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Report on Electrical Generator Reliability Tools Reference: TIPA-EU-0038 Report on Electrical Generator Reliability Tools Issue: 1.0 Page 1 of 34 PUBLIC Available for widespread and public dissemination Report on Electrical Generator Reliability Tools Project Title: Horizon 2020 - TiPA Project Number: Document No: 727793 TIPA-EU-0038 Deliverable: D7.6 Report on Electrical Generator Reliability Tools Current Revision This project has received funding from the European Union’s Horizon 2020 research and innovation programme under Grant Agreement No 727793. Role Name Role / Organisation Revision Approved Date Approved Document Owner Dr. Kaswar Mostafa Research Associate/ University of Edinburgh 1.0 04/10/2019 Reviewed/ Approved By Prof. Markus Mueller

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Report on Electrical Generator Reliability Tools

Reference: TIPA-EU-0038 Report on Electrical Generator Reliability Tools Issue: 1.0

Page 1 of 34

PUBLIC Available for widespread and public dissemination

Report on Electrical Generator Reliability Tools

Project Title: Horizon 2020 - TiPA Project Number: Document No:

727793 TIPA-EU-0038

Deliverable: D7.6 Report on Electrical Generator Reliability Tools

Current Revision

This project has received funding from the European Union’s Horizon 2020 research and innovation programme under Grant Agreement No 727793.

Role Name Role / Organisation Revision Approved

Date Approved

Document Owner

Dr. Kaswar Mostafa Research Associate/ University of Edinburgh

1.0 04/10/2019 Reviewed/ Approved By

Prof. Markus Mueller

Report on Electrical Generator Reliability Tools

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Document Revision Record

Revision Date Issued Purpose of Issue and Description of Amendments

Prepared by Approved by

0.1 21/06/2019 Initial Internal Draft Dr. Kaswar Mostafa Prof. Markus Mueller

0.2 09/08/2019 Initial Draft for NOVA Review Dr. Kaswar Mostafa Prof. Markus Mueller

0.3 02/09/2019 Initial corrected Draft for NOVA Review

Dr. Kaswar Mostafa Prof. Markus Mueller

1.0 04/10/2019 Final Public Report Dr. Kaswar Mostafa Prof. Markus Mueller

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Contents

1. Introduction.................................................................................................................... 5

1.1. Background .......................................................................................................... 5

1.2. Description, Aims and Objectives ........................................................................ 5

2. Tidal to Wire model using MATLAB/SIMULINK ........................................................... 6

2.1. Introduction .......................................................................................................... 7

2.2. Tidal Resource Modelling..................................................................................... 7

2.3. Tidal Turbine Modelling ........................................................................................ 8

2.4. Control Strategy ................................................................................................... 8

2.5. Resistive Braking ............................................................................................... 10

2.6. Cable Modelling ................................................................................................. 10

2.7. Generator side Filter Modelling .......................................................................... 10

2.8. Grid Side Modelling ............................................................................................ 11

2.9. Simulation Results ............................................................................................. 13

2.10. Resistive Braking Simulation Results ................................................................. 17

2.11. Real World Data ................................................................................................. 18

2.12. Conclusion ......................................................................................................... 18

3. Mechanical Reliability Modelling Tools ..................................................................... 20

3.1. Generator Finite Element Model ........................................................................ 20

3.1.1. Introduction ................................................................................................................................... 20

3.1.2. Model and Results ........................................................................................................................ 21

3.1.3. Conclusion .................................................................................................................................... 24

3.2. Multi-body Model ................................................................................................ 25

3.2.1. Introduction ................................................................................................................................... 25

3.2.2. Methodology.................................................................................................................................. 25

3.3. Bearing Lifetime Model ...................................................................................... 28

3.4. Results and Conclusion ..................................................................................... 28

4. Electrical Reliability Modelling Tools ........................................................................ 29

4.1. Loss Model ......................................................................................................... 29

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4.2. Thermal Model ................................................................................................... 29

4.2.1. Setup ............................................................................................................................................. 29

4.2.2. Results .......................................................................................................................................... 30

4.3. Stator Winding Lifetime ...................................................................................... 30

5. Conclusion ................................................................................................................... 32

5.1. Summary............................................................................................................ 32

5.2. Further Work ...................................................................................................... 32

5.3. Recommendations for TiPA Generator Reliability .............................................. 32

References ......................................................................................................................... 33

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1. Introduction

1.1. Background

A Funding Grant was awarded from the European Union’s Horizon 2020 research and innovation programme in June 2016 to deliver a new innovative Direct Drive Power Take-Off (PTO) concept for tidal power devices – Tidal turbine Power take-off Accelerator (TiPA). This was in response to the call LCE-07-2016-2017: Developing the next generation technologies of renewable electricity and heating/cooling to increase the performance and reliability of ocean energy subsystems.

1.2. Description, Aims and Objectives

This report describes work undertaken in WP7 to develop a reliability tool-set for tidal energy converters. This is as outlined in the Reliability Framework, which can be found in Deliverable D7.2, PTO Reliability Framework, and which proposes a framework for analysing the reliability and component lifetime of tidal energy systems, covering Task 7.1. Progress made in Tasks 7.2 to 7.4 are outlined in this report. Design tools are developed linked to lifetime models to address the design of critical components within the generator and the power converter. Finite Element Methods (FEM) are used to model and design for extreme loads. SIMULINK is used for system modelling with output feeding design electromagnetic-structural- thermal design and modelling tools. These tools are verified experimentally from the dry and wet testing programmes, providing confidence that they can be used as part of advanced design tools for next generation products. The key task in this work plan was developing a model for the reliability of electrical generators. Summary of failure modes and consequences of generator subsystems and components, presented in D7.2, illustrated the critical components. High temperature was found to be the failure mode for both the permanent magnets demagnetisation and the stator coils’ insulation breakdown. Permanent magnets are demagnetized, and winding insulation is degraded, when operated above their nominal temperature, and hence understanding the thermal performance of the machine is very important. Drivetrain mechanical design is affected by environmental loads and impacts the electromagnetic performance of the machine. The use of seawater internally adds to the challenge of designing for reliability.

