Modeling of Self-Excited Induction Generator in

International Journal of Electrical & Computer Sciences IJECS-IJENS Vol:20 No:01 1

202401-4747- IJECS-IJENS @ February 2020 IJENS I J E N S

Modeling of Self-Excited Induction Generator in

Synchronously Rotating Frame Including Dynamic

Saturation and Iron-Core Loss into Account Bilal Abdullah Nasir / Northern Technical University / Hawijah Technical Institute.

Abstract-- A dynamic model in a D-Q synchronous

rotating reference is presented for a self-excited induction

generator (SEIG) that takes into account the stator and

rotor iron core and stray load losses and dynamic saturation of magnetizing inductance.

The new model deals with the same number of state-space

differential equations as the conventional SEIG model by a

modification the machine equivalent circuit. The modified

equivalent circuit of SEIG can deal with all machine

parameters without losing the accuracy of the calculation.

This equivalent circuit will become an efficient tool for

performing calculations as well as a suitable for vector control algorithm.

Index Term-- SEIG, Synchronously rotating frame, Iron

Core Loss, Stray Load Loss, Dynamic Saturation.

1- INTRODUCTION

In general, a self-excited induction generator (SEIG)

has been known since the 1930s [1, 2]. In the isolated area

and stand-alone applications that employ wind or hydropower up to (100) KW, SEIG's have many

advantages compared with synchronous generators [3].

The induction generator is rotated by a wind turbine and a

suitable capacitance connected across the generator

terminals. The voltage generated is determined by the

magnetizing saturation characteristics. At no load, for

each capacitance, there is a corresponding rotor speed

and vice versa [4-8].

Many models have been used to analyze the SEIG.

These models can be classified as steady-state models,

which include the loop impedance [9-10] and nodal

admittance [11], and transient models in the D-Q axes

based on the general machine theory [5, 12]. However,

steady-state analysis is not able to show dynamic

characteristics of the SEIG due to the iron loss as well as

stray load loss effects have been neglected.

Seyoum, D. and et al. [13] have been presented a

novel analysis for the dynamics of SEIG taking iron loss

into account in the D-Q axes model. The paper concluded

that the generated electromagnetic torque with iron loss

included is higher than that without iron loss. Mateo

Basic and et al. [14] have been presented a dynamic

model of the SEIG with iron loss in stationary reference frame. Iron losses are simulated as a function of

the supply frequency and the iron core loss current. Sohail

Khan and et al. [15] have been presented a dynamic model

of wind turbine driven SEIG taking the effect of iron core

losses and dynamic mutual inductance. The iron losses are considered as a function of supply frequency and the

magnetizing inductance is considered as a saturated and

an error of 50% observed in the results of this model due

to these considerations.

In the conventional dynamic model the stray load

losses are neglected. Iron core losses are typically up to

5% of the induction machine rated power, and stray load

losses may be between 0.5 - 3% at full load and cannot be neglected [16].

Levi, E. and Lamine, A. [17] have been presented a

suitable model of dynamic equivalent circuit of induction

machines for appropriate calculation of stray load losses.

In this article a novel dynamic modeling of SEIG in

synchronously rotating frame is presented taking into

account the effect of dynamic saturation of magnetizing

inductance and both stator and rotor iron core and stray

load losses .The model is considered to deal with transient

as well as steady-state conditions with high accuracy

without increasing the number of state-space differential

equations.

2- DYNAMIC MODELLING OF SEIG TAKING

INTO ACCOUNT IRON CORE AND STRAY LOAD

LOSSES

The induction machine in figure (1) can operate as

SEIG with appropriate capacitor bank connected across its

terminals, and its rotor is rotating at a suitable speed with

a prime mover. The generator voltage is building-up when

a suitable value of residual magnetism or initial capacitor

voltage is found in the machine.

