King Saud University
College of Engineering
Electrical Engineering Department
Study of Using Induction Generator in Wind
Energy Applications
Prepared By
Mohanad A. Al-Nuaim
420001131
Supervised By
Dr. Ali M. Al-Tamaly
December 2005
1
List of Symbols
Rr
Rotor resistance
Rs
Stator resistance
Rl
Load resistance
Xr
Rotor reactance
Xs
Stator reactance
Xm
Magnetizing reactance
F
Per unit frequency
Fb
Base frequency in Hz
Zb
Base impedance in ohms
V
speed
C
Capacitance of the terminal capacitor
Cmax
Maximum capacitance of the terminal capacitor
Fmin
Minimum frequency
fa
Actual or (generated) frequency, P*Na/120.
Na
Actual or (generated) rational speed, 120 /P.
fr
Rated frequency of induction generator , P*Nr/120.
Nr
Rated speed of induction generator, 120 fr/P.
Nsa
Synchronous speed corresponding to actual frequency.
Nsr
Synchronous speed corresponding to rated frequency.
2
ABSTRACT
The electrical power generated by using the power in the wind to drive a wind turbine to
produce mechanical power. This mechanical power can be converted into electrical power by
using electrical induction generators. Output voltage of the generators changes with any change
in the load, capacitor or rotor speed of the machine.
In this project, computer program have been used to obtain the performance of the generator
under different conditions. Matlab has utilized to get the maximum capacitance required for selfexcited induction generator, minimum frequency under variable load resistance, load reactance
and speed.
3
Chapter 1
Wind Energy Systems
١٫١ Introduction
Renewable energy sources presently provide significant amount of energy in many countries.
Renewable energy sources currently supply about 10 % of the world energy demand [1]. These
energy sources will become increasingly important in the future. There are many types of
renewable energy in a good situation among the energy types like Wind Energy Systems (WES),
biomass energy systems and Photovoltaic Energy Systems (PVES). But much more experience is
needed to predict the future economics and markets for the emerging technologies.
The renewable energy is environmental friendly compared to current level of CO2 emission
associated with electricity generation. Renewable energy sources by year 2020 could reduce the
emission of CO2. Such a contribution from renewable energy systems would also reduce
substantially the low level of other pollutants that cause acid rain, smog and other local
environmental hazards.
The renewable energy has many other benefits such as: Create significant new employment
opportunities in energy infrastructure, manufacturing, installation and etc, Contribute to the
securing of long term, cost-effective environmentally sustainable energy supplies and offer low
operating costs.
The major types of renewable energy sources can be summarized as follows:
•
Wind Energy.
•
Solar Energy.
•
Hydro Energy.
•
Tidal Energy.
•
Biomass Energy
4
1.2 History of Wind Energy System
Windmills have been existence for at least three thousand years, mainly for grinding grain or
pumping water [2]. By the mid-ages, windmills were in wide spread use around the
Mediterranean Sea. These windmills were used for corn grinding. At the end of 18th century,
about 10,000 Wind Turban Generators (WTG) were in use in Netherlands only with the similar
number in use in Britain [3].
Denmark was the first country to use the wind for generating electricity from a wind station
[4]. From 1980 till now there is a competition between Europe and North America in the
generation of electricity from wind. Fig. 1.1 shows the global wind energy market.
Fig. 1.1 The global wind energy market [5].
1.3 Wind Power
Wind energy is a form of solar energy produced by heating of the earth’s surface. As a power
source, wind power is less predictable than solar power, but it is also typically available for more
hours in a given day. Wind resources are influence by the type of the land surface and the
elevation of the land surface. Generally, if the land is in high elevation then it is good for wind
5
energy conversion and visa versa. Since the wind speed is extremely important for the amount of
energy a wind turbine can convert it to electricity.
The power in the wind can be defined as follows,
Pw =
Where
1
ρAV 3
2
(1.1)
ρ : Air density, kg/m3.
A : Cross sectional area of wind parcel, m2.
V : The wind speed, m/sec.
From (1.1), it is clear that the wind power is affected by the wind speed. The wind speed
increases with the height most rapidly near the ground, increasing less rapidly with greater
height.
The wind speed at which electric power production starts called the cut-in wind speed. The
turbine will develop enough mechanical power to rotate itself at slightly lower speeds, but this
wind speed will actually supply all the generator and transmission losses so that useful electric
power cannot be produced. At rated wind speed the power input to the wind turbine will reach the
limit for continuous operation (rated power). When the wind speed exceeds this level the excess
power in the wind must be discarded by varying the pitch angle of the blades to prevent the
turbine overloading. The power is maintained at its rated value until a maximum wind speed is
reached the cut-off wind speed (Vcut-off) then the turbine will shut down. The actual WTG output
power with the wind speed is shown in Fig. 1.2.
6
Fig. 1.2 Actual WTG output power with the wind speed [6].
1.4 Types of Wind Turbine Generators (WTG)
There two main types of (WTGs), which are:
١٫٤٫١ Horizontal Axis WTGs (HA-WTGs):
This is the most famous type of WTGs. There are many configurations for this type, which
are shown in Fig. 1.3.
The main advantages of HA-WTGs are a self-starting, large variety of the rated output power
(Suitable for small WTGs as well as very large WTGs) and it has a comparatively low cost.
The main disadvantages of this type are, it must be reoriented as the wind changes its
direction. The second disadvantage is the generator and gearbox and control system are all
located in the top of the WTG tower, which make the maintenance, is a problem.
7
Fig. 1.3 The HA-WTG configurations [7].
١٫٤٫٢ Vertical Axis WTGs (VA-WTGs):
VA-WTGs type are lower in number than the HA-WTGs due to some problems in design.The
main advantages of VA-WTGs, are no additional cost is required to change the VA-WTGs
direction when the wind direction changes and the gearbox and generator and control system are
in the ground level, then their maintenance is very simple. Fig1.4 Shows the VA-WTGs
configurations. A complete comparison between HA-WTGs and VA-WTGs is shown in table
(1.1).
Fig. 1.4 The VA-WTGs Configurations [7].
8
Table (1.1) Comparison between HA-WTGs and VA-WTGs [7].
