Marine Current Energy Conversion

Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 1353

STAFFAN LUNDIN

ACTA UNIVERSITATIS UPSALIENSIS ISSN 1651-6214 ISBN 978-91-554-9510-7 UPPSALA urn:nbn:se:uu:diva-280763 2016 Dissertation presented at Uppsala University to be publicly examined in Polhemsalen, Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, Wednesday, 4 May 2016 at 13:15 for the degree of Doctor of Philosophy. The examination will be conducted in English. Faculty examiner: Professor AbuBakr S. Bahaj (University of Southampton).

Abstract Lundin, S. 2016. Marine Current Energy Conversion. Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 1353. 66 pp. Uppsala: Acta Universitatis Upsaliensis. ISBN 978-91-554-9510-7.

Marine currents, i.e. water currents in oceans and rivers, constitute a large renewable energy resource. This thesis presents research done on the subject of marine current energy conversion in a broad sense. A review of the tidal energy resource in Norway is presented, with the conclusion that tidal currents ought to be an interesting option for Norway in terms of renewable energy. The design of marine current energy conversion devices is studied. It is argued that turbine and generator cannot be seen as separate entities but must be designed and optimised as a unit for a given conversion site. The influence of support structure for the turbine blades on the efficiency of the turbine is studied, leading to the conclusion that it may be better to optimise a turbine for a lower flow speed than the maximum speed at the site. The construction and development of a marine current energy experimental station in the River Dalälven at Söderfors is reported. Measurements of the turbine's power coefficient indicate that it is possible to build efficient turbines for low flow speeds. Experiments at the site are used for investigations into different load control methods and for validation of a numerical model of the energy conversion system and the model's ability to predict system behaviour in response to step changes in operational tip speed ratio. A method for wake measurements is evaluated and found to be useful within certain limits. Simple models for turbine runaway behaviour are derived, of which one is shown by comparison with experimental results to predict the behaviour well.

Keywords: marine current energy, renewable energy, turbine, energy conversion, wake, Söderfors

Staffan Lundin, Department of Engineering Sciences, Electricity, Box 534, Uppsala University, SE-75121 Uppsala, Sweden.

ISSN 1651-6214 ISBN 978-91-554-9510-7 urn:nbn:se:uu:diva-280763 (http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-280763) List of papers

This thesis is based on the following papers, which are referred to in the text by their Roman numerals.

I M. Grabbe, E. Lalander, S. Lundin and M. Leijon. A review of the tidal current energy resource in Norway. Renewable & Sustainable Energy Reviews, 13(8):1898–1909, 2009.

II S. Lundin, M. Grabbe, K. Yuen and M. Leijon. A design study of marine current turbine-generator combinations. In Proceedings of the 28th International Conference on Offshore Mechanics and Arctic Engineering, OMAE 2009, paper OMAE2009-79350, pages 1–7, June 2009.

III A. Goude, S. Lundin and M. Leijon. A parameter study of the inﬂuence of struts on the performance of a vertical-axis marine current turbine. In Proceedings of the 8th European Wave and Tidal Energy Conference, EWTEC09, Uppsala, Sweden, pages 477–483, September 2009.

IV K. Yuen, S. Lundin, M. Grabbe, E. Lalander, A. Goude and M. Leijon. The Söderfors Project: Construction of an experimental hydrokinetic power station. In Proceedings of the 9th European Wave and Tidal Energy Conference, EWTEC11, Southampton, UK, 5 pages, September 2011.

V S. Lundin, J. Forslund, N. Carpman, M. Grabbe, K. Yuen, S. Apelfröjd, A. Goude and M. Leijon. The Söderfors project: Experimental hydrokinetic power station deployment and ﬁrst results. In Proceedings of the 10th European Wave and Tidal Energy Conference, EWTEC13, Aalborg, Denmark, 5 pages, September 2013.

VI J. Forslund, S. Lundin, K. Thomas and M. Leijon. Experimental results of a DC bus voltage level control for a load controlled Marine Current Energy Converter. Energies, 8:4572–4586, 2015.

VII S. Lundin, N. Carpman, K. Thomas and M. Leijon. Studying the wake of a marine current turbine using an acoustic doppler current proﬁler. In Proceedings of the 11th European Wave and Tidal Energy Conference, EWTEC15, Nantes, France, pages 09A2-3-1–8, September 2015. VIII S. Lundin, A. Goude and M. Leijon. One-dimensional modelling of marine current turbine runaway behaviour. Submitted to Energies, February 2016.

IX S. Lundin, J. Forslund, A. Goude, M. Grabbe, K. Yuen and M. Leijon. Experimental demonstration of performance of a vertical axis marine current turbine in a river. In manuscript, March 2016.

X J. Forslund, A. Goude, S. Lundin, K. Thomas and M. Leijon. Validation of a coupled electrical and hydrodynamic simulation model for vertical axis marine current energy converters. In manuscript, March 2016.

