S V

RQ R P RV

+ ++(1pu)

S V (1pu)

RV R P SIL


173/243

B

Q

Synchronous Generator Reactive Power SupplyCapability


174/243


Fig. 10-5 Reactive power supply capability of synchronous generators.

A

C

0 P

+

Th jX +

I

I

ThjX IThV

Th jX I +

Effect of Current Power Factor on Bus Voltage


175/243


Fig. 10-6 Effect of leading and lagging currents due to the shunt compensating device.

ThV

busV

(a)

busV

jX I V

busV

I

Th jX I

ThV

(b)

busV

1 I

busV

Static Var Compensators (SVC)


176/243


Fig. 10-7 V-I characteristic of SVC.

1 j C

C I

0C I

( )a ( )b

busV

L I

busV busv

Li

i

Thyristor ControlledReactors (TCR)


177/243


Fig. 10-8 Thyristor-Controlled Reactor (TCR).

( )a ( )c

0 L I

090

090 >

( )b

Li

busV

I busV bus

V A B

C

1V

1V

2V 2V

Linear Range

Voltage Control by SVCand TCR Combination


178/243


Fig. 10-9 Parallel combination of SVC and TCR.

1 j C

C I

( )a

L I L I

( )b ( )c I 0 0 I inductivecapacitive inductivecapacitive

1g

V

convV conv I

+ jXI

+

d V

+

V

+

convV

conv I

+ conv jXI

STATCOM


179/243


Fig. 10-10 STATCOM.

busV conv jXI busV

conv

( )a ( )b

Linear Range

busV

STATCOM V-ICharacteristic


180/243


Fig. 10-11 STATCOM VI characteristic.

conv I 0 inductivecapacitive

g

Thyristor-ControlledSeries Capacitor (TCSC)


181/243


Fig. 10-12 Thyristor-Controlled Series Capacitors (TCSC) [source: Siemens Corp.].( )a ( )c( )b

CHAPTER 11


182/243


TRANSIENT AND

DYNAMIC STABILITY OF

POWER SYSTEMS

1V 0 B BV V = L X

X1

V E 0 BV +

+

+

I '( )d tr j X X + / 2 L jX

One-Machine Infinite-Bus

System


183/243


Fig. 11-1 Simple one-generator system connected to an infinite bus.

( )am P

L X

( )be P

post-faultPre-fault

L X Bus 1 0 B BV V = e P

Power-AngleCharacteristic in One-

Machine Infinite-BusSystem


184/243


Fig. 11-2 Power-angle characteristics.

L X

0

m P

0 1

( )a ( )b

m P e P

during-fault


185/243


186/243

e P

P P=C

Pre-fault

post-fault

Rotor Oscillations After

the Fault is Cleared


187/243


Fig. 11-5 Rotor oscillations after the fault is cleared.

e m P P

01

m 2

D

e P

B

Pre-fault

post-fault

Critical Clearing Angle

using Equal-Area Criterion


188/243


Fig. 11-6 Critical clearing angle.

e m P P =

0 0 crit

A

max 1

20

25

30

35

40( )e P puPre-fault

post-fault

B

Example using Equal-Area

Criterion


189/243


Fig. 11-7 Power angle curves and equal-area criterion in Example 11-2.

0 20 40 60 80 100 120 140 160 1800

5

10

15

20

e m P P =

during fault

p

00 22.47 =

0115.28m =075c =A

A

B

Initial Power Flow'Calculate ande P E

for each generator for 1,2,3....k =

Transient StabilityCalculations in LargeNetworks


190/243


Fig. 11-8 Block diagram of transient stability program for an n-generator case.

, ,m k e k P P =

', and held constantm k k P E

Electro-dynamicdifferentialEquations

andk k

,e k P Phasor Calculations'using k k E (load may be assumedas a constant impedance)

Bus-1 Bus-3

1m P 1e P

Example Power System for Transient Stability Analysis


191/243


Fig. 11-9 A 345-kV test example system.

Bus-2

2m P

2e P

4 0 0

5 0 0

6 0 0

7 0 0

8 0 0

Rotor Angle Swings in theExample Power SystemFollowing a Fault


192/243


Fig. 11-10 Rotor-angle swings of 1 and 2 in Example 11-3.

0 0 . 2 0 . 4 0 . 6 0 . 8 1 1 . 2 1 . 4 1 . 60

1 0 0

2 0 0

3 0 0

1 2

Importance of Dynamic

Stability


193/243


Fig. 11-11 Growing Power Oscillations: Western USA/Canada system, Aug 10, 1996 [4].

