Design of a Simulation Startup Model for a Marine Current Turbine

20001

Examensarbete 15 hp Juni 2020

Design of a Simulation Startup

Model for a Marine Current Turbine

Isak Carlénius

Valle Johansson

Preface

This report is the final part of a project course given in the third year of the electrical engineering program at Uppsala university. The chosen project meant working for the department of electricity at Uppsala university.

More specifically, the project consisted of designing a startup circuit for a marine current turbine. The work was initiated in Mars 2020 and concluded in May 2020.

When writing the report students in electrical engineering and employees at the department for electricity was the main targets in mind. Furthermore, this report has the intention of contributing to the ongoing research regarding the fields of marine current turbines and renewable energy.

Through out the project, our supervisors Johan Forslund and Christoffer Fjellstedt has been very supporting and of great help. With their specialized knowledge in marine current turbines and power electronics they have been able to answer the majority of our questions. The success of this project would not have been possible without them.

Uppsala, May 2020

Isak Carlénius, Valle Johansson

Contents

1 Introduction 1

1.1 Purpose . . . . 1

1.2 Project Specifications . . . . 1

1.3 Previous Work . . . . 1

2 Method 2 3 Theory 3 3.1 Hysteresis Current Control . . . . 3

3.2 Synchronous Machine as a BLDC Motor . . . . 3

3.3 Control Theory . . . . 4

3.4 Cp/λ Relation . . . . 5

3.5 Snubber Circuits . . . . 6

4 Implementation 7 4.1 Overview of the Simulink Model . . . . 8

4.2 Synchronous Machine . . . . 9

4.3 BLDC Circuit . . . 10

4.4 DC Load Circuit . . . 12

4.5 Switch Control . . . 13

4.6 Snubber Design . . . 14

5 Results 15

6 Discussion 18

7 Conclusions 20

8 Future Work 21

References 22

Teknisk- naturvetenskaplig fakultet UTH-enheten

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Box 536 751 21 Uppsala

Telefon:

018 – 471 30 03

Telefax:

018 – 471 30 00

Hemsida:

http://www.teknat.uu.se/student

Abstract

Design of a Simulation Startup Model for a Marine Current Turbine

Isak Carlénius, Valle Johansson

This project is aimed at developing a simulation model in Simulink for a new startup system controlling the marine current turbine at Uppsala university's research facility in Söderfors. The goal is to design a circuit that is able to switch between feeding power to and extracting power from the synchronous machine in order to control the rotational speed of the turbine.

The technical solution consisted of two separate circuits combined into the final system. First, the synchronous machine is run as a BLDC motor where power is fed to the motor in order to accelerate the turbine.

Then, at a specified rotational speed threshold the BLDC circuit is disconnected and the turbine continues to accelerate by picking up power from the water alone. Lastly, when the rotational speed reaches the desired setpoint for the rotational speed the synchronous machine is connected to a DC load. By controlling the power extracted in the load with a PI controller the rotational speed of the turbine stays at the setpoint value.

Results from the simulation model shows that it is possible to control the startup process of the turbine with such a system. In future projects improvements can be made regarding removing current spikes, more smooth power usage and faster PI controllers. To further develop the startup system the next step would be to translate the simulation model into LabVIEW code in order to test it at the site in Söderfors.

Ämnesgranskare: Mats Ekberg

Handledare: Johan Forslund, Christoffer Fjellstedt

1 Introduction

The department of electricity at Uppsala university has a facility in the town of Söderfors where they are conducting research on a marine current turbine. The goal is to investigate the possibilities of using underwater streams to generate electricity and how this will effect the surrounding ecosystems. The turbine has five blades and is connected to a permanent magnet synchronous machine.

1.1 Purpose

Recently, during test runs of the turbine, the startup process has failed and caused mechanical damage to the turbine. Therefore, the focus of this project is to design a simulation model in Mathworks Simulink concentrating on active control of the startup of the turbine to prevent further problems. The model should be able to accelerate the turbine from standstill and then control the speed of the turbine during the whole startup process. In order to achieve this the main idea is to control the power flow in and out from the synchronous machine with the intention of controlling the rotational speed of the turbine.

1.2 Project Specifications

The model should continue to build on the existing systems that are already in place in Söderfors. Further- more, the following functions should also be included in the model:

• Hysteresis current controlled BLDC motor.

• 400 V AC voltage source to feed the inverter.

• Feedback control system for the rotational speed using PI controllers.

• Water velocity and rotational speed dependent input torque for the synchronous machine.

Regarding the performance of the model, the desired max speed (upper RPM limit) for the startup process should be 15 RPM with 5 RPM allowed overshoot. As for the lower RPM limit, this value is dependent on the water speed and will be set accordingly. The remaining parameters of the system are to be decided in the design process.