Reprints were made with permission from the publishers. Contents

1 Introduction ...... 13 1.1 Marine current power ...... 13 1.1.1 Characteristics of the energy resource ...... 13 1.1.2 Current topics of research ...... 14 1.2 Previous work at the Division of Electricity ...... 15 1.3 The Söderfors Project ...... 16 1.3.1 Site selection ...... 16 1.3.2 Construction and deployment ...... 18

2 Theory ...... 23 2.1 Terminology ...... 23 2.1.1 Turbine ...... 23 2.1.2 Generator ...... 25 2.2 Torque balance ...... 25 2.3 Turbine power coefﬁcient ...... 27

3 Results from papers ...... 29 3.1 Tidal power in Norway ...... 29 3.2 Design considerations ...... 32 3.2.1 Turbine-generator combinations ...... 32 3.2.2 Inﬂuence of struts ...... 33 3.3 Performance of the Söderfors turbine ...... 35 3.3.1 First results ...... 35 3.3.2 Power coefﬁcient ...... 35 3.3.3 Load control methods ...... 37 3.3.4 Step response ...... 38 3.4 Wake measurements ...... 38 3.5 Turbine runaway behaviour ...... 40

4 Future work ...... 47

5 Concluding remarks ...... 49

6 Summary of papers ...... 51

7 Sammanfattning på svenska ...... 55

Acknowledgements ...... 59

References ...... 61

List of Tables

Table 1.1: Turbine data ...... 19 Table 1.2: Generator data ...... 19

Table 3.1: Number of sites assessed ...... 31 Table 3.2: Rotational speed data ...... 37

List of Figures

Figure 1.1: Location of Söderfors ...... 17 Figure 1.2: Bird’s eye view of central Söderfors ...... 17 Figure 1.3: Overview of test site ...... 19 Figure 1.4: Energy conversion unit ...... 19 Figure 1.5: Discharge in the Dalälven ...... 20 Figure 1.6: Deployment of energy conversion unit ...... 21

Figure 2.1: Illustration of terms ...... 24

Figure 3.1: Map of Norway ...... 30 Figure 3.2: Water levels in Norway ...... 31 Figure 3.3: Contours of CP fora6r.p.m. turbine ...... 33 Figure 3.4: High speed turbines ...... 34 Figure 3.5: Turbines at low speed ...... 34 Figure 3.6: Voltage and current ...... 36 Figure 3.7: Upstream and downstream waterspeed ...... 36 Figure 3.8: Power coefficient curve ...... 36 Figure 3.9: Step response ...... 39 Figure 3.10: Normalised depth-mean speeds ...... 41 Figure 3.11: Cross-flow velocity profiles ...... 41 Figure 3.12: Along-flow velocity profile ...... 41 Figure 3.13: Overshoot model predictions and measured results ...... 44 Figure 3.14: Initial and maximum accelerations ...... 45 Figure 3.15: Maximum angular velocity overshoot ...... 45 Figure 3.16: Runaway development of a wind turbine ...... 45

Nomenclature

Symbol Unit Quantity u m/s Water flow speed u∞ m/s Water freestream flow speed N r.p.m. Rotational speed ω rad/s Angular velocity ωnom rad/s Nominal angular velocity ω0 rad/s Initial angular velocity ω rad/s2 Angular acceleration nb - Number of turbine blades R m Turbine radius h m Blade length (turbine height) c m Blade chord λ - Tip speed ratio σ - Solidity f Hz Electrical frequency A m2 Area 2 At m Turbine cross-sectional area P W Power Pt W Power captured by turbine P0 W Power in freestream flow CP - Power coefficient V m3 Volume V˙ m3/s Volume flow rate m kg Mass m˙ kg/s Mass flow rate ρ kg/m3 Mass density J kg m2 Mass moment of inertia Q N m Torque Erot J Rotational energy Ek J Kinetic energy k, K Various constants

1. Introduction

Energy usage in the world keeps increasing. Development of new as well as existing sources of energy is necessary. Marine currents, i.e. water currents in oceans and rivers, constitute a large energy resource. Furthermore, this resource is renewable, and provided that ways to exploit it can be found which are themselves clean (in some environmental sense), it might provide a significant contribution to the world’s energy mix. This thesis presents research done on the subject of marine current energy conversion in a broad sense. The purpose has been to contribute to the overall understanding of the ﬁeld and to the development of the technology needed to exploit the energy resource in a useful way. The research has been carried out at the Division of Electricity at Uppsala University, and has been mainly centred on or otherwise connected to that Division’s marine current experimental power station in the River Dalälven at Söderfors.

1.1 Marine current power Rivers and oceans have been a source of power to human societies for a long time [1, 2]. Full-scale tidal power plants, exploiting the tidal range in selected locations, were established in the 1960’s [3, 4]. Tidal currents as a source of electricity have been sporadically studied at least since the early 1980’s [5]. Interest was renewed in light of the threat of climate change, and for the last twenty or so years, research and technology development in the ﬁeld of hydrokinetic energy conversion, particularly with regard to tidal currents, has been expanding and intensifying world-wide.

1.1.1 Characteristics of the energy resource Tidal currents are driven by the planetary interaction of the earth, the sun and the moon [6]. Other marine currents are driven by the rotation of the earth, salinity and temperature gradients or other meteorological conditions. These currents all have in common that they are renewable. This makes them a very interesting source of energy at a time in history when there is a strong desire to lower society’s dependence on non-renewable energy [7]. Availability of the resource varies with location. Looking at tidal energy speciﬁcally, global dissipation of energy on the continental shelf is happening

13 at a rate of 2.5 TW [8]. According to one estimate, about one-tenth of this dissipation takes place around the British Isles, and if one-tenth of that energy could be converted it should cover about half of the United Kingdom’s electricity demand [9]. Another study puts the total marine current power resource (rivers, tidal and ocean currents) of the United States at 82 GW, comparable to the country’s installed conventional hydropower capacity covering approx- imately8%oftheannual electricity demand [10]. Comparisons are difﬁcult due to varying premises, but it is clear that the resource will be different in different places. Marine currents are intermittent, i.e. they are not constant in time and will not always provide power. This is a common trait of many renewable power sources [11]. Tidal currents in particular are, however, very predictable, making it possible to plan the power production in advance [12]. This is a charac- teristic not attributable to more weather-sensitive renewables, such as wind or solar power. The resource is not controllable in the sense that it can be turned on and off at will and energy saved for later if power is not needed at the moment, but as high tide appears at different times in different places along a coastline, several marine current power plants could be used to even out the load over the tidal cycle [13, 14]. A small carbon footprint is highly desirable of any energy source or power production method. Life cycle assessments of marine current turbines indicate CO2 emissions in relation to delivered energy comparable with solar and biomass power [15, 16].