1.5 Turbine Shaft Power and Torque at Variable Speeds
Most wind turbines operate at fixed rotational speeds except when starting and stopping. This
simplifies system operation when using synchronous generators paralleled with the utility grid. It
also helps to prevent the turbine from being operated at a speed which will excite a mechanical
resonance that might destroy the turbine. However, fixed speed operation means that the
maximum coefficient of performance C pm is available only at one particular wind speed. A
lower coefficient of performance is observed for all other wind speeds, which reduces the energy
output below that which might be expected from variable speed operation. That is, if the turbine
speed could be adjusted in relation to the wind speed, a higher average coefficient of performance
and a higher average power output could be realized. Variable pitch operation at a fixed speed
also helps improve the average coefficient of performance, but this is not feasible for turbines
such as the Darrieus. Variable pitch operation also increases complexity and cost, hence may not
be the most economical solution for all applications. It is therefore interesting to explore variable
speed turbine operation. We shall now examine the variation of shaft power and torque with
turbine angular velocity, We shall proceed by examining the variation of Pm as a function of
ω m , with the wind speed u as a parameter. The shaft power Pm for this turbine as a function of
shaft rotational speed n is shown in Fig. 1.4. Pm is seen to rise to a maximum for each wind
speed for a particular value of rotational speed. Higher wind speeds have more power in the
9
wind, and the change in tip speed ratio with increasing wind speed causes the maximum to shift
to a higher rotational speed [8].
Fig.1.4 Shaft power output in variable-speed operation [8].
1.6 Methods of Generating Synchronous Power from WTGs
The interfacing of wind energy system with utility grid requires high frequency and voltage
stability to avoid WES get out of synchronization. There are number of ways to get synchronous
power output from WTG. Each has its advantages and disadvantages and each should be
considered in the design stage of a new WES. Some methods can be eliminated for economic
reasons, but there may be several that would be competitive for a given application [4]. Nine
methods of generating synchronous power are shown in Table (1.2) through Table (1.4).
Table (1.2) shows Constant Speed Constant Frequency (CSCF) systems. Systems 1, 2 and 3
differ only in pitch control and gearbox details. A variable-pitch turbine is able to operate at a
10
good coefficient of performance over a range of wind speeds when turbine angular velocity is
fixed. The main problem is that variable pitch turbine is more expensive than fixed pitch turbine.
Table (1.3) shows Variable Speed Constant Frequency (VSCF) systems with series connected
circuit. In system 4 the turbine drives DC generator which drives DC motor at synchronous
speed. The disadvantage of system 4 over system 3 is the requirement of two additional electrical
machines, which increases the cost and weight of equipment on the tower.
System 5 is very similar to system 4 except that an AC generator and three-phase rectifier are
used to produce direct current. The AC generator-rectifier combination may be less expensive
than the DC generator it replaces and may also be more reliable. This is very important for all
equipment located on top of the tower because maintenance can be very difficult over there.
System 6 converts the wind turbine output into DC power by an AC generator and solid-state
rectifier. The direct current is then converted to electric utility alternating current by an inverter.
Modern solid state inverters which become available in mid of 1970 s allowed this system to be
one of the first to supply synchronous power from the WES to the electric utility.
In system-7 the output of AC generator will be synchronized directly in one stage to constant
frequency constant voltage output using a cycloconverter.
11
Table (1.2) constant speed, constant frequency systems [4].
12
Table (1.3) Variable speed, constant frequency WTG with series connected circuit [4].
Table (1.4) shows a VSCF systems by using slip ring induction generator. A constant stator
frequency can be maintained over wide speed range by supplying the rotor circuit with slip
frequency voltage. The system can work in sub-synchronous speed or super-synchronous speed.
In case of sub-synchronous speed, the slip power will subtract from the rotor circuit. In case of
super-synchronous speed, the power is supplied to the rotor. The converter can be a rectifier /
inverter as shown in system-8.
13
In system-9 the slip power frequency can be achieved directly in one stage by using
cycloconverter.
Table (1.4) VSCF systems with slip ring induction generator [4].
Using slip power recovery techniques in system-8 and system-9 extends the range of
rotational speed to upper or lower the synchronous speed. Moreover the ratings of components in
the rotor circuit will be partial rated which will reduce the cost of the power conditioner system
[9].
1.7 Project Objectives
•
Discussing different types of renewable energy.
•
Utilizing the wind energy to generate electricity.
•
Finding the required capacitance to build up the voltage across terminal of induction
generator.
•
Calculating minimum value of capacitor to produce reactive power.
•
Making interconnection between wind turbine generator and utility grid.
14
1.8 Project Organizing
In Chapter One, we discuss different types of renewable energy specially wind energy.
In Chapter Two, we talk about induction generator and obtaining the equivalent circuit of it to
use this generator to transform the mechanical energy (wind energy) to electrical energy.
In Chapter Three, we use the nodal method to find the maximum capacitance required for
self-excited induction generator.
15
Chapter 2
Induction Generator
2.1 Introduction
The induction generator is the most common generator in wind energy system applications
due to its simplicity and ruggedness, more than 50 years life time, same machine can be used as
motor or generator without modification, high power per unit mass of materials and flexibility in
speed range of operation. The main drawbacks in induction generator are its lower efficiency and
the need for reactive power to build up the terminal voltage. However, the efficiency can be
improved by modern design and solid-state converters can be used to supply reactive power
required.
There are two types of induction generator:
1- Normal type (non isolated), where excitation required are provided by an external A.C
source.
2- Isolated type (self excited) in which excitation is provided by a terminal capacitor.
In the first type, the frequency and voltage are equal to that of system. However, in the
second type, the frequency and induced voltage change with speed, excitation capacitor, load
impedance and its associated power factor. The frequency of the induced voltage is always less
than the synchronous frequency (corresponding to input shaft speed) [10].
The generators used in wind energy applications should be simple to use with low
maintenance, and have low initial cost. Induction generator satisfies most of these requirements.
Also, the WTGs employ permanent magnet, synchronous and variable reluctance generator
systems.
16
2.2 Equivalent Circuit of an Induction Machine
2.2.1 Transformer Model of an Induction Machine
The per-phase equivalent circuit, representing the operation of induction machine is shown in
Fig. (2.1)
Fig.2.1 The induction machine with rotor and stator connected by an ideal transformer.
