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ANALOG COMPUTER SIMULATION OF ASWAN HIGH DAM VOLTAGE REGULATORS
September 7 985 Engineering and Research Center
U S . Department of the Interior Bureau of Reclamation
Division of Research and
Laboratory Services Power and Instrumentajion Branch
Analog Computer Simulation of Aswan High Dam Voltage Regulators
September 1985 6. PERFORMING ORGANIZAT ION CODE
D-1550, D-1552 I 9. PERFORMING ORGANIZAT ION NAME AND ADDRESS 110. WORK U N I T NO.
7. AUTHOR^)
J. C. Agee, W. R. Roemish, T. R. Whittemore
8. PERFORMING ORGANIZAT ION R E P O R T NO.
GR-85-7
Same
Bureau of Reclamation Engineering and Research Center Denver, CO 80225
12. SPONSORING AGENCY NAME AND ADDRESS
15. S U P P L E M E N T A R Y NOTES
11. C O N T R A C T OR GRANT NO.
13. T Y P E O F R E P O R T AND P E R I O D C O V E R E D
Microfiche and/or hard copy available at the E&R Center, Denver, Colorado Ed: RNW (c)
16. ABSTRACT
A report prepared for EEA (Egyptian Electricity Authority) by SWED indicated a need for PSS's (Power System Stabilizers) at Aswan High Dam. This recommendation was based on the results of digital-computer load flow and stability studies, which modeled the voltage regulators as IEEE Type AC4 devices. EEA then asked the USBR to determine whether PSS's would be compatible with their existing voltage regulators furnished by the U.S.S.R. This study describes the modeling techniques and results of an analog computer simulation of the existing voltage regulators. These existing regulators incorporate the PSS function and, therefore, do not need the addition of external PSS's.
17. K E Y WORDS A N D DOCUMENT ANALYSIS
a . DESCRIPTORS-- electric generators/ transmission (electrical)/ power system stability/ electric analogs/ control/ excitation/ 'voltage regulators/ stabilization/ 'analog models/ machine-control systems
b. IDENTIFIERS-- / Aswan High Dam/ Egypt/ voltage regulator/ power system stabilizer
c . COSATI Field/Group 09C COWRR: 0903 SR IM:
18. D ISTRIBUT ION S T A T E M E N T IS. S E C U R I T Y CLASS (THIS REPORT)
UNCLASSlFl ED '20. S E C U R I T Y CLASS
(THIS PAGE)
UNCLASSIFIED
121. NO. OF PAGE
67 22. P R I C E
ANALOG COMPUTER SIMULATION OF ASWAN HIGH DAM VOLTAGE REGULATORS
J. C. Agee W. R. Roemish
T. R. Whitternore
Power and Instrumentation Branch Division of Research and Laboratory Services
Engineering and Research Center Denver, Colorado
September 1985
UNITED STATES DEPARTMENT OF THE INTERIOR * BUREAU OF RECLAMATION
As the Nation's principal conservation agency. the Department of theInterior has responsibility for most of our nationally owned publiclands and natural resources. This includes fostering the wisest use ofour land and water resources, protecting our fish and wildlife, preser-ving the environmental and cultural values of our national parks andhistorical places, and providing for the enjoyment of life through out-door recreation. The Department assesses our energy and mineralresources and works to assure that their development is in the bestinterests of all our people. The Department also has a major respon-sibility for American Indian reservation communities and for peoplewho live in Island Territories under U.S. Administration.
The research covered by this report was funded under theBureau of Reclamation PRESS (Program Related Engineeringand Scientific Studies) allocation No. DR-SO, Power SystemControls.
The information contained in this report regarding commercial productsor firms may not be used for advertising or promotional purposes and isnot to be construed as an endorsement of any product or firm by theBureau of Reclamation.
ii
PREFACE
This report describes the models used for and the results of a study of the Aswan High Dam Powerplantexcitation-control system in Upper Egypt. The study is based on information supplied to the USBR (Bureauof Reclamation) by the EEA (Egyptian Electricity Authority). Detailed information describing the existingparameter settings and operating characteristics of the present excitation-control equipment was not sup-plied by the EEA. Therefore, this study deals exclusively with a determination of the optimum theoreticalperformance of the existing equipment with and without additional power system stabilizer equipment. Acopy of Activity No.7 of the SWED POWER Phase II Final Report, dated March 1981, titled" Study on theImprovement of the Reliability of the 500-kV Transmission System from the High Dam to the Cairo Regionand the Possibilities to Increase the Firm Transmission Capacity," [1]* was used to validate the resultsobtained from the Controls Section analog computer model.
This report was prepared by the Controls Section of the Power and Instrumentation Branch of the Divisionof Research and Laboratory Services. It is one of a series of reports documenting hydroelectric synchronousmachine-control system modeling studies. The Controls Section is involved in the development of analogand digital computer models, field testing and alignment of synchronous machine-control systems, andapplied research into improved control techniques. Members of the Controls Section are active in WSCC(Western Systems Coordinating Council) and IEEE(Institute of Electrical and Electronic Engineers) subcom-mittees developing standards for modeling and testing of synchronous machine-control systems.
.Numbers in brackets refer to the bibliography.
III
GLOSSARY OF SYMBOLS AND ACRONYMS
Symbols
8 = torque angleE(MWS) = total kinetic energy of inertia
EBd = direct-axis component of infinite-bus voltage phasorEBq = quadrature-axis component of infinite-bus voltage phasor
--+E Bus = infinite-bus voltage phasor
Emd = direct-axis component of midpoint-bus voltage phasor--+E mid = midpoint-bus voltage phasor
Emq = quadrative-axis component of midpoint-bus voltage phasorH = inertia constant
--+IB = infinite-bus current phasor
Id' I'd = direct-axis component of machine-current phasor--+IL = midpoint-load current phasor
ILd = direct-axis component of midpoint-load current phasorILq = quadrature-axis component of midpoint-load current phasor
IQ' Irq = quadrature-axis component of machine-current phasor--+--+
I" I = machine-current phasorK,1v = voltage regulator gain of terminal voltage deviation
Kv' = voltage regulator gain of derivative of terminal voltageK" = voltage regulator gain of line currentK", = voltage regulator gain of derivative of line currentK,", = voltage regulator gain of second derivative of linecurrentKI'R = voltage regulator gain of derivative of rotor current
KFDBKr= voltage regulator gain of derivative of fieldvoltageKFDBKd= voltage regulator gain of field current
Pe = electrical powerPm = mechanical power
SG1 0 = generator saturation at rated terminal voltageSG12 = generator saturation at 1,2 times rated terminal voltageT"DO = direct-axis subtransient open-circuit time constantT"00 = quadrature-axis subtransient open-circuit time constantroo = direct-axis transient open-circuit time constant
Tm = generator mechanical time constant--+V, = terminal-voltage phasor
V'd = direct-axis component of terminal-voltage phasorVrq = quadrature-axis component of terminal-voltage phasorX = system equivalent reactance
X" 0 = direct-axis subtransient reactanceX"0 = quadrature-axis subtransient reactanceX'D = direct-axis transient reactanceXB = equivalent reactance from midpoint bus to infinite busXo = direct-axis synchronous reactanceXL = armature-leakage reactance
XLine = equivalent reactance from machine to midpoint busXo = quadrature-axis synchronous reactance
v
EEAIEEEPSS
SWEDWSCC
GLOSSARY OF SYMBOLS AND ACRONYMS - Continued
Acronyms
= Egyptian Electricity Authority
= Institute of Electrical and Electronic Engineers= Power System Stabilizer
= Swedish Power Service= Western Systems Coordinating Council
Vi
CONTENTS
Preface.... . . .. ... . .. . .. ....... ......... ... .... iii
Page
Glossary of Symbols v
Introduction. . . .. ....... .. .. . , ... ........ . ... ... 1
Conclusions. . .. . . . .. ..... ........ ... ...... . 1
Background. .. .... ... .. . . ......... ..... ... ... 2
Generator model . 2
Tieline and infinite-bus model 3
Calculation of inertia constant 5
Egyptian power system model 6
IEEEType AC4 regulator model and results 6
Power system stabilizer 8
Existing regulator model and results 8
Bibliography 9
AppendixA - Network reduction of the 500-k V system 57B - Additional analog computer diagrams 61C - Listing of analog computer constants 65
Table
Figure
TABLES
12345
Aswan High Dam synchronous machine parameters..........................................................Saturation curve function generator values.......................................................................Summary of synchronizing and damping power coefficients...............................................Results of study with IEEEType AC4 regulator.................................................................Results of study with existing regulator............................................................................