1.1.2 Current topics of research As mentioned above, the research field of marine current energy is growing. Several topics within the field can be identified, that are the subject of current research interest. A few examples are mentioned below, although there is no claim of exhaustiveness. There are several recent reviews that can be consulted for further details [9, 17–19]. The resource itself is of great interest. The available resource at a given location in naturally interesting [20, 21]. The general characteristics of the resource at a typical site, such as a channel linking two bodies of water has also been studied [22, 23]. Related to this is the development of measurement and assessment techniques for resource estimation [24, 25]. Energy conversion technology is perhaps the most obvious topic for study. Designing turbines and generators to efficiently convert the kinetic energy into electricity must of course be done in a sound way. Individual turbines are being studied numerically [26, 27] as well as experimentally [28–30]. The influence in various ways on the turbine of its surroundings has also been investigated [31, 32].

14 In addition to studies on individual turbines, much research is going into power farm studies [33–35]. It is clear that to provide useful amounts of power, marine current turbines will have to be built in farms in most places, meaning arrays of turbines working next to and sometimes behind each other. The interaction among turbines in an array is a complex matter [36, 37]. Closely related to the array topic is that of turbine wakes. The interaction of turbines in an array is largely governed by the turbine wakes, as some turbines will have to operate in the wake of other turbines [38]. Characterising and understanding wake development is therefore a major research topic [39, 40]. Wakes are also of interest from an environmental impact point of view. The turbine wake will influnce such things as sediment transport and possibly fish life. Understanding and being able to predict local environmental effects of installing a marine current power plant at a site is of growing importance. Noise is another example of potential environmental issues due to hydrokinetic energy conversion [41], which all have to be considered. Generators for marine current energy conversion are also being studied [42]. Permanent magnet generators are under consideration [43, 44] as well as induction generators [45]. On the whole, however, specific marine current generator work is not nearly as common as turbine research.

1.2 Previous work at the Division of Electricity Marine current energy research has been ongoing at the Division of Electricity at Uppsala University for many years. Early on, theoretical and numerical studies were carried out on low-speed generators [46–48]. The benefits of a simple basic concept comprising a vertical axis, or cross-flow type, turbine with a direct-driven permanent magnet generator were identified early [49], and several such machines were studied theoretically and numerically. A 160 kW generator of that type was designed as intended replacement for a generator and gearbox in an existing experimental marine current power station [50]. On the experimental side, work began on a laboratory setup. After further study [51,52], a prototype 5 kW permanently magnetised generator with nominal speed 10 r.p.m. was designed and constructed in the laboratory [53, 54]. Experiments showed good agreement between actual generator performance and predictions by numerical models, validating the design [55–57]. The design has also been the basis for proposals for further improvements in stator design [58]. Meanwhile, research on combining the generators with turbines was also carried out [59]. Vertical axis turbines were modelled numerically [60, 61], as were turbine arrays [62, 63]. In addition to turbine and generator research, the marine current energy resource was studied [64, 65]. Early work was done on resource assessment

15 methodology [66]. It was followed up by studies on the effects of velocity proﬁles and distributions [67, 68]. The tidal energy resource in Norwegian fjords has been studied [69–71]. Preliminary work on the local environmental effects of a marine current power station has also been undertaken [72, 73].

1.3 The Söderfors Project The Söderfors Project, i.e. the design, construction, commissioning and operation of a real-world experimental marine current power station in a river, was initiated based on experience from the previous work. The plans for the project were outlined in [74], and an updated progress report can be found in Paper IV. The following description of the project and the test site closely follows the accounts in Paper IV and Paper V.

1.3.1 Site selection The River Dalälven is one of the largest rivers in Sweden in terms of discharge. There are 35 hydro power plants in the river with a total installed power of 1 100 MW. At Söderfors, approximately 75 km north of Uppsala (see Fig. 1.1), there is a 20 MW hydro power station owned and operated by Vattenfall Vattenkraft AB. The river passes another 4 power stations before flowing into the Baltic Sea at Skutskär [75]. Before selection of the site for the experimental station, several places around Sweden were investigated with regard to water depth, discharge levels, accessibility, potential conflicts of interest with other users etc. In the end, the choice fell on the River Dalälven at Söderfors. The main technical criteria for the selection were: • Suitable water depth (6–7 m). • Water speed typically within the interval 0.5–1.5 m/s. • The location 800 m downstream of a conventional hydro power plant is within the excavated outlet channel of the plant, which makes for a geometrically relatively “clean” riverbed. • Through cooperation with the power plant owner, it is possible to know the current discharge in the river and also to control the flow (within limits). In addition, there were several non-technical reasons for the selection of the site: • There is little or no shipping or other boat traffic on the river at the site. This is due to the river being regulated. • A road bridge crosses the river at the same place (see Fig. 1.2). The energy conversion unit was deployed from this bridge.

16 North Atlantic

SWEDEN

FINLAND NORWAY Söderfors Uppsala Stockholm

Baltic DENMARK Sea

Figure 1.1. The location of Söderfors, approximately 1 hour’s drive north of Uppsala. Fig. 1 from Paper IV.

Assembly site t

Test site t t Measuring station Dalälven

¢¢ ¢ ¢

t Hydro power station Lantmäteriet Gävle 2009. Permission I 2008/1962 c Figure 1.2. A bird’s eye view of central Söderfors. The experimental station is placed some 800 m downstream of the conventional hydro power plant. Fig. 2 from Paper V.

