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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TII.2017.2759502, IEEE
Transactions on Industrial Informatics
Improving Synchronous Generator Parameters
Estimation Using d-q Axes Tests and
Considering Saturation Effect
B. Zaker, G. B. Gharehpetian, Senior Member, IEEE, and M. Karrari, Senior Member, IEEE

Abstract— Fundamentals of parameter estimation of SG have
already been presented in different standards such as IEEE Std.
115. The first proposed methods require short circuit tests and/or
some tests for which the synchronous generator should be out of
service. In recent reports, however, to avoid the shortcomings of
former methods, partial load rejection tests on d-q axes have been
recommended to estimate the electrical parameters of SG such as
different reactances and time constants. In this paper, it is first
shown that the standard well-known methods are valid when there
is no saturation effect. Therefore, a new method is proposed to
improve SG parameters estimation taking into account the
saturation effect. The proposed method uses saturation curve
parameters, rotor angle and analytical equations of the SG
alongside the load rejection tests results. To show the accuracy and
precision of the proposed method, it is applied to experimental
data of an 80 MVA gas turbine unit, and the results are discussed.
Xf
Total reactance of excitation winding.
XD, XQ Total reactances of damper windings.
Xmd, Xmq Mutual reactances of direct and quadrature axes.
rs, rfd
Resistance of stator and excitation windings.
rD, r Q
Resistance of damper windings.
T’do
Transient open-circuit time constants of direct axis.
T”do, T”qoSubtransient open-circuit time constants of direct and
quadrature axes.
S1.0
Saturation parameter in 1.0 pu stator voltage.
S1.2
Saturation parameter in 1.2 pu stator voltage.
Ag, Bg
Parameters of quadrature approximation of the
saturation curve.
csat, ksat Parameters of saturation effect.
ym, ys
Vectors of measured and simulated signal.
Average
of measured signal.
ym
Index Terms—Load rejection test, parameter estimation, rotor
angle, saturation, synchronous generator.
I. INTRODUCTION
NOMENCLATURE
E
ω, ωb, δ
Tm,Te, TD
H
ψd, ψq
ψf
ψ D, ψ Q
ψm, vm
ωb
Pe, Qe
vt, is
vd, vq
id, iq
vfd, ifd
iD, iQ
Xld, Xlq
Xlf
XlD, XlQ
Xd, Xq
X’d
X”d, X”q
Internal voltage of machine.
Rotor speed, base speed and rotor angle.
Mechanical, electrical and friction torques.
Rotor inertia.
Flux linkage of direct and quadrature axis.
Flux linkage of excitation winding.
Flux linkage of damper windings.
Magnetizing flux and induced voltage.
Base speed.
Active and reactive powers.
Terminal voltage and stator current.
Voltage of direct and quadrature axes.
Current of direct and quadrature axes.
Voltage and current of excitation winding.
Current of damper windings.
Leakage reactances of direct and quadrature axes.
Leakage reactance of excitation winding.
Leakage reactances of damper windings.
Steady state reactances of direct and quadrature axes.
Transient reactance of direct axis.
Subtransient reactances of direct and quadrature
axes.
N
R
Number of samples.
ECENT years, due to development and complexity of the
power systems, the monitoring and protection schemes
have gained greater importance. In this regard, the first step is
having an accurate model of the power system which should be
valid for different types of dynamic studies. Therefore,
modeling and parameter estimation of power system
components have been always a challenging issue.
Among all the power system components, SG has been an
important starting point for modeling and identification. Two
categories of offline and online identification methods have
been discussed and published in literature. Different standards
have been provided for modeling and identification of power
plant and SG parameters [1]-[4]. These standards have mostly
used offline procedures to identify different SG parameters
such as reactances, time constants, moment of inertia and
damping factor. Besides the standards, many academic and
industrial studies have been conducted on identification of SG
parameters. In [5], Running Time-Domain Response (RTDR)
tests such as the field short-circuit test, have been used to
estimate the SG parameters. Multi-sinusoidal signals have been
generated by a voltage source inverter for SG identification in
[6]. Also, mixed stochastic-deterministic algorithms have been
used for identification purposes in [7]. In [8], authors have
B. Zaker, G. B. Gharehpetian, and M. Karrari are with the Electrical
Engineering Department of Amirkabir University of Technology, Tehran, Iran
(e-mail: zaker.behrooz@aut.ac.ir, grptian@aut.ac.ir, karrari@aut.ac.ir).
1551-3203 (c) 2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TII.2017.2759502, IEEE
