Application of induction machines in wind turbine driven generators is a good alternative due to their good characteristics such as efficiency, reliability and low cost. Nevertheless, when isolated operation is required, the application of external capacitive bank, connected to the stator windings, to provide selfexcitation results in a rather complex analysis. This paper presents an analysis of selfexcited induction generator connected to a load either directly or by an intermediate of a power converter. At first a dynamic model of the induction generator accounting for magnetic saturation is developed. Then a number of balanced and unbalanced capacitors, passive and active loads are verified. Experimental results obtained from laboratory tests are compared to those simulated; the two are shown to be in good agreement.
1. Introduction
Squirrel cage induction generators, due to their simplicity and advantages, equips a great part of the wind turbine generator on mini powers plants. For gridconnected wind turbine, the magnetizing reactive power is supplied by the grid, and regeneration operation is automatic once the motor shaft is driven to rotate above synchronous speed. For standalone operation, the induction generator must be selfexcited, since there is no external reactive power source. This is typically achieved by connecting capacitors in parallel with the motor magnetizing impedance. A selfexcited induction generator (SEIG) needs a threephase capacitor bank to supply the required reactive power directly and must be driven at a suitable speed by an external prime mover
[1]
. In this case, autonomous operation becomes possible, but, the variations in the voltage and the frequency are highly dependent on the wind speed, the exciting capacitance and the load demand
[2]
.
This paper shows that, due to the saturation of the main magnetic circuits, the induction generator behavior may not be evaluated theoretically with accuracy by means of conventional simplified model. To the contrary, the results obtained by simplified model have been generally quite satisfactory for motor operating conditions; because of small slips and the magnetic flux is equal to the nominal value. During selfexcitation the variation in the value of magnetizing inductance, due to saturation, is the main factor that stabilizes the growing transient of generated voltage.
In last years, many authors have considered the influence of saturation of main magnetic circuits on the behavior of induction machines, and others have evaluated different developed models. The effect has been taken into account in different ways
[3

4]
.
The models of the load and the capacities of selfexcitation are established independently of the induction generator model. After having analyzed the operation of the induction generator under balanced and unbalanced linear load, the behavior of the induction generator feeding a nonlinear load, i.e. static inverter (rectifier or inverter), is outlined.
From the analysis of the results it will be clear how important it is to take into account saturation phenomena if the behavior of the machine has to be simulated with a good approximation. The good agreement of simulated and experimental results has validated the suggested developed models.
2. Self Excited Induction Generator Modeling
 2.1 Induction generator model
The transient behavior of an induction machine is normally represented in the dq reference. As illustrated in
Fig. 1
, a resistor R
_{Fe}
coupled to the magnetizing branch is added to incorporate iron losses. This resistor can be used to takes into account core losses in stator iron. Core losses in rotor are not correct represented by R
_{Fe}
and are neglected in this paper
[5]
.
The dynamic model of the induction machine in the synchronous reference frame is described by the following equations:
Equivalent circuit of an induction machine by considering saturation and iron losses
The symbols in (16) are defined as:

Rs,RrStator and rotor resistances;

Lσs,LσrStator and rotor leakage inductances;

LmMutual inductance;

Φs,ΦrStator and rotor flux vectors;

Stator and rotor voltage vectors;

Stator and rotor currents vectors;

Magnetizing flux and current vectors;

Synchronous and slip angular speeds;

P Number of pole’s pair;

TemElectromagnetic torque;

Fe Index associated to iron loss branch.
Consideration of iron loss leads to an increase of the system order and introduces additional mutual coupling between the axis components d and q.
The treatment of saturation has been considered in detail by a number of authors, and numerous methods with varying level of complexity are available. In this paper, Saturation effect in induction machines is associated with the magnetizing flux, whereas, saturation of leakage flux is neglected. Including saturation in dq axis model consists of expressing the flux linkages and their time derivatives as function of currents
[3

