SYNCHRONOUS GENERATOR PARAMETER
IDENTIFICATION FROM MEASUREMENT
DATA
A dissertation submitted to The University of Manchester for the degree of
Master of Science in Electrical Power Systems Engineering in the faculty of
Engineering and Physical Sciences
2010
Ali H. Almarhoon
School of Electrical and Electronic Engineering
LIST OF CONTENTS
List of contents...........................................................................................................................1
List of figures.............................................................................................................................4
List of tables...............................................................................................................................5
List of abbreviations...................................................................................................................6
Abstract....................................................................................................................................10
Declaration...............................................................................................................................11
Intellectual Property Statement................................................................................................12
Acknowledgments....................................................................................................................13
Chapter 1
Introduction and organisation of dissertation...............................................14
1.1 Background and motivation .......................................................................14
1.2 Aims and objectives the project..................................................................15
1.3 Literature review.........................................................................................16
1.3.1 Introduction........... ............................................................................16
1.3.2 On-line Tests......................................................................................16
1.3.2.1 Standstill Frequency Response (SSFR)......................................16
1.3.2.2 Sudden Three Phase Short Circuit Test......................................19
1.3.2.3 Numerical Impulse Method.........................................................27
1.3.3 Parameters Derivation of Power Plant Equipment.............................27
1.3.4 Summary of the Literature Review....................................................29
1.4 Dissertation organisation...….......................................................................31
Chapter 2
Modelling and simulation of synchronous machine.....................................32
2.1 Introduction................................................................................................32
2.2 Synchronous machine representation...........................................................32
2.3 Tow axes models of synchronous machines...............................................33
2.4 Per-unit notation.........................................................................................34
2.5 Park's transformation..................................................................................35
2.6 Simulation of synchronous machine...........................................................37
2.6.1 Simulation in rotor reference frame.....................................................37
2.7 Experimental data during disturbance........................................................40
2.8 Simulated data during a 3-phase short circuit test......................................41
2.9 Adding and filtering the noise.....................................................................41
2.10 Conclusion..................................................................................................43
Synchronous Generator Parameter Identification from Measurement Data
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Chapter 3
Procedures of parameters estimation in MATLAB/SIMULINK................44
3.1 Introduction.................................................................................................44
3.2 Parameter estimation procedures................................................................44
3.2.1 Creating an estimation project...........................................................44
3.2.2 Importing data into GUI....................................................................45
3.2.3 Parameter estimation.........................................................................47
3.2.3.1 Creating an estimation task........................................................47
3.2.3.2 Specifying data for parameter estimation.................................48
3.2.3.3 Specifying parameters for estimation........................................48
3.2.3.4 Starting the estimation...............................................................50
3.2.3.4.1 Specifying and selecting the solver type..............................50
3.2.3.4.2 Specifying and selecting the optimization method.............51
3.2.3.4.2.1 Cost function specification...........................................51
3.2.3.4.2.2 Optimization method specification..............................52
3.3 Parameter Estimation Flowchart.....................................................................54
3.4 Conclusion.......................................................................................................55
Chapter 4
Parameters estimation results.........................................................................56
4.1 Manufacturer data.......................................................................................56
4.2 Calculation of standard machine parameters..............................................57
4.3 Estimation of Parameters for Different Cases............................................58
4.3.1 Case1...................................................................................................58
4.3.1.1 Estimated parameters without including the effect of noise.........58
4.3.1.2 Estimated parameters with including the effect of noise..............59
4.3.2 Case2...................................................................................................59
4.3.2.1 Estimated parameters without including the effect of noise.........59
4.3.3 Case 3..................................................................................................60
4.3.3.1 Estimated parameters without including the effect of noise.........60
4.3.4 Case 4..................................................................................................61
4.3.4.1 Estimated parameters without including the effect of noise.........61
4.3.5 Case 5..................................................................................................62
4.3.5.1 Estimated parameters without including the effect of noise.........62
4.4 Discussion of the Estimated Results.............................................................62
4.5 Conclusion....................................................................................................63
Synchronous Generator Parameter Identification from Measurement Data
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Chapter 5
Project Conclusion and Further Work...........................................................64
5.1 Project Conclusion.......................................................................................64
5.2 Further Work................................................................................................65
References................................................................................................................................66
Appendices...............................................................................................................................70
Appendix A. m-file for complete synchronous machine simulation………….…70
Appendix B. list of the simulated data…………………………………………...71
Appendix C. m-file for adding noise to simulated data……………………….…78
Words (Including footnotes and endnotes): 17,253.
Synchronous Generator Parameter Identification from Measurement Data
3
LIST OF FIGURES
Fig (1): (a) General d-axis circuit. (b) Simplified d-axis circuit………......................16
Fig (2): General q-axis equivalent circuit……………………………….....................17
Fig (3): (a) q-axis circuit (XqQ=Xq). (b) Simplified q-axis circuit (XqQ=XQ)……..17
Fig (4): Outputs of the actual system and the identified model………………….......18
Fig (5): Basic procedures………………………………………..…...........................20
Fig (6): Results of simulation for the 190MVA turbogenerator ………….................21
Fig (7): Results of simulation for the 32.6 MVA hydrogenerat…………………….21
Fig (8): Generator model 2.1 with one d-axis and one q-axis damper winding [22]...24
Fig (9): Generator model 2.2 with one d-axis and two q-axis damper winding
Adopted from [22]…………………………………………………………..25
Fig (10): Excitation system model [25]…….………………………………………...28
Fig (11): Schematic diagram of a synchronous generator [1]………………………..33
Fig (12): Generator model 2.1 with one d-axis and one q-axis damper winding [22].33
Fig (13): Generator model 2.2 with one d-axis and two q-axis damper winding
Adopted from [22]………………………………………………………….34
Fig (14): Block diagram of voltage park transformation.............................................36
Fig (15): Block diagram of current inverse park transformation.................................36
Fig (16): Complete simulink block diagram of synchronous generator.......................40
Fig (17): Experimental data acquisition from synchronous generator terminals [32].40
Fig (18): Filtering configuration adopted from [1]......................................................42
Fig (19): Block diagram of filtering noise....................................................................43
Fig (20): Block diagram of estimator model................................................................44
Fig (21): Control and estimation toolbox manager GUI..............................................45
Fig (22): Importing input data into the control and estimation toolbox manager........46
Fig (23): Importing output data into the control and estimation toolbox manager......46
Fig (24): The estimation task and settings...................................................................47
Fig (25): Selecting the parameters that need to be estimated......................................49
Fig (26): Selecting the parameters and setting up the initial guess.............................49
Fig (27): Different solvers available in optimization toolbox.....................................50
Fig (28): Different optimization methods available in optimization toolbox..............52
Fig (29): Estimated parameters in optimization toolbox.............................................53
Fig (30): Flowchart of parameters estimation processes [22].....................................54
Synchronous Generator Parameter Identification from Measurement Data
4
LIST OF TABLES
Table (1): Results for the hydrogenerator …………………………………………...22
Table (2): Results for turbogenerator (identification with two rotor circuits)……….22
Table (3): Results for turbogenerator (identification with three rotor circuits)…..….22
Table (4): Estimated parameters for single d-axis and q-axis damper winding….….26
Table (5): Estimated parameters for damper winding D, G and Q…………………..26
Table (6): Fitted excitation system parameters………………………………………29
Table (7): Derived base quantities……………………………………………………35
Table (8): Typical machine parameters from manufacturer data………………….…56
Table (9): Standard parameters from manufacturer stability study data sheet……….56
Table (10): Formulas of standard parameters………………………………………...57
Case 1
Table (11): Estimated parameters of synchronous machine without including noise..58
Table (12): Manufacturer standard parameters vs the estimated standard
Parameters……………………………………………………………….58
Table (13): Estimated parameters of synchronous machine with including noise…..59
Table (14): Manufacturer standard parameters vs the estimated standard
parameters……………………………………………………………….59
Case 2
Table (15): Estimated parameters of synchronous machine without including noise..60
Table (16): Manufacturer standard parameters vs the estimated standard
parameters……………………………………………………………….60
Case 3
Table (17): Estimated parameters of synchronous machine without including noise..60
Table (18): Manufacturer standard parameters vs the estimated standard
parameters……………………………………………………………….61
Case 4
Table (19): Estimated parameters of synchronous machine without including noise..61
Table (20): Manufacturer standard parameters vs the estimated standard
parameters……………………………………………………………….61
Case 5
Table (21): Estimated parameters of synchronous machine without including noise..62
Table (22): Manufacturer standard parameters vs the estimated standard parameters62
Synchronous Generator Parameter Identification from Measurement Data
5
LIST OF ABBREVIATIONS
Stator transformation to zero, direct and quadrature axis parameters
Stator per-phase quantities on conventional a-b-c axis
Damper winding on the direct axis of a synchronous generator
Direct Current
Digital Fault Recorder
Generator internal voltage, leading terminal voltage
Electrical Power Research Institute
Damper winding on the quadrature axis of a synchronous generator
Graphic User Interface
Instantaneous current
Stationary current, proportional to zero sequence current
Vector containing the 0dq currents
Current through stator phase a
Vector containing the abc currents
Current through stator phase b
Stator current base
Current through stator phase c
Current through direct axis
Current through damper winding D
Institute of Electrical and Electronics Engineers
Current through field winding
Current through damper winding G
Neutral Current
Independent Power Producers
Current through quadrature axis
Current through damper winding Q
Stator phase winding a self inductance
Direct axis magnetizing mutual inductance
Quadrature axis magnetizing mutual inductance
Stator inductance base
Stator phase winding b self inductance
Synchronous Generator Parameter Identification from Measurement Data
6
Stator phase winding c self inductance
Direct axis leakage inductance
Direct axis leakage inductance
Equivalent direct axis inductance
Field winding leakage inductance
Field winding to damper winding D mutual leakage inductance
Damper winding G leakage inductance
Equivalent neutral inductance
Damper winding Q leakage inductance
Equivalent quadrature axis inductance
MATrix LABoratory, Software package
Maximum Likelihood
Open Circuit Characteristic
Ordinary differential equation
Output Error Estimation
On-Load Frequency Response
Active power
Park's transformation matrix
Reactive power
Stator resistance phase a
Stator resistance phase b
Stator base resistance
Stator resistance phase c
Damper winding D equivalent resistance
Field winding equivalent resistance
Damper winding G equivalent resistance
Root mean square
Damper winding Q equivalent resistance
Stator and rotor MVA base
Supervisory Control and Data Acquisition
Standstill Frequency Response
Time
Synchronous Generator Parameter Identification from Measurement Data
7
Instantaneous voltage
Voltage phasor
Zero axis voltage, proportional to zero sequence voltage
Vector of 0dq voltages
Stator phase a voltage
Vector of abc voltages
Stator phase b voltage
Stator base voltage
Stator phase c voltage
Direct axis voltage
Damper winding D voltage
Damper winding Q voltage
Field winding voltage
Damper winding G voltage
Neutral voltage component
Quadrature axis voltage
Synchronous quadrature axis reactance
Vector of simulated output
Vector of experimental data
𝛿
Synchronous machine torque angle in electrical radian
Ψ
Instantaneous flux linkage
Flux linkage vector of odq components
Vector of stator flux linkage
Time derivative of flux linkage phase a
Time derivative of flux linkage phase b
Time derivative of flux linkage phase c
Time derivative of flux linkage of damper winding, D
Time derivative of flux linkage of field winding
Time derivative of flux linkage of damper winding, G
Time derivative of flux linkage of damper winding, Q
𝜔
Synchronous angular frequency in radians per second
𝜔
Base synchronous angular frequency in radians per second
Synchronous Generator Parameter Identification from Measurement Data
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𝜔
Rated synchronous angular frequency in radians per second
On-Load Frequency Response
Armature base ohm (impedance), Ω
d-axis synchronous, transient and subtransient reactances
Newly defined open field d-axis subtransient reactance
q-axis synchronous, subtransient reactances
2D
Short circuit d-axis transient and subtransient time constants, S
Open circuit d-axis transient and subtransient time constants, S
d-axis damper winding time constant, S
Open circuit q-axis subtransient time constant, S
Two dimension
Synchronous Generator Parameter Identification from Measurement Data
9
ABSTRACT
Synchronous machines have still been the most common machines used in
generation since 40 years before. For accurate analysis of a synchronous generator,
its parameters should be identified as precise as possible. These parameters can
generally be determined either by off-line or on-line techniques. On-line test is
preferred due to technical and economical reasons.
The main aim of this project is to develop a model that can be used to estimate the
synchronous generator parameters from on-line data. Non linear least square
method has been implemented for the estimation purpose.
This dissertation is started with literature survey to overview some of the previous
research papers discussing synchronous machine parameter identification. Then, the
developed model is simulated including the effect of noise. Both modeling and
simulation is performed by using MATLAB/SIMULINK package.
The simulation outcomes, in general, show a high accuracy of estimation compared
to the original parameters provided by the manufacture. However, further work
needs to be done in order to limit the significant deviation in estimated Rfd by
considering the effect of saturation. AVR and excitation system parameters can also
be estimated in a future work.
Synchronous Generator Parameter Identification from Measurement Data
10
DECLARATION
I, Ali Habib Almarhoon, confirm that no portion of the work referred to in the
dissertation has been submitted in support of an application for another degree or
qualification of this or any university or other institute of learning.
Synchronous Generator Parameter Identification from Measurement Data
11
INTELLECTUAL PROPERTY STATEMENT
Certain copyright is owned by the author of this dissertation (including any
appendices and schedules to this dissertation) and has given The University of
Manchester certain rights to use such copyright, including for administrative
purpose.
Copies of this dissertation, either in full or in extracts and whether in hard or
electronic copy, may be made only in accordance with the Copyright, Designs and
Patents Act 1988 (as amended) and regulations issued under it or in accordance
with instructions and licensing agreement given by the author and The University
of Manchester. This page must form part of any such copies made.
The ownership of any Intellectual Property and any reproductions of copyright
works in the dissertation such as graphs and tables which may be described in this
dissertation may not be owned by the author and may be owned by the third parties.
Such Intellectual Property and Reproductions must not be made available for use by
third parties without the prior written permission of the author or the university,
which all terms and conditions of such agreement will be prescribed.
Further information on the conditions under which disclosure, publication and
commercialisation of this dissertation, the copyright and Intellectual Property and
reproductions described in it may take place is available in the university IP policy
and it is also available in the School of Electrical and Electronic Engineering.
Synchronous Generator Parameter Identification from Measurement Data
12
ACKNOWLEDGEMENTS
I would like to express my gratitude and thanks to my project academic
supervisor, Professor J. V. Milanovic, who has advised, guided and supported me
throughout the project period. Many thanks for his reading and comments on this
dissertation.
Many thanks should be given to PhD students, Mr.Robin and Mr.Gustavo for their
help. Sincere thanks should be also given to Dr. Soon Yee from Siemens for his
help.
I also wish to thank my parents, wife and son for their encouragement and support
during the entire period of my study.
Moreover, my best friend, Zuhair Alnaser, is to be thanked for his help and support
throughout my academic life in the UK.
Finally, I owe special thanks to the government of Saudi Arabia for sponsoring me
during the entire period of my study.
Synchronous Generator Parameter Identification from Measurement Data
13
Chapter 1 Introduction and Organisation of Dissertation
Chapter 1: Introduction and Organisation of Dissertation
1.1 Background and Motivation
Electrical machines consist mainly of two parts: stationary part called a stator and
rotating part called a rotor. Depending on type of power fed and produced by the
machines, they are classified into direct current machines (DC machines) and
alternating current machines (AC machines). AC machines can be categorized into
two main types: synchronous machines and asynchronous machines (induction
machines). As they present an enormous impact on system stability study,
synchronous machines have still been the most common machines used in
generation since 40 years before.
The prime motivation of this project is the high need for accurate models of
synchronous generators and an effective utilization of techniques used to estimate
the parameters of synchronous generators. This is needed for the stability study
which is highly affected by the original parameters of the synchronous generator
given by the manufacture. However, the accuracy of these parameters depends on
the age of the machine. In other words, the parameters of synchronous generator are
not fixed throughout the useful life of the machine. They are varying due to change
of the physical characteristics of the machine as its age moves forward. Moreover,
saturation effect causes some parameters like the magnetizing inductances to vary
at different operating points. Furthermore, significant changes can happen in the
generator parameters after the generator is subjected to repair or replacement of
some components. For these reasons, the accuracy of synchronous generator
parameters has been in interest of many past and recent paper and researches.
This project is further motivated by the need of development and modifications of a
synchronous generator model designed by a previous work done in the electrical
engineering department at the University of Manchester in 2008. The developed
model has shown some leakage of accuracy in estimation the parameters of
synchronous machines and hence it is not accurate enough to be used in
synchronous generator dynamic and stability study. Therefore, it is required to
perform some modifications by considering the effect of noise and magnetic
saturation.
Synchronous Generator Parameter Identification from Measurement Data
14
Chapter 1 Introduction and Organisation of Dissertation
According to [1] many methods had been developed in the period between1969
and 1971 to estimate the parameters values of synchronous machines based on
models developed by Dandeno, Suchuzl and Dineley. A direct and quadrature axis
equivalent circuit for round rotor synchronous generators had been developed by
Jackson and Winchester. Simultaneously, Equivalent circuits for field and damper
windings had been developed by Canay. In 1971, Yu and Mosa reported a systemic
procedure applied to estimate the parameters of the synchronous generator [2].
The parameters of synchronous generators can be generally determined either by
off-line or on-line techniques. The off-line methods require interruption of service
during the test. Moreover, they are impractical and inaccurate since they are not
used under normal operating condition and the saturation effect cannot be
considered on these methods. Thus, they may not be preferred especially in case of
large synchronous generators used as base unit. This makes the on-line methods
more attractive from technical and economical point view.
1.2 Aims and Objectives of the Project
The main aims and objectives of this project can be outlined as follows:

To study and understand the behavior of the synchronous machine.

To implement a methodology for identification of machine parameters based on
continuous monitoring (without staged tests and disconnection of the machine
of the network) of machine output variables such as voltage, current, speed, etc.
This methodology has been modified in order to be accurately applied.

To develop a model using a least square algorithm from MATLAB
optimization toolbox.

To simulate the model in order to identify the synchronous generator
parameters and compare it with actual parameters.The modelling and
simulation will be completely done by using MATLAB/SIMULINK package.
Synchronous Generator Parameter Identification from Measurement Data
15
Chapter 1 Introduction and Organisation of Dissertation
1.3 Literature Review
1.3.1 Introduction
The aim of this review is to examine some recent and relevant literature for
synchronous generator parameter identification based on measurement data. The on
line different tests are described and compared with each other.
1.3.2 On line Tests
In general, the methods used to identify parameters of synchronous machines can
be classified as follows.
* Standstill frequency response (SSFR)
* Sudden Short circuit test.
* Numerical impulse method.
1.3.2.1 Standstill Frequency Response
Modelling and identification of the synchronous machine have been conventionally
used in IEEE standards 115, part II [3]. In 1971, a systematic procedure was
reported by [2] in order to find the synchronous machine parameters depending on
simple field test. The general d-axis equivalent circuit of a synchronous machine
shown in Fig (1a) was simplified as shown in Fig (1b). Moreover, the general qaxis equivalent circuit shown in Fig (2) was simplified as shown in Fig (3).
Fig (1): (a) General d-axis circuit [2].
(b) Simplified d-axis circuit [2].
Synchronous Generator Parameter Identification from Measurement Data
16
Chapter 1 Introduction and Organisation of Dissertation
Fig (2): General q-axis equivalent circuit [2].
Fig (3): (a) q-axis circuit (XqQ=Xq) [2].
(b) Simplified q-axis circuit
(XqQ=XQ) [2].
Mathematical equations were proposed in order to identify the parameters of the
simplified circuits based on field tests. The eight conventional d-axis parameters (
) can be determined from IEEE test code
described in IEEE standards [3]. Nevertheless, an extra test was suggested by [2] to
measure a newly defined parameter (
) by Dalton and Cameron’s method with
the field winding left open and a damper time constant (
) can be measured by
varying slip test or decaying current test [2]. At that time, this method was not
applied to large synchronous machine.
In 1981, two large turbo generators named as Nanticoke and Lambton generators
were used to test an identification technique developed by Dandeno, P.L. et al [4].
Those two generators were modelled by using the transfer functions measured
during on-load frequency response (OLFR) and this model was exactly matching
the one obtained by standstill frequency response (SSFR). [4] Proved that the
existence of continues damper winding under continues rotor slot wedges produces
a countable difference between OLFR and SSFR rotor parameters. Furthermore, the
effect of damper winding dynamics is very important especially in sub transient
studies for a single generator. The major difficulty with the damper winding is that
its currents are not available for measurement. Therefore, an algorithm was
proposed by Said, S.A. et al [5] in order to solve this problem. This algorithm
calculates the electric parameter of the stator by implementing the synchronous
machine equations in steady state where the damper currents can be neglected.
Synchronous Generator Parameter Identification from Measurement Data
17
Chapter 1 Introduction and Organisation of Dissertation
Then, the parameters of field and damper windings can be calculated from the
estimated d-axis and q-axis damper currents. A synchronous generator connected to
an infinite busbar electric network and a limited load was used to test the
performance of this algorithm. The results obtained in this test had shown a very
close matching between the identified model and the actual system performance.
See Fig (4).
q-axis currents
d-axis currents
Output power
Terminal voltage
Fig (4): Outputs of the actual system and the identified model [5].
In 1981, a standstill frequency response test was developed by Coultes, M.E. et al
[6]. The procedure of this test was based on low voltage frequency response
measurements taken from the stator and rotor terminals with fixed rotor. Further
development of these procedures was made by [7] in order to overcome the
disagreements by modifying the model with both stator and rotor values. This
development has also shown a good agreement with [4] regarding the complexity of
modelling the synchronous machines with damper winding.
The maximum likelihood (ML) technique was used in 1989 to estimate the
parameters of the solid rotor linear machine from noise corrupted data. The
technique was applied to the SSFR or time domain test data. Excluding the
saturation effect, ML algorithm was presented to be a very accurate estimation
Synchronous Generator Parameter Identification from Measurement Data
18
Chapter 1 Introduction and Organisation of Dissertation
method involving noise data [8]. In 1994, a direct comparison between the
measured standstill and on-line responses was carried out by [9] on a 5KVA three
phase salient pole synchronous machine and the validation of both the time domain
and the ML estimation was approved. Similar rating machine was used to perform
an on line model identification steps using the ML technique and the small
disturbance responses [10]. Saturation effect was considered in estimating the
mutual inductance. The simplicity of the small disturbance test was shown as there
was no great impact to the interconnected power system during the test.
In 2003, a nonlinear mapping based modelling method was designed to estimate
the parameters of large machine from on-line data [11]. A 460-MVA large steam
turbine was used to test the method. Linear model armature circuit and field
winding parameters were first estimated by using data from small excitation
disturbances. Then, nonlinear mapping functions-based estimators were used to
identify the saturated inductances (
). Finally, an output error method
(OEM) was implemented to estimate the rotor body parameters. The final
simulation results of this paper have proved that the estimated parameters
outperform data supplied by the manufacturer [11].
1.3.2.2 Sudden three-phase short circuit test
Although it is ideal for process identification, SSFR may not be practical under
some conditions such as the adaptation of linear transfer function parameters for
use in generator models operating rather than standstill condition. Instead, a sudden
three-phase short circuit test is commonly used to estimate the dynamic parameters
of the synchronous machine.
An approach of obtaining synchronous machine d and q axis impedances was
suggested based on the concept of line to line short circuit [12]. The short circuit
test is done by applying line to line short circuit to a machine running at reduced
speed while the rotor is excited to produce line to line short circuit current at
fundamental frequency. In addition to the rotor angle, the line voltage and short
circuit current are recorded in order to compute the operational inductances or
impedances. The major advantage of this technique is that it can be used to
determine the machine characteristics at subsynchronous and supersynchronous
frequencies [12]. However, the application of line to line short circuit may lead the
Synchronous Generator Parameter Identification from Measurement Data
19
Chapter 1 Introduction and Organisation of Dissertation
machine out of the operating limit due to dielectric or mechanical stress. Therefore,
a simple and hazardless test procedure was suggested by de Mello, F.P. et al [13].
In this test, the synchronous machine parameter can be derived by tripping the
breaker of loaded generator. The test involves measurement of voltage and field
current transient deviations under no load condition. The results of the simulation
had shown an important technique of determining the q and d axis supposed to help
the industry in resolving the adequacy of machine modelling methods for system
dynamic studies [13]. The q-axis components identification were considered in
details by a further research done by de Mello, F.P. et al [14] although the effect of
saturation was neglected.
Based on three phase short circuit test, a fully automated software was developed
by Simond, J.J. et al [15] to determine the sub-subtransient, subtranisient and
transient parameters of large synchronous machine. Fig (5) shows the main steps
for the software. First, the characteristics reactance’s and time constants of the
machine are identified based on the phase and excitation currents during the three
phase short circuit test. The corresponding equivalent circuit diagram is also
determined according to the theory of the synchronous machine. Then, this
equivalent circuit is converted to a simulation program. Finally, the same three
phase short circuit test is done by a numerical simulation and the results of the
simulation are compared with the measured values taken in field.
Fig (5): Basic procedures [15].
Synchronous Generator Parameter Identification from Measurement Data
20
Chapter 1 Introduction and Organisation of Dissertation
To test the performance of this software, a large hydrogenerator and turbogenerator
were used. The characteristics quantities and simulation results compared to
measurements for the 190MVA turbogenerator are shown in fig (6). In the other
hand, fig (7) shows the characteristics values and the elements of the equivalent
circuit of the 32.6 MVA, 10.5KV hydrogenerator. A comparison between the
simulated and the measured values is also shown in fig (7).
Fig (6): Results of simulation for the 190MVA turbogenerator [15].
Fig (7): Results of simulation for the 32.6 MVA hydrogenerator [15].
Synchronous Generator Parameter Identification from Measurement Data
21
Chapter 1 Introduction and Organisation of Dissertation
Both tests have shown the effective performance of the developed software. The
main advantage of this method appears in the intrinsic time saving, the higher
accuracy of the results [15].
In another research, Simond, J.J. et al [16] used a 2D Finite Element to determine
the parameters of the same rated large machines based on simulations of no load
sudden three phase short circuit test. The saturation effects and the eddy currents in
the rotor solid iron parts were considered in the simulation. The results obtained for
both machines are shown in the following tables. The measured values are included
for comparison.
Table (1): Results for the hydrogenerator [16]
Measured Data
Simulated Data
0.15
0.3
0.5
0.3
1
1
1
1
1
0.905
0.4056
0.4051
0.3777
0.4004 0.3595
0.2738
0.2722
0.2550
0.2777 0.2403
1.6504
1.5838
1.3897
1.2914 1.1002
0.03397 0.03172 0.02724
0.03359 0.02988
Table (2): Results for turbogenerator (identification with two rotor circuits) [16]
Measured Data
Simulated Data
0.2
0.35
0.5
0.7
0.25
1
2.15
2.15
2.15
2.085
2.15
2.09
0.2160
0.254
0.250
0.257
0.232 0.246
0.215
0.196
0.187
0.179
0.190 0.154
1.415
1.327
1.298
1.299
1.519 1.606
1.160
0.094
0.090
0.151
0.109 0.191
Table (3): Results for turbogenerator (identification with three rotor circuits) [16]
Measured Data
Simulated Data
0.20
0.35
0.5
0.7
0.25
1
2.15
2.15
2.15
2.085
2.15
2.084
0.260
0.254
0.250
0.257
0.232 0.246
0.228
0.222
0.219
0.200
0.220 0.178
0.180
0.170
0.162
0.141
0.186 0.145
1.415
1.327
1.298
1.299
1.519 1.606
0.224
0.185
0.209
0.214
0.296 0.258
0.0224 0.0234 0.0258 0.0240
0.0725 0.0764
Synchronous Generator Parameter Identification from Measurement Data
22
Chapter 1 Introduction and Organisation of Dissertation
According to the tables, an outstanding concordance has been shown with the
measurements in case of the large hydrogenerator. However, the accuracy for the
obtained time constant is not so acceptable in case of the turbogenerator. This
inaccuracy is may be due to the not optimal dimension of the mesh analysis in finite
element [16].
A comparison between results of tests was made by [17] on three large
turbogenerator with different rotor construction. Standstill frequency response
(SSFR), on-line frequency response (OLFR) and three phase short circuit tests were
all implemented. As observed in another research [4], Dandeno, P.L. et al [17]
observed that it is more difficult to obtain the equivalent circuit of d and q axis in
case of more complex rotor construction. He also concluded that the standard
model based on the manufactures data is not enough for simulating the dynamic
responses.
An another comparison between standstill frequency response and three phase short
circuit tests was done by Simond, J.J. et al [18] using 2D finite element design.
Without considering the saturation effect, a good agreement between the two tests
was obtained for laminated salient-pole synchronous machines [18].
Although it has been usually used at no load, three phase short circuit test requires
large equipment and therefore it is expensive and risky especially for voltages
higher than 60% of nominal voltage For these reasons, a DC decay test has been
used as an alternative test as it requires light equipment. This test produces the
characteristic values of synchronous machine in the d and q axes. It is done for the
two intense positions of the rotor two axes [19].
A technique based on least-squares estimation was presented by Kyriakides, E. et al
[20]. An observer was designed to measure the damper currents and use them in the
parameter estimation. Two cases were studied in this paper. A good agreement
between the damper current and the simulation result was shown in the case of daxis winding unlike the case of q- axis winding where small difference between the
estimated and the simulated currents was noticed [20]. Further to this paper,
Kyriakides, E. et al [21] used the observer estimator in a Graphic User Interface
(GUI) application. A Visual C++ engine and GUI were both used so that the on-line
Synchronous Generator Parameter Identification from Measurement Data
23
Chapter 1 Introduction and Organisation of Dissertation
measurement can be linked with the estimator. It was shown that the accuracy of
estimation is still acceptable even when multiple parameters are estimated.
Recently, a master thesis about synchronous generator parameters identification has
been written by Nizam, I. [22] for the University of Manchester. The author has
developed a complete Simulink model of synchronous generator including the
damper windings. The parameters have been expressed in per unit system in order
to make it easier to compare between different rated machines. Park’s
transformation has been applied to transform all stator quantities to equivalent dq
quantities. Thus, the generator model can be given as shown in the following matrix
[21].
IEEE Standard models 2.1 and 2.2 shown in figure (8) have been used to represent
the synchronous generator modelling.
Fig (8): Generator model 2.1 with one d-axis and one q-axis damper winding [22].
Synchronous Generator Parameter Identification from Measurement Data
24
Chapter 1 Introduction and Organisation of Dissertation
Fig (9): Generator model 2.2 with one d-axis and two q-axis damper winding
adopted from [22].
Where;
: Stator winding d-axis and q-axis leakage inductances respectively.
: Direct & quadrature axis stator-rotor mutual inductances respectively.
: Field resistance and leakage inductance referred to stator respectively.
: Direct axis damper winding D, resistance and leakage inductance
respectively.
: Quadrature axis damper winding G, resistance and leakage inductance
respectively.
: Quadrature axis damper winding Q, resistance and leakage inductance
respectively.
: Direct axis field –damper mutual leakage inductance.
A balanced load operation has been assumed in the simulation and hence zero
sequence voltages and currents have been ignored. The second order model has
been considered due to a simulation limits and the effect of d-axis field damper
mutual leakage inductance has not been considered. An observer model has been
designed to calculate the damper currents [22].
In this project [22], a 158MVA, 13.8KV and 3600 rpm synchronous machine has
been used to evaluate the developed model. The estimation process has been done
by using the nonlionear least square algorithm from Matlab optimization toolbox.
Table (4) shows the estimation results for single d-axis and q-axis damper winding.
Synchronous Generator Parameter Identification from Measurement Data
25
Chapter 1 Introduction and Organisation of Dissertation
Table (4): Estimated parameters for single d-axis and q-axis damper winding [22]
Parameter Initial Value (p.u)
Estimated Value (p.u)
Deviation (%)
1.64
1.3543
-17.42
1.56
1.5536
-0.41
0.16
0.160889
0.56
0.16
0.15702
-1.86
0.0046
0.0081396
76.95
0.0009722
0.00098341
1.15
0.11791
0.27568
133.81
Table (4) shows an accurate estimation for
difference is obtained for
while an accounted
. This high difference is assumed to be due to
neglecting the saturation effect.
The estimation process has been repeated by including the damper windings D,G
and Q. The results are shown in Table (5).
Table (5): Estimated parameters for damper winding D, G and Q[22].
Parameter
Initial Value
Estimated Value
Deviation (%)
(p.u)
(p.u)
1.64
2.057700
25.47
1.56
1.509100
-3.26
0.16
0.162894
1.81
0.16
0.140320
-12.30
0.0046
0.003821
-16.94
0.000972
0.00099998
2.88
0.257
0.352410
37.12
Except of
, all parameters have shown a very close value to the
initial value. However, the simulation outcomes, in general, are not accurate
enough to be used in synchronous generator dynamic and stability study. Therefore,
it has been concluded that the developed model needs to be modified in order to get
more accurate results [22]. This modification can be done by considering the effect
of noise and magnetic saturation.
Synchronous Generator Parameter Identification from Measurement Data
26
Chapter 1 Introduction and Organisation of Dissertation
1.3.2.3 Numerical Impulse Method
In a numerical impulse method, the obtained parameters describe behaviour of the
machine at the certain operation point. This is an advantage of the numerical
impulse method over the SSFR and the sudden short circuit tests. For this reason,
Olli Makela [23] has chosen the numerical impulse method to estimate two-axis
model parameters for a synchronous machine in his Master degree project where he
used data from linear and nonlinear finite element models to estimate the
parameters. It was noticed that saturation has no big effect when an impulse with
amplitude of 1% of the average RMS value of the line voltages is used.
1.3.3 Parameters Derivation of Power Plant Equipment
In power plant, the generation system is composed of the synchronous generators,
their excitation system and the turbine-governor. Therefore, modeling of
synchronous machine is affected by the modeling of both excitation control system
and turbine-governor control. Similar to the synchronous generator, the excitation
system and turbine-governor control system can be tested either by off-line or online tests.
The excitation system should be tested in conjunction with the commissioning as
the manufactures’ data and manufactures’ representative are available at that time.
Off-line tests are conducted on each part within the excitation system while it is
isolated from field winding and fed by test supplier. On-line tests, in the other hand,
are conducted with the generator synchronized to the network and running at a
range of active and reactive power loadings. The excitation system can also be
tested while the generator is open circuited operating at rated speed and rated
voltage. Automatic voltage regulator (AVR) step response test may be considered
as the most common type of open circuit test. This test is carried out by slightly
changing the AVR reference level for short period. As a result of this change, the
generator terminal voltage will change abruptly and gives a good measure of the
whole response of the excitation system. Another way of open circuit testing is
load rejection with the unit absorbing reactive power. Unlike the AVR step
response, this method doesn’t need any equipment for changing AVR reference
level [24].
Synchronous Generator Parameter Identification from Measurement Data
27
Chapter 1 Introduction and Organisation of Dissertation
Pourbeik, P [25], presented a technique for fitting parameters to power plant
equipment based on off-line tests. The methodology was applied on both brushless
and static exciters. A good agreement between the original data and the measured
values has been shown in most cases. The excitation system model used in this
research is shown in figure (10) below.
Fig (10): Excitation system model [25].
In another paper, Pourbeik, P [26], proposed a novel automated technique for
fitting parameters of power plant equipment based on on-line system disturbances.
A 560MVA and 496MVA large steam-turbine generators in the North American
power system were used to test this method. The test was conducted based on five
loss of generation events occurred due to faults during the period between May to
November 2008. Measurement of speed, field current and field voltage of the
generation system in each event were used to apply the proposed algorithm. After a
number of iterations, the algorithm converged to a very good fit between identified
parameters and the original ones. Table (6) displays identified parameters for some
events in comparison with the original equipment manufacturer [26].
Synchronous Generator Parameter Identification from Measurement Data
28
Chapter 1 Introduction and Organisation of Dissertation
Table (6): Fitted excitation system parameters [26]
Parameter
Description
OEM
0
4.83
4.83
0.01
0
Fit
Event 1
0.02
4.83
4.83
0.01
0
Fit
Event 2
0.02
4.83
4.83
0.01
0
Fit
Event 3
0.02
4.83
4.83
0.01
0
Fit 2
Event 2
0.024
4.36
3.32
0.01
0
Transducer Time Constant
AVR Proportional Gain
AVR Integral Gain
AVR Time Constant
Field Voltage Feedback
Gain
Vfd Feedback Loop P-Gain
Vfd Feedback Loop I-Gain
Potential Forcing Gain
Forcing Angle
Current Forcing Gain
Leakage Reactance
Communication Loss
1
0
6.21
0
0
0
0.09
1
0
6.21
0
0
0
0.09
1
0
6.21
0
0
0
0.09
1
0
6.21
0
0
0
0.09
1
0
5..74
0
0
0
0.05
This research has shown the capability to apply models against real events rather
than against staged tests which were used in the previous work [25].
1.3.4 Summary of the Literature Review
This review has examined some past and recent works and papers published in the
field of synchronous generator parameter identification. The most common on-line
tests such as standstill frequency response (SSFR) and sudden short circuit tests
have been particularly considered and the numerical impulse method has been
briefly described.
The main observations and conclusions can be outlined in the following points:

Since the saturation effect cannot be considered in the off-line test methods and
because of the inaccuracy of this test, the on-line test techniques may be
preferred due to its technical and economical sides.

The existence of continues damper winding under continues rotor slot wedges
produces a countable difference between on-load frequency response (OLFR)
and (SSFR) rotor parameters.

An algorithm that has been used to solve damper winding problem in sub
transient studies for a single generator has an accurate identification results.
Synchronous Generator Parameter Identification from Measurement Data
29
Chapter 1 Introduction and Organisation of Dissertation

Compared to (OLFR), low voltage frequency response, maximum likelihood
and the small disturbance, the nonlinear mapping based modelling method has
shown that the estimated parameters outperform the data supplied by the
manufacturer.

Compared to (SSFR), the sudden three-phase short circuit test is preferred to be
used to estimate the dynamic parameters of the synchronous machine due to its
ability to work in different conditions of the generator operation.

Line to line short circuit technique has an advantage that it is used to determine
the machine characteristics at sub-synchronous and super-synchronous
frequencies.

With no consideration of the effect of the noise and magnetic saturation, the
least square estimation method can show an inaccurate simulation results.

The numerical impulse method has an advantage over (SSFR) and sudden short
circuit tests which describes the behaviour of the machine at the certain
operation point.
In this review, a recent master thesis about synchronous generator parameters
identification written by Nizam, I. [22] has been considered in details. The project
(thesis) has developed a complete Simulink model of synchronous generator
including the damper windings. A 158MVA, 13.8KV and 3600 rpm synchronous
machine has been used to evaluate the developed model. The estimation process
has been done by using the nonlionear least square algorithm from Matlab
optimization toolbox. The results of simulation have shown that the developed
model needs to be modified in order to get more accurate results. This modification
can be done by considering the effect of noise and magnetic saturation.
Synchronous Generator Parameter Identification from Measurement Data
30
Chapter 1 Introduction and Organisation of Dissertation
1.4 Dissertation Organisation
The thesis is structured as follows:

Chapter two describes the modelling and the simulation of synchronous
machine. Development equations of synchronous machine, simulated data
during a 3-phase short circuit and filtering the noise are presented.

Procedures of parameter estimation are covered in chapter three. The
parameters are estimated by using non linear least squares method from
optimization toolbox in MATLAB environment.

In chapter foure, results of parameters estimation are presented.

