Design of Drivetrain and Potential Evaluation of a Gorlov Turbine

Design of Drivetrain and
Potential Evaluation of a
Gorlov Turbine
Inigo Garcia de Madinabeitia
Hannes Hagmar
EEK150 Power Engineering Design Project HT15
Department of Energy and Environment
Chalmers University of Technology
Gothenburg 2015-10-31
Abstract
The Gorlov helical turbine is proposed as a feasible alternative to generate electricity in
smaller rivers where the ecological impact of a dam would be too significant. The report
examines the possibilities of installing and designing a drivetrain for a Gorlov turbine in
the small river of Säveån, close to Nääs castle.
The results show that the energy potential in Säveån is severely limited during significant
periods of the year, and the location is thus found not to be suitable. The design of the
drivetrain and control is thus carried for a hypothetical river with a larger amount of water
flow. The design of the drivetrain and control is intentionally simple, robust and with first
order response, but simulation shows that the control is found to be adapting well to the
applied simulations, and the power output is significantly increased with the controller
implemented. The control needed in order to perform fish behaviour studies is chosen to
be separated from the ordinary control, and instead a mechanical braking system is
proposed.
1
Contents
Abstract .................................................................................................................. 1
1 Introduction ..................................................................................................... 3
1.1 Background ............................................................................................... 3
1.2 Purpose ..................................................................................................... 4
1.3 Scope ........................................................................................................ 4
2 Theory ............................................................................................................... 5
2.1 Helical Gorlov turbine .............................................................................. 5
2.1.1 Turbine power and efficiency ....................................................... 5
2.1.2 Tip-speed ratio .............................................................................. 6
2.2 Generator .................................................................................................. 7
2.2.1 Electric model of a PSMG ............................................................ 7
2.3 Diode rectifier ........................................................................................... 8
2.4 Boost (Step-up) converter ......................................................................... 9
3 Methodology ................................................................................................... 11
3.1 Literature review ..................................................................................... 11
3.2 Water flow measurements and estimations ............................................ 11
3.3 Parameterization of a PMSG .................................................................. 13
3.4 Design of drivetrain and control ............................................................. 14
3.4.1 Design of control system ............................................................ 14
3.4.2 Simulations ................................................................................. 16
4 Results ............................................................................................................. 18
4.1 Water measurements............................................................................... 18
4.2 Parameterization results and values for simulation ................................ 21
4.2.1 Efficiency and Power-Speed curves ........................................... 22
4.2.2 Values and parameters for simulations ....................................... 24
4.3 Simulink simulations .............................................................................. 25
5 Analysis ........................................................................................................... 30
6 Conclusions..................................................................................................... 31
References............................................................................................................. 33
2
1 Introduction
Hydropower is currently one of the most effective ways of generating renewable
electricity in a sustainable way [1]. However, conventional hydropower stations require
the use and construction of dams, resulting in a significant environmental impact. Largescale dam hydropower affects not only the water flow but also the wildlife habitat and the
possibilities for fish migration. This ecological impact may, especially at smaller rivers,
exceed the value of the generated electricity. Consequently, there exists a conflict
between the goal of increasing the amount of renewable electricity and keeping the local
ecosystem unharmed.
Therefore, to still be able to harness power from lesser rivers, a new approach has to be
examined. One possible solution is to use low-head micro hydro installations, such as the
Gorlov helical turbine. The Gorlov turbine is a vertical axis water turbine, using only the
current water flow to operate, therefore eliminating the need of constructing a dam. The
Gorlov turbine has been used commercially mostly in tidal power plants; however, the
potential for small-scale power generation in smaller rivers may still be vast [2].
1.1 Background
Nääs castle is situated close to Säveån, a relatively small river with two small hydropower
stations located in the vicinity. To yield further energy from the river flow, and at the
same time keeping the environmental impact at a minimum, the helical Gorlov turbine
has been proposed as a feasible solution.
Nääs castle is also a popular tourist destination with numerous visits throughout the year.
However, as of now, it still lacks a proper public transport connection with the train
station, and an investment of some sort would be needed. One suggested method of
solving this problem is to use the electricity from the Gorlov turbine to drive an electric
bus and transport train passengers to the castle. This would then not only result in a fully
renewable and clean mean of transportation, but also as a source of goodwill for the castle.
Furthermore, due to the fact that the Gorlov helical turbine is placed in water, it will
undoubtedly have an effect on the aquatic life and the surrounding environment [3]. The
studies of the impact on fish life is somewhat limited and how a system actually affects
the fish is still rather unclear. Previous studies have found that factors such as the size and
speed of the turbine, the size of the fishes, and the visibility all affects the impact. Higher
speed of the turbine will cause higher chance of a collision and a large turbine will
evidently affect a larger area of the river. The visibility is also found to have a significant
impact, where a low visibility commonly results in a higher impact [3].
To further study the impact on fish life of a Gorlov helical turbine, the designed drivetrain
should enable a wide range of speed control. By being able to control the speed of the
turbine, the effect that the speed has on aquatic life can be examined. Up to this moment,
3
the previous studies of the effects that Gorlov helical turbines have on Swedish conditions
are highly limited or even non-existent, and it is therefore most interesting to develop
such studies.
1.2 Purpose
The purpose of the report is to establish the potential of installing a Gorlov turbine in
Säveån, and from the results design a suitable electrical drivetrain. Moreover, a control
system should be chosen and designed to both yield a high energy output and allow a
suitable speed control for future fish studies.