Like any transformer, there is a certain resistance and self-inductance in the primary (stator)
windings, which must be represented in the equivalent circuit of the machine. The stator
resistance will be called R1 and the stator leakage reactance will be called X1. These two
components appear right at the input to the machine model. Like any transformer with an iron
core, the flux in the machine is related to the integral of the applied voltage E1. The
magnetomotiveforce-versus-flux curve (magnetization curve) for this machine is compared to a
similar curve for a power transformer.
2.2.2 Rotor Circuit Model
In an induction machine when the voltage is applied to the stator windings. A voltage is
induced in the rotor windings of the machine. In general, the greater the relative motions between
the rotor and the stator magnetic fields, the greater the resulting rotor voltage. The largest relative
17
motion occurs when the rotor is stationary, called the locked-rotor or blocked rotor condition, so
the largest voltage is induced in the rotor at the condition .The smallest voltage (OV) occurs
when the rotor moves at the same speed as the rotor magnetic field, resulting in no relative
motion. The voltage induced in the rotor at any speed between these extremes is directly
proportional to the slip of the rotor. Therefore, if the induced rotor voltage at locked-rotor
conditions is called Ero, the induced voltage at any slip will be given by the equation
Er = sEro
(2-1)
This voltage is induced in a rotor containing both resistance and reactance .The rotor
resistance Rr is a constant, independent of slip, while the rotor reactance is affected in a more
complicated way by slip.
The reactance of an induction motor rotor depends on the inductance of the rotor and the
frequency of the voltage and current in the rotor. With a rotor inductance of Lr, the rotor
reactance is given by
Xr =wr Lr =2πfroLr
(2-2)
from Equation
(2-2)
Xr = 2πsfe Lr
= s(2πfe)Lr
= sXro
(2-3)
Where Xro is the blocked-rotor reactance.
The resulting rotor equivalent circuit is shown in Fig. (2.2). The rotor current flow can be
found as:
Ir =
Er
Rr + jX r
(2-4)
or
18
Ir =
Ir =
sE ro
Rr + jsX ro
E ro
Rr
+ jX ro
s
(2-5)
Fig.2.2 The rotor circuit model of an induction machine.
The equivalent rotor impedance from this point of view is:
Z r ,eq =
Rr
+ jX ro
s
(2-6)
And the rotor equivalent circuit using this convention is shown in Fig.(2.3).
Fig.2.3 The rotor circuit model with slip effects concentrated in resistance Rr.
19
2.2.3 Final Equivalent Circuit
It is necessary to refer the rotor part of the model over to the stator side. The rotor circuit
model that will be referred to the stator side is the model shown in Fig (2.4), which has all the
speed variation effects concentrated in the impedance term.
Fig.2.4 The per-phase equivalent circuit of induction machine.
Referring the voltage, currents, and impedances on the secondary side of the device to the
primary side by means of the turns ratio of the transformer:
Vp = Vs' = aVs
IP = Is '=
Is
a
and
Z s '= a 2 Z s
(2-7)
(2-8)
(2-9)
Exactly the same sort of transformation can be done for the induction motor’s rotor circuit .If
the effective turns ratio of an induction motor is aeff , then the transformer rotor voltage becomes
E1 = Er' = aeffEro
(2-10)
The rotor current becomes
I2 =
Ir
a eff
(2-11)
And the rotor impedance becomes
20
Rr
(2-12)
+ jX ro )
s
If we know make the following definitions:
2
Z 2 = a eff (
R2 = aeff2 Rr
(2-13)
X2 = aeff2 Xro
(2-14)
Then the final per-phase equivalent circuit of the inducting motor is as shown above in Fig (2.4)
2.3 Operation of Induction Generator
The induction motor can also run as a generator. This simply happens when you, instead
of forcing the rotor to turn at a rotational speed lower than the synchronous speed, exceed
this synchronous speed by applying an outside energy source, the greater the difference between
the rotating magnetic field of the stator and the speed of the rotor, the greater the torque produced
by the rotor.
When it is a working as a generator, the rotating field however acts as a brake in slowing
the rotor. The stator experiences a variable magnetic field from the rotor that 'drags' its rotating
magnetic field and thereby induces an electrical current in the stator. The faster the rotor turns in
relation to the rotating magnetic field of the stator, the greater the induction in the stator and the
greater the production of power.
An induction generator cannot produce reactive power. In fact it consumes reactive power,
and an external source of reactive power must be connected to it at all times to maintain its stator
magnetic field. This external source of reactive power must also control the terminal voltage of
the generator. With no field current, an induction generator cannot control its own output voltage
[10].
2.4 Analysis of Induction generator
For a wind energy conversion system that uses induction generator, a dc link converter is
essential for power conversion. The induction generator produces current at variable frequency.
This current is rectified onto the dc link using a converter with six active switches. To convert the
21
dc to a fixed frequency of the utility, a second converter with six switches is needed. This results
in many switches needed for wind energy conversion system. Hence a new method that uses a
six-switch current regulated pulse width modulated inverter and a zero sequence filter is proposed
to eliminate some of the switches used and still retaining the original functionality of the system
[11]. An approach employing a boost converter to control the DC link is shown in Fig 2.5
Fig 2.5 Interfacing of SCIG to electric utility via diode bridge rectifier and LCI [11].
The study of induction generator steady state analysis and performance characteristics is
important due to the speed fluctuations of unregulated wind turbines, the terminal voltage may
increase to dangerously high levels to cause capacitor failure at wind farms. Over-voltages are the
major cause of excitation capacitor failure. Using a satiable transformer connected to the
terminals of the induction generator will improve voltage regulation and also protection against
over-voltages [12].
2.5 Dynamic Performance of Wind Turbine-Induction Generator
The problem of using wind as an input source of power generation is that wind varies from
time to time due to wind gusts, and is further disturbed by the effect of supporting tower shadow.
However with the advances in power electronics, the use of static VAR compensator to
regulate voltage produced from wind generator system became an alternative solution to
overcome the problem of input variation. To achieved stability of the system, a state and output
PI controller is proposed to control the static VAR controller and the mechanical input power to
the generator. From software simulation results, the proposed controller shows good damping
22
performance for the wind generation system under severe wind gust and large electrical system
disturbances [13].