Figure 1 Reliability framework showing tasks T7.2-T7.5

The main tasks concerned with developing a reliability model are shown in Figure 1 and summarised below, with more detail provided in this report:

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Task 7.2 is concerned with building a tidal to wire system model. This model is built in SIMULINK and has the tidal flow as an input. It can be considered as a model for the electrical part of the design to drive a more detailed generator model. The outputs of this model include the generator currents which are used as inputs for the electromagnetic model (T7.3) and the power converter reliability model (T7.4). The generator currents are used to calculate losses which will drive a thermal model. Task 7.3 is concerned with developing a generator reliability model, integrating electromagnetic models with structural and component lifetime models. An electromagnetic model for the permanent magnet generator is built using open source finite element software, FEMM. The input for this model is the electrical currents in the stator windings which is provided by the tidal to wire model. The main output of this model is the generator unbalanced magnetic pull UMP, which is an input for the multi-body model in order to assess mechanical life of bearings and the drivetrain structure. The main inputs for the multi-body model are the tidal load data provided by NOVA and the generator UMP obtained from the FEM electromagnetic model. Results will feed into Task 7.5 to assess bearing life. Loss models developed as part of the electromagnetic modelling feed into a thermal model used to assess the risks of permanent magnet demagnetization and winding insulation failure. Task 7.4 is concerned with the development of a power converter reliability model. This model relies on the tidal to wire model and is also built in SIMULINK. In wind energy systems the power electronic converter is highlighted as a problem in terms of reliability. Thermal cycling has been identified as one of the main causes of failure. In order to investigate this further a thermal model was developed by TUD to see if thermal cycling is an issue within tidal current systems. The tidal to wire model developed at UOE was adapted to include detailed power converter modelling linked to a thermal model of the devices, and material models. This task was led and completed by TUD as reported in D7.5.

2. Tidal to Wire model using MATLAB/SIMULINK

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2.1. Introduction

The tidal to wire electrical system model is the basis of the reliability and lifetime model. A full water-to-wire dynamic model of a single tidal current turbine is presented in this section. The model is originally based on two models created by Marios Sousounis [1]–[4] for tidal current conversion systems. Sousounis’ first model was based on a three-bladed tidal turbine with active pitch-angle control, a gearbox, a squirrel cage induction generator (SCIG), long subsea cables, and onshore convertor as shown in Figure 2. The second model was based on a three-bladed tidal turbine with active pitch control and a permanent magnet generator (PMG) controlled using direct torque control with space vector modulation (DTC SVM). This model can utilise dynamic loads and investigate the applicability of onshore converters in the tidal current conversion system (TCCS).

Figure 2 The reference tidal current conversion system model [4]

Elements from both these models have been used to develop a tidal to wire model for the Nova system, resulting in the following changes to Sousounis’ model:

- New two-bladed turbine based on TiPA Cp-λ curve provided by NOVA - New direct drive PMG based on data provided by NOVA - Braking system - New power electronic system - Changing the control strategy to meet the inertia characteristic of direct drive.

Details of each part of the model and simulation results to verify operation of the model are presented in the following sections. The tidal turbine shaft is directly connected to the PMG rotor, which means the inertia seen by the control system is the sum of the turbine, shaft, entrained water, and generator rotor inertias.

2.2. Tidal Resource Modelling

A generic formula is used to simulate the tidal current, based upon the same formula used for wind energy systems (Equation 1).

𝑃𝑡𝑖𝑑𝑒 =1

2 𝜌𝑤𝑎𝑡𝑒𝑟𝐴 𝑉𝑐𝑢𝑟𝑟𝑒𝑛𝑡

3 (1)

Where 𝜌𝑤𝑎𝑡𝑒𝑟 water is the sea water density approximately equal to 1027 𝑘𝑔. 𝑚−3, 𝐴 is the swept area by

the tidal turbine blades and 𝑉𝑐𝑢𝑟𝑟𝑒𝑛𝑡 is the fluid speed in 𝑚/𝑠. The input flow is chosen to be a half-cycle with the highest peak flow to represent the most complex period of operation of the system. The flow profile can consist up to 3 components:

1. The mean flow speed which is created based on actual tidal current measurements from an earlier project (Figure 3a).

2. The predicted turbulence which is modelled by adding white noise. 3. The swell effect, by using a first-order Stokes model.

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The flow profile used as input to the model can be seen in Figure 3a. The tidal flow speed with swell effect and turbulence is shown in Figure 3b.

Figure 3 a. Mean tidal flow speed used as input to the TCCS model. b. Tidal flow speed with swell effect and turbulence.

2.3. Tidal Turbine Modelling

The model is based on the steady-state power characteristics of the turbine provided by Nova. The output power of the turbine is given by the following equation:

𝑃𝑚 = 𝐶𝑝(𝜆). 𝑃𝑡𝑖𝑑𝑒 (2) Where 𝑃𝑚 is the mechanical output power of the turbine in Watts and 𝐶𝑝(𝜆) is the power coefficient of the

turbine which is a function of the tip speed ratio 𝜆. In this model a maximum 𝐶𝑝 of 0.39 is assumed and rated

power is achieved at 2.4 m/s.

Figure 4 The tidal turbine block model

Dividing the turbine mechanical output power over the turbine rotational speed gives the generator mechanical input torque 𝑇𝑚:

𝑇𝑚 =60 𝑃𝑚

2𝜋 𝑁𝑟𝑝𝑚 (3)

The tidal turbine block model, shown in Figure 4, has two inputs: the tidal flow speed (m/s) and the tidal turbine rotational speed (rpm), and one output which is the generator input mechanical torque (Nm).

2.4. Control Strategy

In order to ensure variable speed operation, the generator is controlled from a voltage source controller VSC using DTC SVM. DTC SVM methods are based on the classical DTC [5] but they also operate at constant switching frequency. For the generator controller, the DTC SVM scheme with closed-loop torque was implemented, as shown in [6].

