5.modeling of three phase self excited induction generator(26-32)

International Journal Of Communication And Computer Technologies Volume 01 – No.1, Issue: 01 JULY 2012

Page 26 International Journal Of Communication And Computer Technologies

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MODELING of THREE PHASE SELF EXCITED INDUCTION GENERATOR

T. Gopinath*, P. Vetrivellan**

* Research Scholar, **Assistant professor Department of EEE Jayam College of Engineering and Technology, Dharmapuri - 636 813, Tamilnadu, India

EMAIL ID: [email protected]

Abstract - Dynamic characteristics assessment of three phase self excited induction generator is one of the main issue in isolated applications as it proves its importance in recent years. The transient characteristics of SEIG has important role to define its better applicability. In this paper a generalized state-space dynamic model of a three phase SEIG has been developed using d-q variables in stationary reference frame for transient analysis. The proposed model for induction generator, load and excitation using state space approach can handle variable prime mover speed and various transient conditions. Also the effect of variation of excitation capacitance on system is analyzed. The equation developed has been simulated using powerful software MATLAB/SIMULINK and its responses justify the proposed model.

Keywords: Transient characteristics, Excitation capacitance, prime mover speed, variable load.

NOMENCLATURE

Vsd, Vrd : Stator, rotor d-axis voltages

isd, ird : Stator, rotor d-axis currents

Vsq, Vrq : Stator, rotor q-axis voltages

isq, irq : Stator, rotor q-axis currents

Lm : Magnetizing Inductance

Lr, Ls : Rotor, Stator Inductances

Im : Magnetizing current

Te : Electromagnetic Torque

P : Number of poles

L : Load Inductance per

Phase in Henry

Rs : Stator resistance per

phase in ohms

Rr : Rotor resistance per phase referred to

stator in ohms

Xls : stator leakage reactance per phase

Xlr : Rotor leakage reactance per phase

C : minimum value of self Excitation

Capacitance

R : load resistance per phase in ohms

Wr : rotor speed in rad/sec

Ild, Ilq : d-q axes load current per phase

Vld, Vlq: d-q axes excitation voltage per phase

icd, icq : d-q axes capacitor currents per phase

I. INTRODUCTION

It is well known that the three phase self excited induction machine can be made to work as a self-excited induction generator [1, 2], provided capacitance should have sufficient charge to provide necessary initial magnetizing current. In an externally driven three phase induction motor, if a three phase capacitor bank is connected across its stator terminals, an EMF is induced in the machine windings due to the self excitation provided by the capacitors. The magnetizing requirement of the machine is supplied by the capacitors. For self


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excitation to occur, the following two conditions must be satisfied:-

i. The rotor should have sufficient residual magnetism.

ii. The three capacitor bank should be of sufficient value.

If an appropriate capacitor bank is connected across the terminals of an externally driven induction machine and if the rotor has sufficient residual magnetism, an EMF is induced in the machine windings due to the excitation provided by the capacitor. The EMF if sufficient would circulate leading currents in the capacitors. The flux produced due to these currents would assist the residual magnetism. This would increase the machine flux and larger EMF will be induced. This in turn increases the currents and the flux. The induced voltage and current will continue to rise until the VAR supplied by the capacitor is balanced by the VAR demanded by the machine, a condition which is essentially decided by the saturation of the magnetic circuit. This process is cumulative and the induced voltage keeps on riding until saturation is reached. To start with transient analysis, the dynamic modeling of induction motor has been used which further converted into induction generator [1, 4, 9]. Magnetizing inductance is the main factor for voltage buildup and stabilization of generated voltage for unloaded and loaded conditions. The dynamic Model of Self Excited Induction Generator is helpful to analyze all characteristic especially dynamic characteristics.

Different constraints for analyzing transient conditions:

1. The machine is run as an induction motor and then increase the speed above synchronous speed to make it as a generator, after complete excitation the variation of generated voltages observed by applications of various loads.

2. The machine is started as induction generator with the rated load and transient response is observed with various excitation and rotor speed.

3. The machine is started as induction generator with no load and the voltage variations has been observed by applying the load after complete excitation.

