IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 41, NO. 4, JULY/AUGUST 2005
1099
Dynamic Simulation and Analysis of Parallel
Self-Excited Induction Generators for
Islanded Wind Farm Systems
Bhaskara Palle, M. Godoy Simões, Senior Member, IEEE, and Felix A. Farret
Abstract—In this paper, a dynamic mathematical model to describe the transient behavior of a system of self-excited induction
generators (SEIGs) operating in parallel and supplying a common
load is proposed. Wind turbines with SEIGs are increasingly being
used to generate clean renewable energy in rural areas owing to
many economical advantages. Parallel operation of SEIGs is
required where the size of the machine is a constraint. SEIGs
connected in parallel experience various transient conditions such
as generator/load/capacitor switching that are not easy to simulate
using conventional models. An automatic numerical solution to
predict the steady-state and transient behavior of any number of
SEIGs connected in parallel is proposed in this paper. The generators can be of different ratings and can have different prime mover
speeds. The performance of the proposed model when subjected to
various dynamic scenarios is compared with experimental results.
The simulation results are in good agreement with the experimental results, confirming the validity of the proposed model. An
aggregated model of a small wind power system is also proposed.
This model was applied to a two-wind turbine case, which can be
extended to simulate a complete wind generating system.
Index Terms—Induction generators,
state-space methods, transient analysis.
parallel
,
,
,
,
, ,
Excitation capacitance.
Load resistance and load inductance.
Wind turbine power.
Air density.
Wind speed.
Propeller radius.
Wind turbine power coefficient.
Tip speed ratio.
Wind turbine torque.
Electromagnetic torque.
Torque coefficient.
Moment of inertia of the wind turbine.
Viscous friction coefficient.
.
– -axes quantities.
Generator number.
Stator, rotor, and load quantities.
machines,
I. INTRODUCTION
E
NOMENCLATURE
,
,
,
,
Stator and rotor voltage.
Stator and rotor current.
Load voltage and load current.
Magnetization current.
Flux linkage.
Rotor angular frequency.
Stator ad rotor resistance.
Stator and rotor leakage inductance.
Mutual inductance.
Number of poles.
Paper ICPSD-05–04, presented at the 2004 Industry Applications Society
Annual Meeting, Seattle, WA, October 3–7, and approved for publication in
the IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS by the Energy Systems
Committee of the IEEE Industry Applications Society. Manuscript submitted
for review October 15, 2004 and released for publication March 19, 2005. This
work was supported by the Coordination for Improvement of Advanced Education Personal (CAPES) and by the National Science Foundation (NSF) under
Grant ECS -0134130.
B. Palle and M. G. Simões are with the Engineering Division,
Colorado School of Mines, Golden, CO 80401-1887 USA (e-mail:
m.g.simoes@ieee.org).
F. A. Farret is with the Department of Electronics and Computation,
Federal University of Santa María, Santa María 97015-003, Brazil (e-mail:
farret@ct.ufsm.br).
Digital Object Identifier 10.1109/TIA.2005.851040
NVIRONMENTAL concerns and international policies are supporting new interests and developments in
small-scale power generation during the last few years. Although the induction generator is mostly suitable for hydro and
wind power plants, it can be efficiently used in prime movers
driven by diesel, biogas, natural gas, gasoline, and alcohol
motors. Induction generators have outstanding operation as
either motor or generator; they have very robust construction
features, providing natural protection against short circuits, and
have the lowest cost with respect to other generators. Abrupt
speed changes due to variations in load or primary source is
usually expected in small power plants. An induction generator,
with its solid rotor easily absorbs these variations and any surge
in currents is damped by the magnetization path of its iron
core without fear of demagnetization, as opposed to permanent
magnet based generators. Therefore, the study of self-excited
induction generators has re-gained importance, as they are
particularly suitable for generation below 15 kVA for wind and
small hydro plants.
A stand-alone self-excited induction generator (SEIG) is unlikely to supply energy demand for ordinarily growing loads for
long time. Thus, multiple generators operating in parallel may
be required to harvest the maximum energy available at a site.