CHAPTER 12

CONTROL OF


194/243


INTERCONNECTED

POWER SYSTEM AND

ECONOMIC DISPATCH

acinput

phase-controlledrectifier field winding

Generator output

Automatic Voltage

Regulation (AVR)


195/243


Fig. 12-1 Field exciter for automatic voltage regulation (AVR).

slip rings

ac regulator

Control Areas (Balancing

Authorities)


196/243


Fig. 12-2 (a) The Interconnections in North America, (b) Control Areas [Source: 2]

( )a ( )b

Regulator

TurbineGovernor

Frequency

-SupplementaryControl

f

f

a

b0 f

G

Steam-ValvePosition

1

R

slope R=

Load-Frequency Control

and Regulation


197/243


Fig. 12-3 Load-Frequency Control (ignore the supplementary control at present).

m P e P Load P

( )a

Turbine

Control

( )b m P

m P

0

G

m P

slope R


198/243

Area 1 Area 2

12 P 21 P

12 jX

Synchronizing Torquebetween Two Control Areas


199/243


Fig. 12-5 Two control areas.

+

B1

RSupplementaryController

(frequency deviation) f

Change in Steam Valve Position

Automatic GenerationControl (AGC) and AreaControl Error (ACE)


200/243


Fig. 12-6 Area Control Error (ACE) for Automatic Generation Control (AGC).

+

Governor

(tie-line flow deviation) P

(Area Control Error) ACE

Change in Steam Valve Positionk s

1m P 1e P 1 2 P

1 3 P Bus-1 Bus-3

Bus-2M

M

Area 2Area 1

Load

Two Control Areas in the

Example Power System


201/243


Fig. 12-7 Two control areas in the example power system with 3 buses.

2m P

2e P

Power Flow on Tie-Linesbetween Two Control

Areas Following a LoadChange


202/243


Fig 12 9 El t i l q i l t f t i t ti

12 jX 2 jX 1 jX +

1 1 E

+

2 2 E

Electrical Equivalent of

Two Areas


203/243


Fig. 12-9 Electrical equivalent of two area interconnection.

Modeling of Two Control

Areas with AGC+

+

+

1 B1

1 R

1 s P 11

1GT s + 11

1S T s + 1 1 syn

M s D +

11m P

1 Load P

Regulator Governor Steam Turbine Area 1

1 s

1 K s1ACE 1v P 1

11 sT s +

1/ syn


204/243

Copyright Ned Mohan 2006 204Fig. 12-10 Two-area system with AGC. Source: adapted from [6].

+

+

+

s

1

2 B2

1 R

2 s P 2m P

Regulator Governor Steam Turbine Area 22 s

2 Load P

2

2

11GT s + 2

11S T s + 2 2

syn

M s D

+

1 s

1 2( ) 12T

12 12 1 2( ) P T =

2 K s

2ACE2v P

2

11 sT s +

+

1/ syn

0.5

1

1.5

1m P

2P

Results of SimulinkModeling Following a Step

Load Change in Control Area 1


205/243


Fig. 12-11 Simulink results of the two-area system with AGC in Example 12-3.

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000-1

-0.5

0

2m P

12 P

Economic Dispatch: Heat

Rate of a Power Plant

9 0

10.0

11.0

MBTU-per-Hour MW

At this point, to produce 40 MW

Fuel Consumption = 400 MBTU-per-Hour

Heat Rate


206/243


Fig. 12-12 Heat Rate at various generated power levels.

[ ] P MW 0 20 40 60 80 100

9.0

Cost Curve and Marginal

Cost of a Power Plant( )

[$ / ]i iC P

hour

iC i P

( )

[$ / ]

i i

i

C P P

MWh


207/243


Fig. 12-13 (a) Fuel cost and (b) Marginal cost, as functions of the power output.

[ ]i P MW 0

[ ]i P MW 0

( )a ( )b

0 0 0P P P

1( )C P P

2 ( )C P P

3( )C P P

P P P

Load Sharing between

Three Power Plants


208/243


Fig. 12-14 Marginal costs for the three generators.

P P P 1 P 2 P 3 P

CHAPTER 13

TRANSMISSION LINE


209/243


FAULTS, RELAYING AND

CIRCUIT BREAKERS

a

b

c ai

f

bi

i

a

b

c a I

f

b I

I

Fault (Symmetric or Unsymmetric) on aBalanced Network


210/243


Fig. 13-1 Fault in power system.

g

ci

g

c I

( )a ( )b

1a I 1c I

2a I 2b I

a I

c I 0c I

0a I 0b I

Symmetrical

Components


211/243


Fig. 13-2 Sequence components.

2c I

1b I

b I

1a E

+

1 Z

+

+

+

1aV 2aV 0aV 1a I 2a I 0a I

2 Z 0 Z

Sequence Networks: Per-Phase Representation of a

Balanced Three-phaserepresentation


212/243


Fig. 13-3 Sequence networks.

a

b

c a I

f

b I

I

1a E

+

1 Z

+

1 0aV =

1a I

Three-Phase SymmetricalFault (ground may or mayno be involved)


213/243


Fig. 13-4 Three-phase symmetrical fault.

g

c I

( )a

( )b

1a E

+

+

+

2aV

a

b

ca I

f

1 Z

2 Z

1a I

2a I 3 f Z

1aV

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


214/243


Fig. 13-5 Single line to ground fault.

