730IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 18, NO. 2, MAY 2003
Synchronous and Asynchronous Generators
Frequency and Harmonics Behavior
After a Sudden Load Rejection
Vladimir V. Terzija, Senior Member, IEEE, and Magnus Akke, Member, IEEE
Abstract—This paper describes load rejection tests, done at two
hydro power plants in Sweden, one equipped with synchronous
and the other with asynchronous generators. During the tests volt-
ages and currents are digitized, recorded and thereafter off-line
processed. By this, in the processing of distorted and fast param-
eter-varying voltages and currents the powerful estimation tech-
nique, the Newton Type Algorithm, is applied. It was intended to
investigate the frequency changes and the distortions of the mea-
sured signals. The transient processes at both generators are com-
pared. In particular, the frequency changes after the instance of
load rejection are investigated and discussed from the signal pro-
cessing and physical nature point of view.
Index Terms—Asynchronous generator, estimation techniques,
frequency, synchronous generator, transient analysis.
electromechanical and the fast electromagnetic transients are
investigated simultaneously. The analysis result becomes of
more practical relevance, if it is done on field data records,
obtained from real elements of a power system. Nonlinear
properties of algorithms make the problem harder to analyze.
The aforementioned problems have been addressed in work in
which synchronous (SG) and asynchronous (ASG) generators
are investigated during load rejection tests. The measurements
are provided at two small hydro power plants in Sweden.
It was intended to compare the transients on both generator
types. The transients are analyzed by digital processing of the
the signals processed were distorted and frequency modulated.
It was in particular encountered at the ASG, where the inter-
action between generator and its shunt capacitor increased the
distortion of voltages and currents. In load rejection tests, typi-
cally the generator shaft speed is changed and consequently the
frequency of the generator output voltage.
More precisely, after a sudden disconnection of generator
from the external grid, the electrical power is step changed,
whereas at the very beginning of the transient the mechanical
driving power stay constant, so the difference, the so called
HE analysis of transient processes in electrical power
system is a challenging task, especially if both the slow
Manuscript received May 24, 2000; revised April 27, 2002. This work was
supported by the Alexander von Humboldt Foundation.
M. Akke is with ABB Automation Products, Västerås, Sweden.
Digital Object Identifier 10.1109/TPWRS.2002.805013
power of inertia, accelerates the generator. That means that the
expected distortions of signals processed should be determined
during off-nominal frequency conditions, moreover during the
rapid frequency changes.
In modern power plants, microprocessors are commonly
used in protection, monitoring, control and measurement de-
vices. Eachmicroprocessor is programmedwith theappropriate
numerical algorithm (software) providing the desired function.
In this paper a nonlinear estimator, the Newton Type Algorithm
(NTA) , is utilized for the processing of recorded data and
for the simultaneously estimation of signal power spectrum and
frequency. As a derived result, the Total Harmonics Distortion
) is estimated based on the harmonics estimated in
the first stage of the algorithm. It was intended to investigate
the possibilities of applying the NTA algorithm in such an
application in which the signals processed are both severe
distorted and frequency modulated.
In this paper, SG and ASG generators behavior around the
instance of load rejection are analyzed. The author investigated
how a step change in voltage amplitude and phase influences
the frequency estimation.
First, the experiments at hydro power plants are described.
Second, some introductory remarks regarding the frequency es-
processing obtained through NTA algorithm are given: ampli-
tudes, frequencies, spectra and
tained are discussed from the frequency at load rejection, algo-
rithm convergence, frequency definition and data window size
points of view. This is followed by the conclusion. The NTA al-
gorithm is briefly presented in a separate Appendix.
s. Fourth, the results ob-
II. DESCRIPTION OF THE EXPERIMENTS
The experiments investigated in this paper are load rejection
tests at one synchronous (SG) and at one asynchronous (ASG)
generator. In these tests the generators were loaded to 10–20%,
or more, of rated load, then the generator breaker is tripped. As
the breaker opens, the electrical torque goes to zero and the tur-
bine accelerates the generator. This causes an increase in fre-
quency before the turbine governor controls the turbine output.
This test is often done to determine the inertia constant of gen-
eratorand turbine,whichis an important parameter fordynamic
models.In thispaper thetest results areused tocompare thefre-
quency behavior and harmonic content for the SG and ASG.
0885-8950/03$17.00 © 2003 IEEE
TERZIJA AND AKKE: SYNCHRONOUS AND ASYNCHRONOUS GENERATORS731
Fig. 1. Hemsjö test setup (SG).
