Abstract
This thesis investigates the load control of a marine current energy converter using a vertical axis turbine mounted on a permanent magnet synchronous generator. The purpose of this thesis is to show the work done in the so far relatively uncharted territory of control systems for hydro kinetic energy con- version. The work is in its early stage and is meant to serve as a guide for future development of the control system.
An experimental power station has been deployed and the first results are presented.
A comparison between three load control methods has been made; a fixed AC load, a fixed pulse width modulated DC load and a DC bus voltage control of a DC load. Experimental results show that the DC bus voltage control re- duces the variation of rotational speed with a factor of 3.5. For all three cases, the tip speed ratio of the turbine can be kept close to the expected optimal tip speed ratio. However, for all three cases the average extracted power was significantly lower than the average power available in the turbine times the estimated maximum power coefficient. A maximum power point tracking sys- tem, with or without water velocity measurement, should increase the average extracted power.
A simulation model has been validated using experimental data. The sim- ulated system consists of the electrical system and a hydrodynamic vortex model for the turbine. Experiments of no load operation were conducted to calibrate the drag losses of the turbine. Simulations were able to predict the behaviour in a step response for a change in tip speed ratio when the turbine was operated close to optimal tip speed ratio. The start position of the turbine was varied in the simulation to view the influence on the step response from a changed turbine position relative to the direction of the water flow.
To Lucie and Maël
List of papers
This thesis is based on the following papers, which are referred to in the text by their Roman numerals.
I S. Lundin, J. Forslund, N. Carpman, M. Grabbe, K. Yuen, S. Apelfröjd, A. Goude, M. Leijon.
"The Söderfors Project: Experimental Hydrokinetic Power Station Deployment and First Results". Proceedings of the 10th European Wave and Tidal Energy Conference Series, September 2-5 2013, Aalborg, Denmark. (Reviewed conference paper)
II J. Forslund, S. Lundin, K. Thomas, M. Leijon.
"Experimental results of a DC bus voltage level control for a load controlled Marine Current Energy Converter". Energies, 8(5), 4572-4586, May 2015.
III J. Forslund, A. Goude, S. Lundin, K. Thomas, M. Leijon.
"Validation of a Coupled Electrical and Hydrodynamic Simulation Model For Vertical Axis Marine Current Energy Converters".
In manuscript.
Reprints were made with permission from the publishers.
Contents
1 Introduction . . . .13
1.1 Electrical layout and control. . . .14
1.2 Research objective . . . . 15
1.3 Marine Current Power at Uppsala University . . . . 15
1.4 Thesis outline . . . . 15
2 Theory and system overview . . . . 17
2.1 The Söderfors experimental station . . . . 17
2.2 Permanent Magnet Synchronous Generator. . . . 18
2.3 Vertical Axis Turbine. . . .19
2.4 Load Control in Marine Current Power applications. . . .20
2.5 PID Control and step response. . . . 21
2.6 Electrical system overview . . . .22
2.6.1 Load Control System. . . .23
3 Method . . . . 25
3.1 ADCP measurements. . . .25
3.2 AC load control . . . . 26
3.3 DC load control. . . . 26
3.4 Electrical Model. . . . 27
4 Results and Discussion. . . .29
4.1 ADCP measurements. . . .29
4.1.1 Water speed measurements . . . .29
4.1.2 Water speed measurements for determining correction factor. . . .29
4.1.3 Water speed for the AC and DC load cases . . . . 30
4.2 AC load control . . . . 31
4.3 DC load control vs AC load . . . . 31
4.3.1 Rotational speed . . . . 31
4.3.2 Current measurements . . . .32
4.4 Calibration of the simulation model . . . . 34
4.5 Simulation results. . . .36
5 Conclusions . . . .41
6 Future work . . . .43
7 Summary of papers. . . .44
8 Sammanfattning på svenska . . . .47 Acknowledgements. . . .49 References . . . .51
Nomenclature
A [m2] Area of turbine cross section Bmax [T] Maximum magnetic flux density
C - Fraction of upstream and downstream water speed c - Correction factor for water speed
CP - Power coefficient
CPmax - Maximum power coefficient (at λopt) E(s) - Error of a P controller on Laplace form
Ei [V] Generator voltage f [Hz] Electrical frequency
I, i [A] Current
iRMSphase [A] RMS current in one phase of the generator
J [kgm2] Inertia
KP - Proportional constant for P controller Kd - Derivative constant for P controller
Ki - Integral constant for P controller
N - Number of turns in the generator winding n [RPM] rotational speel in RPM
Ntot - Number of measurements
p - Number of poles
P [W] Power
Pkinetic [W] Power across turbine cross section Pturbine [W] Power absorbed by the turbine
Pload [W] Power absorbed in the load
Plosses [W] Power dissipated in the transmission line and generator winding
PCopper [W] Resistive power losses in the generator q - Element of integral
r [m] Turbine radius
R [Ω] Resistance
Rload [Ω] Resistance of load
Rlines [Ω] Resistance of transmission lines Rwindings [Ω] Resistance of generator windings
T [Nm] Torque
Tg [Nm] Generator torque Te [Nm] Electric torque
v [m/s] Water speed
vq - Element q of water speed measurement vturbine - [m/s] Water speed at turbine
vupstream [m/s] Water speed at upstream ADCP vdownstream [m/s] Water speed at downstream ADCP
Y(s) - Output of a P controller on Laplace form
ηsystem - System efficiency defined as < Pturbine> / < Pkinetic>
λ , TSR - tip speed ratio
λopt - optimal Tip Speed Ratio
ρ kg/m3 Density
ω [rad/s] Rotational speed of turbine/generator
Abbreviations
AC Alternating Current
ADCP Acoustic Doppler Current Profiler DC Direct Current
FPGA Field-Programmable Gate Array IGBT Insulated Gate Bipolar Transistor MPPT Maximum Power Point Tracking
PMSG Permanent Magnet Synchronous Generator PWM Pulse Width Modulation
RMS Root Mean Square RPM Revolutions Per Minute TSR Tip Speed Ratio VAT Vertical Axis Turbine VAWT Vertical Axis Wind Turbine
1. Introduction
Marine Current Power with a Vertical Axis Turbine (VAT) is a fairly new and untested concept in renewable energy. It utilizes the kinetic energy in free- flowing water and converts it into electrical energy. This thesis shows the recent work done at Uppsala University. Hopefully this will open up more options for placing an in-stream energy converter, that has less environmental impact on its surroundings than a traditional hydropower dam. The chosen design of a VAT with a Permanent Magnet Synchronous Generator (PMSG) has many similarities of that of a Vertical Axis Wind Turbines (VAWT) with a PMSG in wind power. A study made from 1997 showed that most of the downtime in wind power failures are due to the gearbox [1]. A solution that is becoming more popular is a direct drive variable-speed system that has no gearbox between the turbine shaft and the generator shaft. This will make the system more robust but the generator must be designed to be efficient at low speeds. For wind power, there is alot of research done for both VAWTs [2–4]
and horizontal axis wind turbines [5–7]. A comparison of the two is shown in [8]. However, there is much to explore for in-stream VATs. Even though the similarities are many, there are a number of significant differences.