1.3 Scope
The report will mainly address the electrical aspects of the drivetrain and there will thus
be no analysis of how to physically design the Gorlov turbine. Since the turbine is not
available for testing, specific properties such as efficiency and torque behaviour will have
to be estimated from previous research [4], [5].
Furthermore, due to the limited time frame of the project, the optimization of the
drivetrain will be limited. The main goal of the project is instead to design and simulate
a drivetrain that could be applied once the turbine is in place. There are also a number of
simplifications in the proposed model. Primarily, there is no modulation of the shaft
between the turbine and the generator. Therefore, all the inertia of the whole system is
simulated as if it is contained within the generator. The control system is purposely made
simple due to both due to the lack of data regarding the turbine and due the project time
constraints. Therefore, no regard is taken towards effects such as cross-coupling, backEMF and integrator anti-windup. To enhance the control system further, more effort
should be put to examine these aspects.
Finally, the potential evaluation of the project will not contain an economic estimation.
This technology of small-scale generation of electricity is difficult to compare to other
methods of generating electricity, and the results of such an evaluation would thus be
inconclusive.
Acknowledgements are given to Nusrat Afrin Ani and Iftekhar Zaman Arnab for writing
and editing parts of the report and performing measurements.
4
2 Theory
In the following section the theory required to follow the rest of the report is presented.
The main focus is covering the fundamental aspects of the Gorlov helical turbine and how
maximal power extraction can be achieved. A brief section is also covering the function
of the main parts of the proposed drivetrain.
2.1 Helical Gorlov turbine
The Gorlov helical turbine is an improved version of the Darrieus turbine, with a chosen
number of blades swept in a helix profile along its span, rather than using the curved
aerofoil blades of the Darrieus turbine [6]. Both designs are used as vertical axis turbines,
allowing unidirectional rotation in all flow orientations [2]. However, the Gorlov turbine
is found to have a number of advantages to prior designs. For example; the helical blade
shape allows the turbine to be self-starting, there is a reduction of torque fluctuations
during rotation, a higher efficiency, and a high uniform spinning in slow fluid flows [5].
2.1.1 Turbine power and efficiency
The Gorlov helical turbine can be dimensioned with several different characteristics to
suit the application. The height and diameter of the turbine are significantly affecting the
possible output as the swept area of the turbine is directly proportional to the output of
the turbine. The swept area of the turbine can be calculated as
𝐴 = 2 ∙ 𝑟𝑡𝑢𝑟𝑏𝑖𝑛𝑒 ∙ 𝐻𝑡𝑢𝑟𝑏𝑖𝑛𝑒
(2.1)
where 𝐴 is the swept area, and 𝑟𝑡𝑢𝑟𝑏𝑖𝑛𝑒 and 𝐻𝑡𝑢𝑟𝑏𝑖𝑛𝑒 are radius and height of the turbine.
Furthermore; the number of blades, the material, the chord length, and the blade
inclination angle, all affects the properties of the turbine. The extractable power in a
flowing water stream can then be stated as [2]
𝑃𝑓𝑙𝑜𝑤 =
1
𝜌𝐴𝑣 3
2
(2.2)
where 𝐶𝑝 is the coefficient of power, 𝑃𝑓𝑙𝑜𝑤 is the power of the flowing water in a cross
sectional area, 𝜌 is the water density, 𝐴 the cross sectional area of the stream, and 𝑣 the
fluid stream velocity. The coefficient of power, i.e. the efficiency of the turbine, is then
directly related to the produced mechanical power and thus to the mechanical torque
𝐶𝑝 =
𝑃𝑚
1
3
2 𝜌𝐴𝑣
5
=
𝑇𝑚 Ω
1
3
2 𝜌𝐴𝑣
(2.3)
where 𝜂 is the efficiency of the turbine, 𝑃𝑚 the mechanical power, 𝑇𝑚 the mechanical
torque, and Ω the angular velocity. By rearranging (2.3), the power output of the turbine
is found to be
𝑃𝑚 =
1
𝜌𝐴𝑣 3 𝐶𝑝 = 𝑃𝑓𝑙𝑜𝑤 𝐶𝑝
2
(2.4)
2.1.2 Tip-speed ratio
The tip-speed ratio (TSR) is the ratio between the speed of the tip of the blade and the
velocity of the water flow, and can be stated as
𝜆=
Ω ∙ 𝑟𝑡𝑢𝑟𝑏𝑖𝑛𝑒
𝑣
(2.5)
where 𝜆 is the TSR. The optimal value of TSR is depending on the turbine design and
each value of the ratio is related with a value of the coefficient of power 𝐶𝑝 . In order to
generate the highest amount of energy, the TSR should thus be kept to a ratio that results
in the highest value of 𝐶𝑝 . The highest efficiency is thus obtained when 𝐶𝑝 ,𝑜𝑝𝑡 =
𝐶𝑝 (𝜆𝑜𝑝𝑡 ). By combining (2.4) and (2.5) the expression for the maximal power can then
be stated as
3
𝑃𝑜𝑝𝑡
Ω𝑜𝑝𝑡 ∙ 𝑟𝑡𝑢𝑟𝑏𝑖𝑛𝑒
1
= ∙ 𝜌 ∙ 𝐶𝑝,𝑜𝑝𝑡 ∙ 𝐴 ∙ (
)
2
𝜆𝑜𝑝𝑡
(2.6)
This concept of controlling the tip speed ratio to the value corresponding to the highest
value of 𝐶𝑝 is known as maximum power point tracking (MPPT). The power speed
characteristics of a Gorlov turbine are presented in Figure 13 in section 4.3, and consists
of a curve connecting the highest 𝐶𝑝 -values at different water velocities.