The results are discussed and evaluated in chapter five. Further work is finally
suggested.
Synchronous Generator Parameter Identification from Measurement Data
31
Chapter 2 Modeling and Simulation of Synchronous Machine
Chapter 2: Modeling and Simulation of Synchronous Machine
2.1 Introduction
This chapter presents the representation and models' selection of the synchronous
machines as well as the detailed development of the synchronous machine
equations that will be used in the simulation is presented. The measurements data
during a three-phae short circuit and filtering the noise are also presented.
2.2 Synchronous Machine Representation
A conventional three phase synchronous machine consists of two parts; stationary
part called a stator and rotating part called a rotor. The stator has three-phase
windings that are 120 electrical degrees a part and the rotor has an excitation
winding which DC supply with variable number of damper windings in the direct
and the quadrature axis can be received by the excitation winding. The foundation
of synchronous machine with detailed theory can be found in [27].
The operation of synchronous machine can be represented by the following voltage
equations that can be found as [28]:
(2.1)
(2.2)
(2.3)
(2.4)
(2.5)
(2.6)
(2.7)
Stator and rotor circuit of synchronous generator are shown in figure (11).
Synchronous Generator Parameter Identification from Measurement Data
32
Chapter 2 Modeling and Simulation of Synchronous Machine
Fig (11): Schematic diagram of a synchronous generator [1].
2.3 Two Axes Models of Synchronous Machines
It is necessary to employ a mathematical model in order to formulate the state
estimation equation for a synchronous generator. Depending on the type of study
that is desired to be performed, there are various practical models available for
synchronous generators. The number of rotor circuits in the direct and the
quadarture axes prescribe the order of a synchronous generator model. For stability
studies and representation of various types of generators, lower order models are
often used [1]. Different recommended synchronous generator models are
suggested in IEEE standard, such as models 2.1 and 2.2 and theses models can be
shown in Figs (12) and (13) respectively.
Fig (12): Generator model 2.1 with one d-axis and one q-axis damper winding [22].
Synchronous Generator Parameter Identification from Measurement Data
33
Chapter 2 Modeling and Simulation of Synchronous Machine
Fig (13): Generator model 2.2 with one d-axis and two q-axis damper winding
adopted from [22].
A balanced load operation has been assumed in the simulation and hence zero
sequence voltages and currents have been ignored. The second order model has
been considered due to a simulation limits and the effect of d-axis field damper
mutual leakage inductance has not been considered and due to its accurate
modeling of quadrature axis [1] [22].
2.4 Per-Unit Notation
The per-unit representation of synchronous machine can be used to normalize the
variables of the machine. In addition, the per-unit system offers computational
simplicity by eliminating units and expressing system quantities as dimensionless
ratios compared to the use of physical units (amperes, volts, ohms, webers, henrys,
etc.) [27]. In this project, the parameters have been expressed in per-unit system in
order to make it easier to compare between different rated machines [29]. In order
to derive the other base quantities that have been defined below in table (7), the
base power Sbase, the base voltage Vbase and synchronous angular frequency
Wbase should be specified. Same base power Sbase is selected in order to calculate
the per-unit quantities for rotor but the voltage and the current are referred to
mutual flux linkage. Moreover, more details about conversion to per-unit quantities
can be found in [29].
Synchronous Generator Parameter Identification from Measurement Data
34
Chapter 2 Modeling and Simulation of Synchronous Machine
Table (7): Derived base quantities
Quantity
Formula
Base Current
Base Resistance
Base Inductance
𝜔
Base Flux
2.5 Park's Transformation
The time-varying inductances can be eliminated when the changes of variables are
used in the analysis of ac machines. Changes of variables are also needed in the
analysis of constant parameter power-system components and control systems
associated with electric drives. Indeed, all known real transformations for these
components and controls are contained in the transformation to the arbitrary
reference frame. The same general real transformation can be used for the stator
variables of the induction and synchronous machines and for the rotor variables of
induction machines. One transformation to the arbitrary reference frame can be
formulated which could be applied for all variables [30].
A transformation of the 3-phase variables of stationary circuit elements to the
arbitrary reference frame for a change of variable may be expressed as [30]:
(2.8)
Where:
(2.9)
(2.10)
(2.11)
Synchronous Generator Parameter Identification from Measurement Data
35
Chapter 2 Modeling and Simulation of Synchronous Machine
𝜔
The inverse transformation can be shown in the following equation:
(2.13)
Based on the formulas mentioned above, Simulink models for Voltage and Current
transformations have been designed as shown in figures (14) and (15) respectively.
Fig (14): Block diagram of voltage park transformation (Vabc to Vdqo).
Fig (15): Block diagram of current inverse park transformation (Idqo to Iabc).
Synchronous Generator Parameter Identification from Measurement Data
36
Chapter 2 Modeling and Simulation of Synchronous Machine
2.6 Simulation of Synchronous Machine
The computer simulation for synchronous machine is divided into two types of
simulations. The most common used of simulation derived from the voltage
equations expressed in the rotor reference frame with an arrangement of equations
in the same form of the equations that are used in the induction machine. This kind
of simulation was done by C. H. Thomas [31]. The second type of simulation is that
the stator flux linkages per second are calculated in the arbitrary reference frame
with the rotor flux linkages per second computed in the rotor reference frame [30].
In this dissertation the first type of simulation is only used to be done in
MATLAB/SIMULINK by using the available blocks that have been provided in the
toolbox library.
2.6.1 Simulation in Rotor Reference Frame
The voltage equations expressed in the rotor reference frame are given by [30]:
(2.14)
(2.15)
(2.16)
(2.17)
(2.18)
(2.19)
(2.20)
The equations defining the flux linkages per second are as follows [30]:
(2.21)
(2.22)
(2.23)
Synchronous Generator Parameter Identification from Measurement Data
37
Chapter 2 Modeling and Simulation of Synchronous Machine
(2.24)
(2.25)
(2.26)
(2.27)
The voltage and flux linkage equations can be manipulated in order to obtain
computer simulation. The resulting integral equations are defined as (2.28)-(2.45)
[30]:
(2.28)
(2.29)
(2.30)
(2.31)
(2.32)
(2.33)
(2.34)
Where:
(2.35)
(2.36)
(2.37)
(2.38)
(2.39)
Synchronous Generator Parameter Identification from Measurement Data
38
Chapter 2 Modeling and Simulation of Synchronous Machine
(2.40)
(2.41)
(2.42)
(2.43)
(2.44)
(2.45)
Since the saturation is not taken into account, the torque equation that is used in the
simulation is given by:
(2.46)
And the rotor speed is expressed as:
𝜔
(2.47)
Block diagram showing the computer simulation of the synchronous machine in the
rotor reference frame using Matlab / Simulink is shown in figure (16). The
MATLAB's m-file for the simulation is attached in Appendix A. In general, the
voltages applied to the damper winding are not shown in the block diagram because
the damper windings are always short-circuited and the voltages are zero [30].
Synchronous Generator Parameter Identification from Measurement Data
39
Chapter 2 Modeling and Simulation of Synchronous Machine
Fig (16): Complete simulink block diagram of synchronous generator.
2.7 Experimental Data during Disturbance
Terminal voltages and current of synchronous generator are known as stator
measurements while field winding voltage and current are known as rotor
measurements. Bothe the stator and the rotor measurements can be recorded as
shown in figure (17) [32].
Fig (17): Experimental data acquisition from synchronous generator terminals [32].
Digital Fault Recorder (DFR) can read the experimental data directly from
synchronous generator control panel.
Synchronous Generator Parameter Identification from Measurement Data
40
Chapter 2 Modeling and Simulation of Synchronous Machine
2.8 Simulated Data during a 3-Phase Short Circuit Test
Although it is ideal for process identification, SSFR may not be practical under
some conditions such as the adaptation of linear transfer function parameters for
use in generator models operating rather than standstill condition. Instead, a sudden
three-phase short circuit test is commonly used to estimate the dynamic parameters
of the synchronous machine.
An approach of obtaining synchronous machine d and q axis impedances was
suggested based on the concept of line to line short circuit [12]. The short circuit
test is done by applying line to line short circuit to a machine running at reduced
speed while the rotor is excited to produce line to line short circuit current at
fundamental frequency. In addition to the rotor angle, the line voltage and short
circuit current are recorded in order to compute the operational inductances or
impedances. The major advantage of this technique is that it can be used to
determine the machine characteristics at subsynchronous and supersynchronous
frequencies but the application of line to line short circuit may lead the machine out
of the operating limit due to dielectric or mechanical stress [12]. However, the 3phase short circuit was applied across the machine in this project. High load impact
is presented by this sudden short circuit in order to excite the damper windings
[33].
The simulated data were recorded and attached in Appendix B.
2.9 Adding and Filtering the Noise
The noise has been added to the simulated data of the estimator by typing a
MATLAB code in order to make them as realistic data and this code can be shown
in Appendix C. The noise of the data should be filtered and prepared in a form that
can be used by the estimator.
In order to prepare these data, there are many processes that need to be performed
between the data acquisition and the estimator implementation. The filtering of
simulated data to remove inconsistent measurements and noise is the most
fundamental process. In reality, there are different filters that have been developed
and implemented in order to filter the noise. In this project, the digital discrete
Synchronous Generator Parameter Identification from Measurement Data
41
Chapter 2 Modeling and Simulation of Synchronous Machine
filters are considered and the types of theses filters are classified into; the
Butterworth, Chebyshev, Bassel and Moving average filters [1] [34].
A phase shift to the filtered signals is almost introduced. Since this phase shift is
not desired, a zero phase shift filter is needed to provide no phase difference
between the original and filtered signals. The signal in both the forward and the
reserve directions can be filtered by zero phase digital filters [1]. In Reference [35]
more information about zero shift filters can be found.
In this project, a low pass filter is necessary to be employed whose cut off
frequency is selected to maintain the dynamics of the signals in both steady state
and transient conditions. The types of digital discrete filters that have been
mentioned previously can be considered as low pass filters. The fastest digital filter
available and it has good smoothing in time domain is the moving average filter but
it has a slow roll off. Similar characteristics to butterworth filters can be found in
chebyshev and elliptic filters but they have considerable ripple in their passband.
Therefore, the butterworth filter has been used due to its good transient response
and fast roll off [1]. Figure (18) shows the configuration of the filtering while figure
(19) shows the simulink model of filtering the noise.
Fig (18): Filtering configuration adopted from [1].
Synchronous Generator Parameter Identification from Measurement Data
42
Chapter 2 Modeling and Simulation of Synchronous Machine
Fig (19): Block diagram of filtering noise.
2.10 Conclusion
Various recommended IEEE models and development equations for synchronous
machines are presented in this chapter. A Simulink model for synchronous
generator has been designed based on the development equations. Main parts of
modeling and simulation of synchronous machine have been individually
considered. The function of each part has been built. By the end of this chapter, the
synchronous generator model is ready for simulation.
Synchronous Generator Parameter Identification from Measurement Data
43
Chapter 3 Procedures of Parameters Estimation in MATLAB/SIMULINK
Chapter 3: Procedures of Parameters Estimation in MATLAB/SIMULINK
3.1 Introduction
The main objective of this project is to develop a method & a model that can be
used to estimate the synchronous generator parameters fitting with the
measurements parameters. In order to achieve this objective, the method and the
model will be done in MATLAB/SIMULINK package.
3.2 Parameters Estimation Procedures
The parameters estimation process of the proposed model of the synchronous
generator has been done by using complete model of Synchronous Machine which
is given in figure (16), estimator model that have been built up to be used for the
estimation as shown in figure (20) and Optimization Toolbox (GUI) in MATLAB
by implementing the steps below.
Fig (20): Block diagram of estimator model.
3.2.1 Creating an Estimation Project
Before we start importing data, an estimation project must be created and set up by
configuring the appropriate parameters, solvers, and the cost functions. A Graphical
User Interface (GUI) is provided by Simulink Optimization Software that makes
setting up the estimation project quick and easy.
Synchronous Generator Parameter Identification from Measurement Data
44
Chapter 3 Procedures of Parameters Estimation in MATLAB/SIMULINK
An estimation project can be created by the following steps:

Open synchronous generator and estimator models.

Open the Control and Estimation Tools Manager GUI by selecting Tools ˃
Parameter Estimation in the simulink model window [36].
The Control and Estimation Tools Manager GUI is depicted in figure (21).
Fig (21): Control and Estimation Tools Manager GUI.
3.2.2 Importing Data into the GUI
After creating an estimation project, the estimation data can be imported. In order
to import transient (measured) data for the estimator model, many steps need to be
implemented as follows:

In the Control and Estimation Tools Manager, select Transient Data under the
Estimation Task node of the Workspace tree.

Right-click Transient and select New to create New Data node.

Select New Data node under the Transient Data node.

Import input and output data from data import dialog box.

Select Time / Ts cell from dialog box.
Synchronous Generator Parameter Identification from Measurement Data
45
Chapter 3 Procedures of Parameters Estimation in MATLAB/SIMULINK

Import the time vector for the input and output data [36].
Importing input and output data into the Control and Estimation Tools Manager are
shown in figures (22) and (23) respectively.
Fig (22): Importing input data into the Control and Estimation Tools Manager GUI.
Fig (23): Importing output data into the Control and Estimation Tools Manager
GUI.
Synchronous Generator Parameter Identification from Measurement Data
46
Chapter 3 Procedures of Parameters Estimation in MATLAB/SIMULINK
3.2.3 Parameter Estimation
When the model parameters are estimated, the measured data are compared with
the data generated using a simulink model by Simulink Design Optimization
Software. By using optimization techniques, the parameters and initial conditions of
states are estimated by the software in order to minimize a user-selected cost
function. The cost function typically calculates a least-square error between the
empirical and model data signal [36].
After importing and processing the estimation data, the following steps should be
followed to estimate model parameters:
3.2.3.1 Creating an Estimation Task
An estimation task is created and the estimation settings are configured as follows:

In the Control and Estimation Tools Manager, right-click the estimation node in
the Workspace tree and select New.

Select the New Estimation node [36].
Figure (24) shows the estimation task and settings.
Fig (24): The estimation task and settings.
Synchronous Generator Parameter Identification from Measurement Data
47
Chapter 3 Procedures of Parameters Estimation in MATLAB/SIMULINK
3.2.3.2 Specifying Data for Parameter Estimation
To specify a data set for estimation, the data must be imported in the GUI and an
Estimation Task must be created.
The steps of specifying data are as follows:

Select the selected check box to the right of the New Data of data set.

Specify the weight of each output from the model by setting the weight column
in the output data weights table.

Use less weight when an output is noisy.

Use more weight when an output strongly affects parameters [36].
3.2.3.3 Specifying Parameters for Estimation
Simulink Design Optimization software lets you estimate scalar, vector and matrix
parameters. Estimating model parameter is an iterative process. Usually, it is more
practical to estimate a small group of parameters and use the final estimated values
as a starting point for further estimation of parameters that are more difficult.
However, if a large number of parameters need to be estimated, the parameters that
influence the output should be estimated [36].
The parameters for estimation in the GUI are specified by implementing the
following steps:

In the Control and Estimation Tools Manger, select the Variables node in the
Workspace tree to open the estimated parameters part.

In the estimated parameters pane, click Add to open the select parameters
dialog box.

Select the parameters that need to be estimated and then click OK as shown in
figure (25).

In the New Estimation node of the Control and Estimation Tools Manager GUI,
select the parameters tab and select the parameters that need to be estimated.
Synchronous Generator Parameter Identification from Measurement Data
48
Chapter 3 Procedures of Parameters Estimation in MATLAB/SIMULINK

Enter the initial values for the parameters in the Initial Guess column.

Specifying the Upper/Lower bounds [36].
Selecting the parameters and setting up the initial guess and upper/lower bounds are
shown in figure (26).
Fig (25): Selecting the parameters that need to be estimated.
Fig (26): Selecting the parameters and setting up the initial guess and upper/lower
bounds.
Synchronous Generator Parameter Identification from Measurement Data
49
Chapter 3 Procedures of Parameters Estimation in MATLAB/SIMULINK
3.2.3.4 Starting the Estimation
Before starting the estimation, the estimation options in the new estimation node of
the Control and Estimation Tolls Manager GUI should be specified as follows:
3.2.3.4.1 Specifying and selecting the solver type
In the simulation options of the estimation options, the types of solvers are divided
into two major types according to [36].

Variable-Step which the error can be kept within the specified tolerance by
adjusting the step size of solver uses when it is used.

Fixed-Step which a constant step size can be used.
The variable-step solver is selected due to its ability to keep the error within the
specified tolerance and for faster simulation. For each type of the solvers that have
been mentioned beforehand, different solvers are available for differential equations
in Optimization Toolbox as shown in figure (27). Indeed, the most famous methods
of solving different equations incorporated with Ode 23 and Ode 45 are
implemented in MATLAB package. A solution for a simple second and third order
model can be provided by Ode 23. However, a solution for fourth and fifth order
can be provided by Ode 45 with a higher accuracy. Finally, the Ode 23 is used due
to its economical computation side and fast convergence for Lower-Order model
with less data [36].
Fig (27): Different solvers available in Optimization Toolbox.
Synchronous Generator Parameter Identification from Measurement Data
50
Chapter 3 Procedures of Parameters Estimation in MATLAB/SIMULINK
3.2.3.4.2 Specifying and Selecting the Optimization Method
3.2.3.4.2.1 Cost Function Specification
In order to set up the optimization method the cost function should be specified.
Ideally, the most common methods that can be used in this project to minimize the
deviations of the estimated measurements from the actual measurements are as
follows:
1. The weighted least-squares method
It is used to minimize the sum of the squares of the weighted deviations of the
estimated data from actual data and it can give the best linear unbiased estimate for
any distribution with finite variance [1].
2. The maximum likelihood method
It can be used to maximize the probability of estimating the state variable [22].
3. The maximum variance method
The anticipated value of the sum of the squares of the error between the estimated
components of the state variable vector and the actual components of the state
variable vector can be minimized by using this method [22].
In this project, the least-squares method will be used due to its ability to give the
best minimization of the sum of the squares of the difference between the estimated
output and experimental data compared to other methods [1].
The error signal is given by:
(3.1)
Where:
the deviation between the simulated model outputs.
the current set of model parameters.
the experimental measurements.
Synchronous Generator Parameter Identification from Measurement Data
51
Chapter 3 Procedures of Parameters Estimation in MATLAB/SIMULINK
Since the negative and positive deviations need to be taken into account, the cost
function is given by [22]:
(3.2)
3.2.3.4.2.2 Optimization Method Specification
In order to minimize the objective function
, the nonlinear least squares method
is selected as shown in figure (28), and it is selected due to its ability to be used for
discontinuous and highly nonlinear functions, and also for the functions that have
unreliable and undefined derivatives.
Fig (28): Different optimization methods available in Optimization Toolbox.
From figure (28), it can be seen that there are different methods available in
MATLAB's Optimization Toolbox.

Pattern Search Method which can be used to compute the first approximation
of parameters as initial simulation.

Gradient Descent Method which can be used to optimize the response signal
subject to the constraints.