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The proposed control strategy is based on the measured value of the shaft rotational speed. Control is achieved according to the general equation of motion for a rotary generator (Equation 4) by controlling the generator electrical torque 𝑇𝑒

𝑇𝑚 − 𝑇𝑒 = 𝐽𝑑𝑤

𝑑𝑡 (4)

Where 𝐽 is the moment of inertia of all rotating parts (tidal turbine rotor, shaft, generator rotor and entrained water). Two MATLAB functions called “SupervisoryController” and “RegionDetector” are used in the model as shown in Figure 5. Those functions implement the control strategy for a fixed-pitch, variable-speed system. The control strategy is based on dividing the operation process into regions, detecting the working region according to the actual rotational speed, then setting the reference torque limitations. Depending on the working region, the overall controller controls the circuit breakers to connect and disconnect the tidal turbine to the grid.

Figure 5 Block diagram showing the control strategy for a variable-speed system

The operation process can be divided into the following regions:

1- Region 1: When the rotational speed is under 10rpm, 𝑇𝑒 = 0 and increases quickly. (StartUp1=0, StartUp2=1).

2- Region 2: When the rotational speed is greater than or equal to cut-in speed and is less than or equal to maximum operating speed, the tidal turbine is connected to the grid (StartUp1=, StartUp2=0). The reference rotational speed 𝑁𝑟𝑝𝑚𝑟𝑒𝑓

, as shown in Figure 6, is extracted from the

actual mechanical turbine torque as:

𝑁𝑟𝑝𝑚𝑟𝑒𝑓= 𝐾𝑜𝑝𝑡 . √𝑇𝑚 (5)

Where 𝐾𝑜𝑝𝑡 is the torque factor, which sets shape of speed-torque curve for optimum operation.

The speed controller is then used to compare the actual rotational speed 𝑁𝑟𝑝𝑚 and the reference

rotational speed 𝑁𝑟𝑝𝑚𝑟𝑒𝑓 to extract the reference electrical torque using a PI controller.

Figure 6 The control strategy

3- Region 3: When the tidal flow speed is greater than the nominal operating speed, and the speed power limit is greater than maximum operating speed, the reference rotational speed is fixed at the maximum operating speed. Speed power limit is the rotational speed value that limits the generated power to a certain value.

𝑆𝑝𝑒𝑒𝑑 𝑝𝑜𝑤𝑒𝑟 𝑙𝑖𝑚𝑖𝑡 =𝑃𝑜𝑤𝑒𝑟 𝐿𝑖𝑚𝑖𝑡 [𝑘𝑊] ∗ 1000 ∗ 30

𝑇𝑚 ∗ 𝐸𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑎𝑙 𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 ∗ 𝜋 (6)

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4- Region 4: When the speed power limit is less than the maximum operating speed, the reference speed then equals the speed power limit.

2.5. Resistive Braking

Power limitation in high tidal current flows could be achieved by using resistive braking. This action

corresponds to increasing the generator electrical torque 𝑇𝑒 reducing the shaft rotational speed according to Equation 4. According to the tip speed ratio equation:

𝜆 =𝑤. 𝑟

𝑣 (7)

According to the tip speed ratio 𝜆 (Equation 7), decreasing while the tidal flow 𝑣 is increasing, will lead to

a reduction in 𝜆, and thus 𝐶𝑝will be reduced causing lower mechanical power captured.

2.6. Cable Modelling

The subsea cables are modelled with a network of π-sections in order to accurately represent the uniform distribution of the cable resistance 𝑅𝐶, inductance 𝐿𝐶 and capacitance 𝐶𝐶.

Figure 7 The 3-phases subsea cables block as seen the model

The number of identical π-sections required to accurately represent frequency transients is given by the following equation:

𝑁 =8 𝑙𝑐 𝑓𝑚𝑎𝑥

𝑣𝑐 (8)

Where 𝑣𝑐 is the travelling velocity of the waves in the cables and is defined in equation (9).

𝑣𝑐 =1

√𝐿𝑐 𝐶𝑐

(9)

The subsea cables block in the model is shown in Figure 7.

2.7. Generator side Filter Modelling

The optimised passive filter for the generator side is based on a second-order LCR (Low Voltage LCR) filter for overvoltage mitigation, which is described in detail for a converter-cable-generator system in [7], for a converter-cable-motor system in [8] and for a converter-transformer-cable-motor system in [9]. In this project, we are modelling a generator-converter-cable system. In this case the LV LC R filter is designed to reduce the overvoltage at the generator terminals and minimise the effects of resonance in the cables while at the same time the single tuned filter, tuned at the switching frequency of the controller, will mitigate the harmonics generated by the VSC that controls the generator. Figure 8 shows the generator side of the TCCS with the different options of filtering techniques.

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Figure 8 Block diagram of the generator side of the TCCS. a. System without filters b. System with a LV LC R filter c. System with an

LV LC R filter and a single tuned filter.

Figure 9 Generator side filter block diagram

The parameters of the LV LC R filter are calculated using equations (10) – (12) which are described in detail in [8].

𝑅𝑓𝑖𝑙𝑡𝑒𝑟 = 2 √𝐿𝑓𝑖𝑙𝑡𝑒𝑟

𝐶𝑓𝑖𝑙𝑡𝑒𝑟= |𝑍𝑐| (10)

√𝐿𝑓𝑖𝑙𝑡𝑒𝑟 𝐶𝑓𝑖𝑙𝑡𝑒𝑟 ≥ 𝑡𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙 (11)

𝑡𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙 = 15 𝑙𝑐 √𝐿𝑐𝐶𝑐 (12)

The PMG side filter components as presented in the model are shown in Figure 9.

2.8. Grid Side Modelling

The power generated by the TCCS is delivered to the grid through a VSC. The grid-tied inverter is connected to the grid through a filter that reduces harmonics, a step-up transformer and transmission lines as shown in Figure 10. The inverter is controlled by a PWM scheme called voltage oriented control (VOC) with decoupled controllers [10] which ensures a constant DC link voltage, constant frequency output on the AC side and control over the amount of reactive power flowing based on grid requirements.