1.3 Previous Work

From the beginning of the research in Söderfors, the system in charge of the startup process has not been

changed. The current system is only able to accelerate the turbine and there is no feedback functionality to

control the speed of the turbine. Because of the discovered problems in the startup system being so close in

time, this is the first project assigned to solve the problem.

2 Method

The beginning of the project included a planning phase and the search for relevant information regarding the facility in Söderfors. This phase was a key factor for the success of the project and made it possible for a smooth start on the technical solution for the startup system.

First, the project was divided into smaller sections with one or two associated milestones. Then, using these milestones a Gantt chart was created according to the given time frame and deadlines. The first version of the Gantt chart was then revised and approved in the presence of our supervisors. Throughout the design phase minor changes in the technical plan have been made.

The information search mainly consisted of reading research articles written on the subject of the facility in Söderfors, e.g. the articles [1] and [2]. When needed, more in depth papers covering specific theoretical areas was also looked up. This meant using the Uppsala university scientific search engine and the Google scientific data bank. In this project the majority of the references used are papers published in journals, conference proceedings and books.

After the planning and information search phases were over, the project transitioned into the implementation

phase. Here, the work followed the Gantt chart which allowed for an efficient work flow and weekly meetings

with the supervisors. The design of the technical solution was conducted in Mathworks Simulink.

3 Theory

3.1 Hysteresis Current Control

Hysteresis current control can be used in applications were the magnitude of a current needs to be controlled.

The aim is for a generated current to follow a predetermined reference current. A common way of achieving this is by creating a hysteresis band limited by a lower and upper set point. These set points are often symmetrically located around the reference current, and constitutes the allowed deviation of the generated current compared to the reference current. To keep the generated current within the hysteresis band, no action is taken to alter the behavior of the generated current when it is inside the two set points.

However, when reaching the lower or upper limit, switching devices are used to ramp the current up or down respectively, creating a triangular shape of the current [3]. An example of how the resulting current and pulses sent to the switching devices can look like is illustrated in Fig. 3.1.

Figure 3.1: Hysteresis current control [4]

Two of the advantages with this kind of system is the ease of implementation and its satisfactory dynamic performance. One drawback is the risk of an alternating switching frequency. Since the time it takes for the current to reach either of the set points might vary, the time between each switch can vary as well. This is not necessarily a problem but might be a source of error when choosing frequency dependent components for the rest of the system at hand [5].

3.2 Synchronous Machine as a BLDC Motor

The synchronous machine can be used both as a motor and a generator. When using it as a motor there are many various control techniques to choose from. It depends on the configuration of the machine and what components are available.

In this project the turbine is connected to a PMSM (permanent magnet synchronous machine) which makes it similar to how a BLDC motor (brushless DC motor) works. This technique measures the position of the rotor with hall sensors and then uses an inverter to control the current going to the coils in the stator.

Knowing the position of the rotor using hall sensors, basic logic is then used to calculate the control signal

to the inverter. By doing this, the inverter switches in a pattern that makes the stator currents induce a

magnetic field following the rotor, and thus making it rotate. In Simulink, BLDC control can be implemented

using hysteresis current control [6].

3.3 Control Theory

In control design a Proportional-Integral-Derivative (PID) controller is the most used controller for a variety of applications which uses a closed loop feedback system. In general a closed loop feedback system has a specific set point as the input and an physical process variable as the output. Then by continuously correcting itself the system aims at changing its output to follow the desired set point [7].

Figure 3.2: Closed loop system with PID controller [8]

The basic principle of the PID controller is to read a sensor value and calculate an error e(t) by taking the difference between the sensor value y(t) and the set point value r(t). Then, the mathematical operations multiplication, integration and derivation are performed on the error in order to get the final control variable u(t) , see Fig. 3.2.

u(t) = K p e(t) + K i

Z t 0

e(t ⁰ )dt ⁰ + K d

d

dt e(t) (1)

When the system changes accordingly to the control variable, a new error is then calculated for each iteration of the feedback loop and this process continues until the control algorithm no longer has an effect on the output. The performance of this control process is often valued by looking at the rise time, overshoot and steady state error for the system, see Fig. 3.3.

Figure 3.3: Step response for closed loop system using PID conroller [9]

One of the strengths of the PID controller is how easy it is to change the performance of the system by manipulating the control parameters K p , K i and K d . The proportional term only depends on the error of the system. In general, increasing K p will result in a faster rise time but will also increase the overshoot.