FIGURES
1234567
Two-axis synchronous machine model .....Open-circuit saturation curve...........................................................................................Tieline and infinite-bus model..........................................................................................Tieline single-line diagram and equation.. .........Analog computer diagram for midpoint load.....................................................................Single-line diagram of the tieline with midpoint load..........................................................500-k V power system....................................................................................................
VII
1011121314
15161718192020
CONTENTS- Continued
89
10111213141516171819202122232425
Model of the modified 500-kV power system...................................................................IEEE Type AC4 regulator model.......................................................................................IEEEType AC4 regulator analog computer diagram
""""' ,,.
Off-line time-domain responses with IEEE Type AC4 regulator (4 sheets)............................Off-line frequency response with IEEE Type AC4 regulator.................................................On-linetime-domain responses with IEEE Type AC4 regulator (5 sheets)
',.
System performance for various values of line impedance and damping (8 sheets) .,............Bode plots of the machinetransfer function (3 sheets)
""""'".. ..
"".. ...
Phasor diagram with both lines in service.........................................................................Phasor diagram with only one line in service.....................................................................System performance at full capacity with both lines in service...........................................System performance at full capacity with only one line in service.......................................Analog computer diagram of PSS function.......................................................................Block diagram of existing regulator..................................................................................Analog computer diagram of existing regulator.................................................................Off-line time-domain responses of the existing regulator (2 sheets) ,............On-linetime-domain responses of the existing regulator (2 sheets) ,.Phase-angle response of machine power to rotor position for various line impedances
to the infinite bus.......................................................................................................Successive steps in reduction of equivalent circuits..........................................................Analog computer diagram of power to the infinite bus......................................................Analog computer diagram to enable pole-slipping.............................................................Analog computer constants............................................................................................
A1B1B2C1
viii
2122222327283341444546474849505153
5559636467
INTRODUCTION
As a part of Activity No.7 of the SWED Phase IIFinal Report [1], dated March 1981, performed
for EEA, a recommendation was made to install PSS's (power system stabilizers) at Aswan High
Dam. This recommendation was based on the results of digital-computer load flow and stability
studies, which modeled the voltage regulators as IEEE Type AC4 devices. EEAthen asked theUSBRto determine whether PSS's were compatible with their existing voltage regulators furnished
by the U.S.S.R. This study was undertaken to determine the effect of the existingvoltage regulators
on power system stability and to explore the addition of PSS's.
CONCLUSIONS
The existing Russian regulators are not simply voltage-regulating devices. They incorporate feed-
back from the terminal voltage, the derivative of terminal voltage, the 500-kV line current, the
first and second derivatives of line current, and the derivative of rotor (field) current. Therefore, if
properly aligned, these regulators can contribute to the dynamic stability of the power system
and to its steady-state and transient stability. A typical IEEE Type AC4 voltage regulator increases
only the transient and steady-state stability of the power system and decreases the dynamic
(power-oscillation) stability limit. By adding a PSS to the type AC4 regulator, dynamic stability can
be increased while retaining the increased transient and steady-state limits. By using additional
feedback quantities, the existing High Dam regulators incorporate these dynamic-stability
considerations.
Unanswered questions center on the alignment of the existing High Dam regulators and the typical
system conditions. If the current-feedback quantities are not properly adjusted, the dynamic sta-
bility of the system could be worse than it would be without these quantities. The alignment also
depends on the oscillation modes of the system. A strong mode between Aswan High Dam and
Aswan Power Stations could hinder efforts to stabilize the 500-kV system; however, the use of
500-kV line current, rather than generator current, input to the regulator should eliminate this
problem.
A record of actual line flows on the High Dam-Nag Hammadi, the Nag Hammadi-Samalut, and the
Samalut-Cairo sections that show the damping or development of oscillations would help validate
the model results. The SWED report seems to give conservative line limits based on the study
of the actual voltage-regulating equipment. PSS's do not seem to be needed with the existing
regulators; however, if these regulators are replaced with conventional equipment, there will be
a definite need for PSS's.
1
BACKGROUND
The Egyptian power system of concern consists of thermal generation in the Cairo area in Lower
Egypt and hydroelectric generation at the Aswan High Dam, Aswan, and Aswan II Powerplants
in Upper Egypt. The system data were taken from the forecast for the 1985 system conditions
in the SWED report.
The generation capacity in Upper. Egypt is approximately 3070 MV. A, and the capacity in the
Cairo area is approximately 4770 MV. A. The major load is in the Cairo area. The Upper Egypt
generation is connected to the load in the Cairo area by two 500-kV transmission lines. There is
limited generation at Assiut (110 MV.A). a midpoint on the 500-kV transmission line.
The load in Upper Egypt is predominately at Nag Hammadi and is less than 25 percent of the
capacity in Upper Egypt. Nearly 50 percent of the capacity in Upper Egypt goes unused unless it
is transmitted to the Cairo area. The present system can transmit less than 25 percent of the
capacity of Upper Egypt to Cairo. The objective is to increase this percentage.
The problem is similar to a classical stability problem, in which two large masses are connected
by a weak spring. The inertia of the Cairo area system is nearly the same as the inertia of the
system in Upper Egypt. There is more generation in the Cairo area, but the inertia of the individual
steam generators there is less than that of the individual hydroelectric generators in Upper Egypt.
The two 500-kV lines provide the only tie between these two large inertias. The limiting case for
stability analysis is the system condition in which one of two parallel line sections is out of service.