Transactions on Industrial Informatics
applied step-voltage tests to SG and have estimated the
parameters by means of a hybrid genetic algorithm-based
method. DC excitation test has been utilized as a standstill
method for identification in [9].
In addition to offline methods, many online ones have also
been presented by researchers. In online identification methods,
usually a small disturbance such as a step change in reference
voltage of Automatic Voltage Regulator (AVR) is applied to
SG and measured output signals such as terminal voltage and
reactive power are used for identification. Indeed, these
methods are a kind of modeling procedure with the aim of
finding the best set of parameters to fit the output signals of the
simulated system to the measured signals of the plant [10]. A
third-order SG model has been identified using nonlinear least
square method in [11]. Online measurements alongside rotor
angle measurement have been utilized to identify the SG
parameters in [12]. Authors in [13], have used measured signals
of active and reactive power, terminal and field voltage, field
current and rotor angle following of a small perturbation of field
voltage to identify a third-order model of SG. Phasor
Measurement Unit (PMU) data has been processed using an
unscented Kalman filter for online parameter estimation of a
fourth-order SG in [14]. SG parameters have been identified
based on state space model using online measurements in [15]
and [16]. In [17], Heffron-Phillips model of a single-machine
infinite bus has been identified using small perturbation of the
reference voltage. A multistage genetic algorithm-based
identification procedure has been proposed in [18] to
simultaneously identify the parameters of SG and excitation
system without measuring the field voltage signal. This method
is useful for brushless exciters where the field voltage is not
accessible. In [19], a nonlinear term selection method has been
used to determine the parameters which have considerable
impacts on the machine response as an improvement in
parameter estimation. Among the aforementioned researches,
[10], [11], [13] and [15]-[18] have not considered the saturation
effect of the synchronous generator in their proposed models
and identification procedure. Although the saturated parameters
have been estimated in [12], [14] and [19], but the saturation
characteristic and unsaturated parameters have not been
identified. In [23], only three parameters of synchronous
generator, i.e. Xmd, Xmq and rfd, have been estimated. A
parameter has been iteratively estimated for different operating
points to consider the saturation effect.
In this paper, the parameters of the SG is identified using two
load rejection tests; one for d-axis parameters and another for
q-axis. These tests have already been recommended in [1].
However, it is shown in the next sections that the proposed
procedure of [1] is not accurate enough when the saturation
effect is taken into account. Therefore, a new method is
presented in this paper to overcome this drawback. Firstly, the
saturation curve and corresponding parameters are extracted
using experimental test results of an 80 MVA, 10.5 kV gas unit.
Using these parameters, results of load rejection tests, and
model of SG, the d-q parameters are identified. In the proposed
method, d-q components of terminal voltage and stator current
should be determined. In order to extract the d-q components of
these signals, it is vital to measure the rotor angle. So, an
accurate rotor angel metering technique has been designed to
measure the rotor angle. Besides the load rejection tests, step
changes are applied to reference voltage of excitation system
and the measured results are compared to the simulated ones for
the validation of the estimated parameters.
The rest of the paper is organized as follows: model of SG
and basics of load rejection tests are explained in Section II. In
Section III, problem statement is outlined. The load angle
metering technique is presented in Section IV. Experimental
results and validation tests are discussed in Section V. Finally,
Section VI concludes the paper.
II. SG MODEL AND LOAD REJECTION TESTS
A. SG Model
The fundamentals of the SG model have well been explained
in [20] and [21]. Considering the seventh-order nonlinear model
of the SG, the mechanical part is represented by two state
equations as follows:
  1 2 H Tm  Te  TD 
(1)

   b    1
Besides the mechanical part, five state equations represent the
electrical part of the SG as follows:
 d  b  v d  rs i d   q
 q  b  v q  rs i q   d
(2)
 fd  b  v fd  rfd i fd
 D  b   rD i D
 Q  b   rQ i Q
where,
 d

 fd
 D
X m d X m d   i d

Xd
  1 X
Xf
X m d   i fd
   md
b
 X m d X m d
X D   i D

X mq   i q 
 q 
1 Xq
X

  

