8. L IST OF R EFERENCES

8.

L

IST OF

R

EFERENCES

[1]

Bacchini, G., Out-of-step and Power Swing Relaying, Switzerland: ABB 1MRB520338-Aen. 17 p.

[2]

Redfern, M.A. & Checksfield, M.J. “A New Pole-slipping Protection Algorithm for Dispersed

Storage and Generation using the Equal Area Criterion”, IEEE Transactions on Power Delivery, 10

(1): 194-200, January 1995

[3]

SABS specification, “Conventions for description of synchronous machines, SABS IEC 34-10,

February 1993

[4]

Sen, P.C.. Principles of electric machines and power electronics, 2

nd

ed. Canada: Wiley. 615 p.

1997

[5]

Glover, D.J. & Sarma, M.. Power system analysis & design, 2

nd

ed. Boston: PWS. 583 p. 1994

[6]

CYMSTAB users guide and reference manual. 244 p. August 2004

[7]

Say, M.G.. Alternating current machines, 5

th

ed. London: Pitman. 632 p.1983

[8]

Say, M.G.. The performance and design of alternating current machines, 3

rd

ed. London: Pitman.

631 p. 1970

[9]

ABB brochure: “ABB high voltage machines”, Publication no: ZA-IND.02/94.06

[10]

Griffiths, D.J.. Introduction to electrodynamics, 2

nd

ed. New Jersey: Prentice Hall. 532 p. 1989

[11]

Wildi, T.. Electrical machines, drives, and power systems, 3

rd

ed. New Jersey: Prentice Hall. 814 p.

1997

[12]

Cathey, J.J.. Electric machines analysis and design applying Matlab®, 1

st

ed. New York: McGraw

Hill. 544 p. 2000

[13]

Sarma, M.S.. Electric Machines: Steady-State Theory and Dynamic Performance, 2

nd

ed. United

States: Thomson Learning. 649 p. 1994

[14]

Adkins, B. & Harley, R.G.. The general theory of alternating current machines. Chapman & Hall.

279 p. 1975

[15]

Kundur, P.. Power System Stability and Control. EPRI Power System Engineering Series: McGraw

[16]

ANSI/IEEE Standard 1110-1991, “IEEE guide for Synchronous Generator Modelling Practices in

Stability Analysis”, 89 p. 1991

[17]

ANSI/IEEE Standard 115-1983, “IEEE guide: Test Procedures for Synchronous Machines”

[18] Shigley, J.E. & Mischke, C.R., Mechanical engineering design, 6

th

ed. New York: Mc Graw Hill. 1248

p. 2001

[19]

IEEE SSR Working Group,. “Proposed Terms and Definitions for Subsynchronous Resonance,” IEEE

Symposium on Countermeasures for Subsynchronous Resonance, IEEE Pub. 81TH0086-9-PWR, ,p

92-97. 1981

[20]

Anderson, P.M., Agrawal, B. L., Van Ness, J. E.. Subsynchronous Resonance in Power Systems.

Wiley-IEEE Press. 288 p. 1999

[21]

EMTDC Transient Analysis for PSCAD Power System Simulation, User’s Guide, Version 4.2.0, 2005

[22]

Mozina, C.J., Advanced Applications of Multifunctional Digital Generator Protection, Beckwith

Electric Company

[23]

Mason, T.H. et al, “Asynchronous Operation of Turbo Generators”, CIGRE Vol. 1 (11-02), 1972

[24]

Cooper, C.B. et al, “Problems associated with limited Pole-slipping of Turbo-Generators following

system faults”, CIGRE Vol. 3 (306): 1-16, 1966

[25]

Mason, T.H. et al, “Turbo Generator performance under exceptional operating conditions”, IEE

Conf. Proc. Vol. 106: 357-373, 1959

[26]

Abolins, A et al, “Effect of clearing short-circuits and automatic reclosing on torsional tress and life

expenditure of turbine generator shafts”, IEEE Transactions of Power Apparatus and Systems, PAS

Vol. 97 (1): 14-25, February 1976

[27]

Masrur, M.A. et al, “Studies on asynchronous operation of synchronous machines and related

shaft torsional stresses”, IEE Conf. Proc. Part C Vol. 138: 47-56, January 1991

[28]

Ilar, F, “Innovations in the detection of power swings in electrical networks”, Brown Boveri Revue,

Part 2:87-93, 1981

[29]

ABB Power Automation, REG216 Numerical Generator Protection Operating Instructions,

1MDU02005-EN. 1090 p. 2001

[31]

Laughton, M.A., Warne, D.F. , Electrical Engineer’s Reference Book, 16

th

ed, Elsevier, 1441 p. 2007

[32]

Blondel, A. “The two-reaction method for study of oscillatory phenomena in coupled alternators”,

Revue génerale de l’ électricité, Vol. 13: 235-251, 515-531, March 1923

[33]

Doherty, R.E.., & Nickle, C.A., “Synchronous Machines I: An extension of Blondel’s two-reaction

theory,” AIEE Transactions, Vol. 45: 927-942, 1926

[34]

Park, R.H., “Two-reaction theory of synchronous machines – Part I,” AIEE Transactions, Vol. 48,

716-727, 1929

[35]

Real Time Digital Simulator, [Available on internet:]:

www.rtds.com [Date of access: 4 March

2008]

[36]

Thévenin Theory, [Available on internet:] http://hyperphysics.phy-astr.gsu.edu [Date of access: 8

September 2008]

[37]

IEEE Standard C37.111-1999, “IEEE Standard Common Format for Transient Data Exchange

(COMTRADE) for Power Systems”, 47 p. 1999

[38]

Mooney, J & Fischer, N, “Application Guidelines for Power Swing Detection on Transmission

Systems”, Schweitzer Engineering Laboratories, 2005

[39]

de Kock, J.A., private communication, June 2007

[40]

Rigby, B., private communication, Feb 2008

[41]

Harris, M.R., Lawrenson, P.J., Stephenson, J.M., “Per-unit systems with special reference to

electric machines”, IEE Monograph, Cambridge University Press, 1970

[42]

Canay, I.M., “Causes of discrepancies on calculation of rotor quantities and exact equivalent

diagram of synchronous machines”, IEEE Transactions, Vol. PAS-88, pp. 1114-1120, July 1969

[43]

Canay, I. M., “Equivalent Circuits of Synchronous Machines for Calculating Quantities of the Rotor

During Transient Processes and Asynchronous Starting, Part II, Salient Pole Machines,” Brown

Boveri Review, vol. 57, March 1970.

[44]

IEEE Committee Report: “Current Usage and Suggested Practices in Power System Stability

Simulations for Synchronous Machines,” IEEE Transactions on Energy Conversion, vol. EC-1, pp.

77–93, March 1986.

[45]

Kilgore, L. A., “Calculation of Synchronous Machine Constants—Reactances and Time Constants

Affecting Transient Characteristics,” AIEE Transactions, vol. 50, pp. 1201–1213, Dec. 1931.

[46]

ABB South Africa, electric machine designer, private communication, Feb 2007

[47]

IEEE Standard 421.5™-2005, “IEEE Recommended Practice for Excitation System Models for

Power System Stability Studies”

[48]

Kar, N.C., Murata, T., M.A. & Tamura, J., “A New Method to Evaluate the q-Axis Saturation

Characteristic of Cylindrical-Rotor Synchronous Generator”, IEEE Transactions on Energy

Conversion, Vol. 15, No. 3, September 2000

[49]

IEEE Standard 122-1991, “IEEE Recommended Practice for Functional and Performance

Characteristics of Control Systems for Steam Turbine-Generator Units”

[50]

Lara, O., Acha, E., “Modeling and Analysis of Custom Power Systems by PSCAD/EMTDC”, IEEE

Transactions on Power Delivery, Vol. 17, No. 1, January 2002

[51]

Kaberere, K.K., Folly K.A., Ntombela, M. & Petroianu, A.I. “Comparative analysis and numerical

validation of industrial-grade power system simulation tools: Application to small-signal stability”,

15

th

Power Systems Computation Conference, Liege, August 2005

[52]

Liu, J., Krogh, B.H., & Ilic, M.D., “Saturation-Induced Instability in Electric Power Systems”,

American Control Conference, Seattle, Washington, USA, June 2008

[53]

Redfem, M.A., Checksfield, M.J., “A review of pole slipping protection”,

Institude for Electrical

Engineers,

University of Bath, Bath, UK, 1996

[54]

Redfem, M.A., Checksfield, M.J. & Yip, H.T., “Field trials to demonstrate the performance of a new

pole slipping protection”, Developments in Power System Protection, IEE Publication No. 434,

March 1997

[55]

Girgis, A.A., Wang, L., “A new method for Power System Transient Instability Detection”, IEEE

Transactions on Power Delivery,

Vol. 12, No.

3,

July

1997

[56]

Eskom South Africa Transmission line data

[57]

Fixed Series Compensation, [Available on internet:]:

www.abb.com, [Date of access: 28 March

2011]

A

PPENDIX

A

–

ABB

REM543

P

OLE

-S

LIP

L

OGICS

Explanation of function blocks

ABS:

The output of the ABS function block is equal to the absolute value of the input.

ACOS:

The output of the ACOS function block is equal to arc-cos of the input.

ADD:

The output of the ADD function block is equal to the sum of the inputs.

AND:

The output of the AND function block is true if all the inputs are true.

ATAN:

The output of the ATAN function block is equal to arc-tan of the input.

DIV:

The DIV function block divides the top input by the bottom input.

GE:

The output of the GE function block is true if the top input is greater or equal to the

bottom input.

LT:

The output of the LT function block is true if the top input is less than the bottom input.

MOVE:

The output of the MOVE function block is equal to the input.

MUL:

The MUL function block multiplies the inputs with each other.

OR:

The output of the OR function block is true if at least one input is true.

SEL:

If the input of the SEL function block is true, the output has the value of IN1. If the input is

false, the output has the value IN0.