Figure 1.1 shows typical water and wind speed measurements during 45 sec- onds. There is clearly a difference in characteristics between the two; in par- ticular, the highest and lowest values obtained during the relatively short time span differ more for wind speed than for water speed. For a direct drive sys- tem under these conditions, the difference in power absorption (and output voltage) between the high and the low velocity would be even bigger for wind power. This would suggest that the design of a control system for a marine current power converter would be different from that of wind power converter, which in turn indicates the need for research on control systems for marine current applications.
Time [s]
0 5 10 15 20 25 30 35 40
1.3 1.4 1.5 1.6
0 5 10 15 20 25 30 35 40 45
7 6 5 4 3
Time [s]
Water speed [m/s]Wind speed [m/s]
(a)
(b)
Figure 1.1. A: Water velocity upstream of the Söderfors turbine on 2014-04-16. B:
Wind speed measurement taken from p. 53 of [9].
1.1 Electrical layout and control
Since the choice of a VAT with a PMSG is similar to that of a VAWT with a PMSG for wind power, the electrical systems share the same basic topology.
The control system is typically operated by rectifying the generator voltage and controlling the rotational speed of the turbine by switching the Direct Current (DC) bus voltage, see figure 1.2. The DC bus is connected to the grid side power electronics that converts the DC voltage to grid voltage and frequency using an inverter, a filter and a transformer. The author’s work is focused on the control side.
Grid Generator
Turbine
Rectifier DC bus Inverter Filter Transformer
Control side Grid side
Switch
Figure 1.2.The control side and the grid side connected using the DC bus.
To optimize the energy capture one can use Maximum Power Point Track- ing (MPPT). There is not much published in the area of control methods for VAT with PMSG in marine currents, but it has been a popular field of research the last two decades in wind power. Once the turbine has reached the nominal operation region, there are a few different ways of trying to achieve MPPT and different components are required depending on the application. In wind power it is common to use a DC/DC converter or a tap-transformer [10–12].
Control of a VAWT with PMSG using tip speed ratio control (tip speed ratio is explained in section 2.3) is suggested in [13] and [14]. A method for finding 14
the optimal operation point without wind speed measurement or turbine pa- rameters is presented in [15]. Using the rotational speed of the turbine as wind speed measurement is suggested in [16]. Combining MPPT and tip speed ratio control is presented in [17]. A novel way of using MPPT for tidal power is proposed in [18] and an electric system for grid connection is proposed in [19].
1.2 Research objective
The area of interest for the author is the control and optimization of power ab- sorption of a marine current energy converter. The goal is to design a control system for marine current application. The work thus far includes the deploy- ment described in paper I, the first results of the implemented control system in paper II and validation of a simulation model that combines a hydrodynamic model of the turbine with an electrical model of the system in paper III. The work will serve as a guide for the continued work of more complex control systems and for creating an autonomous power station.
1.3 Marine Current Power at Uppsala University
In 2001 the Division of Electricity at the Department of Engineering Sciences in Uppsala University started investigating hydro-kinetic energy conversion, also called marine current power. One prototype generator has been built and tested in a lab environment, and an experimental station was deployed in Söderfors during 2013 that features an improved generator prototype, a tur- bine and an electrical system. Acoustic Doppled Current Profilers (ADCPs) were also deployed in the river for measuring water speeds. The research of the group has included hydrodynamic models, investigation of the marine cur- rent resource, developing a low speed generator design and electrical system.
The research has resulted in 6 PhD theses [20–25].
1.4 Thesis outline
Chapter 2 presents the theoretical foundations of the research carried out in this thesis. It also describes the experimental station and its electrical layout.
Chapter 3 describes the conducted experiments and chapter 4 shows and dis- cusses the experimental results. Chapter 6 outlines the work of the PhD thesis to come. Chapter 7 summarizes the three papers in this thesis and chapter 8 summarizes the thesis in Swedish.
2. Theory and system overview
This section describes the theoretical background and provides an overview of the system. Chapter 2.1 describes the experimental station. Chapter 2.2 briefly describes the generator. Chapter 2.3 concerns the turbine design. Chapter 2.4 explains how control theory is applied to VATs with PMSGs in marine current applications. Chapter 2.5 describes PID controllers and step repsonse. Chapter 2.6 describes the electrical system.
2.1 The Söderfors experimental station
The experimental station comprises two ADCPs, a turbine and generator placed at a depth of 7 m, and a measurement cabin containing control and measure- ment systems. The turbine and generator are placed approximately 800 m downstream of a conventional hydro power plant, and the ADCPs are placed about 15 m upstream and 15 m downstream of the turbine, see figure 2.1.
There is an electrical enclosure on the bridge where the cables from the gen- erator and the ADCPs are forwarded to the measuring station on shore.
The experimental station is fully described in [26, 27].
Figure 2.1.Overview of the experimental station in Söderfors.
2.2 Permanent Magnet Synchronous Generator
The prototype generator is a PMSG that uses permanent magnets to electri- cally excite the rotor. The generator voltage, Ei, depends on the amplitude of the magnetic flux density, Bmax, the electrical frequency, f , and the number of turns in the winding, N,
Ei∼ Bmaxf N. (2.1)
The generator is a three phase machine, i.e. it has three phases 120 electrical degrees apart. The electrical frequency depends on the rotational speed, n, and the number of poles, p, as
f= p 2
n
60. (2.2)
The rotational speed of the prototype generator at nominal operation will be lower than that of a typical generator for hydropower or wind power because of the low speed of the water currents. By increasing the number of poles the output voltage is increased and a higher efficiency can be obtained.