Fig. 2.An interior view of the generators at Hemsjö.
A. Measuring System
As a measurement unit a multichannel
lows up 16 inputs using a 16-bit AD converter is used. The sam-
pling frequency is set to
Hz cycle. The Daqbook is connected to the parallel port of a
portable PC. Two inputs are used for voltage measurement. The
inputs had industrial “5B-modules” for signal conditioning and
galvanic isolation. The data acquisition started a short time be-
fore the load has been rejected from the generator. The recorded
data are later on processed off-line.
kHz, or 40 samples per a 50
B. Hemsjö Test (The Synchronous Generator Case)
Hemsjö hydro power plant is one of the oldest power stations
in southern Sweden. It is commissioned in 1906 and it consists
of 4 units, each one with a rated power of 880 kVA. During the
test only one unit was operating. Fig. 1 shows the test setup at
The components in Fig. 1 are as follows: IU1 is a temporarily
connected to the secondary circuit of a permanent current trans-
former. The transducer gives 100 mV per ampere and the fre-
quency range is from DC to 100 kHz. The maximal current is
20 A. E1 and E2 are permanent voltage transformers 3850/110
V/V. Before the voltage signals are connected to the Daqbook
signal conditioning modules, the voltage is further decreased in
resistive voltage dividers. The phase-to-phase voltage signal is
The generators at Hemsjö are not equipped with automatic
voltage regulators (AVR). Each generator is magnetized by a
manually controlled rotating exciter. Fig. 2 shows an interior
view of the four generators and exciters.
The load rejection test started at
after that a transient process started. At
s the exciter is
Fig. 3. Recorded SG output voltage.
Fig. 4. Knisslinge test setup (ASG).
blocked, so the voltage amplitude rapidly decreased (see the SG
voltage presented in Fig. 3.). All variables are changed, which
will be shown in the next Section. Relatively small distortions
of the signals recorded are detected.
C. Knisslinge Test (The Asynchronous Generator Case)
Knisslinge is a small hydro power plant in southern Sweden.
Fig. 4 shows the test setup at Knisslinge. The station has two
standard induction machines used as ASG. This is a common
practice in smaller power plants, typically with ratings of less
than 1 MVA. The rated voltage is 400 V, the rated power 440
generator is connected to a 10 kV bus via a transformer with a
circuit breaker at thelow voltage side. Amongsuch plants many
hydro power plants are found nowadays, but also many of the
rapidly growing number of wind power plants.
An induction generator does not have a separate excitation
systemasaSG. Themagnetization currentoftheinductiongen-
erator rotor (i.e., the reactive power) is taken from the power
system to which the generator is connected . In order to im-
provethepowerfactorofthegenerator, itisoftenequipped with
shunt capacitors (SC). Three delta-connected capacitors with a
total rating of 150 kVAr compensate for approximately half of
point. When the induction generator is feeding a synchronous
system at steady state, the reactive power needed by the gener-
ator is taken both from the capacitors and the network. A strong
external network helps to keep the voltage constant at the ASG
terminal. An interior view of Knisslinge hydro power plant is
plotted in Fig. 5.
In this test only generator G1 is disconnected from the ex-
ternal grid. By this, SC was left connected to the network. The
test started at
s. A short segment of the recorded ASG
and SC voltage and current is presented in Figs. 6 and 7, respec-
tively. In this test a severe distortion of the signals recorded are
in particular at the moment of the load rejection. This change is
732IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 18, NO. 2, MAY 2003
Fig. 5.An interior view of the generators at Knisslinge.
Fig. 6. Voltage and current of ASG.
Fig. 7. Voltage and current of SC bank.
Fig. 8. Recorded voltage of ASG.
obvious by observing the currents depicted in Figs. 6 and 7. The
recorded ASG voltage is presented in Fig. 8. The accumulated
reactive energy slowly disappears and consequently the voltage
amplitude slowly decreases. For this test a detailed spectral es-
timation and analysis is provided and presented in Section VI.
III. INTRODUCTORY REMARKS ABOUT THE FREQUENCY
ESTIMATION AT LOAD REJECTION
of algorithms estimating frequency from the generator output
voltage at the instant of load rejection and during the short time
In order to apply a numerical algorithm efficiently, first the na-
ture of the problem analyzed must be investigated. After that,
the next step is the optimal selection of the algorithm parame-
ters (e.g., the data window size, the sampling frequency, etc.).
voltage point A) circuit breaker B and load impedance ? .