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Figure 10 Control structure of the grid side controller

Figure 11 Grid side filter

Figure 12 Grid side voltage-oriented control

Figure 13 PWM (pulse width modulation) of the grid side VSC

The equations that describe the output of the VOC with decoupled controllers are:

𝑣𝑑𝑖 = −𝑃𝐼(𝑠). (𝑖𝑑𝑔∗ − 𝑖𝑑𝑔) + 𝑤𝑔. 𝐿𝑔. 𝑖𝑞𝑔 + 𝑉𝑑𝑔 (13)

𝑣𝑞𝑖 = −𝑃𝐼(𝑠). (𝑖𝑞𝑔∗ − 𝑖𝑞𝑔) + 𝑤𝑔. 𝐿𝑔. 𝑖𝑑𝑔 + 𝑉𝑞𝑔 (14)

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Based on equations (13) and (14) the control structure implemented can be seen in Figure 13. Figures 11-13 show the grid side components.

2.9. Simulation Results

The actual tidal flow time is reduced by a factor of 30 in order to reduce the simulation run time. The simulation run time is set to 820 seconds for the half cycle which represents 6.83 hours. Figure 14 shows the tidal flow speed which starts at 0.35m/s then increase gradually up to 4m/s and after 4.25 hours the speed starts to decrease for about 2.55 hours to the end of the half cycle. Changing the tidal flow according to the site will have significant effect on the simulation results.

Figure 14 Tidal flow speed [m/s]

The simulation results show that the control system is perfectly doing what is expected from it because the actual speed is matching the reference speed during the operating period. When starting the simulation, the actual speed is 0rpm while the reference speed is set to cut-in speed. According to the simulation results, it takes the turbine about 12min to get to cut-in speed when starting from stall with low flow speed. The reference speed then starts to increase (region 2) as explained in the control strategy section 2.4. The turbine mechanical torque, and the turbine power, shown in Figure 15, also increase with the tidal flow increasing. The turbine gets to maximum operating speed before rated tidal flow (region 3) and the control works to keep the speed constant while the tidal flow is increasing which leads to decrease in the TSR, which also leads in reduction in the power coefficient. At this point there is a need to increase the power up to the nominal power limit. According to the simulation results, it takes the turbine about 8min to get to the nominal power limit after reaching the maximum operating speed limit. Region 4 starts when the turbine power reaches the nominal power limit. At this point, the only way to keep the output power constant while the tidal flow is increasing is to reduce the turbine power coefficient which happens by reducing the TSR according to the turbine (𝐶𝑝 − 𝜆). Reducing TSR require

reducing the rotational speed.

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Figure 15 Turbine power [W]

The generator side three phase currents are shown in Figure 16. The currents increase with the increase of the turbine power. The controller reaction when the turbine speed gets to the maximum operating speed is clear on the generator currents where a noticeable reduction occurs. Figure 17 shows the generator currents for 1 second period of time.

Figure 16 Generator side three phase currents [A]

Figure 17 1 second generator side three phase currents [A]

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Figure 18 Generator-side three-phase voltages [V]

Figure 19 1 second Generator-side three-phase voltages [V]

Figure 20 DC voltage [V]

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Figure 21 Grid-side three-phase currents [A]

Figure 22 0.2 second Grid-side three-phase currents [A]

The generator three phase voltages zoomed of 1 second period are shown in Figure 19. The DC voltage is shown in Figure 20. The grid side three phase currents with a 0.2 second zoomed period are shown in Figures 21 and 22. The grid side frequency is 50Hz. The peak voltage is controllable be the grid side transformer and the DC link voltage.

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2.10. Resistive Braking Simulation Results

A simplified MATLAB model for the resistive braking alone was created as shown in Figure 23.

Figure 23 Resistive braking model

Resistive braking can be functional when the tidal flow is below a certain value. The model shows that applying the resistive braking when the flow speed is above that value will not on its own reduce the rotational speed. Under this condition the tip speed ratio and the 𝐶𝑝 value will not decrease and, hence, braking will not occur as tidal power is greater than resistor absorption power. Depending on the control strategy, the rotational speed can be controlled to stay below the maximum operating speed with higher tidal speed to extract maximum possible energy. Resistive braking is practical and reliable with the limitation of providing sufficient braking force only up to a certain tidal flow speed. Hence, it is essential to have another emergency braking system to help stop the turbine in case of a fault when the tidal flow speed is above the resistive braking limit. The electrical braking limit can be increased by adding capacitive load bank to the resistive load bank. That requires further research and is recommended for future work.

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2.11. Real World Data

The model results are compared to real world data from WP5. Figure 24 shows a picture of multiaxial load demonstrator test rig with TiPA as the PTO under test. The actual generator design has included stator waterproofing solution to protect and isolate the stator coils. This waterproofing is not included in the water to wire model.

Figure 24 Picture of multiaxial load demonstrator test rig with tidal turbine subsystem prototype as PTO under test

The output power and overall performance of the PTO was tested at discrete operating points of the speed/torque characteristic of the turbine controller. The dry (generator filled with air instead of water) power curve test is used to create a baseline for performance data for comparing different power curve tests (with multiaxial loads and/or water filled generator). Both the design curves used for test design, and the lab test results were used to validate the water-to-wire model results. It has been demonstrated that not only does the water-to-wire model match the design curves for the system, but that it also shows good correlation (less than 5% error at rated operation) with lab test results once un-modelled losses (e.g. stator waterproofing and test equipment losses) are accounted for.

2.12. Conclusion

In this model, an alternative way of integrating TCCS with direct drive PM generator is proposed. The analysis of this model focuses on controlling the turbine’s rotational speed in order to maximise the captured tidal power according to the turbine (𝐶𝑝, 𝜆) characteristics when the tidal flow is lower than rated flow speed and

limit the captured tidal power when the tidal flow is over the rated flow speed. From the analysis results acquired, it is concluded that the adopted control strategy is appropriate for controlling and stabilizing the direct drive system. The resistive braking unit is found to be useful for emergency braking when tidal flow speed is lower than a certain limit, taking the largest possible turbulence in account. The higher the turbulence the lower the tidal speed limit for the electrical braking system. Extending the electrical braking system to work for higher tidal flow speed is not included in this study and it is recommended for future research. The advantage of extending the electrical braking system to work at highest possible tidal flow speed “including the turbulence”

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would cancel the need for a mechanical braking system for the tidal turbine. That would reduce both the capital and operational costs leading to a reduction in the Levelized Cost of Energy LCoE, which is the main goal. The stator waterproofing solution that insulates and protects the stator is not included in this model. The model results match the lab testing results when disregarding the stator waterproofing and test rig losses. The outputs from this model are used as inputs to the following reliability modelling tools.