A

PPENDIX

D

–

PSCAD

A

LGORITHM

S

OURCE

F

ILE

CD

Contents of CD:

New Pole-slip protection function logics for:

• PSCAD source file as well as PDF version of a Round Rotor Generator (590MVA example)

• PSCAD source file as well as PDF version of a Salient Pole Generator (158MVA example)

System requirements:

A licensed version of PSCAD (or a 30 day trial) is required to compile the simulations. The PSCAD models

contain more nodes than the maximum number of nodes that the PSCAD demo version can simulate. The

PSCAD software can be downloaded at www.pscad.com

Hints on using the pole-slip algorithm model:

Setting the fault duration

A fault is applied on one of the transmission lines. It is assumed that the faulted transmission line

protection will clear the fault (which will leave only one transmission line in service after the fault is

cleared). For example, if the fault is chosen to occur at 15 s for a duration of 200 ms, the timer that opens

CB2s and CB2r must be set at 15.2 s.

Waiting for steady state before applying fault

It is important to wait for the simulation to reach steady state before applying a fault. It is recommended

to apply the fault no earlier than 15 s after the simulation started. After the simulation is started while

steady state is being approached, the controls switches must be set as follows:

RESET = 1

STEADY = 0

Toggle the switches about 2 seconds before the fault occurs to the following state:

RESET = 0

STEADY = 1

Viewing the graphs (results)

Changing generator active power output

The active power outputs of the four generators in the model can be independently changed by sliding

the “T

primover

”- sliders up and down. It is not recommended to change generator powers during the

simulation to ensure that steady state is obtained before the fault occurs.

Changing shunt loads at Generator 1

The shunt load active- and reactive power magnitudes can be changed to verify the pole-slip function

works accurately regardless of the shunt load at the generator terminals.

Changing Generator, Transformer and Transmission Line Parameters

If the user wishes to change any parameters on the Generators, Transformers or Transmission lines, the

parameters must be modified in the PSCAD three-line diagram as well on the pole-slip algorithm inputs.

The pole-slip algorithm inputs are located in the top-left corner of the model. For example, if the

transmission line length is changed, the effective per unit value of the transmission line reactance and

resistance must be calculated by the user and entered into the “Xline” and “Rline” parameters of the

pole-slip algorithm.

NOTE: The MVA base is chosen to be the same as the MVA rating of Generator 1. If the MVA rating of

generator 1 is changed, the following needs to be modified:

• Change the MVA base on all the Power Meters (this includes the power meters at the generator

terminals, at the transformer HV terminals, at the generator shunt load, at the transmission line

feeders, and at the infinite bus transmission line sections)

• Change the MVA base in the transmission line models

• Change the MVA base in the infinite bus source

• Change the MVA base in the pole-slip algorithm variable “S

base

”

Adjusting Generator 2 overshoot factor

The pole-slip function is designed to predict the time that the rotor will remain above synchronous speed

after the fault is cleared. This is, however, only calculated for Generator 1 in the PSCAD model. In a real

power system, Generator 2 will have its own pole-slip relay, which will communicate the rotor angle to

the pole-slip relay on Generator 1.

If the graph below is considered, the yellow area indicates the area during which the fault occurred, while

the red area indicates the period after the fault is cleared until the rotor speed deviation reached 0 rad/s.

The “Gen2_rotor_overspeed” variable in the model must be calculated by the user as follows:

Re

2 _

_

=

d Area

Gen

rotorspeed overshoot

Yellow Area

(a)

-8

-6

-4

-2

0

2

4

6

8

9.0

9.5

10.0

10.5

11.0

11.5

12.0

Time (s)

S

p

e

e

d

d

e

v

ia

ti

o

n

(

ra

d

/s

)

ω

∆

_max

0

t

_t

_c

-8

-6

-4

-2

0

2

4

6

8

9.0

9.5

10.0

10.5

11.0

11.5

12.0

Time (s)

S

p

e

e

d

d

e

v

ia

ti

o

n

(

ra

d

/s

)

ω

∆

_max

0

t

_t

_c

Generator speed deviation due to an electrical fault

Note that the calculation in equation (a) must be done after a simulation was run during which Generator

1 did not loose stability. Only after this calculation was performed, the simulation must be re-compiled

with the correct variable “Gen2_rotorspeed_overshoot” entered into the pole-slip algorithm.

Recap

_Page:

Project: PROJECT

POE\INPUT\INPUT.GB

1/1

Software

Author:

Sbase REAL#1072000000.0

REAL#24000.0 Vbase Ibase

REAL#1.732

S_base (VA) - THREE PHASE V_base (V) - LINE TO LINE

I_base CALCULATION

Xq REAL#2.28

Qudrature axis Reactance (p.u.)

Xd REAL#2.46

Direct axis Reactance (p.u.)

X_total_steady

Network, generator and transformer reactances

H REAL#5.61

Inertia H-value of generator and prime mover combined

poles REAL#2.0

Number of poles

Base Frequency REAL#50.0 freq_base

Base Speed for mechanical angle calculation (rad/s)

REAL#12.5664

poles

speed_base

Base Speed for electrical angle calculation (rad/s)

omega_base freq_base REAL#6.2832 freq_base Xd_prime REAL#0.348

Direct axis Transient Reactance (p.u.)

Network Rn REAL#0.0126 Rn

Network Xn (Step-Up Transformer + Transmission lines and shu

Xn Xd_prime X_total_transient Xn Xd SWGRP1_1 SWGRP2_1 TRUE REAL#1.0 REAL#0.0 REAL#2.0 REAL#0.0 REAL#4.0 REAL#0.0 REAL#8.0 REAL#0.0 REAL#16.0 REAL#0.0 REAL#32.0 REAL#0.0 REAL#64.0 REAL#0.0 REAL#128.0 REAL#0.0 REAL#256.0 REAL#0.0 REAL#512.0 REAL#0.0 REAL#1024.0 REAL#0.0 REAL#2048.0 REAL#0.0 REAL#4096.0 REAL#0.0 REAL#8192.0 REAL#0.0 REAL#16348.0 REAL#0.0 REAL#32768.0 REAL#0.0 REAL#100000.0 Xn IN1 IN2 IN3 IN4 IN5 IN6 IN7 IN8 GROUP OUT1 OUT2 OUT3 OUT4 OUT5 OUT6 OUT7 OUT8 CHKSUM IN1 IN2 IN3 IN4 IN5 IN6 IN7 IN8 GROUP OUT1 OUT2 OUT3 OUT4 OUT5 OUT6 OUT7 OUT8 CHKSUM G IN0 IN1 G IN0 IN1 G IN0 IN1 G IN0 IN1 G IN0 IN1 G IN0 IN1 G IN0 IN1 G IN0 IN1 G IN0 IN1 G IN0 IN1 G IN0 IN1 G IN0 IN1 G IN0 IN1 G IN0 IN1 G IN0 IN1 G IN0 IN1 MOVE MOVE DIV MUL MOVE MOVE MOVE MOVE MOVE DIV MUL MUL MOVE MOVE ADD ADD SWGRP1 SWGRP2 SEL SEL SEL SEL SEL SEL SEL SEL SEL SEL SEL SEL SEL SEL SEL SEL ADD DIV

Recap

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Project: PROJECT

POE\MEASURE\MEASURE.GB

1/1

Software

Author:

CURRENT MEASUREMENT

CURRENT Ia TO MIMIC

MEASUREMENTS PAGE (CYCLE TIME 20mS)

Ia IL3

MEASURING CHANNEL 4

IL1

MEASURING CHANNEL 2

IL2

MEASURING CHANNEL 3

CONVERT TO P.U.

Ibase MECU3A_1

CT Ratio Correction

25788/3000 = 8.6

REAL#8.6 Ia1

VOLTAGE MEASUREMENT

VOLTAGE Vab (P.U.)

Vab U1 U2 U3 Vbase

CONVERT TO P.U.

REAL#1732.05 REAL#3.0 MEVO3A_2 IL1 IL2 IL3 RESET IL1MEAS IL2MEAS IL3MEAS HighWarning HighAlarm LowWarning LowAlarm ERR UL1_U12 UL2_U23 UL3_U31 RESET UL1_U12MEAS UL2_U23MEAS UL3_U31MEAS HighWarning HighAlarm LowWarning LowAlarm ERR MECU3A DIV MUL MEVO3A DIV DIV ADD DIV

Recap

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Project: PROJECT

POE\PROT\PROT.GB

1/4

Software

Author:

POLE SLIP PROTECTION PAGE (CYCLE TIME 5mS)

Fault_cleared P0 "C"-Key F001V011 RS_Fault_Cleared MMIALAR3_1 MMIALAR4_1 IL1 IL2 IL3 NOC3Inst_Trip "C"-Key F001V011 NOC3Inst_1 Fault_detect "C"-Key F001V011

FAULT OCCURRED AND FAULT CLEARANCE DETECTION

"C"-Key

F001V011 Reset_Fault

MM1ALAR2_1

POWER MEASUREMENT

ACTIVE POWER (P.U.)

Power_Factor

MEPE7 USES IL3 AND U12 TO CALCULATE POWER FACTOR

Q

REACTIVE POWER (P.U.)

P Sbase

CONVERT TO P.U.

Sbase

CONVERT TO P.U.