Turbine T, generator G, gen. internal impedance ? , gen. terminal
Fig. 10.Principal frequency response for SG.
A time continuous definition of frequency of the signal
presented by a complex rotating phasor with phase angle
. See ,  for a more rigorous definition. Starting
from this definition, many numerical algorithms determine
frequency from the pre-filtered input signal, from which
the complex phasor is determined after every incoming new
sample. At least two successively determined phase angles (at
and ) are required for the unknown signal
This approach of frequency calculation is often followed with
the additionally post-filtering. Otherwise, it is very sensitive to
system depicted in Fig. 9.
At the instance of the load rejection, the breaker B opens and
the current goes rapidly to zero. The voltage drop over the gen-
erator internal impedance
becomes zero, as well, causing a
sudden step change in generator output voltage amplitude and
phase. The sudden step change in phase causes a spike in cal-
culated frequency for algorithms of the above type. Linear/non-
linear post-filtering will smoothen out the spike. Fig. 10 shows
the principal frequency response for SG load rejection without
any post-filtering. Note that the sole purpose of Fig. 10 is to
illustrate the principal behavior. The rate of frequency change
after the load rejection depends on the inertia constant and on
the generation—load imbalance. The larger inertia constant, the
smaller slope and the larger imbalance, the larger slope (the
same observations are valid for ASG, too). The simple model
processing point of view (see (1) which delivers frequency from
the known phases).
In contrast to synchronous machine, as the name indicates,
an asynchronous machine runs at asynchronous speed. Below
However, the mechanical speed of the ASG is higher than the
TERZIJA AND AKKE: SYNCHRONOUS AND ASYNCHRONOUS GENERATORS733
Fig. 11. Principal frequency response for ASG.
synchronous. Thespeed differenceis a partof the asynchronous
machine operating principle.
After the disconnection of an ASG from the external grid, the
In addition to the phase step change caused by the step change
in the internal voltage drop, a step jump in frequency occurs, as
well. The frequency jumps from the external network frequency
frequency jump of approximately 1 Hz. The principal behavior
of the ASG frequency response after a load rejection is illus-
trated in Fig. 11.
Numerical algorithms require a convergence period to track
changes in unknown parameter, such as frequency and ampli-
tude. Fast convergence is one of important features of algo-
rithms. It is predominantly determined by the data window size,
as well as by the dynamics properties of the process analyzed.
IV. RESULTS OF DATA PROCESSING
By a roughly analysis of recorded signals presented in Figs. 6
and 7, one concludes that generator frequency should be esti-
mated from a distorted signals. That means that the frequency,
as well as the voltages and the phases of harmonics, should be
included into the signal model. The idea was the measurement
established in a form of an efficient estimation numerical algo-
rithm. In order to provide it, Newton Type Algorithm (NTA)
, briefly described in Appendix I, is applied. In , NTA is
applied as an estimation numerical algorithm suitable for the
processing of a pure sine wave. In this paper the signal model
is extended with higher harmonics. In this form it is applied in
the processing of distorted signals. The NTA, extended with the
higher harmonics, provides simultaneously estimation of power
spectrum and frequency. The most of known algorithms  are
not in the position to provide user with such a feature. In ad-
dition, the NTA, based on the closed mathematical structure
capable of solving not-constrained optimization problems, pos-
sesses the second order convergence. This important feature of-
fers the opportunity of processing signals with fast changes of
In the signal processing the NTA algorithm is firstly simulta-
neously applied to all three-phase signals (arbitrary voltages or
currents). The length of data window is selected to be
ms. After that the second stage analysis of the parameters
estimated followed (e.g., calculation of total harmonics distor-
In thetextbelow, theresults ofsignals processingare system-
Fig. 12. Estimated SG output voltage amplitude.
Fig. 13. Estimated SG frequency.
Fig. 14. Estimated network frequency.
A. Hemsjö (Synchronous Generator)
In Figs. 12 and 13 the estimated ASG voltage amplitude and
frequency are respectively presented. At the instance of load re-
jection, a step change of the reactive power flow through gen-
erator causes a step change in the fundamental voltage ampli-
tude. Due to a huge load generation imbalance, the generator
accelerates. The acceleration is proportional to the magnitude
of power imbalance and inverse proportional to the generator
size, defined by the generator inertia constant
s the exciter is blocked, so the SG voltage amplitude
decrease rapidly to a very low level, proportional to the rema-
nent magnetism. In Fig. 13 at
frequency acceleration can be noticed.