The results from previous studies regarding optimal TSR of Gorlov turbines are
somewhat inconclusive. Two studies, using a three-bladed turbine, found that the TSR
should be chosen to a value 2.0-2.2 to achieve the highest 𝐶𝑝 -value [5] and [4]. In
contrast, another study, with the same amount of blades, found that the highest 𝐶𝑝 -value
was achieved at about 1.1-1.2 TSR [7]. The efficiency of the turbines is also varying
significantly, with an efficiency span ranging from 11.6 - 39 % [2]. The efficiency varies
significantly depending on aspects such as number of blades, blade type, helical angle
and water flow velocity. However, one of the more recent reports states that the efficiency
for a 3-bladed helical turbine is closer to 27 % [4].
6
2.2 Generator
The generator transforms the mechanical power from the shaft into electric power that is
then fed to either the grid or to a battery cell. The most common generator types for
driving wind turbines are the induction generator (IG) and the permanent magnet
synchronous generator (PMSG). The PMSG has generally a larger torque density and
requires less maintenance, but is generally more expensive than IG.
Due to the proximity to open air and water, the aspects of corrosion and sealing are
important. The easiest solution to handle this would be to either select a generator with a
high IP rating or construct a suitable sealing. The dust protection should be at least enough
for dust not to interfere with the performance and the water protection should at least be
enough to withstand splashing of water [8].
2.2.1 Electric model of a PSMG
The PMSG is a synchronous generator that uses permanent magnets, rather than windings
in the rotor, to create the required magnetic field [9]. The related stator equation can be
stated [10] as
𝐸𝑎̇ = 𝑗𝑋𝑠 ∙ 𝐼𝑠̇ + 𝑅𝑠 ∙ 𝐼𝑠̇ + 𝑉𝑠̇
(2.7)
where 𝐸𝑎̇ is the electromotive force (EMF) of the generator, 𝑗𝑋𝑠 is the reactance of the
generator, 𝑅𝑠 is the stator resistance, 𝑉𝑠̇ is the stator voltage , and 𝐼𝑠̇ is the line current.
Note that all currents and voltages are expressed as phasors by using the notation of the
dot above the symbol [10].
The generated EMF voltage 𝐸𝑎 is directly proportional to the rotor speed [9]
𝐸𝑎̇ = 𝑘𝐸 ∙ ωr
(2.8)
where 𝑘𝐸 is a machine dependent constant and ωr the rotor speed measured in
radians/second. Using (2.7) and (2.8) we can state the line current as
𝐼𝑠̇ =
𝑘𝐸 ωr − 𝑉𝑠̇
𝑅𝑠 + 𝑗𝜔𝑟 𝐿𝑠
(2.9)
From (2.9) it is found that if 𝑉𝑠 is varied, the current will change accordingly. This is
however only true for lower values of ωr ; at higher frequencies the 𝑗𝜔𝑟 𝐿𝑠 -term will
increase as much as the generated 𝑘𝐸 ωr -term and the control will be lost. The electrical
torque 𝑇𝑒 produced by the machine can similarly be stated as
𝑇𝑒 = 3 ∙ 𝑘𝐸 ∙ 𝐼𝑠̇
The mechanical relationship between the torque and the speed is
7
(2.10)
𝐽
𝑑𝜔𝑟
= 𝑇𝑒 − 𝑇𝐿
𝑑𝑡
(2.11)
where 𝐽 is the inertia of the machine, and 𝑇𝐿 is the load torque.
If the PMSG is connected to a rectifying unit, then speed of the PMSG is possible to
estimate by measuring the DC current and voltage. The relation for the speed is governed
by the following equation [11]
ωr =
2𝜋 (𝑉𝑑𝑐 + 2𝑅𝑠 𝐼𝑑𝑐 )
𝑃𝑝
3√3 ̂
60 ( 𝜋 Ψ
m − 2 𝐿𝑠 𝐼𝑑𝑐 )
(2.12)
where 𝑉𝑑𝑐 and 𝐼𝑑𝑐 is the DC voltage and current, and 𝑃𝑝 is the number of pole pairs
2.3 Diode rectifier
In order to transform the AC-output of the generator to a DC-voltage, a rectifying unit is
required [12]. The design of the rectifying unit is often made with respect to the
application it is going to be used in. Normal power diodes have an on-state forward
voltage drop of about 0.7-1 V depending on the design [12]. The Schottky diode has a
significantly lower on-state voltage drop, around 0.3-0.4 V, and is therefore more
preferable in the sense of reduced losses. However, the Schottky diode has higher reverse
leakage current and a smaller breakdown voltage. Since the output voltage of the rectifier
should be as ripple free as possible, a large capacitor should be connected on the DC side.
