Download The Design, Construction and Analysis of Horizontal Wind Turbine

Acta Physica Universitatis Comenianae
Volume (2016) 57–69
The Design, Construction and Analysis
of Horizontal Wind Turbine
for Small Scale Electric Energy Production*
¼. Staòo, V. Chudoba, M. Morvová
Department of Astronomy, Physics of the Earth and Meteorology, Faculty of Mathematics,
Physics and Informatics, Comenius University Bratislava, [email protected]
Abstract: This paper is handling with the design, construction and study of a low-cost horizontal wind
turbine as a small scale power source without the use of mechanical gears. It is focused on custom design
of individual components of the system including the turbine rotor, alternator, regulation, measuring
equipment and electric energy storage system. Manufacture and technological process is also described.
Turbine output has been compared with the record of wind speed obtained from the anemometer that is
installed on the same site, triggering the establishment of performance characteristics. Based on data
analysis, the potential for energy production for various wind speed has been evaluated in order to assess
the potential of using the turbine in different wind conditions.
1. Introduction
The wind manifests a transformation of solar radiation into kinetic energy of an air
mass. Thermal power transformed into airflow represents only about 1–2 % of the Sun radiation reaching the Earth's surface [8]. Nevertheless, that represents in absolute numbers
1015 W [1]. In fact, it is about 100 times the worldwide human energy consumption in all
its forms.
Wind flow is generally unstable, mainly due to the general circulation, climatic zone,
landscape relief etc. In the lowest layer of the atmosphere (up to 50 m), the wind velocity
increases roughly logarithmically over an open landscape. That is why it is important to
locate WT as high above the terrain as possible. In urban areas, the situation is quite
different due to the potential to form funnel effect between buildings [8]. Unstable wind
velocity generates operational problems in practice. To manage this problem, it is
necessary to develop sophisticated regulation and control systems that eliminate power
fluctuations by means of energy storage or transformation. However, the advantage of
wind is that it occurs in different intensity almost everywhere, making it one of the most
affordable and sustainable source of renewable energy worldwide [1]. The conversion of
this form of energy into electricity is handled for decades by means of wind turbines
(hereinafter referred to as WT) of various types.
Horizontal axis wind turbine (HAWT) is a type of WT with the axis of rotation directed horizontally. The advantage of HAWT compared to vertical wind turbines VAWT
is that it achieves higher performance, according to comparable cross-section area. The
base is very similar - the wind flows through blades and rotates it together with an axis.
*) Dedicated to Prof. V. Martišovitš 75-th anniversary
58
¼. STAÒO, V. CHUDOBA, M. MORVOVÁ
The axis is connected to an electric generator, either directly or by means of a gear system.
However, physical principle of the wind interaction with the blade is significantly different. Considering vertical wind turbines VAWT, pressure effects (except of Darrieus WT)
are utilized predominantly. In contrast, the principle of wing lift effect occurs on HAWT
and that force component, which is perpendicular to the axis of rotation, generates the
torque. Principles of aerodynamics, relevant to the wing lift effect generation, tend to be
disrupted by turbulent airflow, resulting in disadvantage of HAWT.
Our intention was to prove, that even at urban areas, this type of turbine could be harvested throughout this deficiency.
2. Theoretical background
2.1 Wind energy and efficiency of turbines
The kinetic energy of air mass that flows at velocity u through an active area A and per
unit of time is given as follows
PW =
1
rAu 3
2
(1)
To prevent any distortion of airflow, the kinetic energy cannot be converted to the
torque completely, based on the theory of inertia conservation. As it can be obtained, optimal performance is achieved, when the wind speed leaving the turbine u out reaches certain
value, defined as Betz condition.
u out = 1 / 3 u
a
u1 = 2 / 3 u
(2a)
The efficiency of energy transformation in turbines is defined by the relationship
Ptot
= cp
PW
(2b)
where c p is the power coefficient and relates the power that can be extracted from turbine
Ptot to the theoretical wind power PW . One can further derive the Betz limit upon (2a),
c p( Betz) = 0.59, that is the maximum of the power coefficient.
2.2 The rotor blade profile
The efficiency of airflow energy transformation in the turbine of cross sectional area
A (swept area) is strongly dependent on the rotational speed. The dependence is more significant by decreasing the number of blades. With the speed of rotation, the blade velocity v
proportionally changes. At given distance from the axis of rotation r, relative velocity of
air ua at a given speed of the wind changes, that is crucial for the lift effect (Fig. 1).