The losses in the generator are divided into copper losses and iron losses.
The copper losses are mainly resistive losses in the windings that dissipate as heat and depend on the resistance and the current according to
PCopper= RI2. (2.3)
Not only do the copper losses reduce the efficiency of the generator, they also pose a problem of where and how to remove the heat that can put con- straints on the capacity of maximum power delivered by the generator. The copper losses can be reduced by reducing the resistance of the windings.
The iron losses are divided into eddy current, hysteresis and excess dynamic losses. They are not dependent on the power delivered by the generator, but on the layout of the generator and the electrical frequency. Iron losses are not included in any of the papers since at the rotational speeds used in the papers the copper losses are assumed to dominate the generator losses.
Power for a rotating body is P = ωT where T is torque. When the gen- erator and turbine are rotating the difference between torque delivered to the generetor, Tg, minus the electric torque, Tewill determine the acceleration of the rotor, ω, written as
dω
dt J= Tg− Te (2.4)
where J is the inertia. The electrical torque can be controlled by control- ling the size of the load, hence determining the acceleration and the rotational speed of the turbine. The generator is a directly driven permanent magnet synchronous generator. Nominal operation is at water speed 1.3 m/s and the 18
specifications for the generator can be found in table 2.1. A detailed descrip- tion of the generator and its losses can be found in [28]. The generator is connected to the measurement cabin on shore by a three phase power cable
∼200 m long with a resistance of 0.1 Ω/phase. A description of the generator losses and how it interacts with a VAT is desribed in [22, 25] and PMSGs for wind power applications is described in [9, 29, 30].
Table 2.1. Generator specifications at nominal operation Generator specification Value Unit Mechanical rotational speed 15 RPM
Electrical frequency 14 Hz
Poles 112
Line-to-line rms voltage 138 V
Stator rms current 31 A
Power rating 7.5 kW
Stator phase resistance 0.335 Ω
Armature inductance 3.5 mH
Flux linkage 1.28 Vs
Estimated inertia 2445 kgm2
2.3 Vertical Axis Turbine
The power in free-flowing water of cross section A is
Pkinetic=1
2Aρv3, (2.5)
where v is water speed and ρ is density of water. The fraction of power delivered to the generator from the turbine is called power coefficient, CP, defined as
CP=Pturbine Pkinetic
. (2.6)
CP is a function of the Tip Speed Ratio, λ (or TSR) , i.e. the ratio of blade speed to undisturbed water speed, defined as
λ = ω r
v (2.7)
where ω is the rotational speed of the turbine and r the turbine radius. Maxi- mum power absorption from the water, CPmax, occurs at some optimal tip speed ratio λopt. A typical relation between CPand λ can be seen in figure 2.2.
Tip speed ratio (λ) C
PFigure 2.2. Power coefficient, CP, as a function of tip speed ratio, λ . The designed turbine has optimal tip speed ratio λopt = 3.5 for a power coefficient of CPmax = 0.36. The turbine has five vertical blades with fixed pitch and a NACA0021 profile, it is 3.5 m high, it has a radius of 3 m and a chord length of 0.18 m. For more detailed information on power absorption of turbines, see [31]. Turbines in a channel using a streamtube model are discussed in [32].
2.4 Load Control in Marine Current Power applications
The mechanical power Pturbine delivered to the generator by the turbine shaft is converted to electricity. It is dissipated in the load, and as losses in the generator windings and the transmission lines. At steady-state it can be written as
Pturbine∼ Plosses+ Pload (2.8)
(see [33]). Combining equations (2.5), (2.6) and (2.8) we see that 1
2CPρ Av3∼ Plosses+ Pload, (2.9) and since CP= CP(λ ), one can control the rotational speed of the turbine by varying the load. This way the system can be kept at λopt and the highest amount of energy from the water can be extracted.
Defining the system efficiency ηsystem as average electric power delivered to the generator over average power available in the water as,
ηsystem= < Pturbine>
< Pkinetic>. (2.10) 20
This means that the average power absorption will be dependent on the ability of the control system to keep the rotational speed over time at the speed corresponding to λopt.
2.5 PID Control and step response
To control a process that is not only controlled by the defined input, but also af- fected by its surroundings, one can use Proportional-Integral-Derivative (PID) control. It is a feed-back control loop that is commonly used throughout var- ious industry processess. The PID controller can be written using Laplace transform as
Y(s) =
KP+Ki s + Kds
E(s) (2.11)
where Y(s) is the output, KP is the proportional gain, Ki is the integral gain, Kd is the derivative gain and E(s) is the error between output and a set reference value. You can display the controller and its defined inputs and outputs in a block diagram as in figure 2.3.
Reference value Error
Measured value
Process KP
Ki Kd
+ -
+ + +
∑ ∑
Figure 2.3.Block diagram of a PID controller.
The purpose of the constants are to minimize the error, often as quickly as possible, and to make sure it reaches the set point with as little overshoot, con- stant error and oscillations as possible. The proportional term KPis multiplied with the error and determines how fast the system will react to the current error. A too high KP can result in oscillations and leave a constant error the controller is unable to remove. The integral part, Ki, takes into account both the size of the error and the duration of the error. The purpose of Ki to pre- vent the constant error left over by KP. A too high value of Ki may result in an overshoot (the output passes the reference value). The derivative part, Kd, takes the size of the error and the slope of the error into account. Kd can reduce the rise time but is sensitive to high frequencies and noise, and is there- fore often accompanied by a low pass filter. A step response can be used to test the constants of a PID controller where the overshoot, constant error, response time and oscillations will be visible, see figure 2.4.
Constant error
Overshoot Oscillations
Rise time
Figure 2.4.The characteristics of a step response.
2.6 Electrical system overview
The only equipment inside the generator housing are Hall sensors for detecting rotational speed and a camera powered by LED lights, see figure 2.5a. All other electrical measurements are made inside the measurement cabin.
Figure 2.5.(a) The Hall sensors inside the generator as seen by the camera.
(b) The electrical enclosure.
An enclosure containing all electrical components, called the main enclo- sure, is located in the measurement cabin, see figure 2.5b. The entire system is controlled by LabView using a CompactRIO and Field-Programmable Gate Array (FPGA). An overview of the electrical system is shown in figure 2.6.