 Q  b  m q X Q   i Q 
X d  X ld  X m d
X d  X ld  ( X m d || X lf )
X d  X ld  ( X m d || X lf || X lD )
X q  X lq  X m q




(3)
(4)
X q  X
lq  ( X m q || X lQ )
According to (2), the steady state values of the voltage, active
and reactive powers are as follows:
Pe  v d i d  v q i q
Qe  v q i d v d i q
v q   X d i d  rs i q  X
(5)
m d i fd
v d  X q i q  rs i d
B. Load Rejection Tests
As recommended in [1]-[3], the d-axis load rejection test
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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TII.2017.2759502, IEEE
Transactions on Industrial Informatics
should be applied to SG in order to identify the reactances and
time constants of the d-axis. Before the breaker tripping, the
excitation system should be switched to manual control and the
SG operating point should set to 0.0 pu of active power and
about 0.1 pu absorption of reactive power. The zero value of the
active power leads to the zero value of the rotor angle with vt=vq
and vd=0. Also the stator current is aligned with the d-axis on
this condition. The negative value of the reactive power causes
under excited situation that consequently leads to voltage drop
after breaker tripping. Using Fig.1, the steady state, transient
and subtransient reactances are calculated as follows [1]-[3]:
v 1
X d 
I
(6)

v
2
X d 
I
v 3
Xd 
I
According to annex F of [1], Δv2 and Δv3 are determined using
the extended transient and subtransient periods of vt.
Similar to aforementioned procedure, the q-axis test is
recommended to identify the q-axis parameters. It is necessary
to measure the rotor angle in order to set the steady state
conditions for q-axis test [3]. The stator current is aligned with
the q-axis by matching the rotor angle with power factor angle
[3]. To meet this condition, about 0.1 pu of active power and
reactive power absorption of a few percent of rated power is
needed [3]. However, as it will be explained in Section III, these
procedures have some shortcomings that makes them not
applicable to real and none-ideal conditions. These drawbacks
are as follows:
 The identification procedure of both direct and
quadrature parameters using (6) is only valid when the
saturation effect does not exist while the saturation
exists in a real SG.
 To meet the steady conditions of the d-axis test, the
active power should be set to zero while it is almost
impossible in a power plant due to reverse power and
low forward protection functions.
In the next section, a new method will be proposed to
overcome these shortcomings.
III. PROBLEM STATEMENT
To show the saturation effects on results of the d-q axes tests,
a 50 MVA SG connected to infinite bus through a transformer
is simulated by DIgSILENT software with known and preset
parameters. The steady state conditions are set to 0 MW and -5
MVAr to meet the d-axis situation. The load rejection is
simulated two times; once with and without considering
saturation.
The results are compared in Fig. 2. It can be seen that the
steady state values of terminal voltage after breaker tripping
have considerable difference. For analytical studies, it is
assumed that the terminal voltages before and after breaker
tripping are vq1 and vq2, respectively, in d-axis test. The stator
current is equal to zero after breaker tripping. So, using (5), we
have:
v q 1  (X
md
v q2  X
i fd
md
 X l )i d  rs i q  X
md
i fd
(7)
If the saturation does not exist, Xmd remains constant during
the test. Therefore, neglecting the stator resistance, the
reactance of the d-axis can be calculated, as follows (as
recommended in [1]):
v  v q 2 
(8)
X d  v
 q1
id
I
However, since the saturation affects the mutual reactances
of SG, above equations are not valid for real saturated
conditions. Considering the saturation, the mutual reactances
are not the same before and after breaker tripping while the
terminal voltage changes from nominal value to a lower value
during the load rejection tests. Therefore, (7) could be written
as follows:
v q 1  (X
v q2  X
m ds 1
 X l )i d  rs i q  X
i
m ds 1 fd
(9)
m ds 2 i fd
where, the s subscript indicates the saturated values. Using (9),
the following equation can be written.
v q 1  v q 2   X mds 1  X mds 2  i fd  ( X mds 1  X l )i d  rs i q (10)