Since the lifting force L (that results from airflow around the blade profile) is perpendicular
to u a , the value of angle F between v and u a is important. As far as the component L sin F
is parallel to the velocity v, only this component is involved to the torque generation. In
Fig. 1 it can be seen that for angle F applies:
THE DESIGN, CONSTRUCTION AND ANALYSIS ...
59
Fig. 1. The balance of forces on the HAWT blade aerodynamic profile (the profile represents a blade
section).
tgF =
u1
v
(3)
At low speed or start-up, the ratio of inertia transferred to the turbine, compared to the inertia of air is small. It is because conditions are not suitable for lift generation and more over,
pressure effect on the profile is negligible. In fact, the only parameter for a specific blade
profile, which affects the lift force at given wind speed, is the angle of attack a. Because a
(angle between the blade chord and u a ) is large at start-up situation, airflow around the
profile forms turbulences on its end, which prevents from formation of lift. In such circumstances, the angle F is large, but the useful component of lift is also increased. Therefore,
there is the speed v of blade section, at which the angle is optimal to reach maximum of useful lift component.
Low torque at start-up is the main disadvantage of lift-effect turbine types. When the
rotational speed approaches the speed for which blades are designed, the angle of attack
became optimized and the torque rises to the maximum. Practically, the angle of attack is
continuously optimized by tilting blades according to actual wind and rotor speeds. However, it applies only on large scale power plants over 10 kW for economical reasons [9].
2.3 The wind speed and rotation
TSR (Tip-Speed Ratio l), namely the ratio of the blade tip-speed v t to the wind speed u
is one of the parameters of WT design. TSR refers to the maximal rotational speed of the
turbine of radius R, which is kept constant after the balance of forces is achieved.
l=
v t 2 pRf
=
u
u
(4)
Angle F may then be expressed using (3) and (4) together with Betz condition u 1 = 2u / 3 as:
tgF =
2R
3rl
(5)
Eqn. (5) shows that for fixed point in the distance r, F is only a function of l. Therefore,
TSR is critical in the design of lift type WT. To maintain the value of angle a optimized for
the whole blade (tgF »1/r) it can be seen that along the blade, the angle between blade
chord and a plane of rotation called tilt angle is given as (Fig. 1):
Q=F -a
(6)
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¼. STAÒO, V. CHUDOBA, M. MORVOVÁ
where the optimal value of a ranges from 6 to 10 [9]. The maximal lift during start-up (F = p / 2)
is therefore situated near to the rotor base, where the tilt angle is maximal.
2.4 The dependence of power coefficient on the tip-speed ratio
Subtracting air friction losses D (Drag), the power spinning the turbine will be:
v (R)
p=
ò L sin F (1 - gl)dv
(7)
v ( 0)
where g = D / L (Fig. 1) is the draft to lift ratio. Of course, analytical expression of g does
not exist and numerical methods (computer simulations) should be used to determine it [1].
We mentioned that the maximum of theoretical performance PBetz resulting from the Betz
limit is proportional to c p( Betz) . That is, under real conditions, decreased due to friction
looses to reduce the maximal efficiency of turbine, expressed by the Eqn. 8 and visualized
in Fig. 2 (for various WT designs).
c p (max) = (1 - gl )c p ( Betz)
(8)
Fig. 2. The power coefficient and TSR dependence for various WT types.
3. The design and construction
3.1 Rotor design
We decided to use a three-bladed rotor. It was designed to cooperate with electrical
generator, which converts generated torque into electric energy, so that optimization is
needed to extract the power efficiently. The wind speed at which the electrical energy generation starts upon this system is called cut-on wind speed u c . For fixed number of turbine
blades with radius R and resulting typical value of TSR, there is cut-on speed of rotation
THE DESIGN, CONSTRUCTION AND ANALYSIS ...
61
fc obtained, at which electromagnetic braking is stimulated and the generator starts to
slow down the turbine.
fc =
lu c
2 pR
(9)
In our system as discussed later, this rotational speed changes a little as a result of variable
actual accumulator battery voltage. We consider average wind speed to be u c as principal
parameter, which plays an important role in our calculations and is based on long term
wind speed measurements and observations on Faculty of Mathematics, Physics and Informatics meteorological station. The average wind speed during period of years 2010–2013
shows to be between 2.7 and 3.1 m/s.