Also, in the last few years, the trend has shifted from installing
a few wind turbines to planning large wind farm installations
0093-9994/$20.00 © 2005 IEEE
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IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 41, NO. 4, JULY/AUGUST 2005
Fig. 2. Aggregated model of parallel SEIGs.
Fig. 1.
Induction machines supplying a common load.
with many induction generators connected electrically in parallel [1]. Hybrid power plants that integrate wind farms with diverse storage devices to allow for the control of the power output
of the ensemble further support the possibility of large-scale installations [2]. With the resulting increased penetration of wind
power into power networks, an accurate dynamic model of the
overall wind farm system is required to analyze the interaction
between the wind farm and the power system. A system of parallel-operated SEIGs in a wind or small hydro plant is subjected
to various transient conditions such as initial self-excitation,
load transient and generator/capacitor switching. Transient interaction and resonant states may also be reasons for concern
for small power plants as they may create unstable oscillations,
deteriorate mechanical elements and trigger protection circuits.
Therefore, it is important to perform modeling and simulation
analysis of parallel-operated induction generators under transient conditions. [3]–[5] developed a wind farm model that can
be used in power system dynamic simulations with steady-state
representation of the generator but does not deal with the transient behavior of SEIGs. Understanding the transient behavior
of parallel SEIGs helps on the proper design of the power plant.
Several papers [6]–[10] have been published on stand-alone operation of self-excited generators and only a few references are
available on parallel-operation of SEIGs. Steady-state analysis
of parallel-operated SEIGs has been discussed [11], [12] and
previous works related to transient analysis do not present clear
numerical modeling and experimental observations [13], [14].
The current literature does not allow transient analysis of parallel operation due to approximated representation of the induction machine models. This paper proposes an algorithm that can
be used to simulate a wind generation system with SEIGs operating in parallel.
With the proposed algorithm, any new generators can be
added or old generators can be removed from the existing parallel generator model just by changing one variable in the state
variable matrix [15]. Fig. 1 shows wind turbines equipped
with SEIGs ready to be connected in parallel according to the
load requirements or when more energy becomes available.
The schematic shown in Fig. 1 seems to cope with the vast
majority of practical cases since it is always expected to have
a new generator connected or disconnected from an already
existing parallel association.
Section II gives a generalized model to simulate a wind generation system with parallel SEIGs. Detailed models of SEIG and
Fig. 3. d–q axes equivalent circuit of an SEIG.
wind turbine are developed in Sections III and IV, respectively.
The transient model developed for a stand-alone generator is
extended to generators operating in parallel in Section V. To
validate the proposed model, simulation results of two induction generators operating in parallel are compared with experimental results in Section VI. The proposed model is tested for
various conditions normally encountered in a real wind generation system.
II. MODEL OF A WIND GENERATION SYSTEM
One of the primary goals of this work is to develop a general model to represent parallel operated SEIGs in a wind farm.
Fig. 2 shows a group of wind turbines equipped with SEIGs supplying an isolated load. Wind energy systems are usually composed of turbine, generator and load. Detailed models of each
of these components are developed in the following sections.
These models are integrated to obtain the complete model of a
wind turbine driving an SEIG. It is shown that this aggregated
model could be extended to simulate multiple SEIGs connected
in parallel in a wind farm.
III. SEIG MODELING
Fig. 3 shows the – -axes equivalent circuit of a self-excited
induction generator supplying an inductive load. The dynamics
of an induction machine can be expressed in a classic matrix
PALLE et al.: DYNAMIC SIMULATION AND ANALYSIS OF PARALLEL SEIGs SUPPLYING AN ISOLATED LOAD
formulation using – -axes modeling [16] as shown in (1), at
the bottom of the next page. The representation includes the
self and mutual inductances as coefficients, which are widely
used in machine theory. The following assumptions are made in
this analysis: 1) core and mechanical losses in the machine are
neglected,; 2) all machine parameters except the magnetizing
inductance are assumed to be constant; and 3) stator windings,
self- excitation capacitors, and the load are star connected (although a common ground through delta connection is also acceptable). Individual variation in the magnetizing inductance is
incorporated in the analysis.