In this limiting case the tie is weak.
The SWED study addresses several methods for improving the stability of the system and in-
creasing the transmission to Cairo. One of the proposed solutions involves the addition of PSS's.
This study attempts to validate the recommendation that PSS's be used.
GENERATOR MODEL
Figure 1 shows the 2-axis machine model used in this study. This model is described in detail in
[2]. Table 1 shows the parameters used in this model. X"q was unavailable in the SWED report;
therefore, a value equal to X'd was used.
The model chosen uses inputs of direct- and quadrature-axis machine currents and applied field
voltage. The model outputs values of direct- and quadrature-axis machine voltage. The tieline
model used is compatible with this approach.
2
Figure 2 shows the open-circuit saturation curve for the High Dam units based on the parameters
SGlO and SGl2 given in the Swedish study. Table 2 lists the function generator values used in the
model.
TIELINE AND INFINITE-BUS MODEL
Figure 3 shows the tieline and infinite-bus representation initially used in this study. The swing
equation is represented by amplifiers A35, A34, and A36 and potentiometers P36, P37, and P17.
This group of elements solves the torque angle equation:
8 = J 314 J Pm ; Pe , when the damping constant, represented by P17, is set to zero.m
The damping constant, P 17, is incorporated in the model to determine the relative stability. Neg-
ative damping can be inserted until a normally stable system begins to oscillate. This allows
measurement of the damping in a stable system.
Amplifiers A3, A 13, A41 , and A45 create electrical power from the terminal direct- and quadrature-
axis voltages and currents. Mechanical power from the turbine is assumed to be constant for the
range of oscillation frequencies that voltage regulators cause. This is represented by P16.
The output of the swing equation is the total angle between the machine quadrature axis and the
infinite-bus voltage phasor. This angle allows the infinite-bus voltage to be decomposed into its
direct- and quadrature-axis components. At this point the tie line equation shown on figure 4 can
be solved. This equation can be stated in direct- and quadrature-axis form as follows:
v: = lx + Eaus
(V:d + jV:q) = jx7f: + 71:)+ (Ead+ jEaq)
V:d = -x~ + Ead
V:q = + Xl: + Eaq
These equations are solved using amplifiers A51 , A55, A 103, and A 113 and potentiometers P61 ,
P74, and P75. Switches S51 and S55 provide a means to take the generator off line for testing.
3
- -- Vtq E8q I LdX8Itd = +
X8+XLine X8+ XLine X8+ XLine
- -- -Vtd E8d ILqX8I tq = + +
X8+XLine X8+ XLine X8+ XLine
During the testing it was determined that a midpoint load was needed so that the identities of the
High Dam-Cairo power flow and impedance were not lost in the total system representation. The
model section on figure 5 was installed for this purpose. This model applies a constant current
load at a point between the machine and the infinite bus. It was necessary to back-calculate the
values of midpoint voltage and infinite-bus current to avoid numerical instability when using high
tieline-impedance values. The equations for the midpoint load system are as follows:
- - -V t = Emid + }I tXLine - v: - flrXLine = E:id
- - -Emid = E8us + }18X8 - E:id - E:us=Ia
jX8
7;=Ia+~
E:id7;= -jX8
E8us----:---x + ILJ 8
- v:I -t -}X8
flrXLine E:us-- -+ IL
}X8 jX8
XLine v: E:us-7;+7; +ILX8 }X8 }X8
-I =t
v: E:us ~+jX8 (1 + XLine/X8) (1 + XLine/X8)
}X8 (1 + XLine/ X8)
-- VtI =tj(X8 + XLine)
E:us ~ X8+
j(X8 + XLine) (X8 + XLine)
7;d + flrq =V:d }V:q
+} (X8 + XLine) } (88 + XLine)
E:dj(X8 + XLine)
jE:q ~dX8+
j(X8+ XLine) X8+ XLine+
hqX8
X8+ XLine
4
High Dam 2060 7.41 1700
Aswan IIA 150 3.3 136
Aswan IIB 150 3.3 136
Aswan I 297 4.4 222
U. Egypt Equiv. 2657 6.61 2194
L. Egypt Equiv. 4164 2.85 3305
Assiut 112.5 4.0 90
Ayat 600 4.0 316
L. & M. Egypt Equiv. 4877 3.02 3711
Total System 7534 4.29 5905(U., L. & M. Egypt)
H=E (MWS)
SBase
E:d = V:d +TrqXLine
E:q = V:q - 'tdXLine
Figure 6 shows the single-line diagram of this system.
CALCULATION OF INERTIA CONSTANT
The equivalent inertia constant, H, for the High Dam-Cairo system when converting the equivalent
two-finite-machine system to an equivalent finite-infinite machine system calculated as:
Rating
MV.A H
Study
Power
Hon
2060 MV. ABase
8.52
7.15
HuHLHeq = = 3.89 on 2060 MV. ABase
Hu + HL
Note that the kinetic energy of Upper Egypt is 22,638 MJ; whereas, the kinetic energy of Lower
Egypt is only 14,729 MJ. Thus, Aswan High Dam more closely approximates an infinite mass
than does Cairo.
5
EGYPTIAN POWER SYSTEM MODEL
The basis for the power system model used was found in appendix 1 of the Swedish study. Figure
7 shows these data on a diagram of the 500-kV system. Appendix A of this report shows a
network reduction for this system. The resulting equivalent finite machine-to-infinite bus system
has a reactance between machine model Thevenin voltages of 0.673 per unit ( on a
2060 MV. ABase) with both High Dam-Nag Hammadi lines in service or a reactance of 0.784 per
unit with one line out of service. Unfortunately, this model is inaccurate because the total power
generated in Upper Egypt is not transmitted through the equivalent reactance of the model. There-
fore, an intermediate load was added to the transmission system (at Nag Hammadi) to more
accurately model the Egyptian 500-kV system. Figure 8 shows the system chosen to model the
500-kV system more accurately. Results obtained with this model corroborate the Swedish report
much better than those obtained with the simple machine infinite-bus system having no inter-
mediate load.
IEEE TYPE AC4 REGULATOR MODEL AND RESULTS
Figure 9 shows the block diagram of the regulator model used in the Swedish study. This diagram
fits the form of the IEEE Type AC4 model [3]. Figure 10 shows the analog computer representation
used in this study.
First, off-line data were gathered using the IEEE Type AC4 regulator. Figure 11 shows the off-line
time-domain performance of this regulator with varying amounts of gain. Figure 12 shows the
closed-loop frequency response of this regulator with the gain set to 31 (the value used in the
SWED study).
Figure 13 shows the on-line time-domain performance of the regulator when the generator is
running at no load. Note that as the line impedance increases, the gain of the overall excitation
system increases also.
For the finite-machine tieline, infinite-bus system on figure 4, the regulator gave the results shown
on figure 14. Table 3 summarizes the synchronizing-power coefficient and damping-power coef-
ficients observed in these and other tests.
