ST2A Excitation System Model Validation
Iman Naziri Moghaddam, Zia Salami, Saeed Mohajeryami
University of North Carolina at Charlotte
Technical Report
{inazirim, zsalami, smohajer } @uncc.edu
Abstract— Power Systems are the most complex and critical
infrastructure ever created. Model simplification and order
reduction are widely used among researchers to deal with
nonlinearity and uncertainties of power system components.
Voltage dip and transients are known for their importance in
dynamic studies and as a result of short circuits or starting a
large induction motor, generator excitation systems come into
effect in order to compensate voltage oscillations and voltage
dips during such transients. This report will address model
parameter reduction of generator excitation systems. An
objective function and a simple method for sensitivity analysis
will be proposed to identify which excitation parameters are
more sensitive and have more impact on generator voltage
response. Moreover, the proposed method can be used to
determine which parameters do not have significant effect on
the excitation system. The objective function will stress voltage
dip and overshoot rather than small oscillations and transients.
A small stand-alone micro gird, with three induction motors and
a generator with IEEE ST2A excitation system have been
selected to simulate and verify the method performance.
Index Terms-- Sensitivity Analysis, Model Order Reduction,
Electrical Distribution System (EDS), Excitation System, Micro
Grid and Island Operation.
I.
INTRODUCTION
Dynamic modeling and analysis of the power system to
reflect the actual system responses is one of the features of
simulation software. In general, to have an accurate EDS
model, many parameters and their related data must be
gathered and considered. However, in some parts of a model,
there is no need to have all parameters in order to perform an
accurate simulation. For instance, among all of the generator
excitation system parameters, only several may impact the
generators voltage response behavior.
Designing and locating controllers in large power systems
can be simplified by eigenvalue sensitivity analysis, which
provides important and useful information for optimizing
controller parameters [1]. Traditional methods of eigenvalue
sensitivity in power systems have been proposed in [3], [4].
Various methods of sensitivity analysis and its application
in a broad range of fields are presented in [5].
Located in section II of this paper, the problem statement
is described and some basics related to voltage dips and
transients are discussed. Next, a small scale power system in
island operation (i.e. micro grid) is selected and discussed for
this analysis. Furthermore, in the last part of section II, ST2A
is introduced as an excitation system. In section III, a
sensitivity analysis method for model simplification is
proposed. In section IV, the proposed method is applied to the
system case study and results are discussed. Conclusions and
future work are mentioned in section V.
II.
CONVERTING SCANNED PLOTS TO DIGITAL DATA
Estimating the parameters of a real excitation system is
objective of this report. In this report actual field data is
gathered during a test which were done many years ago.
Therefore, many test responses such as terminal voltage, field
voltage, field current, frequency, active power, and reactive
power are available. However, these graphs like many old
documents are only available in printed hard copy format. In
order to use them in different software, they should be
converted to digital data. This process is commonly known as
“plot digitizing” or “graph digitizing”. Figure 1 shows a
sample data in the mentioned test case.
Sensitivity Analysis could be utilized and useful to find
out how parameters and uncertainties will affect the output,
test the robustness of a model or system, and understand the
relationship between inputs and outputs. Likewise, sensitivity
analysis is useful for model simplification and order reduction
since some parameters, in every system, do not have any
meaningful impact on the outputs.
This paper will address sensitivity analysis to simplify the
model of an exciter and identify which parameters will have
more influence on the output voltage response specifically.
For this study, the IEEE type ST2A excitation system model
and Electrical Transient Analyzer Program (ETAP) as the
simulation software are selected.
