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CHAPTER 1 INTRODUTION Power demand is increasing day by day, considering this power demand with present environment conditions and exhausting of conventional energy resources made scientists to investigate on renewable and non-conventional energy sources like wind, solar, hydro, geothermal etc in recent years. Normally for non-conventional and renewable energy applications, induction generators are preferred for its advantages over synchronous generators. It offers many advantages for wind and hydro applications like cost and simplicity. Induction generator plays an important role in renewable energy sources. 1.1 Working principle of induction motor Induction motor works on the principle of electromagnetic induction. When the three phase supply is given to the three phase stator winding it produces a R.M.F. with constant magnitude. Then the speed of R.M.F is synchronous speed (N s r.p.m), N s = 120 f P = speed of R.M.F in stator winding Where f = supply frequency, P = number of poles for which stator winding is wound By this time rotor is stationary and stator flux R.M.F is rotating. So it is clear that there exists a relative motion 1

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Page 1: Full Theroy Doc

CHAPTER 1

INTRODUTION

Power demand is increasing day by day, considering this power demand with present

environment conditions and exhausting of conventional energy resources made scientists to

investigate on renewable and non-conventional energy sources like wind, solar, hydro, geothermal

etc in recent years.

Normally for non-conventional and renewable energy applications, induction generators are

preferred for its advantages over synchronous generators. It offers many advantages for wind and

hydro applications like cost and simplicity. Induction generator plays an important role in

renewable energy sources.

1.1 Working principle of induction motor

Induction motor works on the principle of electromagnetic induction. When the three phase supply

is given to the three phase stator winding it produces a R.M.F. with constant magnitude. Then the

speed of R.M.F is synchronous speed (Ns r.p.m),

Ns = 120 f

P = speed of R.M.F in stator winding

Where f = supply frequency,

P = number of poles for which stator winding is wound

By this time rotor is stationary and stator flux R.M.F is rotating. So it is clear that there

exists a relative motion between stator R.M.F and rotor conductors. Whenever conductor cuts the

flux an e.m.f is induced in the rotor conductors, this is known as electromagnetic induction. As

rotor forms a closed circuit then induced e.m.f circulates current through rotor called rotor current.

Any current carrying conductor produces its own flux, so rotor generates its flux called as rotor

flux.

By using right hand thumb rule we can determine the direction of rotor flux and now there

are two fluxes, one is R.M.F and rotor flux. These two fluxes interact each other and moves in

same direction. As all the rotor conductors experiences a force then the entire rotor experiences a

torque and starts rotating. Therefore the interaction of two fluxes is very essential for a motoring

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action. The direction of force experienced is same as that of rotating in the same direction as

R.M.F.

1.2 Synchronous speed

A synchronous speed is the rotary motion rate of stator magnetic field of an AC motor,

which is expressed in r.p.m

Ns = 120 f

P r.p.m

Where f is motor supply frequency in hz and P is the number of magnetic poles.

When rotor starts rotating, if it catches the speed of r.m.f then the relative motion between

rotor and r.m.f will become zero (Ns-N = 0). But actually relative motion is the main cause for

inducing e.m.f in rotor then the induced e.m.f will be gone and therefore rotor current and rotor

flux will be absent which is essential to produce the torque on the rotor. Ultimately the motor will

stop, but instantly there is an existence of relative motion between rotor and stator r.m.f, due to this

motor will start again. But due rotor inertia, it doesn’t happen in practical and rotation of rotor

continues with a speed slightly less than the synchronous speed of the r.m.f in steady state. And the

induction motor never rotates at synchronous speed. The rotation speed of rotor is sub synchronous

and it is also known as asynchronous motor (N < Ns).

1.3 Slip and torque characteristics

1.3.1 Slip

The ration of difference between synchronous speed and operating speed, at the same

frequency can be expressed in r.p.m or in percent or synchronous speed is known as slip(s).

s = N s−N r

N s

Where Ns is stator electrical speed, Nr is rotor mechanical speed. This speed judges the magnitude

of the induced e.m.f and the rotor current, which in turn judges the torque produced.