If u c is considered to be too low according to the average wind speed, the torque of
turbine is actually not sufficient and it stalls rapidly. In other case, too high u c means that
the probability of exceeding it in local conditions becomes smaller. We chase 3 m/s as optimal cut-on wind speed. According to Eqn. 9, the value of cut-on frequency fc = 3.14 Hz
was calculated. Three-bladed rotor usually has a typical TSR ranging 6–10, the higher the
value, the more precisely fabricated rotor in general. Perfect blade design was not expected, so that resulting aerodynamics should not be overestimated, because drag to lift
ratio affects the efficiency of turbine. The design of aerodynamic profile was based on
Eqn. 5 and Eqn. 6 (tilt along the blade).
3.2 Generator
In our project we designed a three-phase alternator to work within 12 V system. It is a
type of axial-direction magnetic flux alternator with permanent neodymium magnets.
Each of three phases represents three series-connected coils mutual angle of 120°. This
layout determines the total induced voltage. Dimensions of the alternator components are
summarized in Fig. 4.
Fig. 3. The layout of magnets on the rotor disc.
The source of magnetic flux is a set of 12 magnets made of neodymium iron boron
(NdFeB) alloy with a magnetization of N45 and dimensions (l/w/h) 30/12/5 mm. Magnetic poles are located on 30´12 mm surfaces. Their contact force is 8.5 kg in touch. Adja-
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¼. STAÒO, V. CHUDOBA, M. MORVOVÁ
cent magnets according to each other are attached to a rotor disc with opposite polarity
orientation as shown in Fig. 3 in order to obtain required alternating magnetic flux.
Based on the strength of magnetic flux, we obtained the value of cut-in rotor speed and
thus the design of stator winding. Considering the speed of circular motion of magnet
v m = 2pfc rm , the total induced voltage Ui on phase can be calculated (Eqn. 10) if the rotor
magnets are located at a distancerm = ( R i + R o ) / 2 = 8 cm from the axis of rotation. Shape
of the coil is designed so that it corresponds with magnet dimensions (especially length
l = 3 cm) to maximize magnetic induction flux through the coil.
U i = 3U ic = 3
- Dj
= -3NBl 2 prm fc
Dt
(10)
One can find that the number of turns in one coil should be N = 200 if Ui =14 V has to be
achieved at fc =3.14 Hz. The number of turns gives the final thickness of the coil 8 mm and
15 mm in width around the perimeter. The diameter of wire is a compromise between the
number of turns and minimizing the total winding resistance (to achieve minimal losses in
winding that converts electric power into heat. The maximal net power that can be obtained
depends on the system voltage. When the current I produced at voltage U, the net power is
given as P = UI, where maximal current is determined by the nominal current load of the
wiring and is roughly directly proportional to its cross section. The total electrical resistance of the copper wire R cu causes ohm losses in the winding Pcu , relating to the current
consumption as Pcu=I2Rcu. Thus, electrical generator effectiveness relates to the current
consumption as 1/I. The final layout of the coils was connected and embedded all together
Fig. 4. The assembled alternator scheme (stator red, rotor disc blue, dimensions in mm).
in a bed of epoxy resin and glass fiber composite. Phase terminals were led out for later
contact connections. GND contacts are led separately for each phase to allow any changes
between star and delta phase connection. In the star connection, phases are connected as
parallel, so there is a sum of currents in the main terminal.
3.3 The regulation and storage system
Because of the fact, that weather conditions are generally unstable, renewable energy
sources such as wind cannot be simply used directly in small scale system. In our system,
THE DESIGN, CONSTRUCTION AND ANALYSIS ...
63
Fig. 5. The scheme of alternator and regulator electrical connection circuit.
electric energy is stored in two parallel connected 12 V lead-acid battery bank, each capacity of 90 Ah, thus together providing capacity of 180 Ah, 2.16 kWh.