It can be seen that the reactance of the d-axis could not be
easily calculated in this case. Indeed, due to saturation effect,
the mutual reactance of the d-axis is not identical before and
after breaker tripping.
The saturation model could be approximated by different
representations such as exponential and quadratic based on two
parameters S1.0 and S1.2 of Fig.3 [21], [22]. Considering the
scaled quadratic approximation [22], we have:
Sat  x  
B g  x  Ag 
2
x
(11)
1.2  Ag 
S1.2

S1.0 1.2  1.0  A 2
g
2
1.2  1.2 
Ag 
1.0  1.2 
S1.2
S1.2
S1.0
S1.0
Bg 
,
1  A 
S1.0
2
At each operating point, the magnetizing flux is
approximately equal to the induced voltage as follows:
 m v m 
v
d
 X l i q  rs i d
  v
2
q
 X l i d  rs i q 
2
(12)
Finally, the saturation parameters are calculated as follows
[22]:
if v m  A g then c sat 
B g v m  A g
vm

2
, k sat 
1
1  c sat
(13)
if v m  A g then c sat  0 , k sat  1
For each operating point, the saturated values of mutual
reactances are calculated using saturation parameters as
follows:
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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TII.2017.2759502, IEEE
Transactions on Industrial Informatics
X
m ds
 k sat  X
mdu
X
m qs
 k sat  X
mqu
(14)
where, the u subscript indicates the unsaturated values [22].
Fig. 1. Terminal voltage and stator current during d-axis test.
The key point of the SG parameter estimation is calculation
of steady state reactances of d-q axes. The proposed method is
summarized for a real power plant, as follows:
Step1: Determination of saturation curve: Turbine and
generator are started to reach the nominal speed (3000 rpm),
while the excitation system is switched to manual control in
order to control the excitation current. The generator breaker is
kept open and the unit is on no load condition. The reference of
the field current is manually and continuously changed so that
the terminal voltage varies from 0.7 pu to 1.2 pu. The terminal
voltage, excitation voltage and current are recorded by a high
rate data logger during this test. Using these recorded signals,
the saturation curve, S1.0, S1.2, Ag and Bg are determined.
Step2: Determination of Xdu: After determining the saturation
parameters, the next step is calculation of unsaturated value of
Xd. At first, the unit is paralleled to the grid and it is tried to set
the operating point to the ideal conditions of the d-axis test.
However, as mentioned before, it is almost impossible to
exactly set the active power to zero in a power plant due to
reverse power and low forward protection functions. When the
active power is not exactly equal to zero, the terminal voltage
is not completely in the direction of the q-axis. Since the
quadrature component of the terminal voltage is required to
calculate the Xdu, a rotor angle metering device is designed and
built, which will briefly be explained in the next section. Using
the measured rotor angle, terminal voltage, stator current, active
and reactive powers, the d-q components are calculated as
follows:
  tan 1 Q / P 
(16)
v  v  sin   , v  v  cos  
d
t
q
t
i d  i s  sin     , i q  i s  cos    
Fig. 2. Comparison of saturation effect on load rejection test results.
Fig. 3. Obtaining the saturation parameters using open-circuit characteristic.
Considering the aforementioned relations, (10) can be
written as follows:
v q 1  v q 2   X mdu  k sat 1  k sat 2  i fd
(15)
 ( X mdu k sat 1  X l )i d  rs i q
Due to under-excited condition of the test, the terminal
voltage drops to much lower value than 1.0 pu after the breaker
tripping. Hence, the operating point moves to knee point, where
the open-circuit curve meets the air gap line. Therefore, it is
assumed that the saturation effect after breaker tripping is
negligible and ksat2=1:
v q 1  v q 2   X mdu  k sat 1  1 i fd
(17)
 ( X mdu k sat 1  X l )i d  rs i q
The above equation includes two unknown variables Xmdu
and Xl. Considering (12) and (13) it can be said that ksat1 is a
nonlinear function of d-q components of (16) and Xl. The rs
could also be neglected or set to a very small typical value. To
solve this equation with two variables, it is assumed that Xl is
proportional to Xmdu. The standards and references such as [2]
and [21] presents typical values of Xdu and Xl. These data can
be used for this purposes.
Now, (17) is a nonlinear equation with one variable which
could be solved by mathematics tools such as MATLAB
software and then Xmdu will be determined. Using this value, Xl
and Xdu could be calculated.
Step 3: Determination of X’du and X”du: It should be noted that
as shown in Fig. 1, Δv1 and Δv2 are considerably smaller than
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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TII.2017.2759502, IEEE
Transactions on Industrial Informatics
Δv3, which means the smaller values of X’du and X”du rather than
Xdu. Therefore, these reactances are not significantly affected by
the saturation effect. Firstly, using the measured signals and (6),
the saturated values of X’d and X”d are calculated. Then, Xlf is
calculated using the following equation:
(18)
X ds  X l   X mds || X lf 
where, Xmds is the result of the previous step as well as Xmdu.
Finally, X’du could be determined as follows:
(19)
X du  X l   X mdu || X lf 
The same procedure is also carried out for X”du.
Step 4: Determination of time constants: The time constants are
calculated using extended periods of terminal voltage response
as shown in Fig. 1. These parameters may need fine tuning
during time-domain validation simulations in order to reach the
highest accuracy.
Step 5: Determination of q-axis parameters: The operating
point is set to ideal conditions of q-axis test as mentioned
before. The terminal voltage trend is similar to the d-axis test.
However, the direct component of the terminal voltage is used
in this step. Using (5), the equation which should be solved is
as follows:
(20)
v d 1  0   (X mqu k sat 1  X l )i q  rs i d
Since the excitation current is not included in vd of (5), the direct
component of the terminal voltage drops to zero after breaker
tripping. In addition, Xl has already been determined in Step 2.
Therefore, ksat1 is simply calculated using (12) and (13). Solving
the linear equation of (20) leads to Xmqu and consequently, Xqu.
It should be noted that the aforementioned steps can be used
for round-rotor SGs. For salient-rotor SGs, Xld and Xlq are not
identical. Therefore, the leakage reactances of (17) and (20) are
Xld and Xlq respectively. For a salient-rotor SG, the estimation
procedure of d-axis parameters is the same as ones described in
Step 2-Step 4. The difference between these two cases is in the
solving method of (20). Unlike the round-rotor case, in case of
salient-rotor SG, Xlq is still unknown in Step 5. Thus, it is
assumed that Xlq is proportional to Xmqu to eliminate one variable
and solve (20). The standards and references such as [2] and
[21] presents typical values of Xqu and Xlq. These data can be
used for this purpose. Besides that, for a salient-rotor SG, ksatq
is used to consider the saturation effect on q-axis parameters.
According to [22], ksatq, as follows, is used instead of (13), while
ksatd is calculated the same as before.
1
(21)
k satq 
X m qu
1
c sat
X m du
It should be noted that Xmdu has been already determined in
Step 2. Therefore, considering (21) and (20) and the
aforementioned assumption between Xlq and Xmqu, (20) is
changed to a nonlinear equation with one variable which could
be solved by tools such as MATLAB software and then Xmqu
will be determined. Using this value, Xlq and Xqu could be
calculated.
IV. LOAD ANGLE METER
Load angle is defined as the angle difference between
internal voltage E and terminal voltage (vt) of SG. Indeed, load
angle could be interpreted as the difference of electrical angle
between the terminal voltage and the reference axis on the rotor.
In no load condition, vectors of E and vt are identical, so the
angle difference between them is zero that means the load angle
is equal to zero. When the SG is under load, the reference axis
on the rotor advances in phase comparing to the zero crossing
of vt. Therefore, as shown in Fig. 4, the load angle could be
calculated by measuring the phase angle between a fixed point
on the shaft and the zero crossing of vt. A real-time DSP-based
load angle meter has been designed and built according to this
theory. Two signals are used to obtain and calculate the load
angle in this device as shown in Fig. 5. An optical encoder
determines physical position and period of the rotor as the first
input. The second input is SG voltage transformer (VT) output.
Input signals are applied to a DSP based processor board. These
signals are processed by DSPIC33J256 processor. Finally, the
load angle is calculated as follows:
(22)
  UL   NL
Fig. 4. Basics of load angle measuring.
Fig. 5. Load angle meter connections.
V. EXPERIMENTAL RESULTS AND VALIDATION
The experimental tests have been applied to an 80 MVA
Kraftwerk Union gas unit. The SG type is TLRI 93/36, 50 Hz,
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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TII.2017.2759502, IEEE
Transactions on Industrial Informatics
10.5 kV with nominal power factor of 0.85. The machine rated
values are given in Table I which are used in (1) and (3) as the
base values. According to [21], base values of field voltage and
currents are such chosen that at these vales, the terminal voltage
on the air gap line is equal to nominal value of 10.5 kV. The
static excitation system makes the measurement of the filed
voltage and current possible. All the required signals have
synchronously been measured by a 1 kHz data acquisition
device.
TABLE I
BASE VALUES OF SG
Variable
Sb
vb
ib
ifdb
Value
80 MVA
10.5 kV
4.4 kA
194 A
Variable
ωb
zb
Tb
vfdb
Value
314 rad/s
1.3778 Ω
25.48x104 N.m
68 VDC
A. Saturation Curve Test
The results of the saturation curve test is presented in Fig. 6.
As it is shown in this figure, due to overvoltage and isolation
concerns, the terminal voltage has been increased to only about
11.5 kV. However, to determine the S1.2, it should be increased
to 12.6 kV (1.2 pu). So, the corresponding field current for 12.6
kV is extrapolated by means of curve fitting toolbox of
MATLAB using the measured trends of the terminal voltage
and field current. The extrapolated point is shown in red in Fig.
6. Therefore, S1.0 and S1.2 are calculated as follows [21]:
BC 220.2  194