Simplex Search Method which can use a direct search method to optimize the
response and it is the most useful for simple problems [36].
Nevertheless, Nonlinear Least Squares Method with lower and upper bounds is
used to achieve accurate parameters representing models with nonlinear equations.
Finally, after setting up the simulation and optimization options, the estimation can
be started and the estimated parameters will be appeared as shown in figure (29).
Synchronous Generator Parameter Identification from Measurement Data
52
Chapter 3 Procedures of Parameters Estimation in MATLAB/SIMULINK
Fig (29): Estimated parameters in Optimization Toolbox.
Synchronous Generator Parameter Identification from Measurement Data
53
Chapter 3 Procedures of Parameters Estimation in MATLAB/SIMULINK
3.3 Parameter Estimation Flowchart
The estimation processes of the parameters that have been applied into the
Optimization Toolbox in Simulink can be outlined in the following flowchart:
Obtain Va, Vb, Vc, Wr, Efd, Ifd, Ia, Ib & Ic
(Experimental Measurements)
Add Noise to Experimental
Measurements
Filter the Noise of Experimental
Measurements
Ifd, Ia, Ib & Ic
Va, Vb, Vc, Efd, & Wr
Priori System Knowledge
Complete Synchronous Generator Model
(MATLAB/SIMULINK)
Simulated Output: Ifd, Ia, Ib & Ic
No
Parameter Adjustment
Algorithm
℮˂ε
Yes
Estimated Parameters
Fig (30): Flowchart of parameters estimation processes [22].
Synchronous Generator Parameter Identification from Measurement Data
54
Chapter 3 Procedures of Parameters Estimation in MATLAB/SIMULINK
3.4 Conclusion
A Simulink model for the estimator has been designed in this chapter. The
estimator has been designed based on the obtained measurements data from on-line
test. These measurements have been used in the estimator as inputs and outputs
data. Furthermore, the procedures of parameters estimation have been described
based on non-linear least squares method from Optimization Toolbox in Matlab.
Main steps of parameters estimation have been individually considered.
Synchronous Generator Parameter Identification from Measurement Data
55
Chapter 4 Parameters Estimation Results
Chapter 4: Parameters Estimation Results
4.1 Manufacturer Data
In this project, a 158MVA, 13.8KV and 3600 rpm synchronous machine has been
used to evaluate the developed model. The typical machine parameters that have
been obtained from manufacturer data are listed in table (8). These parameters have
been used as priori knowledge and were subjected to changes during optimization
process at each iteration. Moreover, the available parameters from manufacturer
stability study data sheet are given by [1] and shown in table (9) and the
experimental data from 3-ph short circuit test that have been used for the simulation
and estimation are attached in Appendix B.
Table (8): Typical machine parameters from manufacturer data
Parameters
Original Values (p.u.)
1.64
1.56
0.11791
0.16
0.0009722
0.0046
Table (9): Standard parameters from manufacturer stability study data sheet
Parameters
Original Value
1.8 p.u.
0.27 p.u.
0.1971 p.u.
1.72 p.u.
0.49 p.u.
0.1793 p.u.
4.7963 S
0.049 S
0.49 S
0.059 S
0.1085 S
Synchronous Generator Parameter Identification from Measurement Data
56
Chapter 4 Parameters Estimation Results
4.2 Calculation of Standard Machine Parameters from Estimated Derived
Parameters
The available machine parameters in table (9) are referred as standard machine
parameters and the direct and quadrature axis reactances and their transient and
subtransient components are included as well as the transient and subtransient time
constants. Indeed, the estimated parameters that have been obtained through the
developed model derived from the standard parameters. Wherefore, it is necessary
to calculate the standard parameters obtained through the selected algorithm [1].
The formulas that are needed to perform the conversion from derived parameters to
standard parameters are outlined in table (10) [28].
Table (10): Formulas of standard parameters
Parameters
Formula
Note: all time constants are in p.u. and they are divided by 2*π*f in order to get the
values in seconds.
Synchronous Generator Parameter Identification from Measurement Data
57
Chapter 4 Parameters Estimation Results
4.3 Estimation of Parameters for Different Cases
The parameters have been estimated in the Optimization Toolbox by using
nonlinear least square method with setting up the initial guesses of parameters
values that have been provided table (8) with different cases as follows:
4.3.1 Case 1
In this case, the initial guesses in the estimation process have set up to be matched
with the initial values of the original parameters.
4.3.1.1 Estimated Parameter without Including the Effect of Noise
The parameters of the developed synchronous machine model were estimated
without including the effect of the noise to the measurements data. The results are
shown in table (11) and the estimated standard parameters are compared with
manufacturer standard parameters as shown in table (12).
Table (11): Estimated parameters of synchronous machine without including noise
Parameters
Original
Initial Guess Estimated Values Deviation (%)
Values (p.u.)
(p.u.)
(p.u.)
1.64
1.64
1.6407
-0.0426
1.56
1.56
1.5645
-0.288
0.11791
0.11791
0.11786
0.0424
0.16
0.16
0.16001
-0.000625
0.0009722
0.0009722
0.00075286
22.56
0.0046
0.0046
0.0047643
-3.57
Table (12): Manufacturer standard parameters vs the estimated standard parameters
Parameters
Original Values
Estimated Values
Deviation (%)
0.27 (p.u.)
0.27 (p.u.)
0
0.1971 (p.u.)
0.1972 (p.u.)
-0.0507
0.49 (p.u.)
0.4902 (p.u.)
-0.0408
0.1793 (p.u.)
0.1796 (p.u.)
-0.1673
4.7963 (s)
6.196 (s)
-29.18
0.049 (s)
0.049 (s)
0
0.49 (s)
0.4911 (s)
-0.22
0.059 (s)
0.059 (s)
0
0.1085 (s)
0.1048 (s)
0.34
Note: the deviation has been calculated by using the following equation:
Synchronous Generator Parameter Identification from Measurement Data
58
Chapter 4 Parameters Estimation Results
4.3.1.2 Estimated Parameters with Including the Effect of Noise
With including the effect of noise, the parameters estimation process has been
repeated. The results are listed in table (13) and the estimated standard parameters
are depicted in table (14).
Table (13): Estimated parameters of synchronous machine with including noise
Parameters
Original
Initial Guess Estimated Values Deviation (%)
Values (p.u.)
(p.u.)
(p.u.)
1.64
1.64
1.6399
0.006
1.56
1.56
1.538
1.41
0.11791
0.11791
0.1179
0.008
0.16
0.16
0.16003
-0.018
0.0009722
0.0009722
0.00098936
1.32
0.0046
0.0046
0.0046037
-0.08
Table (14): Manufacturer standard parameters vs the estimated standard parameters
Parameters
Original Values
Estimated Values
Deviation (%)
0.27 (p.u.)
0.27 (p.u.)
0
0.1971 (p.u.)
0.1973 (p.u.)
-0.1014
0.49 (p.u.)
0.4891 (p.u.)
0.183
0.1793 (p.u.)
0.1792 (p.u.)
0.055
4.7963 (s)
4.8602 (s)
-1.332
0.049 (s)
0.049 (s)
0
0.49 (s)
0.4848 (s)
1.06
0.059 (s)
0.0588 (s)
0.338
0.1085 (s)
0.1084 (s)
0.092
4.3.2 Case 2
The initial guesses of the original parameters in the estimation process have been
set up by taking 80% of (Xmd, Xmq, Xlfd, Xls, rfd and rs) initial values.
4.3.2.1 Estimated Parameter without Including the Effect of Noise
The estimated parameters are shown in table (15) and the estimated standard
parameters are compared with manufacturer standard parameters as can be shown
in table (16).
Synchronous Generator Parameter Identification from Measurement Data
59
Chapter 4 Parameters Estimation Results
Table (15): Estimated parameters of synchronous machine without including noise
Parameters
Original
Initial Guess Estimated Values Deviation (%)
Values (p.u.)
(p.u.)
(p.u.)
1.64
1.312
1.6404
-0.024
1.56
1.248
1.5646
-0.29
0.11791
0.094328
0.11788
0.025
0.16
0.128
0.15999
0.0063
0.0009722
0.00077776
0.00060011
38.27
0.0046
0.00368
0.0047631
-3.54
Table (16): Manufacturer standard parameters vs the estimated standard parameters
Parameters
Original Values
Estimated Values
Deviation (%)
0.27 (p.u.)
0.27 (p.u.)
0
0.1971 (p.u.)
0.1972 (p.u.)
-0.0507
0.49 (p.u.)
0.4902 (p.u.)
-0.041
0.1793 (p.u.)
0.1792 (p.u.)
0.055
4.7963 (s)
7.7719 (s)
-62
0.049 (s)
0.049 (s)
0
0.49 (s)
0.4912 (s)
-0.244
0.059 (s)
0.059 (s)
0
0.1085 (s)
0.1084 (s)
3.4
4.3.3 Case 3
The initial guesses of the original parameters in the estimation process have been
set up by taking 120% of (Xmd, Xmq, Xlfd, Xls, rfd and rs) initial values.
4.3.3.1 Estimated Parameter without Including the Effect of Noise
The estimated parameters are shown in table (17) and the estimated standard
parameters are compared with manufacturer standard parameters as can be shown
in table (18).
Table (17): Estimated parameters of synchronous machine without including noise
Parameters
Original
Initial Guess Estimated Values Deviation (%)
Values (p.u.)
(p.u.)
(p.u.)
1.64
1.968
1.6409
-0.054
1.56
1.872
1.5645
-0.288
0.11791
0.141492
0.11786
0.0424
0.16
0.192
0.16002
-0.0125
0.0009722
0.00116664
0.00066337
31.766
0.0046
0.00552
0.0047659
-3.61
Synchronous Generator Parameter Identification from Measurement Data
60
Chapter 4 Parameters Estimation Results
Table (18): Manufacturer standard parameters vs the estimated standard parameters
Parameters
Original Values
Estimated Values
Deviation (%)
0.27 (p.u.)
0.27 (p.u.)
0
0.1971 (p.u.)
0.1972 (p.u.)
-0.0507
0.49 (p.u.)
0.4902 (p.u.)
-0.041
0.1793 (p.u.)
0.1792 (p.u.)
0.055
4.7963 (s)
7.0327 (s)
-46.6
0.049 (s)
0.049 (s)
0
0.49 (s)
0.4911 (s)
-0.002
0.059 (s)
0.059 (s)
0
0.1085 (s)
0.1048 (s)
3.4
4.3.4 Case 4
The initial guesses of the original parameters in the estimation process have set up
by taking 80% of (Xmd, Xmq & Xlfd) and 120% of (Xls, rfd & rs) values.
4.3.4.1 Estimated Parameter without Including the Effect of Noise
Table (19) shows the estimated parameters and table (20) shows the estimated
standard parameters.
Table (19): Estimated parameters of synchronous machine without including noise
Parameters
Original
Initial Guess Estimated Values Deviation (%)
Values (p.u.)
(p.u.)
(p.u.)
1.64
1.312
1.641
-0.06
1.56
1.248
1.5644
-0.28
0.11791
0.094328
0.11785
0.051
0.16
0.192
0.16003
-0.01875
0.0009722
0.00116664
0.0006
38.28
0.0046
0.00552
0.0047662
-3.6
Table (20): Manufacturer standard parameters vs the estimated standard parameters
Parameters
Original Values
Estimated Values
Deviation (%)
0.27 (p.u.)
0.27 (p.u.)
0
0.1971 (p.u.)
0.1972 (p.u.)
-0.0507
0.49 (p.u.)
0.4902 (p.u.)
-0.041
0.1793 (p.u.)
0.1792 (p.u.)
0.055
4.7963 (s)
7.7758 (s)
-62.12
0.049 (s)
0.049 (s)
0
0.49 (s)
0.4911 (s)
-0.002
0.059 (s)
0.059 (s)
0
0.1085 (s)
0.1048 (s)
3.4
Synchronous Generator Parameter Identification from Measurement Data
61
Chapter 4 Parameters Estimation Results
4.3.5 Case 5
The initial guesses of the original parameters in the estimation process have set up
by taking 80% of (Xmd, Xlfd & rfd) and 120% of (Xmq, Xls & rs) values.
4.3.5.1 Estimated Parameter without Including the Effect of Noise
The estimated parameters can be seen in table (21) and the estimated standard
parameters can be found in table (22).
Table (21): Estimated parameters of synchronous machine without including noise
Parameters
Original
Initial Guess Estimated Values Deviation (%)
Values (p.u.)
(p.u.)
(p.u.)
1.64
1.312
1.641
-0.06
1.56
1.872
1.5644
-0.28
0.11791
0.094328
0.11785
0.051
0.16
0.192
0.16003
-0.01875
0.0009722
0.00077776
0.0006
38.28
0.0046
0.00552
0.0047662
-3.6
Table (22): Manufacturer standard parameters vs the estimated standard parameters
Parameters
Original Values
Estimated Values
Deviation (%)
0.27 (p.u.)
0.27 (p.u.)
0
0.1971 (p.u.)
0.1972 (p.u.)
-0.0507
0.49 (p.u.)
0.4902 (p.u.)
-0.041
0.1793 (p.u.)
0.1792 (p.u.)
0.055
4.7963 (s)
7.7758 (s)
-62.12
0.049 (s)
0.049 (s)
0
0.49 (s)
0.4911 (s)
-0.002
0.059(s)
0.059 (s)
0
0.1085 (s)
0.1048 (s)
3.4
4.4 Discussion of the Estimated Results
The estimated parameters of the synchronous generator without including the effect
of noise with different cases of setting up the initial guesses of the original values
are shown in tables 11, 15, 17, 19 & 21. All parameters confirm a high accuracy of
estimation compared to the original values except rs and rfd. These high deviations
may be due to:

Their small p.u. values.

Imprecision in the modeling of the synchronous generator.
Synchronous Generator Parameter Identification from Measurement Data
62
Chapter 4 Parameters Estimation Results

Estimating more than one parameter at the same time.

Inaccurate adjustment of the function tolerance in algorithm.
Nevertheless, various tests have been tried in order to reduce these high deviations
but the results have shown the same high deviations. These various tests are as
follows:

Converting their values from p.u. to Ohms and re-estimating them.

Changing in certain features of algorithm.

Converting all p.u. values to their absolute values.
Moreover, tables 12, 16, 18, 20 & 22 show the calculated standard parameters
without considering the effect of noise. All parameters emphasize the high accuracy
of the estimation except
. This is because it is related with rfd.
However, the estimated parameters and the calculated standard parameters with
including the effect of noise are depicted in tables 13 & 14 respectively. All
parameters show a high accuracy compared to the original values.
4.5 Conclusion
The simulation has been performed on a 158 MVA, 13.8 KV and 3600 rpm
synchronous machine in order to evaluate the proposed model. Parameters
estimation outcomes have been presented and analyzed in this chapter based on
non-linear least squares method. The main observations can be outlined as follows:

High accuracy of the proposed model and method has been proved for
parameters estimation.

All estimated parameters without considering the effect of noise have shown
high accuracy estimation except rs and rfd.

High deviation found in estimated rfd may be due to its small p.u. value and
estimating more than one parameter at the same time in addition to inaccurate
adjustment of the function tolerance in algorithm.

