A Practical Method for Calculation of Over-Excited Region in the Synchronous Generator Capability Curves

A Practical Method for Calculation of Over-Excited
Region in the Synchronous Generator Capability
Curves
Davoud Esmaeil Moghadam
Institute of Electrical Power Systems and
High-Voltage Engineering
Technische Universität Dresden
Dresden, Germany
[email protected]
Abbas Shiri
Department of Electrical Engineering
Islamic Azad University- Hadishahr
Branch
Hadishahr, Iran
[email protected]
investigation of the effect of some issues such as load variation
or transmission line characteristics on the capability curves [1].
Abstract— The capability curves are used for loading the
synchronous generators as a useful and essential tool. Moreover,
one of the important applications of the capability curves is
setting the relays. The main purpose of the proper loading and
accurate setting of the relays is stable operating of the
synchronous generators in desired margins. Therefore, the
accurate calculation of the curves is significant. Although in the
papers some methods and formula for calculating and drawing
the capability curves have been presented, the obtained results do
not coincide with the original capability curves provided by the
manufacturers. It could be potentially because of disregarding
the real conditions of synchronous generators such as saturation,
temperature, mechanical considerations, altitude and etc. Also,
there is no complete source about the capability curves which
cover all parts of the curve.
In this paper, in addition to briefly assess all parts of the
capability curve, the latter is precisely calculated by taking into
account all parameters and operational conditions of the
generator. The results in the armature current limit and the
under-excitation limit are in agreement with the original
capability curves provided by the manufacturers. In spite of this
coincidence, the over-excitation part of the graph drawn on the
basis of the above-mentioned considerations and calculations
does not follow the manufacturer's curves, although the
conditions and limitations of the generator are considered.
Accordingly, in this paper, a new simple and applicable
procedure is proposed for calculating the over-excitation part of
the curve, based on authors' experience in designing the
synchronous generators. The results of the calculations are in
good agreement with over-excitation limit of the manufacturers'
curves.
Simplicity, fast calculation time, precision and error
minimization main features of this method.
Capability curves are provided by manufacturers in
standard condition1. They are used for loading the synchronous
generators in different operating conditions without exceeding
the designed limits. Some of the most important aspects which
are presented in the P-Q plan by the capability curves are
dynamic stability, steady state stability, stator and rotor current
limits and thermal restrictions.
Capability curves play important role in setting of the
synchronous generators relays such as under-excited
controllers, automatic voltage regulators (AVR) and internal
functions of protection systems which contain the loss of field
(LOF) relay, minimum excitation limiter (MEL) and over
excitation limiter [2]. Different parameters affect the regions
and limits determined by capability curves. Variations in the
structure of the synchronous generator, such as cooling gas
pressure or magnetic saturation, directly affects the
synchronous generator capability curves [3]. One of the most
significant effects of the power plant elements on the capability
curves is the variation of the over-excited region based on the
type of the used turbines [4].
Although many attempts have been done in calculating and
drawing the synchronous generators capability curves, there is
no comprehensive reference to calculate and draw these curves.
Normally, in literature, one or two regions of the capability
curves have been briefly considered. However the obtained
results are not completely match with prepared curves by
manufacturers. In this paper, theoretical bases of each part of
the capability curves and their calculating method will be
presented and discussed comprehensively. Moreover, in order
to obtain accurate results, all technical and important factors of
the capability curves are considered.
Keywords—Capability Curve; Over-excited Region; Underexcited Region; Armature Region; Stability
I.
Sajad Sadr, Davood Arab Khaburi
Department of Electrical Engineering
Iran University of Science & Technology
Tehran, Iran
[email protected]
INTRODUCTION
Stability of generators and power systems is one of the
most important and fundamental topics in the power system
studies. Hence, consideration of various parameters which
affect the system stability is worthwhile. In the last few years,
the stability of the generators has been indirectly evaluated by
978-1-4799-2399-1/14/$31.00 ©2014 IEEE
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Standard condition:
− Ambient Temperature: 40°C
− Nominal Voltage
− Altitude above sea level: 0 m
By close scrutiny of generator designn documents and
regarding authors’ experiences, a practical annd accurate method
based on the exciting current–power curvess of the generators
for calculating over-excited region is preseented. Considering
mentioned method and technical factors, cappability curve for a
sample generator will be calculated and draawn. The modeled
synchronous generator is a 160 MW turbbo generator with
nominal voltage of 15.75 kV and power factor 0.8. It is shown
that the achieved results completely follow thhe factory’s curve.
localized heating create. Othher limits for this region of
capability curves are rated voltage,
v
dynamic stability and
steady-state stability. The under-excited region of the
synchronous generator covers topics related to LOF relay and
function of MEL [7].