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3. Mechanical Reliability Modelling Tools

3.1. Generator Finite Element Model

3.1.1. Introduction

An electrical machine produces both tangential and radial electromagnetic forces. In a radial flux permanent magnet RFPMG machine, the tangential force generates a beneficial rotating torque while the radial force produces wasted torque. In theory, the radial electromagnetic forces in a perfectly centred rotor in a symmetrical RFPMG machine are cancelled out and the machine generates zero net radial force. In practice, however, a net radial electromagnetic force always exists, and most machines run with some degree of rotor eccentricity. The stator and rotor in a PMG are physically separated by a very small gap that does not exceed a few millimetres. The non-uniformity of this gap results in unbalanced magnetic pull (UMP) inside the machine. The probability of radial shaft misalignment can be a major contributor to eccentricity. Shaft misalignment gives rise to a dynamically eccentric rotor disturbing the equilibrium of the magnetic attraction forces that result in a periodical radial load on the bearings, undesirable noise and vibration due to the increase in space harmonics [11].

Figure 25 Schematic drawing for a rotor eccentricity

Several types of rotor eccentricities can be distinguished [12]. Static, dynamic, and mixed rotor eccentricities are the main types considered in the literature [11]–[15]. Figure 25 shows a schematic drawing for the rotor position inside the stator bore before and after a dislocation. Here the value 𝑤𝑟 is the rotor rotational speed around its own axis, 𝑔 is the uniform mechanical gap length when the rotor is concentric, 𝑒 is the rotor

eccentricity and 𝑤𝑒 is rotor axis rotational speed around the stator axis.

Ideally, the rotor should be concentric, and its rotational axis is identical to the stator bore axis, i.e., 𝑒 = 0. However, when the rotor is rotating around a shifted axis relative to the stator bore axis, by some fixed distance 𝑒, then a static eccentricity is said to exist. Essentially, static rotor eccentricity occurs when 𝑒 =𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 and 𝑤𝑒 = 0. If the rotor rotational axis is not stable and moving around the stator bore axis with constant angular velocity 𝑤𝑒 and constant distance 𝑒, then the eccentricity is a uniform dynamic eccentricity. The value 𝑤𝑒 is normally

less than or equal to the rotor angular velocity 𝑤𝑟. The most realistic rotor eccentricity type is a mix of static and dynamic variants. In such scenarios, the variable, 𝑒, changes over time. As long as 𝑒(𝑡) < 𝑔, there is no severe or catastrophic failure as a result of contact between the rotor and the stator. Bearing wear, however, is a possibility where 𝑒(𝑡) > 0, and one

expects increasing wear with larger 𝑒(𝑡) values.

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3.1.2. Model and Results

An open source Finite Element Methods Magnetics software (FEMM) was used to model the generator.

Figure 26 (a) Shaft displacement, (b) concentric rotor, (c) eccentric rotor

As shown in Figure 26, the rotor rotational direction is counter-clockwise around the x-axis and the

eccentricity occurs in the Y-Z plane. Assuming y(t) and z(t) to be the incremental shaft displacements, in the Y-Z plane, measured at any instant t. Then the dynamic change in the gap, denoted as g(t) can be obtained from the incremental shaft displacement along the Y and Z axis as

𝑔(𝑡) = √𝜕𝑦2(𝑡) + 𝜕𝑧2(𝑡) (15)

Static eccentricity simulations were carried out as they represent the worst possible condition that can be experienced by the generator. The rotor was displaced from 10% up to 60% of the mechanical gap length. Practically, considering the stator waterproofing solution, the mechanical gap is less than 70% of the magnetic gap. That is the reason behind considering only up to 60% rotor eccentricity. Figure 27 shows the change in the water-gap magnetic flux density magnitude when applying 20% static rotor eccentricity compared to the concentric case.

Figure 27 Magnitude of normal flux density with concentric case and 20% static rotor eccentricity case

The resultant force in the generator was obtained from the water-gap flux density variation and was approximated as a function of the static rotor eccentricity (𝑒𝑠𝑡𝑎𝑡𝑖𝑐 ) as shown in Figure 28, and given by:

𝑈𝑀𝑃 = 14.04 × 𝑒𝑠𝑡𝑎𝑡𝑖𝑐 − 0.917 [𝑘𝑁] (16)

Armature reaction effect on UMP is very small [11]–[13], [15], therefore, it was disregarded in this model. A simple method for converting static eccentricity into dynamic eccentricity was done by considering the frequency of shaft displacements, 𝑤𝑠. The two different components of the resultant dynamic force along Y-axis and Z-axis were then resolved for the generator as:

𝑈𝑀𝑃𝑌𝑑𝑦𝑛𝑎𝑚𝑖𝑐= (14.04 × 𝑒(𝑡) − 0.917) cos 𝑤𝑠𝑡 [𝑘𝑁] (17)

𝑈𝑀𝑃𝑧𝑑𝑦𝑛𝑎𝑚𝑖𝑐= (14.04 × 𝑒(𝑡) − 0.917) sin 𝑤𝑠𝑡 [𝑘𝑁] (18)

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Figure 28 Static rotor eccentricity and the induced UMP in TiPA generator

The bearings in TiPA project are located at one end, hence, it is important to consider tilting eccentricity shown in Figure 29, especially when studying the UMP effect on the bearing lifetime. Calculating the UMP induced by a tilting rotor eccentricity requires using a 3D FEA software. The open source FEMM software is a 2D software. Hence, to calculate the UMP using a 2D software, an analytical model had to be included. Dividing the rotor into large number of slices (𝑚 + 𝑞) then calculating the UMP induced on each slice due to the eccentricity is the analytical way chosen to calculate the force applied on the bearing due to tilting rotor eccentricity. Assuming the tilting is occurring around an imaginary axis, then 𝑚, 𝑞 are the generator slice

numbers on the two sides of the tilting axis. 𝑚 & 𝑞 are constants if the tilting eccentricity is static, whereas, they are variables with dynamic tilting eccentricity. Torque around the axis of rotation is given by:

𝑇 = ∑ 𝐴𝑛𝐹𝑛

𝑚

𝑛=1

+ ∑ 𝐴𝑛𝐹𝑛

𝑞

𝑛=1

(19)

Where, 𝐹𝑛 is the net magnetic force induces on the slice number 𝑛 because of the eccentricity and 𝐴𝑛 is the

distance between this slice and the axis of tilting. 𝑚 is the number of slices in one side of the axis of rotation

whereas 𝑞 is the number of slices on the other side depending on the location of the axis of rotation. There is a linear relationship between rotor static eccentricity and the induced UMP and can be expressed as: 𝐹𝑈𝑀𝑃 = 𝐵𝑥 + 𝐶 (20)

Where, 𝐵 and 𝐶 are constants related to the machine size and type. 𝑥 is the rotor eccentricity as a percentage

of the generator mechanical gap. Assuming the length of the rotor is 𝐿, then the length of each slice and the eccentricity 𝑥 are:

𝑑𝐿 =𝐿

𝑚 + 𝑞 (21)

𝑥 =

𝑛. 𝑑𝐿. tan 𝜃

𝑎

(22)

where, 𝜃 is the tilting angle and 𝑎 is the normal gap length. Substituting Equations (20), (21), and (22) in (19) results:

𝑇 = ∑(𝑛. 𝑑𝐿)(𝐵. 𝑛. 𝑑𝐿.𝑡𝑎𝑛𝜃

𝑎+ 𝐶)

𝑚

𝑛=1

+ ∑(𝑛. 𝑑𝐿)(𝐵. 𝑛. 𝑑𝐿.𝑡𝑎𝑛𝜃

𝑎+ 𝐶)

𝑞

𝑛=1

(23)

When (𝑚 = 𝑞), the torque becomes:

𝑇 = 2 ∑ 𝐵. 𝑛2. 𝑑𝐿2.𝑡𝑎𝑛𝜃

𝑎+ 𝑛. 𝑑𝐿. 𝐶

𝑚=𝑞

𝑛=1

(24)

The force applied on the bearing because of the tilting eccentricity will be:

𝐹𝑏𝑒𝑎𝑟𝑖𝑛𝑔 =2 ∑ 𝐵. 𝑛2. 𝑑𝐿2.

𝑡𝑎𝑛𝜃𝑎

+ 𝑛. 𝑑𝐿. 𝐶𝑚=𝑞𝑛=1

𝐿

(25)

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Figure 29 Schematic drawing for tilting rotor eccentricity

The generator was divided into 100 slices axially then the UMP induced in each slice due to a certain static eccentricity was calculated using FEMM. Figure 30 shows the UMP induced in one slice due to static eccentricity. Assuming that the tilting is occurring around the centre of gravity of the generator, that means 𝑚, 𝑞, which are the generator slice numbers on the two sides of the tilting centre, are equals. Applying Equation (25) gives the total induced UMP because of different rotor tilting angles in the generator as shown in Figure 31.

Figure 30 UMP induced in one slice of the generator due to static eccentricity showing the best fit line and equation

Figure 31 UMP induced in the generator due to tilting rotor eccentricity showing the best fit line and equation

The resultant UMP in the generator due to 𝑒𝑡𝑖𝑙𝑡𝑑𝑒𝑔

number of degrees was obtained from the water-gap flux

density variation of each slice and was approximated as a function of the tilting degree and given by:

𝑈𝑀𝑃𝑡𝑖𝑙𝑡 = 32.477 × 𝑒𝑡𝑖𝑙𝑡𝑑𝑒𝑔− 0.9268 [𝑘𝑁] (26)

Comparing the UMP induced in the generator because of similar static, dynamic, and tilting rotor eccentricities shows that the static eccentricity is generating the highest UMP.

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For example, 20 % rotor eccentricity induces about double UMP value than the UMP induced by a tilting rotor eccentricity where the furthest slice from the rotational axis is 20% eccentric. Hence, it is enough to consider the static rotor eccentricity in the multi-body model. In conclusion, as having the maximum effect, it is enough to consider the maximum static rotor eccentricity when it comes to bearing design.

3.1.3. Conclusion

The inputs for this model are the generator specifications and the currents in the stator coils. The water to wire model provides the stator currents for each tidal flow speed. The magnetic field generated by the rotor’s permanent magnets is in the order of 20 times higher than the magnetic field generated by the stator currents (the armature reaction). Hence, the armature reaction can be disregarded. Comparing the effect of different types of rotor eccentricities (static, dynamic, and tilting), the static rotor eccentricity generates the highest UMP. Therefore, the generator (UMP/Static rotor eccentricity) Equation 16 is considered in the multi-body model in the next section. This equation is the output of this model and the input for the multi-body model.

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3.2. Multi-body Model

3.2.1. Introduction

Operational experience from existing direct-drive wind turbines to corroborate the claim of the possible consequences of the generator eccentricity and unbalanced magnetic pull (UMP) on vibration, noise and bearing wear is not broadly published [16]. Designers, therefore, tend to rely on numerical simulation techniques to make inferences on the dynamics of the drive-train [17]. For such a problem, multi-body simulation (MBS) techniques are commonly used in the industry. Similarly, the dynamics of a tidal turbine drivetrain can be examined using MBS technique. Tidal turbine components, in this technique, are modelled as rigid or elastic bodies connected by kinematic constraints or force elements. The motion equations of the components, then, are solved using a set of computation algorithms. MBS tools deliver efficient understandings of the dynamic loading of the drivetrain taking in account all related loading conditions and system-wide interactions that exist in a tidal turbine system. There are no studies available from tidal energy projects regarding the dynamics of direct drive generators. On the other hand, limited studies on the dynamics of direct-drive generators in wind turbines have been conducted in the past. There is similarity in multi-body modelling between wind and tidal. Poore and Lettenmaier [18] in 2001 analyzed and compared different drive-train and generator design combinations for wind turbines rated between 0.75-3 MW. The proposed 1.5 MW direct-drive design used two inverted-arrangement main-shaft tapered roller bearings engineered to meet the specified life as shown in Figure 32. A connection torque tube made of ductile iron is mounted on the bearings and connected to the main shaft through the bearings on one side and to the generator rotor on the other side. Even though, a single large diameter bearing design would allow a direct connection between the rotor hub and the tower support structure, it was disregarded because the benefits were not obvious to the authors and the risk was seen as relatively high. Experimental tests on this design showed no vibration problems with the generator, although up to 50% eccentricity was permitted during extreme loads [19] [20].