CT Ratio Correction

REAL#8.6

CT Ratio Correction

REAL#8600.0 REAL#1000.0

25788/3000 = 8.6

25788/3000 = 8.6

CYCLE_ERROR MEPE7_1 fault_cycles REAL#10.0 REAL#2.0 P_min P_min P0 P_threshold SET RESET1 Q1 ON ACK AALARM ON ACK AALARM IL1 IL2 IL3 BS1 BS2 TRIGG GROUP DOUBLE BSREG RESET BSOUT START TRIP CBFP ERR SET RESET1 Q1 ON ACK AALARM RESET P3 Q3 DPF HighWarning HighAlarm LowWarning LowAlarm ERR GE AND RS OR MMIALAR3 MMIALAR4 NOC3Inst RS MMIALAR2 MEPE7 DIV DIV MUL MUL MUL GT ADD _DIV GT OR AND MIN

Recap

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2/4

Software

Author:

"C"-Key F001V011 fault_cycles REAL#0.0 fault_cycles "C"-Key F001V011 delta_rotor REAL#0.0 delta_rotor "C"-Key F001V011 speed_diff REAL#0.0 speed_diff "C"-Key F001V011 Area1_transient REAL#0.0 Area1_transient "C"-Key F001V011 Area1 REAL#0.0 Area1 G IN0 IN1 G IN0 IN1 G IN0 IN1 G IN0 IN1 G IN0 IN1 SEL SEL SEL SEL SEL

Recap

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Project: PROJECT

POE\PROT\PROT.GB

3/4

Software

Author:

SPEED DEVIATION CALCULATION FOR ELECTRICAL ROTOR ANGLE CALCULATION

speed_diff delta_rotor delta_rotor speed_diff REAL#0.005 delta_rotor delta_c delta_rotor REAL#2.0

rad/s

Fault_cleared omega_base H P0 P REAL#0.005 Fault_cleared speed_diff speed_diff REAL#1.0 Fault_cleared REAL#0.0 fault_cycles fault_cycles delta0 Area1 P0 P Area1 Stability_Trip speed_diff REAL#0.005 Area1 Fault_cleared Area1 G IN0 IN1 G IN0 IN1 G IN0 IN1 G IN0 IN1 G IN0 IN1 ADD MUL ADD SEL MUL DIV SUB MUL SEL ADD ADD SEL SUB MUL SEL ADD SEL

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4/4

Software

Author:

Area2 EMF X_total_transient delta_c delta_L P0 delta_L delta_c

STABILITY TRIP CONDITION

Area2 Area1

Stability_Trip PS1_4_HSPO3

RELAY TRIP OUTPUT - X4.1: 6-7

POLE_SLIP_TRIP1 "C"-Key F001V011 Stability_Reset "C"-Key F001V011 ON ACK AALARM SET RESET1 Q1 DIV MUL SUB COS COS SUB MUL SUB GT MMIALAR1 RS

Recap

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Project: PROJECT

POE\SLOWCYCL\SLOWCYCL.GB

1/3

Software

Author:

P0

P0 P

Fault_detect

SLOW CYCLE PAGE - STEADY STATE CALCULATIONS (CYCLE TIME 1000mS)

Vq Vab delta_actual_generator Id Ia delta_actual_generator PF_Angle

IMPEDANCE CALCULATION

Vab Ia Z_relay REAL#0.0 Q delta_actual_generator PF_Angle

ADD WHEN Q > 0; SUBTRACT WHEN Q < 0

Power_Factor Rc Xc PF_Angle Z_relay REAL#0.0 Q REAL#1.0 REAL#-1.0 Z_relay Ia PF_Angle Power_Angle Power_Factor Vab Numerator Denumerator REAL#0.0 Numerator Denumerator REAL#0.0 REAL#57.29578

Radians to Degrees

Power_Angle REAL#180.0 REAL#0.0 Numerator Denumerator REAL#0.0 REAL#0.0 REAL#180.0 REAL#0.0 Power_Angle Power_Angle Power_Angle

TRIGONOMETRIC CORRECTIONS FOR ARC TAN (EXTEND POWER ANGLE TO +-180)

REAL#0.0

Q

ADD WHEN Q > 0; SUBTRACT WHEN Q < 0

Xq REAL#57.29578 Power_Angle delta_actual_generator G IN0 IN1 G IN0 IN1 G IN0 IN1 G IN0 IN1 G IN0 IN1 G IN0 IN1 SEL MUL COS MUL ABS SIN ADD DIV ABS ABS SEL SUB LT ABS ABS ABS MUL MUL SIN LT SEL ABS ABS ABS MUL ACOS SIN MUL SUB DIV ATAN GE LT AND ADD MUL SEL LT LT AND SEL SUB SEL ADD LT DIV

Recap

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2/3

Software

Author:

delta_L REAL#3.14159 P0 X_total_transient EMF REAL#1.0 delta_imp_transfer X_total_transient Xc Rc Rn PF_Angle delta_imp_generator Xd_prime Xc Rc _{PF_Angle} Xs_actual Rc PF_Angle Xc

Determine if machine is in steady state

delta_actual_generator Vq Id Xd EMF Fault_detect EMF Xd Xd_prime Id

Eq'

G IN0 IN1 SUB ASIN MUL MUL DIV ABS ATAN SUB DIV SUB ADD ABS ATAN SUB DIV ADD ABS ABS MUL TAN SUB ADD ADD MUL SEL SUB MUL SUB

Recap

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POE\SLOWCYCL\SLOWCYCL.GB

3/3

Software

Author:

delta0

Pre-fault Actual Transfer Angle

delta_Gen Fault_detect delta0 delta_Trfr delta_Tline G IN0 IN1 ADD SEL

aplt UnlockRotor Tmstdy omegar CCT 1 CCT 2 telec Source2Machine Timer C B A CB2s C B A CB2r F A U L T S C B A A B C -> G A B C A B C 275 [kV] #2 #1 22 [kV] 590 [MVA] T im e d F a u lt L o g ic Timer d/dt T m _ In Ef 1 .0 CB2s CB2r * 1.0 Timer If V A A B C A B C A B C V A A B C RL RL A B C RL A B C V A A B C A B C P+jQ A B C P+jQ V A A B C A B C V A A B C A B C 0.001 [H] 0.001 [H] 0.001 [H] 0.001 [H] 0.001 [H] 0.001 [H] V A A B C A B C V A A B C A B C Reset Steady A B C trl C trl = 1 Excitation Excitation 2.5 aplt2 Tmstdy2 omegar2 telec2 d/dt T m _ In 2 Ef2 1 .0 If2 V A A B C A B C A B C V A A B C 0 .0 5 [ H ] 0 .0 5 [ H ] 0 .0 5 [ H ] A B C P+jQ 59 [MW] /ph 59 [MVAR] /ph 0 .0 1 [ o h m ] 0 .0 1 [ o h m ] 0 .0 1 [ o h m ] A B C A B C Power A B P Q Pshunt Qshunt N D N/D N D N/D Sbase_MVA Sbase_MVA Tm_In Tm_In2 Tm_In3 Tm_In4 a p lt 3 Tmstdy3 o m e g a r3 telec3 A B C A B C 2 7 5 [k V ] # 2 # 1 ₂4.0 [ k V ] 2 2 2 0 .0 [ M V A ] A B C S If E f T e A V T m E f0 T m w E f If d/dt T m _ In 3 V T _IT 3 If E f E f0 V re f E x c it e r_ (A C 1 A ) E f3 1 .0 If3 V A A B C A B C A B C V A A B C A B C P+jQ 1000[MW] /ph 100[MVAR] /ph V A a p lt4 Tmstdy4 o m e g a r4 telec4 A B C A B C 2 7 5 [k V ] #2 # 1 2 4 .0 [k V ] 2 2 2 0 .0 [M V A ] A B C S If E f T e A V T m E f0 T m w E f If d/dt Tm_In4 V T IT 3 If E f E f0 V re f E x c ite r_ (A C 1 A ) E f4 1.0 If 4 V A A B C A B C V A A B C A B C A B C P+jQ 1000[MW] /ph 100[MVAR] /ph V A V A A B C A B C C B A C B g e n 2 CBgen2 CBshunt A B C A B C SECTION PI COUPLED A B Ctrl Ctrl = 1 S te a d y Pshunt0 Pshunt0 VT IT 3 If Ef Ef0 Vref Exciter_(AC1A) VT IT 3 If Ef Ef0 Vref Exciter_(AC1A) A B C S If Ef Te A V Tm Ef0 Tm w Ef If A B Ctrl Ctrl = 1 Qshunt0 Qshunt0 Sshunt0 Y X M P M P Y X Ang_Shunt A B C A B C 275 [kV] #2 #1 22 [kV] 590 [MVA] A B C S If Ef Te A V Tm Ef0 Tm w Ef If A B C A B C SECTION PI COUPLED

Open breakers 0.0 seconds after fault is cleared

RESET must be 1 and STEADY must be 0 until steady state is reached. Then switch RESET to 0 and steady to 1 BEFORE FAULT OCCURS

Main : Controls 1.5 0 T primover4 0.5 p u 1.5 0 T primover3 0.5 p u 1.5 0 T primover 1 p u 1.5 0 T primover2 0.5 p u

Y-Y makes angle calculation de-bugging easier Algorithm works with a Delta-Y configuration as well

Y-Y makes angle calculation de-bugging easier Algorithm works with a Delta-Y configuration as well

Main : Controls RESET 0 RUN RESET STEADY 1 RUN STEADY CBgen2 0 OFF ON Excitation 1 OFF ON

telec aplt Ef D + F + Pgen1 X2 X X2 Qgen1 N D N/D _PF PF S S Vs iam vam vamLL 1.732 * vamLL N D N/D N D N/D iam Vinf Pinf Qinf Infdelta Vgen_pu Igen_pu Igen_pu Vgen_pu ArcCos PF PF_angle Pline2 Pline1 Pgen1 Qgen1 Qline2 Qline1 Vinf_rms_pu Vtrfr1_pu Pline4 Pline3 Qline4 Qline3 Pgen_meter Qgen_meter Pgen2 Qgen2 Pgen3 Qgen3 Pgen4 Qgen4 Pgen_busbar Qgen_busbar If2 Ef2 vam2 vamLL2 1.732 * vamLL2 _N D N/D Vgen2_pu Ptr2 Qtr2 Ptr Qtr vamLL Phase_GI Phase_GT Phase_Tline If genpowerangle Vgen2_pu genpowerangle2 D + F + Pgen2 X2 X X2 Qgen2 N D N/D _PF2 S2 ArcCos PF2 PF_angle2 Vgen Vgen Igen * 1.0 0.15 Rline * 1.0 0.014 Xd * 1.0 2.11 Xd_prime * 1.0 0.28 Xq 2.02 Xline * 1.0 * 1 Xtrfr Sbase_MVA 590.0 _1.0* * 1.0 Xd_prime_2 Xd2 * 1.0 Xtrfr2 * 1.0 * 0.5 Vgen * 1.0 22.0 2.11 0.28 V_LL 0.071 2.0

***SELF-TUNING CORRECTION CONSTANT C1*** Only applicable for round rotor machines. Salient rotors uses C1 = 1

Xline2 * 1.0 Rline2 * 1.0 D + F -Tm_In C1 transferangle1 omegar D + F -Pi * 120.0 D + F + Phase_GI transferangle Power_Angle speed_deviation1 omegar2 D + F - speed_deviation2 Pi * 120.0 omegar3 D + F - speed_deviation3 Pi * 120.0 omegar4 D + F - speed_deviation4 Pi * 120.0 D + F -Pi * 2.0 N D N/D iam2 Igen2_pu transferangle2 D + F -Pi * 2.0 Igen Vgen N D N/D Sbase_MVA * 1.732 Igen Gen2_rotorspeed_overshoot 1 .0 *************************************************************************************************************************************** The rotor speed overshoot (area under rad/s curve) after fault is cleared for Gen 2:

NOTE: This value is determined by the pole-slip relay on Gen2 and must be communicated automatically to the relay on Gen1.