6
It was noticed that the oscillation frequencies obtained in this study did not match the frequencies
found in the SWED report. It seems that combining all of the 500-kV system into a single equivalent
voltage and impedance is not adequate for maintaining the correct swing frequency. Therefore, a
frequency-domain technique was used to discover the effect of voltage-regulator action on damp-
ing power.
Figure 15 shows Bode plots of the machine transfer function, Pel8 . It should be noted that anytime the machine has a lagging phase angle, the overall machine tieline-infinite bus system is
unstable. On figure 15 (sheet 1) this region can be observed as swing frequencies below
0.075 Hz (with a regulator gain of 31). Figure 15 (sheet 2) indicates that as machine power
increases, the frequency range of unstable operation increases. At 1.0 per unit (on a 2060
MV. ABase)power, the machine is unstable for swing frequencies below 0.95 Hz. This result can
also be seen in table 3.
Unfortunately, this frequency-response technique provides no insight into power transfers or sys-
tem configuration. However, it is a powerful tool for pointing out frequencies at which sufficient
damping is unavailable. The oscillation modes within regions that are actually present on the system
depend on the particular system configurations used.
To investigate actual line flows, the system on figure 6 was connected. Figure 16 shows a phasor
diagram of the system with both High Dam-Nag Hammadi lines in service, and figure 17 shows
a phasor diagram with one line out of service. With both lines in service, the transfer from High
Dam-Nag Hammadi was limited to 1700 MW, and the transfer from Nag Hammadi-Cairo was 1025
MW. The oscillation frequency observed was 0.72 Hz under these conditions. Figure 18 shows
this condition.
With one High Dam-Nag Hammadi line out of service, the power transfer from High Dam-Nag
Hammadi was limited to 1350 MW, and the Nag Hammadi-Cairo transfer was 660 MW. The
oscillation frequency for this case was 0.63 Hz. Figure 19 shows this case.
Unfortunately, direct comparison of the findings of this study with those of the SWED study cannot
be made because of the inability to model many machines on the analog computer and the una-
vailability of most of the SWED study load-flow data. (Only two cases are included in the ap-
pendices of the SWED Report). However, the findings in this section are reasonably close to the
SWED study summary of 1700 MW for both lines in service and 1550 MW with one line out of
service.
7
POWER SYSTEM STABILIZER
A PSS of the speed type was connected to the Type AC4 regulator model by using the analog
diagram of figure 20. The resulting power-transfer increase is shown in table 4 for various stabilizer
gain settings. In real applications this gain will be limited by local plant swing modes. This limitation
is not now known. From examining the SWED study, it appears that a gain of 1.5 per unit was
used. If that was the case, a transfer increase of about 150 MW would be obtained as stated in
the SWED study.
EXISTING REGULATOR MODEL AND RESULTS
A block diagram of the existing Aswan High Dam regulators is shown on figure 21 [4]. The inputs
from derivatives of line current, terminal voltage, and field current make this an extremely difficult
regulator to understand and align. The analog model used is shown on figure 22. Terminal voltage
and current were obtained by using vector modules remote from the analog computer. Direct-and quadrature-axis voltages and currents were input to the vector modules, and the terminal
quantities were output.
An off-line alignment of this regulator was done by using the derivative of voltage. This adjustment
provided a sort of transient gain reduction. Figure 23 shows the off-line time-domain response of
this regulator for various values of Kv'. Figure 24 shows the on-line no-load time-domain responses
of this regulator with various line impedances.
The on-line alignment of the current feedback elements was made by loading the unit into the
machine, infinite-bus, midpoint load system and adjusting the parameters until a damping im-
provement was seen. Table 5 shows the power transfer limits for various regulator parameters.
Actual parameters in use on the regulators would be helpful to this part of the study.
The frequency-response technique presented earlier was also used with the existing regulator.
Figure 25 shows that for low values of line impedance (approximately 25%) to the infinite bus,
the High Dam regulators would be unstable at frequencies above 1.0 Hz. There appears to be a
significant increase in damping at frequencies below 1 Hz for all values of impedance. This is an
interesting phenomenon, which should be investigated further.
8
BIBLIOGRAPHY
[1] "Study on the Improvement of the Reliability of the 500-kV Transmission System from the
High Dam to the Cairo Region and the Possibilities to Increase the Firm Transmission Capacity,"
SWED POWER Phase IIFinal Report, March 1981.
[2] PTI Course Notes, "Power System Dynamics: Volume 1," Power Technologies, Inc., Sche-
nectady, New York, 1978.
[3] "Excitation System Models for Power System Stability Studies," IEEE Committee Report, IEEE
Transactions on Power Apparatus and Systems, Vol. PAS-100, No.2, February 1981.
[4] "Main Generator Automatic Voltage Regulator Type APFrr-TC," V. I. Lenin All-Union Elec-
trotechnicallnstitute, Moscow, U.S.S.R.
9
Table 1. - Aswan High Dam synchronous machine parameters.
SWED Brown Boveri Model Data Used
Xv 1.1025 1.0 1.1025
Xa 0.6615 0.66 0.6615
X'v 0.3638 0.33 0.3638
X"o 0.2392 0.22 0.2392
X"a N/A 0.33 0.24
XL 0.1690 N/A 0.169
Too 8.5 2.8 8.5
T" 0.06 0.15 0.0600
T" 0.1 N/A 0.100
MV. ABase 171.7 each 206 each 171 .7 each
SG1.0 0.0857 N/A 0.0857
SG1.2 0.2432 N/A 0.2432
10
Table 2. - Saturation curve function generator values.
GENERATOR SATURATION - ASWAN HIGH DAK
SG=B*<Et-A)*<Et-A)/EtA= .763415467333 B= 1.53111610898SG1.0= .0857 SG1.2= .2432
Et <PU)0.05.1.15.2.25.3.35.4.45.5.55.6.65.7.75.8.85.9.9511. 051.11.151.21.251.31. 351.41.451.51. 551.61.651.71. 751.81.851.91. 952
5"T rUNC 5g (PU)00000000000000002.56161089769E-31.35042302602E-23.17372036323E-25. 61094224863E-2B.56999999997E-2.119763456364.157689853555.198975329723.2432.29001116109.339110371745.39024340423B.443192349084.497769353281.553811610B97.611177323212.669742416344.729397855685.7900474342.851605939977.913997629067.9771549460651.041017446671.105530885981.1706464436
Sg*Efd (PU)00000000000000002.04928871815E-31.14785957212E-2.028563483269.053303951362B.56999999998E-2.125751629182.173458838911.228821629182.29184.362513951363.440843483268.526828595723.620469288718.721765562258.830717416345.947324B509781.071587866151.203506461881.343080638141.490310394961.645195732321.807736650221.977933148672.155785227662.3412928872
<1+5g)*Et (PI0.05.1.15.2.25.3.35.4.45.5.55.6.65.7.75.80204928872.86147859572.9285634832681.003303951371. 0BS71.175751629181.273458838921.378821629181.491841.612513951361.740843483281.876828595732.020469288712.171765562262.330717416352.497324850982.671587866152.85350646193.043080638153.240310394983.445195732333.657736650233.877933148684.105785227654.3412928872
11
Table 3. - Summary of synchronizing and damping power coefficients.