High accuracy of all estimated parameters with including the effect of noise
has been emphasized compared to original values.
Synchronous Generator Parameter Identification from Measurement Data
63
Chapter 5 Project Conclusion and Further Work
Chapter 5: Project Conclusion and Further Work
5.1 Project Conclusion
The purpose of this project was to develop a model and modify a methodology that
can be used to estimate the synchronous generator parameters from on-line data.
The model has been developed by using MATLAB/SIMULINK package while the
methodology has been implemented and modified from Optimization Toolbox in
MATLAB.
The work has been started by reviewing some of the research papers written and
experimental works done on synchronous machine parameters identification. The
parameters of synchronous machine can generally be determined either by off-line
or on-line techniques. The on-line techniques are mainly considered in this work
due to technical and economical reasons.
Various recommended IEEE models and development equations for synchronous
machine are presented in chapter three first for the purpose of modeling. Then, a
Simulink model for synchronous generator has been designed based on the
development equations. After that, the theory of main parts of modeling and
simulation of synchronous machine has been individually explained. In addition,
the function of each part has been described and its Simulink model has been built.
By the end of chapter three, the proposed model has been ready for simulation.
After it is used for obtaining the simulated data from on-line test, a Simulink model
for the estimator has been designed and built in chapter four first in order to be used
for parameters estimation. Then, the procedures of parameters estimation have been
described based on non-linear least squares method from Optimization Toolbox in
MATLAB environment. Furthermore, main steps of parameters estimation have
been individually explained.
The simulation has been performed on a 158 MVA, 13.8 KV and 3600 rpm
synchronous machine in order to evaluate the proposed model. Parameters
estimation outcomes have been presented and analyzed. High accuracy of the
proposed model and method has been proved for parameters estimation. Compared
to original values, high accuracy of all estimated parameters with including the
effect of noise has been emphasized. However, imprecision has been noticed in
Synchronous Generator Parameter Identification from Measurement Data
64
Chapter 5 Project Conclusion and Further Work
estimation the parameters rs and rfd when the effect of noise is ignored. The
significant deviation that can be found in rs and rfd may be justified by their small
p.u. values and estimating more than one parameter at the same time in addition to
inaccurate adjustment of the function tolerance in algorithm. Therefore further
work is suggested.
5.2 Further Work
Further work needs to be done in order to limit the significant deviation in
estimated rs and rfd by including the effect of saturation and adjusting the function
tolerance of the proposed method in addition to adjusting the max/min bounds of
the parameters. Other models in power plant, such as AVR and excitation systems,
are linked to the synchronous generators and it is worth to estimate their parameters
in a future work.
Synchronous Generator Parameter Identification from Measurement Data
65
REFERENCES
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on Power Apparatus and Systems, Vol.PAS-100, No. 2, February 1981.
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Simond J.J., Xuan Mai Tu, Schwery A. and Regli P.; “Fully Automated
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Hydropower & Dams 2003, Croatia.
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Ramirez C., Xuan M.Tu., Simond J.J, Schafer D. and Stephan C. –E.;
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Xuan M.Tu., Ramirez C., Kawakabani B. and Simond J.J; “Automatic
Determination of Laminated Salient-Pole Synchronous Machines
Parameters Based on the Finite Element Method”, LME Publications from
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Electrimacs 1999.
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Identification of the Synchronous Machine Parameters Using Standstill DC
Decay Test”, LME Publications from EPFL, Swiss Federal Institute of
Technology, Lausanne, Switzerland, ICEM 2006.
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Kyriakides E. and Heydt G. T.; “An Observer for the Estimation of
Synchronous Generator Damper Currents for Use in Parameter
Identification”, IEEE Transactions on Energy Conversion, Vol.18, No.1,
pp.175-177, March 2003.
[21]
Kyriakides E., Heydt G. T. and Vittal V. ; “On-Line Estimation for
Synchronous Generator Parameters Using a Damper Current Observer and a
Graphical User Interface”, IEEE Transactions on Energy Conversion,
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[22]
Nizam, I.; “Synchronous Generator Parameters Identification from
Measurement Data”, MSc. Thesis submitted to the University of
Manchester, 2008, pp 20-44.
[23]
Makela, O.; ” Parameter Estimation For a Synchronous Machine”, MSc.
Thesis submitted to Helsinki University of Technology in Malaysia, 2007,
pp 1-2.
[24]
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Testing”, IEEE Task Force on Generator Model Validation Testing of the
Power System Stability Subcommittee.
[25]
P. Pourbeik, “Automated Parameter Derivation for Power Plant Models
Based on Staged Tests”, IEEE.
[26]
P. Pourbeik, “Automated Parameter Derivation for Power Plant Models
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[27]
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Milanovic. J. V., “MSc Course Notes on Power System Dynamics, Chapter 2”,
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[34]
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Synchronous Generator Parameter Identification from Measurement Data
69
APPENDICES
APPENDICES
Appendix A. M-file for complete synchronous machine simulation
w=1; % angular speed in p.u
we=2*pi*60;
wb=2*pi*60;
Po=2; % number of poles
% Parameters of the machine
rs=0.0046; %r
Xls=0.16; % lq and ld
Xq=1.72; % LAQ+0.16
Xd=1.80; % LAD+0.16
rfd=9.722E-4; % rF
Xlfd=0.11791; % lF
rQ2=0.01632; % rQ (0 for salient pole machine)
rD=0.0125; % rD
XlQ2=0.033; % lQ (inf for salient pole machine)
XlD=0.121; % lD
XlQ1=0.4185; % lG
rQ1=0.01071; % rG
Xmq=Xq-Xls;
Xmd=Xd-Xls;
% Calculate Initial Conditions of the machine
Im=1;
Vm=1;
lang=-acos(0.85);
Ea=1+(rs+j*Xq)*Im*(cos(lang)+j*sin(lang));
eang=angle(Ea);
t=0;
c=wb*t+eang;
Vabc=[Vm*cos(wb*t);Vm*cos(wb*t-2*pi/3);Vm*cos(wb*t+2*pi/3)];
Iabc=[Im*cos(wb*t+lang);Im*cos(wb*t2*pi/3+lang);Im*cos(wb*t+2*pi/3+lang)];
P=2/3*[1/2 1/2 1/2; cos(c) cos(c-120*pi/180) cos(c+120*pi/180);
sin(c) sin(c-120*pi/180) sin(c+120*pi/180)];
Voqd=P*Vabc;
Ioqd=P*Iabc;
% Steady State Conditions (p 218)
vd=Voqd(3);
vq=Voqd(2);
io=Ioqd(1);
iq=Ioqd(2);
id=Ioqd(3);
Exfd=abs(Ea)+(Xd-Xq)*id;
vfd=Exfd*rfd/Xmd;
ifd=Exfd/Xmd;
fq=-Xls*iq+Xmq*(-iq); % state 1 --> x(1)
fd=-Xls*id+Xmd*(-id+ifd); % state 2 --> x(2)
fo=-Xls*io; % state 3 --> x(3)
fQ1=Xmq*(-iq); % state 4 --> x(4)
fQ2=Xmq*(-iq); % state 5 --> x(5)
ffd=Xlfd*ifd+Xmd*(-id+ifd); % state 6 --> x(6)
fD=Xmd*(-id+ifd); % state 7 --> x(7)
Te=fd*iq-fq*id; % Initial Electrical Torque
wb=2*pi*60;
Tm=Te;
H=5.6;
dt=0.0004;
Synchronous Generator Parameter Identification from Measurement Data
70
APPENDICES
Appendix B. List of the experimental data that have been used for the simulation
and estimation
Time
0
0.0004
0.0008
0.0012
0.0016
0.002
0.0024
0.0028
0.0032
0.0036
0.004
0.0044
0.0048
0.0052
0.0056
0.006
0.0064
0.0068
0.0072
0.0076
0.008
0.0084
0.0088
0.0092
0.0096
0.01
0.0104
0.0108
0.0112
0.0116
0.012
0.0124
0.0128
0.0132
0.0136
0.014
0.0144
0.0148
0.0152
0.0156
0.016
0.0164
0.0168
0.0172
0.0176
0.018
Simulated Data from Synchronous Generator Model
Va
Vb
Vc
Wr
Efd
Ia
Ib
Ic
-0.738
-0.569
-0.385
-0.2
-0.041
0.0816
0.1697
0.2287
0.2651
0.2871
0.299
0.2981
0.2891
0.2751
0.2476
0.2029
0.1418
0.066
-0.02
-0.112
-0.208
-0.306
-0.404
-0.499
-0.584
-0.658
-0.719
-0.765
-0.794
-0.807
-0.803
-0.78
-0.739
-0.682
-0.611
-0.527
-0.429
-0.318
-0.198
-0.072
0.0562
0.1825
0.3053
0.4222
0.5305
0.6263
-0.738
-0.601
-0.491
-0.403
-0.326
-0.253
-0.187
-0.13
-0.082
-0.044
-0.013
0.0132
0.034
0.0483
0.0773
0.131
0.2008
0.2794
0.3593
0.4349
0.5022
0.5562
0.5952
0.6181
0.6232
0.6097
0.5774
0.525
0.4533
0.3656
0.2655
0.1571
0.0422
-0.076
-0.194
-0.309
-0.418
-0.521
-0.616
-0.698
-0.764
-0.813
-0.844
-0.856
-0.849
-0.824
-0.74
-0.6
-0.5
-0.43
-0.37
-0.31
-0.26
-0.21
-0.17
-0.13
-0.1
-0.07
-0.05
-0.03
-0.02
-0.03
-0.06
-0.08
-0.1
-0.11
-0.11
-0.09
-0.06
-0.01
0.043
0.112
0.192
0.279
0.371
0.463
0.552
0.631
0.698
0.754
0.798
0.829
0.841
0.834
0.807
0.76
0.695
0.615
0.52
0.415
0.301
0.181
-0.68
7.195
26.09
52.61
83.95
117.8
152.4
186.3
218.4
248.2
275.1
299
319.6
337.2
351.7
363.6
373
380.1
385.4
389.1
391.4
392.6
392.9
392.6
391.8
390.7
389.4
387.9
386.5
385
383.7
382.4
381.3
380.3
379.5
378.8
378.3
377.8
377.5
377.2
377
376.9
376.8
376.8
376.8
376.8
-0.74
-0.54
-0.28
0.006
0.311
0.618
0.915
1.193
1.449
1.677
1.877
2.049
2.196
2.316
2.412
2.487
2.543
2.583
2.61
2.625
2.634
2.636
2.635
2.627
2.614
2.6
2.584
2.566
2.55
2.536
2.524
2.514
2.505
2.496
2.488
2.481
2.476
2.474
2.475
2.475
2.475
2.476
2.477
2.477
2.476
2.476
-0.74
-0.57
-0.4
-0.22
-0.04
0.155
0.376
0.623
0.89
1.17
1.455
1.736
2
2.236
2.437
2.602
2.734
2.833
2.902
2.944
2.961
2.958
2.936
2.895
2.834
2.758
2.667
2.566
2.458
2.351
2.251
2.164
2.096
2.05
2.031
2.041
2.083
2.159
2.265
2.4
2.557
2.726
2.9
3.07
3.229
3.371
-0.74
-0.61
-0.52
-0.46
-0.42
-0.39
-0.37
-0.33
-0.27
-0.18
-0.05
0.133
0.367
0.657
0.997
1.365
1.74
2.108
2.458
2.782
3.076
3.338
3.569
3.768
3.935
4.072
4.176
4.246
4.281
4.281
4.249
4.185
4.089
3.961
3.807
3.632
3.442
3.245
3.047
2.854
2.675
2.519
2.393
2.3
2.245
2.227
Ifd
-0.738
-0.59
-0.458
-0.35
-0.278
-0.257
-0.301
-0.423
-0.625
-0.905
-1.259
-1.678
-2.153
-2.668
-3.205
-3.741
-4.257
-4.739
-5.174
-5.558
-5.889
-6.168
-6.394
-6.566
-6.689
-6.762
-6.784
-6.763
-6.706
-6.614
-6.491
-6.343
-6.178
-6.005
-5.833
-5.672
-5.526
-5.402
-5.309
-5.249
-5.227
-5.242
-5.292
-5.375
-5.486
-5.617
-0.74
-0.56
-0.35
-0.13
0.09
0.318
0.554
0.794
1.038
1.29
1.55
1.818
2.096
2.381
2.671
2.957
3.227
3.474
3.69
3.866
3.996
4.077
4.103
4.075
3.993
3.86
3.676
3.443
3.167
2.852
2.509
2.144
1.766
1.385
1.011
0.65
0.31
0.001
-0.27
-0.5
-0.68
-0.81
-0.89
-0.91