C. Over-excited Region (Rotor
(
Current)
The copper losses of thhe rotor winding impose the
limitation on the field windinng current. The correspondence
between the active and reactivve powers for a specified field
current is defined by a circle centered
c
on the negative Q-axis.
Circles which determine arm
mature and rotor current limits
intersect at point B (Fig.1). Point B shows the nominal output
s
generator [8].
power and power factor of the synchronous
III.
The armature current regionn of the capability curve refers to
the stator current limitations. This
T region is defined by a circle
centered at the origin with reduuce equal to the nominal power
(MVA). The notable point is that in the calculation of the
radius, only the voltage and cuurrent have been considered. The
first effectual factor which impposes changes on the capability
curve is terminal voltages and its
i variations (Fig. 2). Moreover,
the apparent power depends on the other parameters, such as
the inlet air temperature of thhe cooling system. Non-thermal
factors such as mechanical limitations
l
of the turbine, the
maximum tension of the coupleed rotor on fault conditions, also
maximum field current and coooling system capacity are other
factors that limit the capabilityy curve in the armature region.
For instance, maximum poower of turbines is limited.
Consequently it could be potentially a limitation for output
power of generators. Consiidering these conditions, the
maximum output power can be determined. It should be
notified that a margin has beeen assigned for the temperature
difference between the inlet coooling air temperature and inlet
cooling water temperature in a synchronous generator.
According to the manufacturerrs design documents, it has been
approximated between 6ºK and 8 ºK.
Fig.1. A typical capability curve
II.
PRACTICAL DESC
CRIPTIONS AND CALCULATIONS
FOR ARMAT
TURE CURRENT REGION
THE CAPABILITY CURVEE REVIEW
Synchronous generators are able to provide
p
maximum
designed power at a rated voltage and power factor in which
they can work continuously without overheatting. Active power
is limited by the prime mover capability. In Fig.1, the vertical
line crossing the point B presents the limit off the active power.
It should be mentioned that the ability of continuous active
power producing in synchronous generatorss is determined by
three different indexes which in the below inn the sequel, these
different limits are reviewed [5].
• Armature current region (Stator currennt)
• Under-excited region
• Over-excited region (Rotor current)
A. Armature Current Region
One of the parameters which can limit a generator rating is
the maximum allowable current (Ohmic loosses) that can be
carried by the armature winding without exceeeding the thermal
limits. In the P-Q plane, it appears as a circcle centered at the
origin and radius equal to the MVA rating (BC part in Figure 1)
[6].
B. Under-excited Region
Heating the stator end core imposes thee limitation on the
under-excited region of the synchronous geenerator capability
curves (CD part in Figure 1). The magnetic flux
f
is a radial flux
which passes through the stator core in parallel with
laminations. However, the leakage flux of thee stator end core is
axial flux and crosses in the core laminatioons. Consequently,
Fig.2. Effects of the generator voltagee terminal (Et) and armature resistance
(Ra) on the armature lim
mit of the capability curve
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Fig.4. Attitude correction factor
IV.
DESCRIPTIONS AN
ND CALCULATIONS FOR UNDEREX
XCITED REGION
Many factors impose limitss on the under-excited region of
capability curve. Limitation off the stator end core heating and
the stability aspect are some samples for the limits. After
determining each of the aboove limits, whichever is more
restrictive will be used in thhe under-excited region of the
capability curve (Fig.5).