Figure 1. Scanned data which require to be digitized
Basically, graph digitizing is an analog to digital
conversion process. There is number of software available to
digitize printed graphs. In earlier versions, operators used a
pen or mouse-like device on a digitization board. By moving
along the curve x,y coordinates of some points of that curve
were extracted. In newer versions, computer programs use
image processing to convert scanned plots to data. Plot
digitizer, Graphclick, Didger, Engauge Digitizer, Data Thief,
many other software are available for converting printed
graphs into data. In this report, we used CurveSnap V1.0
which is C++ based open source software and anyone can
easily find it on the internet. This program takes scanned
image of a plot (JPEG, GIF, and PNG are acceptable) and
after calibration with four coordinates, it accurately digitizes
values of the plot by simple clicking on a point in that plot.
However, during digitizing some practical concerns came into
the consideration. Noise in old printed documents is
inevitable; moreover, most of documents are published in
thick books and it’s difficult to load them perfectly in scanner
and they result in non-orthogonally. Using Adobe Photoshop
in raw images, above-mentioned problems is relatively solved
and scanned images get ready to be digitized.
Another problem with CurveSnap is a sampling rate and
line-following routines. Sampling intervals is known as the
time between successive samples. Likely, sampling rate can be
found by inversing the sampling interval time and it is
expressed by Hz. Basically, in analog to digital conversion, we
need higher sampling rate when rate of change in a signal goes
higher. Typically, each signal can be considered as summation
of its fundamental signals. According to Nyquist sampling
rate:
Min sampling rate> 2 x highest frequency of a signal
Therefore, if a part of signal which includes frequency
more than half of the Nyquist rate, it cannot be correctly
sampled and reconstructed. This failure in sampling for
frequency of higher than a half of Nyquist rate is referred as
aliasing.
Sampling rate in most of digitizing software is fixed and
cannot be adjusted. In CurveSnap sampling time intervals are
0.033 seconds and sampling frequency is 30 Hz. Based on the
Nyquist theory if a part of graphs frequency exceed than 15
Hz, original curve cannot be retrieved and also digitized curve
might include some dents. Ideal frequency-selective filter is a
quite well solution for aforementioned problem in A/D
conversion. In order to implement frequency-selective filter,
frequency selection should be determined based on power
spectral density. However, simple low pass filter can easily
filter the unpleasant imposed signal which is also known as
aliasing.
Figure 2. shows the output of CurveSnap which is the
digitized data of the first 7-second of Figure 1. In section 4,
we will show that system identification process is done by 1motor acceleration (first 7-second) and model validation
process is done by 5-motor accelerations (whole30 seconds).
Sampling rate problem of Curvesnap in A/D converting
process is shown in Figure 2. Red circle in Figure 2. is aliasing
and it requires to be passed from a low pass filter.
(a)
(b)
Figure 2. Digitized field voltage (output of CurveSnap)
A low pass filter with the following frequency and magnitude
specifications is designed:
𝐹𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 = {
𝐹𝑝𝑎𝑠𝑠 = 0.01
Hz
𝐹𝑠𝑡𝑜𝑝 = 0.06
𝐴𝑝𝑎𝑠𝑠 = 1
𝑀𝑎𝑔𝑛𝑖𝑡𝑢𝑑𝑒 = {
dB
𝐴𝑠𝑡𝑜𝑝 = 60
Filtered signal is shown in Figure 3. Clearly, there is no
aliasing in the filtered signal; however, slight phase shifting
happens when a signal passes from a low pass filter.
Figure 3. Digitized field voltage after passing from Low pass filter
III.
EXCITATION SYSTEM
Generators’ dynamic voltage response behaviors are
greatly affected by their excitation systems. Excitation
systems have a great impact on the generator voltage profile
and reactive power. IEEE excitation systems are categorized
as AC type, DC type, and ST type. Functions and
characteristics of different types of excitation systems are not
the subject of this report. However, a method for sensitivity
analysis for various parameters of excitation systems is
addressed here. IEEE type AC5A has been chosen as a test
case for the sensitivity analysis and parameter estimation.
Extensive use of AC5A in the industry was the reason of
choosing in this report.