4. The analysis has been extended to variation of the excitation capacitance under no load

and rated load by keeping rotor speed above synchronous speed and by keeping capacitance constant and the rotor speed is varied above synchronous speed. The resultant voltage and current waveforms has been observed.

5. The transient periods of voltage build up and voltage collapses has been observed when switching periods between the excitation and application of load varies.

An uncontrolled self excited induction generator shows considerable variation in its terminal voltage, degree of saturation and output frequency under varying load conditions. It is convenient to represent the circuit model in terms of base frequency for the analysis.

The per-phase, steady-state, stator-referred equivalent circuit of a self-excited induction generator connected to a load is given below. A capacitor of capacitance Co is connected to provide the excitation VAR.

Fig 1. Stator referred circuit model normalized to base

Frequency

II. GENERALIZED SEIG MODELLING

The d and q axis current are given by the set of differential equations [1, 3] shown below,

] ... (2.1)



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] ... 2.2)

... (2.3)

] ..(2.4)

Where K =

The variation of the magnetizing inductance is the main factor in the dynamics of the voltage build up and stabilization in SEIG. The non linear relationship between magnetizing inductance (Lm) and magnetizing current (Im) is given as,

… (2.5)

3 … (2.6)

The following equations represents the self excitation capacitor currents and voltages in d-q axes representation,

… (2.7)

… (2.8)

Where,

… (2.9)

… (2.10)

From the above equations,

… (2.11)

… (2.12)

Equations (5.24) and (5.25) represents the d-q axes load voltages and currents,

… (2.13)

… (2.14)

III. SIMULATION OF SELF EXCITED

INDUCTION GENERATOR

Simulation and the equations described above has been implemented in MATLAB/SIMULINK block sets. The current equations have been implemented in subsystem “Induction Generator” whose outputs are currents in d & q axis. The load and excitation model is implemented in subsystem ‘Excitation and Load’ as shown in fig. 3.2 & 3.3 by using equations (2.7) to (2.14). Further these currents are the function of constants viz. stator and rotor inductances, resistances, speed, excitation capacitance and load impedance.



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Fig.3.1 SIMULINK

model of Self Excited Induction Generator

Fig.3.2 Excitation model

Fig. 3.3 Load model

IV. DETERMINATION OF CAPACITANCE

There are two main methods used in the calculation of the minimum capacitance necessary for self-excitation. The first method is based on the generalized machine theory in which the characteristic equation of the operational impedance matrix has to be solved numerically for its roots. In this method the characteristic equation which represents the self-excitation process is a tenth order differential equation for inductive and capacitive loads, while an eighth order differential equation results for resistive load conditions.

The second method is based on the

analysis of the generalized per phase equivalent circuit, (in which all parameters are divided by the base frequency), of the three phase induction machine and either the loop impedance or the nodal admittance concept is applied. When the loop impedance concept is used in the analysis of the equivalent circuit, the process of self excitation is satisfied by equating the sum of the loop impedance's to zero. Then both the real and imaginary parts of the total impedance are equated to zero, resulting in two nonlinear simultaneous equations in both self-excitation capacitor reactance and frequency. The degrees of both the equations are two and six in the case of R-L load respectively. Using the nodal admittance concept [8] and by equating the real and imaginary parts of the total admittance to zero, a sixth order polynomial in the per unit frequency is obtained after a series of algebraic manipulations by decoupling the load and excitation capacitor branches.

From fig 3.2, the loop equation for the current I can be written as

IZ = 0 …. (4.1)

Where Z is the net loop impedance given by

…. (4.2)

Since under steady state excitation the current is not equal to zero, it follows from the above equation that Z=0 or both real and imaginary parts of Z are zeros.

Considering Xm = Xsmax, the equation obtained from the real part is,

…. (4.3)

Similarly the equation obtained from the imaginary part is,

…. (4.4)

Equating the above equations the following fourth order equation given below is obtained,



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…. (4.5)

Where are positive constants.

Let {Fi, i ≤ 4} be the set of positive real roots of the equation and {Ci , i ≤ 4} be the corresponding set of positive capacitor values. Since all these values of C are sufficient to guarantee self-excitation of the induction generator, it follows that the minimum capacitor value required is given by

Cmin = min {Ci, i ≤ 4} ….(4.6)

If the eqn. (4.5) has no real roots, then no excitation is possible. In fact, there is a minimum speed value, below which the equation (4.5) has no real roots. Correspondingly, no excitation is possible.