The Pole-slip Relay on Gen2 is not included in this PSCAD simulation. "Gen2_rotorspeed_overshoot" must therefore be manually updated by the user as follows; (Speed Area after fault clearance until speed reaches 0 rad/s) / (Speed Area during fault)

"Gen2 overshoot factor to be adjusted"

* 0.5 2.0 _D + F -Tm_In2 * 2.0 not to be adjusted Xq_prime N D N/D VD CQ2 Xq_calc Tm_In * Xq

Just for graph purposes "Xq_avg" for use in round rotor

Equal area criteria

X1 X2 X3 Ph1 Ph2 Ph3 Mag1 Mag2 Mag3

(7) (7) (7) (7) (7) (7) dc1 dc2 dc3 F F T F = 60.0 [Hz] 1 2 3 Vs 1 1 1 vam vbm vcm 1 1 1 vap vbp vcp X1 X2 X3 Ph1 Ph2 Ph3 Mag1 Mag2 Mag3

(7) (7) (7) (7) (7) (7) dc1 dc2 dc3 F F T F = 60.0 [Hz] 1 2 3 Is 1 1 1

iam ibm icm

1 1 1 iap ibp icp X1 X2 X3 Ph1 Ph2 Ph3 Mag1 Mag2 Mag3

(7) (7) (7) (7) (7) (7) dc1 dc2 dc3 F F T F = 60.0 [Hz] 1 2 3 Vtr 1 1 1 Vtra Vtrb Vtrc 1 1 1 vtrap vtrbp vtrcp VtraLL N D N/D 275.0 Vtrfr1_pu Vtra VtraLL 1.732 * X1 X2 X3 Ph1 Ph2 Ph3 Mag1 Mag2 Mag3

(7) (7) (7) (7) (7) (7) dc1 dc2 dc3 F F T F = 60.0 [Hz] 1 2 3 Vs2 1 1 1 vam2 1 1 1 Phase_GI 1 2 3 Vs 1 2 3 Vinf P h a s e D iff e re n c e A 1 B 1 C 1 A 2 B 2 C 2 Phase_GT 1 2 3 Vs 1 2 3 Vtr P h a s e D iff e re n c e A 1 B 1 C 1 A 2 B 2 C 2 Phase_Tline 1 2 3 Vline44 1 2 3 Vline1 P h a s e D iff e re n c e A 1 B 1 C 1 A 2 B 2 C 2 1 2 3 vam vbm vcm 1 2 3 vap vbp vcp vm vp 1 2 3 iamibmicm 1 2 3

iap ibp icp im ip X1 X2 X3 Ph1 Ph2 Ph3 Mag1 Mag2 Mag3

(7) (7) (7) (7) (7) (7) dc1 dc2 dc3 F F T F = 60.0 [Hz] 1 2 3 Is2 1 1 1 iam2 Vgen_pu Cos * _Vq Vgen_pu Sin * _Vd1 genpowerangle genpowerangle Vgen2_pu Cos * _Vq2 Vgen2_pu Sin * _Vd2 genpowerangle2 genpowerangle2 Calculation of EMF (Eq_prime) for generator1 and 2

A B Ctrl Ctrl = 1 A B Compar-ator Qgen1 0.0 D + F + PF_angle D -F + PF_angle Sin * Igen_pu Id genpowerangle genpowerangle A B Ctrl Ctrl = 1 A B Compar-ator Qgen2 0.0 D + F + PF_angle2 D -F + PF_angle2 Sin * Igen2_pu Id2 genpowerangle2 genpowerangle2 D + F + Id2 * Xd2 Vq2 A B Ctrl Ctrl = 1 Eq2 Steady B + D -Id2 * Xd2 B + D -Eq2_prime Eq2_prime Xd_prime_2 A B Ctrl Ctrl = 1 A B Compar-ator Qgen1 0.0 D + F + PF_angle D -F + PF_angle Cos * Igen_pu genpowerangle genpowerangle * _{IqXq_prime} Vd1 D -F + N D N/D Vd1 Xq_prime A B Ctrl Ctrl = 1 Steady Iq_steady Iq Iq_steady IqXq_prime IqXq_prime * Xq

Pgen_i0 Eq_prime Vgen_fault * N D N/D Xd_prime * Sin delta_gen_i0 D + F + Vgen_fault X2 N D N/D 2.0 D + F -* N D N/D 1.0 Xq_prime N D N/D 1.0 Xd_prime * Sin * 2.0 delta_gen_i0 delta_gen_i1 delta_gen_i0 D + F -D + F -Pgen_i0 Ptx_i0 * K1 D -F + delta_tx_i1 Pgen_i1 Eq_prime Vgen_fault * N D N/D Xd_prime * Sin delta_gen_i1 D + F + Vgen_fault X2 N D N/D 2.0 D + F -* N D N/D 1.0 Xq_prime N D N/D 1.0 Xd_prime * Sin * 2.0 delta_gen_i1 delta_gen_i2 delta_gen_i1 D + F -D+ F -Pgen_i1 Ptx_i1 * K1 D -F + Pgen_i2 Eq_prime Vgen_fault * N D N/D Xd_prime * Sin delta_gen_i2 D + F + Vgen_fault X2 N D N/D 2.0 D + F -* N D N/D 1.0 Xq_prime N D N/D 1.0 Xd_prime * Sin * 2.0 delta_gen_i2 **************** ITERATION #2 ***************** **************** ITERATION #1 ***************** **************** ITERATION #3 ***************** Pgen_i3 Eq_prime Vgen_fault * N D N/D Xd_prime * Sin delta_gen_i3 D + F + Vgen_fault X2 N D N/D 2.0 D + F -* N D N/D 1.0 Xq_prime N D N/D 1.0 Xd_prime * Sin * 2.0 delta_gen_i3 delta_gen_i4 delta_gen_i3 D + F -D + F -Pgen_i3 Ptx_i3 * K1 D -F + delta_tx_i4 **************** ITERATION #4 ***************** ITERATIONS TO DETERMINE delta_Gen1 & detla_Tx DURING THE FAULT

K1 N D N/D 7.0 Vgen_fault Ptx_i0 * N D N/D Xtrfr * Sin delta_tx_i0 Vtx_sec_fault Vgen_fault Ptx_i1 * N D N/D Xtrfr * Sin delta_tx_i1 Vtx_sec_fault Vgen_fault delta_tx_i2 delta_gen_i3 delta_gen_i2 D + F -D + F -Pgen_i2 Ptx_i2 * K1 D -F + delta_tx_i3 Ptx_i2 * N D N/D Xtrfr * Sin delta_tx_i2 Vtx_sec_fault Vgen_fault Ptx_i3 * N D N/D Xtrfr * Sin delta_tx_i3 Vtx_sec_fault Vgen_fault delta_tx_HV delta_tx_HV delta_tx_HV delta_tx_HV Pgen_i4 Eq_prime Vgen_fault * N D N/D Xd_prime * Sin delta_gen_i4 D + F + Vgen_fault X2 N D N/D 2.0 D + F -* N D N/D 1.0 Xq_prime N D N/D 1.0 Xd_prime * Sin * 2.0 delta_gen_i4 delta_gen_i5 delta_gen_i4 D + F -D + F -Pgen_i4 Ptx_i4 * K1 D -F + delta_tx_i5 **************** ITERATION #5 ***************** delta_gen_i5_rad * 0.017453 Ptx_i4 * N D N/D Xtrfr * Sin delta_tx_i4 Vtx_sec_fault Vgen_fault * 0.017453 delta_trfr1 Fault_detected A B Ctrl Ctrl = 1 * 0.017453 delta_tx_i5_rad delta_tx_HV delta_c Vgen_fault_ang D + F -delta_gen_i0 delta_c D + F -* 57.3 * 57.3 Vtx_sec_fault_ang D -F + delta_tx_i0 delta_tx_HV

Y X M P M P Y X delta_c2 D + F + C + D + E + Xtrfr2 Y X M P M P Y X Ithfprime_m1 Ithfprime_m2 Ithfprime_p1 Ithfprime_p2 N D N/D I_Th_fault_mag_prime D + F -I_Th_fault_ang_prime A B Ctrl Ctrl = 1 Fault_cleared A B Ctrl Ctrl = 1 Fault_cleared I_Thevenin_prime (fault) is the generator 2 current connected only to the shunt load (disconnected from transmission lines and generator 1)

Xd_prime_2 0.0 Ithfprime_m1 Ithfprime_m2 Ithfprime_p1 Ithfprime_p2 I_Th_fault_mag_prime I_Th_fault_ang_prime * Sin Cos * Eq2_prime R_Shunt X_Shunt Cos A B Ctrl Ctrl = 1 Fault_cleared * * D + F + Xtrfr2 Sin _D + F + Eq2_prime * * D + F + Xtrfr2 V_fault_Th_ang_prime Xd_prime_2 Xd_prime_2 Y X M P M P Y X A B Ctrl Ctrl = 1 Fault_cleared delta_c2 D + F + Cos * D -F ₊ Eq2_prime Sin * V_fault_Th_mag_prime 0.0 V_fault_Th_mag_prime V_fault_Th_ang_prime I_Th_fault_mag_prime I_Th_fault_mag_prime I_Th_fault_ang_prime I_Th_fault_ang_prime