P - EBus Efd j Ws Sp
Sp = Pmax cas 8 w = 2H Ws (50 Hz) = 314.16max-X Xn
q + Line
Heq (Aswan High Dam with system effects) = 3.31nH 4H
Ks = K =-15 Tosc
0td
Data Records Actual
XLine XLine+ Xq Efd ""Pmax 8 @ 1.0 pu load Sp Wn fn Ks Ko fn Ko
0.25 0.91 1.55 1.70 46.1° 1.18 7.5 1.19 0.94 6.3 1.36 6.62
.30 .96 1.58 1.65 48.7" 1.09 7.2 1.14 .90 5.9 1.30 5.50
.35 1.01 1.61 1.59 51.3° 0.996 6.9 1.09 .86 4.4 1.24 4.42
.... .40 1.06 1.64 1.55 53.9° .913 6.6 1.05 .83 3.7 1.20 3.74N
.45 1.11 1.67 1.50 56.7" .824 6.3 0.995 .79 2.9 1.14 2.87
.50 1.16 1.70 1.47 59.5° .745 5.9 .95 .76 2.2 1.095 2.20
.60 1.26 1.77 1.41 65.6° .582 5.3 .84 .68 1.2 0.98 1.04
.70 1.36 1.86 1.36 72.2° .418 4.5 .71 .60 0.08 .86 0.09
H XLine+Xq Efd ""Pmax 8 Pe Sp Wn fn Ks Ko fn Ko
3.31 1.36 1.86 1.36 72.2° @ 1.0 0.418 4.5 0.71 0.60 0.08 0.86 0.09
4.0 1.36 1.85 1.36 71.9° @ 0.996 .42 4.07 .65 0.65 0 .78 0
5.0 1.36 1.82 1.34 70.7" @ .98 .44 3.73 .59 0.75 0 .71 0
6.0 1.36 1.80 1.32 69.6° @ .96 .46 3.48 .55 0.83 0 .66 0
7.0 1.36 1.79 1.32 68.9° @ .95 .47 3.26 .52 0.89 0 .61 0
8.0 1.36 1.78 1.31 68.6° @ 0.95 .48 3.06 .49 0.96 0 .57 0
Table4. - Resultsof study with IEEE type AC4 regulator.
(a) One line out of service
PSS Gain HD-NH NH-Cairo NH Load
10.0 1747 MW 1178 MW 569 MW
5.0 1683 MW 1079 MW 604 MW
2.0 1524 MW 873 MW 651 MW
1.0 1442 MW 775 MW 667 MW
0.0 1350 MW 660 MW 690 MW
(b) Both lines in service
PSSGain HD-NH NH-Cairo NH Load
10.0 >2200 MW >1600 MW 600 MW
5.0 2125 MW 1503 MW 622 MW
2.0 1920 MW 1261 MW 661 MW
1.0 1788 MW 1108 MW 680 MW
0.0 1700 MW 1025 MW 675 MW
13
Table 5. - Results of study with existing regulator.
Conditions
No current FB
K!Jv = 25
Kv' = 10
(a) One line out of service
HD-NH NH-Cairo NH Load
1154 MW 453 MW 700 MW
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Kit = 0.25 pu
Krt = 5.0 pu
Krt = 0.0 pu
1298 MW 618 MW 680 MW
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Kit = 0.25 pu
Krt = 5.0 pu
Krt = -2.5 pu
1732 MW 1151 MW 581 MW
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ; - - - - - - - - - - - - - - - - - - - - - - -
K't = 0.25 puKrt = 5.0 pu
Krt = -1.0 pu
1655 MW 1046 MW 609 MW
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Conditions
No current FB
(b) Both lines in service
HD-NH NH-Cairo NH Load
K!JV = 25
Kv' = 10
1400 MW 713 MW 690 MW
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Kit = 0.25 pu
Krt = 5.0 pu
Krt = 0.0 pu
1755 MW 1079 MW 676 MW
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Kit = 0.25 pu
K/'t = 5.0 pu
K"t = -2.5 pu
2190 MW 1580 MW 610 MW
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Kit = 0.25 pu
Krt = 5.0 pu
Krt = -1.0 pu
2108 MW 1482 MW 626 MW
14
~
01
+Efd
-10 0 +10
(2V/pu) 17V'I,+s.,)lN
(2VIpulP22
-2(Xd-Xd)
5
+Efd (2V/plI)+
P30
+ (X~-XL)Xd-XL
022
02710
~-1.
O-Axis Subtranslent Model(PTI)
5V/pu
E'.
+1.
Figure 1. - Two-axis synchronous machine model.
X'qP3.
-( Xq-X'q)
Q- Axis Subtronslent Mode I(PTI)
x".
+1.
/ ..--'~...--'
/ ~~~./
/ /v
/./
i v '/
)/
/ B(Et -AlsG=
Et
1/ A= .7634/5467333 SGI.O= .08578=/.53/116/0898 SGI.2= .2432
/
~ 1.5
CJ)
~0>l-=>a-l-=>0 1.0a::0I-«a::wzwc:>-w
2.0GENERATOR SATURATION -ASWAN HIGH DAM
.5
0.00.0 2.01.5 2.5 3.0 3.5 4.0.5 1.0
GENERATOR FIELD CURRENT (PU)
Figure 2. - Open-circuit saturation curve.
16
Analog Trunks anrl Variables
+ Vd 401 from A 32
- V 402 from A 26q
- Id 403 from AI03
- I 404 from A1l3q
Vt from Vector Module
It 3 from Vector Module
+ P from A45 (5 V/pu)e
+ AN A34 (50 V/pu)
- 6 A31i lAo/V
Ea P60 5 V/pu
- Xl Plil 10 V/pu
Integrators
I 0 I' ckt. E + 0t
I 4 Efd 2V/pu E + 1
110 dV/dt ckt. E + 0
114 rate Fa ckt. E + 0
116 IN ckt. E + 0t
120 E' 5 V/pu E + 0q
124 EN 5 V/pu E + 2q
130 EN 5 V/pu E + 2d
134 +AN 50 V/pu E + 1
131i -6 ISo/V E + 2
Coefficients
C 0 KI (AVR)
C 1 K' (AVR)I
Coeffi cients - Continued
(X' - X" )C27 -(X: - X~)2C 2 KN (AVR)
I
C 3 -KE (AVR) Xd - Xlfd C30
~C4 -Kf (AVR)
(AVR) C31 XNC 5 +11l00/T f
d
C 6 -K' (AVR) C32 I.C. of Ed [Vd]y
C 7 Manual (AVR)C33 -1
Fxci tat ion 100 Tooqo
ClD -Ref. (AVR)C34 - (Xq - X~)
Cll -I.C. of Efd (AVR)
C35 X"C12 +I.C. of Efd (AVR)
q
(AVR) C31i -I Swing Eq.C13 +I.C. of Vt I mC14 - 1110 TA (AVR)
Int.C37 + Scale (0.2) Swing Eq.