The contribution from the integral term is driving the steady state error to zero. This is because the integral

term sums all errors over time and does not stop producing an output until the accumulated sum of errors

is zero. Increasing K i will increase both the rise time and overshoot. The derivative term is proportional to

the rate of change in the process variable and predicts system behavior. Increasing K d decreases overshoot

and improves the stability of the system [10].

3.4 Cp/λ Relation

When a turbine operates in water, not all power in the water current is captured. Instead only a small part will produce a torque on the turbine. This fraction is determined by the power coefficient Cp which depends on the water velocity v, the rotational speed of the turbine Ω and the radius of the turbine r. These three variables are then combined into what is called the tip-speed ratio λ, see Equation (2). Then, by using the tip speed ratio an expression for the power coefficient can be obtained consisting of a third order polynomial, see Equation (3) [11].

λ = Ωr

v (2)

Cp = 0.0836 · λ ² − 0.0183 · λ ³ (3)

The equation for Cp is unique for the turbine and is derived from measurements taken in the location of the turbine. The relation between Cp and λ for the facility in Söderfors is shown in Fig. 3.4.

Figure 3.4: Relation between Cp and λ in Söderfors

As can be seen in Fig. 3.4, there exists a certain tip-speed ratio λ 0 which corresponds to a maximum of the

power coefficient Cp. When designing a turbine the goal is to have the turbine operate in an interval around

this λ 0 . The use of the Cp/λ relation is also widely used in the wind turbine industry and serves as a reliable

tool for measuring the efficiency for a vertical axis wind turbine. Because of the many similarities between

wind and water turbines, the Cp/λ relation can be applied to both cases using the same principles.

3.5 Snubber Circuits

In circuits containing inductive loads and switching devices, care must be taken so that the energy dissipation from the inductive load do not damage the switching devices at their switch off point. Because when the circuit is opened by a switch the energy dissipation from a charged coil can result in rapidly changing currents and inducing high voltages in the circuit. By placing a snubber in parallel with the switching device, an alternative path for the current coming from the inductor, as the switch opens, is available. So the general purpose of a snubber is to handle the energy dissipation from the inductor to reduce the stress on the switching device.

The configuration of snubber circuits vary depending on the application it is used in. One of the most frequently used setup is the use of a series RC-circuit. The capacitor causes a decreasing transient current to pass through the snubber for a fraction of a second, not enabling the voltage to rise instantaneously across the switch. Thereby the rate at which the current and voltage rises across the snubber and switch is reduced.

Placing a resistor in series with the capacitor limits the discharge current passing through the snubber and it dissipates the energy stored in the snubber circuit [12]. An illustration of the mentioned setup can be seen in Fig. 3.5.

Figure 3.5: RC-snubber circuit [13]

Below, a method to calculate the values for the resistor and capacitor is described [14]. The resistance can be calculated with

R = V _o

I c (4)

where V o is the voltage across the open switch and I c the current through the closed switch. The amount of energy the resistance is to dissipate depends on the energy stored in the capacitor. A guideline is to choose the capacitor so that the resistor dissipates half of its wattage rating [12]. The average power dissipation from the resistor is given by

P = CV _o ² f s (5)

where P is the power dissipation, C the snubber capacitance and f s the switching frequency. Using this, the capacitance value can be calculated with

C = P

V _o ² f s

. (6)

This is a quick method for calculating values for the resistor and capacitance and does not take in consid-

eration all the AC-characteristics of the circuit. However, it yields estimates for the values and thereby a

starting point for the tuning of these components.

4 Implementation

The new startup system designed in this project is based on the existing system used at the site in Söderfors.

Therefore, the same parameter and component values from the existing system will be used when possi- ble. The turbine in Söderfors is a vertical axis current turbine and the generator is a permanent magnet synchronous machine. The parameters for the existing system are presented in Table 1.

Table 1: Turbine and synchronous machine specifications [2]

Turbine and generator rating 7.5 kW Turbine

Rated rotational speed 15 RPM

Rotor radius 3 m

Rotor height 3.5 m

Number of blades 5

Synchronous Machine

Nominal electrical frequency 14 Hz

Poles 112

The main idea for the new startup system is to first run the synchronous machine as a BLDC motor in order to accelerate the turbine from standstill. This is the first phase in the startup process. An AC voltage source on 400 V will be used in combination with a three-phase transformer to feed the inverter in the BLDC circuit. Furthermore, hysteresis current control will be integrated in the BLDC controls.

Figure 4.1: Flowchart for the startup process

The startup system enters the second phase of the startup process when the lower RPM limit is reached.