V_Thevenin_prime (fault) is the Transformer 2 HV Voltage connected only to the shunt load (disconnected from transmission lines and generator 1)

Y X M P M P Y X delta_c2 D + F + C + D + E + Xtrfr2 Y X M P M P Y X Ithpfprime_m1 Ithpfprime_m2 Ithpfprime_p1 Ithpfprime_p2 N D N/D I_Th_postfault_mag_prime D + F -I_Th_postfault_ang_prime A B Ctrl Ctrl = 1 Fault_cleared A B Ctrl Ctrl = 1 Fault_cleared I_Thevenin_prime (postfault) is the generator 2 current connected only to the shunt load (disconnected from transmission lines and generator 1)

Xd_prime_2 Ithpfprime_m1 Ithpfprime_m2 Ithpfprime_p1 Ithpfprime_p2 I_Th_postfault_mag_prime I_Th_postfault_ang_prime * Sin Cos * Eq2_prime R_Shunt X_Shunt delta_rotor2 * Gen2_rotorspeed_overshoot Cos A B Ctrl Ctrl = 1 Fault_cleared * * D + F + Xtrfr2 Sin _D + F + Eq2_prime * * D + F + Xtrfr2 V_postfault_Th_ang_prime Xd_prime_2 Xd_prime_2 Y X M P M P Y X A B Ctrl Ctrl = 1 Fault_cleared delta_c2 D + F + Cos * D -F ₊ Eq2_prime Sin * V_postfault_Th_mag_prime V_postfault_Th_mag_prime V_postfault_Th_ang_prime I_Th_postfault_mag_prime I_Th_postfault_mag_prime I_Th_postfault_ang_prime I_Th_postfault_ang_prime

V_Thevenin_prime (postfault) is the Transformer 2 HV Voltage connected only to the shunt load (disconnected from transmission lines and generator 1)

delta_rotor2 * Gen2_rotorspeed_overshoot N D N/D Ithpf_m1 Ithpf_m2 I_Th_postfault_mag D + F -Ithpf_p1 Ithpf_p2 I_Th_postfault_ang A B Ctrl Ctrl = 1 Fault_cleared I_Th_postfault_mag A B Ctrl Ctrl = 1 Fault_cleared I_Th_postfault_ang I_Thevenin (postfault) is the generator 2 current (without generator 1)

Y X M P M P Y X Cos D+ F + D+ F -Sin * 1.0 D + E + Xline Rline Y X M P M P Y X Ithpf_m1 Ithpf_m2 Ithpf_p1 Ithpf_p2 * 0.0 _{V_postfault_Th_mag_prime} V_postfault_Th_ang_prime V_postfault_Th_mag_prime R_Th_prime X_Th_prime D + E + Y X M P M P Y X Cos D + F + D + F -Sin * 1.0 Ithf_m1 Ithf_p1 I_Thevenin (fault) is the generator 2 current (without generator 1)

* 0.0 _{V_fault_Th_mag_prime} V_fault_Th_ang_prime V_fault_Th_mag_prime Y X M X P Y M P X_Shunt R_Shunt Ang_Shunt Z_shunt_mag X2 N D N/D Sshunt0 Vtrfr1_pu Z_shunt_mag A B Ctrl Ctrl = 1 Vtrfr1_SS Vtrfr1_SS Steady

P_delta_c Eq_prime * N D N/D Xd_prime * Sin B + D + F +

*******************ROTOR OVERSHOOT PREDICTION*******************

Area1_gen N D N/D delta_rotor_max0 B + D -Tm_In B + D + A B Ctrl Ctrl = 1 Fault_cleared delta_rotor_max0 Xline Xtrfr delta_c 1.0 delta_cc P_delta_c P_delta_max0 Eq_prime * N D N/D Xd_prime * Sin B + D + F + Xline Xtrfr 1.0 delta_rotor_max0 B + D -P_delta_c P_delta_max0 B + D -delta_rotor_max0 * B + D ₊ delta_rotor_max0 delta_rotor_max delta_cc A B Ctrl Ctrl = 1 delta_rotor_max Fault_cleared N D N/D B -D + Tm_In P_delta_c N D N/D C1 2.0 C1 * * N D N/D Ithf_m1 Ithf_m2 I_Th_fault_mag D+ F -Ithf_p1 Ithf_p2 I_Th_fault_ang A B Ctrl Ctrl = 1 Fault_cleared I_Th_fault_mag _A B Ctrl Ctrl = 1 Fault_cleared I_Th_fault_ang Cos A B Ctrl Ctrl = 1 Fault_cleared * * Sin B -D + F + * * V_fault_Th_ang I_Th_fault_ang I_Th_fault_mag I_Th_fault_ang I_Th_fault_mag Y X M P M P Y X A B Ctrl Ctrl = 1 Fault_cleared V_fault_Th_mag D + F + Cos * D -E -F + Sin * V_fault_Th_mag V_fault_Th_ang 0.0 V_fault_Th_mag_prime V_fault_Th_ang_prime V_fault_Th_mag_prime R_Th_prime X_Th_prime Cos * I_Th_fault_ang I_Th_fault_mag * X_Th_prime Sin * * I_Th_fault_ang I_Th_fault_mag R_Th_prime * B + D + speed_deviation1 delta_rotor B + D + A B Ctrl Ctrl = 1 Fault_cleared 1.0 0.0 fault_cycles fault_cycles A B Ctrl Ctrl = 1 Reset 0 .0 1 2 Fault_detected Delta-T A B Ctrl Ctrl = 1 Reset delta_rotor 0.0 Transfer_Angle B + D + * 0.017453 delta_c * 57.3 delta_c_deg * B + D + speed_deviation2 delta_rotor2 Delta-T A B Ctrl Ctrl = 1 Reset delta_rotor2 0.0 Transfer_Angle2 B + D + * 0.017453 delta_c2 * 57.3 delta_c2_deg B -D + V_fault_Th_ang delta_Th delta_Th_deg * 57.296 A B Ctrl Ctrl = 1 Fault_cleared delta_cc delta_cc Cos A B Ctrl Ctrl = 1 Fault_cleared * * Sin B -D + F + * * V_postfault_Th_ang I_Th_postfault_ang I_Th_postfault_mag I_Th_postfault_ang I_Th_postfault_mag Y X M P M P Y X A B Ctrl Ctrl = 1 Fault_cleared V_postfault_Th_mag D+ F + Cos * D -E -F ₊ Sin * V_postfault_Th_mag V_postfault_Th_ang 0.0 V_postfault_Th_mag_prime V_postfault_Th_ang_prime V_postfault_Th_mag_prime R_Th_prime X_Th_prime Cos * I_Th_postfault_ang I_Th_postfault_mag * X_Th_prime Sin * * I_Th_postfault_ang I_Th_postfault_mag R_Th_prime D + E + Xline Rline Y X M P M P Y X Ithf_m2 Ithf_p2 R_Th_prime X_Th_prime D + E +

* * PF ArcCos Sin * * D + F + D -F + A B Ctrl Ctrl = 1 N D N/D ArcTan _57.296* Power_Angle0 A B Compar-ator Qgen1 0.0 Numerator Denumerator Igen_pu Igen_pu Vgen_pu Xq A B Compar-ator Numerator 0.0 A B Compar-ator Denumerator 0.0 A B C trl C trl = 1 0 .0 1 8 0 .0 A B Compar-ator Numerator 0.0 A B Compar-ator Denumerator 0.0 A B C trl C trl = 1 0 .0 1 8 0 .0 D + F + G -Power_Angle0 Power_Angle A B Ctrl Ctrl = 1 Steady Power_Angle

GENERATOR 1 POWER ANGLE CALCULATION

* N D N/D B + D + X2 N D N/D * N D N/D _D+ F -1.0 Xq_prime N D N/D 1.0 Xd_prime 2.0 Sin * 2.0 delta_L N D N/D D + F -Pi delta_L X D + F -1.0 m c N D N/D _D + F + delta_L delta_LS Vgen_postfault Xd_prime Eq_prime * Vgen_postfault delta_L Tm_In | X | ArcSin 3.14159 * N D N/D Eq_prime D -F + Xd_prime * Sin delta_L Xtrfr * Vgen_postfault delta_L_tx Tm_In | X | ArcSin 3.14159 * N D N/D _D -F + * Vgen_postfault Vtx_sec_postfault Za_mag_corrected_pu Vtrfr1_pu B + F -Pline_Total N D N/D Y X M P M P Y X Za_angle_corrected_rad * -1.0 X2 0.0 Qline_Total -1.0 * * 57.296 Za_angle_corrected_deg ArcTan D+ F -N D N/D 57.296 * Xa_corrected_pu Ra_corrected_pu D+ F -Rline_par alpha Xline_par | X | A + B + D+ Transfer_Angle Power_Angle Za_angle_corrected_deg alpha _A B Ctrl Ctrl = 1 -1.0 * delta_trfr1 Imp_line B + D + A B Ctrl Ctrl = 1 Transfer_Angle Steady A B Compar-ator Xa_corrected_pu Xline_par A + B + D + Transfer_Angle2 Za2_angle_corrected_deg alpha2 A B Ctrl Ctrl = 1 A B Compar-ator Xa2_corrected_pu Xline_par -1.0 * delta_trfr2 Imp_line2 B + D + A B Ctrl Ctrl = 1 Transfer_Angle2 Steady genpowerangle2 * 57.296