When the generator is kept at stand still, it is short circuited in the bridge enclosure using the bridge parking brake. The resistance in the 50 m cables from the generator is a big enough electrical load to keep the generator from self-starting. For redundancy, there is also a short circuit in the main enclosure, 22
Grid
Generator Turbine
Parkingp brake
main enclosure
Emergencyp brake ACpLoad
DCpLoad
Rectifier Inverter
Transformer Startuppcircuit
Operationpcircuit
Softpstartp Parkingp
brake bridge enclosure
~50pmpcable ~150pmpcable
Figure 2.6.Overview of the electrical system in the experimental station.
called the main enclosure parking brake. To start up the system both short circuits must be manually disconnected.
The generator windings double as a startup circuit. Three-phase power is drawn from the grid, rectified and connected to the generator directly from the three-phase inverter. At the same time, power is also drawn from the grid to the soft start that charges the capacitor bank for the DC load. The contactors in the enclosure are used for connecting the load once sufficient rotational speed has been reached. There is an emergency brake consisting of low resistance, high power resistors that can be connected both using LabView and manually in case the regular load is unsufficient.
Manual switches are used (prior to startup) to connect a fixed resistive load either in an Alternating Current (AC) three-phase Wye formation or a DC connection.
Further details about the control and measurement system can be found in [34].
2.6.1 Load Control System
The AC load comprises no active control during load operation. Once the switch from the startup circuit to AC load has been made, the generator is connected directly to fixed resistive AC load.
The DC load control comprises the resistive load, a rectifier with a capaci- tor bank, voltage measurement on the rectifier and an Insulated Gate Bipolar Transistor (IGBT) with a snubber circuit in parallel (see figure 2.7).
Gen
Capacitor bank
Snubber IGBT
AC iAC
iDC
VDC VDC,Target
Rectifier
Load
Figure 2.7. The DC load control consisting of a rectifier, capacitor bank, IGBT with snubber circuit and resistive load.
The DC load operation uses the FPGA module of the CompactRIO to con- trol the switching frequency of the IGBT. Two control algorithms have been implemented for DC load control: Constant duty cycle and Target DC volt- age. The Constant duty cycle is an open loop controller where the user sets a desired duty cycle, thus it has no feedback control. The Target DC voltage aims to keep the DC bus voltage within a set range using a P-controller loop that uses the error of measured DC bus voltage minus a target DC bus voltage reference as input, see figure 2.8. The loop has three states depending on the size of the error. If the error is negative, the duty cycle is set to 0 %, i.e. no load operation (or free spin operation). If the error is more than 5 Volts the duty cycle is set to 100 %, i.e. full load operation. In between 0 V and 5 V the loop enforces a linear relationship between error and duty cycle. The control system is described in more detail in paper II.
Process +- KP Error handling
Figure 2.8. P-controller loop of the DC bus voltage.
24
3. Method
This section presents the methods used in the thesis. Section 3.1 describes the water speed measurements and sections 3.2 and 3.3 describe the AC load and DC load experiments respectively. The electrical model is described in 3.4.
Three methods for load control have been implemented and are referred to as follows: The AC load control case is the "AC case", the fixed Pulse Width Modulated (PWM) DC load control is the "fixed PWM" case and the Target DC voltage control is the "constant DC" case. For both papers the losses are assumed to be purely resistive and limited to the transmission lines and generator windings. All average powers are calculated with
P= 1 Ntot
Ntot
∑
q=1
R i2q. (3.1)
where R is resistance and i is current.
3.1 ADCP measurements
The cross section of the river at the upstream and the downstream devices dif- fers, i.e. if the discharge is the same at both points the velocity of the water will be different. Paper II makes an estimate of the velocity at the turbine, v, by assuming that the turbine is located exactly between the upstream and down- stream ADCPs and that the change in cross section is linear so the average value of the fraction of the upstream and downstream device can be written,
C= vupstream
vdownstream. (3.2)
The average value of C can be used to find a correction factor, c, so that the velocity of the water at the turbine can be written as
vturbine= c vupstream. (3.3)
The average power at the turbine can be calculated as
< Pkinetic>= 1 Ntot
Ntot
∑
q=1
1
2Aρv3q. (3.4)
The ADCPs devices are Workhorse Sentinel 1200 Hz with an accuracy of 0.3 % of the water speed. Measurements are taken minimum every 3.6 seconds (set by user) and give a velocity profile from one meter above the bot- tom of the river to one meter below the surface. It does not make a difference if the downstream or the upstream values are used, in paper II it was decided to use the upstream values for all measurements of vturbine. In Paper III, the speed of the water at the upstream ADCP was assumed to be constant until reaching the turbine. An average value of the water speed in the intervall of interest was used to determine the average time it took for the water to reach the turbine.
3.2 AC load control
In paper I, resistive AC loads of 2.0 Ω and 2.5 Ω are connected in Wye- formation. The following was measured during load operation: current and line-to-neutral voltages in the load, water speed from the upstream and down- stream ADCPs and rotational speed of the turbine. From that we can calculate the average power consumed by the load and the average tip speed ratio.
3.3 DC load control
Paper II aims to compare the two DC load controls with the fixed AC load control.
Each control strategy was evaluated by the variation in rotational speed, losses and the extracted electric power. An average value of the upstream ADCP water speed measurement was used to calculate the average power ab- sorbed by the turbine. The variation of delivered of power to the DC bus was determined using equations 2.7 and 2.9 and the rotational speed. For each load case the average power consumed in the load, the transmission lines and the generator windings were calculated.
Symmetry between the generator voltages was assumed when calculating the AC power. λopt= 3.5 was used together with an average value of the water velocity to determine at which rotational speed to switch over to load control.
Data was recorded after a wake had been built up after the turbine.
For both of the DC control cases, a PWM frequency of 500 Hz was used.
A duty cycle of 17 % was used in the fixed PWM case and in the constant DC case the target DC voltage was set to 173.5 V and KP= 1.
26
3.4 Electrical Model
In paper III a simulation model was developed that couples an electrical model with a hydrodynamic vortex model of the turbine. The purpose of developing such a tool is the ability to easily change parameters in the simulation that are in reality either not so easily changed, or cannot be changed at all. For example, the water speed in the river is one parameter that we are not in control of, but a parameter which we can choose as input in a simulation model.