17 • The power plant owner, local and regional authorities as well as private and corporate neighbours to the site in Söderfors all took a sympathetic attitude towards the project. • Being relatively close to Uppsala, the site is accessible from the Univer- sity on a daily basis. The ﬁnal decision to pick Söderfors was reached in early 2009. The site was then studied further [76] in order to assess such things as what the test station would mean for the hydro power plant [77], divers inspected the riverbed etc. Necessary permits were also obtained to establish the test station, erect a measurement cabin, run cabling along the bridge and so on.

1.3.2 Construction and deployment For an overview of the test site at the bridge, see Fig. 1.3. The energy conversion unit, pictured in Fig. 1.4, comprises a straight-bladed Darrieus type cross-flow axis turbine with 5 blades connected to a direct-driven permanent magnet synchronous generator placed on a steel tripod foundation. Acoustic doppler current profilers (ADCP) are permanently placed in the river upstream and downstream of the turbine to monitor water speed. Cables from the generator and instruments run up a bridge pillar and into an electrical enclosure on the bridge railing, from where further cables run along the bridge to shore and ultimately to the measurement cabin, housing the starting circuit, load control and measurement equipment and the dump load. The tripod foundation was selected due to the riverbed characteristics at the site. The bottom has a hard gravel surface with larger rocks spread about. A gravity base solution was chosen to avoid underwater construction work, and the tripod was favoured instead of e.g. a large concrete foundation due to its smaller size and lower sensitivity to riverbed smoothness. The vertical axis turbine runner is made mainly from carbon fibre composite material, with a steel hub. The blades have a fixed pitch; before deployment the blades were mounted with 0◦ pitch (i.e. the blade chord is tangential to the turbine periphery). The design of the blade-strut connexion allows for a few degrees of pitch variation, which may be implemented at a later stage. Table 1.1 summarises data for the turbine. The generator is a cable wound permanent magnet generator, essentially of the same type as the prototype generator constructed in the laboratory (see Section 1.2). Due to its relatively large diameter and number of poles (see Table 1.2), it can generate electricity efficiently at comparatively low rotational speed. For further details on the Söderfors generator, see [78, 79]. The generator housing supports the generator and the turbine. It must thus be able to cope with the hydrodynamic and electromagnetic forces involved. Furthermore, the housing keeps the generator dry.

18 Table 1.1. Turbine data. Table 1.2. Generator data. Table I from Paper IV, prepared by K. Yuen. Parameter Value Number of blades 5 Parameter Value Hydrofoil NACA0021 Dimensions Blade chord length 0.18 m Axial length 197 mm Blade height 3.5 m Stator outer diameter 1 800 mm Diameter 6.0 m Stator inner diameter 1 635 mm Cross section 21 m2 Air gap 7 mm Number of poles 112 Magnet thickness 10 mm Magnet width 30 mm Nominal performance Speed 15 r.p.m. Armature voltage 138 V Frequency 14 Hz Apparent power 7.5 kW Power factor 1 B in air gap (load) 0.73 T B in tooth (load) 1.7 T Downstream ADCP Iron losses 0.29 kW Copper losses 0.96 kW Nominal torque 5.6 kNm Turbine Efﬁciency 86 % Upstream ADCP Load angle 8.0◦

XyXX XXX Horizontal Pillars ADCP ¢ ¢ ¢ Direction of ﬂow ¢ ¢

02040m

Figure 1.3. An overview of the test site. The turbine is placed immediately downstream of the bridge. Vertically oriented Figure 1.4. The energy conversion ADCPs are located upstream and down- unit with turbine and generator housing stream of the turbine, and a horizontally mounted on a tripod foundation. Figure oriented ADCP is upstream mounted on appears in several papers; illustration by the bridge pillar. Fig. 2 from Paper VI. A. Nilsson. See also Fig. 2.1.

19 In the measurement station on shore, the starter, load control system and monitoring equipment are located. Since a Darrieus turbine cannot always be expected to self-start, a starting circuit was designed which uses the ordi- nary generator windings to run the generator as a motor and rotate the turbine. Once the water starts to drive the turbine, the starter is disconnected and the load control system is connected instead. There are two different possibilities, either to connect an unregulated AC-configured resistive three-phase load, or to connect an actively regulated resistive DC load. The control system is described in further detail in [80–82]. Components for the machine were ordered from suppliers but the assembly was carried out in the laboratory in Uppsala (generator and housing) and on- site in Söderfors (foundation and turbine runner). Due to some high voltage power lines crossing the road between the measuring station and the bridge across the river, the whole unit could not be transported in its finished shape from the measuring station to the deployment point. Consequently, the machine had to be assembled on the other side of the river a few hundred meters away (see Fig. 1.2). The assembly site was a parking lot outside a small su- permarket, which ensured local public interest in the scientific project. Based on historical data on the discharge levels in the river, it was decided to deploy the unit in late summer or early autumn when discharge might be expected to be low. The hydro power plant operator agreed to shut the flow off in the river for a few hours, given about one week’s notice. As it turned out, precipitation in the summer and autumn of 2012 was unusually high, and so was the river discharge, making it impossible to shut off the river without flooding the area upstream of the hydro power dam. Fig. 1.5 illustrates the

800 Discharge 700 Ready to deploy Deployment 600 /s) 3 500 Too high to deploy 400

300 Discharge (m 200 Too low to run

100

0 ASONDJ FMAMJJASONDJ FM 2012 2013 2014

Figure 1.5. Discharge in the Dalälven at Näs over time. The energy conversion unit was ready for deployment in August 2012, but due to high discharge deployment was not possible until March 2013. Discharge levels were then below cut-in level for the unit for most of the year. Data from http://www.vattenreglering.se/.