( )a

( )b

+

0aV g

f Z

0 Z

0a I


215/243

ab

c

g

b I

f

c I 1a E

+

+1 Z

1a I

1aV

+2 Z

2a I

2aV

+ 1 f a Z I

Double-Line Fault (ground

not involved)


216/243


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

( )a ( )b


217/243

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

n Z

( )b

+

0aV

0 Z

0a I

3 n Z

Neutral Grounded through

an Neutral Impedance)


218/243


g g g p

1 Load P pu=

0 Load Q =Bus-1

Bus-2

Bus-31 0.12 gen X pu =

2 0.12 gen X pu=

0 0.06gen X pu=1 0.10tr X pu=

0 10X pu=

1 0.10 Line X pu=

2 0.10 Line X pu=

0 0.20 Line X pu=

1 1.0 0V pu= 0

3 0.98 11.79V pu=

One-Line Diagram of a

Simple System)


219/243


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

0 gen2 0.10tr X pu

0 0.10tr X pu=

i 13 11 i i i i f l l i 3 h f l b 2

0.12 j pu

1 1.0 0V pu=

+

+

Load I

fault I

0.10 j pu 0.10 j pu

E 0.9604 Load R pu=

Thee-phase Fault on Bus-2

in the Simple System


220/243


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

Single-Line to Ground(SLG) Fault in the SimpleSystem

1 1.0 0V pu=

+

+

0.10 j pu

E 0.9604 Load R pu=

0.12 j pu 0.10 j pu

1aV

+

V

+0.10 j pu0.12 j pu 0.10 j pu

1a I

2a I

0V =

+

/ 3 ( / 3)a fault I I =


221/243


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

0.9604 Load R pu=

0.9604 Load R pu=

2aV

0aV

+

0.10 j pu0.06 j pu 0.20 j pu

0a I

0aV =

1m P 1e P

Bus-1Bus-3

Bus-2

An SLG Fault in the

Example 3-Bus System


222/243


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

2e P

2m P

Fig. 13-14 Protection equipment.

CB

R

CT

PT

Protection in Power

System


223/243


CT

Burden

Current Transformers

(CT)


224/243


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

(b)

Capacitor-Coupled Voltage

Transformers (CCVT)


225/243


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

(a) (b)

Fig 13 17 Differential relay

CT

CT

CT

Relay

Differential Relays


226/243


Fig. 13-17 Differential relay.


227/243

Time

instantaneous

Ground Directional Over-Current Relays for GroundFaults


228/243


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

X

R

Impedance (Distance)

Relays


229/243


Fig. 13-20 Impedance (distance) relay.

Microwave Terminal for Pilot Relays


230/243


Fig. 13-21 Microwave terminal [5].

Fig. 13-22 Zones of protection.

Time

A B C

Zone 1: instantaneousZone 2: 20-25 cycles

Zone 3: 1-1.5 sec

Zones of Protection


231/243



232/243

A B

P jQ+

Zone1Zone2

Zone2

Relaying in the 3-BusExample Power System


233/243


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


234/243

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 CurrentOffset in R-L Circuits


235/243


Fig. 13-26 Current in an RL circuit.

( ) ( )

CHAPTER 14

TRANSIENT OVER-VOLTAGES,

SURGE PROTECTION AND

INSULATION COORDINATION


236/243


INSULATION COORDINATION

Fig 14-1 Lightening current impulse

[ ]t s

0.5 peak I

peak I i

1t 2t

Lightning Current

Impulse


237/243


Fig. 14-1 Lightening current impulse.

Fig. 14-2 Lightening strike to the shield wire.( )a ( )b

Lightening Strike to ShieldWire and Backflash


238/243


Fig. 14-3 Over-voltages due to switching of transmission lines.( )b

av

bv

cv

L

( )a

L

L

A B

C

500kV Line100 miles (open)

Switching Surges


239/243


Frequency Dependence of Transmission LineParameters


240/243


Fig. 14-4 Frequency dependence of the transmission line parameters [Source: 2].

Fig. 14-5 Calculation of switching over-voltages on a transmission line.

Bus-1 Bus-3

Calculation of SwitchingOver-Voltages on Line 1-3in the Example 3-BusPower System


241/243


i

0t

pe ak V

0.5 pe ak V

1 .2 s 40 s

Standard Voltage Impulseto Define Basic InsulationLevel (BIL)


242/243


Fig. 14-6 Standard Voltage Impulse Wave to define BIL.


243/243

slides psbook2006 revised july2007

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