 0.1351
S 1.0 
AB
194
(23)
EF 352.58  227

 0.5532
S 1.2 
DE
227
Consequently using (11), we have Ag=0.8356 and Bg=4.9998.
Fig. 7. Raw results of d-axis test.
Fig. 8. Results of d-axis test in pu.
B. d-Axis Test
The raw results of the d-axis test is presented in Fig. 7. The
terminal voltage is recorded from the VT. Therefore, the output
is an AC signal and the RMS value of this signal is used for
calculations. The active and reactive powers are measured as
DC signals. The filtered and scaled values of these signals are
presented in Fig. 8 in per-unit. As it is shown in Fig. 8, the
breaker is opened in Pe=2.8 MW (0.035 pu) and Qe=-20 MVAr
(-0.25 pu).
Fig. 9. d-q components and rotor angle of d-axis test.
Fig. 6. Saturation test result.
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Transactions on Industrial Informatics
Fig. 10. Excitation current of d-axis test.
Using the measured rotor angle and (16), the d-q components
of the terminal voltage and stator current of the d-axis test are
calculated and presented in Fig. 9. It can be seen in this figure
that due to small value of active power before load rejection, vd
and iq are not exactly zero. The excitation current during this
test is also shown in Fig. 10. Due to manual control mode of
excitation, the current remains constant before and after
tripping. The steady states values of Figs. 9 and 10 are given in
Table II. Using these values, Ag, Bg and (12), (17) could be
solved. It should be noted that as mentioned in step 2 of Section
II, the ratio of Xl to Xmdu is considered as about 0.055 using the
typical values to solve (17). The typical value of 0.001 pu is
also considered for rs. The results of this solution are Xmdu, Xl,
Xdu and ksat1, which are listed in Table III. The obtained values
of the Xdu, Xl and the other parameters will be validated using
three tests in different operating points in part D of this section.
From (18), (19) and Fig. 11, which is the zoomed part of vq of
Fig. 9, the transient and subtransient reactances of the d-axis are
calculated as follows:
X ds  X l   X
mds
|| X
lf