Substituting the given values of the machine, the values of F obtained are 0.4965 and 1.084 for which the values of capacitances obtained are 657µF and 45.6 µF respectively.

The degree of eqn.4.5 determines the number of capacitor values from which the minimum value is selected.

V. SIMULATION RESULTS

The figure given below shows the simulated responses of the studied induction machine operated from an induction-motor mode to an IG mode. The stator phase current at starting is of high vale but latter it settles downs to a very small steady value.

Fig.5 (a). Stator phase current

Fig 5(b) Stator phase current (ias)



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Fig.5.1 Stator phase voltages

The rotor speed starts from 0 rpm at t=0.0s and approaches to 1499 rpm at t=0.5 S. the rotor speed changes to be 1550 rpm at t= 1.5s. The electrical torque changes to be negative at t= 1.5s when the machine acts as an IG. Fig. 5.2 & 5.3 plots the dynamic variation of rotor speed and Te during various modes of operation.

Fig. 5.2 Rotor Speed

Fig. 5.3 Variation of Torque

VI. CONCLUSION

This paper has presented generalized state space dynamic modeling of three phase self excited induction generator. With this model it is possible to isolate induction generator, excitation and load. This feature is guaranteed by the separate parameter representation of the machine model, the self excitation bank of the capacitor and the load. The main advantages of this approach are (i) representation of SEIG in the form of classical state equation (ii) separation of machine parameters from the self excitation capacitors from the load parameters, the transient analysis can be effectively analyzed (iii) this model works effectively even with the consideration of main and cross flux saturation and gives better result.

APPENDIX

Generator Rating and Parameters

Rated Power 5.5 HP

Rated Line to Line Voltage 400V

Rated Frequency 50 Hz

Stator Resistance, Rs 0.063 ohms

Stator Leakage Reactance, Xls 0.163 ohms

Rotor Resistance, Rr 0.1179 ohms



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Rotor Leakage Reactance, Xlr 0.163 ohms

Number of Poles, P 4

REFERENCES

1) S.S. Murthy, C. Nagamani, K.V.V. Satyanarayana, “Studies of the use of conventional induction motors as self excited induction generators”, IEEE transactions on energy conversion vol. 3, No 4, December 1998.

2) R. Chaturvedi, S.S. Murthy, “Use of conventional induction motor as a wind driven self excited induction generator for autonomous operation”, 1998 IEEE.

3) Avinash kishore, G. Satish kumar ”Dynamic modeling and analysis of three phase self excited induction generator using generalised state space approach” International symposium on power electronics.

4) P.C. Krause, Analysis of Electric Machinery, McGraw hill Book Company, 1986

5) Bhim Singh, Madhusudan Singh “Transient Performance of Series Compensated Three-Phase Self-Excited

induction Generator Feeding Dynamic Loads” IEEE Transactions on Industry Applications, Vol. 46, July/August 2010

6) S.N. Mahato, M.P. Sharma, S.P. Singh “Determination Of Minimum And Maximum Capacitances Of A Self-Regulated Single-Phase Induction Generator Using A Three-Phase Winding” Proceedings of India International Conference on Power Electronics 2006

7) B.Venkatesa perumal and Jayanta K.Chaterjee “Voltage and frequency control of a standalone wind electric generation using generalized impedance controller” IEEE transactions on energy conservation, Vol. 23, June 2008

8) Kh Al Jabri, A I Alolah, “Capacitance requirement for isolated self excited induction generator”, IEEE proceedings, Vol. 137, Pt. B. No. 3, March 1990

9) L. Sridhar, Bhim Singh, C. S. Jha, “Transient performance of the self regulated short shunt self excited induction generator’, IEEE transactions on energy conversion vol. 10, No. 2, June 1995.

10) J. L. Bhattacharya, J. L. Woodward, “Excitation Balancing of a self excited induction generator for maximum power output”, IEE proceedings, Vol. 135, Pt. c, No. March 1998.

5.modeling of three phase self excited induction generator(26-32)

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