23
Chapter 3
Maximum Capacitance Required for Self-Excited Induction
Generator
3.1 Introduction
Induction generator has a widely acceptance in using with wind energy conversion systems
for many reasons. Induction generator is very simple, very rugged, reliable, cheap, lightweight,
long lifetime, produces high power per unite mass of materials and requires very little
maintenance. All above advantages are very important especially in wind energy conversion
systems where the generator is in the top of the tower where the weight, maintenance and life
time are very important aspects. Induction generator can be used with stand alone as well as grid
connected wind energy conversion systems. Also, induction generator works with constant speed
constant frequency systems as well as variable speed constant frequency systems.
The main drawback of induction generator in wind energy conversion systems applications is
its need for leading reactive power to build up the terminal voltage and to generate electric
power. Using terminal capacitor across generator terminals can generate this leading reactive
power. The capacitance value of the terminal capacitor is not constant but it is varying with many
system parameters like shaft speed, load power and its power factor. If the proper value of
capacitance is selected, the generator will operate in self-excited mode. The capacitance of the
excitation capacitor can be changed by many techniques like switching capacitor bank [14],
thyristor controlled reactor [15] and thyristor controlled DC voltage regulator [16]. In last decade
many researches uses PWM technique to provide the desired excitation by controlling the
modulation index and the delay angle of the control waveform [17].
24
3.2 Calculating Maximum Capacitance
The obtained circuit in chapter two as shown below in Fig.3.1 can be used in steady state
operation. But, in case of varying operating frequency of the generator, this circuit can be
modified to be as the circuit shown in Fig.3.2 [18]. The elements of this circuit are corresponding
on the rated frequency. In this circuit, the machine core losses have been ignored. In fact, for
maximum capacitance required, the machine must operate at threshold of saturation. Therefore,
ignoring such losses will result in no serious errors in estimating Cmax [19].
RL
-jXc
jXr
jXs
Rs
Vt
Is
Rr
s
jXm
jXL
Fig. 3.1 The equivalent circuit of one phase of induction generator.
YL
YC
Rs
a
Vt/a
RL
a
Yin
JXc
a2
Xr
Xs
Is
Xm
Rr
a-b
JXL
Fig. 3.2 Modified equivalent circuit of induction generator.
25
3.3 Nodal Analysis Method
The proposed technique uses nodal analysis instead of loop analysis to obtain just one
formula for the maximum capacitance required for induction generator operation at different load
and speed conditions. In this technique, we used the real part of Yt =0 to determine the frequency
due to the resultant equation does not contains XC and substituting this frequency in imaginary
part to calculate Cmax in a simple form as shown in (3-7).
Applying the nodal analysis at the terminal voltage Vt of the circuit shown in Fig.3.2 we
get the following equation:s=
N sa − N a
N sa
(3-1)
Divide equation (3-1) by Nsr then:
a −b
a
(3-2)
Vt
Yt = 0
a
(3-3)
s=
Where all these admittances are shown in Fig.3.2
Then, Real of Yt = 0
(3-4)
And Imaginary of Yt = 0
(3-5)
After some algebraic operations we can get the following:١. From real part we get the following equation:-
C 4 a 4 + C 3 a 3 + C 2 a 2 + C1 a + C 0 = 0
(3-6)
The Coefficients Cn, n=0, 1, 2, 3, 4 are shown in Appendix I. The coefficients of this
equation do not contain XC. The frequency can be obtained directly by solving (3-6) to get the
operating frequency. There are four roots; the positive real roots only have the physical meaning.
If there is no any positive real root, then there is no self-excitation.
26
٢. From the imaginary part we can drive a simple formula for the maximum value of
terminal capacitor as shown in (3-7).
C max =
M4
1 X La
(
)
+
2
2π M 3 M 1 + M 2 2
(3-7)
The coefficients M1, M2, M3 and M4 of (3-7) are shown in the appendix.
This new formula can be used on line to calculate the maximum capacitor required for
induction generator to build up. This new formula does not require any numerical analysis
iteration.
3.4 Maximum Value of Terminal Capacitor
To validate the above formula (3-7), we can use the same data used in reference [20] :
Xm =3.23 pu, Rs =0.071 pu, Rr =0.0881 pu,
Xs = Xr =0.1813 pu, Zb=43.3 N=1800 rev/min,
fb =60Hz, RL=1 pu, XL=2 pu, b = 1 pu.
By using matlab program, we wrote a program as shown in the appendix contains nodal
analysis equations (3-6) and (3-7). And finally we get Cmax values as curves varying with
different speed.
27
Chapter 4
RESULTS
350
RL=0.5 , XL=0
maximum capacitance (uF)
300
250
200
150
100
50
0
0
500
1000
1500
2000
speed (rpm)
2500
3000
3500
Fig.4.1 Relation between speed and maximum capacitance
90
RL=0.5 , XL=0
80
minimum frequency (Hz)
70
60
50
40
30
20
10
0
0
500
1000
1500
2000
speed (rpm)
2500
3000
3500
Fig.4.2 Relation between speed and minimum frequency.
28
350
RL=0.5 , XL=0.5
250
200
150
100
50
0
0
500
1000
1500
2000
speed (rpm)
2500
3000
3500
Fig.4.3 Relation between speed and maximum capacitance.
90
RL=0.5 , XL=0.5
80
70
minimum frequency (Hz)
maximum capacitance (uF)
300
60
50
40
30
20
10
0
0
500
1000
1500
2000
speed (rpm)
2500
3000
Fig.4.4 Relation between speed and minimum frequency.