This phase consists of disconnecting the BLDC circuit and letting the turbine accelerate the synchronous machine with only the power from the water. This is possible when the rotational speed of the turbine is sufficient in order for the turbine to produce enough torque. To simulate this behavior the Cp/λ relation described in Section 3.4 will be used.

When the upper RPM limit is reached, the startup system proceeds to the final phase of the startup process.

This is where the synchronous machine is connected to the DC load which then controls the rotational speed

of the turbine and keeps it below 15 RPM. Here, a PI controller will be used to control an IGBT which

then control the current flow through a resistor. Only the PI part of the controller was used because it

was thought to be sufficient to solve the task. By drawing a specific amount of power in the resistor the

rotational speed of the turbine will be controlled to meet the desired speed.

4.1 Overview of the Simulink Model

This section will give a brief introduction to the main blocks in the complete Simulink model. The final version of the model is shown in Fig. 4.2, and it serves as a useful overview of all the main blocks and functions in the startup system. In Simulink, data flow between components is represented with lines and the direction of the data flow is indicated by an arrow in one end of the line. Some lines in the model do not have an arrow which mean data can flow both directions, e.g. AC currents. The simulation was run in Simulink 2018b with a discrete time solver, in Simulink called "discrete (no continuous states)", with default settings and 5 µs sampling time. The green boxes represent scopes that creates plots and they were used throughout the whole design process. To make the model more user friendly and also a bit cleaner the majority of the code was divided into smaller subsystems, the blue boxes. These subsystems were then turned into masks. This makes it possible to change parameters in the subsystems from a menu instead of needing to find the specific component in the subsystem to change its value.

Figure 4.2: The complete Simulink model

The basic idea for the startup system is to first feed the synchronous machine, the red block in Fig. 4.2, with power in order to accelerate the turbine. This is done by running the machine as a BLDC motor and using an inverter to control the stator currents using hysteresis control. Everything from the AC voltage source to the inverter is inside the input power block, the blue block with number 3 in the model. The components inside the red rectangle with number 6 in the model controls the hysteresis current control and the gate signal to the inverter. When the rotational speed of the turbine reaches a specified lower RPM limit, the system switches off the BLDC circuit and lets the turbine run only with the power from the water. At the same time as the BLDC circuit is switched off the torque input to the synchronous machine is changed to the torque computed with the Cp/λ relation, the blue block with number 2. All of this is controlled by the blue block with number 5 in Fig. 4.2 which consists of several switches.

The second part of the startup process is activated when the rotational speed of the turbine reaches the

upper RPM limit which is 15 RPM. At this point, the three phase cables from the synchronous machine is

connected to the DC load through a switch. A feedback loop then controls the power extracted in the load

in order to control the rotational speed of the turbine. Everything concerning the DC load and controls for

the power extraction is in the blue block with number 4.

4.2 Synchronous Machine

To simulate the generator in place in Södefors, the permanent magnet synchronous machine block was used in Simulink. This made it possible to use parameters from the real generator such as stator phase resistance, flux linkage and inertia. The synchronous machine block, see Fig. 4.3, has four ports on the left side and one port on the right side. The three ports A, B, C are for the three-phase cables and works as both inputs and outputs depending on the mode of the machine, i.e. if it is run as a motor or generator. In the top left corner, the mechanical torque input is located, indicated by the symbol T m . The sign of this input value determines which mode the block is in. A negative value corresponds to the machine running as a motor and represents a braking torque on the drive shaft, vice-versa applies for a positive value [15]. The port on the right side is the output bus for everything that is measured in the synchronous machine, e.g.

stator currents and voltages, hall effect signals and rotor speed. Bus selectors can be used in order to get the desired measurements from this output port.

Figure 4.3: The synchronous machine block in Simulink

When running the synchronous machine as a BLDC motor the input torque is set to 0 Nm. This is not a negative value and thus the machine should not operate like a motor. However, both the values 0 Nm and

−1 Nm was tested as the input torque during the BLDC circuit part of the startup process without noticing any differences in the results. Therefore, 0 Nm was used because it was most accurate to how the system would behave in reality. This has to do with the Cp/λ relation and how the turbine does not capture enough power from the water in order to accelerate the turbine before a certain rotational speed is reached. The part of the model calculating the torque picked up from the water is seen in Fig. 4.4. In the "Cp/lambda" block the Cp parameter is calculated using Equation (3) in Section 3.4. This, together with the water velocity and rotor speed, is then used in the "Pt/w" block to calculate the torque produced by the turbine.