By neglecting the voltage drop and the losses of the rectifying unit, the DC voltage can
easily be referred to the AC side by using the concept of power balance. Thus, from the
rule of conservation of energy, the power on the DC side must be equal to the power on
the AC side
3𝑉𝑠 𝐼𝑠 = 𝑉𝐷𝐶 𝐼𝐷𝐶
(2.13)
where 𝑉𝐷𝐶 and 𝐼𝐷𝐶 is the DC voltage and current respectively. Note that there is no need
for a cosine term at the AC side due to the unity power factor. The mean value of the
voltage on the DC side is found by integrating the rectified AC voltage as
𝑉𝐷𝐶 =
3 𝜋/6
3√6
∫ 𝑉𝑠 ∙ √3 =
𝑉
𝜋 −𝜋/6
𝜋 𝑠
By combining (2.13) and (2.14), the DC current can then be stated as
8
(2.14)
𝐼𝐷𝐶 =
3𝑉𝑠 𝐼𝑠
3𝑉𝑠 𝐼𝑠
𝜋
=
=
𝐼𝑠
𝑉𝐷𝐶
3√6
√6
𝜋 𝑉𝑠
(2.15)
2.4 Boost (Step-up) converter
A boost (step-up) converter is mainly used for DC power regulated supplies and for
regenerative breaking of DC motors [12]. As the name indicates, the output voltage of the
converter is always greater than the voltage input. In order to be able to keep the voltage
on the high voltage side, a large capacitor is generally needed. The basic circuit diagram
of a boost converter is found in Figure 1.
Figure 1. Circuit diagram of boost (step-up) converter
The converter equations are
1
𝑉
(1 − 𝐷) 𝐷𝐶1
(2.16)
𝐼𝐷𝐶2 = (1 − 𝐷)𝐼𝐷𝐶1
(2.17)
𝑉𝐷𝐶2 =
𝐷=
𝑡𝑜𝑛
𝑇
(2.18)
where 𝑉𝐷𝐶2 and 𝐼𝐷𝐶2 are converter output voltage and current, respectively; 𝑉𝐷𝐶1 and 𝐼𝐷𝐶1
are converter input voltage and current, respectively; 𝐷 is the duty cycle; 𝑡𝑜𝑛 is the
converter on time per period; and 𝑇 is the converter switching period. Using these
equations, the DC resistance can be varied by changing the duty cycle of the converter
9
𝑅𝐷𝐶2
1
𝑉𝐷𝐶2 (1 − 𝐷)
=
=
𝑅
= (1 − 𝐷)2 ∙ 𝑅𝐷𝐶1
𝐼𝐷𝐶2
(1 − 𝐷) 𝐷𝐶1
(2.19)
where 𝑅𝐷𝐶2 is the DC effective output resistance and 𝑅𝐷𝐶1 is the DC input resistance. To
reduce the current ripple to a certain value, the inductance should be designed according
to [12]
∆𝑖 =
(𝑉𝐷𝐶2 − 𝑉𝑑𝑐1 + 𝑉𝑑 )𝑇
𝐿
10
(2.20)
3 Methodology
In the following section, the used methodology is thoroughly described. A short literature
review is presented to give the reader an overview of the general progress within this field
of research. Furthermore, the procedure for the water flow measurements are discussed
and argued for and the method for the parameterization of the proposed PMSG is
described. Finally, the choice, design, and selections for the drivetrain and control system
are presented.
3.1 Literature review
The project will commence with a significant literature study, covering mainly previous
research of the Gorlov turbine, as well as how to actually design a working drivetrain for
a small generator. The previous studies regarding the efficiency of the Gorlov turbine are
somewhat limited [5] , [6] and [7]. The results differ significantly from each study and
the results are therefore also somewhat questionable. Thus, for the purpose of this report,
the required values will have to be estimated.
The literature covering the design of drivetrain is vast, and a huge number of articles and
reports are available. However, most reports cover advanced methods of control and few
are focusing on the simple and robust control needed in this project.
3.2 Water flow measurements and estimations
The water flow measurements were carried out by using an electromagnetic water current
meter from a bridge overpassing Säveån, see the marked location in Figure 3. In order to
find the most suitable spot for placing the turbine with the highest water velocity, the
water flow of several of the bridge openings were tested; for reference see Figure 2. The
measurements were also performed at different depths in order to examine if there was
variations in water flow. Moreover, the depth of the river was measured in order to find
a feasible location to physically place the turbine.
Due to the time constraint of the project, it is impossible to measure the water flow during
a long period. The proposed method to still be able to estimate the annual water flow is
to compare the actual measurements with data from the southern hydro power station in
Floda located nearby (see Figure 3). Thus, from the correlation between these data, it will
be possible to make an estimation in the differences of total annual water flow. By
assuming a linear relationship between the measured water speed value and the data from
the power station, a reference value for the water velocity can be found.
11
Figure 2. Bridge over Säveån where the measurements where performed
Figure 3. Map over Säveån and surroundings
12
3.3 Parameterization of a PMSG
The generator chosen for this project is a 12 V, 600 W permanent magnet synchronous
generator. Due to the higher efficiency and the robustness it was found to be the most
suitable choice in this application. In order to simulate its behaviour in Simulink,
measurements of the machine parameters were required.
The mechanical parts of the PMSG were assembled and then connected to an 87 kW
driving motor. Due to the low power rating of the motor, it is not possible to directly
measure the resistance with a multimeter. Therefore, a current was applied between two
phases and the voltage was then measured. By then using Ohm’s law the resistance could
be calculated.
The inductance was measured by using an autotransformer as a source of a variable AC
power supply, and then measuring the impedance between two phases. The inductance is
sensitive to physical movement, may vary significantly due to outer vibrations. Therefore,
the measurements of the inductance were conducted both during vibrating and nonvibrating conditions. A current of about 2 A was applied and the voltage was then
measured. Using the data from the resistance measurements, the inductance is possible to
distinguish from the measured impedance, see following equations
𝑍𝑚 =
𝑉𝑚
𝐼𝑚
2 − 𝑅2
𝑗𝑋𝑠,𝑚 = √𝑍𝑚
𝑚
𝐿𝑠,𝑚 =
𝑋𝑠,𝑚
2𝜋𝑓
(3.1)
(3.2)
(3.3)
where 𝑍𝑚 is the measured complex impedance, 𝑉𝑚 is the measured applied voltage, 𝐼𝑚 is
the measured applied current, 𝑅𝑚 the measured resistance, 𝑋𝑠,𝑚 the estimated stator
reactance of the generator, and 𝐿𝑠,𝑚 the estimated inductance.