1.3.2 Torque

The torque generated in the induction motor depends on the following terms:

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i. The part of r.m.f which reacts with rotor and is responsible to generate induced e.m.f in

rotor.

ii. The magnitude of rotor current in running condition.

iii. The power factor of the rotor circuit in running condition.

And the torque produced by an induction motor at starting is known as starting torque, where N=0

and slip s = 1in torque equation. So the expression of starting torque Tst as,

Tst = (3/2πns).[(s E22R2)/(R2

2+(s X2)2)]

If the R2 value changes at starting can possible in slip ring induction motor, in this case slip is used

to control the starting torque Tst.

1.3.3 Characteristics

Figure 1.1 torque-slip characteristics

The induction motor is loaded from no load to full load due to this speed decreases hence

slip increases. By increasing load motor will produce more torque to require load demand.

Ultimately torque depends on slip and the behavior of motor can be judge by plotting torque

against slip from s =1 to s =0 is called torque-slip characteristics of induction motor.

1.4 induction generator

An induction generator or asynchronous generator is one of the types of AC electrical

generator; the principle of induction generator is similar to induction motor. Induction generator

works mechanically turning of rotor faster than the synchronous speed which gives negative slip

value. Induction generators are most preferred in applications of nonconventional resources and 3

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renewable energy sources like hydro, wind and in reducing high pressure gas streams to lower

pressure, because they can make progress energy with relatively simple controls. An induction

generator must be excited with a leading voltage to an electrical grid and sometimes they are self

excited by using phase correcting capacitors.

In induction generators, the air gap magnetic flux is provided by capacitor bank connected

to the machine to establish the reactive power which is required for standalone system and in grid

connected system it draws reactive power to maintain its air gap flux from grid. Frequency and

voltage at the machine will be dictated by the electric grid and it is compared to the entire system.

For self systems, frequency and voltage are complex function of machine parameters, for

excitation capacitance is used and load value.

1.4.1 self excited induction generator

The purpose of SEIG is of four main items they are the prime mover, the induction

machine, the load and the self excited capacitor bank. A squirrel cage induction generator is much

promising than a conventional synchronous generator because of its low unit cost, absence of DC

excitation source, brushless cage rotor construction and requires less maintenance. A suitable sized

three phase capacitor bank is connected at the generator terminals is used as variable lagging

source to meet excitation demand of cage machine and the load. This mode of machine operation

is known as self excited induction generator (SEIG). But, the main drawback of the standalone

SEIG is its poor voltage and frequency regulations under variable loads. The change in the load

impedance directly affects the excitation of the machine due to the reactive power of the excitation

Figure 1.2 standalone diagram of a self excited induction generator

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capacitors is shared by both the machine and the load. Thus the voltage drops when impedance of

the load is increased resulting in poor voltage regulation. Poor frequency regulation occurs due to

increasing load.

If the machine is self-excited and loaded then the magnitude of the steady state voltage

produced by the SEIG is determined by the nonlinearity of the magnetizing curves, the value of

self excitation capacitance, speed, machine parameters and terminal loads.

1.4.2 SEIG system performance

The SEIG system performance characteristics mainly depends on

a) The parameters of the induction machine

It directly affects the machine operating voltage, power factor, rated power, rotor speed and

operating temperature and the induction machine parameters.

b) The Self-excitation process

The connecting a capacitor bank across the induction machine stator terminals is required in the

standalone operation of the system. The capacitor connection scheme (delta or star) and the use of

fixed or controlled self-excitation capacitors have a direct impact on the performance of a SEIG

system.

c) Load parameters

It directly affects the power factor, starting or maximum torque and current, generated harmonics

and load type.

d) Type of prime mover

It directly affected either the primary source is hydro, wind, biomass or combinations.

1.5 Comparison of Synchronous and Induction Generator

Normally generators are of two types they are: synchronous and induction generators.

Synchronous generators have the DC excitation field supplied from batteries i.e. DC

generators or a rectified AC source. DC is applied to the field through brushes riding on slip rings

attached to the rotor.