The simulation tool Matlab SIMULINKTMwas used for the simulation be- cause it can handle power electronic devices with fast switching rates. The rectifier, IGBT, capacitors, snubber and generator were simulated using the values of the components used in the experimental set-up. The drag losses of the turbine model are calibrated by letting the turbine spin freely so the turbine is accelerated by the water and slowed down by the losses until it reaches an equilibrium tip speed ratio. Comparing the experimental rotational speed with the simulated rotational speed allows for the drag losses in the hydrodynamic model to be estimated. After the drag losses have been calibrated, the gener- ator model is calibrated by comparing the experimental and simulated gener- ator voltage. Once the model is calibrated, it is validated by evaluating step responses of a change in tip speed ratio. The turbine is controlled by setting a certain output voltage from the generator using the control system, and then setting a new value for the target voltage. The set value will instantly change and the time it takes for the turbine to reach the new target value reveals how accurately the model can describe the system.
For every rotation of the turbine each blade has two peaks in generated torque, one upstream (bigger) and one downstream (smaller). The step re- sponse will be affected by the turbine position at the moment of the step. If the target value is changed in between the peaks of torque it will slow down the rise time of the step respone. For now, the position of the turbine before a step can not be controlled in the experimental set-up but can be changed in the simulation by changing the turbine starting position.
4. Results and Discussion
This section presents the results and discussions from papers I, II and III. Sec- tion 4.1 shows the results of the ADCP measurements for papers I and II.
Section 4.2 shows the results of the AC load control for paper I and section 4.3 shows the results of the comparison between AC load control and the two DC load control methods in paper II. Section 4.4 shows the results from the simulation calibration and section 4.5 shows the simulation results from paper III.
4.1 ADCP measurements
4.1.1 Water speed measurements
For paper I, the mean values for water speed during an hour are plotted in figure 4.1. On average, the speed of the undisturbed flow was 1.14 m/s at the upsteam ADCP and 1.05 m/s at the downstream ADCP. During load operation, a significant decrease in the water speed at the downstream ADCP is distin- guishable. For the operational period beginning at 14:02, the average mean speed downstream of the turbine was 0.71 m/s.
4.1.2 Water speed measurements for determining correction factor
In paper II, one week of measurements of the water speed with frequency 0.1 Hz from the upstream and downstream devices were recorded during the week leading up to the AC and DC load experiments. The average value of the correction factor was Cmean= 1.090. Equation 3.3 gives c = 0.9587 and the water speed at the turbine can now be estimated as v = 0.9587 vupstream.
13:30 13:45 14:00 14:15 14:30 0
0.5 1 1.5
Time of day
Water speed (m/s)
Upstream Downstream
Figure 4.1. Mean water speed measured by ADCP upstream (blue line) and down- stream (green line) of the turbine on 29 April 2013. The horizontal dashed lines show the time-averaged mean speed for the undisturbed flow at the two locations. The shaded areas indicate time periods during which the machine was operated.
4.1.3 Water speed for the AC and DC load cases
Table 4.1 from paper II shows the average values of vupstreamand vturbinefor the three load cases, measured with (1/3.6) Hz. The calculated average power at the turbine was calculated using equation 3.4, vupstream, c = 0.9587, A = 21m2 and ρ=1000 kg/m3. The statistical analysis in the paper concludes that the variance in each data set was the same. The average water velocity was higher for the fixed PWM case than for the AC case, and for the other cases the average values were the same. These values were used in paper II together with Pturbineto determine ηsystemfor each load case, see section 4.3.
Table 4.1. Average velocity measured by the ADCP and calculated average power across the turbine at respective speed.
Load case AC Fixed PWM Constant DC
vupstream(m/s) 1.394 1.406 1.399
Variance (m/s) 0.005 0.005 0.005
Measurement points 601 501 502
vturbine(m/s) 1.336 1.348 1.341
< Pkinetic> (kW) 27.44 28.15 27.78
30
4.2 AC load control
Paper I shows the results of Wye-connecting 2.0 Ω/phase and 2.5 Ω/phase. A summary of measured and calculated values is shown in table 4.2.
Table 4.2. Measurement results from AC load control
Parameter Value
2.5 Ω load
Electrical frequency 11.8 Hz Mechanical frequency 12.7 RPM
Tip speed ratio 3.5
Line-to-neutral voltage (RMS) 103 V
Current (RMS) 23.7 A
2.0 Ω load
Electrical frequency 8.3 Hz Mechanical frequency 8.9 RPM
Tip speed ratio 2.5
Line-to-neutral voltage (RMS) 68.2 V
Current (RMS) 19.5 A
4.3 DC load control vs AC load
This section shows the comparison of the AC load, fixed PWM control and the constant DC bus voltage control from paper II.
4.3.1 Rotational speed
Figure 4.2 shows a histogram of the rotational speed and table 4.3 shows cal- culated average values, variances and the average λ . The average λ was de- termined for each load case using equation 2.7 together with the average rota- tional speed in Revolutions Per Minute (RPM) and the average water velocity at the turbine.
Table 4.3. Rotational speed of the turbine and number of measurements of the three load cases. Calculated average λ from average water speed and average rotational speed, ω.
Load case AC Fixed PWM Constant DC
< ω > 15.35 15.68 15.65
Variance 2.34 2.11 0.65
< λ > 3.61 3.65 3.67
RPM 12 14 16 18 20 400
300
200
100
0
400
300
200
100
0
400
300
200
100
12 14 16 18 20 0
Measurements per bin
(a) (b) RPM (c)
12 14 16 18 20 RPM
Figure 4.2.Histogram of rotational speed of turbine during load conditions.
(a) AC load (b) fixed PWM (c) constant DC.
The statistical analysis in paper II shows that for all three cases the rota- tional speed measurements have different variance and that the fixed PWM case and the constant DC case have comparable average values. Figure 4.2 shows that the DC voltage control was able to reduce the variance in rota- tional speed. Table 4.3 shows that the variance in the constant DC case is reduced with a factor 3.5 compared to the AC case. The variance of the fixed PWM case was 10 % lower than the AC case.