20 Figure 1.6. Deployment of the energy conversion unit into the River Dalälven at Söderfors on 7 March 2013. Photograph by Uppsala University/M. Wallerstedt.

21 development of river discharge during the latter part of 2012 and in 2013; the data is from Näs, two power plants upstream from Söderfors. The discharge ﬁnally began to go down in late 2012, but winter is high-season for public utilities and for this reason the power plant could not be shut down at this time. While the energy conversion unit was ready for deployment in August 2012, it was not until March 2013 that an opportunity to actually deploy the machine opened up. Deployment was carried out on 7 March 2013. Since temperatures were still below freezing, a tent had to be erected the night before deployment, covering the coils of cable attached to the generator, with gas heaters inside to make sure the cables were not too cold and brittle to be rolled out. The machine was lifted by a mobile crane and transported on a trailer to the bridge. The crane then lifted the unit over the railing and lowered it into the river. A photograph of the event is shown in Fig. 1.6. Ropes were tied to the upstream foot of the tripod to ensure correct orientation (not clearly seen in the picture). The cable bundle was covered with a protective plastic coating and paid out from the bridge. Once the tripod was on the riverbed, a diver went down to inspect the unit’s placement, relase the lifting lines and secure the cable bundle on the riverbed. The permanently mounted ADCPs were also deployed on the same occasion. Finally, all cables were routed up a bridge pillar and connected to the enclosure on the bridge railing. After discharge levels had gone down enough for deployment, they stayed low through most of 2013, creating difﬁculties in operating the Söderfors experimental station. Not until Christmas time 2013 did the water speed start to pick up enough that useful experiments could be carried out.

22 2. Theory

This chapter outlines the theoretical background of the included papers and introduces some often used terminology. More detailed theoretical background is given in the papers.

2.1 Terminology This section introduces a few basic terms and concepts used throughout this thesis and in the included papers. As far as possible, standard symbols are used, but complete consistency in this respect is probably not entirely achiev- able. In particular, use of symbols may show slight variations in the included papers.

2.1.1 Turbine The Söderfors turbine is of the cross-flow axis type, i.e. its axis of rotation is perpendicular to the main direction of flow. Fig. 2.1 shows the machine with the directions of flow and rotation marked. The axis is oriented vertically, and so the turbine type is often referred to as vertical axis rather than cross-flow axis. Both are of course correct regarding the Söderfors turbine, but obviously a cross-flow axis does not have to be vertical. More specifically, the turbine is a straight-bladed Darrieus type turbine. Looking at Fig. 2.1 we see that the supporting arms extending from the hub to the turbine blades are called struts. The chord c of a blade or strut is a line from the leading edge to the trailing edge. The aspect ratio of a turbine blade is the ratio of its length h to its chord. The blades, struts and hub together constitute the turbine runner. The ratio of the total blade surface area to the area swept by the turbine is called the solidity of the turbine. It influences the efficiency of the turbine and at what rotational speed peak efficiency occurs. For a straight-bladed Darrieus turbine, the surface area of a blade is the product of its length and chord. The swept area is the circumference of the turbine times its height (equal to the blade length). The solidity σ is thus defined as n hc n c σ = b = b , (2.1) 2πRh 2πR where nb is the number of blades on the turbine.

23 R

strut

ω XyX ⎫ ⎪ ⎪ ⎪ © ⎪ ⎪ ⎪ ⎪ ⎬⎪ H ¨ h u∞ ⎪ ⎪ ⎪ ¨* ⎪ ¨¨ ⎪ ¨ ⎪ blade ¨ ⎪ ⎭⎪

Figure 2.1. The Söderfors energy conversion unit (cf. Fig. 1.4) with some added terminology. R – turbine radius; h – blade length (turbine height); ω – angular velocity; u∞ – freestream ﬂow speed.

The rotational speed N and angular velocity ω of the turbine are essentially the same thing, a measure of how quickly the machine is turning. Usually, rotational speed is given in revolutions per minute (r.p.m.), while angular velocity is given in radians per second (rad/s). Since there are 60 seconds to a minute and 2π radians to a revolution, the two are related to each other as ω 30 π N = · 60 = ω ⇐⇒ ω = N (2.2) 2π π 30 or very roughly by a factor of 10. The rotational speed is governed by the water flow speed and the applied elctrical load as described in Section 2.2. During operation at operational speed, the driving torque of the water is balanced by the electrical torque of the load. If the load is lost or disconnected a runaway situation occurs, and the rotational speed will increase to what is known as runaway speed. To relate the rotational speed to the flow speed, the tip speed ratio λ is used. It is a non-dimensional number defined as the ratio between the speed of the turbine blade tips and the freestream water speed u∞, ωR λ = . (2.3) u∞ For a flow-aligned axis or axial-flow type turbine (often called horizontal axis, but a cross-flow axis turbine could also have its axis horizontally oriented), the blade tips move at a speed equal to the angular velocity ω times the turbine radius R. On a straight-bladed cross-flow axis turbine, the whole blade moves at that speed, but the term tip speed ratio is nevertheless retained.