29
3500
350
RL=0.5 , XL=1
250
200
150
100
50
0
0
500
1000
1500
2000
speed (rpm)
2500
3000
3500
Fig.4.5 Relation between speed and maximum capacitance
90
RL=0.5 , XL=1
80
70
minimum frequency (Hz)
maximum capacitance (uF)
300
60
50
40
30
20
10
0
0
500
1000
1500
2000
speed (rpm)
2500
3000
3500
Fig.4.6 Relation between speed and minimum frequency
30
350
RL=0.5 , XL=2
250
200
150
100
50
0
0
500
1000
1500
2000
speed (rpm)
2500
3000
3500
Fig.4.7 Relation between speed and maximum capacitance
90
RL=0.5 , XL=2
80
70
minimum frequency (Hz)
maximum capacitance (uF)
300
60
50
40
30
20
10
0
0
500
1000
1500
2000
speed (rpm)
2500
3000
3500
Fig.4.8 Relation between speed and minimum frequency
31
350
RL=0.5 , XL=inf
250
200
150
100
50
0
0
500
1000
1500
2000
speed (rpm)
2500
3000
3500
Fig.4.9 Relation between speed and maximum capacitance
90
RL=0.5 , XL=inf
80
70
minimum frequency (Hz)
maximum capacitance (uF)
300
60
50
40
30
20
10
0
0
500
1000
1500
2000
speed (rpm)
2500
3000
3500
Fig.4.10 Relation between speed and minimum frequency
32
350
XL=0
XL=0.5
XL=1
XL=2
XL=inf
250
200
150
100
50
0
0
500
1000
1500
2000
speed (rpm)
2500
3000
3500
Fig.4.11 Relation between speed and max. capacitance at fixed RL=0.5
120
XL=0
XL=0.5
XL=1
XL=2
XL=inf
100
minimum frequency (Hz)
maximum capacitance (uF)
300
80
60
40
20
0
0
500
1000
1500
2000
speed (rpm)
2500
3000
3500
Fig.4.12 Relation between speed and min. frequency at fixed RL=0.5
33
350
XL=0
XL=0.5
XL=1
XL=2
XL=inf
250
200
150
100
50
0
0
500
1000
1500
2000
speed (rpm)
2500
3000
3500
Fig.4.13 Relation between speed and max. capacitance at fixed RL=1
120
XL=0
XL=0.5
XL=1
XL=2
XL=inf
100
minimum frequency (Hz)
maximum capacitance (uF)
300
80
60
40
20
0
0
500
1000
1500
2000
speed (rpm)
2500
3000
3500
Fig.4.14 Relation between speed and min. frequency at fixed RL=1
34
350
XL=0
XL=0.5
XL=1
XL=2
XL=inf
250
200
150
100
50
0
0
500
1000
1500
2000
speed (rpm)
2500
3000
3500
Fig.4.15 Relation between speed and max. capacitance at fixed RL=2
120
XL=0
XL=0.5
XL=1
XL=2
XL=inf
100
minimum frequency (Hz)
maximum capacitance (uF)
300
80
60
40
20
0
0
500
1000
1500
2000
speed (rpm)
2500
3000
3500
Fig.4.16 Relation between speed and min. frequency at fixed RL=2
35
500
speed=900rpm
speed=1800rpm
speed=2700rpm
speed=3600rpm
400
350
300
250
200
150
0
0.5
1
1.5
Load Resistance
2
2.5
Fig.4.17 Relation between load resistance and max. capacitance at XL=0.5
400
speed=900rpm
speed=1800rpm
speed=2700rpm
speed=3600rpm
350
Maximum Capacitance (uF)
Maximum Capacitance (uF)
450
300
250
200
150
0
0.5
1
1.5
Load Resistance
2
2.5
Fig.4.18 Relation between load resistance and max. capacitance at XL=1
36
250
150
100
speed=900rpm
speed=1800rpm
speed=2700rpm
speed=3600rpm
50
0
0
0.5
1
1.5
2
2.5
XL
Fig.4.19 Relation between load reactance and max. capacitance at RL=0.5
210
200
190
Maximum Capacitance (uF)
Maximum Capacitance (uF)
200
180
170
160
speed=900rpm
speed=1800rpm
speed=2700rpm
speed=3600rpm
150
140
130
0
0.5
1
1.5
2
2.5
XL
Fig4.20 Relation between load reactance and max. capacitance at RL=1
37
Chapter 4
Experimental Part
4.1 The equivalent circuit parameters test
The equivalent circuit parameters of the squirrel cage induction machine are calculated
from terminal measurements of DC, no-load and locked-rotor test as described in the
following subsections.
This test was applied to substitute the parameters used in the MATLAB program of the
1st part of the graduate project by the others found in this test due to discover the variance
between the theoretical and practical results.
4.1.1 D.C Test:
D.C Voltage is applied across two phases of the machine and several readings of the
current and voltage are taken.
The stator resistance (RS) is then calculated by taking the slope of the line relating the
voltage across the current through the motor winding.
4.1.2 No-Load Test:
Fig 4.1 The no-load test equivalent circuit
38
By using a synchronous motor as a driver of the test motor with speed of 1800 r.p.m. A
variable sinusoidal voltage source at 60 Hz, is connected to the stator. Fig.(4.1) shows
test requirements.
In this test, the slip is zero, which means that the branch corresponding to the rotor in
the equivalent circuit can be considered as open.
This test is used to calculate the magnetizing reactance due to applied voltage by
following several steps:
The motor has been running at no-load using rated line to line voltage VNL . Then by
measuring the no-load current INL and calculating the total 3-phase active power PNL.
The primary phase voltage can be obtained from the following equation:
VT =
V LL
3
V/ Phase (4-1)
Then the no-load impedance can be obtained as following:
ZNL =
VT
IS
(4-2)
The no-load resistance is:
RNL =
PNL
3I S2
(4-3)
The no-load reactance is:
XNL =
2
2
Z NL
− R NL
(4-4)
In the equivalent circuit it’s assumed that:
XS + Xm = XNL
(4-5)
Then from the no-load test, the value of XS + Xm has been calculated.
39
4.1.3 Locked-rotor test:
In this test, the rotor and the stator is connected to a low voltage and the equivalent
circuit of this test is shown in fig.(4.2), from which we can find the referred parameters
i.e. (Rr and Xr) following the next steps and equations:
Fig.4.2 The locked-rotor test equivalent circuit
Under rated line voltage, when the rotor of an induction motor is locked, the stator
current IS is almost six times its rated value. Furthermore, the slip s is equal to one. This
means that Rr / s is equal to Rr . Because IS is greater then the exciting current Io, we can
neglect the magnetizing branch. This leaves the equivalent circuit shown in Fig.(4.2)
without the magnetizing branch.
By applying 3-phase voltage to the stator and gradually increase it from zero until the
stator current is about its rated value.
Then the readings of VLL |BL, IS|BL has been taken and the total 3-phase power PBL.