Traditional – -axes modeling of induction generators is not
convenient for the automatic building up of a general model of
parallel-operated induction generators. Every time a new generator is switched on/off from the system, the set of differential
equations for that particular generator have to be added to/removed from the system, which might become cumbersome if
the size of the system is large. Isolation of machine parameters from the self-excitation capacitor and load parameters is required to make the process of simulating parallel operated generators convenient. To isolate those parameters, (2), shown at the
1101
bottom of the page, has been formulated using eight first-order
differential equations that relate the stator and rotor currents and
voltages. The matrix representation can be used for steady-state
as well as transient behavior of the parallel generator system.
The simultaneous solution of this system of equations can be obtained using the Runge–Kutta fourth-order integration method
with automatic adjustment of step, which gives the instantaneous values of – -axes voltages and currents for stator and
rotor. See (1), shown at the bottom of the page. Equation (1) can
be expressed as a state variable matrix, which takes the form of
(2), shown at the bottom of the page, which is in the form of
, or
classical state-space equation
(3)
refer, respectively, to the partition of
where , , and
into matrices for the induction generator parameters,
matrix
is
the self-excitation capacitance, and the load. Vector
the transposed matrix
and the submatrixes
,
and
are defined as the set of equations shown at the
(1)
(2)
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IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 41, NO. 4, JULY/AUGUST 2005
bottom of the page. The excitation vector
of (3)
, shown
is multiplied by the excitation parameter matrix
defines the voltages corresponding
following (therefore,
to the residual magnetism in the machine core)
The variation of the magnetizing inductance is the main
factor in the dynamics of the voltage build up and stabilization
in SEIGs. The relationship between magnetization inductance,
, and the magnetization current for each induction machine
was obtained experimentally. The nonlinear relationship between magnetizing inductance and magnetizing current for the
generator G1 used in the experimental setup is shown below
(4)
Fig. 4 shows the experimental and simulated plots of the transient self-excitation process of a stand-alone SEIG. The terminal
voltage of the generator stabilizes when the machine reaches the
saturation level. The induction generator was operated at 1780
r/min with a dc motor as prime mover. A capacitor bank of 160
F in star connection is supplying reactive power for the machine and a 120- 22.5-mH star load was connected at 7.6 s
after the generator was completely excited. Variation of speed
observed in the laboratory when load was applied is incorporated in the numerical simulation as seen in Fig. 4(a). Remnant
and
Fig. 4. Self-exciatation and load response of a stand-alone SEIG. (a) Rotor
speed profile. (b) Variation in phase voltage measured during self-excitation and
load switching on generator G1 (see Section V). (c) Variation in phase voltage
simulated using MATLAB.
magnetism in the machine core is also taken into account and is
explained below.
To begin the self-excitation process of the induction generator, it is necessary that a certain amount of residual magnetism
be present. That is, it is a condition “sine qua non.” This effect
must also be taken into account in the simulation of the self-excitation process, without which it is not possible to start the numerical integration process. At the beginning of the integration
process of (2) and (4), an impulse function was used to represent the transient existence of the residual magnetism that fades
away after the first iterative step. Any other representation of the
way the residual magnetism fades way may be acceptable. This
observation is vital in understanding the dynamics of self-excitation phenomenon because, it would justify the use of a small
voltage source to the real machine for recovery of its active state
during the occurrence of a fortuitous core de-excitation.
PALLE et al.: DYNAMIC SIMULATION AND ANALYSIS OF PARALLEL SEIGs SUPPLYING AN ISOLATED LOAD
1103
IV. MODEL FOR PARALLEL SEIGS
The model used for an isolated machine can be extended for
multiple generators operating in parallel. The model to be presented is according to the representation of SEIGs supplying a
common load as shown in Fig. 1. Equation (3) is generalized for
generators operating in parallel as explained below. Incoming
generators can be incorporated into the model by appending the
generator parameter matrix ’ ’ diagonally as shown in (5). This
is made possible by the isolating the generator, excitation capacitance and load parameters. The matrix representation allows us
to simulate the behavior of generators in parallel during the
self-excitation process and in steady state, besides allowing us
to analyze the transient performance under varying load conditions and generator switching. Equation (5) is also in the form
of the classical state-space equation. State-space representation
is very useful for eigenvalue and eigenvector analysis. It is also
a powerful technique that provides deep insight into the system
behavior and greatly aid the system design
Fig. 5. Capacitance requirements of an SEIG supplying a load.
is the torque coefficient and the electromagwhere
netic torque generated by the induction generated is
(8)
..
