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Estimation of SynchronousGenerator Parameters fromOn-line MeasurementsMohammad Hasan Mosaddeqi, Reza Laali , Mohammad Mehdi Masoudi

Shahed university of Tehran

2 TABLE OF CONTENTSChapter 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

3 TABLE OF CONTENTSChapter 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

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.

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.

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

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.

8 Block diagram of the overall system

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.

10 Representation of a synchronous generator

11 Park’s transformation is definedThe 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

12 Schematic diagram of a synchronous generator

13 Transformed voltages and flux linkages are

Similarly, the transformed voltages and flux linkages are

Equation (2.1) in its expanded form becomes

14 the flux linkage equations forthese windings result in

15 Transformed flux linkages are

16 The mathematical model can bederived as

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.

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).

19 Algorithm for estimator implementation for actual measurements

20 Pictorial of an estimator for synchronous generator parameter identification

21 Concept of an observer for a dynamic system

22 Solving for the several damper currents

23 Observer implementation and parameter identification algorithm

24 Simulated and estimated Q-winding damper currents using transient data

25 STATE ESTIMATIONState 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

26 Example of State EstimationFor 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.

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

28 Distinguishing characteristics of the three candidate models

29 Generator model

Model 2.1 Model 2.2

30 Estimated parameters for the three proposed models for generator FC5HP

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

32 Calculation of standard parametersfrom the estimated derived parameters

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

34 Block diagram for processing measured data

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.

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.

37 The Brushless Exciter Case

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

39 Input-Output Data CollectionThe 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.

40 Simulink model of brushless exciter

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.

42 Parameter Estimation with Nonlinear FunctionsA 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,

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.

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

46 Thank you for Your Attention