From the locked-rotor test, the locked-rotor resistance is:
RBL =
PBL
3I S2 | BL
(4-6)
40
The locked-rotor impedance at frequency of locked-rotor test is:
ZBL|fBL =
VT | BL
I S | BL
(4-7)
The locked-rotor reactance at frequency of locked-rotor test is:
XBL|fBL =
2
2
( Z BL
| fBL − R BL
)
(4-8)
Its value at rated frequency is:
XBL = XBL|fBL*
XBL ≅ XS + Xr
f rated
f BL
(4-9)
(4-10)
Assuming, XS = Xr (at rated frequency)
Then XS and Xr can be obtained
From no-load test its known that XS + Xm = XNL and XS is known then the magnetizing
reactance is:
Xm = XNL - XS
(4-11)
41
The locked-rotor resistance is the sum of RS and an equivalent resistance, say R, which is
the resistance of Rr + jXr in parallel with Xm as shown in Fig.(2.4); therefore,
R=
X m2
* Rr
Rr2 + ( X r + X m ) 2
(4-12)
If Xr + Xm ⟩⟩ Rr , as is usually the case,
Rr = (
X r+ X m 2
) *R
Xm
(4-13)
Now R= RBL – RS. so the value of R can be used to determine Rr from equation (4-13)
and all different parameters has been obtained due to the three previous tests above.
42
4.2 Min. and Max.Capacitance Required for Self-Excited Induction Generator Test
In chapter 3, the nodal approach was applied on the induction generator to obtain the
min. and max. capacitance required for the build-up voltage using a software program for
calculating the required values.
In practical, the test has been done in the lab to find the higher and lower value of the
capacitor that the build-up voltage appears and make a comparison between the
theoretical and practical results.
In fact, the only problem finding the maximum value of the capacitor in the lab, is that
the induction motor reaches its rated current value without a voltage collapse happens, so
to deal with this problem, the capacitance value at the rated current has been choose as
the maximum capacitance required for self-excited induction generator, and that’s for
preventing any damage may happen to the machine.
To find the required capacitance values, the following steps have been done:
a-First, the circuit shown in Fig.(4.3) has been connected and the necessary steps to
operate the induction machine has been applied.
b-Without switching ON the load switch, the speed has been set at 800 rpm, and then
the capacitor bank switch is switched ON.
c-The value of capacitance has been increased until the build-up voltage appears in the
induction machine, then in gradually steps the value of capacitance has been decreased
until the build-up voltage disappear, and this value has been recorded as the minimum
capacitance required for the self-excited induction generator at 800 r.p.m.
43
Fig. 4.3 The circuit used for testing in the lab
d-The speed has been increased in steps of 100 rpm and the step (c) has been repeated at
each speed value with recording the capacitance value at each speed, and this will be the
no load test.
e-The load has been set at 1 p.u and the steps from (b) to (d) has been repeated with
switching ON the load switch.
f-The load values has been changed from 1 p.u to 1.5 p.u and 2 p.u and the previous steps
has been repeated and finally, the results has been plot for each load used in this test.
44
And to find the maximum capacitance value, the following steps has been taken:
a-With the circuit shown above, the same necessary steps has been applied to operate this
machine.
b-without switching ON the load switch, the speed has been set at 800 r.p.m and the
capacitor bank switch has been ON.
c-The value of capacitance has been increased until the build-up voltage happens, then in
gradually steps the value of the capacitance is increased until the rated current of the
induction machine has been reached, and this value will be record as the maximum value
of capacitance at 800 r.p.m.
d-The speed has been increased in steps of 100 r.p.m until the rated speed of the machine,
and the step (c) has been repeated for each speed value, and with recording each value of
capacitance at each speed, this will be the no-load test.
e-The load has been at 1 p.u. and the steps from (b) to (d) has been repeated, with
switching ON the load switch.
f-The load values has been changed from 1 p.u. to 1.5 p.u. and 2 p.u. and the previous