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A small AC generator used by Brushless generators determined directly from the shaft. The

output of AC is rectified and the DC is applied directly to the main generator field. The

arrangement of exciter generator is reversed from the normal generator in the armature is rotated

with the main generator shaft and the field is fixed. Thus, the AC output can be given to a rectifier

assembly which also rotates and the resulting DC connected directly to the main generator field

without brushes or slip rings.

An induction generator receives its excitation or magnetizing current from the system to

which it is connected. It uses before supplying reactive power (KVAR) and supplies only real

power (KW) to the system. The KVAR required by the induction generator plus the KVAR

requirements of all other loads on the system must be supplied from synchronous generators or

static capacitors on the system.

When a squirrel cage induction motor is excited from a power system and is mechanically

driven above its synchronous speed it will carry power to the system. Running as a generator at a

given percentage slip above synchronous speed, current, torque, efficiency and power factor

doesn’t change much from that when working as a motor. The same slip below the shaft torque,

synchronous speed, and electric power flow is reversed.

1.6 Applications

a) externally-excited generators this type of generators requires a little backup equipment. They

run in parallel with an existing 3-phase system. Thus, voltage and frequency of induction

generators cannot be controlled. Only the active power can be vary through the speed control of

prime-mover driving the 3-phase induction generator. Externally excited induction generators are

also used in unattended small remote hydro plants thereby interconnected a small power station to

a large power distribution network. Induction generator principle is used for regenerative braking

of hoists or electric locomotives drives by 3-phase induction motors.

b) self- excited generators with the depletion of energy sources; every effort is made to convert

other forms of unconventional energies into electrical energy. Therefore, energy recovery schemes

are becoming an important aspect of present day industrial processes. In the coastal areas, wind

energy is available in abundance. For the conversion of this wind energy into electrical energy, an

induction generator coupled with a wind-mill offers ideal solution.

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CHAPTER 2

LITERATURE SURVEY

[1] Lahcene Ouazene (1983) et al. presented an arrangement using a capacitor-excited induction

generator and a variable speed driven to supply resistive loads is described and a method for

determining the output voltage and frequency in the steady state is presented. By this power flow

and losses in the machine are summarized. The voltage source is applied at stator of the induction

machine during its rotor is driven by the dc motor at a constant speed equivalent to the

synchronous speed of the machine at the rated frequency. Here the application of the method to

predict a graph of the generated voltage and frequency at different range of speeds of load

resistances and excited capacitors.

[2] N.H.Malik (1990) et al. presented the excitation capacitor on the steady state performance of an

standalone self excited induction generator feeding with balanced loads. This depends on the range

of capacitance value and the selected value of capacitance shows much influence on the generator

performance characteristics. By keeping terminal voltage Vt constant, C value depends on the

generator parameters, speed, output power and load power factor. And for a constant speed, the

efficiency of generator and frequency decrease almost linearly with output power.

[3] L. Shridhar (1995)et al. explained about a system consisting of both shunt and series capacitors

for a desired voltage regulation. Short and Long shunt configuration is techniques of improving

voltage regulation of SEIG where the capacitors are placed between the machine terminals and the

shunt capacitors. But while comparing both the short and long shunt configurations, short shunt

configuration is preferred compared to long shunt, because of economy and performance of the

SEIG.

[4] T. F. Chan (2001)et al. explains the behavior of steady state analysis of a standalone three

phase self excited induction generator with unbalanced capacitances and unbalanced loads.

Analysis can be explained by a function minimizing technique by the equivalent circuit determines

the excitation frequency and magnetizing reactance. Then a balance phase scheme supplying a

single-phase load which is modified steinmetz connection (MSC) involves only passive circuit

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elements this is an economical and effective method to achieve perfect phase balance in 3-phase

which supplies to 1-phase loads.