Regarding the network voltage, as expected, some essential
changes in its amplitude are not detected. A slightly frequency
increase after the generator load rejection is detected, as plotted
in Fig. 14.
nals recorded has been slightly changed. In Table I the values
of the total harmonic distortion for generator (
) voltages are presented. Somewhat higher values
in generator voltage are caused by the relatively fast
changes in voltage amplitude. For this test the harmonic content
is not essential, so it is not separately analyzed, as for the rejec-
tion test with the ASG.
s . At
s a slight increase in the
) and net-
B. Knisslinge (Asynchronous Generator)
In Figs. 15–17 the estimated ASG fundamental voltage
amplitude, harmonics and frequency filtered from the voltage
734IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 18, NO. 2, MAY 2003
SYNCHRONOUS GENERATOR AND NETWORK VOLTAGE ??? (%)
Fig. 15. Estimated ASG output voltage.
Fig. 16. Estimated ASG output voltage harmonics.
Fig. 17. Estimated ASG frequency (filtered from its output voltage).
Fig. 18. Estimated ASG output current.
signal, are respectively presented. As depicted in Fig. 15, the
amplitude of ASG voltage has a fast step change, due to a
sudden change in the reactive power consumed by the gener-
ator. The later damped amplitude decrease is determined by
the slowly disappearing of ASG reactive energy. The reasons
for the frequency increase (see Fig. 17) are the same as with
SG—the generation—load imbalance.
In Figs. 18 and 19 the estimated ASG fundamental current
amplitude and harmonics filtered from the current signal are re-
spectively presented. The values are presented for (
Current fundamental harmonic goes to zero and frequency esti-
mated diverges. The same is valid for the spectra. Correct fre-
quency estimates are obtained, but not presented, as well.
In Figs. 20–22 the estimated SC fundamental voltage am-
plitude, harmonics and frequency filtered from the SC voltage
Fig. 19. Estimated ASG output current harmonics.
Fig. 20. Estimated SC voltage.
Fig. 21. Estimated SC voltage harmonics.
Fig. 22. Network frequency estimated from the SC voltage.
Fig. 23. Estimated SC current.
and SC voltages were the same (compare Figs. 15 and 20).
In Figs. 23 and 24 the estimated SC fundamental current am-
plitude and harmonics obtained from SC current, are respec-
From the harmonics estimated, the corresponding
values are respectively calculated and shown in Fig. 25. The
strongest harmonics flow occurred through the shunt capaci-
tance, both before and after the load rejection.
The estimated levels of
plications in which signals processed are both distorted and
frequency deviated the suitable digital signal processing algo-
rithms should be applied. Significant frequency changes can
s indicates that in the ap-
TERZIJA AND AKKE: SYNCHRONOUS AND ASYNCHRONOUS GENERATORS735
Fig. 24. Estimated SC current harmonics.
Fig. 25. Estimated Total Harmonic Distortion.
Fig. 26.SG output voltage.
introduce errors in the process of spectra determination. This
could be followed with the wrong conclusions. That is why
the NTA nonlinear estimator has been applied in the problem
V. DISCUSSION OF THE RESULTS OBTAINED
At the beginning of this discussion it is tested if the phase
angle step change in the generator output voltage signals occurs
after the load rejection. In Figs. 26 and 27, the output voltages
of SG and ASG are respectively plotted. The phase angle step
change exists, it is obvious and it is more stressed in the case
of ASG, so in this case the larger frequency peaks are expected,
as remarked in Section III of the paper. In Figs. 26 and 27,
denotes the instance of the load rejection.
Knowing that the signal model included into NTA algorithm
starts from the assumption that the frequency is defined as the
first derivative of phase angle, after the load rejection a step fre-
quency increase (almost a peak) for both generators occurs (see
Figs. 28 and 29). The maximum peak value for SG and ASG
detected for the shortest data window size were 50.85 and 55.5
Hz, respectively. At the same time the influence of data window
size on the peak form, as well as on the convergence is investi-
sizes, the faster convergence and the larger peak and vice versa.
With the data window size decreased, the theoretically expected
peak should be larger. The longer data windows smooth out the
peak. It is also concluded that after the load rejection, the am-
plitude step change for SG and ASG was 3.61% and 10.77%,
Fig. 27. ASG output voltage.
Fig. 28. Estimated frequency, NTA algorithm, SG.
Fig. 29. Estimated frequency, NTA algorithm, ASG.