 v 2 0.9219  0.8094

 0.0946  1.6848 || X
i d
0.2701  0
X
lf
lf

 0.3976 pu
X du  X l   X
mdu
|| X
lf
(24)
  0.0946  1.6848 || 0.3976 
X du  0.4176 pu
The same procedure is done for X”du and the result is 0.3067
pu. The T’do and T”do have been calculated as 3.5 s and 0.45 s
using extended periods of voltage as shown in Fig. 11.
TABLE II
STEADY STATE VALUES OF D-AXIS TEST
Value before
tripping
2.51 deg
0.0405 pu
0.9219 pu
-0.2701 pu
0.0498 pu
106.4432 A
Signal
δ
vd
vq
id
iq
Ifd
Value after
tripping
0.00 deg
0.0000 pu
0.4527 pu
0.0000 pu
0.0000 pu
106.4432 A
TABLE III
SOLUTION RESULTS OF (17) FOR D-AXIS TEST
Parameter
Xmdu
Xl
ksat1
Xdu
Xmds1
Value
1.7202 pu
0.0946 pu
0.9794
1.8148 pu
1.6848 pu
Fig. 11. Zoomed part of vq during d-axis test.
C. q-Axis Test
The measured rotor angle and d-q components of terminal
voltage and stator current of q-axis test are presented in Figs.
12 and 13. The operating point of this test before breaker
tripping is Pe=7.5 MW (0.094 pu) and Qe=-1.5 MVAr (-0.019
pu). The steady states values of Fig. 12 are given in Table IV.
Using these values, Ag, Bg and (12), (20) is solved and we have:
Xmqu=1.4905 pu. Using the predetermined value of Xl in
previous step, we have: Xqu=1.5851 pu. Due to small value of
voltage drop of d-axis and signal filtering, it is actually not
possible to distinguish the portion of X”q in this drop.
Therefore, T”qo and X”qu are considered identical to T”do and
X”du. The ultimate parameters of the SG are given in Table V.
They will be validated by time-domain tests in the next section.
D. Validation Tests
For validation purposes, a step additive signal is applied to
the reference of AVR in different operating points and desired
signals are recorded. The validation tests are carried out in
different operating points (especially reactive power) to show
the accuracy of the estimated saturation parameters as well as
reactances. The measured excitation voltage is used as the input
for simulations in DIgSILENT software. The outputs of the
simulated SG with parameters of Table V are compared to the
measured ones. The results are presented in Figs. 14-16. To
evaluate the errors between the measured signals and simulated
ones, R-squared index is used for both terminal voltage and
reactive power as follows:
N
SS res    y m  y s 
2
i 1
N
SS tot    y m  y m 
2
(25)
i 1
R2  1
SS res
SS tot
where, the value of R2 varies from 0 to 1 and 1 indicates the best
fitness and accuracy. The R-squared values for all three
validation tests are given in Table VI. As it is shown in Figs.
14-16 and according to the R-squared values, the accuracy of
1551-3203 (c) 2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TII.2017.2759502, IEEE
Transactions on Industrial Informatics
the parameters of Table V are completely acceptable.
To show and verify the sensitivity of simulation results, the
simulations are carried out for operating point of Pe=47 MW
and Qe=20 MVAr, while in each simulation, a certain
parameter of Table V changes. The results for +10% and -10%
change in Xd, -10% change in Xq and +20% change in T’do are
shown in Figs. 17-20 respectively. As it is shown and expected,
Xd has significant effect on the terminal voltage and reactive
power, while Xq has the less. Besides that, when T’do changes
from the estimated value of Table V, the settling times of
terminal voltage and reactive power differ from the measured
signals.
Fig. 12. d-q components and rotor angle of q-axis test.
Fig. 14. Validation test in operating point of Pe=47 MW and Qe=20 MVAr.
Fig. 13. Zoomed part of vd during q-axis test.
TABLE IV
STEADY STATE VALUES OF Q-AXIS TEST
Signal name
δ
vd
vq
id
iq
Value before the
trip
9.04 deg
0.1537 pu
0.9621 pu
-0.0073 pu
0.1024 pu
Value after the
trip
0.00 deg
0.0000 pu
0.9621 pu
0.0000 pu
0.0000 pu
Fig. 15. Validation test in operating point of Pe=39 MW and Qe=2 MVAr.
TABLE V
FINAL PARAMETERS OF SG
Parameter
Xdu
Xqu
X’du
X”du
X”qu
Xl
Value
1.8148 pu
1.5851 pu
0.4176 pu
0.3067 pu
0.3067 pu
0.0946 pu
Parameter
T’do
T”do
T”qo
S1.0
S1.2
-
Value
3.50 s
0.45 s
0.45 s