6]
.
The principles of magnetizing flux saturation modeling and derivation procedure remain the same as for induction machine without iron loss. The function L
_{m}
=F(I
_{m}
), which models saturation, is applied to the set of Eqs. (16). Model of a saturated induction machine can be formed in various different ways, depending on the selected set of statespace variables
[4]
. The model selected here is the one with stator and rotor current dq axis components as statespace variables. It may be given in matrix form as
[5]
:
The variable terms in (7) are:
M
_{dy}
and L
_{m}
are the dynamic and the static mutual inductance's, respectively. M
_{dq}
is the term that explains the “cross effect” between the axis in quadrate. α is the angle between the d axis and the magnetizing current I
_{m}
.
From a practical point of view the developed model can be easily used. It requires only a preliminary experimental evaluation of the noload magnetizing characteristic of the machine L
_{m}
=F(I
_{m}
) and the equivalent iron loss resistance R
_{Fe}
. The evaluation can be made by performing standard noload tests on an induction machine. Therefore in the following analysis the parameters of the induction machine are assumed constant except the magnetizing inductance which varies with saturation.
In generator operating conditions, Eqs. (16) cannot be solved because the voltage space V
_{s}
is not known; it is possible to obtain solution only with an external network that provides reactive power. In the self excited induction generator, this power is obtained form a capacitance bank
 2.2 Capacities model
The model of capacities of selfexcitation is established in a way completely independent of the machine model. The stator windings of the induction generator are connected to a star capacitive bank. The equations of self excitation, at no load conditions, are given by:
Where I
_{sg}
is the generator current (magnetizing current), I
_{c}
is the capacitance current, and a, b, c are phases indices. In the noload conditions, the generator current is equal to the capacitance current (
Fig. 2
).
This system can be transformed in the synchronous reference frame (d,q) by applying Park Transformation:
The value of the excitation capacitance must be greater than a minimum limit so that the generator current is sufficient for the operation in the nonlinear portion of the magnetization curve.
 2.3 Linear load model
The SEIG can be loaded by connecting a resistive, inductive and capacitive load, across the excitation capacitor C. In this case of linear load (
Fig. 2
), the dynamic model of a threephase balanced load is given by:
Where I
_{sL}
is the load current, and R
_{L}
, L
_{L}
, C
_{L}
are the load components. Hence, the self excitation model takes the followings form at load conditions (
Fig. 2
):
Linear load fed by self excited induction generator
Nolinear load (Rectifier + RL) fed by self excited induction generator
 2.4 No linear load model
The three phase diode bridge rectifier is used to convert variable magnitude, variable frequency voltage at the induction generator terminal into DC voltage (
Fig. 3
).
The rectified output voltage is expressed as:
The Dc Link current is governed by the following equation:
Where, R
_{L}
and L
_{L}
are the load resistance and inductance respectively.
Then, the Load current that fed the rectifier is deduced:
The Eqs. (12) remain still valid.
Fig. 4
shows the scheme of the SEIG feeding an electronic converter. This system is made up of a threephase voltage source inverter connected to RL load. The PWM signals are used to switch on the IGBT’s in the inverter. The IGBT’s are connected anti parallel with the diodes. The converter is modeled by three switching functions (F
_{1}
, F
_{2}
and F
_{3}
) to determinate the state of the IGBTs (on or off) in each branch of the bridge. Considering the commutation basic rules of converters, the switches of a branch must change of complementary form. F
_{i}
is the switching functions to determinate the state of IGBTs:
Nolinear load (Rectifier + Converter + RL) fed by self excited induction generator
The converter output voltages, applied to the load, are given by:
The differential voltage equations of the inverter are as follow:
The dc side current of the inverter and its relationships with the ac side currents is expressed by:
3. Simulation results
Many example test cases have been studied to evaluate the modeling approach. A select few are presented in this section
 3.1 Noload operation
The operation of the asynchronous generator, based on a simplified model (not taken into account of saturation), leads to a divergence of the characteristics because the saturation which fixes the operating point in steady operation.
Selfexcitation is excited by reciprocal relation of rotor residual magnetism and selfexcited capacitor. When the machine is driven by an external mover, the current is induced in the stator winding because of residual flux of the rotor. Connection of suitable capacitors to stator winding causes leading current. This current increases the core flux, and the voltage difference between induction voltage and capacitors can be constant. The continuous increasing of voltage is controlled by magnetic saturation and voltage finally reaches steady state. The voltage depends on speed, capacitance, machine parameters, magnetic characteristics and loads. Such magnetic excitation phenomena are caused by continuous energy circulation between the electric field (capacitors) and the magnetic field (machine). When the operating point is reached, the machine delivers a stator voltage which its rms value is constant.