-0.88
-0.78
Synchronous Generator Parameter Identification from Measurement Data
71
APPENDICES
0.0184
0.0188
0.0192
0.0196
0.02
0.0204
0.0208
0.0212
0.0216
0.022
0.0224
0.0228
0.0232
0.0236
0.024
0.0244
0.0248
0.0252
0.0256
0.026
0.0264
0.0268
0.0272
0.0276
0.028
0.0284
0.0288
0.0292
0.0296
0.03
0.0304
0.0308
0.0312
0.0316
0.032
0.0324
0.0328
0.0332
0.0336
0.034
0.0344
0.0348
0.0352
0.0356
0.036
0.0364
0.0368
0.0372
0.0376
0.038
0.0384
0.0388
0.7073
0.7724
0.8206
0.8516
0.8645
0.8568
0.8282
0.779
0.7101
0.6246
0.527
0.4179
0.2989
0.1732
0.0444
-0.086
-0.215
-0.339
-0.454
-0.557
-0.646
-0.724
-0.787
-0.834
-0.86
-0.865
-0.85
-0.815
-0.762
-0.691
-0.608
-0.512
-0.404
-0.286
-0.161
-0.031
0.1021
0.2325
0.359
0.4769
0.5833
0.6773
0.7555
0.8159
0.8562
0.8751
0.874
0.8545
0.8191
0.7658
0.6942
0.6065
-0.78
-0.717
-0.637
-0.541
-0.432
-0.311
-0.182
-0.048
0.0874
0.2193
0.3456
0.464
0.5723
0.6653
0.7404
0.7972
0.8368
0.8604
0.8659
0.8526
0.821
0.7699
0.7008
0.6153
0.517
0.4078
0.2906
0.1668
0.0387
-0.091
-0.221
-0.348
-0.466
-0.573
-0.668
-0.748
-0.811
-0.855
-0.879
-0.882
-0.864
-0.826
-0.77
-0.698
-0.613
-0.513
-0.402
-0.28
-0.15
-0.018
0.1156
0.247
0.054
-0.07
-0.2
-0.32
-0.43
-0.54
-0.64
-0.72
-0.78
-0.83
-0.86
-0.86
-0.85
-0.82
-0.77
-0.71
-0.63
-0.53
-0.42
-0.3
-0.18
-0.05
0.082
0.21
0.333
0.449
0.552
0.642
0.718
0.777
0.818
0.842
0.847
0.834
0.802
0.752
0.685
0.601
0.504
0.394
0.274
0.148
0.015
-0.12
-0.25
-0.37
-0.48
-0.59
-0.68
-0.76
-0.82
-0.86
376.8
376.8
376.9
376.9
376.9
376.9
376.9
376.9
376.8
376.8
376.7
376.7
376.6
376.6
376.5
376.5
376.5
376.4
376.4
376.4
376.4
376.4
376.4
376.4
376.4
376.5
376.5
376.6
376.6
376.7
376.7
376.8
376.9
376.9
377
377.1
377.1
377.1
377.2
377.2
377.2
377.2
377.2
377.2
377.1
377.1
377
377
376.9
376.8
376.8
376.7
2.477
2.477
2.48
2.484
2.486
2.491
2.494
2.496
2.496
2.496
2.496
2.496
2.496
2.496
2.496
2.495
2.49
2.485
2.481
2.477
2.472
2.467
2.462
2.458
2.454
2.451
2.449
2.448
2.449
2.452
2.456
2.458
2.459
2.46
2.464
2.468
2.472
2.476
2.478
2.478
2.476
2.472
2.471
2.471
2.474
2.479
2.48
2.481
2.485
2.487
2.489
2.49
3.492
3.589
3.657
3.695
3.702
3.683
3.641
3.577
3.496
3.403
3.301
3.198
3.096
2.995
2.896
2.799
2.703
2.609
2.516
2.42
2.321
2.222
2.119
2.012
1.906
1.803
1.71
1.633
1.574
1.538
1.53
1.553
1.606
1.689
1.798
1.929
2.079
2.241
2.408
2.574
2.734
2.88
3.006
3.108
3.18
3.223
3.24
3.23
3.198
3.148
3.085
3.01
2.243
2.292
2.37
2.47
2.588
2.716
2.848
2.978
3.103
3.218
3.322
3.413
3.491
3.559
3.618
3.668
3.711
3.748
3.78
3.808
3.831
3.847
3.854
3.851
3.834
3.798
3.741
3.659
3.552
3.424
3.276
3.109
2.931
2.748
2.568
2.398
2.244
2.113
2.008
1.929
1.883
1.87
1.888
1.936
2.009
2.102
2.211
2.328
2.452
2.574
2.688
2.794
-5.759
-5.905
-6.051
-6.19
-6.315
-6.422
-6.506
-6.57
-6.611
-6.632
-6.632
-6.615
-6.584
-6.543
-6.496
-6.442
-6.385
-6.327
-6.268
-6.203
-6.129
-6.045
-5.952
-5.845
-5.725
-5.592
-5.449
-5.298
-5.142
-4.988
-4.84
-4.703
-4.583
-4.487
-4.418
-4.379
-4.373
-4.4
-4.46
-4.55
-4.661
-4.789
-4.926
-5.066
-5.204
-5.334
-5.45
-5.549
-5.63
-5.693
-5.739
-5.769
-0.64
-0.45
-0.21
0.061
0.365
0.691
1.035
1.389
1.745
2.093
2.426
2.74
3.026
3.277
3.486
3.648
3.761
3.824
3.835
3.795
3.706
3.569
3.388
3.163
2.904
2.617
2.308
1.981
1.646
1.313
0.989
0.681
0.393
0.132
-0.1
-0.29
-0.43
-0.53
-0.59
-0.59
-0.55
-0.46
-0.33
-0.16
0.053
0.297
0.566
0.854
1.154
1.463
1.772
2.072
Synchronous Generator Parameter Identification from Measurement Data
72
APPENDICES
0.0392
0.0396
0.04
0.0404
0.0408
0.0412
0.0416
0.042
0.0424
0.0428
0.0432
0.0436
0.044
0.0444
0.0448
0.0452
0.0456
0.046
0.0464
0.0468
0.0472
0.0476
0.048
0.0484
0.0488
0.0492
0.0496
0.05
0.0504
0.0508
0.0512
0.0516
0.052
0.0524
0.0528
0.0532
0.0536
0.054
0.0544
0.0548
0.0552
0.0556
0.056
0.0564
0.0568
0.0572
0.0576
0.058
0.0584
0.0588
0.0592
0.0596
0.5026
0.3859
0.259
0.1271
-0.007
-0.14
-0.27
-0.394
-0.508
-0.61
-0.697
-0.767
-0.818
-0.855
-0.874
-0.873
-0.852
-0.811
-0.751
-0.673
-0.581
-0.478
-0.365
-0.241
-0.109
0.0267
0.1605
0.2884
0.4089
0.5209
0.6215
0.7082
0.777
0.8266
0.8572
0.867
0.8578
0.831
0.7863
0.7228
0.6438
0.5517
0.4469
0.3316
0.2084
0.0783
-0.055
-0.187
-0.316
-0.439
-0.552
-0.654
0.3728
0.4899
0.5959
0.6869
0.7619
0.8192
0.8566
0.8745
0.8727
0.851
0.8109
0.754
0.6804
0.5912
0.4883
0.3742
0.2521
0.1237
-0.008
-0.138
-0.265
-0.384
-0.494
-0.596
-0.685
-0.76
-0.814
-0.85
-0.865
-0.86
-0.836
-0.793
-0.731
-0.653
-0.557
-0.449
-0.334
-0.214
-0.091
0.035
0.1608
0.2837
0.4016
0.5118
0.6117
0.6999
0.7739
0.8286
0.8603
0.8717
0.8625
0.833
-0.89
-0.89
-0.87
-0.83
-0.77
-0.7
-0.61
-0.51
-0.4
-0.28
-0.15
-0.01
0.119
0.247
0.368
0.479
0.579
0.665
0.735
0.789
0.825
0.841
0.839
0.818
0.781
0.725
0.651
0.559
0.451
0.336
0.216
0.091
-0.04
-0.17
-0.29
-0.41
-0.52
-0.62
-0.71
-0.78
-0.83
-0.87
-0.88
-0.87
-0.84
-0.8
-0.74
-0.66
-0.57
-0.46
-0.34
-0.22
376.6
376.6
376.5
376.4
376.4
376.3
376.3
376.3
376.2
376.2
376.2
376.2
376.2
376.3
376.3
376.3
376.4
376.4
376.5
376.5
376.6
376.7
376.7
376.8
376.8
376.9
376.9
377
377
377
377
377
377
377
377
376.9
376.9
376.8
376.8
376.7
376.7
376.6
376.5
376.5
376.4
376.4
376.3
376.3
376.2
376.2
376.2
376.2
2.492
2.494
2.495
2.496
2.495
2.494
2.493
2.493
2.493
2.492
2.489
2.486
2.483
2.481
2.482
2.483
2.482
2.48
2.478
2.476
2.475
2.477
2.48
2.482
2.485
2.489
2.493
2.498
2.502
2.506
2.508
2.508
2.508
2.507
2.504
2.503
2.503
2.505
2.507
2.509
2.51
2.514
2.519
2.52
2.519
2.517
2.513
2.508
2.505
2.505
2.505
2.505
2.928
2.84
2.748
2.654
2.56
2.469
2.376
2.281
2.186
2.09
1.99
1.889
1.784
1.678
1.573
1.476
1.39
1.319
1.268
1.241
1.24
1.265
1.319
1.399
1.506
1.635
1.78
1.933
2.091
2.246
2.394
2.526
2.64
2.732
2.801
2.843
2.86
2.854
2.825
2.778
2.723
2.658
2.584
2.504
2.421
2.335
2.246
2.158
2.067
1.972
1.873
1.771
2.891
2.977
3.054
3.123
3.184
3.236
3.284
3.326
3.364
3.399
3.428
3.448
3.46
3.459
3.44
3.401
3.339
3.254
3.15
3.026
2.883
2.724
2.558
2.387
2.218
2.058
1.913
1.786
1.684
1.613
1.571
1.559
1.576
1.621
1.69
1.777
1.877
1.985
2.096
2.206
2.314
2.417
2.511
2.596
2.675
2.747
2.811
2.87
2.925
2.975
3.018
3.053
-5.782
-5.783
-5.771
-5.75
-5.72
-5.683
-5.641
-5.593
-5.539
-5.475
-5.401
-5.319
-5.226
-5.119
-4.997
-4.859
-4.712
-4.559
-4.402
-4.249
-4.104
-3.973
-3.861
-3.772
-3.711
-3.682
-3.683
-3.713
-3.771
-3.855
-3.96
-4.081
-4.208
-4.341
-4.473
-4.598
-4.71
-4.809
-4.893
-4.958
-5.007
-5.04
-5.061
-5.07
-5.068
-5.054
-5.03
-5
-4.964
-4.921
-4.868
-4.805
2.357
2.622
2.862
3.069
3.241
3.374
3.465
3.509
3.507
3.461
3.372
3.243
3.079
2.882
2.654
2.4
2.126
1.84
1.548
1.26
0.979
0.712
0.465
0.245
0.056
-0.1
-0.21
-0.29
-0.33
-0.32
-0.27
-0.17
-0.04
0.121
0.313
0.531
0.769
1.025
1.291
1.559
1.823
2.078
2.316
2.534
2.728
2.894
3.031
3.132
3.199
3.225
3.212
3.16
Synchronous Generator Parameter Identification from Measurement Data
73
APPENDICES
0.06
0.0604
0.0608
0.0612
0.0616
0.062
0.0624
0.0628
0.0632
0.0636
0.064
0.0644
0.0648
0.0652
0.0656
0.066
0.0664
0.0668
0.0672
0.0676
0.068
0.0684
0.0688
0.0692
0.0696
0.07
0.0704
0.0708
0.0712
0.0716
0.072
0.0724
0.0728
0.0732
0.0736
0.074
0.0744
0.0748
0.0752
0.0756
0.076
0.0764
0.0768
0.0772
0.0776
0.078
0.0784
0.0788
0.0792
0.0796
0.08
0.0804
-0.74
-0.807
-0.856
-0.885
-0.895
-0.884
-0.853
-0.804
-0.737
-0.652
-0.554
-0.445
-0.327
-0.204
-0.073
0.0623
0.1969
0.3248
0.4428
0.5498
0.6453
0.7254
0.7859
0.8265
0.8492
0.8548
0.8427
0.812
0.7631
0.6966
0.6148
0.5181
0.4089
0.2899
0.1635
0.0339
-0.095
-0.223
-0.345
-0.458
-0.562
-0.653
-0.731
-0.793
-0.837
-0.862
-0.866
-0.849
-0.812
-0.757
-0.685
-0.598
0.7855
0.723
0.6455
0.5521
0.4458
0.3295
0.2057
0.0764
-0.056
-0.188
-0.316
-0.439
-0.549
-0.646
-0.729
-0.794
-0.841
-0.868
-0.875
-0.862
-0.829
-0.778
-0.71
-0.629
-0.534
-0.427
-0.311
-0.186
-0.056
0.0756
0.2061
0.3323
0.4507
0.5584
0.6543
0.7351
0.7982
0.8448
0.8741
0.8829
0.8711
0.8392
0.7882
0.7208
0.6359
0.5361
0.4264
0.3075
0.1829
0.0548
-0.077
-0.21
-0.09
0.045
0.177
0.306
0.426
0.534
0.63
0.711
0.776
0.823
0.854
0.865
0.857
0.826
0.775
0.706
0.62
0.521
0.414
0.3
0.179
0.053
-0.07
-0.2
-0.32
-0.43
-0.54
-0.63
-0.71
-0.78
-0.83
-0.86
-0.86
-0.86
-0.83
-0.78
-0.71
-0.62
-0.52
-0.41
-0.29
-0.16
-0.03
0.102
0.232
0.356
0.47
0.574
0.665
0.741
0.8
0.84
376.2
376.2
376.2
376.2
376.3
376.3
376.3
376.4
376.4
376.5
376.5
376.6
376.6
376.7
376.7
376.8
376.8
376.8
376.9
376.9
376.9
376.9
376.9
376.8
376.8
376.8
376.7
376.7
376.7
376.6
376.6
376.5
376.5
376.4
376.4
376.3
376.3
376.3
376.2
376.2
376.2
376.2
376.2
376.2
376.2
376.2
376.2
376.3
376.3
376.4
376.4
376.5
2.504
2.503
2.504
2.505
2.505
2.503
2.502
2.501
2.503
2.506
2.507
2.506
2.506
2.506
2.504
2.504
2.505
2.507
2.506
2.505
2.503
2.501
2.497
2.493
2.49
2.486
2.484
2.484
2.485
2.486
2.486
2.488
2.491
2.493
2.494
2.493
2.493
2.494
2.497
2.497
2.496
2.495
2.493
2.491
2.488
2.484
2.48
2.476
2.473
2.471
2.47
2.469
1.667
1.564
1.46
1.354
1.253
1.161
1.082
1.021
0.981
0.963
0.97
1.001
1.061
1.145
1.252
1.379
1.518
1.665
1.816
1.962
2.099
2.225
2.333
2.42
2.486
2.53
2.551
2.548
2.523
2.482
2.428
2.366
2.298
2.225
2.147
2.063
1.976
1.888
1.794
1.696
1.596
1.492
1.385
1.278
1.169
1.062
0.96
0.869
0.793
0.734
0.696
0.679
3.081
3.1
3.107
3.1
3.076
3.035
2.973
2.89
2.786
2.664
2.526
2.375
2.212
2.048
1.888
1.737
1.602
1.488
1.397
1.334
1.297
1.288
1.307
1.351
1.415
1.494
1.585
1.686
1.792
1.899
2.003
2.103
2.2
2.291
2.375
2.451
2.519
2.582
2.638
2.69
2.736
2.776
2.808
2.83
2.837
2.825
2.792
2.739
2.666
2.573
2.464
2.339
-4.73
-4.644
-4.545
-4.434
-4.312
-4.18
-4.039
-3.891
-3.743
-3.597
-3.46
-3.338
-3.238
-3.161
-3.112
-3.092
-3.101
-3.135
-3.197
-3.282
-3.385
-3.501
-3.628
-3.759
-3.891
-4.016
-4.131
-4.233
-4.318
-4.389
-4.441
-4.474
-4.493
-4.501
-4.496
-4.481
-4.458
-4.425
-4.386
-4.34
-4.284
-4.217
-4.141
-4.053
-3.955
-3.846
-3.724
-3.592
-3.454
-3.314
-3.175
-3.041
3.07
2.946
2.792
2.61
2.404
2.181
1.944
1.696
1.445
1.198
0.959
0.733
0.525
0.341
0.184
0.056
-0.04
-0.1
-0.12
-0.11
-0.06
0.025
0.139
0.284
0.456
0.649
0.858
1.081
1.312
1.547
1.779
2.001
2.208
2.399
2.567
2.71
2.823
2.903
2.951
2.966
2.946
2.895
2.815
2.706
2.572
2.412
2.231
2.033
1.823
1.607
1.391
1.18
Synchronous Generator Parameter Identification from Measurement Data
74
APPENDICES
0.0808
0.0812
0.0816
0.082
0.0824
0.0828
0.0832
0.0836
0.084
0.0844
0.0848
0.0852
0.0856
0.086
0.0864
0.0868
0.0872
0.0876
0.088
0.0884
0.0888
0.0892
0.0896
0.09
0.0904
0.0908
0.0912
0.0916
0.092
0.0924
0.0928
0.0932
0.0936
0.094
0.0944
0.0948
0.0952
0.0956
0.096
0.0964
0.0968
0.0972
0.0976
0.098
0.0984
0.0988
0.0992
0.0996
0.1
0.1004
0.1008
0.1012
-0.498
-0.387
-0.266
-0.139
-0.009
0.1223