Finally, the flux linkage has to be estimated. This was done by performing a no load-test
and measuring the voltage at different speeds of the machine. From the results, a voltagevs-speed curve could be found and the flux factor estimated. Moreover, the number of
pole pairs was found by using the following formula
𝑃𝑝 =
60 ∙ 𝑓
Ω𝐺
where 𝑃𝑝 is the number of pole pairs and 𝑓 the frequency.
13
(3.4)
3.4 Design of drivetrain and control
The drivetrain should be designed to be as efficient, reliable, and robust as possible. The
turbine is therefore to be connected directly to the PMSG without the interconnection of
a gearbox. Due to the high number of poles of the PMSG, the efficiency is still high even
at low speeds. The generator is then connected directly to a three-phase rectifier, which
in turn is connected to a boost converter and a battery bank. A simple design of the
proposed drivetrain is found in Figure 4.
Figure 4. Proposed drivetrain for a PMSG
The effective load of the battery bank may be, due to the simple connection of the
rectifying unit, modelled as an AC voltage source with a unity power factor [13]. The
stator current 𝐼𝑠 , and thus the torque, can then be controlled by regulating the duty cycle
value of the boost converter.
By then using the data from the water flow measurements, simulations will be performed
in order to accomplish the potential evaluation. Initially, a Simulink model will be
designed in order to test the properties of the drivetrain and the control system. Since the
turbine is not available for testing, specific properties such as efficiency and torque
behaviour will have to be estimated from previous research. If the results are satisfying,
the real drivetrain will be constructed and tested. In order to imitate the turbine behaviour,
a motor with specified speed and torque inputs will instead be connected to the drivetrain.
With respect to the given results, further improvements will be suggested.
3.4.1 Design of control system
The control system should be designed to be both efficient and allow a wide range of
speed control in order to allow more degrees of freedom in future fish behaviour studies.
The speed control required for future fish behaviour studies has been chosen to be
separated from the proposed maximum power point tracking system. Since the fish
behaviour studies will likely take place during a reasonably short time span, it will not
affect the total generated power in such a high degree. Therefore, a mechanical manual
braking system is instead proposed to control the turbine during fish studies. This results
in a decreased power output during the time of the studies, but since the time frame is
limited, there is a small effect on the total energy output. Due to the generally small output
14
of the turbine, the mechanical torque is fairly small and the breaking system can be
dimensioned accordingly. During the period of mechanical control, the regular control
system will be disconnected to avoid disturbances.
The aim of the actual control system that is going to be in place during normal operation
is instead to generate maximum power at all water flow velocities. The whole circuit in
its entity in Simulink is presented in Figure 5 below.
Figure 5. Simulink model of a Gorlov turbine and PMSG connected to a DC load
The aim of the control system is to control the switch of the boost converter and thereby
the output voltage and current of the PMSG. By measuring the power output on the DCside and considering the power-speed characteristics of the generator, the rotor speed
reference can be determined. The estimated power-speed characteristics for the Gorlov
turbine is found in section 4.3 and Figure 13.The error between the actual speed and the
reference speed is then fed to a PI controller to obtain the reference torque, expressed as
[14]
𝑇𝑒,𝑟𝑒𝑓 = (𝐾𝑝Ω +
𝐾𝑖Ω
) (Ωref − Ω)
𝑠
(3.5)
where 𝑇𝑒,𝑟𝑒𝑓 is the reference electromagnetic torque, 𝐾𝑝Ω and 𝐾𝑖Ω are the proportional
and integral gains for the speed control, and Ωref is the reference rotor speed. The values
for the proportional and integral gain are chosen experimentally and the results are
presented in section X. From the torque reference, the DC current reference is calculated
by using (2.10) and (2.15)
15
𝐼𝐷𝐶,𝑟𝑒𝑓 =
𝜋
̂m
3√6Ψ
𝑇𝑒,𝑟𝑒𝑓
(3.6)
The DC current reference is then compared with the actual DC current and the error is
finally provided to a hysteresis controller. Thus, when the error between the reference and
actual current is too large, a signal will be transmitted to the switch in the boost converter.
The inner current loop controller is used to ensure a higher level of robustness and a
quicker response. The control circuit in its entity in Simulink is illustrated in Figure 6.
Figure 6. The simple control circuit used in Simulink for the PMSG
To avoid the need of measuring the speed of the PMSG, a speed estimation block is
connected. The speed estimation block is derived by using (2.12) and is found in Figure
7.
Figure 7. Speed estimation block in Simulink for the PMSG
3.4.2 Simulations
The performed simulations use the water speed profile from Figure 15 as input to the
previously presented Simulink model. The simulation output was chosen to 5000 points
per second, with a total of 100 000 points in 20 seconds. This resolution is believed to be
enough to observe the system and controller behavior and performance. The Power
16
Systems Toolbox is used in Simulink for the electrical components, as well as the PMSG
block for the generator.