The sudden disconnection of synchronous and asynchronous
generators from an external grid is followed with the severe
frequency acceleration. Significant frequency changes can
introduce errors in the process of spectra determination and this
could be followed with the wrong conclusions. The nonlinear
effects and interaction between shunt capacitors introduce dis-
tortion of generator voltages and currents. The distortion level
) estimated was higher at the asynchronous generator
that was compensated with the shunt capacitors. The chal-
lenging problem of the simultaneously estimation of the signal
frequency and the spectrum has been with success solved by
using the nonlinear nonrecursive Newton Type Algorithm. Its
fast convergence gave a possibility to track the fast frequency
changes. It is concluded that at the instance of load rejection
the frequency change at asynchronous generator is faster than
at the synchronous generators.
NEWTON TYPE ALGORITHM
Newton Type Algorithm (NTA)  is an efficient nonlinear
estimator. The starting point of this technique is in advance
adopted mathematical model of the input signal. Let us assume
the following observation model of the measured signals
736IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 18, NO. 2, MAY 2003
varying parameter vector to be estimated and
function of time and unknown model parameters, expressed as
is a zero mean random noise, a suitable time
Herethe vector ofunknownparametersis
. Its dimension, i.e., the
. For example,
. The model order depends on the
model order, is
application and the nature of the signal processed. Here
are the amplitude and the phase angle of the
-th harmonic, respectively, whereas
an efficient nonrecursive nonlinear estimator . One of the
key assumption here is that the unknown parameters (i.e., the
unknown vector ) are constant in data window. The estimates
are obtained from a measurement vector
() uniformly sampled signal samples with the
during a finite period of time,
based on the following vector equation:
is frequency. NTA is
. It is
is the vector of estimated unknown model parameters,
is the nonlinear signal model,
trix of the Jacobi matrix (its elements are the first derivatives of
the signal model through the unknowns) and
index . The parameter vector estimated in the step
The algorithm has excellent convergence properties. The order
of convergenceis 2and thedurationof convergenceis nolonger
than the duration of data window (
initialized with the initial guess for
the initial frequency to a nominal value (
unknown parameters during fast and slow transients in power
is the pseudoinverse ma-
is the iteration
). The algorithm must be
. It is reasonable to select
(or 60) Hz),
The authors wish to thank Dr. H.-J. Koglin, University of
Saarland, Germany, for helping to make the research presented
 V. Terzija, M. Djuric, and B. Kovacevic, “Voltage phasor and local
system frequency estimation using Newton Type Algorithm,” IEEE
Trans. Power Delivery, vol. 9, pp. 1368–1374, July 1994.
 P. Crause, Analysis of Electrical Machinery.
 B. Boashash, “Estimating and interpreting the instantaneous frequency
of a signal—Part 1: Fundamentals,” Proc. IEEE, vol. 80, pp. 520–538,
, “Estimating and interpreting the instantaneous frequency of a
signal—Part 2: Algorithms and application,” Proc. IEEE, vol. 80, pp.
540–568, Apr. 1992.
 T. S. Sidhu, “Bibliography of relay literature, 2000 IEEE committee re-
port,” IEEE Trans. Power Delivery, vol. 17, pp. 75–84, Jan. 2002.
New York: IEEE Press,
Vladimir V. Terzija (SM’00) was born in Donji
Barac, Yugoslavia, in 1962. He received the B.Sc.,
M.Sc., and Ph.D. degrees in electrical power
engineering from the Department of Electrical
Engineering, University of Belgrade, Yugoslavia, in
1988, 1993, and 1997, respectively.
In 1988, he joined the University of Belgrade,
where he was an Assistant Professor teaching
courses in electric power quality, power system
control, electromechanic transient processes in
power systems, and estimation techniques in power
engineering. In 2000, he was a Research Fellow at the Institute of Power En-
gineering, Saarland University, Saarbruecken, Germany. He is now employed
with ABB Calor Emag Mittelspannung, Ratingen, Germany, as an expert
for protection, control, and monitoring of medium voltage switchgears. His
areas of scientific interest are power system protection, control, electric power
quality, and DSP applications in power systems.
Magnus Akke (M’92) received the M.E.E., Licen-
tiate, and Ph.D. degrees from the Lund Institute
of Technology, Sweden, in 1986, 1989, and 1997,
At present, he is in the Relay Development
Department, ABB Automation Products, Västerås,
Sweden. Before that he worked for nine years
with relay protection and power system analysis
at a Swedish power utility. He has been a visiting
scientist at the University of Newcastle, Australia
and Cornell University, Ithaca, NY.