To ensure optimal charging cycle of batteries to prolong its lifetime and to gain maximum of the stored energy during charge-discharge cycle, electronic regulation circuit is
used (the scheme is shown in Fig. 5). The main element of the circuit is an electromagnetic
switch controller, which leads rectified current from the alternator either into the battery
bank or, when fully charged, to feed a dummy load, which is basically a variable resistor
and has a function of an electro-dynamic brake. The battery voltage is controlled to hold
an optimal charging cycle. For lead-acid batteries, it is appropriate to maintain the voltage
between 12 and 14 V though, at peak maximum up to 14.7 V. At discharged state (11 V),
any extra discharging should not be longer allowed. This is when relay is switched to
"charging" state and the generator terminal is connected to the battery positive. The state
"dummy load" (putting the switch into active state) switches if the battery voltage exceeds
the maximum of 14 V. It is possible to change the states, when voltage is in defined range
using momentary buttons, while designed to perform a hysteresis effect automatically. To
avoid discharging the battery below 11 V, internal protection of an inverter 300 W
(DC/AC 12V/230V) electronics has been used. The inverter is used for generation AC of
50 Hz from DC battery voltage, which is then usable for most appliances. When the stored
energy used directly from the battery (12 V appliances), an additional undercharge protection is needed.
3.4 Measurement setup
The whole construction consisting of the rotor, alternator, rectifiers and a hall-effect
sensor are placed on a bearing that provides vertical rotation according to wind direction
by means of a tail. Rectified voltage is transferred over two-pole rotary contacts.
The net power delivered to the battery was quantified as a product of battery voltage
and charging current. The analog voltage signals are processed through an AD converter
with the microcontroller interface, which is connected through a COM port to a computer.
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¼. STAÒO, V. CHUDOBA, M. MORVOVÁ
To correlate the net power extracted from the turbine with the wind speed, measurement by wind speed sensor connected to a wireless Vantage Pro2 weather station from
DAVIS also has been digitalized. Values of the speed and direction are averaged over
minute intervals before storing in memory by associated software.
4. Experimental results
4.1 Alternator testing and calibration
An important parameter that characterizes the alternator is the dependence of voltage
on the rotational speed. After the alternator has been assembled, we measured voltage signals of respecting phases by means of an oscilloscope in order to verify the values calculated at specific rotor frequency.
Fig. 6a. The voltage signal on one phase.
Fig. 6b. The net power (blue), the loss power (red) and the efficiency (green) as a function of gained
current.
THE DESIGN, CONSTRUCTION AND ANALYSIS ...
65
In one phase winding, there are 6 periods of AC voltage signal generated per one revolution of the rotor with 12 magnets. The frequency of the voltage is thus firmly determined
and corresponds to six times the rotor frequency in Hz or, 1/10 of revolutions per minute
(rpm). This is typical for synchronous machines. As a result, the time-voltage diagram
(shown in Fig. 6a) contains the information about the speed of rotation.
Table 1. The technical parameters of constructed alternator.
Dimensions of magnets
Number of poles
Rotor disc diameter
30´12´5 mm
12
100 mm
Air gap
12 mm
Magnetic induction
0.5 T
Number of phases
3
Winding turns number
500
Wire diameter
0.8 mm
Winding resistance
Rated current
Voltage frequency by 200 rpm
3.6
11.4 A
20 Hz
Rated power
140 W
Weight of winding
1.08 Kg
Total weight
7 Kg
Since the storage system is designed to use DC voltage, the phase outputs are rectified
(the wiring diagram is shown in Fig. 5). All phases have the same waveform voltage and
the same amplitude at given speed. Measurement of DC signal involving all phases shows
a linear dependence on the speed with coefficient of 3.78 V/Hz, or 0.063 V/lrpm. Charging voltage 14 V is generated at the frequency of 3.7 Hz. Compared to the value in computations considered ( fc = 3.18 Hz) it represents a deviation of 16 %. 12 V is achieved at
3.3 Hz (200 rpm). This is because in calculations amplitudes are considered, while after
rectification it is the effective value of AC. To specify the effective value of such non-harmonic signal would be more complicated problem and would require more complex
method to determine it. In addition, rectified voltage signals of three phases overlaps, so
that the effective value is higher. Additional voltage drop is caused by semiconducting
rectifier.
4.2 Wind speed measurements
In local wind conditions, where the turbine is situated, there is turbulent wind, because
of buildings and others objects higher than the turbine. The turbine is situated 20 m from
south-east corner of a building, so east and north-east winds are not utilized. South wind
provides optimal conditions, with low wind speed fluctuation. However, there is west and
north-west preference of airflow on this site.
Measuring of the wind speed was carried out from 27.3.2015 00:00 to 2.4.2015 17:00.
From anemometric data we calculated the average wind speed of 2.61 m/s and a histogram
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¼. STAÒO, V. CHUDOBA, M. MORVOVÁ
that shows the wind speed duration (Fig. 7). Produced energy in kWh has been evaluated
for this period using calibration curve (Fig. 8).