Figure 4.4: The Cp/λ implementation in Simulink

4.3 BLDC Circuit

As mentioned in Section 4.1, the synchronous machine is first run as a BLDC motor. This mode is used until the rotational speed reaches a predetermined RPM setpoint. The startup circuit for the BLDC motor is represented by block 3 in Fig. 4.2. The leftmost block is the AC power supply representing the power grid. It delivers a 400 V phase-to-phase voltage to the next block which is a wye-connected transformer. The transformer decreases the amplitude of the voltage to make sure the diode bridge it is connected to delivers 200 V DC to the next block, the inverter.

Figure 4.5: The input power block in Simulink

The three-phase inverter consists of three legs with two IGBTs in each one. These IGBTs are controlled by signals generated using hysteresis current control to regulate the currents going to the synchronous machine from the inverter. The controller is represented by the two blocks at number 6 in Fig. 4.2. Fig. 4.6 shows the content of the rightmost of the two blocks. Here, the gates to be open and the ones to be closed is decided depending on the signals from the hall sensors positioned in the synchronous machine.

Figure 4.6: Hall sensor interpretation

The control signals are then multiplied with the value generated from the PI controller in block 5 in Fig.

4.2. This multiplication results in reference currents for each phase going to the synchronous machine. Each

reference current and the actual current in each phase are used as inputs to the leftmost block at number 6 in Fig. 4.2. The content of this block can be seen in Fig. 4.7. Here, the difference between the reference current and the actual current in each phase is computed and the results are used as inputs to three relays.

The relays have an upper and a lower limit resulting in a hysteresis band within which the actual current is to be contained, according to Section 4.1. If the actual current in one phase is outside the hysteresis band, a one or a zero is outputted from the relay. The current in each corresponding phase is increased if a one is outputted and decreased if a zero is outputted. The amplitude of the reference current is calculated using the difference of the reference rotational speed and the actual rotational speed of the synchronous machine as input to the previously mentioned PI controller.

Figure 4.7: Relays controlling gate signals to the inverter

Between the diode bridge and the inverter in Fig. 4.5, a resistor of 12 Ω in series with a capacitor of 3.3 mF is mounted in parallel with the two terminals. The capacitor is there to smooth out the voltage from the diode bridge, and thereby achieving a smoother power delivery to the synchronous machine when run as a motor. Measurements made earlier in Söderfors showed that the charge time of the capacitor was 200 ms.

To replicate the performance at the Söderfors site, the charge time was to be kept below that. The value of the capacitor was chosen according to the actual component at the site, so the resistor value had to be calculated to achieve the desired charge time. This was done by using the RC time constant, τ which is the time it takes for the capacitor to charge to a certain percentage of its supply voltage. The time constant τ was calculated using τ = RC were R is the resistance in the RC branch and C is the capacitance. Since the time it takes for the capacitor to be fully charged is approximately five time constants and both the charge time and the value of the capacitor was known, the resistance could be calculated with R = _5C ^τ which resulted in the resistor value of 12 Ω.

The only information available regarding the transformer was its no-load losses of 64 W and copper losses of

110 W at 3.5 kVA. Using these parameters the magnetization resistance could be calculated using R = ^U _P

,

were U is the primary side rms voltage and P the no-load losses. This resulted in a magnetization resistance

of 827 Ω. Due to the lack of further information, no more parameter values were calculated. Instead, the

default settings of the transformer were used.

4.4 DC Load Circuit

Since the max speed of the generator is 15 RPM a system was needed to regulate its speed. This was achieved with the DC load circuit represented as block number 4 in Fig. 4.2. The content of this block can be seen in Fig. 4.8. The three inputs to the left in the DC load circuit, going to the diode bridge, is the three-phase voltage and current generated by the synchronous machine when run as a generator. These are then rectified by the diode bridge resulting in a DC current and voltage going to the DC load.

Figure 4.8: The DC load block in Simulink

To actually maintain a speed of 15 RPM the load circuit was constructed to vary the power consumed depending on the rotational speed of the generator. More power consumed in the load leads to a slower rotational speed of the generator, and vice versa. Since the power consumption depends on the voltage and current across and through the load, hysteresis current control was used to alter the current flowing through the load. This was implemented using an IGBT whose control signal is generated using a PI controller and a relay. The PI controller generates a reference current depending on the rotational speed of the generator.

Afterwards, the difference between the reference current and the actual current in the load is computed and used as input to a relay. This relay works in the same way as the relays used in the BLDC startup circuit.

If the difference between the two currents are above or below the upper or lower setpoint of the relay, a zero or one is sent to the IGBT to decrease or increase the current respectively.

To achieve a less varying current when the IGBT switches, an inductor of 60 mH was placed after the diode

bridge. This value was not calculated but tested until the current’s fluctuation was as small as possible. The

capacitor was used to replicate the capacitor bank with a value of 16 mF at the site in Söderfors. To model

a resistance in the load a resistor of 0.83 Ω was used. The resistor value was based on information regarding

the DC load at the site in Söderfors [11].