24 2.1.2 Generator The generator has a rotor which is directly driven by the turbine via the shaft. The poles of the generator are the 112 permanent magnets ﬁxed around the periphery of the rotor. The magnets are alternately north or south pole, making for 56 electrical periods in one revolution of the rotor. Consequently, since there are 2π radians to one period, the electrical frequency f of the generator is related to angular velocity and rotational speed as 56ω 28 14 f = = ω = N. (2.4) 2π π 15

2.2 Torque balance In this section we consider the torque driving the energy conversion unit. When the driving torque equals the braking torque, rotational speed remains constant. This is usually the desired state during steady operation. If condtions change – for instance, the water ﬂow speed or the output power level –, the torque balance is no longer zero and a change in rotational speed will occur, again changing the conditions of operation. At a given rotational speed, the rotating system – turbine runner, generator rotor and connecting shaft – has the rotational energy Jω2 E = , (2.5) rot 2 where J is the mass moment of inertia of the rotating system and ω is the angular velocity of the turbine. The time derivative of Erot is the power P: dE dω P = rot = Jω . (2.6) dt dt But power is also torque Q times angular velocity, so we get dω dω P = Jω = Qω =⇒ J = Q. (2.7) dt dt Here, Q is the sum of all torque acting on the rotating system, and as stated above, Eq. (2.7) says that there is no change in angular velocity if the total torque is zero. The torque can be analysed in terms of a hydrodynamic component, a mechanical component and an electrical component:

Q = Qhydro + Qmech + Qel. (2.8) These components in turn have different contributions. The hydrodynamic driving torque is created by lift forces on the turbine blades, more speciﬁcally the tangential components of those forces. Hydrody- namic drag also contributes to the torque, but in a negative manner. According

25 to momentum theory (see, for instance, chapter 3 in [83]), the hydrodynamic driving torque is proportional to the ﬂow speed u and the angular velocity. Hydrodynamic drag causes a torque loss proportional to the angular velocity squared. We get 2 Qhydro = k1uω − k2ω (2.9) where k1 and k2 are constants. The mechanical torque component is due to frictional losses in bearings and seals. It is constant, i.e. it is the same regardless of angular velocity. The electrical torque component, ﬁnally, is due to power being dissipated in the load and electrical losses in the generator. Electrical losses are divided into copper losses (in the windings) and iron losses (in the stator). Since torque is power through angular velocity, we can write + + + = −Pload Ploss = −Pload PCu PFe . Qel ω ω (2.10)

Here, the minus sign indicates that the torque contribution is negative in the sense that it causes power to leave the rotating system. Neglecting iron losses other than those proportional to the electrical frequency, we can write + = − Pload PCu Qel QFe ω (2.11) where QFe = −PFe/ω is a constant. If we sum the constant torque losses they can be written

Qconstloss = Qfric + QFe = −k3, (2.12) where k3 is a constant. Substituting back into Eq. (2.8), we now get

dω P + P J = k uω − k ω2 − k − load Cu , (2.13) dt 1 2 3 ω which is the governing equation for turbine rotational speed when a load is connected. If the electrical load is disconnected, the last term disappears since there is no longer any power dissipated in the load and there are no copper losses unless a current is ﬂowing in the generator windings. The iron losses in the stator, however, are present even with no load connected. Eq. (2.13) becomes

dω J = k uω − k ω2 − k . (2.14) dt 1 2 3 This is the governing equation during runaway.

26 2.3 Turbine power coefficient The performance of a marine current power turbine is often measured in terms of its power coefficient CP. The power coefficient gives the fraction of power in the undisturbed water flow that is captured by the turbine and is defined as

Pt CP = , (2.15) P0 where Pt is the power captured by the turbine and P0 is the power available in the flow without the turbine. P0 is ususally defined as 3 u∞ P = ρA , (2.16) 0 t 2 where ρ is the mass density of water, At is the cross-sectional area of the turbine as seen in the direction of flow and u∞ is the free stream water speed, i.e. the water speed far from the turbine or more precisely the speed which water would have at the location of the turbine if the turbine were not there. To derive Eq. (2.16), we start by noting that power P is the time derivative of energy. Kinetic energy Ek is mass m times velocity u squared divided by two, so dE d mu2 u2 P = k = = m˙ , (2.17) dt dt 2 2 wherem ˙ is the mass flow rate, assuming that u is constant in time. Mass flow rate is density times volume flow rate V˙ , which in turn is velocity times area A perpendicular to the direction of flow, i.e. m˙ = ρV˙ = ρAu. (2.18) Combining these two equations we get u2 u3 P = ρAu = ρA , (2.19) 2 2 which is exactly Eq. (2.16) when u = u∞ and A = At. The turbine captures power equal to the hydrodynamic torque times angular velocity. Multiplying through with ω assuming u = u∞, Eq. (2.9) yields 2 3 Pt = Qhydroω = k1u∞ω − k2ω . (2.20)

But by Eq. (2.3) ω = λu∞/R,so

3 3 u∞ u∞ P = k λ 2 − k λ 3 (2.21) t 1 R2 2 R3 which, when substituted into Eq. (2.15) together with Eq. (2.16), gives the following expression for the power coefﬁcient as a function of tip speed ratio: 2 3 CP(λ)=K1λ − K2λ , (2.22)

27 where the constants are

= 2k1 = 2k2 . K1 2 and K2 3 (2.23) ρR At ρR At It should be noted that the above reasoning implicitly assumes that the ﬂow speed is constant over the area or cross-section under consideration. If it is not, it is necessary to integrate over the area (instead of just multiplying), and Eq. (2.19) becomes ρ P = u3 dA. (2.24) 2 A For most practical purposes, however, Eq. (2.16) will do nicely.

28 3. Results from papers

This chapter contains a summary of the results from the papers on which the thesis is based. Paper IV is extensively referenced in Section 1.3 and is not discussed in this chapter.