Fig. 5
shows the buildup of voltage and current achieved when 65μF of capacitance was switched across the motor stator winding while it was turning at 1500 rpm.
As can be observed in
Fig.6
, the magnetizing inductance starts from a linear value then decreases to reach its saturated value. This change in L
_{m}
is due to the characteristics of the magnetizing curve, at the start of selfexcitation point where the voltage is close to zero, L
_{m }
is close to its linear value. Once selfexcitation starts the generated voltage will grow and then Lm starts to decrease while the voltage continues to grow until it reaches its steady state saturated value.
Generator voltage and current built up process at noload by taking into account magnetic saturation at 1500 rpm
Magnetizing Inductance variation in built up process at noload
Evolution of the rms generator voltage depending on the speed and the excitation capacities
Fig. 7
shows the variation of the rms generator voltage against the variations in the speed and excitation capacitors. As can be seen, the rms generator voltage increases as the values of the selfexcitation capacitor and speed increase. Increasing self excitation capacitance value results in high voltage. Therefore, the capacitance value must be correctly adjusted.
Same conclusion can be outlined for the variation of built up time of generator voltage with the selfexcitation capacitances and speed that is shown in
Fig. 8.
When one of the three capacities is sudden disconnected, the process of selfexcitation is maintained if the value of two remaining capacities is sufficient to maintain the stator voltage (
Fig. 9
. left). If the unbalanced operation, obtained with the two remaining capacities, is not sufficient to maintain the phenomenon of selfexcitation, the stator voltage falls down and causes the demagnetization of the generator (
Fig. 9.
right). Furthermore, unbalanced excitation capacities lead to an unbalanced stator voltage as shown in
Fig. 10
.
Evolution of the built up time depending on the speed and the excitation capacities
Sudden disconnection of one of the three excitation capacitors: voltage fall down (right) voltage maintenance (left)
Unbalanced capacities effect
 3.2 Load operation
Two possible connections of the induction generator to load can be found: either connected on the load directly or by means of an electronic converter. The first one has advantages of costs, maintenance and reliability while the second one, by making speed regulation possible, increases the efficiency of the wind turbines
[7
,
8]
.
 ALinear load
The call of reactive energy, poses a problem for the induction generator. Because, even for its own requirements in reactive, it depends on an external source (capacities of excitation). The more important the load is, the more the requirement in reactive energy of the induction generator is important, which results in a decrease of the output generator voltage (
Fig. 11
. a and b). Without load the SEIG requires only its own reactive power for selfexcitation, but loaded SEIG requires a more reactive power for selfexcitation and for inductive load. When R and L is large the characteristic is similar to the no load self excitation case. If RL is small, larger is the load.
Generator voltage response (left) and current response (right) to load connection at t=1s
Capacitance current (left) and load current (right) to resistive load connection at t=1s
Evolution of the maximum generator voltage depending on the value of the impedance Z (left) and the power factor cosφ(right)
To compensate the supplement of reactive called by the generator, one can insert series condensers with the load (
Fig. 11.c
). This technique of compensation is a simple method to improve the generator voltage regulation.
Fig. 12
shows the capacitance and the load currents when the resistive load is applied. The capacitance current varies in the same ratio as the generator current and the load current appear with load.
As can be seen form
Fig. 13
, the generator voltage decreases when the value of the load impedance Z increases, in other hand, it indicates that the generator voltage tends to fall steeply with balanced inductive load as compared with the resistive load (when cosφ decrease, generator voltage is more affected). With inductive load, excitation capacitors must provide the reactive power to the inductive load in addition to the reactive power to the generator.
 BNolinear load
In
Figs. 14
,
15
and
16
, the generator and load currents and theirs harmonic spectrum, in case of diode rectifier, thyristor rectifier or converter insertion, are respectively presented.
Generator and Load currents and theirs harmonic spectrum in case of a (diode rectifierRL) load
Generator and Load currents and theirs harmonic spectrum in case of a (thyristor rectifierRL) load with α =30°