[5] Tarek Ahmed (2003)et al. proposed the nodal admittance approach steady state frequency

domain analysis of the minimum excitation capacitance required for the squirrel cage rotor type 3-

phase SEIG driven by variable speed prime movers(VSPMs) such as a wind turbine and a micro

gas turbine is presented. Initially this paper explains about the VSPM with the exciation

capacitance requirements of 3- phase SEIG driven directly. Then in addition to SVC is used for

voltage regulation and SVC was established for cost effectiveness wind turbine power conditioner

used in the rural alterative energy effective utilization area from an earth environmental protection

point of view.

[6] Tarek Ahmed (2004) et al. explained the steady state operating performances of single-phase

squirrel cage SEIG to estimate by the per-unit slip frequency steady state analysis at the prime

move speed and inductive load power variations. By using PI controller based feedback control

scheme with single phase SVC composed of the FC connected in parallel with the TCR and the

TCS was employed. A single phase SEIG prototype was established for the low cost, ruggedness,

reliable and simple control strategy in stable wind turbine driven power conditioner in the riral

alternative protection.

[7] Bhim Singh (2005)et al. presents a transient analysis of SEIG with electronic load

controller(ELC) used in standalone micro hydro power generation employing uncontrolled

turbines. To analysis transient analysis both the dynamic and static loads from switching in of

loads is of interest. By considering a mathematical model of the system has been developed by

combining the modeling of prime mover, ELC and load. By analyzing ELC is capable of handling

the transients caused by load switching. The voltage THD of SEIG is found within acceptable

limits under reasonable amount of consumer loads.

[8] S. S. Murthy (2006)et al. presents an analysis and design of an electronic load controller (ELC)

for three-phase self-excited induction generators (SEIGs) suitable for stand-alone pico-hydro

power generation with constant input powerAn analysis and design procedure to design the ELC

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for SEIG has been presented for constant power applications. Using the design criteria given in this

paper, the voltage and current rating of the uncontrolled rectifier and chopper, value of dump load

Resistance, and the value of dc filtering capacitance for the three phase ELC and single-phase ELC

for both the three-phase SEIG system can be calculated for power generation in pico hydro

applications.

[9] D. Joshi (2006)et al. explains the performance analysis of SEIG using ANN technique. The

steady state analysis such machines are to estimate the behavior under actual operating conditions.

By using a new technique steady state analysis of 3-phase SEIG feeding balanced unity power

factor. ANN modeling has been found to be very effective for accounting the non-linearity of

magnetic characteristics. Comparison of the computed results using ANN modeling along with

iteration method has been compared with the experimental results.

[10] Ali Nesba (2006)et al. proposed the dynamic performances of a three phase self excited

induction generator(SEIG) during sudden connection of static loads. This could be explained by

dynamic flux model of SEIG as well as the models of R, RL, RC and RLC in the α – β axis

stationary reference frame is presented. The SEIG output voltage is highly influenced by the

impedance and the power factor of the load. This series capacitor must have an adequate

capacitance value. The amplitudes of the signals, their shapes as their duration present practically

the same values for both simulation and experimentation.

[11] S. S. Murthy (2008)et al. presents the analysis of dynamic and steady state performance of

feeding single phase loads in a Self Excited Induction Generator (SEIG) with digitally controlled

Electronic Load Controller (ELC) feeding single phase loads. It is proven by a detailed modeling

and analysis that the proposed scheme can regulate the output voltage from no load to full load

range with a fairly good accuracy and quick response. It also provides TRIAC triggering of

additional capacitances in order to provide better power factor. The system has been successfully

fabricated and laboratory tests are carried out.

[12] Dheeraj Joshi (2009)et al. presents the induction generators operated in grid or self excited

mode, are found to be successful machines for wind energy for large variations in operating speed.

Steady-state analysis of self excited induction generator reveals that such generators are not 9

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capable to maintain the terminal voltage and frequency in the absence of expensive controllers.

Genetic algorithm along with artificial neural network has been proposed to estimate the values of

shunt and series excitation capacitance to maintain the terminal and load voltage. Terminal and

load voltage maintained near to the rated value without exceeding the rated current of induction

generator.