C40 -9.A5 V Into Reset Ckt.resetCIS Subst i tute 6 (Open loop testing) C41 +9.85 V Int. Reset CH.
Cl6 -Pload (Swing Eq.) C44 +q.9 V Into Reset CH.cH.
01100 (Swing Eq.)C45
C17
C20 -I.C. of E' (O-Axis) [-VtJC50 Step Input
qC51
C71 5(O-Axis) C54
~C55
C27-2 (Xd - Xd) CliO +ER (5 V/pu)
5
C23 X' - XlClil -XL
(10 V/pu)d
C24 +I.C. of E~ (O-Axis) [Vtj Cli4
C65 Vt correction - 0.003pu
C25 -I100 Trio C70
- Cd- Xd)
C7l
C21i C74 Pu correction~C75 Pu correction
Figure 3. - Tieline and infinite-bus model.
17
IdVd +Iq Vq= +P.
FRAINPUT
POLE-SLIPPING~ 75HARDWARE PI5
\ I Substitute b
IC= 0 -I) for open-loop
E+2 lBO/VOLTt t 'PI37 es In9
3,IB3V/pu+SCALE A36
0,2150Hz)
-~ 5V/pur- - --zI +VI (A32)~
5V/pu
I
i
I-=-~ 5V/pu
I I -vI I (A26)~ 5V/pu
IILt- --~ 5V/pu OFFLINE
IIIL_-~
5V/pu OFFLINE
!
+6N
314*3,IB3V/pu100 *50V /pu(50Hz)
Vq
EBq = EBCOS b5V /pu
- EBd= - EBSIN J
5V/ pu
Machine
Vt x
....I
....
Vt= jIX + [BUS
[BUS
Figure 4. - Tieline single-line diagram and equation.
18
InfiniteBus
A51
+ESq (5V/ pu) AI03C74
(A23)Vtq - ESq + ILd Xs DIV - 21 td S51
-Itd-r
N
(5V/pu) (5V/pu)
-Vtq (5V/pu) 0.5 1-(A26) 10V/pu D
P61
-ILd Xs
(5V/pu) XS+XL AI26
2+ISd
-r+ ILd
+IOV
Figure 5. - Analog computer diagram for midpoint load.
19
Vt Emid EBUSXB
.... ....It IB
HIOAM5 NAHAM 5 SAMAL 5 CAIRO 5
H.D.828MW 70.53 -'L 815 486 ) 101.2O..JL. 479 424 ) 61.98..JL 420
1700 GEN 828 MW ) 70.53...IL 815 517)62.50..JL. )38.40...JI... )25.08..JL.ASWAN 451 202 200 3300 GEN493 GEN
ASSlU5 AYAT5
+IL
Figure 6. - Single-line diagram of the tieline with midpoint load.
11985I
TOTAL SYSTEM GENERATION = 5985 MW
Figure 7. - 50o-kV power system.
20
AVAT CAIRO-6.50 -7.70
424 MW--390 202
---- ---200
---
27.50HD
22.20
1700 MW 1655MW--- ----
(41 MW
0.7075 One out0.4135 One in
.1700 MW
HD --- NH
NH9.240
700MWt
AST+2.00
SAM-1.80
486 MW---
517MW-- 453MW----
(627MW~
58MW
0.67pu
..7000
(117MW
0.4135pu Both lines in
0.7075 pu One line ou t
NH -- CAIRO 0.67 pu
Load at NH - ::::::; 700 MW -- O.34pu
Power to Cairo -- ::::::;1000MW- 0.485pu
Total Generation 1700MW 0.825pu
Figure 8. - Model of modified 500-kV power system.
21
!
14MW
Vtref
K1+ TE5
1+ TA5
1+ Te5
2V /pu EfdGEN
K = 31 TE = 0.05 second
TB=13.0 second TA = 0.254 TB = 3.3 second
+ 30 dB.0122Hz
I
. .0482 HzTransientGain Re~ ~
+ 20dB
+IOdB.001 Hz .01Hz .1 Hz I Hz
Figure9. - IEEE Type AC4 regulator model.
- 2.17
(2V/pu) +2.17
TO ~A21
87 A Efd
~ ~t
+IOV
L50
tBLI P 2
(.254) A.217
PI03
1+ A Tlag
1+ TloO
T109= 13.0 second
A = O. 254
Figure 10. - IEEEType AC4 regulator analog computer diagram.
22
Figure 11. - Off-line time-domain responses with IEEE Type AC4 regulator (sheet 1 of 4).
23
""
Figure 11. - Off-line time-domain responses with IEEE Type AC4 regulator (sheet 2 of 4).
24
Figure 11. - Off-linetime-domain responses with IEEE Type AC4 regulator (sheet 3 of 4).
25
Figure 11. - Off-line time-domain responses with IEEE Type AC4 regulator (sheet 4 of 4).
26
0 . .Phase Log (.)
100
200
0
Gain (dB)
-10
-20
0.01
Lead @ 0.2 Hz/.26 rod /second
V 0.8 second
. .. . .
0.1 FREQUENCY {Hz}
Log @ 2Hz/2.6 rod/second0.08 second
Type AC4 Exc. System
KA =3/Tc = 3.3 second
Ts =/3.0 second
I1.0
110.
Figure 12. - Off-line frequency response with IEEE Type AC4 regulator.
27
. r
,~
" +:~
;1
. , " 1: 1"
Cleveland. Ohio Printed in U.SA
Figure 13. - On.line time-domain responses with IEEE Type AC4 regulator (sheet 1 of 5),
28
n
-I-~
'~ ~~ tit,
hi ;i"
Figure 13. - On-line time-domain responses with IEEE Type AC4 regulator (sheet 2 of 5).
29
. . tt T-E tf~~.
+;'
+.
Cleveland. Ohio Printed in U.S.A.
Figure 13. - On-line time-domain responses with IEEE Type AC4 regulator (sheet 3 of 5).
30
+r.
Figure 13. - On-line time-domain responses with IEEE Type AC4 regulator (sheet 4 of 5).
31
Figure 13. - On-line time-domain responses with IEEE Type AC4 regulator (sheet 5 of 5).
32
Figure 14. - System performance for various values of line impedance and damping (sheet 1 of 8).
33
Figure 14. - System performance for various values of line impedance and damping (sheet 2 of 8).
34
Figure 14. - System performance for various values of line impedance and damping (sheet 3 of 8).
35
ACCUCHART Gould IIIc.. Cleveland, Ohio
Figure 14. - System performance for various values of line impedance and damping (sheet 4 of 8).
36
Figure 14. - System performance for various values of line impedance and damping (sheet 5 of 8).
37
Figure 14. - System performance for various values of line impedance and damping (sheet 6 of 8).
38
".
Figure 14. - System performance for various values of line impedance and damping (sheet 7 of 8).
39
Figure 14. - System performance for various values of line impedance and damping (sheet8 of8).
40
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Figure 15, - Bode plots of the machine transfer function (sheet 2 of 3).
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'.. '1<)
'1- - ~..~..I
~" -... ..