AC types of excitation systems employ an AC alternator
and a rectifier to generate DC field voltage. In this model
significant load effects are taken into the consideration by
using effects of generator field current. Other than AC4A,
other AC types do not deliver negative field current.
Figure 4. shows Type AC5A which is a model for
brushless excitation systems. There are some signals in all
AC-Type exciters which are common in various models from
AC1A to AC8B. SE[EFD] is one of these signals and it
represents saturation and it was implemented based on IEEE
recommended practice for excitation systems [6].
This model, like DC models, utilizes samples directly from
load (namely EFD which is the output of the block diagram) for
saturation and limiting the output voltage. Conversely, other
models of AC-Type use open circuit exciter saturation.
Tf
IAE 

ymeasured (t )  yreference (t )
(1)
o
Tf
SAE   ymeasured (t )  yreference (t )
(2)
t 0
Also, Integral of Square Errors (ISE) and Sum of Square
Errors (SSE) are commonly employed as a criterion to be
minimized. These indices penalize for larger errors rather than
smaller ones.
Tf
IAE 
y
measured
(t )  yreference (t ) 
2
(3)
o
Tf
SAE    ymeasured (t )  yreference (t ) 
2
(4)
t 0
Figure 4. IEEE AC5A excitation system block diagram[6]
IV.
SENSITIVITY ANALYSIS
In order to find out how much each parameter can affect
the output, an objective function should be defined. This
sensitivity analysis can be done to simplify the complicated
model of the exciter for further studies and calculations. For
instance, due to nonlinearity and a complicated model of an
excitation system, parameter identification is complex and not
possible. Technically, having an accurate model with all of the
parameters for such system is impractical. Therefore, by using
measured data including inputs and outputs and applying
system identification methods such as Recursive Weighted
Least Square (RWLS), the mathematical model of the system
can be derived. In this regard, more sensitive parameters will
get more weight in comparison with other parameters in
RWLS, WLS (Weighted Least Square), and other methods.
On the other hand, less sensitive parameters can be considered
as constants in order to reduce the size of unknown
parameters.
There are many criteria which are used as a performance
index. Integral of Absolute Errors (IAE) or Sum of Absolute
Errors (SAE) is summation of the deviations between
measured signal and expected signal. IAE and SAE are the
same in concept; however, IAE and SAE are used for
continuous signals and sampled signals, respectively. They
can be defined as follows:
There should be an objective function to emphasize on
different parts of the voltage response (Error! Reference
source not found.Needless to say, voltage dips and swells
need more weight in comparison with small steady state
errors. In this regard, the following objective function is
proposed:
t1
t2
J  W1  yout (t )  yref (t )   W2  yout (t )  yref (t ) 
2
t  t0
t3
 W3  yout (t )  yref (t ) 
2
t t1
2
(5)
t  t2
Minimizing the objective function results in less error in
voltage dips and overshoots, which means the system has less
response time and more accurate voltage response. W1, W2,
and W3 are weights, where W1 is greater than W2 and W2 is
greater than W3. This means larger errors, specifically in
voltage dips, are more important than other errors. Although
the amount of voltage drop is directly related to the size and
dynamic model of induction motors, the voltage dip duration
can be decreased by modifying the excitation parameters.
There are two common analytical sensitivity functions, the
absolute sensitivity function and the relative sensitivity
function [5].
Choose appropriate
excitation model
A. The Absolute Method
If we have the following function:
y  f ( x1 , x2 ,
- sort parameters
- i=1
- k=0
-Set parameters as IEEE
sample data
, xn )
i=i+1
Find J
The absolute sensitivity function of y related to xi is:
y
S 
xi
y
xi
|Sk-Sk-1|<e
Or |Sk-Sk-1|>10
- Increase parameter
number I
- k=k+1
(6)
OP
Where OP stands for ‘operating point’ which means all
variables have their normal values. Function f also can be time
varying and partial differential should apply to y just with
respect to xi.