4.5 Switch Control

The switching block in Fig. 4.2 has two inputs to the left and four outputs to the right, see Fig. 4.9.

The lower RPM limit used for the switching block in the figure is 10 RPM as can be seen by the threshold numbers "10" and "9" in the two switches. Input number 2 is the rotational speed of the rotor measured in RPM and this is the main control variable in the switching block. The circuit at the top in Fig. 4.9 controls the reference signal passed through to the hysteresis current control block for the BLDC circuit. When the lower RPM setpoint is reached (in this case 10 RPM) the output of the switch is changed to zero. The reason for this is to turn the BLDC circuit off when the first phase of the startup process is done.

In the middle in Fig. 4.9 is the switch controlling the torque to the synchronous machine. Input number 1 is the calculated torque coming from the Cp/λ block, being number 2 in Fig. 4.2. When the rotational speed of the rotor reaches 9 RPM the output of the switch changes from zero and starts outputting the torque from the Cp/λ block. The reason for having "9" instead of "10" as the RPM threshold for the switch is based on observations during testing of the startup system. It was discovered that switching from the BLDC circuit to the DC load and changing the input torque to the synchronous machine could not occur at the same moment. The cause of the problem was not found. Instead, one solution to the problem was to let the torque switch before the system switched from the BLDC circuit to the DC load.

Figure 4.9: The switching block in Simulink

The final circuit at the bottom of the switching block, see Fig. 4.9, controls the two three-phase switches

connected to the synchronous machine. These two switches has an inverse relation, i.e. when one is open the

other is closed. Output number 3 is controlling the BLDC motor cables and output number 4 is controlling

the DC load cables. At the beginning of the start-up process, the synchronous machine is run as a BLDC

motor hence output number 3 is false and output number 4 is true. When the rotational speed then reaches

the lower RPM limit (13 RPM) the "GreaterThan" block outputs true. This makes the OR-gate output true

and this changes the output number 3 to true and output number 4 to false. Because of the transition phase

in the system where the generator is accelerated only by the power from the water these two outputs needs

to be locked in order to stop the system from switching back to the BLDC cables. By placing a memory

block and then make it loop back into the OR-gate the OR-gate is guaranteed to always output true after

it receives its first true value.

4.6 Snubber Design

Because of switching components used in the input power block, DC power block and the two breakers in Fig. 4.2, spikes occurred in the current going to the synchronous machine when run as a BLDC motor. To eliminate them, snubbers were used in the inverter and diode bridge in the BLDC startup circuit. Snubbers were also used in the diode bridge and IGBT in the DC load and in the two breakers between the Input power block and the DC load block. For the snubbers in the inverter, diode bridges and the IGBT, values for the resistors and capacitors were chosen according to ones already existing at the site in Söderfors. The resistance in the resistors is 47 kΩ and the capacitance is 3.3 mF. For the two breakers positioned between the input power block and DC load block, the snubber resistance was calculated using Equation (4). This resulted in resistors for the left and right one of 16 Ω and 15 Ω respectively. Since the breakers only switch once, Equation (6) was difficult to use for calculating snubber capacitor values. Instead the capacitor value was gradually increased and decreased until the current spikes were eliminated resulting in capacitances of 2 µF and 50 mF in the left and right breaker respectively. All snubber components and were they are located are summarized in Table 2.

Table 2: Snubber values

Location Capacitance Resistance

Inverter 3.3 mF 47 kΩ

Diode bridges 3.3 mF 47 kΩ Left breaker 2.0 µ F 16 Ω

Right breaker 50 mF 15 Ω

IGBT 3.3 mF 47 kΩ

5 Results

All of the plots presented in this section are from the same simulation run of the startup system. The parameters used for this run are as follows:

• Water velocity: 1.3 m/s

• Lower RPM limit: 10 RPM

• Upper RPM limit: 15 RPM

In Fig. 5.1 the rotational speed of the turbine and the input torque to the synchronous machine is plotted.

Here, the three phases of the startup system is visible. First, the BLDC circuit accelerates the turbine up to 9 RPM (lower RPM limit minus one) which it reaches after 4.5 s. During this phase the input torque is set to zero, as mentioned in section 4.2. Then, the turbine continues to accelerate with only the power from the water and the BLDC circuit is switched off at the lower RPM limit (10 RPM). At this phase the torque computed with the Cp/λ relation is switched on. Finally, when the rotational speed reaches the upper RPM limit (15 RPM) at 4.8 s the DC load circuit is switched on and the PI controller keeps the rotational speed of the turbine below 15 RPM. Because the torque produced on the turbine depends on the rotational speed of the turbine the two curves have the same shape for t > 5 s which is shown in the plot, Fig. 5.1.