.
..
.
..
..
.
.
..
.
The machine swing equation is given by
(9)
Equation (9) represents the wind turbine as a single lumped inertia. However, if required, (9) may be expanded to include the
masses of the generator, gearbox and blades with the associated
parameters. Using an iterative process, the instantaneous prime
mover speed can be calculated.
..
.
..
.
(5)
where
V. TURBINE MODEL
The power generated by the wind turbine is given by
(6)
is the wind turbine power coefficient usually exwhere
pressed as a function of the tip speed ratio, ( ). Power coefficient is not constant, but varies with the wind speed, rotational
speed of the turbine, and turbine blade parameters. The torque
generated by a turbine is given by
(7)
VI. RESULTS AND DISCUSSION
Simulations in this paper have been developed in MATLAB®.
Remnant magnetism in the machine is taken into account in the
simulation process without which it is not possible for the generators to self-excite. As was said above, an impulse function is
used to represent the remnant magnetic flux in the core. Fig. 5
shows capacitance and speed requirements of a loaded SEIG
needed to sustain self-excitation. At lighter loads, speed and
excitation capacitance can vary over a wide range without the
generator losing excitation. However, for heavy loads, higher
capacitances are needed as SEIG absorbs more reactive power
and there are maximum and minimum speed limits for the generator to produce self-excitation. The generator might collapse
under heavy loads when sufficient reactive power is not supplied
as depicted in Fig. 6. Other parameters remaining constant, the
maximum load that the generator can supply is dictated by the
excitation capacitance.
Two similar induction machines driven by two dc motors
were used to investigate the proposed model experimentally.
DC motors act as prime movers emulating wind-driven turbines.
Variation in magnetizing inductance due to changes in load and
prime mover speed has been taken into account by obtaining
the nonlinear relationship between air-gap voltage and magnetizing current experimentally. The induction machine parame-
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IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 41, NO. 4, JULY/AUGUST 2005
Fig. 6. Voltage collapse in a stand-alone SEIG under heavy load. (a) Rotor
speed profile. (b) Variation in phase voltage measured during collapse of G1.
(c) Variation in phase voltage simulated.
TABLE I
GENERATOR G1 RATINGS AND PARAMETERS
Fig. 7. Parallel connection of two SEIGs with different voltage levels. (a)
Rotor speed profile. (b) Variation in phase voltage of G1 measured. Load is
applied at t = 1:95 s and paralleling switch is closed at t = 3:85 s. (c)
Simulated variation in phase voltage of G1. (d) Simulated variation in phase
voltage of G2.
TABLE II
GENERATOR G2 RATINGS AND PARAMETERS
ters shown in Tables I and II are used for simulation. In addition
to the stand-alone operation of an SEIG discussed in Section III,
four other scenarios are discussed in this section.
First, the maximum load that an isolated SEIG can supply
with a fixed excitation capacitance was tested in the laboratory. Load on the generator was increased until the machine can
no longer supply the required load power. The generator was
excited with a 160- F capacitance bank and a 45- 45.5-mH
star-connected inductive load was applied after the generator
s. Fig. 6 shows the experimental
was fully excited at time
and simulated plots of terminal voltage collapse of a stand-alone
SEIG (G1) when this heavy load was applied. Speed variations
observed in the laboratory were taken into account for simulation, as illustrated in Fig. 6(a).