The simulations are performed to both examine the potential of the drivetrain and to
control that the proposed control system is operating properly. To examine whether the
control is fast enough, simulations are performed for a step and a filtered water speed
profile with shrunk time axis. The reason of using this shrunk time axis is to make it more
challenging for the control. Furthermore, the properties and functionality of the speed
estimation block is examined. In order to observe the difference for with and without
control, the control block is turned on first after 10 seconds for the filtered speed profile
case, whereas it is always on for the step responses.
The following four different simulations are performed in order to examine the control
system:
A. 1 to 1.5m/s step with measured speed
B. 1 to 1.5m/s step with estimated speed
C. Filtered water speed profile and measured speed
D. Filtered water speed profile and estimated speed
17
4 Results
In the following section the results from the water measurements, the parameterization of
the motor, and the Simulink simulations are presented. The results are further analysed
and discussed in the next section.
4.1 Water measurements
Figure 8 show the water speed results from the measurements in Säveån for a depth of
0.5 meters. These measurements were performed on the first opening to the right of the
largest bridge opening, for reference see Figure 2. To reduce the noise of the
measurements, a cubic Savitzky–Golay filter with a moving average of 99 elements has
been implemented [15]. The moving average is illustrated by the red line in the figure.
The average water speed value of the measurement is calculated to 0.198 m/s.
0.4
0.35
Water speed [m/s]
0.3
0.25
0.2
0.15
0.1
0.05
0
Measurement data
Filtered data
50
100
150
200
250
Time [s]
Figure 8. Water measurement plot from Säveån, 2015-09-16. Blue line is measured data points
and red line is the filtered water speed
Another measurement was performed the 15th October 2015 with an estimated average
water speed value of 0.369 m/s. Figure 9 shows the speed measurements for this date with
the same moving average as previous. The water flow from this figure will later be used
in the upcoming simulations and an added constant will used to simulate a river with a
higher water velocity.
18
0.6
0.55
Speed [m/s]
0.5
0.45
0.4
0.35
0.3
0.25
0
200
400
600
800
1000
1200
1400
1600
Time [s]
Figure 9. Water measurement plot from Säveån, 2015-10-15. Blue line is measured data points
and red line is the filtered water speed
The water flow in the Säveån measurement point, Figure 3, in cubic meter per second
was found by using the SMHI application “SMHI Vattenwebb – Hydrologiskt nuläge”
[16]. During the date of the first measurement the flow at the southern water power station
in Floda was measured to 8.7 𝑚3 /𝑠 [16]. During the date of the second measurement the
flow at the southern water power station in Floda was measured to 8.1 𝑚3 /𝑠 [16].
By assuming a linear relationship between these values and the estimated average values
from the actual measurements in Säveån, a reference value for the water velocity can be
found. Monthly water flow data for the southern power station is presented in Table 1
together with the estimated average water speed, average power for an assumed turbine,
and the possible energy generation per month. The estimated water average speed in
Säveån near Nääs castle is also found in Figure 10.
19
Table 1. Monthly water flow of Säveån in Floda and estimated values of water speed and energy
generation for Nääs castle [16]
Average
Estimated
Average
Average Power of
Energy
Water Flow Water Speed
power
Generated*
Month
Water Flow
in Floda
in Floda
Generated*
[W/m2]
[kWh/month]
[m³/s]
[m/s]
[W/m2]
Jan
32.88
1.12
712.13
178.03
129.96
Feb
30.16
1.03
549.61
137.40
100.30
Mar
25.25
0.86
322.59
80.64
58.87
Apr
23.03
0.78
244.85
61.20
44.67
May
16.62
0.56
92.12
23.03
16.81
Jun
11.85
0.40
33.33
8.33
6.08
Jul
11.67
0.39
31.87
7.96
5.81
Aug
11.06
0.37
27.13
6.78
4.95
Sep
11.44
0.39
30.06
7.51
5.48
Oct
14.78
0.50
64.76
16.19
11.81
Nov
21.44
0.73
197.58
49.39
36.06
Dec
27.79
0.95
430.11
107.53
78.49
499.34
Total generation* [kWh/year]:
* Assuming a turbine- and drivetrain total efficiency of 25 % efficiency and a swept area of 1 m2
1.2
Water Speed [m/s]
1
0.8
0.6
0.4
0.2
0
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Figure 10. Estimated average water speed for Nääs castle
20
Nov
Dec
4.2 Parameterization results and values for simulation
In the following section, the results from the parameterization of the PMSG are presented.
Furthermore, the values chosen for the Simulink model and control are presented.
4.2.1 Generator measurements
The results from the inductance measurements are presented in Table 2. As can be found
in the table, the value of the inductance is varying somewhat between the measurements
and to determine what value is most correct is hard to state. Due to the lower variation in
the results for the no vibration cases, the average of these values will be used in the
simulations.
Table 2. Results from the inductance measurements
Inductance
(No
vibration)
Measurement
Conditions
I [A]
U [V]
L [mH]
2
2.1
2.31
2.3
2.3
0.36
0.356
0.381
0.407
0.34
0.263
0.245
0.2376
0.258
0.207
Average
0.242
The measured speed-voltage characteristics of the generator are found in Figure 11. By
evaluating the slope, the flux linkage can be estimated and the value is presented in Table
2.
21
20
18
16
Voltage [V]
14
12
10
8
6
4
2
50
100
150
200
250
Rotor Speed [rmp]
300
350
400
Figure 11. Voltage-speed characteristics for the measured PMSG
4.2.2 Efficiency and Power-Speed curves
The 𝐶𝑝 -vs-𝜆 curve is found by using experimental values from [4] and adding two
fictional points (marked with black rings in Figure 12) to the experimental values. This is
made so that the control strategy can be made analogous to a wind turbine controller.