Fig. 7. The histogram of wind duration (wide) and extracted power (narrow) according to the wind
speed.
Fig. 8. The turbine calibration curves (net power, total power, wind power and power coefficient as a
function of wind speed).
4.3. Turbine performance characteristics
Precise correlation of the power with wind speed is very complicated because of the
presence of wind speed fluctuation. The turbine has its own momentum of inertia, like anemometer has, so measurement is actually just an average through certain time intervals
and there is not the same response for the whole speed range. The reason why this happens
is discussed in the section of the rotor blade profile. To minimize inaccuracies, the calibration was performed at roughly constant speed. It is difficult to quantify the turbine reaction on gusty wind, but there are studies dealing with the problem of time reaction
THE DESIGN, CONSTRUCTION AND ANALYSIS ...
67
characteristics of HAWT [9]. To obtain relevant wind turbine calibration it is necessary to
use a wind tunnel with well-defined conditions.
This wind turbine is not designed for wind speed lower than u c , thus the reaction time
is long. If fluctuations of the wind speed are around u c = 3.4 m/s (determined as the
cut-in speed according to measurements) the turbine reaches necessary rotational speed
for optimal operation, so reaction is dramatically different. At this speeds, fluctuations are
captured efficiently. This is observed on rapid electric current increase. Data of all variables were collected every 2 seconds. The result is the calibration curve shown in Fig. 8.
The power loss (heat dissipation in windings) Pcu and total electrical power
Ptot = P + Pcu gathered from the turbine were also computed. The power coefficient cp has
been specified according to the Eqn. (2b). It is clearly visible that cp increases up to wind
speed of about 5.5 m/s. Above 5.5 m/s it remains almost constant. That means the turbine
reaches optimal operating speed for maximum performance. The ratio of total electrical
power to Betz limit Ptot/PBetz reaches a value »44 %. Energy efficiency h is the ratio of
P/Pw. Ideally this is the product of the turbine power coefficient cp and the alternator efficiency h a . The value cp is characteristic for the turbine itself and refers to the conversion
of kinetic energy of the wind into mechanical energy. Total efficiency h characterizes a
whole system including more energy losses as were considered. Nevertheless, the value h
is more accurate because the value was set from ratio of precisely-measured net power and
wind energy (calculated from theory). In fact, there are additional losses on contacts,
losses by the transfer, friction in bearings etc. that indicate inaccuracy of the power coefficient value.
The efficiency of alternator rapidly decreases at high electric current. Maximum
h = 17 % has been recorded at wind speed 5.5 m/s and power P = 48 W. Higher wind
speed, around 8 m/s were also recorded, but just like gusty wind, therefore these data were
excluded from calculations. Rated power has been observed at gusty wind 12 m/s.
Fig. 9. The wind turbine power system constructed.
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¼. STAÒO, V. CHUDOBA, M. MORVOVÁ
Table 2: Parameters of the wind turbine.
Rotor radius
0.9 m
Swept area
2.5 m2
Height of the axis of rotation above ground
8.5 m
Tip speed ratio
5.8
Power coefficient
0.26
Cut-in wind speed
3.4 m/s
Cut-in revolutions (12V)
200 rpm
Cut-out wind speed
Rated power
Maximum efficiency factor of the system
12 m/s
140 W
17 %
5. Conclusions
In this project, we used long term measurements of the wind speed in order to design
the turbine rotor and adapted alternator (system for generating electrical energy) for a specific urban site. On the constructed alternator, we performed measurements intended to
diagnose voltage signals. Three-bladed rotor using lifting principle, own design, has been
tested in cooperation with three phase generator and calibrated on output performance
according to wind speeds.
Within the evaluation, the power coefficient of the turbine relative to consumed output
cp = 0.26 and overall energy efficiency of the system h = 17 % has been determined. We
consider important to mention that at constant wind speed, the turbine is able to spin-up already at 2 m/s. This would be impossible by using an alternator with cored winding. Even
high speeds of the wind provide very low torque to run up steady HAWT. The start-up is
possible only at sufficiently low static resistance, in our case there are coreless coils meaning no additional inductive losses when alternator not loaded and the resistance is generated only in bearings.
Acknowledgement
Effort sponsored by the Slovak Research and Development Agency APVV-0134-12,
and Slovak grant agency VEGA 1/0918/15.
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