Dynamic model for parallel SEIGs presented in Section IV
was used to simulate parallel operation two SEIGs. The first
case that was studied was the transient process of generator
switching. Generator G1 was self-excited with 160- F capacitance at 1800 r/min and a 130- 22.5-mH star-connected load
was applied at time
s. Drop in the terminal voltage of G1
Fig. 8. Parallel connection of two SEIGs with similar voltage levels. (a) Rotor
speed profile. (b) Variation in phase voltage of G1 measured. Load is applied at
t = 1:2 s and paralleling switch is closed at t = 4:6 s. (c) Simulated variation
in phase voltage of G1. (d) Simulated variation in phase voltage of G2.
can be observed at this instant. Generator G2 which was previously self-excited with 160 F at 1800 r/min was suddenly cons. Fig. 7 shows the transient
nected in parallel at time
behavior of the two generators during the generator switching.
Sudden collapse in the phase voltages of the two generators can
be observed when the second generator is switched on. This is
due to the differences in phase voltages of the two generators
at the paralleling instant. Full common voltage was recovered
s. Also, from Fig. 7(a), a heavy dip in the
at about time
overall speed of the machines can be observed at the paralleling
instant. It can be noticed from Fig. 7 that the model is able to
successfully simulate the load and generator switching.
Synchronization techniques could be applied so as to switch
the generators when the phase voltages are at the same levels.
The purpose of this result was to demonstrate the possibility of
representing this worst case scenario using the proposed model.
PALLE et al.: DYNAMIC SIMULATION AND ANALYSIS OF PARALLEL SEIGs SUPPLYING AN ISOLATED LOAD
1105
in Fig. 2 has been used to simulate the wind turbine with real
wind conditions. This could be extended to simulate an entire
wind farm with multiple wind turbines equipped with SEIGs.
The wind speed profile of the two turbines is shown is Fig. 9(a).
The simulated voltage variation closely follows the wind speed,
thus confirming the validity of the turbine and the generator
model. The generator begins to self-excite after the rotor has
reached a certain speed . The dip in voltage at corresponds
to share the load
to load switching. G2 is connected to G1 at
resulting in a slight increase in voltage.
Fig. 10 shows the simulated variation in phase currents of
generator G1 and G2 during the load and generator switching
process. The current surge experienced by the two machines
during the switching of the second generator was very high (approximately twice the rated current). However, it settled down
in a few milliseconds; the system is able to sustain its excitation.
Fig. 9. Simulation of two wind turbines operating in parallel. (a) Wind speed
profile. (b) Simulated phase voltage of G1. Load is applied at t = 36 s and
paralleling switch is closed at t = 38 s. (c) Simulated phase voltage of G2.
Fig. 10. Simulation of two wind turbines operating in parallel. (a) Simulated
phase current of G1. (b) Simulated phase current of G2.
The next result (Fig. 8) shows the experimental and simulated plots of the transient generator switching process when
parallel connection was made between SEIGs operating at identical voltage levels. As in the previous case, G1 was self-excited
with 180- F capacitance and a 130- 22.5-mH star load was
s. Generator G2 was already self-excited
applied at time
with 160 F and was connected in parallel at time
s. Compared to the previous case, higher capacitance value was chosen
to excite G1, so that the two generators would be operating at
similar voltage levels at the paralleling instant. No synchronization techniques were used. Full common voltage was recovered
s. As the voltages were similar, there was
at about time
no collapse in the terminal voltages as observed in the previous
case and the voltage and speed dips are not very pronounced.
Fig. 9 shows the simulated plots of two 20-kW wind turbines
operating electrically in parallel. The aggregated model shown
VII. CONCLUSION
This paper has presented an innovative algorithm for analyzing the steady-state and transient performance of a wind
power system with parallel-operated SEIGs. The approach
presented in this paper enhances previous works based only
on steady-state conditions that cannot be used for transient
analysis. It has been shown that a new wind turbine or a generator can be incorporated into the existing parallel generator
model by appending the generator matrix simplifying the
simulation process. Performance of the parallel SEIG system is
analyzed during the initial self-excitation, load switching, and
generator switching. Reactive power requirements and load
demand limits are also analyzed. The simulation results closely
match the experimental results validating the proposed matrix
partition scheme and opening new possibilities to incorporate
advanced control to monitor and optimize a parallel installation
of SEIGs. A model for a wind turbine equipped with an SEIG
was presented. Simulations results for a two-wind turbine case
were presented that demonstrate the usefulness of the proposed
model in modeling a small wind generating system.