From these points, a fitted curve for a theoretical 𝐶𝑝 -vs-𝜆 curve is found. The fitted curve
will be later used to find the power-speed characteristics of the turbine.
Cp vs. lambda
FIT
0.25
Cp
0.2
0.15
0.1
0.05
0
0
0.5
1
1.5
2
2.5

Figure 12. Estimated 𝐶𝑝 -vs-𝜆 curve for a Gorlov turbine
22
3
The 𝐶𝑝 -vs-𝜆 curve is found and can be mathematically stated as
𝐶𝑝,𝑓𝑖𝑡𝑡𝑒𝑑 = 0.2713 ∙ 𝑒
(𝜆−2.06) 2
) )
(−(
0.7059
+ 0.03035𝑒
(𝜆−2.724) 2
) )
(−(
0.252
(4.1)
Using the 𝐶𝑝 -vs-𝜆 curve from Figure 12, the power-speed characteristics is generated for
turbine at different water velocities. This power-speed curve (see Figure 13) is later used
in the simulations together with the measured DC power to find the reference value of the
turbine speed.
Figure 13. Power-Speed characteristics of for a Gorlov Helical Turbine
This equation for the power-speed curve is found by taking the maximum value of each
water velocity and fitting a curve with fourth order polynomial which can be
mathematically stated as
𝑃𝑝𝑜𝑤𝑒𝑟_𝑠𝑝𝑒𝑒𝑑 = −0.07083 ∙ Ω𝑚𝑒𝑐 4 + 16 ∙ Ω𝑚𝑒𝑐 3 − 1.069 ∙ Ω𝑚𝑒𝑐 2
+ 0.8488 ∙ Ω𝑚𝑒𝑐 − 0.1778
23
(4.2)
4.2.3 Values and parameters for simulations
The data to be used in the Simulink simulations are summarized in Table 3. Note that the
values for system inertia and viscous damping are estimated, and that the values for
proportional and integral gain are experimentally gathered. The values of the boost
converter are deducted experimentally to suit the application.
Table 3. Summarized table of measured and estimated values to be used in simulations
Generator
Controller
Turbine
Converter
Parameter
Estimated values
Resistance [Ω]
0.071
Inductance [mH]
0.242
Flux linkage [Wb]
0.4643
Pole pairs [-]
8
System Inertia [kg∙m2]
40
Viscous damping [Ns/m]
0.006
Proportional gain Speed C.
3000
Integral gain Speed C.
30
Radius of turbine [m]
1
Height of turbine [m]
0.5
Forward voltage rectifier [V]
0.3
Boost converter inductor [mH]
200
Boost converter capacitor [µH]
10
24
4.3 Simulink simulations
In the following section, the results from the Simulink simulations are presented. The
water flow is simulated by using the data from Figure 9 with an added constant of 1 m/s.
The measurement device was operated at 1 measurement/s and this is believed not to be
demanding enough for the control, and therefore the time axis will be reduced to match
the Simulink simulation time. Thus, the time data is scaled down with a 1/80 factor. The
compressed water speed used in the simulation is found in Figure 14. The step water
profile is shown in Figure 15.
Figure 14. Filtered water curve used for the upcoming simulations, with a compressed time axis
to match the simulation time.
Figure 15. Step water speed profile for performed simulations.
25
A. Step water speed profile and measured speed
Figure 16 shows the 𝐶𝑝 evolution. As seen, it can easily follow the reference, and the 𝐶𝑝
gets back to the optimal value within a short period of time, around 1.5s. As for the
generated power, illustrated in Figure 17, there is a steady state error, but the shape is of
a first order response, which is the expected from the proposed PI controller.
Figure 16. 𝐶𝑝 -value with step water speed profile with speed sensor.
Figure 17. Power with step water speed profile with speed sensor. Actual DC power in blue,
maximum theoretical value in red.
26
B. Step water speed profile and estimated speed
The 𝐶𝑝 evolution is displayed in Figure 18. In this case, there is an overshoot every time
the control is started or a new step is applied. However, is it not due to integrator windup
or a second order system control, but due to the 𝐶𝑝 -curve. The step takes the operation
point to a lambda value smaller than the optimal, arrow 1 in Figure 19. This way, the
controller has to move the operation point to the optimal, arrows 2 and 3, but owing to
the speed estimation, it does not stop there and continues to a lower 𝐶𝑝 , arrow 4. As for
the generated power, illustrated in Figure 20, there is a steady state error, but the shape is
of a first order response, which is the expected from the proposed PI controller.
Figure 18. 𝐶𝑝 -value with step water speed profile with speed estimation.
0.25
3
2
0.2
Cp
4
Cp vs. lambda
FIT
1
0.15
0.1
0.05
0
0
0.5
1
1.5
2
2.5
3

Figure 19. 𝐶𝑝 -trajectory during step change from Figure 15.
27
Figure 20. Power with step water speed profile with speed estimation. Actual DC power in blue,
maximum theoretical value in red.
C. Filtered water speed profile and measured speed
Figure 21 illustrates the change of the 𝐶𝑝 -value over time in the case of using the filtered
water speed profile and speed sensor. The controller is turned on at 𝑡 = 10, and as can be
seen in the figure the control succeed to significantly improve the 𝐶𝑝 -value.