0.2498
0.3708
0.4836
0.5852
0.6754
0.7508
0.8081
0.8463
0.8643
0.8624
0.8416
0.8039
0.7491
0.6759
0.5884
0.4899
0.3801
0.2591
0.1305
-0.001
-0.133
-0.261
-0.383
-0.495
-0.598
-0.688
-0.764
-0.823
-0.863
-0.883
-0.886
-0.87
-0.831
-0.773
-0.697
-0.604
-0.497
-0.379
-0.255
-0.126
0.0074
0.1414
0.2717
0.3943
0.507
0.6083
-0.339
-0.459
-0.567
-0.66
-0.739
-0.8
-0.845
-0.872
-0.879
-0.865
-0.831
-0.778
-0.707
-0.621
-0.521
-0.409
-0.286
-0.156
-0.022
0.113
0.245
0.3718
0.4907
0.5985
0.6933
0.7719
0.8316
0.8732
0.8947
0.8947
0.8748
0.8356
0.7786
0.7055
0.6167
0.5126
0.3967
0.2709
0.1386
0.0049
-0.128
-0.256
-0.376
-0.485
-0.583
-0.669
-0.738
-0.793
-0.832
-0.85
-0.847
-0.825
0.861
0.864
0.849
0.816
0.765
0.699
0.617
0.52
0.409
0.289
0.161
0.029
-0.1
-0.23
-0.35
-0.47
-0.57
-0.66
-0.74
-0.8
-0.84
-0.86
-0.86
-0.84
-0.8
-0.74
-0.66
-0.57
-0.47
-0.35
-0.23
-0.1
0.036
0.168
0.295
0.414
0.521
0.616
0.696
0.763
0.814
0.849
0.868
0.868
0.847
0.808
0.75
0.674
0.582
0.476
0.359
0.234
376.5
376.6
376.6
376.7
376.7
376.7
376.8
376.8
376.8
376.8
376.8
376.8
376.8
376.8
376.8
376.7
376.7
376.7
376.6
376.6
376.5
376.5
376.5
376.4
376.4
376.3
376.3
376.3
376.3
376.2
376.2
376.2
376.2
376.2
376.2
376.3
376.3
376.3
376.4
376.4
376.4
376.5
376.5
376.5
376.6
376.6
376.7
376.7
376.7
376.7
376.7
376.7
2.469
2.469
2.472
2.475
2.478
2.481
2.483
2.482
2.478
2.471
2.465
2.46
2.456
2.453
2.451
2.449
2.449
2.452
2.457
2.464
2.47
2.475
2.478
2.48
2.479
2.477
2.477
2.476
2.476
2.477
2.48
2.484
2.484
2.483
2.482
2.482
2.482
2.483
2.485
2.487
2.487
2.487
2.486
2.485
2.486
2.487
2.488
2.488
2.488
2.488
2.486
2.483
0.69
0.728
0.792
0.881
0.991
1.117
1.254
1.401
1.547
1.687
1.818
1.935
2.036
2.117
2.18
2.221
2.242
2.242
2.223
2.189
2.141
2.081
2.014
1.941
1.865
1.785
1.704
1.618
1.526
1.431
1.333
1.234
1.134
1.032
0.929
0.83
0.739
0.658
0.59
0.538
0.506
0.498
0.515
0.557
0.622
0.709
0.815
0.937
1.071
1.209
1.348
1.483
2.2
2.051
1.897
1.744
1.594
1.454
1.33
1.225
1.144
1.088
1.057
1.052
1.071
1.113
1.172
1.245
1.332
1.427
1.528
1.629
1.73
1.828
1.922
2.011
2.094
2.17
2.24
2.303
2.358
2.41
2.456
2.494
2.524
2.543
2.549
2.538
2.507
2.457
2.389
2.304
2.201
2.08
1.945
1.801
1.652
1.505
1.364
1.234
1.119
1.022
0.945
0.889
-2.917
-2.809
-2.721
-2.654
-2.613
-2.597
-2.606
-2.642
-2.703
-2.785
-2.885
-2.997
-3.117
-3.24
-3.36
-3.475
-3.581
-3.675
-3.755
-3.82
-3.871
-3.911
-3.938
-3.954
-3.959
-3.954
-3.938
-3.911
-3.874
-3.828
-3.774
-3.71
-3.633
-3.543
-3.442
-3.331
-3.209
-3.079
-2.947
-2.814
-2.686
-2.566
-2.457
-2.363
-2.284
-2.226
-2.19
-2.176
-2.188
-2.226
-2.287
-2.368
0.978
0.789
0.614
0.46
0.331
0.23
0.159
0.119
0.11
0.133
0.185
0.266
0.372
0.503
0.653
0.821
1.002
1.193
1.388
1.586
1.782
1.972
2.149
2.31
2.452
2.573
2.668
2.734
2.773
2.781
2.76
2.709
2.629
2.523
2.396
2.25
2.087
1.912
1.728
1.54
1.352
1.171
0.995
0.829
0.678
0.545
0.434
0.348
0.291
0.262
0.261
0.286
Synchronous Generator Parameter Identification from Measurement Data
75
APPENDICES
0.1016
0.102
0.1024
0.1028
0.1032
0.1036
0.104
0.1044
0.1048
0.1052
0.1056
0.106
0.1064
0.1068
0.1072
0.1076
0.108
0.1084
0.1088
0.1092
0.1096
0.11
0.1104
0.1108
0.1112
0.1116
0.112
0.1124
0.1128
0.1132
0.1136
0.114
0.1144
0.1148
0.1152
0.1156
0.116
0.1164
0.1168
0.1172
0.1176
0.118
0.1184
0.1188
0.1192
0.1196
0.12
0.1204
0.1208
0.1212
0.1216
0.122
0.6961
0.7677
0.821
0.8576
0.8733
0.8695
0.8478
0.8073
0.7466
0.6669
0.5715
0.4638
0.3446
0.2175
0.0852
-0.049
-0.18
-0.307
-0.424
-0.531
-0.626
-0.708
-0.776
-0.827
-0.86
-0.872
-0.864
-0.836
-0.787
-0.721
-0.637
-0.537
-0.426
-0.306
-0.182
-0.052
0.0777
0.2047
0.3256
0.4397
0.5464
0.6417
0.7225
0.7844
0.828
0.8519
0.8537
0.8363
0.8008
0.7484
0.681
0.6
-0.785
-0.727
-0.651
-0.562
-0.459
-0.346
-0.225
-0.099
0.028
0.1519
0.2713
0.3848
0.4895
0.5824
0.663
0.7286
0.778
0.8116
0.8276
0.8246
0.8021
0.7591
0.6974
0.6209
0.5321
0.4309
0.3167
0.1935
0.0662
-0.063
-0.192
-0.316
-0.435
-0.545
-0.644
-0.73
-0.798
-0.847
-0.877
-0.886
-0.874
-0.841
-0.79
-0.721
-0.634
-0.531
-0.415
-0.289
-0.157
-0.025
0.1049
0.2317
0.103
-0.03
-0.16
-0.29
-0.41
-0.52
-0.62
-0.71
-0.78
-0.84
-0.87
-0.87
-0.86
-0.84
-0.79
-0.72
-0.65
-0.55
-0.45
-0.33
-0.21
-0.08
0.057
0.187
0.312
0.43
0.541
0.639
0.722
0.789
0.838
0.869
0.881
0.874
0.852
0.811
0.747
0.664
0.565
0.452
0.328
0.197
0.065
-0.07
-0.2
-0.32
-0.44
-0.54
-0.64
-0.71
-0.77
-0.82
376.7
376.7
376.7
376.7
376.7
376.7
376.7
376.6
376.6
376.6
376.5
376.5
376.5
376.4
376.4
376.4
376.4
376.3
376.3
376.3
376.3
376.3
376.3
376.3
376.3
376.3
376.3
376.4
376.4
376.4
376.5
376.5
376.5
376.6
376.6
376.6
376.7
376.7
376.7
376.7
376.7
376.7
376.7
376.7
376.7
376.7
376.7
376.7
376.7
376.7
376.6
376.6
2.482
2.482
2.483
2.486
2.487
2.488
2.487
2.487
2.487
2.487
2.487
2.489
2.492
2.496
2.498
2.497
2.496
2.495
2.491
2.486
2.481
2.477
2.476
2.475
2.473
2.472
2.47
2.469
2.469
2.469
2.47
2.469
2.465
2.461
2.459
2.46
2.461
2.463
2.464
2.466
2.468
2.47
2.47
2.471
2.47
2.47
2.472
2.476
2.482
2.487
2.49
2.489
1.606
1.716
1.811
1.888
1.945
1.984
2.004
2.007
1.991
1.961
1.919
1.867
1.805
1.734
1.659
1.58
1.496
1.405
1.309
1.209
1.107
1.006
0.903
0.803
0.708
0.619
0.538
0.466
0.408
0.369
0.353
0.357
0.381
0.427
0.495
0.582
0.683
0.798
0.922
1.053
1.184
1.312
1.43
1.536
1.628
1.703
1.759
1.795
1.813
1.813
1.799
1.774
0.856
0.85
0.867
0.902
0.956
1.025
1.104
1.193
1.288
1.386
1.485
1.581
1.673
1.763
1.848
1.929
2.003
2.071
2.132
2.186
2.232
2.269
2.294
2.305
2.303
2.286
2.253
2.2
2.127
2.041
1.939
1.822
1.693
1.558
1.421
1.283
1.15
1.027
0.919
0.83
0.764
0.719
0.696
0.692
0.71
0.747
0.802
0.87
0.95
1.037
1.129
1.226
-2.466
-2.577
-2.692
-2.81
-2.923
-3.03
-3.132
-3.223
-3.301
-3.366
-3.42
-3.461
-3.492
-3.511
-3.519
-3.518
-3.506
-3.482
-3.447
-3.401
-3.345
-3.279
-3.201
-3.11
-3.005
-2.893
-2.772
-2.646
-2.515
-2.385
-2.261
-2.144
-2.039
-1.949
-1.878
-1.825
-1.792
-1.784
-1.802
-1.844
-1.908
-1.99
-2.086
-2.192
-2.304
-2.421
-2.534
-2.64
-2.739
-2.831
-2.911
-2.978
0.339
0.416
0.515
0.635
0.772
0.922
1.084
1.252
1.424
1.599
1.77
1.929
2.077
2.21
2.325
2.42
2.493
2.542
2.565
2.562
2.533
2.481
2.408
2.313
2.199
2.069
1.927
1.776
1.618
1.455
1.293
1.136
0.987
0.848
0.721
0.613
0.526
0.46
0.419
0.401
0.405
0.431
0.479
0.547
0.635
0.744
0.87
1.006
1.149
1.297
1.447
1.597
Synchronous Generator Parameter Identification from Measurement Data
76
APPENDICES
0.1224
0.1228
0.1232
0.1236
0.124
0.1244
0.1248
0.1252
0.1256
0.126
0.1264
0.1268
0.1272
0.1276
0.128
0.1284
0.1288
0.1292
0.1296
0.13
0.1304
0.1308
0.1312
0.1316
0.132
0.1324
0.1328
0.1332
0.1336
0.134
0.1344
0.1348
0.1352
0.1356
0.136
0.1364
0.1368
0.1372
0.1376
0.138
0.1384
0.1388
0.1392
0.1396
0.14
0.1404
0.1408
0.1412
0.1416
0.142
0.1424
0.1428
0.505
0.3981
0.2822
0.1602
0.0349
-0.091
-0.216
-0.337
-0.45
-0.555
-0.651
-0.732
-0.798
-0.844
-0.869
-0.875
-0.862
-0.829
-0.777
-0.707
-0.62
-0.52
-0.409
-0.291
-0.166
-0.036
0.0932
0.2198
0.3405
0.4532
0.5559
0.6485
0.729
0.7903
0.832
0.8535
0.8546
0.8367
0.8008
0.7469
0.6771
0.592
0.4926
0.3824
0.2633
0.1385
0.0106
-0.119
-0.249
-0.372
-0.485
-0.588
0.3525
0.4662
0.5697
0.6597
0.7346
0.7934
0.8355
0.8588
0.8628
0.8483
0.8162
0.7663
0.6983
0.6129
0.5115
0.3984
0.2769
0.1499
0.0191
-0.111
-0.236
-0.356
-0.469
-0.571
-0.661
-0.735
-0.794
-0.838
-0.865
-0.873
-0.861
-0.828
-0.777
-0.708
-0.623
-0.521
-0.408
-0.284
-0.154
-0.021
0.1123
0.2434
0.3678
0.4832
0.5871
0.6761
0.7481
0.8039
0.8417
0.8599
0.8576
0.8353
-0.85
-0.85
-0.84
-0.81
-0.76
-0.7
-0.61
-0.51
-0.4
-0.28
-0.16
-0.03
0.104
0.233
0.358
0.476
0.584
0.677
0.754
0.812
0.85
0.87
0.873
0.858
0.825
0.774
0.704
0.615
0.513
0.4
0.278
0.148
0.015
-0.12
-0.25
-0.37
-0.49
-0.59
-0.68
-0.75
-0.81
-0.85
-0.87
-0.88
-0.86
-0.82
-0.77
-0.7
-0.61
-0.51
-0.39
-0.27
376.6
376.5
376.5
376.5
376.4
376.4
376.4
376.4
376.4
376.4
376.4
376.4
376.4
376.4
376.4
376.4
376.4
376.4
376.5
376.5
376.5
376.5
376.6
376.6
376.6
376.7
376.7
376.7
376.7
376.8
376.8
376.8
376.8
376.8
376.8
376.8
376.7
376.7
376.7
376.7
376.7
376.6
376.6
376.6
376.6
376.5
376.5
376.5
376.5
376.5
376.5
376.5
2.487
2.486
2.485
2.485
2.484
2.484
2.483
2.482
2.483
2.483
2.484
2.487
2.49
2.491
2.492
2.493
2.493
2.493
2.491
2.488
2.489
2.489
2.488
2.486
2.484
2.481
2.479
2.478
2.476
2.474
2.471
2.467
2.463
2.458
2.454
2.45
2.448
2.445
2.444
2.444
2.445
2.447
2.449
2.45
2.45
2.449
2.449
2.447
2.446
2.445
2.442
2.44
1.737
1.687
1.626
1.556
1.477
1.392
1.301
1.206
1.108
1.007
0.906
0.806
0.706
0.61
0.519
0.436
0.362
0.3
0.252
0.218
0.206
0.216
0.246
0.295
0.364
0.45
0.549
0.661
0.783
0.91
1.036
1.159
1.273
1.374
1.459
1.528
1.581
1.616
1.634
1.636
1.622
1.594
1.549
1.491
1.425
1.353
1.275
1.192
1.106
1.015
0.917
0.816
1.323
1.418
1.508
1.594
1.677
1.755
1.827
1.897
1.96
2.014
2.057
2.087
2.105
2.112
2.103
2.077
2.034
1.971
1.888
1.788
1.675
1.551
1.418
1.279
1.14
1.005
0.879
0.766
0.668
0.589
0.53
0.49
0.473
0.478
0.503
0.549
0.613
0.691
0.781
0.879
0.981
1.085
1.187
1.284
1.378
1.468
1.553
1.63
1.701
1.763
1.817
1.861
-3.035
-3.081
-3.112
-3.129
-3.137
-3.136
-3.125
-3.102
-3.066
-3.02
-2.961
-2.892
-2.81
-2.717
-2.613
-2.501
-2.381
-2.257
-2.131
-2.004
-1.88
-1.767
-1.668
-1.587
-1.526
-1.485
-1.464
-1.468
-1.494
-1.544
-1.611
-1.695
-1.791
-1.895
-2.004
-2.115
-2.226
-2.334
-2.435
-2.525
-2.606
-2.674
-2.728
-2.77
-2.801
-2.818
-2.82
-2.81
-2.789
-2.757
-2.716
-2.664
1.743
1.883
2.013
2.127
2.225
2.304
2.362
2.4
2.418
2.412
2.383
2.333
2.263
2.176
2.075
1.96
1.835
1.702
1.565
1.424
1.283
1.146
1.017
0.898
0.79
0.698
0.624
0.567
0.527
0.51
0.515
0.54
0.581
0.642
0.722
0.818
0.929
1.051
1.181
1.315
1.453
1.59
1.72
1.842
1.952
2.048
2.127
2.19
2.236
2.262
2.268
2.255
Synchronous Generator Parameter Identification from Measurement Data
77
APPENDICES
0.1432
0.1436
0.144
0.1444
0.1448
0.1452
-0.677
-0.751
-0.808
-0.847
-0.868
-0.866
0.7912
0.7271
0.6461
0.5504
0.443
0.3266
-0.14
-0.02
0.113
0.241
0.365
0.478
376.5
376.5
376.5
376.5
376.5
376.5
2.443
2.45
2.457
2.463
2.467
2.471
0.714
0.613
0.513
0.416
0.324
0.242
1.893
1.915
1.924
1.922
1.906
1.875
-2.601
-2.527
-2.444
-2.352
-2.25
-2.139
2.224
2.177
2.114
2.036
1.945
1.841
Synchronous Generator Parameter Identification from Measurement Data
78
Appendix C. M-file for adding noise to the simulated data
% Adding noise to the simulated data
Van=Va+0.05.*randn(length(Va),1);
Vbn=Vb+0.05.*randn(length(Vb),1);
Vcn=Vc+0.05.*randn(length(Vc),1);
Efdn=Efd+0.05.*randn(length(Efd),1);
Wrn=Wr+0.05.*randn(length(Wr),1);
Ian=Ia+0.05.*randn(length(Ia),1);
Ibn=Ib+0.05.*randn(length(Ib),1);
Icn=Ic+0.05.*randn(length(Ic),1);
Ifdn=Ifd+0.05.*randn(length(Ifd),1);