THIS CALCULATION WILL BE INCLUDED IN POLESLIP RELAY ON GENERATOR 2 IN A REAL INSTALLATION ArcTan D+ F -N D N/D 57.296 * Xa2_corrected_pu Ra2_corrected_pu D+ F -Rline_par alpha2 Xline_par | X | Za2_mag_corrected_pu Za2_angle_corrected_deg B + F -* 57.296 Pline_Total N D N/D Y X M P M P Y X Za2_angle_corrected_rad * -1.0 Vtrfr1_pu X2 0.0 Qline_Total -1.0 * Pgen1 ArcSin * Xtrfr N D N/D Vgen_pu * 57.296 * delta_trfr1 Vtrfr1_pu Pgen2 ArcSin * Xtrfr2 N D N/D Vgen2_pu * 57.296 * delta_trfr2 Vtrfr1_pu Xa_corrected_pu Ra_corrected_pu Y X M X P Y M P Za_mag_corrected_pu Za_angle_corrected_rad Xa2_corrected_pu Ra2_corrected_pu Y X M X P Y M P Za2_mag_corrected_pu Za2_angle_corrected_rad Pline2 Pline1 Qline2 Qline1 D + F + Pline_Total D + F + Qline_Total Y X M P M P Y X Y X M X P Y M P Xline_par Rline_par Rline Xline Y X M P M P Y X Rline2 Xline2 * N D N/D D + F + Rline Rline2 D + F + Xline Xline2 Y X M P M P Y X Zline1_ang Zline2_ang Zline1_ang Zline2_ang B -D + F + Paralleled pre-fault transmission line impedance

Y X M P M P Y X Cos D+ F -Sin * C + D + E + Xtrfr Xd_prime Y X M P M P Y X Ifault_m1 Ifault_p1 * * Ifault_m2 Ifault_p2 R_Th X_Th delta_c D + F + Eq_prime Cos * D -F + Eq_prime Sin delta_c D+ F + N D N/D D + F -A B Ctrl Ctrl = 1 Fault_cleared A B Ctrl Ctrl = 1 Fault_cleared Ifault_m1 Ifault_p1 Ifault_m2 Ifault_p2 I_fault_ang I_fault_mag I_fault_mag I_fault_ang 0.0 0.0 V_fault_Th_mag V_fault_Th_mag V_fault_Th_ang ArcTan N D N/D B + D + F -ArcTan C + D + E + N D N/D Z_Th_ang_prime A B Ctrl Ctrl = 1 Fault_cleared X_Shunt R_Shunt X_Shunt R_Shunt 1.5708 Xd_prime_2 Xtrfr2 Z_Th_ang_prime X2 X2 _D + X F + D+ F + N D N/D A B Ctrl Ctrl = 1 Z_Th_mag_prime Fault_cleared D + F + * X2 X2 X Z_Th_mag_prime Z_Th_ang_prime Y X M X P Y M P X_Th_prime R_Th_prime X_Shunt R_Shunt C + D + E + R_Shunt X_Shunt Z_Th_mag_prime Xd_prime_2 Xtrfr2 Xd_prime_2 Xtrfr2 C + D + X2 X2 _D + X F + D + F + N D N/D A B Ctrl Ctrl = 1 Z_Th_mag Fault_cleared D + F + * X2 X2 X Z_Th_mag Z_Th_ang Y X M X P Y M P X_Th Z_Th_mag R_Th X X2 X2 C + D + ArcTan N D N/D B + D + F -ArcTan D + E + N D N/D Z_Th_ang A B Ctrl Ctrl = 1 Fault_cleared Z_Th_ang ArcTan N D N/D D + E + R_Th_prime X_Th_prime R_Th_prime X_Th_prime Rline Rline Xline Xline Xline Xline Rline Rline X_Th_prime X_Th_prime R_Th_prime R_Th_prime

N D N/D D + F -A B Ctrl Ctrl = 1 Fault_cleared A B Ctrl Ctrl = 1 Fault_cleared Ipostfault_m1 Ipostfault_p1 Ipostfault_m2 Ipostfault_p2 I_postfault_ang I_postfault_mag I_postfault_mag I_postfault_ang Y X M P M P Y X Cos D + F -Sin * C + D + E + Xtrfr Xd_prime Y X M P M P Y X Ipostfault_m1 Ipostfault_p1 * * Ipostfault_m2 Ipostfault_p2 R_Th X_Th Eq_prime Cos * D -F + Eq_prime Sin V_postfault_Th_mag V_postfault_Th_mag V_postfault_Th_ang delta_rotor_max delta_c D + F + A B Ctrl Ctrl = 1 Steady delta_rotor_max delta_c D+ F + delta_rotor A B Ctrl Ctrl = 1 Steady delta_rotor Eq_prime D + F + * * Sin I_postfault_ang I_postfault_mag * * Cos I_postfault_ang I_postfault_mag Vgen_postfault Xd_prime Xd_prime * Cos Sin * Eq_prime D + F -A B Ctrl Ctrl = 1 Fault_cleared Vgen_postfault Y X M P M P Y X delta_rotor_max delta_c D + F + A B Ctrl Ctrl = 1 Steady delta_rotor D+ F + Id * Xd Vq A B Ctrl Ctrl = 1 Eq Steady B + D -Id * Xd B + D -Xd_prime Eq_prime Eq_prime Vtx_sec_postfault D+ F + Xtrfr Xd_prime Eq_prime D + F + * * Sin I_postfault_ang I_postfault_mag * * Cos I_postfault_ang I_postfault_mag * Cos Sin * Eq_prime D+ F -D + F + Xtrfr Xd_prime A B Ctrl Ctrl = 1 Fault_cleared Vtx_sec_postfault Y X M P M P Y X delta_rotor_max delta_c D + F + A B Ctrl Ctrl = 1 Steady delta_rotor Vgen_fault I_fault_ang I_fault_mag I_fault_ang I_fault_mag Vtx_sec_fault Eq_prime D + F + * * Sin I_fault_ang I_fault_mag * * Cos I_fault_ang I_fault_mag Xd_prime Xd_prime * delta_c D + F + Cos Sin * Eq_prime D+ F -A B Ctrl Ctrl = 1 Fault_cleared Vgen_fault 0.0 D + F + Xtrfr Xd_prime Eq_prime D + F + * * Sin * * Cos * delta_c D + F + Cos Sin * Eq_prime D + F -D + F + Xtrfr Xd_prime A B Ctrl Ctrl = 1 Fault_cleared Vtx_sec_fault 0.0 Y X M P M P Y X Y X M P M P Y X _A B Ctrl Ctrl = 1 Fault_cleared Vtx_sec_fault_ang Vtx_sec_fault_ang A B Ctrl Ctrl = 1 Fault_cleared Vgen_fault_ang Vgen_fault_ang

B + F -Tm_In * B + D + Area1_gen A B Ctrl Ctrl = 1 Area1_gen A B Ctrl Ctrl = 1 Reset 0.0 A B Ctrl Ctrl = 1 A B Compar-ator 0.0 0.0 Pgen1 Pgen1 Area2_gen Eq_prime N D N/D * B -D + Cos Cos * Tm_In B + D -B + D -F + Area2_tx N D N/D * B -D + Cos Cos * Tm_In B + D -B + D -* X2 N D N/D 4.0 N D N/D 1.0 Xq_prime Xd_prime N D N/D 1.0 D -F + Cos * 2.0 * D + F -Cos * 2.0 Vgen_postfault delta_LS delta_LS * Vgen_postfault Xd_prime delta_LS delta_gen_i5_rad delta_gen_i5_rad delta_gen_i5_rad B + F -Tm_In * B + D + Area1_tx A B Ctrl Ctrl = 1 Area1_tx A B Ctrl Ctrl = 1 Reset 0.0 A B Ctrl Ctrl = 1 A B Compar-ator 0.0 0.0 Pgen1 Pgen1 delta_gen_i5_rad Fault_cleared Fault_cleared * Xtrfr delta_L_tx delta_tx_i5_rad delta_tx_i5_rad delta_tx_i5_rad delta_L_tx B + D + A B Ctrl Ctrl = 1 Fault_cleared Area1_tx_rad A B Ctrl Ctrl = 1 Reset 0.0 Area1_tx_rad delta_tx_i5_rad0 delta_tx_i5_rad B + F -delta_tx_i5_rad0 A B Ctrl Ctrl = 1 1.0 0.0 * A B Ctrl Ctrl = 1 delta_tx_i5_rad0 Delay * Fault_detected Delay T Vtx_sec_postfault Vgen_postfault delta_gen_i5_rad0 A B Ctrl Ctrl = 1 1.0 0.0 A B Ctrl Ctrl = 1 delta_gen_i5_rad0 Delay B + F - * * Fault_detected Delay T B + D + A B Ctrl Ctrl = 1 Fault_cleared Area1_gen_rad A B Ctrl Ctrl = 1 Reset 0.0 Area1_gen_rad delta_gen_i5_rad delta_gen_i5_rad0 Sample

FAULT DETECTION AND FAULT CLEARED ALGORITHM

B + F -Tm_In * B + D + Area1 * speed_deviation1 A B Ctrl Ctrl = 1 Reset 0.0 A B Ctrl Ctrl = 1 A B Compar-ator 0.0 0.0 Pgen1 Pgen1 Area1 Delta-T Igen_puA B Compar-ator 1.2 Q Q C S R Fault_cleared Fault_detected Reset Q Q C S R Reset Area1_fault_cleared

Only for FAULT DETECT purposes

A B Compar-ator Area1_fault_cleared Q Q C S R Reset fault_cycles A B Compar-ator 700.0 Area1_0 A B Ctrl Ctrl = 1 Area1_0 Area1 Area1

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M a in : G ra p hs 5. 40 5. 60 5.8 0 6.0 0 6. 20 6. 40 6.6 0 6. 80 ... ... ... -1 .0 0.₀ 1.₀ 2.₀ 3._{0 0} 4. 5.₀ 6.₀ 7.₀ 8.₀ 9.₀ y (rad/s) S pe ed D ev ia tio n S p ee d D e via tio n 2 S pe ed D ev ia tio n 3 S p ee d D e via tio n 4 -1 .0 0.₀ 1.₀ 2.₀ 3.₀ 4.₀ 5.₀ 6.₀ y (pu) F au lt_ c le a re d A re a2 _g en A re a 1_ ge n Fa u lt_ d ete c t -2 .0 0.₀ 2.₀ 4.₀ 6.₀ 8.₀ 10.0 12.0 14.0 16.0 y (pu) F au lt_ c le a re d Fa u lt_ d ete c t A re a 1_ tx A re a2 _tx 0. 00 0.20 0.40 0.60 0.80 1.00 1.20 y (pu) V g e n_ pu V g en _p os tfa ult V trf r_ p u V tx _s e c_ po st fa u lt -1 0 0 -50 ₀ 50 100 150 200 y (deg) d elta _g e n_ i5 G e n P o w e r A n gle (d e g) d elta _t x_ i5 Tr an sf o rm e r a n g le