Figure 21. 𝐶𝑝 -value with filtered water speed profile with speed sensor.
In Figure 22 the optimal and actual output power output are illustrated. In the figure, it is
clearly seen that the difference between the optimal and actual power are significantly
28
reduced once the controller is turned on at 𝑡 = 10. It is also possible to distinguish a
steady-state error between the optimal and actual output power.
Figure 22. Power with filtered water speed profile with speed sensor. Actual DC power in blue,
maximum theoretical value in red.
D. Filtered water speed profile and estimated speed
When the speed sensor is disabled and the control uses speed estimation, results get
altered, mainly due to the fact that the speed estimation is not as accurate in lower speeds.
Figure 23 shows the 𝐶𝑝 -value at estimated speed.
Figure 23. 𝐶𝑝 -value with filtered water speed profile with speed estimation.
29
In Figure 24 the optimal and actual output power output with estimated speed are
illustrated. In the figure, it is clearly seen that the difference between the optimal and
actual power are significantly reduced once the controller is turned on at 𝑡 = 10.
However, due to the speed estimation, the output DC power is somewhat reduced.
Figure 24. Power with filtered water speed profile with speed estimation. Actual DC power in
blue, maximum theoretical value in red.
5 Analysis
The water flow is found to varying significantly during the year, with the lowest water
flow during June to September and the highest during December to Mars. Furthermore,
the results show that the extractable power is almost non-existent during large periods of
the year and the estimated total energy generated during one year for the proposed turbine
would only be 500 kWh. This number is also based on the assumption of an efficiency of
25 % for the whole drivetrain. However, due to the low water velocity and therefore the
low speed of the turbine, the efficiency of the generator might be decreased significantly.
When this generated energy during one year is compared with the consumption of an
electric bus, with 4 daily 2-way trips between Floda train station and Nääs castle, 5.5km,
for 100 days per year, it found seen that the turbine does not suffice to cope for the bus’
consumption. The used parameter for traction consumption is 0.072 kWh/km·ton [17]. A
bus with a mass of 19 ton would thus require a yearly consumption of 6019.2 kWh. Hence,
12 Gorlov turbines like the studied one would be needed.
The established linear relationship between the water measurements and the data from
the power station in Floda might also be a source of uncertainty. The first measurement
registered a water velocity of 0.198 m/s whilst the power flow at Floda was found to be
8.7 m3/s. During the second measurement, the water velocity was measured to 0.369 m/s
whilst the power flow was found to be 8.1 m3/s. Therefore, the positive linear relationship
between the water velocity at Nääs and the water flow in Floda cannot be proved with
30
this data. However, due to the time constraints of the project no more measurements could
be performed to further verify this.
Due to the undesirable results of the water measurements, the simulation and design of
the drivetrain was instead performed with a hypothetical river in consideration.
Furthermore, since no Gorlov turbine was available for testing, several of the parameters
for the simulation had to be estimated. For example, the 𝐶𝑝 -curves and the resulting
power-speed characteristics had to be estimated from previous experiments and parameter
values such as the system inertia and viscous damping had to be estimated. Thus, for
future setups and installations, these values would have to be reconsidered.
The results from the Simulink model show that the simple controller and the drivetrain is
generally working well. In figures 16 - 24, the controller is tested for a filtered and a step
water speed profiles, and for the scenarios with or without the proposed speed sensor. In
all the filtered scenarios, the controller is activated after 10 seconds. In the step
simulations, the control is always activated. Generally, the 𝐶𝑝 -value is found to be
significantly increased when the control is activated in all simulations. Furthermore, the
results show that, despite that the water velocity varies significantly in the filtered water
speed profile, the controller has no problem of responding to these variations. Therefore,
it can be concluded that the controller is well adapted to handle quick changes in the water
speed.
However, there is a somewhat decrease in the efficiency of the controller when the speed
estimation block is connected. At lower speeds the estimation block is found to not
estimate the speed perfectly. In the case when the speed sensor is connected, the 𝐶𝑝 -value
is increased from 75% to 95% of the optimal 𝐶𝑝 -value. Though, in the case when instead
the speed estimation block is connected the 𝐶𝑝 -value is increased only up to 92% of the
optimal 𝐶𝑝 -value. Therefore, it is possible to conclude that the speed estimation is
generally operating well, but is somewhat misjudging the actual speed. However, this
would probably be acceptable for most setups as speed measurement devices generally
are both rather expensive and require some maintenance.
For all simulations, a steady state error between the optimal power output and the actual
generated power output is found. This steady state error is believed to be a result of both
the limits of the controller and due to losses in the drivetrain. As the controller is designed
as a hysteresis-controller, the operating point of the system will always be close to the
desired, but never perfect. Furthermore, the losses in the boost converter and the rectifier
will also contribute to the discrepancies.
6 Conclusions
The water flow in Säveån close to Nääs castle is found to be considerably too small to for
it to be feasible to install a Gorlov turbine. A river with both a higher and more consistent
water flow would be desirable.
31
Due to the lacking results of the water measurements, the simulation and design of the
drivetrain were performed on a theoretical setup instead. The simple and robust drivetrain
and control were found to be adapting well to the applied simulations, and the power
output was significantly increased with the controller implemented. The system has a first
order response, which was expected to have with the PI tuning that was performed. The
operation with a speed estimation block instead of a speed measurement was found to be
generally working well, however, with a small decrease in the power output. The control
needed in order to perform fish behaviour studies is separated from the ordinary control,
and instead a mechanical braking system is proposed.
32
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34