Figure 5.1: Turbine rotational speed

The measured power delivered to the inverter is shown in Fig. 5.2. The reason for the power peak in the

beginning of the simulation run is because of the current drawn by the transformer. The charging current

peaks at 14 A and disappears after 0.2 s. When the BLDC circuit is switched off the power to the inverter

goes down to almost zero as can be seen in Fig. 5.2.

Figure 5.2: Power from BLDC power supply to the inverter

In Fig. 5.3 the power from the synchronous machine is plotted. The direction of the power is defined as positive going out from the synchronous machine. This results in a negative power when the startup system is in the BLDC phase which can be seen in the graph the first 4.5 s. Around the 5 s mark, the startup system switches to the DC load and the synchronous machine starts working as a generator resulting in a positive current. This can be seen by the positive sign of the power at the second half of the graph.

Figure 5.3: Power to/from synchronous machine

The power consumption in the DC load is plotted in Fig. 5.4. The DC load is not connected until the

rotational speed of the turbine reaches the lower RPM limit. Hence there is no power consumption in the

DC load the first 4.5 s of the simulation. Then, the DC load is switched on and a small power is consumed during the acceleration from the water. Then, when the rotational speed reaches the upper RPM limit at 4.8 s the DC load starts to extract power in order to keep the turbine at 15 RPM.

Figure 5.4: Power consumed in DC load

The current going from the inverter to the synchronous machine is in 5.5. Until 4.5 s the synchronous machine is run as a BLDC motor drawing at most around 10 A. After 4.5 s the speed of the rotor has reached the lower RPM limit and the BLDC startup circuit is disconnected, resulting in a current close to 0 A from the inverter.

Figure 5.5: Three-phase current from inverter to synchronous machine

6 Discussion

In Fig. 5.1 an overshoot of 0.8 RPM is visible. Since it is below the specification of a 5 RPM overshoot, no actions were taken to reduce it. Depending on water velocity the lower setpoint at which the power supply is disconnected might have to be altered. This is because the power from the water captured by the turbine varies with water velocity, as described in Section 3.4. You want a high enough Cp/λ ratio for the turbine to produce a torque on the drive shaft. Furthermore, as the water velocity increases the produced torque is increased as well which is why the lower setpoint might have to be altered.

The torque generated by the water is, in this simulation, connected 1 RPM before the power supply is disconnected, rather than the torque to the machine being zero until disconnecting the power supply. This is because during testing it showed that it was not possible to connect the torque generated by the water and disconnect the power supply simultaneously. In this case, the rotational speed of the synchronous machine would decrease until it reached 0 RPM. The lower RPM limit was changed to see if it would solve the problem but it did not. No further actions were taken to find the reason for the behavior. At this moment the most likely reason is because of limitations in Simulink and not the actual behavior of the system. Because of this the breaking point in Fig. 5.1 occurs at 9 RPM instead of at the lower RPM limit of 10 RPM.

As mentioned in Section 5 much power is drawn from the power supply at the beginning of the simulation, see Fig. 5.2. The early power characteristics most likely depends on an inrush current drawn by the transformer at startup. Another noticeable characteristic of the input power are the power spikes shown in 5.2. These peaks constitutes a small enough fraction of the supplied power to not have a significant effect on the overall performance of the system. Therefore they were not further investigated and no action was taken to eliminate them. After around 4.5 s the lower RPM limit is reached and the power supply is disconnected from the circuit, and the power decreases to almost zero. In the beginning a large current spike was present at the switching point from BLDC mode to generator mode. This was removed with snubbers in the breakers connected to the BLDC startup circuit and the DC load. Because of limited information regarding the transformer in the input power block some simplifications were made. In this model there is no saturation simulated. If it was, the model might need to be altered to handle a possible change in the behavior of the system. Also, only the magnetization resistance of the transformer was calculated. If more information regarding the transformer was available more parameters could have been chosen closer to the real transformer. This could also require adjustments in the Simulink model.

Looking at the graph showing the power from the synchronous machine, in Fig. 5.3, there are some positive power spikes visible in the first phase of the startup process. When the synchronous machine is run as a motor the power from the synchronous machine should only be negative per definition. The origin of these spikes was not found during troubleshooting. A possible reason is the simulation itself and the sampling frequency used. With a higher sampling frequency the resolution would be improved and the spikes might decrease or disappear. A higher sampling frequency was never tested because of the large increase in computing time.