Fig.3. Generator output (MW) vs. inlet cooling airr temperature (°C)
If the cooling inlet air temperature and poower factor do not
follow designed values (Tkg = 40ºC & P.F. = 0.8),
0
the maximum
output power will be determined in accorddance with related
curves. Therefore, according to the new pow
wer factor and also
new inlet cooling air temperature, the maxim
mum output power
at the rated voltage will be calculated. Figuree 3 demonstrates a
sample of these kinds of curves which calculated, simulated
and presented by a manufacturer. These currves determine the
maximum output power (according to the generator
g
thermal)
based on different inlet cooling air temperatuures and variations
of the power factor. It is worthwhile to mention that the curves
mitations related to
with power factor greater than 0.8, refer to lim
stator winding temperature and curves with power factor less
than 0.8, refer to rotor winding temperature.
s
end core heating, some
In order to control the stator
measures have been taken intoo account. Using non-magnetic
retainer rings or step pockets inn the end part of the stator core
to increase the air gap are som
me of the mentioned preventive
measures. These changes can increase reluctance of the flux
path in under-excited conditionn. Hence it can be expressed that
the stability issues have more effective rules in under-excited
region. In references, a circlle centered at (0, E ⁄2 (1⁄X
1⁄X )) with the radius equal to
t E ⁄2 (1⁄X 1⁄X ) is used to
draw the stability limit.
It should be mentioned that the curvves in Fig. 3 are
referable only in the sea level. Heat transferr in the air-cooled
turbo generators is done by air convection. Thus,
T
heat transfer
ratio will be decreased by reduction in the air density due to
t homogenize the
installation altitude (Hgeo). Hence in order to
temperature of the different parts of the generator in high
altitude of installation, maximum output power should be
modified by a correction factor (Khgeo). Mannufacturers present
curves to determine the correction factor bassed on the altitude
of installation (Fig.4). By multiplying modiified output power
based on inlet cooling air temperature (Figg.3) in the altitude
correction factor (Khgeo), real output power off the generator will
be calculated. The obtained output power determines curve
radius in the armature current region.
Fig.5. Under-excited limits
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The stability limit of the steady-state is obtained by using
the active and reactive power of the synchhronous generator.
Another kind of the steady-state stability lim
mit is a straight line
which presents the concept of stability cleaarly. To determine
the steady state stability limit, the direct axis of the saturated
reactance is used. For a safe margin, the sttability limit angle
can be considered less than 90 degree (α2).. It is assumed 80
degrees (α1), approximately. In addition, thhe practical steady
state limit is more restrictive than the theoreetical case and it is
considered 0.9 of the theoretical value (Fig. 6).
where K is the saturation factoor which can be determined by
the no-load curve of generatorss. In spite of consideration of the
saturation effect, the over-exciited region obtained from these
equations does not follow thee curve given by manufacturers
(Fig. 7). Therefore, the necessitty for a method which fulfills all
condition of the generator is com
mpletely obvious.
Fig.7. Overr-excited area
Obviously, there is no specific relation between the
excitation current and generatoor output power. Manufacturers
present a graph, which illustraates the relation between these
two parameters for various pow
wer factors (Fig. 8). This curve
can be prepared for different vooltage levels.
Fig.6. Stability limits in underexcited area
V.
PROPOSESD METHOD FOR CALLCULATION AND
DRAWING OF THE CAPABILITY CURVES IN THE
OVER-EXCITED REG
GION
According to experiences of the synchronous generator
g
tests and the curves
design and scrutiny of the generator
achieved from the different tessts, it can be found out that this
curve is necessary to determine the over-excited region of the
r
current in the full load
capability curve. The rated rotor
condition is an important facctor for drawing the capability
curve. For these purpose, in fiigure 8, we draw a vertical line
from the rated current. The inteersection points of this line with
the graph lines show the geenerator power at the desired
terminal voltage and desired field
f
current at different power
factors. So by using (4)-(6) andd in accordance with Fig. 9, we
can draw the capability curve acccurately.
The over-excited region of the capabiliity curve refers to
constant field current. This area limits excitting current due to
temperature limits. The field current restrictioon is applied when
the generator operates at the nominal conditioon.