4.3.2 Current measurements
Figure 4.3 shows the AC currents in one phase for each load case. The AC case has the highest amplitude for the current, fixed PWM second highest and the constant DC case the lowest. The rectifier causes the non-sinusodial shape of the currents drawn in the fixed PWM and the constant DC cases and results in a higher RMS-current which gives higher copper losses. The losses are calculated with equation 3.1 and are shown in table 4.4.
32
0 100 200 ms 0 100 200 ms 0 100 200 ms
A A A
-30 -20 -10 10 20 30
0
-30 -20 -10 10 20 30
0
-30 -20 -10 10 20 30
0
(a) (b) (c)
Figure 4.3.Currents in one phase from the generator.
(a) AC load (b) fixed PWM (c) constant DC.
Figure 4.4 shows the load currents in the DC cases. Figure 4.4a shows that the duty cycle is constant and figure 4.4b shows that the duty cycle is changing, following the design of the control methods. The difference in amplitude for the currents in figures 4.4a and 4.4b is roughly 30 A higher (∼ 16 % higher) for the fixed PWM case. Even though, as a result of the varying duty cycle in the constant DC case, the average power delivered to the load was merely
∼ 2 % higher in the fixed PWM case compared to the constant DC case. The average power calculated using the current and equation 3.1 is shown in table 4.4.
0 2 4 6 8 1 0 12 14 16 18 20
0 2 4 6 8 10 12 14 16 18 20
200 150 100 50 Ampere [A] 0
200 150 100 50 Ampere [A] 0
Time [ms]
Time [ms]
(a)
(b)
Figure 4.4.Current in the load in the (a) fixed PWM case (b) constant DC case.
Table 4.4. Current, power and ηsystemfrom paper II.
Load case AC Fixed PWM Constant DC
Rload(Ω/phase) 3.52 0.86 0.86
Rlines+ Rwindings(Ω/phase) 0.435 0.435 0.435
iRMSphase(A) 20.77 23.23 23.53
Pload(kW) 4.60 4.55 4.44
Plosses(kW) 0.56 0.70 0.72
Plosses+ Pload(kW) 5.16 5.26 5.17
< Pturbine> (kW) 27.44 28.15 27.78
ηsystem 0.188 0.187 0.186
Table 4.4 shows measured resistances, calculated RMS phase current in the transmission line, calculated average powers, Pturbine from table 4.1 and calculated ηsystemfrom equation 2.10.
Out of the three cases, the losses were the biggest for the constant DC case, both in terms of magnitude and in terms of losses/total electric power deliv- ered. Despite having different size of losses and shapes of currents both drawn from the generator and delivered to the load, ηsystem was about the same for the three load control methods.
4.4 Calibration of the simulation model
An interval of minimum water speed can be seen from 13:09:20 to 13:09:33, see figure 4.5a. At an average speed of 1.4 m/s the water needs 11-12 seconds to reach the turbine from the ADCP. The result can be seen in the difference in time between the water speed measurement in figure 4.5a and in the rotational speed measurement in figure 4.5b. In the minimum water speed interval the average water speed is about 1.31 m/s. An interval of peak water speed can be seen just before the minimum interval. The intervals points are used for calibrating the drag losses of the turbine in the simulation. The peak ω is between 21.5-22.0 RPM and the minimum ω is between 19.5-20.5 RPM. The two water speeds, referred to as high and low speed, were used as input in two separate simulations of operation with a load of 10 kΩ that symbolizes no load operation. The simulation was run for 60 s to let the simulation values stabilize and to let the vortex code build up a wake. The last 30 s of the simulations are plotted in figures 4.6a and 4.6b. With drag losses of 900 Nm the high water speed simulation predicts 21.5-22.5 RPM and the low water speed simulation predicts 19.5-20.5 RPM. The estimation of the drag losses are good enough to simulate the turbine ω and generator voltage in the experimental free spin measurement.
34
08:58 09:07 09:15 09:24 09:33 09:41 09:50 09:59 10:07 20
20.5 21 21.5 22 22.5
08:41 08:49 08:58 09:07 09:15 09:24 09:33 09:41 09:50 1.3
1.32 1.34 1.36 1.38 1.4 1.42 1.44
m/s
Time (minutes:second)
(a) (b) Time (minutes:second)
r.p.m.
Figure 4.5. (a) Measured water speed during 60 seconds. (b) Measured ω during 60 seconds.
Seconds 30 35 40 45 50 55 60
r.p.m.
21 21.5
22 22.5
23
Seconds 30 35 40 45 50 55 60
r.p.m.
19 19.5
20 20.5
21
(a) (b)
Figure 4.6. Simulated ω during free spin operation during (a) peak water speed (b) minimum water speed.
Measured line to line voltage peaks at high water speed was 278-284 V and simulated line to line voltage peaks was 281-289 V, see figure 4 .7a. The simulation can predict the voltage of the generator in the high water speed interval within 2 % of the experimental measurement. Measured line to line voltage peaks at low speed was 263-273 V and simulated line to line voltage peaks was 261-265 V, see figure 4 .7b. The simulation can predict the voltage of the generator in the low water speed interval within 3 % of the experimental measurement.
Seconds
50.2 50.25 50.3 50.35
Volt
-300 -200 -100 0 100 200 300
Simulated Measured
Seconds
50.2 50.25 50.35
Volt
-300 -200 -100 0 100 200 300
(a) (b)50.3
Simulated Measured
Figure 4.7. Simulated and measured line to line voltage of the generator during free spin operation and (a) high water speed (b) low water speed.
4.5 Simulation results
The experiment was carried out during 826 seconds of operation on 2014-01- 20. The target value was changed with discrete steps and kept for a time period of at least one minute. The water speed interval of 1.1-1.25 m/s, seen to the left in figure 4.8, and a DC bus voltage range of ∼ 75 V up to 180 V, seen to the right in figure 4.8, covers operation in high λ , low λ and at λopt.
Seconds
0 100 200 300 400 500 600 700 800 900
m/s
1 1.05
1.1 1.15
1.2 1.25
1.3 1.35
1.4
0 100 200 300 400 500 600 700 800 900 60
80 100 120 140 160 180 200
Volt
Seconds
(a) (b)
Figure 4.8. (a) Measured water speed. (b) Set target DC bus voltage.
The two step responses seen in figures 4.9a and 4.9b correspond to an in- crease (4.9a) and a decrease (4.9b) of target dc voltage that corresponds to first a λ increase from 3.3 to 3.6 and then a λ decrease from 3.5 to 2.7. The speed of the step response and the initial and final values of the voltage are well predicted by the simulation when the turbine is simulated to operate close to λopt.