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Bhaskara Palle was born in Hyderabad, India, in
1980. He received the B.Tech. degree in electrical
and electronics engineering from Jawaharlal Nehru
Technological University, Hyderabad, India, in 2001.
He is currently working toward the M.S. degree
in engineering systems at the Colorado School of
Mines, Golden.
His main areas of interest are power electronics
and power systems.
Marcelo Godoy Simões (S’89–M’95–SM’98)
received the B.S. and M.Sc. degrees in electrical
engineering from the University of São Paulo, São
Paulo, Brazil, in 1985 and 1990, respectively, the
Ph.D. degree in electrical engineering from the
University of Tennessee, Knoxville, in 1995, and the
Livre-Docência (D.Sc.) degree from the University
of São Paulo in 1998.
He joined the faculty of the Colorado School of
Mines, Golden, in 2000 and has been working to establish research and education activities in the development of intelligent control for high-power electronics applications in renewable and distributed energy systems. He is the author of Renewable Energy Systems: Design and Analysis with Induction Generators (Boca Raton, FL: CRC
Press, 2004).
Dr. Simões is a recipient of a National Science Foundation (NSF)—Faculty
Early Career Development (CAREER) Award, which is the NSF’s most
prestigious award for new faculty members, recognizing innovative research of
young teachers/scholars. He is serving as the Program Chair for the 2005 IEEE
Power Electronics Specialists Conference, General Chair of the 2005 Power
Electronics Education Workshop, Chair of the IEEE Power Electronics Chapter
of the Denver Section, IEEE Power Electronics Society Intersociety Chairman,
as Associate Editor for Energy Conversion, as well as Editor for Intelligent
Systems, of the IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC
SYSTEMS, and as Associate Editor for Power Electronics and Drives of the
IEEE TRANSACTIONS ON POWER ELECTRONICS. He is the Program Chair for
PESC’05, the IEEE Power Electronics Specialists Conference, to be held in
Brazil. He has been actively involved in the Steering and Organization Committee of the IEEE/DOE/DOD 2005 International Future Energy Challenge.
Felix A. Farret received the B.E and M.Sc. degrees
in electrical engineering from the Federal University of Santa María, Santa María, Brazil, in 1972
and 1986, respectively, the M.Sc. degree from the
University of Manchester, Manchester, U.K., and
the Ph.D.degree from the University of London,
London, U.K.
Since 1974, he has taught in the Department of
Electronics and Computation, Federal University
of Santa Maria. He works in an interdisciplinary
educational background related to power electronics,
power systems, nonlinear controls, and integration of renewable energy. He
was a Visiting Professor at the Engineering Division, Colorado School of
Mines, Golden, during 2002–2003. He is currently committed to undergraduate
and graduate teaching and research. Energy engineering systems are the focus
of his present interests for industrial applications. He is the author of Use of
Small Sources of Electrical Energy (santa maría, Brazil: UFSM Univ. Press,
1999) and coauthor of Renewable Energy Systems: Design and Analysis with
Induction Generators (Boca Raton, FL: CRC Press, 2004). In more recent
years, he has coordinated several technological processes in renewable sources
of energy and transferred them to Brazilian enterprises, such as AES-South
Energy Distributor, Hydro Electrical Power Plant Generation of Nova Palma,
RGE Energy Distributor, and CCE Power Control Engineering Ltd. These
processes have been related to integration of micro power plants from distinct
primary sources, voltage and speed control by the load for induction generators,
and low-power PEM fuel-cell applications and model development. Injection
of electrical power into the grid is currently his major interest. In Brazil, he
has been developing several intelligent systems for industrial applications
related to integration, location, and sizing of renewable sources of energy for
distribution and industrial systems, including fuel cells, hydropower, wind
power, photovoltaics, battery storage applications, and other ac–ac and dc–ac
links.