In some references, in order to explain ovver-excited region,
a synchronous generator connected to a netw
work is modeled. It
calculates supposed that the over-excited region
r
is a circle
centered at the lead part of the Q-axis at E ⁄X and with the
radius EI E ⁄X . The internal voltage, synchhronous reactance
and terminal voltage are denoted, respectivelly, by EI, Xd, Et. In
calculation internal voltage, the saturationn effect has been
considered and defined as below.
2
sin
(E cos θ)
Sin φ
E sin θ
E S
IX
E
IX
P
R. Sin ρ
C
R
(1)
C
Q
(4)
Q
(5)
(6)
As shown in Figs. 10 andd 11, the under-excited region
curve obtained by using thee field current-power graph is
completely matched with the curves presented by
manufacturers.
where
E
R. Cos ρ
(2)
VI.
TYPICAL CAPPABILITY CURVE DRAWING
Regarding mentioned issuees in the previous sections, the
capability curve for a 160 MW
W synchronous generator, with
rated voltage 15.75 kV and poweer factor 0.8 is calculated.
(3)
730
intersection points of the over--excited region of the capability
curve with deferent powers inn the obtained curve follow the
curve presented by the manuffacturer. The stability region of
this curve complies fully with the intended reactance and the
intended stability limit.
Fig.10. Calculated capability curve for the sample generator
Fig.8. relation between output power and excitationn current – 16 kV
Fig.11. Presented capability curve for the
t sample generator by the manufacture
Fig.9. Curve related to equation 4-6
VII.
According the previous sections, if the capability
c
curve is
calculated by the current equations, the obttained curves will
differ from the manufacturer curves. By usiing the points and
correction factors which have been specifiedd in the paper, the
capability curve of the synchronous generatoor is calculated and
drawn. To do this, it is assumed that the gennerator operates in
the rated condition. Also, the synchronous reeactance and angle
stability limit are, respectively, equal to 1.9778 per-unit and 80
degrees. Based on the design docum
ments, when the
synchronous generator operates at the ratedd voltage, the field
current is equal to 1417 A. According to this
t
condition, the
capability curve is prepared (Fig. 10).
CONCLUSION
In literature, several methods have
h
been proposed to draw the
generator capability curve. Theese methods are often based on
theoretical formulas and do noot cover special conditions such
as the effect of altitude, temperrature, saturation and mechanical
conditions of the synchronous generator. In this paper, we
considered the capability curvve in three parts. The results of
consideration of the armature current region showed that the
studied conditions in this papeer completely met the machine
operating condition. To draw
w the under-excited region, a
simple method is used based onn theoretical methods, concept of
the stability and the practical operation of the generator. The
accuracy of the proposed methhod which have high speed and
high accuracy is confirmed byy the calculation results. It was
proved that the previous curvee of the over-excited region had
differences with the curve pressented by manufacturers. So, by
scrutiny of design documentts of several manufacturers, a
The capability curve presented by thee manufacturer is
shown in Figure 11. As it is shown, tow curves
c
completely
match. The rated power factor in the over-excited region in
both curves exactly occurs at the 161 MW. Additionally, the
731
simple method was presented. Moreover, in this method, the
probable errors due to some assumptions and conditions of
generators such as saturation, etc. are eliminated.
[3]
[4]
The mentioned issues cause the generator capability curve
to be accurately and efficiently determined, which lead to
optimized exploitation of power plant units.
[5]
REFERENCES
[1]
[2]
J. R Poblete and S. M. Deckmann."Stability Margin Reduction Due to
Synchronous Machine Saturated". IEEE Transaction on Circuits and
Systems. Rio de Janeiro, Brazil. vol. 2, pp. 1090-1093. 1995.
Roman Sandoval and Armando Guzman. "Dynamic Simulations Help
Improve Generator Protection". Power Systems Conference: Advanced
Metering, Protection, Control, Communication, and Distributed
Resources. Madren Center, Clemson University, USA. pp. 16-38, March
2007.
[6]
[7]
[8]
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Generators and Generator/Motors for Hydraulic Turbine Applications
Rated 5 MVA and Above", 2005.
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Generators", IEEE Power Engineering Society. Revision of IEEE Std
67-1990 – 2005.
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