Fig. 1. SEIG driven by a prime mover

Figure (2) shows dynamic D-Q axes equivalent circuit of

the SEIG with capacitor bank and inductive load, taking

into account the iron and stray load losses in a

synchronously rotating reference frame. The iron loss is

represented by an equivalent variable resistances



( ) connected in parallel with the dynamic

saturated magnetizing inductance ( ). The stray loss represented by an equivalent variable

resistance ( ) connected in series with stator and rotor leakage inductances. Both resistances are

derived after a modification in the SEIG equivalent

circuit, and they depend on the stator angular speed, while

the rotor stray load loss resistance depends largely on the

rotor speed.

a) D- axis equivalent circuit

b-) Q-axis equivalent circuit

Fig. 2. Equivalent circuit of SEIG in D-Q axes including stator and rotor

iron core and stray load loss resistances.

The modified equivalent circuit is shown in figure (3).

In this circuit the parallel branches of the stator and rotor

iron core resistances ( ) are replaces by series

resistances ( ) in the magnetizing branch and

the dynamic magnetizing inductance ( ) is replaced by

series equivalent dynamic magnetizing inductance ( ) in the magnetizing branch.

Also, in this circuit the parallel resistances ( )

connected with stator leakage inductance ( ) are

replaced by a series equivalent resistance ( ) to represent the stray load loss in stator-equivalent circuit,

while the parallel resistances ( ) connected

with rotor leakage inductance ( ) replaced by a series

equivalent resistance ( ) to represent the stray load loss in the rotor circuit. This idea is stated as the first time,

due to, from a literature serve related with stray loss in

induction machines, I concluded that the stray loss

produces from two components, one of them due to the

leakage fluxes generate voltage drops in stator and rotor

iron cores and then stray power losses are generated in these iron cores depending on leakage voltage drops and

iron core resistance, and the other reason due to the

leakage fluxes generate eddy currents in stator and rotor

windings and these eddy currents generate stray power

losses in these windings depend on the leakage voltage

drop and winding resistances ( ).

Also, in this modified equivalent circuit, the modified

series equivalent of stator and rotor iron core resistances

( ) can be reflected as a voltage drops in the stator and rotor circuits respectively.

From the figure (2), the equivalent series of the stator and

rotor iron core resistances ( ) as well as the

series equivalent dynamic inductance ( ) can be calculated as:

(1)

= =

(2)

(3)

where is the power loss in the stator iron core and can be measured from no-load machine test at synchronous

speed.

is air-gap voltage and can be calculated from no-load

test as:

(4)

is power loss in the rotor iron core and can be

determined in terms of rotor frequency ( ) , where (s) is the machine slip.

(5)

(6)

(7)

Where = the angular-frequency of the stator.

The modified stray load loss resistances ( ) of stator and rotor circuits can be calculated from figure (2)

as:

(8)

(9)

Where and = stator and rotor leakage inductances, respectively.

and are stator and rotor winding resistances, respectively.



If the machine operates near the synchronous speed the

slip is very small and rotor circuit stray load loss

resistance ( ) can be neglected.

a-) D-axis model

b-) Q-axis model

Fig.(3)Modified equivalent circuit of SEIG in D-Q axes synchronously rotating reference frame

The components of stator and rotor voltages of SEIG with

excitation capacitors bank and inductive load can be

written from the modified equivalent circuit of the figure (3) as:

(10)

(11)

(12)

(13)

Where is the slip speed = ( ) rad./sec. (14)

= electrical angular speed of the generator (rad./sec.)

, , and are the stator and rotor flux

linkage in d-q axes respectively , and can be defined as:

(15)

(16)

(17)

(18)

(19)

(20)

= the residual rotor linkage fluxes in the

D and Q axes, respectively.

(21)

(22)

(23)

(24)

Where and are the initial voltages of the

capacitor bank in D-Q synchronously reference frame.

= D-Q components of load current and can

be calculated from the following differential equations:

(25)

(26)

(27)

Then substitute equations (15-20) into equations (10-13)

and re-arrange, after series manipulations, the stator and

rotor currents in first-order differential equations can be

derived in D-Q synchronously rotating reference frame as:

(28)

(29)

(30)

(31)

Where rotor inductance

stator inductance



The electromagnetic torque generated by SEIG can be

calculated as:

(32)

The active output power of SEIG can be calculated as:

(33)

The reactive output power can be calculated as:

(34)

The machine power factor can be calculated as:

(35)

3- DYNAMIC SATURATION OF SEIG

The magnetizing characteristics of SEIG are non-

linear in nature and it operates in saturation region. The

stator magnetizing current ( ) and magnetizing

inductance ( ) cannot be considered constant. The variation in magnetizing inductance is the main factor in

generating voltage build-up and stabilization.