[13] S.N.Mahato (2010)et al. presents the transients analysis of a three-phase self excited induction

generator (SEIG) feeding single phase inductive load with an Electrical Load Controller (ELC)

used in stand-alone micro-hydro power generation employing uncontrolled turbines. A detailed

mathematical model of an ELC for a single phase SEIG using a three phase, star connected

induction machine has been developed and verified with the experimental results obtained on the

fabricated ELC. The dynamic behavior of the SEIG with load controller reveals that this system

can be used satisfactorily in constant power applications such as micro-hydro with uncontrolled

turbines.

[14] Aref Biglari (2012)et al. presents steady-state operation of SEIG (with general RL load) under

varying operating speed, excitation capacitance and balanced load is presented using a simple and

fast nodal analysis and piecewise linearization of magnetization characteristics. This method is

faster and simpler than conventional models used such as d-q model and Genetic Algorithm (GA).

However, due to using piecewise linear magnetization curve, its accuracy is inferior to Artificial

Neural Network technique (ANN). Capacitor switching provided simple, cheap and acceptable

voltage control.

[15] K. Trinadha (2012)et al. presents the performance of a stand-alone self-excited induction

generator (SEIG) driven by fixed pitch wind turbine. The main purpose of the paper is: (i) dynamic

study of SEIG under balanced R-L/R-C loads (ii) dynamic study of SEIG under balanced and

unbalanced excitation, (iii) Fixed pitch wind turbine model has been considered for driving

induction generator. The SEIG representation with balanced/un-balanced load and excitation

results is:

[i] The performance of SEIG has been determined for five different cases. It is experimental that

the Performance of SEIG under balanced R-L and R-C and balanced excitations, the stator voltage,

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stator currents, load currents and capacitor currents are balanced. In this case the voltage build up

is reasonably fast because of balanced excitation.

[ii] At un-balanced excitation the electromagnetic torque is having oscillations compared to the

case with balanced excitation and capacitor currents are unbalanced.

[iii] At un-balanced load and balanced excitation the electromagnetic torque have more oscillations

and are more as compared to other case.

[iv] It is observed that the stator currents and load currents are un-balanced under un-balanced

load. It is balanced under balanced excitation and balanced load only.

[16] M. Rizwan Khan (2013)et al. presents that a self excited induction generator (SEIG) may be

operated in various configurations such as shunt, short shunt and long shunt. And the steady state

SEIG model used for the analysis is based on double field revolving theory while the performance

equations are developed through branch impedance method. By using developed model the

different SEIG characteristics are obtained to assess its performance under two different modes;

the shunt connection and short shunt connection. The optimum capacitance selection is affected

not only by the SEIG parameters such as speed, frequency and machine constants but load power

factor also has considerable bearing on output characteristics. As the load power factor shifts in

lower ranges; the SEIG terminal voltage tends to drop almost instantaneously due to resonance.

This phenomenon occurs sooner in output power range as the power factor is decreases.

[17] Deepika (2013) et al. presents an efficient analytical technique using Secant method is used to

describe the generated frequency and saturated magnetizing reactance of self-excited induction

generator for a given capacitance, speed, and load. The nodal method is used on the single phase

equivalent circuit of SEIG which gives two nonlinear equations One equation contain only

generated frequency term solve by Secant method using initial values calculation by real power

balance equivalent circuit. This proposed technique is simple and used for any kind of balanced

load. This paper introduced the efficient approach to calculate initial values of generated frequency

with the help of real power balanced circuit.

[18] Lalit Goyal (2013)et al. presents the usage of renewable energy sources is increasing such as;

bio-gas energy, wind energy, solar energy, and hydro potential have become essential to adopt a

low cost generating system, which operates in the remote areas, and in combination with the 11

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variety of prime movers. The use of induction generator as potential alternative to the synchronous

generator to utilize the small hydro and wind energy to accomplish the future energy requirement,

and gives the power to isolated locations and far flung areas, where expansion of grid is not

economically possible. Applications of self-excited induction generator for energy conversions in

remote locations offer many advantages over a synchronous generator. The better methods of

reactive power/voltage control techniques will make the SEIG more suitable for isolated

applications.