36
123.45 123.46 123.47 123.48 123.49 123.5 123.51 123.52 123.53 123.54 123.55
Volt
125 130 135 140 145 150
Simulated DC bus voltage Target DC voltage Experimental voltage
Seconds
210.74 210.745 210.75 210.755 210.76 210.765 210.77
Volt
105 110 115 120 125 130 135 140 145 150
Simulated DC bus voltage Target DC voltage Experimental voltage
(a) Seconds (b)
Figure 4.9. Simulated and experimental step response close to λopt. (a) An increase of λ . (b) A decrease of λ .
The two step responses seen in figures 4.10a and 4.10b correspond to a small increase (4.10a) and a large increase (4.10b) of target dc voltage that corresponds to first a λ increase from 1.8 to 2.4 and then a λ increase from 2.6, passing λopt = 3.5, up to 3.8. Figure 4.10a shows how the simulated ω increases much faster than the experimental ω. This is because the hydrody- namic simulation will estimate a too high power capture in low λ operation.
Seconds
534.3 534.5 534.7
Volt
75 80 85 90 95
Simulated DC bus voltage Target DC voltage Experimental voltage
Seconds
594.25 594.35 594.45 594.55
Volt
90 100 110 120 130 140 150 160 170
Simulated DC bus voltage Target DC voltage Experimental voltage
(a) (b)
Figure 4.10. Simulated and experimental step response. (a) Far from λopt and an increase of λ . (b) An increase of λ , passing λopt.
The step response in figure 4.11 shows a change in λ above λopt, from 3.7 to 4.0. The speed of the step response and the initial and final values of the voltage are well predicted by the simulation at operation above λopt.
Seconds
726.24 726.26 726.28 726.30
Volt
160 165 170 175 180 185
Simulated DC bus voltage Target DC voltage Experimental voltage
Figure 4.11.Simulated and experimental step response of an increase of λ above λopt.
For most of the step changes in λ , the experimental and simulated ω show an increase of ω of the same time scale. If you add rotational speed to the step response in figure 4.9 you get the figure 4.12a where it takes less than half a second to reach the new ω. The only step where the experimental and simulated ω result do not agree is for the large step of low λ , past λopt, to a high λ , see figure 4.12b. As in the previsous steps, the initial and resulting dc bus voltage in the simulation agrees with the experimental result, but there is a big overshoot in ω and it takes a few seconds for it to stabilize. The control system in the simulation does not brake the turbine ω as it is desgined to.
However the dc bus voltage is not overshooting which indicates that there is a voltage drop missing in the model of the generator.
38
Seconds
120 121 122 123 124 125 126 127 128 129 130
Volt
120 125 130 135 140 145 150 155 160
Simulated DC bus voltage Target DC voltage Experimental voltage Experimental rpm (x10) Simulated rpm (x10)
Seconds
592 593 594 595 596 597 598 599 600
Volt
80 100 120 140 160 180 200
Simulated DC bus voltage Target DC voltage Experimental voltage Experimental rpm (x10) Simulated rpm (x10)
(a) (b)
Figure 4.12. Step response of the simulated and experimental voltage and ω (a) No overshoot. (b) Overshoot in the simulated ω.
In the large step from low λ to high λ it takes about 0.3 s for the turbine to increase the rotational speed to reach the target dc voltage. With ω = 11 RPM and a five bladed turbine the time period between blades of will be 1.09 s, and for ω = 16 RPM the time period will be 0.75 s. The step time of 0.3 s represents 27.5 % and 40 % of the time between blades for ω = 11 RPM and ω = 16 RPM respectively. This means that it is likely that the turbine position will be between the peaks of maximum power capture of the turbine.
Changing the starting position of the turbine in the simulation changes the angle between the blade and the water flow at the time of the step. In figure 4.13 the response time of the voltage decreases when the starting position of the turbine is moved with 15 and 30 degrees respectively. 15 and 30 degrees corresponds to a 20.8 % and 41.7 % relative move of the starting position.
Seconds
594 594.1 594.2 594.3 594.4 594.5 594.6 594.7 594.8 594.9 595
Volt
90 100 110 120 130 140 150 160 170
Targetp DCp voltage Experimentp voltage
SimulatedpDCpbuspvoltagep-p0pdegrees Simulatedp DCp bus voltage - 15 degrees Simulatedp DC bus voltage - 30 degrees
Figure 4.13. Step response of the dc bus voltage from low λ to high λ for different starting positions of the turbine.
5. Conclusions
In paper I, an experimental station was deployed and the first measurements showed that the generator and and turbine was able to deliver power to a re- sistive dump load without active control. The measurements from the down- stream ADCP clearly show a reduction in water speed during load operation.
In paper II, experimental results from three different control methods are analyzed in this paper, and the results indicate that DC bus voltage control is the best suited control for marine current applications. It has been experi- mentally verified that the DC bus voltage control system was able to lower the variations of rotational speed with a factor of ∼ 3.5. The results show that the average tip speed ratio for all three cases was close to λopt = 3.5 but resulted in only ηsystem=∼ 19 %. An MPPT system should be able to increase ηsystem. In paper III, a simulation model coupling the electrical and hydrodynamic parts of a vertical axis marine current energy converter has been validated. The model can be used for describing the behaviour of the turbine and generator for different flow conditions by predicting the step response of the DC bus voltage and the rotational speed for a change in tip speed ratio. The simulation cannot predict the behaviour when the turbine is operated far from optimal tip speed ratio where the vortex model overestimates the power capture. By changing the starting position of the turbine in the simulation it shows how the rise time of the step response changes.
6. Future work
The work presented in this thesis has been focused on the first experimental results of the implemented control system and validating a simulation model.
The simulation model can be used to inverstigate control methods for dif- ferent MPPT topologies.
There is a lower limit to at what water speed the turbine will start to absorb power. This limit will be investigated to determine what water speeds are suitable for extracting power. This limit will depend on the turbulence in the water and the ability of the system to stay at a certain λ .
The experiments in this thesis have recorded data during 30 minutes. It would be interesting to do longer experiments with an autonomous drive of an MPPT to investigate the utilization factor for marine currents in a river using a vertical axis turbine.