3.1 Tidal power in Norway A study regarding tidal power in Norway is reported in Paper I. The overall conclusion of the study is that tidal current energy conversion should be of interest to Norway as a country. There is a palpaple, if not very well understood, tidal energy resource, and the long coastline creates a phase lag which could be exploited to even out the load over time. Norwegian offshore industry has considerable experience which might be put to use in this context, and there is a political will to increase the fraction of renewable energy in the Norwegian energy mix. Norway has a long coastline, full of fjords and inlets. The tidal wave prop- agates along the eastern borders of the Atlantic Ocean, up along the coast of Norway (see Fig. 3.1). The North Sea is not strongly affected by tides, but the tidal amplitude is signiﬁcant all along the Norwegian west coast and gener- ally increases with latitude. Fig. 3.2 shows sea level along the coast (locations marked in Fig. 3.1) based on data from Norwegian pilot books (Den Norske Los, DNL). It is noteworthy that there is a time difference for the occurrence of high or low water among different locations along the coast, due to the propagation of the tidal wave; thus, high water at Bodø occurs nearly two hours later than at Bergen (see Fig. 3.2). This also means peak tidal ﬂow occurs at different times in different places, which could be used to even out the load: When production at one tidal power plant is going down as the tide is turning, another plant is approaching its peak production. Due to the tidal range and abundance of narrow constrictions (fjords and inlets), there are many places along the coast of Norway where strong tidal currents occur. Some are world-famous, such as the Moskenstraumen tidal current at the tip of Lofoten which has the mythical capacity to create a Mael- strom vortex strong enough to pull ships down under the sea. Pilot books quote surface currents of 5 m/s in Moskenstraumen. Other sites with strong currents are Gimsøystraumen in Lofoten (2.3 m/s) and Saltstraumen on the mainland

29 Barents ◦ N80 Sea

Vardø SVALBARD Heleysundet Hammerfest

Freemansundet ◦ N70 Longyearbyen

Stor- Tromsø fjorden Lofoten RUSSIA Sørkapp FINLAND E10◦ E20◦

Norwegian Bodø Sea

NORTH ATLANTIC ◦ N65 Rørvik

Trøndelag

Møre Trondheim SWEDEN

NORWAY Bergen

◦ Oslo N60

0 250 500 km North Skagerrak Sea E10◦ E20◦

Figure 3.1. A map of the Norwegian coastline including Svalbard (inset). Fig. 1 from Paper I.

30 HWL 200 4 HAT 100 2 phase delay Reference water level 0 0

− − time / hours

water level / cm 100 2 LAT −200 −4 LWL

Oslo Bodø Bergen Tromsø Vardø Trondheim Hammerfest

Figure 3.2. Sea level shown as Highest and Lowest Water Level (HWL/LWL) and Highest and Lowest Astronomical Tide (HAT/LAT) in comparison with the reference (mean) water level [cm]. Also in the figure are the variations in time [h] for the occurrence of high/low water, where time for high water is taken as 0 in Bergen. Data from DNL. Fig. 3 from Paper I; diagram by E. Lalander. coast at latitude N 67◦ (4 m/s). It is clear that there are sites in Norway, where tidal power could be produced. While measurements of tidal currents are important, to develop tidal power in Norway it would be necessary to numerically model tidal flows. Paper I reviews a few different models for ocean flow used in Norwegian universities, in particular one developed at the University of Oslo and one fron the University of Bergen known as the Bergen Ocean Model, BOM. Both these models were originally developed with other goals than assessing the tidal energy resource. The University of Oslo model was, for instance, used for predicting tidal currents for navigational purposes. However, adapting the models for a different purpose should be quite possible, and having been developed in Norwegian universities the models indicate that Norway has the academic capabilities for such an undertaking. The paper reviews two previous tidal energy potential assessments for the Norwegian coast, [66] and [84] (see Table 3.1). Using the same methodology (described in [66]), another assessment is made specifically for Paper I. The

Table 3.1. The number of sites and calculated resource as presented in the three different resource assessments. Table 1 from Paper I, prepared by M. Grabbe. [66] [84] Present study No. of sites 12 22 104 Theoretical resource (TWh) 2.3 – 17 Extractable resource (TWh) 0.23–1.1 – – Technical resource (TWh) 0.18–0.89 > 1– Economical resource (TWh) 0.16–0.82 < 1–

31 number of evaluated sites differ among the studies, as do the results regarding the size of the tidal energy resource. However, the results are not necessarily contradictory since the assessments in part discuss different types of resource (theoretical, technical etc.). That a large number of evaluated sites should indicate a bigger resource than just a few sites also seems reasonable. Paper I has been quite widely cited in contexts such as tidal and ocean energy reviews [19, 85]. While obviously focussed on Norway, it has also been cited in papers on tidal power in many other places, e.g. China [86], Ire- land [87] and Brunei Darussalam [88]. For more on the tidal energy resource in Norway, see for instance [64, 65, 69, 70].

3.2 Design considerations When designing a marine current energy converter, many things have to be taken into consideration. This section summarises results concerning the com- bination of turbine and generator and concerning the inﬂuence of struts on the efﬁciency of a turbine.

3.2.1 Turbine-generator combinations Paper II reports a design study of marine current turbine-generator combinations. The underlying assumption is that the turbine and the generator cannot be designed separately when a marine current power station is designed, since both components are influenced by the performance of the other. Conse- quently, they must be seen as a system and be optimised together. In the study, three different combinations of turbines and generators, giving the same output power at a given water flow speed, were designed and compared. The following design process was applied: 1. Three generators were designed, giving the same output power but at different rotational speeds. 2. Given the estimated efficiency of the generators at nominal speed, three turbines were designed to deliver the required power at that speed. 3. The power delivered by the turbines at different flow speeds was calculated. 4. Given input from the turbine simulations, the output power from the generators at different speeds was computed. The chosen design case was output power of 10 kW at 1 m/s flow speed, which was considered to be a reasonable case for a small river. The chosen nominal rotational speeds were 6, 12 and 18 r.p.m, all at a tip speed ratio of 4.0. The generators were designed as variants of the prototype generator built in the lab [54, 56]. The turbines were then matched to the generators by varying the solidity and cross-sectional area and selecting a solution which satisfied

