The main objective of this research work is to develop a method to identify synchronous generator parameters from on-line measurements. Secondary objectives of the research include • Development of an observer for damper currents • Calculation of the error characteristics of the estimation • Development of an index of confidence • Calculation of a range of values for each estimated parameter • Study of which machine parameters can be estimated, and which can not

1. Estimation of Synchronous
Generator Parameters from
On-line Measurements
Mohammad Hasan Mosaddeqi, Reza Laali , Mohammad Mehdi Masoudi
Shahed university of Tehran
1

2. TABLE OF CONTENTS
Chapter 1
Synchronous generators History
Model History
Objectives
Executive Summary
Chapter 2
Block diagram of the overall system
Park’s transformation
Chapter 3
Estimation Techniques
Parameter Estimation Algorithm
Concept of an observer
STATE ESTIMATION
Example of State Estimation
2

3. TABLE OF CONTENTS
Chapter 3 - Continue
SATURATION OF SYNCHRONOUS GENERATOR INDUCTANCES
Distinguishing characteristics of the three candidate models
Estimated parameters for the three proposed models for generator FC5HP
Calculation of standard parameters
digital fault recorder
processing measured data
Bad Data Rejection
Data Filtering Analysis
The Brushless Exciter Case
Reference
Conclusion
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4. Synchronous generators History
Synchronous generators are the mainstay of electric
power generation in the World.
These machines were invented in the late 1800s and
further refined in the early 1900s.
There is a huge literature of synchronous generators prior to
1930, but the main initial advance in synchronous machine
analysis was the development of Park’s model.
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5. Model History
Park’s model was not the only synchronous machine
model: Jackson and Winchester developed direct and
quadrature axis equivalent circuits for round rotor
synchronous generators.
During the same period, Canay focused on developing
equivalent circuits for field and damper windings to
estimate generator parameters. A significant contribution
was made by Yu and Moussa in 1971 who reported a
systematic procedure that can be implemented to
determine the parameters of the equivalent circuits of
synchronous generators.
5

6. Objectives
The main objective of this research work is to develop a
method to identify synchronous generator parameters
from on-line measurements.
Secondary objectives of the research include
• Development of an observer for damper currents
• Calculation of the error characteristics of the estimation
• Development of an index of confidence
• Calculation of a range of values for each estimated
parameter
• Study of which machine parameters can be estimated,
and which can not
6

7. Executive Summary
The method uses a mathematical tool from state
estimation technology to formulate a minimum squared
error solution. A particular difficulty relates to modeling
magnetic saturation.
Applications of this work include:
Utilization of accurate data and accurate models in
transient stability studies, thus allowing more accurate and
‘safe’ operating practices.
7

8. Block diagram of the overall system8

9. Park’s transformation
Park’s transformation eliminates the time-varying
inductances from the voltage equations.
In the case of the synchronous machine, the time-varying
inductances can be eliminated only if the reference frame
is fixed in the rotor and therefore Park’s transformation will
be used.
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10. Representation of a synchronous
generator
10

11. Park’s transformation is defined
The angle θ is given by
where ωR is the rated (synchronous) angular frequency in
rad/s and δ is the synchronous torque angle in electrical
radians. The transformed currents are
where the current vectors are defined as
11

12. Schematic diagram of a synchronous
generator
12

13. Transformed voltages and flux linkages
are
Similarly, the transformed voltages and flux linkages are
Equation (2.1) in its expanded form becomes
13

14. the flux linkage equations for
these windings result in
14

15. Transformed flux linkages are15

16. The mathematical model can be
derived as
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17. Estimation Techniques
Estimation techniques such as state estimation, least
squares, and maximum likelihood are used in engineering
applications interchangeably.
For the purposes of this research the mathematical model
is desired to be transformed in a form realizable by a state
estimation algorithm.
State estimation is a process during which a number of
unknown system state variables or parameters are
assigned a value based on measurements from that
system.
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18. Parameter Estimation Algorithm
The parameter estimation algorithm was tested using real
data collected from the terminals of a committed
synchronous generator. The machine under consideration
is the cross-compound generator.
Measurements were collected using a digital fault recorder
(DFR). The data were collected at steady state operation,
while the machine served its load. The sampling frequency
was 10 kHz and eight signals were measured: stator line
currents and voltages (Ia, Ib, Ic, Vab, Vbc, Vca), and field
current and voltage (IF, VF).
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19. Algorithm for estimator implementation
for actual measurements
19