steps has been repeated and finally, the results has been plot for each load used in this
test.
45
Chapter 5
Conclusion
The main advantages of renewable are available, clean, low cost and continuous
energy. The reasons for choosing induction generator in wind energy system are that its
very reliable tends to be comparatively inexpensive, light weight, and low maintenance.
The generator also has some mechanical properties which are useful for wind turbines.
So, the induction generator is the most common generator in wind energy system
applications due to its simplicity and ruggedness. The used formula to calculate the
maximum capacitance required for self-excited induction generator is simple and it
doesn’t need numerical iteration. For this reason, this formula helps to determine the
maximum capacitance required for self-excited induction generator on line. The formula
gives typical results as the results obtained from iterative technique without any iteration
or divergence problem.
46
Appendix 1
% This program is to calculate the maximum capacitance and the minimum
% frequency
% it will plot the relation between the speed and the maximum capacitance
% required & the relation between the speed and the frequency
% here we assume that the load resistance is constant and load inductance
% is variable
% and for the same program we let the load inductance fixed and change the
% load resistance
rr=0.0881;
zb=43.3;
rs=0.071;
xs=0.1813;
xr=0.1813;
xm=3.23;
rl=0.5;
fb=60;
xl=0;
fmax=0;
vv(1)=0;
for x=2:100;
vv(x)=vv(x-1)+0.02;
v=vv(x);
l1=xs*(xr+xm)+xr*xm;
l2=xr+xm;
l3=xm+xs;
c4=xl^2*rr*(l2*l3-l1)+xl^2*rs*l2^2+rl*l1^2;
c3=xl^2*rr*v*(l1-l2*l3)-2*v*(xl^2*rs*l2^2+rl*l1^2);
c2=rl^2*(rs*l2^2-rr*l1+rr*l2*l3)+xl^2*rs*(rr^2+l2^2*v^2)+2*rl*rr*rs*(l2*l3l1)+rl*(l1^2*v^2+rr^2*l3+rs^2*l2^2);
c1=rl^2*rr*v*(l1-l2*l3)-2*rl*rs*l2^2*v*(rl+rs)+2*rl*rs*rr*v*(l1-l2*l3);
c0=(rl+rs)*rl*rs*(rr^2+v^2*l2^2);
p=[c4 c3 c2 c1 c0];
r=roots(p);
cmin=1000000000000;
cmax=0;
for i=1:4;
f=r(i);
if angle(f)==0;
m1=rs*rr-f*(f-v)*l1;
m2=rr*f*l3+rs*(f-v)*l2;
m3=rl^2+xl^2*f^2;
m4=rr*m2-l2*f*(f-v)*m1;
yc=xl*f^2/m3+m4*f/(m1^2+m2^2);
47
xc=zb/yc;
c=1/(2*3.14*f*fb*xc)*10^6;
if c<cmin;
cmin=c;
fmax=f;
end
if c> cmax;
cmax=c;
fmin=f;
end
end
end
fmx(x)=fmax;
fmn(x)=fmax;
cmn(x)=cmin;
cmx(x)=cmax;
xc=1/(2*3.14*60*cmin*zb);
vt(x)=fmax;
freq1=fmn*60;
cmx1=cmx
end
rr=0.0881;
zb=43.3;
rs=0.071;
xs=0.1813;
xr=0.1813;
xm=3.23;
rl=0.5;
fb=60;
xl=0.5;
fmax=0;
vv(1)=0;
for x=2:100;
vv(x)=vv(x-1)+0.02;
v=vv(x);
l1=xs*(xr+xm)+xr*xm;
l2=xr+xm;
l3=xm+xs;
48
c4=xl^2*rr*(l2*l3-l1)+xl^2*rs*l2^2+rl*l1^2;
c3=xl^2*rr*v*(l1-l2*l3)-2*v*(xl^2*rs*l2^2+rl*l1^2);
c2=rl^2*(rs*l2^2-rr*l1+rr*l2*l3)+xl^2*rs*(rr^2+l2^2*v^2)+2*rl*rr*rs*(l2*l3l1)+rl*(l1^2*v^2+rr^2*l3+rs^2*l2^2);
c1=rl^2*rr*v*(l1-l2*l3)-2*rl*rs*l2^2*v*(rl+rs)+2*rl*rs*rr*v*(l1-l2*l3);
c0=(rl+rs)*rl*rs*(rr^2+v^2*l2^2);
p=[c4 c3 c2 c1 c0];
r=roots(p);
cmin=1000000000000;
cmax=0;
for i=1:4;
f=r(i);
if angle(f)==0;
m1=rs*rr-f*(f-v)*l1;
m2=rr*f*l3+rs*(f-v)*l2;
m3=rl^2+xl^2*f^2;
m4=rr*m2-l2*f*(f-v)*m1;
yc=xl*f^2/m3+m4*f/(m1^2+m2^2);
xc=zb/yc;
c=1/(2*3.14*f*fb*xc)*10^6;
if c<cmin;
cmin=c;
fmax=f;
end
if c> cmax;
cmax=c;
fmin=f;
end
end
end
fmx(x)=fmax;
fmn(x)=fmax;
cmn(x)=cmin;
cmx(x)=cmax;
xc=1/(2*3.14*60*cmin*zb);
vt(x)=fmax;
freq2=fmn*60;
cmx2=cmx
end
49
rr=0.0881;
zb=43.3;
rs=0.071;
xs=0.1813;
xr=0.1813;
xm=3.23;
rl=0.5;
fb=60;
xl=1;
fmax=0;
vv(1)=0;
for x=2:100;
vv(x)=vv(x-1)+0.02;
v=vv(x);
l1=xs*(xr+xm)+xr*xm;
l2=xr+xm;
l3=xm+xs;
c4=xl^2*rr*(l2*l3-l1)+xl^2*rs*l2^2+rl*l1^2;
c3=xl^2*rr*v*(l1-l2*l3)-2*v*(xl^2*rs*l2^2+rl*l1^2);
c2=rl^2*(rs*l2^2-rr*l1+rr*l2*l3)+xl^2*rs*(rr^2+l2^2*v^2)+2*rl*rr*rs*(l2*l3l1)+rl*(l1^2*v^2+rr^2*l3+rs^2*l2^2);
c1=rl^2*rr*v*(l1-l2*l3)-2*rl*rs*l2^2*v*(rl+rs)+2*rl*rs*rr*v*(l1-l2*l3);
c0=(rl+rs)*rl*rs*(rr^2+v^2*l2^2);
p=[c4 c3 c2 c1 c0];
r=roots(p);
cmin=1000000000000;
cmax=0;
for i=1:4;
f=r(i);
if angle(f)==0;
m1=rs*rr-f*(f-v)*l1;
m2=rr*f*l3+rs*(f-v)*l2;
m3=rl^2+xl^2*f^2;
m4=rr*m2-l2*f*(f-v)*m1;
yc=xl*f^2/m3+m4*f/(m1^2+m2^2);
xc=zb/yc;
c=1/(2*3.14*f*fb*xc)*10^6;
if c<cmin;
cmin=c;
fmax=f;
end
if c> cmax;
cmax=c;
fmin=f;
end
end
end
50
fmx(x)=fmax;
fmn(x)=fmax;
cmn(x)=cmin;
cmx(x)=cmax;