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CHAPTER 3

RESEARCH METHODOLOGY

In the previous paper different methods have been used to study the performance of SEIG with

balanced loads and unbalanced loads. In my paper “ Modeling of Self Excited Induction Generator

with Unbalanced Loads”, solve the steady state analysis to predict the values of capacitance

reactance required for self excitation at different operating conditions, speed and frequency with

this values voltage and frequency is controlled by this the behavior of SEIG can be analyzed.

Different methods for SEIG:

1. Excitation capacitance method.

2. Modified Steinmetz connection(MSC).

3. Eigen values sensitivity analysis.

4. Electronic load controller (ELC).

5. P – Q load model.

6. Artificial neural network (ANN) technique

7. Genetic algorithm.

3.1 Steady state circuit model

The steady state analysis of an induction generator can be solved by using any of two

methods in per phase equivalent circuit model they are i) loop impedance method and ii) nodal

admittance method. The steady state model is presented here in Fig. 3.1. This model makes

assumptions that the RL load and neglecting machine core loss component and the machine

parameters (except for magnetizing reactance) remain constant.

3.1.1 Mathematical model

To self-excite the machine on the load the impedance line associated to the parallel

combination of the load impedance and excitation capacitance should cross each other the

magnetization characteristic well in to the saturation region. For the self-excitation of the machine

on no load, the excitation capacitance should be greater than the minimum value, by this minimum

value decreases with decreasing speed. For the circuit shown in Fig. 3.1, by using Kirchhoff’s

current law, the sum of currents at node (1) should be equal to zero, therefore

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R

Lj2πfL2

j2π fLm

j2πfL1

-j2πfC R2/S

R1

E1

Vt

Fig 3.1 Equivalent Circuit of Self-Excited Induction Generator

VY = 0 (3.1)

Where Y is the admittance given by

Y = YL+ YC+ Y2 (3.2)

The terminal voltage cannot be zero i.e.

Y = 0 (3.3)

By equating the real and imaginary terms in equation (3.3) respectively to zero, we have

Real(YL+ YC+Y2) = 0

Imag(YL+ YC+Y2) = 0

3.1.2 Nodal Admittance Method

In this circuit, only the capacitive reactance is considered to be affected by magnetic saturation and

all other parameters to be constant. And also, core losses and the effect of the harmonics are

ignored. From equivalent circuit in Fig. 3.2 the total current at node ‘a’ may be given by

Where the admittances at different

Y1 = (Y L+Y C )(Y S)(Y L+Y C+Y S )

, YC = 1

R L /F , YS =

1

( R LF )+ j X 1 , YM =

1j X M , YR =

1(R 2/ F−V )+ j X 2

(3.4)

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j2πfL1R1

RL/ F V1/F

R2/(F-V)

ab

c d

IL

I1

-jXc/F2 Eg/FE1 = jXm

I2

YL YCYM YR

jX2

Fig 3.2 per-phase equivalent circuit of SEIG

At a constant shaft speed the generator is operates, F and Xc varies with the load and hence they

are represented as the two unknowns. A sixth order polynomial equation, independent of Xc, is

extracted from real part as shown in equation (3.2) where as equation (3.3) is used to obtain X c

from imaginary part. This is an advantage of nodal admittance method that one non-linear equation

is independent of other and thus the problem solves easily.

A6F6 + A5F5 + A4F4+ A3F3+ A2F2+ A1F+A0 = 0 (3.5)

3.1.3 Loop Impedance Method

As there is no e.m.f source, applying Kirchhoff’s e.m.f law around the loop abcd in Fig. 3.2

the per-phase equivalent circuit yields the loop equation from where the stator current can be

separated yielding a separate equation with total impedance equal to zero, from there the real and

imaginary parts are equated separately to zero. The Newton-Raphson method has been used to

compute the values of frequency F and capacitance reactance XC from where the capacitance value

is determined. If the required capacitance for a specified value of the terminal voltage under a

given load and speed is the requirement then both the steady-state values of XC and F are unknown

where magnetizing reactance XM is a specific value lying in the saturated region and both

unknowns have to be determined for the given speed and load from the equivalent circuit. From

the generator equivalent circuit the loop equation for the current I1 can be written as,

Z1I1 = 0 (3.6)

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By using Newton-Raphson method we can find the values of XC and frequency F.