1'.. =1==m. -+
~. ~-+- .E'J"
,I
~'t-,-,~'.~ cI. ~~_. -+=:.
+- ~+-1 -1--- +-~S ~...,... .. . ..
+- L...- ." ft --- -, -1::t4.-.. -~-+-+- 1/. '~L----i.--+-+- +-+t4
..d-- ~-; ,~ t-~ .. ~~.~ ~.-r-- :-
'=Ie
.: .." =+j-ff Hi ~' .
L f= 4- ~'"
., -'-+-I
-+ ;c~+ -'-+-+- ++-' H~+-
--+-' ~L~,~
~--+- + ~,L-+-
.. - -+- '4-+ T":::: t:f- rif -t-
1-. ~-~.. .~ .. ..
2r 4- H--
...J+-
~+
.j- r-+I .H+ +- r-TT--- .t-
I H-!- h- ", {L
t- ttL;.,.. -. H
I. I)J' J ' I
i I r- I Vi I ' i -I , I , I,)1
11
I
I
0'"~ .- .......
41 ~ ~V>~ ~0..<:0<>
0\S
'"<:.JIt,
'"+
0 0"21'"'_CO~~
\n+
43
M-0MQjQ)~!!2.c0.;::uc::J-...Q)-<J)c~Q)cEucoEQ)£-0<J)0a.Q)
"0aJI
LIi
~::JOJu::
+q
E I (unsat)
Both Lines In ServiceMax Power
IEEE Type AC4 Regulator
1.0
0.5
0.5
Figure 16. - Phasor diagram with both lines in service.
44
EBUS
1.0
+d
+q
[I (unsat)One Line Out
Max PowerIEEE Type AC4 Regulator
1.0
0.5
0.5
[BUS
Figure 17. - Phasor diagram with only one line in service.
1.0
45
+d
Figure 18. - System performance at full capacity with both lines in service.
46
~
'.. I j
i I
it
t;:,-.i--1-~
'r ",
+..;... ~
II t :-. t
t .~t-
It,
r'
Figure 19. - System performance at full capacity with only one line in service.
47
+~N(A34) ( 50V / pu) -I
100TIog
E+2
AI24 -I100TIog
Tleod = ATlog
Tlog = 0.08 second - Pot = -0.125
Tleod= 0.8 second = IOTl09 - Pot = 1.0
A10
PI06
Figure 20. - Analog computer diagram of PSS function.
48
~10
PI07
AI25
TOAIOI50V/pu
- Forincrease in
Vt
P.T.500 KV
C.T.500 KV
Ifd
Efd
AuxIn put
Joint Control-Plant Central V.R.
Rf:;ference
7.2
Kv'S
2.7
K'SIR
KFDBKtS
KFDBKd
Regulator Output(to Exciter)
Figure 21. - Block diagram of existing regulator.
49
V TIt
+:>.OOV
Gain this stage = 25
+IOV
tJ.V Gain 25pu
5V /pu
50V / pu
- Ref.
KV' tI
-KVt
KEfd
,-KEfd
+IOV
2551+.0255
Ki:fd
-5.0VKIt
KI't2551+.0255
2.5pu Max gain2.552
(I +.0255)( 1+.055)
T3
+ It
(5V/pu)
5
1 +.0255
5
1+.055
-2.17V
Ipu max gain
P3
-KEfd
1051+.015
AI2AI5
III
+ t
Figure 22. - Analog computer diagram of existing regulator.
50
+2.047V
Efd
2V/pu
87A~A21
B~
\+IOV
L50t
81i p 2
't I::'::1:::
~~..
T-.-
1ft:,,
..
.
:::1+1 j
,!;
I+ '+
"'4 H+'
n
r:
Q
+
..
tiE .;~:
f:tt.I.g!
H~
A~CUCHART,
:1-:+-+-.
!,:
..
+',
...
.,.
'i !kU~ni:!lt
c:>"'~... p'"...
. ,
H-' +'-. !tt 11-:~:+\:tt1 ...J..,
.. -t,.. i+t+ 1: .
h' ... '~4 ill #1 ii: 1: ~H
.-tl~. .,. '.r t
ni1-i-
-d
h m m 1'1 ,~1 iil: :+1..
t: II!
H +:..iF n:
.".
1f1
,. ,.H
-d---,- ttl +1m
+
.
f',-t-, I.j...j+1- It +j
+-.,
I"l'
ff!
11:t~-1-
+
"II; t;
...
,.,F
""II,
lH~:
;" i 1 Ii; !...~
l+t ~H: + : ~i~ Uiij:rhl ~ili!i~
~: Eft: ! 1 -rS-
.. ..
"
.---P.c
.i:'p- . -il.
,
~.+.
"" t~' ~jj tff Li;
t-li :tt ;:i ~11
~~l+;:
.,
fUP;:-H-i-..
11-1 ! ttnm~l~
+~ :If :-: tft +"-+
":T
..
ire --:~ 4f1
ih
E~." ..
E,..
~+Ir,;
h~ tti ~~~fit ffPt
Ii;
. Gould I~. Cleveland,Ohio,\
I
H'..'
... ."'T
,,-
"". ....
'"
:;;
" ;::: .., ,.
"..
,
::1...
,.+
, ~.
I"+;-
tt~; m
TiT 11'
1+
H
.+..'..,.
!!':..
"
,. ~
..
.
;:~t I.
..
."
i.
,
H~t-t
1++ t,.-" +
"
11':
I + -H+. t+t: n~ f... J+
.~; ::~t
.
.
.
~'§IE
~: ~mE
. .-,-,-.
~il '"1'1
:E m
Figure 23. - Off-line time-domain responses of the existing regulator (sheet 2 of 2).
52
III . "".""""1''''1''''1"'1'11'''1''..1""j."'t" ''."&.""."".""""11'1""1""1'."11"'1""1:1""1"" "'"
I I
Figure 24. - On-line time-domain responses of the existing regulator (sheet 1 of 2).
53
1..'.'."11"1.1..1111.1""'1"..'" 1"1."'"1'.1'."111"'"T "'"
'.1'
xl, Ohio Printed in U.S
Figure 24. - On-line time-domain responses of the existing regulator (sheet 2 of 2).
54
, Ii
Q t> "",,,, .q
<: ~'"... C ~0
~f~~C)
<t..J
55
'"::IJ:IQ)...'c~,SQ)
J::...
()
2'"Q)uc:t1:I.0Q)
c.,~Q)
:E
'"::I.gt1:I>0-c:0
'+:'iii0c.
()
0e2....Q)
::0c.Q)c:
Eut1:IE'0
Q)
'"c:0C.