Find Jnew
i=i+1
Find Sk and record data
for further analysis
B. The Relative Method
Jnew>J
|Sk-Sk-1|<e
Yes
Or |Sk-Sk-1|>10
In order to compare the effects of the parameters, the
relative method can be more useful. The relative function is
defined as follows:
S xyi 
y
xi
OP
xi
y
percent changein y

percent changein xi
Decrease parameter
number i
y
y
xi
(7)
Jnew and Sk and record
data for further analysis
xi
For our purpose, the relative method would be more
appropriate. Figure 5. shows the algorithm for the sensitivity
analysis for the excitation system parameters. By using this
algorithm, we have two options, increasing or decreasing the
parameters. If a parameter is sensitive, it would cause a large
change in the objective function whether the parameter is
increased or decreased. However, sometimes parameters are
more sensitive in one direction. For example, when one
parameter is increased, there is no impact on the output.
Figure 5. Sensitivity analysis flow chart
However, it does not mean that the parameter is not
sensitive because we do not see the impact of decreasing for
that parameter. Nevertheless, most of the sensitive parameters
show their sensitivity in both directions.
V.
SIMULATION RESULT
Based on what has been discussed in introduction, in order
to identify a system’s parameters, we should have the
mathematical model and input-outputs of that system. One of
the necessary conditions for each identification method is to
have informative disturbed input-output sets.
In this report, real field data is collected from a 7 MW
Emergency Diesel Generator which worked in an island
mode. To have disturbed input-output sets, some pumps were
run during test.
Dynamic Parameter Estimation and Tuning (DPET) is a
new identification tool of ETAP which recently has been
added to User-defined Dynamic Model (UDM) module.
DPET is a tool for parameter estimation of exciters and
governors of generators. One can build an exciter/ agoverner
model in UDM and upload appropriate measured input-output
set into DPET and update initial values of parameters to
estimate them. DPET takes the input and calculate the ouput
based on the updated initial values. Then, it compares the
measured output (which it had been uploaded at first of the
process) to calculated output and starts adjusting parameters
to minimize error between calculated and measured outputs.
DPET keeps tuning parameters, unless error is reasonably
reduced or time runs out. Based on authors’ experience, there
are several cases which DPET may fails in them. Initial
values for the first itteration is so important in DPET. If they
result in instability, DPET cannot change parameters
appropriately to reduce the error. Suggested data set by IEEE
would be the best option for intial values.
Complex systems with large amount of unknown
parameters is another example that DPET cannot handle.
Reduced order model of a system can dynamically behave
like the original model. Nevertheless, simplified model can
be replaced in DPET and parameter estimation processing
can be significantly diminished.
In order to evaluate performance of proposed method,
two different simulations is performed. First, original model
of AC5A was modeled in UDM and parameter estimation
using field data was performed. In the second simulation,
original model is simplified utilizing the proposed method
and it is modeled in UDM and system identification was
performed, accordingly. These two simulation demonstrates
simplified model can be, successfully, used as a replacement
of original model in parameter estimation. The reason of
choosing AC5A was that both original and simplified model
work in DPET;consequently, validation of the proposed
method in simplification can be evaluated. Moreover, AC5A
is widely used in industry and known as one of the most
favourite exciters for manufacturers.
Part I. Original Model
A simple stand-alone micro grid that was introduced in
section II part B has been simulated in ETAP. For sensitivity
analysis the largest induction motor was considred since it
has more voltage dip. After running the model in ETAP,
voltage responses are saved and utlizing Matlab code to find
J and S k from [5] and [7].
In this paper, IEEE ST2A is selected for the excitation
system. Error! Reference source not found. shows block
diagram of IEEE ST2A excitation system. Different
parameters of ST2A and their initial values based on IEEE
recommendation sample data are shown in table 1 [6].