Figures show that generator and load currents present a high loworder harmonic content, due to the presence of the converter. Before and after load application, the harmonic content in the currents has been slightly changed. It can be seen from these figures that for both the rectifier and the converter, the generator current wave form is distorted and becomes not sinusoidal. However, in the case of inverter, the generator output voltage of the generator is rectified and inverted using the PWM inverter. The modulation index is adjusted such that the voltage and the frequency at the output are maintained.
Generator and Load currents and theirs harmonic spectrum in case of a (rectifierconverterRL) load
4. Experimental results
The experimental bench has been realized with an induction generator mechanically coupled with a dc motor. Linear loads, capacitance bank, numerical scope with PC connection complete the bench (
Fig. 17
). The experiments investigated in this section are done in noload and loading conditions with linear loads. The data acquisition started a short time before the built up process or load application.
The induction generator is operated at 1000 rpm driven by a DC motor as a prime mover. Then a star connected capacitor bank of 65μF was switched across the terminals of the stator of the induction machine. The excitation capacitors are selected to provide the generator rated terminal voltage at no load condition
Experimental bench
Fig. 18
shows the experimental built up process of the stator voltage and current under noload conditions. As can be observed, the magnitude of the voltage obtained experimentally is in agreement with the simulated one shown in
Fig. 5
.
From
Fig. 19
, we can see that in the case of insufficient capacities, the accumulated reactive energy slowly disappears and consequently the voltage amplitude slowly decreases to a very low level, proportional to the remanent magnetism. In the opposite case, the voltage is maintained.
Experimental voltage and current built up process at noload and at 1000 rpm
Experimpental Sudden disconnection of one of the three capacitors: voltage fall down (left) voltage maintenance (right)
Experimental generator voltage response to load connection: Resistive load R (left) capacitive load RC (right)
Experimental current response to load connection: (a) Generator current; (b) Capacitance current; (low) and load current (top)
Experimental generator voltage in case of unbalanced capacitance
Experimental generator voltage in case of unbalanced load
In load tests, the generator is loaded at t=1s. As shown in
Fig. 20
and
Fig. 21
, immediately after that a transient process started, the voltage and current amplitude rapidly decreased. The generator decelerates; the reason for the decrease in rotational speed is due to the change in load torque, as a result a slightly frequency decrease after the load application is detected.
Fig. 20
.right shows that an additional shunt capacitance with the load would be required for improved the generator voltage regulation.
Fig. 22
shows the unbalanced operation caused by unbalanced excitation capacities.
Fig. 23
shows the behavior of SEIG under an unbalanced load. In this case, the generated voltage and its frequency decrease. Moreover, the three phase terminal voltage and stator currents are also unbalanced. As a result of this unbalanced currents yield a current that flow by the neutral conductor if existed.
5. Conclusion
In this paper, the authors have investigated modeling of the self excited induction generator used in wind generation. The developed model has been validated by experimental results. The analysis of the results presented in the paper clearly evidences that saturation phenomena have a considerable effect on the performances and must be taken into account.
The limits relate to the variations of the rms voltage and the frequency at load application and the possible variations of speed were outlined. The behavior of the induction generator depends considerably on the nature of the load, in the case of a passive load (linear), the output voltage as well as the current decrease but remain sinusoidal. Whereas, in the case of an active load (nonlinear), a bad quality of the energy is related to the nosinusoidal form of the voltage wave because of the presence of a static converter. However, the voltage level and the frequency at the output can be maintained.
BIO
Samir Moulahoum was born in Algiers in 1971. He received the Engineer degree in Electrical Machines in 1995 and the Magister degree in Electrical Engineering in 1998 and the Doctorate degree in Power Elctronics and Drives in 2006 from University of Sciences and Technology of Algiers USTHB. He was with GREEN laboratory, UHP University, Nancy, France, as invited researcher for two years. He is actually an associate professor in Department of Electrrical Engineering at the University of Médéa. His research interests are Power Electronics, Electrical Drives, Power Generation and Power Quality.
Nadir Kabache received the Engineer, Magister and Doctorate degrees in Electrical Engineering in 1997, 2001 and 2007 respectively from M’hamed Bouguerra University of Boumerdès. He is currently an associate professor in Electrical Engineering Department at The University of Médéa. His research interests include Electric Machines, Variable Speed Drives. He is also Director of Research Laboratory in University of Médéa since 2010
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