20. Pictorial of an estimator for synchronous
generator parameter identification
20

21. Concept of an observer for a dynamic
system
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22. Solving for the several damper currents22

23. Observer implementation and
parameter identification algorithm
23

24. Simulated and estimated Q-winding
damper currents using transient data
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25. STATE ESTIMATION
State estimation is a process during which a number of
unknown system state variables or parameters are
assigned a value based on measurements from that
system.
The system is usually arranged in the form [H][x] = [z],
where H is a matrix of dimensions m× n , x is a vector of
dimension n, and z is a vector of dimension m.
In this notation m is the number of measurements and
n is the number of parameters to be estimated.
Therefore
if H is invertible then
it is not possible to invert H since m ≠ n then
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26. Example of State Estimation
For example, if parameters LAD, LAQ and rF are to be
estimated, the damper current expressions can be
rearranged in the form Hx = z to obtain
In this way, the four unknown parameters and their coefficients are isolated on
the left hand side, and all elements of the right hand side are known.
Moreover, the right hand side reduces to a vector and therefore the system
takes the final form Hx = z.
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27. SATURATION OF SYNCHRONOUS
GENERATOR INDUCTANCES
The main effect of saturation in a synchronous generator is
the decrease of its mutual inductances depending on the
operating level of the generator. Such a decrease may be
considerable as the generator is driven higher into
saturation. Therefore, it is imperative that the effect of
saturation be modeled in the parameter estimation
procedure The effects of saturation are represented as
27

28. Distinguishing characteristics of the
three candidate models
28

29. Generator model
Model 2.1 Model 2.2
29

30. Estimated parameters for the three
proposed models for generator FC5HP
30

31. Calculation of unsaturated parameters from
the estimated parameters of generator
FC5HP
31

32. Calculation of standard parameters
from the estimated derived parameters
32

33. Block diagram of the generator, the data
measurement using a digital fault recorder
(DFR), and the data processing system
33

34. Block diagram for processing
measured data
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35. Bad Data Rejection
Due to measurement errors, high amplitude spikes may
contaminate the recorded signal. These spikes in the signal
may cause filter misoperation.
These spikes are termed as bad data, and have to be
eliminated form the signal. To accomplish this, a maximum
deviation is set for the given signal and the adjacent
samples are compared. If the difference exceeds the
deviation, the latter datum is erased from the data. The
maximum deviation is set by observation and experience
for the particular application.
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36. Data Filtering Analysis
The measurements are taken at a sampling frequency (fS)
of 10 kHz. The data are analyzed in two distinct sets.
The first set is the field quantities that are DC in nature; the
other set is the three-phase ac voltages and currents at 60
Hz. The data records are 0.32 seconds in length.
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37. The Brushless Exciter Case37
A brushless exciter is an alternator-rectifier exciter, as
shown in Fig, and this type of exciter employs rotating
rectifiers with a direct connection to the synchronous
machine field thus eliminating the need for field brushes.

38. Type AC1A-alternator-rectifier
excitation system
38

39. Input-Output Data Collection
The first step in parameter estimation is to collect the input
and output data that are physically measurable in the
actual system. The measurable signals are listed in Table
F.1, where EFD is the exciter output voltage; IFD is the
exciter output current; VR is the regulator output; VFE is the
signal proportional to exciter output current; VF is the
excitation system stabilizer output; VE is the exciter voltage
back of commutating reactance.
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40. Simulink model of brushless exciter40

41. Parameter Estimation With Linear
Function
To determine the parameters of each part (except the rectifier operation
function and the saturation function of the main exciter), the least square
method is employed. The task is to minimize the objective function as follows.
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42. Parameter Estimation with Nonlinear
Functions
A common expression of the saturation function is the
exponential function as,
where a and b are constants.
For the exciter load saturation curve, only values (S1, S2) for
two points (E1, E2) are provided. Based on the two points
given, the following can be obtained,
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43. Estimation result43

44. Conclusion
A method to identify synchronous machine parameters
from on-line measurements is shown. The method is based
on least squares estimation and a simple formula for the
derivative operator.
An observer for identification of the unmeasurable damper
winding currents is also presented. A saturation model was
implemented for the generator inductances.
Parameter estimation results using on-site measured DFR
data show that the machine parameters are estimated
accurately for most parameters of interest.
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45. Reference
E. Kyriakides and G. T. Heydt, “Estimation of synchronous generator parameters
using an observer for damper currents and a graphical user interface” Journal
of Electric Power System Research, Power Systems Engineering Research
Center
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46. Thank you for Your Attention46