Figure 32 Section view of nacelle and main shaft area. Modified from: [18]

Sethuraman et al. [16], [17], [21], [22] also used MBS to study the dynamics of a 5 MW direct-drive floating wind turbine. The results showed very small effect of the extra motions of the floating wind turbine on the rotor eccentricity and UMP with the generator design tolerances being fairly preserved. Extensive comparisons between land-based wind turbine and floating wind turbine were presented showing additional excitation caused be extra axial loads and tilting moments in the floating wind turbine.

3.2.2. Methodology

Time-domain multi-body simulation tool, SIMPACK [23], is used to examine the drive-train dynamic behavior as shown in Figure 33. SIMPACK is a multi-body simulation software that generates detailed kinematic and dynamic analysis of drive-train components by means of integrated tidal turbine simulation, incorporating the various forces and control elements. The global motion response and drive-train loads are supplied by NOVA and fed to a detailed stand-alone drive-train model in SIMPACK. The response statistics for shaft displacements, eccentricity, forces due to UMP, and the main bearing reactions are computed.

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For modelling the permanent magnet generator (PMG) in SIMPACK, reference is made to [17]. The generator mass and inertia properties were required to complete this step. The bearings are modelled as 6 degree of freedom (DoF) springs with certain stiffness values. The bearing radial, axial and tilting stiffness values were required to complete this task. A simplified analytical model for UMP force is implemented, based on [22], by measuring the eccentricity due to shaft displacement at every time-step. The analytical model relates the dynamic change in the water gap caused by radial shaft displacement to unbalanced magnetic forces, using a linear relationship given in Equations 17 &18. Two main reactions are included in SIMPACK model which are (a) eccentricity that induces unbalanced magnetic pull and (b) shaft vibrations that appear as bearing load and torsional vibrations in the drivetrain.

Figure 33 Multi-body model of the direct-drive tidal turbine in SIMPACK

Figure 34 shows the coordinate system that is used in this model to define the directions of the loads and bending moments. Figure 35 shows an example of hub load case Mx at a certain tidal speed. Figure 36 shows a screenshot of SIMPACK software running TiPA generator model.

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Figure 34 Definition of coordinate system, according to IEC 61400

Figure 35 Example of hub load case

Figure 36 Screenshot of SIMPACK software with simplified TiPA generator

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3.3. Bearing Lifetime Model

The generator system generates significant amounts of heat that might change the dimensions of the air gap causing a variation and UMP. Further expansion can occur at the shaft and in the housing. Humidity effects and moisture can cause bearing materials to oxidize and degrade over time. Such considerations require sealing of bearing elements [24] . More can be added to these considerations of the speed of operation of the tidal turbine. The specific bearing should be selected to accommodate the rated rotational speed of the turbine – in the case of TiPA tidal turbine; this is relatively slow. The lower speed implies a higher loading per roller over a given time frame that can lead to various issues such as flattened areas in rolling elements and indentations in raceways (that is unlikely to happen in TiPA design). Generally, such damage may also occur in an irregular fashion. Such deformations can also lead to higher vibration and noise levels as well as jamming. For large loads at slow speeds, the static load conditions should be a primary consideration when choosing or designing a bearing. These reliability considerations are discussed further project deliverable D7.2. Assuming appropriate design to avoid the above reliability issues, the analytical formula for a cylindrical bearing 𝐿𝑐𝑦 is shown in Equation (31). Likewise, the formulation for the other two bearings

(𝑆𝑝ℎ𝑒𝑟𝑖𝑐𝑎𝑙 𝐿𝑠𝑝𝑎𝑛𝑑 𝑡𝑎𝑝𝑒𝑟𝑒𝑑 𝐿𝑡𝑝) can be represented as shown in Equation (32).

𝐿𝑐𝑦 =106

60𝑛(

𝐶

𝑃)

𝑝

(31)

𝐿𝑠𝑝 = 𝐿𝑡𝑝 = 2106

60𝑛(

𝐶

𝑃)

𝑝

(32)

For a cylindrical roller, the value of the exponent 𝑝 is 10/3, the value n is the rated speed of operation of the turbine, C is the basic dynamic load rating and P is the equivalent dynamic load. The resultant lifespan is given in hours of operation. This understanding can be used to further evaluate the life span of both the spherical and tapered single bearing using simple geometric considerations.

3.4. Results and Conclusion

Both rotor side RS and generator side GS bearings are high stiffness bearings supplied by SKF. Different axial, radial and tilt stiffness cases were considered for a sensitivity analysis. In all cases, the displacement in X, Y, and Z directions were smaller than 50µm. That results in over 8 million life span hours according to the analytical formula Equation (31). In conclusion, the inputs for the multi-body model were a load case provided by NOVA and the UMP equation produced from the FEA generator model. The main finding of this model is that the bearing units are very reliable with high lifetime suggesting that there is potential to optimize the bearing design further.

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4. Electrical Reliability Modelling Tools

4.1. Loss Model

Ohm loss in the stator windings can be calculated as:

𝑃𝑜ℎ𝑚 = 3 ∗ 𝐼2 ∗ 𝑅 = 3 ∗ 𝐼2 ∗ (𝜌𝑐𝑜𝑝𝑝𝑒𝑟 ∗ 𝑙

𝐴) (30)

Ohm loss was found to consume about 4% of the rated power when working at full load. An additional source of losses that is not included in the models presented was identified as being non-negligible during testing. This loss, which relates to the design of the stator waterproofing solution is modelled and presented as part of D7.7, alongside design iteration to remove or minimize this source of loss. The modelled losses from the generator are relatively low, which is to be expected for a machine design driven by extreme events e.g. braking. Decreasing the winding losses further can be achieved by increasing copper but this adds cost, so it is not recommended. The loss values calculated are used as inputs to the thermal model below.