Magnetizing current should be calculated in all steps of

integration in terms of stator and rotor D-Q current components as [18]:

(36)

The relation of magnetizing inductance with magnetizing

current is obtained experimentally from the no-load test at

synchronous speed.

Figure (4) gives the magnetizing inductance variation

with magnetizing current, which can be represented by

fifth-order polynomial curve fitting as:

(37)

Where

Figure (4) The Relation of magnetizing inductance with the magnetizing current.

The dynamic saturated magnetizing inductance ( ) can be computed as:

(38)

(39)

The dynamic saturation magnetizing inductance can be

calculated as [19]:

(40)

And the modified dynamic magnetizing inductance ( ) can be calculated as:

(41)

Where can be calculated from equation (7).

4- CAPACITOR BANK REQUIREMENTS

The residue magnetism and in the rotor of

SEIG and the initial voltage and in the capacitor

bank must be taken into account in the simulation process

for building up the voltage at the SEIG terminals. The

minimum capacitance of 3-phase delta connected

capacitor bank needed to generate the rated terminal

voltage at no-load and rated machine speed conditions is

defined as [20-21]:

(42)

Where = the rotor speed in elec. rad./sec.

Also, the stator angular frequency ( ) can be calculated from the model as [18]:

(43)

Figure (5) shows the practical relation between excitation capacitance and generator rotor speed. The minimum and

maximum excitation capacitance and generator rotor

speed can be obtained from this figure.

Figure ( 5 ) Variation of excitation capacitance with generator speed.

5- SIMULATION AND EXPERIMENTAL RESULTS

The dynamic model of SEIG system has been

simulated in Matlab / Simulink. The experimental setup

consists of DC Motor coupled with the SEIG system.

The DC motor is separately excited type and used as a

prime-mover to SEIG.



The SEIG is driven at speed above synchronous speed,

and then the capacitor bank is connected to the SEIG

terminals to build-up the machine terminal voltage at a

constant speed. The parameters of DC motor and SEIG

are given as follow:

DC motor parameters: 2.2KW, 1500 r.p.m ,

, ,

.

SEIG: 3-phase, squirrel-cage, Δ-connected, 220 V,

induction machine with the following parameters:

, , ,

, , ,

,

, , at rated voltage

at no-load,

Figure (6-a.b) show the simulation and experimental

results for starting-up condition of building the generator

terminal voltage. Figure (7-a.b) show the simulation and

experimental results of steady-state terminal voltage of the

SEIG. From these figures, there is a close agreement between the theoretical and practical results, which

indicate the validity of the proposed dynamic simulation

model.

Figures (8-11) show the simulation results of SEIG

electromagnetic torque, air-gap voltage, active power, and

trajectory of stator flux linkage in the D-Q plane.

(a)

(b)

Fig. 6-a,b. Experimental result (a) and Matlab simulation result (b) of

building–up generator terminal voltage at the transient condition.

(a)

(b)

Fig.(7-a,b) Experimental result (a) and Matlab simulation result (b) of the

steady-state generator terminal voltage.

Fig.( 8) Simulation results of electromagnetic torque

Fig.(9) Simulation result of air-gap phase voltage

Fig.(10) Simulation result of active power per phase



Fig.(11) Simulation result of the trajectory of stator flux linkage in the D-Q plane

6- CONCLUSION

An advanced and comprehensive dynamic model of

SEIG has considered in this paper takes into account the

losses in the stator and rotor iron core and stray load

losses and the dynamic saturation in magnetizing inductance without increasing the number of state-space

differential equations. The SEIG equivalent circuit is

modified to deal with all machine parameters without

losing the accuracy of performance calculation.

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Modeling of Self-Excited Induction Generator in