0.1351
0.5532
-
TABLE VI
R-SQUARED VALUES OF VALIDATION TESTS
Operating point
Pe=47 MW, Qe=20 MVAr
Pe=39 MW, Qe=2.0 MVAr
Pe=44 MW, Qe=7.5 MVAr
R-squared for vt
0.9861
0.9923
0.9915
R-squared for Qe
0.9926
0.9950
0.9961
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Transactions on Industrial Informatics
Fig. 20. Simulation sensitivity to +20% change in T’do in operating point of
Pe=47 MW and Qe=20 MVAr.
VI. CONCLUSION
Fig. 16. Validation test in operating point of Pe=44 MW and Qe=7.5 MVAr.
Fig. 17. Simulation sensitivity to -10% change in Xd in operating point of Pe=47
MW and Qe=20 MVAr.
In this paper, a new method has been proposed to improve
estimation of SG parameters using d-q axes tests considering
saturation. It has been shown that the conventional method has
shortcomings in presence of saturation. A load angle meter has
been designed and built to extract the d-q components of the
terminal voltage and stator current. The proposed method has
been applied to an 80 MVA Kraftwerk Union gas turbine unit.
The validation tests have been carried out in different operating
point and the results have been compared to simulations of
estimated parameters. It has been shown that the proposed
method can accurately estimate the SG parameters taking into
account the saturation effect. Besides the saturation effect,
temperature variations are also impactful on SG parameters.
These effects may be considered in the future works.
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Fig. 18. Simulation sensitivity to +10% change in Xd in operating point of Pe=47
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1551-3203 (c) 2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TII.2017.2759502, IEEE
Transactions on Industrial Informatics
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Prof. G. B. Gharehpetian received his
Ph.D. degree in electrical engineering 1996
from Tehran University, Tehran, Iran,
graduating with First Class Honors. As a
Ph.D. student, he has received scholarship
from German Academic Exchange Service
from 1993 to 1996 and he was with High
Voltage Institute of RWTH Aachen,
Aachen, Germany.
He has been holding the Assistant Professor position at AUT
from 1997 to 2003, the position of Associate Professor from
2004 to 2007 and has been Professor since 2007.
He was selected by the ministry of higher education as the
distinguished professor of Iran and by IAEEE as the
distinguished researcher of Iran and was awarded the National
Prize in 2008 and 2010, respectively. Based on the ISI Web of
Science database (2005-2015), he is among world’s top 1%
elite scientists according to ESI (Essential Science Indicators)
ranking system.
He is the author of more than 1000 journal and conference
papers. His teaching and research interest include Smart Grid,
DGs, Monitoring of Power Transformers, FACTS Devices,
HVDC Systems, and Power System Transients.
Prof. M. Karrari received the Ph.D.
degree in control engineering from
Sheffield University, Sheffield, U.K., in
1991. Since 1991, he has been with the
Amirkabir University of Technology,
Tehran, Iran. He is author or coauthor of
more than 150 technical papers and three
books. His main research interests are
power system modeling, modeling and
identification of nonlinear dynamic systems, and large-scale
and distributed systems.
B. Zaker was born in Shiraz, Iran in 1989.
He received the B.S. degree in electrical
power engineering from Shiraz University,
Shiraz, Iran, in 2011; the M.S. degree in
electrical power engineering from
Amirkabir University of Technology
Tehran, Iran, 2013. He is currently
pursuing the Ph.D. degree in electrical
power engineering at Amirkabir University
of Technology.
He has a lot of practical experience in modeling and parameter
estimation of power plants in Iran. His research interests
include system identification, power system dynamics,
distributed generation systems, and microgrids.
1551-3203 (c) 2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
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