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M a in : G ra p hs 5. 40 5. 60 5.8 0 6.0 0 6. 20 6. 40 6.6 0 6. 80 ... ... ... -1 .0 0.₀ 1.₀ 2.₀ 3._{0 0} 4. 5.₀ 6.₀ 7.₀ 8.₀ 9.₀ y (rad/s) S pe ed D ev ia tio n S p ee d D e via tio n 2 S pe ed D ev ia tio n 3 S p ee d D e via tio n 4 -1 .0 0.₀ 1.₀ 2.₀ 3.₀ 4.₀ 5.₀ 6.₀ y (pu) F au lt_ c le a re d A re a2 _g en A re a 1_ ge n Fa u lt_ d ete c t -2 .0 0.₀ 2.₀ 4.₀ 6.₀ 8.₀ 10.0 12.0 14.0 16.0 y (pu) F au lt_ c le a re d Fa u lt_ d ete c t A re a 1_ tx A re a2 _tx 0. 00 0.20 0.40 0.60 0.80 1.00 1.20 y (pu) V g e n_ pu V g en _p os tfa ult V trf r_ p u V tx _s e c_ po st fa u lt -1 0 0 -50 ₀ 50 100 150 200 y (deg) d elta _g e n_ i5 G e n P o w e r A n gle (d e g) d elta _t x_ i5 Tr an sf o rm e r a n g le

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M a in : G ra p hs 0. 60 0. 80 1.0 0 1.2 0 1. 40 1. 60 1.8 0 2. 00 ... ... ... -1 0 .0 -8.0 -6.0 -4.0 -2.0 ₀ 0. 2.₀ 4.₀ 6.₀ 8.₀ 10.0 y (rad/s) S pe ed D ev ia tio n S p ee d D e via tio n 2 S pe ed D ev ia tio n 3 S p ee d D e via tio n 4 -1 .0 0.₀ 1.₀ 2.₀ 3.₀ 4.₀ 5.₀ 6.₀ y (pu) F au lt_ c le a re d A re a2 _g en A re a 1_ ge n Fa u lt_ d ete c t 0. 0 2.0 4.0 6.0 0 8. 10.0 12.0 14.0 16.0 y (pu) F au lt_ c le a re d Fa u lt_ d ete c t A re a 1_ tx A re a2 _tx 0. 00 0.20 0.40 0.60 0.80 1.00 1.20 y (pu) V g e n_ pu V g en _p os tfa ult V trf r_ p u V tx _s e c_ po st fa u lt -5 0 -25 ₀ 25 50 75 100 125 150 175 y (deg) d elta _g e n_ i5 G e n P o w e r A n gle (d e g) d elta _t x_ i5 Tr an sf o rm e r a n g le

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M a in : G ra p hs 0. 60 0. 80 1.0 0 1.2 0 1. 40 1. 60 1.8 0 2. 00 ... ... ... -1 0 .0 -8.0 -6.0 -4.0 -2.0 ₀ 0. 2.₀ 4.₀ 6.₀ 8.₀ 10.0 y (rad/s) S pe ed D ev ia tio n S p ee d D e via tio n 2 S pe ed D ev ia tio n 3 S p ee d D e via tio n 4 -1 .0 0.₀ 1.₀ 2.₀ 3.₀ 4.₀ 5.₀ 6.₀ y (pu) F au lt_ c le a re d A re a2 _g en A re a 1_ ge n Fa u lt_ d ete c t 0. 0 2.0 4.0 6.0 0 8. 10.0 12.0 14.0 16.0 y (pu) F au lt_ c le a re d Fa u lt_ d ete c t A re a 1_ tx A re a2 _tx 0. 00 0.20 0.40 0.60 0.80 1.00 1.20 y (pu) V g e n_ pu V g en _p os tfa ult V trf r_ p u V tx _s e c_ po st fa u lt -5 0 -25 ₀ 25 50 75 100 125 150 175 y (deg) d elta _g e n_ i5 G e n P o w e r A n gle (d e g) d elta _t x_ i5 Tr an sf o rm e r a n g le

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M a in : G ra p hs 0. 60 0. 80 1.0 0 1.2 0 1. 40 1. 60 1.8 0 2. 00 ... ... ... -1 0 .0 -8.0 -6.0 -4.0 -2.0 ₀ 0. 2.₀ 4.₀ 6.₀ 8.₀ 10.0 y (rad/s) S pe ed D ev ia tio n S p ee d D e via tio n 2 S pe ed D ev ia tio n 3 S p ee d D e via tio n 4 -1 .0 0.₀ 1.₀ 2.₀ 3.₀ 4.₀ 5.₀ 6.₀ y (pu) F au lt_ c le a re d A re a2 _g en A re a 1_ ge n Fa u lt_ d ete c t 0. 0 2.0 4.0 6.0 0 8. 10.0 12.0 14.0 16.0 y (pu) F au lt_ c le a re d Fa u lt_ d ete c t A re a 1_ tx A re a2 _tx 0. 00 0.20 0.40 0.60 0.80 1.00 1.20 y (pu) V g e n_ pu V g en _p os tfa ult V trf r_ p u V tx _s e c_ po st fa u lt -5 0 -25 ₀ 25 50 75 100 125 150 175 y (deg) d elta _g e n_ i5 G e n P o w e r A n gle (d e g) d elta _t x_ i5 Tr an sf o rm e r a n g le

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M a in : G ra p hs 0. 60 0. 80 1.0 0 1.2 0 1. 40 1. 60 1.8 0 2. 00 ... ... ... -1 0 .0 -8.0 -6.0 -4.0 -2.0 ₀ 0. 2.₀ 4.₀ 6.₀ 8.₀ 10.0 y (rad/s) S pe ed D ev ia tio n S p ee d D e via tio n 2 S pe ed D ev ia tio n 3 S p ee d D e via tio n 4 -1 .0 0.₀ 1.₀ 2.₀ 3.₀ 4.₀ 5.₀ 6.₀ y (pu) F au lt_ c le a re d A re a2 _g en A re a 1_ ge n Fa u lt_ d ete c t 0. 0 2.0 4.0 6.0 0 8. 10.0 12.0 14.0 16.0 y (pu) F au lt_ c le a re d Fa u lt_ d ete c t A re a 1_ tx A re a2 _tx 0. 00 0.20 0.40 0.60 0.80 1.00 1.20 y (pu) V g e n_ pu V g en _p os tfa ult V trf r_ p u V tx _s e c_ po st fa u lt -5 0 -25 ₀ 25 50 75 100 125 150 175 y (deg) d elta _g e n_ i5 G e n P o w e r A n gle (d e g) d elta _t x_ i5 Tr an sf o rm e r a n g le

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M a in : G ra p hs 16 .8 0 1 7. 00 1 7. 20 1 7.4 0 17 .6 0 1 7. 80 1 8. 00 1 8.2 0 18 .4 0 ... ... ... -1 0 .0 -8.0 -6.0 -4.0 -2.0 ₀ 0. 2.₀ 4.₀ 6.₀ 8.₀ 10.0 y (rad/s) S pe ed D ev ia tio n S p ee d D e via tio n 2 S pe ed D ev ia tio n 3 S p ee d D e via tio n 4 -1 .0 0.₀ 1.₀ 2.₀ 3._{0 0} 4. 5.₀ 6.₀ 7.₀ 8.₀ 9.₀ y (pu) F au lt_ c le a re d A re a2 _g en A re a 1_ ge n Fa u lt_ d ete c t -2 .5 0.₀ 2.₅ 5.₀ 7.₅ 10.0 12.5 15.0 17.5 20.0 y (pu) F au lt_ c le a re d Fa u lt_ d ete c t A re a 1_ tx A re a2 _tx 0. 00 0.20 0.40 0.60 0.80 1.00 1.20 y (pu) V g e n_ pu V g en _p os tfa ult V trf r_ p u V tx _s e c_ po st fa u lt -4 0 -20 ₀ 20 40 60 80 100 y (deg) d elta _g e n_ i5 G e n P o w e r A n gle (d e g) d elta _t x_ i5 Tr an sf o rm e r a n g le

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M a in : G ra p hs 16 .8 0 1 7. 00 1 7. 20 1 7.4 0 17 .6 0 1 7. 80 1 8. 00 1 8.2 0 18 .4 0 ... ... ... -1 0 .0 -8.0 -6.0 -4.0 -2.0 ₀ 0. 2.₀ 4.₀ 6.₀ 8.₀ 10.0 y (rad/s) S pe ed D ev ia tio n S p ee d D e via tio n 2 S pe ed D ev ia tio n 3 S p ee d D e via tio n 4 -1 .0 0.₀ 1.₀ 2.₀ 3._{0 0} 4. 5.₀ 6.₀ 7.₀ 8.₀ 9.₀ y (pu) F au lt_ c le a re d A re a2 _g en A re a 1_ ge n Fa u lt_ d ete c t -2 .5 0.₀ 2.₅ 5.₀ 7.₅ 10.0 12.5 15.0 17.5 20.0 y (pu) F au lt_ c le a re d Fa u lt_ d ete c t A re a 1_ tx A re a2 _tx 0. 00 0.20 0.40 0.60 0.80 1.00 1.20 y (pu) V g e n_ pu V g en _p os tfa ult V trf r_ p u V tx _s e c_ po st fa u lt -4 0 -20 ₀ 20 40 60 80 100 y (deg) d elta _g e n_ i5 G e n P o w e r A n gle (d e g) d elta _t x_ i5 Tr an sf o rm e r a n g le