4.2. Thermal Model

4.2.1. Setup

This has involved using a thermal model to simulate the solid conduction of heat from the power source within the generator both outwards towards the sea as well as inwards towards the centre of the machine. The goal is to ascertain the worst-case scenario temperature rise of the machine components during operation, to make conclusions regarding the thermal reliability of the machine. In the current simulation, a simplified version of NOVA’s machine design was recreated. The design comprises a stationary part (stator), a rotating part (rotor), and an active part representing the power coils. The magnets are not included. The design is shown in Figure 37.

Figure 37 Generator modelling geometry

When performing simulations, an imported CAD file can be examined to highlight hollow or empty volumes within the solid geometry and give them material properties, often that of a fluid. These volumes were

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extracted using CFD. Three additional parts were created as a result. The three regions comprise two air gaps, one in each of the rotor and stator, as well as one water gap. A separate CFD simulation was carried out to define an appropriate heat transfer coefficient for the outside of the machine based on forced convection due to a constant tidal current. The average heat transfer coefficient from this simulation was applied to the outside surface of the machine to perform the thermal simulations. The thermal simulations were also run in steady state. This means with a continuous constant heat source on the inside of the machine and a continuous constant value of cooling on the outside, the temperature distribution throughout the machine would then stabilise. All values shown are steady state.

4.2.2. Results

Comparing the results of two independent thermal models, the maximum winding temperature seen was less than 30degC above ambient. This represents the most arduous long-duration operation point for the machine, where it will be subject to relatively high losses for a long duration. An example plot from a model setup test-case is shown in Figure 38. For all sites where sea temperatures remain below 30degC, this would result in winding temperatures remaining below 60degC. This value will be fed into the lifetime model, providing a conservative lifetime value.

Figure 38 Temperature distribution on outer surface

4.3. Stator Winding Lifetime

Electrical insulation systems are subjected to different types of stresses: thermal, electrical, ambient, and mechanical. Each of them can cause one or more kinds of degradation process and could lead to a machine winding failure. In the case of TiPA generator, thermal loading is the critical factor for the stator winding lifetime. Thermal stress is directly linked to Ohm losses in the wires. The thermal model and CFD simulation show that the insulation temperature does not exceed 60degC. That gives a high lifetime prediction as shown in Figures 39 & 40. Machine manufacturers produce standard curves showing lifetime vs temperature for common insulation materials, for example, Figure 39 shows insulation life in hours vs total temperature for four different classes of insulation [25]. Figure 40 shows similar information, but in terms of failure rate. Such curves will be used to determine insulation life using the results of temperature from thermal modelling. These curves can be determined from lifetime models developed by Dakin and described by Portugal in [26].

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Even assuming the lowest winding class (A), a winding temperature of 60degC leads to an expected lifetime that is greater than shown on typical lifetime graphs. Extrapolating from the graph below, the Class A curve would reach a lifetime of approximately 400,000hrs; this is more than twice the design life of the machine. As expected for a low current density, well-cooled machine, winding temperature is not a dominant factor in generator lifetime. It is noted however that for the region of operation of the TiPA generator, a 10degC increase in operating temperature results in a halving of expected winding life. This strong dependence means that any thermal design changes should be considered carefully as a small change can have a large impact.

Figure 39 Insulation life for different insulation classes.

Figure 40 Failure rate data for different insulation classes [27]

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5. Conclusion

5.1. Summary

This report summarises the generator reliability modelling tools developed during the TiPA project. The first model presented in this report is the water to wire model. The model results match the expected results without the stator waterproofing solution. The generator electrical currents as an output of this model was input for the generator electro-magnetic Finite Element model. For the generator electro-magnetic Finite Element model, different rotor eccentricity types and the induced UMP were presented. Static rotor eccentricity was found to generate the highest UMP. An output of this model was the UMP/Eccentricity equation which was an input for the multi-body model. Sensitivity analysis and prediction of the bearing’s stiffness matrix required to stabilise the system were the outputs of the multi-body model. The output of the winding loss model was an input for the thermal model, which concluded that the temperature inside the generator is less than 30 degrees C above ambient. Some results were able to be verified by real world data from WP5. It is noted that losses within the stator waterproofing solution are not currently modelled, however the design iteration of the waterproofing solution, and modelling of any remaining losses will be covered as part of D7.7. The generator is found to be of high reliability, with room for design optimisation to reduce LCoE without compromising lifetime reliability.

5.2. Further Work

- The main focus for immediate further work is to, modify the water to wire model to include the stator waterproofing then re-validate the model with WP5 test rig results. This tool can then be used to assess the optimised design developed as an output of WP7.

- Beyond this, the existing tools could be used to develop an optimised design of electrical braking system that works at a greater range of tidal flow speeds with turbulence.

- A specific tool for the reliability of the rotor’s permanent magnets could be developed and linked to

the thermal model.

- The generator electromagnetic finite element tool could be extended to optimize the copper content in the stator windings to improve the LCoE.

- The modelling tools could be extended to cover a broader range of generator designs.

- Following further tool iteration and validation, it may be desirable to make a mature toolset more

available to a broad range of users. This could include, further parameterisation, development of user manuals, and potentially translation into open-source software. For example, using MBDyn software for the multi-body model instead of SIMPACK.

5.3. Recommendations for TiPA Generator Reliability

The reliability of TiPA generator is found to be high for the system lifetime. In order to further improve the reliability of TiPA generator, the only recommendation out of the modelling tools is to replace the stator waterproofing solution to minimise the heat loss in the generator. This and other recommendations for TiPA generator design optimization are covered as part of D7.7.

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Reference: TIPA-EU-0038 Report on Electrical Generator Reliability Tools Issue: 1.0

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