3.2 Loads

Loads have been classified into two types they are balanced and unbalanced loads.

Practically loads never are in balanced state they vary according to the load demand in the power

system but, to understand we are assuming the loads are balanced. The three phase loads have the

same impedance and power factor in each phase are called as balanced loads. The problems on

balanced loads can be solved by considering one phase only, the conditions in the other two phases

being similar. And when loads are unbalanced then each load phase has different impedance and/or

power factor, in this case power in each phase will be different.

The unbalanced loads are classified into 3 types they are:

i. Four-wire Y-connected unbalanced load

ii. Unbalanced ∆-connected load

iii. Unbalanced 3-wire, Y-connected load

3.2.1 Four-wire star-connected unbalanced loads

The three-phase four-wire star system is widely used for distribution of electric power in

commercial purposes. The single phase load is connected between any line and neutral wire while

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Figure 3.3 4-wire 3-phase star connected unbalanced load

a 3-phase load is connected across the three lines. The 3-phase, 4-wire system always carries

Unbalanced loads, because it is rarely possible that single phase loads on all the three phases have

the same magnitude and power factor. Because the load is unbalanced, the line currents of

magnitude and displaced from one another by unequal angles will be different.

The currents in the neutral wire will be the phasor sum of the three line currents i.e. current in

neutral wire is,

IN = IR+IY+IB (3.7)

3.2.2 Unbalanced ∆ connected load

When a ∆ connected supply feeds a ∆ connected load which is not usual, then the line

voltages are known so that the currents inside the delta can be obtained directly from Ohm’s law.

The line currents can be obtained by phasor summing of the currents inside the delta. The line

currents will not be equal nor will they have a 1200 phase difference as was the case with balanced

loads.

Figure 3.4 unbalanced ∆ connected load

3.2.3 Unbalanced 3-phase, Y-connected load

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With only the three lines A, B and C connected to an unbalanced Y load the common point

of the three load impedances is not at the potential of the neutral and is marked “O” takes place of

N. The Voltages across the three impedances can vary considerably from line to neutral magnitude

Figure 3.5 unbalanced 3-phase.Y-connected load

as shown by the voltage triangle which relates all of the voltages in the circuit and the

displacement of “O” from N, the displacement neutral voltage.

Actually the main difference of balanced and unbalanced loads are balanced loads are used

for transmission lines and the unbalanced loads are used for distribution systems. Because in

transmission system the load can be controlled but in distribution system the load changes

according to the demand required. To explain SEIG with unbalanced we are using unbalanced ∆

connected load by the loop impedance approach or the nodal admittance

approach.

3.3 Objective

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The main objective of the thesis is to analyze the performance of self excited induction

generator with unbalanced loads which is to be obtained by but here we are using S.S.MURTHY

which is well known as Murthy’s method. From the steady state analysis with either of two

methods they are nodal admittance method and loop impedance method. By this we can analyze

the behavior of dynamic characteristics and control the frequency and speed of the self excited

induction generator.

REFERENCES

[1] Lahcene Ouazene, George McPherson, “ANALYSIS OF THE ISOLATED INDUCTION

GENERATOR”, IEEE Transactions on Power Apparatus and Systems, Vol. PAS-102, No. 8,

August 1983.

[2] N.H. Malik, A.H. AI-Bahrani, “Influence of the terminal capacitor on the performance

characteristics of a self excited induction generator”, IEE PROCEEDINGS, Vol. 137. Pt. C, Nu. 2,

MARCH 1990.

[3] L. Shridhar, Bhim Singh, c. s. Jha, B. P. Singh. SM and S.S. Murthy, “SELECTION OF

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