TABLE I. ST2A PARAMETERS SAMPLE DATA
Parameter
Description
Controllers parameters
Voltage regulator time
T𝐴
constant
Voltage regulator gain
K𝐴
Damping filter gain
T𝐹
Damping filter time constant
K𝐹
Voltage regulator output
V𝑅 𝑀𝐴𝑋
limits
Voltage regulator output
V𝑅 𝑀𝐼𝑁
limits
Exciter and rectifier
Exciter time constant
T𝐸
Self Excitation gain
K𝐸
Potential circuit gain
K𝑃
Rectifier loading factor
K𝑐
Current circuit gain
K𝐼
coefficient
Value
0.15 sec
120
1 sec
0.05
1
0
0.5 sec
1
4.88
1.82
8
Utilizing sensitivity analysis method introduced in the
previous section, we can see how much sensitivity index \is
different for various parameters. Table II shows sensitivity of
different paraameters respect to voltage response. As it was
disscussed in [..], different aspects of voltage response have
different weight on sensitivity analysis and voltage dip has
more priority.
Used-defined dynamic model of AC5A is implemented
in UDM module of ETAP as shown in Figure 6.
Since the objective of sensitivity analysis in this paper is
model order reduction, we should eliminate those parameters
which have lowest sensitivity index. We are looking for a
system with same dynamical behaviour but less complex.
Simplification should be done in order to a specific objective.
Figure 6. AC5A implemented in ETAP (UDM)
Therefore, some parameters are not that much sensitive
and can be eliminated for specific studies. However, some
parameters might be so sensitive and they can be affect to
output significantly. Hence, these sensitive parameters not
only should not be eliminated, but also should be kept fixed
in parameter tuning process. Needless to say, system
identification is done for stable systems and parameter
estimation
impossible for unbouhnded outputs. Small
variation in a sensitive parameter may cause an extensive
impact on output, and failure to parameter estimation,
consequensly. Thus, … and …. Have been kept fixed during
parameter estimation.
Some of the parameters like self excitation constant (K 𝐸 )
are relatively constant and they were not considered for
sensitivity analysis. According to Table 2, potential circuit
gain (K 𝑃 ) is the most sensitive parameter among ST2A
parameters and this depends on the excitation circuit design.
Figure 9 shows the voltage response for vaious amount of K 𝑃 .
Table 2 shows the sensitivity index for the parameters of
ST2A during starting motor scenario as discussed above. In
this paper, parameters are divided into 4 groups:
- Very sensitive if
- Sensitive if
- Medium Sensitivity if
- Not sensitive if
S k >0.25
0.25> S k >0.05
0.05> S k >0.01
S k <0.01
Figure 7. Voltage response with various K P s.
Exciter time constant (TE ) and current circuit gain
coefficient (K I ) are sensitive (Figure 10).
TABLE II.OBJECTIVE FUNCTION FOR ST2A PARAMETERS
Parameter
Controllers parameters
T𝐴
K𝐴
T𝐹
K𝐹
Exciter and rectifier
T𝐸
K𝑃
K𝑐
K𝐼
| Sk |
0.014
0.006
0.0095
0.021
0.194
0.323
0.032
0.15
Figure 8. Sensitive parameters voltage response
Also, Rectifier loading factor (K c ), Voltage regulator time
constant (TA ), and Damping filter time constant (K F ) has
medium sensitivity (Figure 11). Lastly, Voltage regulator
gain (K A ) and Damping filter gain (TF ) are among non
sensitive parameters (Figure 12).
Figure 10. Non-sensitive parameters voltage response
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Figure 9. Medium sensitive parameters voltage response
VI.
CONCLUSION
In this report, we proposed a sensitivity analysis method
to simplify a generator excitaion system based on voltage
response. Stability analysis and voltage step response
analyses need an accurate mathematical model of a system.
The proposed sensitivity analysis method is useful not only
for model simplification, but also for system identification
which provides an accurate mathematical model. The
proposed method is tested on IEEE ST2A excitation system
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micro grid. This method can be utilized in other excitation
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