Nevertheless, the spikes are few and far apart. Also, the width of the lines in the graph is not proportional to time length of the spikes. Zooming into the graph, it was found these spikes represents less than 1 % of the total power. No further actions were made in order to investigate the impact of these spikes as they were assumed to not have a crucial impact on the performance of the startup system.

Fig. 5.4, showing the power consumed in the DC load, shows there’s almost no power drawn when the

synchronous machine is run as a BLDC motor and the DC load is disconnected. At 4.8 s the speed of the

rotor reaches the upper RPM limit and the power consumed in the load increases to keep the speed at

15 RPM . The curve is very similar to the curve representing the power to/from the synchronous machine

after 4.5 s. It’s possible to see that the power consumed in the load is slightly lower than the power generated

by the synchronous machine. This is due to the resistive losses in the breaker and the diode bridge. Before

using hysteresis current control as a mean of controlling power consumption, a PWM signal was used to

control the IGBT in the DC load. So instead of using the PI controller to determine a reference current a

pulse width was generated. Using a PWM signal lead to a very fluctuating power withdrawal were the power

went from a few kW to zero at each each switch of the IGBT. So by using hysteresis current control instead

of a PWM signal a much smoother power consumption was achieved in the DC load.

The hysteresis current controlled three phase current in Fig. 5.5 starts from zero and then slowly increases

following a constant slope until it reaches 10 A. The current spike in the beginning is most likely an inrush

current drawn by the transformer. The reason for the currents not switching until 1.5 s is due to the moment

of inertia in the synchronous machine and how it affect the rotational speed of the turbine. In Fig. 5.1

it is shown that the rotational speed does not start to increase until around 1.5 s. This is when the Hall

sensors gets updated. As the turbine accelerates, the switching frequency of the current increases until the

rotational speed of the turbine reaches the lower RPM limit and the BLDC circuit is disconnected.

7 Conclusions

The most significant results includes being able to control the rotational speed of the rotor during the startup system to satisfy the specifications for the project. With PI controllers, the rotational speed of the rotor reached the desired final speed of 15 RPM having an overshoot below 5 RPM. Furthermore, hysteresis current control was used in the BLDC startup circuit and in the DC load with success. A 400 V AC voltage source was also used as specified in series with a transformer to feed the inverter. Finally, an equation for the Söderfors Cp/λ relation was used for the water torque in the simulation model.

When designing the startup system the most crucial solution to figure out was the main layout of the simulation model and how to make it possible to run the synchronous machine as both a motor and a generator. Using two three phase switches to control the functionality of the synchronous machine, i.e.

switching between motor and generator, proved to be a sufficient solution.

Through out the whole design process, troubleshooting focused on minimizing the presence of current spikes

was the most time consuming problem. To solve this problem, snubbers was introduced in the startup system

in places where switching mechanism occurred, e.g. three phase switches, rectifiers and inverter. For the

most part, measurements were taken directly in the simulation model in order to acquire design parameters

for the snubbers. In the DC load, introducing an inductor and a capacitor bank contributed to reduce

the current spikes. The conclusion from this process is to from the beginning of the project start thinking

about where to place snubbers in the system. This would have saved us time and also made it possible to

integrate the switching mechanisms when the system was in a earlier state which also would have improved

the optimization of the snubbers.

8 Future Work

Because of the short time frame for this project, many areas of the simulation model has the potential for improvements. One example is the power usage which hasn’t been looked into. It would be interesting to investigate if the same results could be achieved using less power in the Input power block. Also, different values for the resistance in the DC load and how it affect the system’s performance could be further looked into. Another aspect of the startup system to investigate is the speed of the startup process, i.e. optimization of the PI controllers. The current time it takes for the system to reach the desired RPM set point at 15 RPM is approximately 10 s. By eliminating the overshoot in Fig. 5.1 the overall time could be halved for the startup system. It would also be possible to shorten the overall time by increasing the slope of the acceleration of the turbine during the BLDC motor phase. This would most likely mean increasing the current to the motor.

Finally, a third area for improvements is the power spikes in Fig. 5.3 and the inrush current spikes visible in Fig. 5.2 and Fig. 5.5. How these spikes impact the system and if it’s possible to eliminate them, are two questions to investigate.

This project has only focused on designing a simulation model and therefore the concepts addressed in this

project has not been proved to work in the real world. Although realistic parameters have been used and

the model has been designed based on the system already in place in Söderfors, the implementation of such

a system is a complex process. In a future project concerning the startup system for the turbine in Söderfors

one idea would be to translate the simulation model into a functional program. The software used to control

the system in Söderfors is a CompactRIO module and hence LabVIEW code would be the natural choice to

translate the simulation model into.

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