'"~Q)
~c:t1:IQ)
'"t1:IJ::a...I
Lt)('oj
~::IC)i.i:
APPENDIX A
NETWORK REDUCTION OF THE 500-kV SYSTEM
597 MW 625MW 90MW 115MW 600MWGEN LOAD GEN LOAD GEN
Xd =.27 90MW X'd=.23LOAD 185 LOA D
X'd = .26 785180
Uni t Xfmr .097 on 600 MVA500/130Xfmr.095 on 600MVA
X'd .27 on 600 MVANeglect lines
total .462 on 600 MVA1.59 on 2060 MVA
(a) Step 1
HD NH SAM CAIRO
H.D..294 .83 .51
OR.1195 .588 AST AYAT
.52 .31 .45 .21
Appendix A
Network Reduction of the 500-kV System
HD500
NH500
1700----
.83 486
AST.52 500 .31
H.D. ---
--2060MW
GEN~
41 MW
1.59 5.221.77
SAM500
.51
AYAT.45 .21
CAIRO
620 LOAD--4114GENX'd = 22.5
10 1.44 .25
1.59 1.77 5.22
(b) Step 2
/0 1.44
Figure A 1. - Successive steps in reduction of equivalent circuits.
59
.25
H.D. HD500
1.59
.1195
1.59
.1195
.588OR
.294
.294or
.588
Appendix A
.83 .51
.25
Ie) Step 3
.83 .51.294
OR.588 .86 .476 .73
1.77 .25
Id) Step 4
.554
Weak System --- 0.784(2637 MW)Pmox = I.28py
Strong System 0.673 Pmox = 1.49py
(3061 MW)
Figure A 1. - Successive steps in reduction of equivalent circuits - Continued.
Ie) Step 5
60
APPENDIX B
ADDITIONAL ANALOG DIAGRAMS
Bd -EBdI Bd A6/
MUL2 PBUS
2.5 Vlpu2 -X
+IBd -
+[ BqAI33 A/31
EBqI Bq -EBqIBq
+IBq MUL -X -2.5vlpu
A33
A/26
A/27
Appendix B
Additional Analoq Diagrams
P = EBd I Bd + VBq I Bq
-E AI23
A23
Figure B1. - Analog computer diagram of power to the infinite bus.
63
INTOUTPUT +T<Y.oV
-IOV
+ 9.858
L34
-=
Appendix B
LlO
sFF
R
LII
S FFR
Ll3
TO INT HD
LI4
545
L52
L22
Figure 82. - Analog computer diagram to enable pole-slipping.
64
HIGH-- RUN MODELOW --I.C. MODE
L51
FF S
RBLI P 3
IC
To 541 ControlHIGH-IC=+9.9VLOW-IC=-9.9V
APPENDIX C
LISTING OF ANALOG COMPUTER CONSTANTS
HHlCllEOlCOOO = +0.1019lCOOl = +0.2019lC002 = +0.0018lCOO:3 = -0.0000lC004 = -0.0001lC005 = +0.9994lC006 = -0.4006lC007 = +0.2171lC010 = -0.5228lC011 = -0.2166lC012 = +0.0000lC01:3 = +0.4'399lC(114 = -0.5001lC015 = +0. :3::::01
lC016 = +0.0094lC017 = -0.0009lC020 = -0.5000lC021 = +0.29:36lC022 = -0.2954lC02:3 = +0.1948lC024 = +0.4998lC025 = -0.1666lC026 = -0.6:394lC027 = +0.:3279lCO:30 = +0.:3604
lCO::::l= +0.2:390
lCO:32 = +0.0000lCO.3:3= -0.1000lCO:34 = -0.4212lCO:35 = +0.2400lC036 = -0.12851CO:37 = +0.20001C040 = -0.9850lC041 = +0.98501C044 = +0.9900lC045 = +0.0000lC050 = -0.01001C051 = +0.0000lC054 = +0.0000lC055 = +0.00001 C 06 0 = + O. 5 00 0
lC061 = -0.6888lC064 = +0.00001C065 = +0.00:301C070 = -0.0000lC071 = +0.0000
Appendix C
Listinq of Analog Computer Constants
lC074 = +0.5000lC075 = +0.5000lC100 = +0.:3100lC10l = -0.0769lC102 = -0.0769lC10:3 = +0.2540lC104 = -0.1251lC105 = -0.1251lC106 = +0.9'3991CI07 = +0.0000lC110 = -0.5175lCll1 = -0.2168lC112 = +0.2169lCl1:3 = +0.2170lCl14 = -0.2000lC115 = +0.0000lC116 = +0.0000lC117 = +0.0000lC120 = +0.0000lC121 = +0.0000lC122 = +0.0000lC12:3 = +0.0000lC124 = +0.0000lC125 = +0.0000lC126 = +0.0000lC127 = +0.0000lC130 = +0.0000lCl:31 = +0.0000lCl:32 = -0.7074lCl:3:3= -0.7075lC134 = -0.6700lCl:35 = -0.6700lCl:36 = -0.0000lC1:37 = +0.0000lRVOO=OOOOOlRuOl=onooo IFOO:
. .- - 1B=41
lRV02=00000 1\101=-0.8682lRV04=OOOOO 1\102=-0.8212
.............................................
.............................................
. .
. ASWAN HIGH DAM .
. .
. bEN INF BUS TIELINE MIDPT LOAD.
. .
. MAY/JUNE 1984 .
. .
. JCA .
. .
.............................................
....................................Figure C1. - Analog computer constants.
lRV05=00OOOlRY06=:32624lRV10=000001RVll=:30672lRV12=:32760lRTO=00500lRT1=05000IF.:T2=00000
11OOO=E+011004=E+111010=E+011014=E+011016=E+01 I 020=E+0
11024=E+211030=E+2l1034=E+l11036=E+21 I 040=E+0
l1044=E+0l1050=E+0l1054=E+01 I 060=E+0
11064=E+011070=E+011074=E+011I00=E+0l1104=E+211II0=E+0l1114=E+01 I 120=E+2
l1124=E+21 I 13 O=E + 0
1 I 1::::4=E+0
1V0:3=- o. 77561\/04=-0.7:3151\/05=-0.68901\106=-0.64811\/07=-0.60861\/08=-0.57071\109=-0.53431\/10=-0.49951\/11=-0.46611\112=-0.43441\113=-0.40411'",'14=- O. 37541\115=-0.34821\116=-0.32251\/17=-0.29841\/18=-0.27581\119=-0.25471\120=-0.23521\121=-0.2171IV22=-0.20071\/23=-0.18571\/24=-0.17231\125=-0.16041\/26=-0.15001\127=-0.14001\128=-0.13001\129=-0.12001\/30=-0.11001\131=-0.10001'1132=-0.09001'1133=-0.08001'1134=-0.07001\135=-0.06001\136=-0.05001'1137=-0.04001\138=-0.03001"/39=-0.02001\140=-0.01001\141=+0.0000IS;lin
67 GPO 849-172
Minion of the Bureau of Reclamation
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The Bureau's original purpose "to provide for the reclamation of arid and semiarid lands in the West" today covers a wide range of interre- lated functions These include providing municipal and industrial water supplies; hydroelectric power generation; irrigation water for agri- culture/ water quality improvement; flood control; river navigation; river regulation and control; fish and wildlife enhancement; outdoor recreation; and research on water-related design, construction, mate- rials, atmowheric management, and wind and solar power.
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