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M a in : G ra p hs 5. 50 5 .7 5 6 .0 0 6 .2 5 6. 50 6 .7 5 7 .0 0 7 .2 5 7. 50 ... ... ... -1 0 .0 -8.0 -6.0 -4.0 -2.0 0.₀ 2.₀ 4.₀ 6.₀ 8.₀ y (rad/s) S pe ed D ev ia tio n S p ee d D e via tio n 2 S pe ed D ev ia tio n 3 S p ee d D e via tio n 4 -1 .0 0.₀ 1.₀ 2.₀ 3._{0 0} 4. 5.₀ 6.₀ 7.₀ 8.₀ 9.₀ y (pu) F au lt_ c le a re d A re a2 _g en A re a 1_ ge n Fa u lt_ d ete c t -2 .5 0.₀ 2.₅ 5.₀ 7.₅ 10.0 12.5 15.0 17.5 20.0 y (pu) F au lt_ c le a re d Fa u lt_ d ete c t A re a 1_ tx A re a2 _tx 0. 00 0.20 0.40 0.60 0.80 1.00 1.20 y (pu) V g e n_ pu V g en _p os tfa ult V trf r_ p u V tx _s e c_ po st fa u lt -4 0 -20 ₀ 20 40 60 80 100 120 140 y (deg) d elta _g e n_ i5 G e n P o w e r A n gle (d e g) d elta _t x_ i5 Tr an sf o rm e r a n g le

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M a in : G ra p hs 5. 00 5 .2 5 5. 50 5 .7 5 6 .0 0 6. 25 6 .5 0 6. 75 7 .0 0 7 .2 5 7. 50 ... ... ... -1 5 .0 -1 0 .0 -5.0 0.₀ 5.₀ 10.0 15.0 y (rad/s) S pe ed D ev ia tio n S p ee d D e via tio n 2 S pe ed D ev ia tio n 3 S p ee d D e via tio n 4 -1 .0 0.₀ 1.₀ 2.₀ 3._{0 0} 4. 5.₀ 6.₀ 7.₀ 8.₀ 9.₀ y (pu) F au lt_ c le a re d A re a2 _g en A re a 1_ ge n Fa u lt_ d ete c t -2 .5 0.₀ 2.₅ 5.₀ 7.₅ 10.0 12.5 15.0 17.5 20.0 y (pu) F au lt_ c le a re d Fa u lt_ d ete c t A re a 1_ tx A re a2 _tx 0. 00 0.20 0.40 0.60 0.80 1.00 1.20 y (pu) V g e n_ pu V g en _p os tfa ult V trf r_ p u V tx _s e c_ po st fa u lt -1 0 0 -50 ₀ 50 100 150 200 y (deg) d elta _g e n_ i5 G e n P o w e r A n gle (d e g) d elta _t x_ i5 Tr an sf o rm e r a n g le

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M a in : G ra p hs 4. 00 4 .2 0 4 .4 0 4 .6 0 4 .8 0 5 .0 0 5. 20 5 .4 0 5. 60 5. 80 ... ... ... -6 .0 -4.0 -2.0 0.₀ 2.₀ 4.₀ 6.₀ 8.₀ y (rad/s) S pe ed D ev ia tio n S p ee d D e via tio n 2 S pe ed D ev ia tio n 3 S p ee d D e via tio n 4 -0 .2 0 0.00 0.20 0.40 0.60 800. 1.00 1.20 1.40 1.60 1.80 y (pu) F au lt_ c le a re d A re a2 _g en A re a 1_ ge n Fa u lt_ d ete c t 0. 0 2.0 4.0 6.0 8.0 10.0 12.0 y (pu) F au lt_ c le a re d Fa u lt_ d ete c t A re a 1_ tx A re a2 _tx 0. 00 0.20 0.40 0.60 0.80 1.00 1.20 y (pu) V g e n_ pu V g en _p os tfa ult V trf r_ p u V tx _s e c_ po st fa u lt -2 0 ₀ 20 40 60 80 100 120 140 160 180 y (deg) d elta _g e n_ i5 G e n P o w e r A n gle (d e g) d elta _t x_ i5 Tr an sf o rm e r a n g le

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M a in : G ra p hs 4. 40 4. 60 4.8 0 5.0 0 5. 20 5. 40 5.6 0 5. 80 ... ... ... -6 .0 -4.0 -2.0 0._{0 0} 2. 4.₀ 6.₀ 8.₀ 10.0 y (rad/s) S pe ed D ev ia tio n S p ee d D e via tio n 2 S pe ed D ev ia tio n 3 S p ee d D e via tio n 4 -0 .2 0 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 y (pu) F au lt_ c le a re d A re a2 _g en A re a 1_ ge n Fa u lt_ d ete c t 0. 0 2.0 4.0 6.0 8.0 10.0 12.0 y (pu) F au lt_ c le a re d Fa u lt_ d ete c t A re a 1_ tx A re a2 _tx 0. 00 0.20 0.40 0.60 0.80 1.00 1.20 y (pu) V g e n_ pu V g en _p os tfa ult V trf r_ p u V tx _s e c_ po st fa u lt -2 0 0 -150 -100 -50 ₀ 50 100 150 200 250 y (deg) d elta _g e n_ i5 G e n P o w e r A n gle (d e g) d elta _t x_ i5 Tr an sf o rm e r a n g le

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M a in : G ra p hs 3. 80 4. 00 4.2 0 4.4 0 4. 60 4. 80 5.0 0 5. 20 ... ... ... -8 .0 -6.0 -4.0 -2.0 ₀ 0. 2.₀ 4.₀ 6.₀ 8.₀ y (rad/s) S pe ed D ev ia tio n S p ee d D e via tio n 2 S pe ed D ev ia tio n 3 S p ee d D e via tio n 4 -0 .2 5 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 y (pu) F au lt_ c le a re d A re a2 _g en A re a 1_ ge n Fa u lt_ d ete c t 0. 0 2.0 4.0 6.0 8.0 10.0 12.0 y (pu) F au lt_ c le a re d Fa u lt_ d ete c t A re a 1_ tx A re a2 _tx 0. 00 0.20 0.40 0.60 0.80 1.00 1.20 y (pu) V g e n_ pu V g en _p os tfa ult V trf r_ p u V tx _s e c_ po st fa u lt -2 0 0 -1 5 0 -1 0 0 -50 ₀ 50 100 150 200 250 y (deg) d elta _g e n_ i5 G e n P o w e r A n gle (d e g) d elta _t x_ i5 Tr an sf o rm e r a n g le

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M a in : G ra p hs 3. 80 4. 00 4.2 0 4.4 0 4. 60 4. 80 5.0 0 5. 20 ... ... ... -8 .0 -6.0 -4.0 -2.0 ₀ 0. 2.₀ 4.₀ 6.₀ 8.₀ y (rad/s) S pe ed D ev ia tio n S p ee d D e via tio n 2 S pe ed D ev ia tio n 3 S p ee d D e via tio n 4 -0 .2 5 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 y (pu) F au lt_ c le a re d A re a2 _g en A re a 1_ ge n Fa u lt_ d ete c t 0. 0 2.0 4.0 6.0 8.0 10.0 12.0 y (pu) F au lt_ c le a re d Fa u lt_ d ete c t A re a 1_ tx A re a2 _tx 0. 00 0.20 0.40 0.60 0.80 1.00 1.20 y (pu) V g e n_ pu V g en _p os tfa ult V trf r_ p u V tx _s e c_ po st fa u lt -2 0 0 -150 -100 -50 ₀ 50 100 150 200 250 y (deg) d elta _g e n_ i5 G e n P o w e r A n gle (d e g) d elta _t x_ i5 Tr an sf o rm e r a n g le

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M ain : G ra ph s 0.8 0 1 .0 0 1 .2 0 1 .4 0 1 .6 0 1.8 0 2.0 0 2 .2 0 2.4 0 2.6 0 ... ... ... -8 .0 -6.0 -4.0 -2.0 0.0 2.0 4.0 6.0 8.0 y (rad/s) S p ee d D e via tio n S pe ed D ev ia tio n 2 S pe ed D ev ia tio n 3 S p ee d D e via tio n 4 -2 .0 0 -1 .5 0 -1 .0 0 -0 .5 0 0.0₀ 0.5₀ 1.0₀ 1.5₀ 2.0₀ y (pu) F au lt_ c le a re d A re a 2_ ge n A re a 1_ ge n F au lt_ d ete c t 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 y (pu) F au lt_ c le a re d Fa ult _ de te ct A re a 1_ tx A re a2 _tx 0.0 0 0.20 0.40 0.60 0.80 1.00 1.20 y (pu) V ge n_ pu V g en _p os tfa ult V trf r_ pu V tx _ se c_ po stf a ult -2 0 0 20 40 60 80 100 120 140 160 180 y (deg) d elt a _g en _i5 G e n P ow er A n gle (d eg ) de lta _ tx _i5 T ra n sf or m e r a ng le

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M a in : G ra p hs 4. 50 4 .6 0 4. 70 4 .8 0 4 .9 0 5. 00 5 .1 0 5. 20 5 .3 0 5 .4 0 5. 50 ... ... ... -4 .0 -2.0 0.₀ 2.₀ 4.₀ 6.₀ 8.₀ 10.0 12.0 14.0 y (rad/s) S pe ed D ev ia tio n S p ee d D e via tio n 2 S pe ed D ev ia tio n 3 S p ee d D e via tio n 4 -0 .5 0 0.00 0.50 1.00 1.50 2.00 2.50 y (pu) F au lt_ c le a re d A re a2 _g en A re a 1_ ge n Fa u lt_ d ete c t 0. 0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 y (pu) F au lt_ c le a re d Fa u lt_ d ete c t A re a 1_ tx A re a2 _tx 0. 00 0.20 0.40 0.60 0.80 1.00 1.20 y (pu) V g e n_ pu V g en _p os tfa ult V trf r_ p u V tx _s e c_ po st fa u lt -2 0 0 -150 -100 -50 ₀ 50 100 150 200 250 y (deg) d elta _g e n_ i5 G e n P o w e r A n gle (d e g) d elta _t x_ i5 Tr an sf o rm e r a n g le