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
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.