xc=1/(2*3.14*60*cmin*zb);
vt(x)=fmax;
freq3=fmn*60;
cmx3=cmx
end
rr=0.0881;
zb=43.3;
rs=0.071;
xs=0.1813;
xr=0.1813;
xm=3.23;
rl=0.5;
fb=60;
xl=2;
fmax=0;
vv(1)=0;
for x=2:100;
vv(x)=vv(x-1)+0.02;
v=vv(x);
l1=xs*(xr+xm)+xr*xm;
l2=xr+xm;
l3=xm+xs;
c4=xl^2*rr*(l2*l3-l1)+xl^2*rs*l2^2+rl*l1^2;
c3=xl^2*rr*v*(l1-l2*l3)-2*v*(xl^2*rs*l2^2+rl*l1^2);
c2=rl^2*(rs*l2^2-rr*l1+rr*l2*l3)+xl^2*rs*(rr^2+l2^2*v^2)+2*rl*rr*rs*(l2*l3l1)+rl*(l1^2*v^2+rr^2*l3+rs^2*l2^2);
c1=rl^2*rr*v*(l1-l2*l3)-2*rl*rs*l2^2*v*(rl+rs)+2*rl*rs*rr*v*(l1-l2*l3);
c0=(rl+rs)*rl*rs*(rr^2+v^2*l2^2);
p=[c4 c3 c2 c1 c0];
r=roots(p);
cmin=1000000000000;
cmax=0;
for i=1:4;
f=r(i);
if angle(f)==0;
m1=rs*rr-f*(f-v)*l1;
51
m2=rr*f*l3+rs*(f-v)*l2;
m3=rl^2+xl^2*f^2;
m4=rr*m2-l2*f*(f-v)*m1;
yc=xl*f^2/m3+m4*f/(m1^2+m2^2);
xc=zb/yc;
c=1/(2*3.14*f*fb*xc)*10^6;
if c<cmin;
cmin=c;
fmax=f;
end
if c> cmax;
cmax=c;
fmin=f;
end
end
end
fmx(x)=fmax;
fmn(x)=fmax;
cmn(x)=cmin;
cmx(x)=cmax;
xc=1/(2*3.14*60*cmin*zb);
vt(x)=fmax;
freq4=fmn*60;
cmx4=cmx
end
rr=0.0881;
zb=43.3;
rs=0.071;
xs=0.1813;
xr=0.1813;
xm=3.23;
rl=0.5;
fb=60;
xl=100000000;
fmax=0;
52
vv(1)=0;
for x=2:100;
vv(x)=vv(x-1)+0.02;
v=vv(x);
l1=xs*(xr+xm)+xr*xm;
l2=xr+xm;
l3=xm+xs;
c4=xl^2*rr*(l2*l3-l1)+xl^2*rs*l2^2+rl*l1^2;
c3=xl^2*rr*v*(l1-l2*l3)-2*v*(xl^2*rs*l2^2+rl*l1^2);
c2=rl^2*(rs*l2^2-rr*l1+rr*l2*l3)+xl^2*rs*(rr^2+l2^2*v^2)+2*rl*rr*rs*(l2*l3l1)+rl*(l1^2*v^2+rr^2*l3+rs^2*l2^2);
c1=rl^2*rr*v*(l1-l2*l3)-2*rl*rs*l2^2*v*(rl+rs)+2*rl*rs*rr*v*(l1-l2*l3);
c0=(rl+rs)*rl*rs*(rr^2+v^2*l2^2);
p=[c4 c3 c2 c1 c0];
r=roots(p);
cmin=1000000000000;
cmax=0;
for i=1:4;
f=r(i);
if angle(f)==0;
m1=rs*rr-f*(f-v)*l1;
m2=rr*f*l3+rs*(f-v)*l2;
m3=rl^2+xl^2*f^2;
m4=rr*m2-l2*f*(f-v)*m1;
yc=xl*f^2/m3+m4*f/(m1^2+m2^2);
xc=zb/yc;
c=1/(2*3.14*f*fb*xc)*10^6;
if c<cmin;
cmin=c;
fmax=f;
end
if c> cmax;
cmax=c;
fmin=f;
end
end
end
fmx(x)=fmax;
fmn(x)=fmax;
cmn(x)=cmin;
cmx(x)=cmax;
xc=1/(2*3.14*60*cmin*zb);
vt(x)=fmax;
freq5=fmn*60;
cmx5=cmx
end
y=0:36:3599;
53
plot(y,cmx1,y,cmx2,y,cmx3,y,cmx4,y,cmx5)
ylabel('maximum capacitance (uF)')
xlabel('speed (rpm)')
axis([0 3600 0 350])
legend('XL=0','XL=0.5','XL=1','XL=2','XL=inf')
figure
plot(y,freq1,y,freq2,y,freq3,y,freq4,y,freq5)
ylabel('minimum frequency (Hz)')
xlabel('speed (rpm)')
axis([0 3600 0 120])
legend('XL=0','XL=0.5','XL=1','XL=2','XL=inf')
54
Appendix 2
%This program is to calculate the maximum capacitance and the minimum
% frequency
% it will plot the relation between load resistance and max. capacitance at
% fixed speed
% the same program also can plot the relation between load reactance and
% max. capacitance at fixed speed
rr=0.0881;
zb=43.3;
rs=0.071;
xs=0.1813;
xr=0.1813;
xm=3.23;
xl=0.5;
fb=60;
fmax=0;
v=0;
for t=1:4;
vv(t)=v+0.5;
v=vv(t);
rl=0;
for x=1:20;
rrl(x)=rl+0.1;
rl=rrl(x);
l1=xs*(xr+xm)+xr*xm;
l2=xr+xm;
l3=xm+xs;
c4=xl^2*rr*(l2*l3-l1)+xl^2*rs*l2^2+rl*l1^2;
c3=xl^2*rr*v*(l1-l2*l3)-2*v*(xl^2*rs*l2^2+rl*l1^2);
55
c2=rl^2*(rs*l2^2-rr*l1+rr*l2*l3)+xl^2*rs*(rr^2+l2^2*v^2)+2*rl*rr*rs*(l2*l3l1)+rl*(l1^2*v^2+rr^2*l3+rs^2*l2^2);
c1=rl^2*rr*v*(l1-l2*l3)-2*rl*rs*l2^2*v*(rl+rs)+2*rl*rs*rr*v*(l1-l2*l3);
c0=(rl+rs)*rl*rs*(rr^2+v^2*l2^2);
p=[c4 c3 c2 c1
c0];
r=roots(p);
cmin=1000000000000;
cmax=0;
for i=1:4;
f=r(i);
if angle(f)==0;
m1=rs*rr-f*(f-v)*l1;
m2=rr*f*l3+rs*(f-v)*l2;
m3=rl^2+xl^2*f^2;
m4=rr*m2-l2*f*(f-v)*m1;
yc=xl*f^2/m3+m4*f/(m1^2+m2^2);
xc=zb/yc;
c=1/(2*3.14*f*fb*xc)*10^6;
if c<cmin;
cmin=c;
fmax=f;
end
if c> cmax;
cmax=c;
fmin=f;
end
end
end
resis(x)=rl
cap(x)=cmax;
end
56
if t==1;
cap1=cap;
end
if t==2;
cap2=cap;
end
if t==3;
cap3=cap
end
if t==4;
cap4=cap;
end
end
plot(resis,cap1,'k-*',resis,cap2,'g-o',resis,cap3,'r-',resis,cap4,'b--');
%axis([0.4 2 20 90]);
xlabel('Load Resistance');
ylabel('Maximum Capacitance (uF)');
legend('speed=900rpm','speed=1800rpm','speed=2700rpm','speed=3600rpm');
57
References
[1] International Energy agency report " Key Issues in Developing Renewables", 1997.
[2] John F. Walker and Nicholas Jenkins "Wind Energy Technology", John Wiley & Sons, 1997.
[3] P. J. Musgrove, " Wind Energy Conversion an Introduction “, IEE, Proceedings, VOL. 130,
Pt. A, No. 9, December 1983, PP 506-517.
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