7. Summary of papers
In the following text the papers in the thesis are summarized and the author’s contribution is presented.
Paper I
The Söderfors Project: Experimental Hydrokinetic Power Station Deployment and First Results.
During 2013 an experimental hydrokinetic power station was deployed for in-stream experiments at a site in a river. This paper briefly describes the deployment process and reports some initial results from measurements made at the test site.
The paper was presented by the author at EWTEC in Aalborg, September, 2013. The author and the main author Staffan Lundin did the majority of the experimental work and Staffan did the majority of the writing. The Marine Current Power group deployed the experimental station in a joint effort.
Paper II
Experimental Results of a DC Bus Voltage Level Control for a Load-Controlled Marine Current Energy Converter.
This paper investigates three load control methods for a marine current en- ergy converter using a vertical axis turbine mounted on a permanent magnet synchronous generator. The three cases are; a fixed AC load, a fixed pulse width modulated DC load and a DC bus voltage control of a DC load. Exper- imental results show that the DC bus voltage control reduces the variation of rotational speed with a factor of 3.5. For all three cases, λ can be kept close to the expected λopt. However, for all three cases the average extracted power was about half of the estimated 36 %. A Maximum Power Point Tracking (MPPT) system, with or without water velocity measurement, should increase the average extracted power.
The paper was published in Energies in May 2015.
The author did the majority of the work.
44
Paper III
Validation of a Coupled Electrical and Hydrodynamic Simulation Model For Vertical Axis Marine Current Energy Converters.
This paper validates a simulation model for a Vertical Axis Turbine (VAT) connected to a Permanent Magnet Synchronous Generator (PMSG) in a direct drive configuration. The simulated system consists of the electrical system and a hydrodynamic vortex model for the turbine. Experiments of no load op- eration were conducted to calibrate the drag losses of the turbine. Simulations were able to predict the behaviour of a step response for a change in Tip Speed Ratio (TSR) when the turbine was operated close to optimal TSR. The turbine starting position could be changed to view the influence of changed relative position of the turbine to the water flow in the step response.
The paper is a manuscript.
The author designed the electrical system and did the majority of the writ- ing.
8. Sammanfattning på svenska
Marin strömkraft med vertikalaxlad turbin är ett nytt koncept inom förnybar el. Tanken är att med hjälp av en turbin och generator placerad på botten kunna utnyttja energin i fritt strömmande vatten för att konvertera till elektrisk energi.
Tekniken är i grunden lik vertikalaxlad vindkraft med den stora skillnaden att turbin och generator befinner sig under vatten. För att maximera effektup- ptaget av turbinen behöver man hålla kvoten mellan rotationshastigheten hos turbinen och vattenhastigheten, löptalet, vid ett visst värde. För att utveckla ett styrsystem som kan hålla optimalt löptal behöver man veta hur turbinen och generatorn beter sig i vattnet, hur förlusterna och eventuella risker relaterar sig till olika typer av drift. Den här avhandlingen består av tre artiklar; Den första beskriver sjösättningen av experimentstationen och presenterar de första re- sultaten, den andra visar prestanda från det implementerade styrsystemet som finns idag och den tredje artikeln visar hur en kombinerad simulering av sys- temets elektriska och hydrodynamiska egenskaper kan valideras med hjälp av experimentella data. Artikel två konstaterar att det är möjligt att hålla tur- binen vid ett fixt varvtal med väldigt små variationer på bekostnad av högre förluster. Nästa steg blir att utveckla ett system som kan maximera effektup- ptaget men samtidigt minimera förlusterna. Simuleringsmodellen som tagits fram kan förutse turbinens och generatorns egenskaper för ett steg i löptal nära optimalt löptal. Simulerings-koden kan användas för att förutse systemets be- teende vid situationer som vi antingen inte kan, eller vill riskera, att utsätta systemet för, t.ex. vattenhastigheter utöver vad systemet är designat för. Mod- ellen kan också användas för att testa olika kontrollmetoder för att optimera effektupptaget av turbinen.
Författarens huvudfokus kommer i fortsättningen ligga i att utveckla styrsys- temet och undersöka startförloppet av turbinen.
Acknowledgements
Thank you to my main supervisor Mats Leijon and my second co-supervisor Jan Sundberg for giving me this opportunity. A special thanks goes to my first co-supervisor Karin Thomas for all the help and guidence during a sometimes quite stressfull period.
I would like to say thank you to the Marine Current Power Group: Thank you Nicole, Anders, Staffan, Emilia, Thao and Irina.
A special thank you to two previous members of the group: Dr Katarina Yuen and Dr Mårten Grabbe. Thank you for all the help and guidance during my first time as a PhD student. Thank you for keeping a positive and motivat- ing attitude towards science. Thank you for answering all my clever questions, especially the stupid ones.
Thank you Senad Apelfröjd for knowing your stuff, and thank you Martin Fregelius for solid lab work.
Dear Sir Mr Chairman, Rickard Ekström, thank you for your help, your sportmanship and your "great" sense of humor. I hope you are still enjoying your mug.
My roomates, Liselotte, Nicole, Valeria, Linnea, the ADCP raft, Stefan and Anders: thanks for making it fun to go to the office. And thank you for all the wednesday-fika. And thank you for motivating me to work on fridays. I like sushi. I hope you will not miss me too much when I move to my new office so far away, I will try to come visit.
Eduard, thanks for all the super interesting and rewarding meetings lately, they have greatly helped my progress at work. We managed to save the world once, and there is surely more to come! Vi får ta en liten jävel snart.
Victor and Kaspar, my Whats App guys! Thanks for all the fun times!
I’ve gotten to know great people from of an impressively wide range of nationalities! Francisco, Maria, Markus, Saman, Johan, Johan, Johan, Johan (i think i got them all), Wei, Flore, Malin, Weijia and Juan. As we say in swedish: "Variation förnöjer"!
Ling, i trust i can call you Dr Hai by now! Congratulations and good luck in China, i will miss you.
Shiuli and Michael, such a great couple that are always happy and easy going. Always great to see you, inside and outside of Ångström.
Ola, Claire and Amélie, thank you for making taking care of a baby look so easy!
Ante, Perra, Ubbe and A-skott. Mina äldsta vänner. Great people that made me who I am today! Perra, nihao and good luck in China!