32 C in htwl ieatrieotu oe hc ntr ie 0k upta the at output kW 10 a gives II. turn Paper in from which 2 power Fig. efficiency. output generator turbine estimated a give will that tions hc ili uncryacs ntrso yrdnmcdrag. hydrodynamic struts, of for terms in requirements cost the a set carry will turn the in blades paper, will that turbine the which in of for discussed As slenderness struts models. and supporting the length in particular, included the In not for were structure blades simplicity. supporting turbine for of effects neglected the was II, Paper turbine of modelling turbine the In struts of Influence 3.2.2 coefficient power the how shows 3.3 Fig. generator. the of requirements the 3.3. Figure ainlsed steeetia fcec ftegnrtrwsbte o the for better was ro- generator the increasing with of with but efficiency down machines. long electrical faster-rotating went was the area one as cross-sectional The fastest speed, Turbine the tational lot. a while radius. quite wide small varied The and a turbine, short the output. was especially power turbine machine, overall slowest the the of shape influence and significantly ro- size nominal not chosen did the i.e. speed power, negligible, output tational was of machines terms the in that among found difference was the It studied. were conditions speed flow selected. was turbine shortest For kW. the 10 to giving of deliver solution output would the designated that the turbine, solutions achive each to marks required line power kW the this 10 generator in the the size diagram, turbine the the of In measures the equivalent from context. are and (2.3) length area Eq. axial cross-sectional or by the height given consequently turbine directly and was speed, rotational radius chosen turbine the the fixed, was ratio speed P ihtegnrtr n ubnsdsge,terbhvorudrvarying under behaviour their designed, turbines and generators the With aiswt oiiyadtriesz o h ...trie ic h tip the Since turbine. r.p.m. 6 the for size turbine and solidity with varies otusof Contours

Turbine cross-sectional area (m2) 40 50 60 70 80 90 234567 C P o h ...trie h 0k ieidctssolu- indicates line kW 10 The turbine. r.p.m. 6 the for Solidit y (%) 0.35

10 kW 0.3

0.25 0.2 3.1 3.9 4.7 5.5 6.3 7.1

Turbine height/length (m) 33 In Paper III, the influence of struts on turbine efficiency was studied. It was noted that, as a rule of thumb, the efficiency of the turbine might be expected to improve with increased aspect ratio of individual blades. The more slender the blades, however, the more support structure will be required. To investigate this, two theoretical turbine configurations were studied, one with 6 blades and one with 3 blades. Each was designed in two variants, one intended for operation at optimum tip speed ratio at 1.5 m/s flow speed and the other at 2.5 m/s. The solidity of the turbines was optimised for tip speed ratios from 2.5 to 4.5 without any strut losses. These solidities were then used to calculate the maximum normal (radial) force on the blades. Based on the normal force, the minimum number of struts for operation at each speed vas computed, and finally the losses due to the struts as well as blade tip effects were included. The calculations were done for two flow speeds, 1.5 m/s and 2.5 m/s. The maximum power coefficients of the turbines optimised for the higher flow speed are plotted in Fig. 3.4. Due to the discrete addition of strut losses, the curves assume a stair-step character. As might be expected, the steps occur more frequently for the 6-bladed turbine with the thinner, leaner blades, than for the 3-bladed turbine, and as a consequence the power coefficient drops off considerably more quickly as the tip speed ratio increases. Since the turbines were optimised for 2.5 m/s, they might be expected to perform less well at a lower flow speed. Fig. 3.5 shows the power coefficients of all turbines at 1.5 m/s. Again, the 6-bladed turbines exhibit more steps in the curves and a quicker drop-off in power coefficient with increasing tip

0.45 0.45 3 blades 3 blades (2.5) 6 blades 6 blades (2.5) 3 blades (1.5) 6 blades (1.5) 0.4 0.4

Power coefficient 0.35 Power coefficient 0.35

0.3 0.3 2.5 3 3.5 4 4.5 2.5 3 3.5 4 4.5 Tip speed ratio Tip speed ratio

Figure 3.4. Maximum power coefficients Figure 3.5. Power coefficients of turbines of the turbines designed for flow speed optimised for flow speeds of 1.5 m/s and 2.5 m/s. The stair-step shape of the curves 2.5 m/s, all run at 1.5 m/s. Fig. 5 from due to the inclusion of more struts with Paper III; diagram by A. Goude. increasing tip speed ratio is clearly visible. Fig. 4 from Paper III; diagram by A. Goude.

34 speed ratio than their 3-bladed counterparts. Not surprisingly, the turbines designed for 1.5 m/s perform consistently better than those designed for higher speed. The difference is less pronounced for the 3-bladed turbines, and the two curves behave almost identically at tip speed ratios below approximately 3.2. Depending on the ﬂow characteristics at a particular site, it might be better to optimise the turbine for operation at a lower speed than peak ﬂow speed.

3.3 Performance of the Söderfors turbine This section reports results based on experiments made on the test station at Söderfors.

3.3.1 First results The energy conversion unit at the Söderfors test site was deployed in March 2013 as described in Section 1.3.2. Paper V describes the deployment but also reports the first measurement results from the test station. As can be seen from Fig. 1.5, soon after deployment discharge in the river dropped off and it was not possible to operate the turbine. A few weeks later, water speeds picked up again and in late April the first measurements were taken. Fig. 3.6 shows voltage and current over two electrical periods. At the time, a three-phase resistive load of 2.5 Ω per phase without rectification was connected. Shown voltage is line-to-line while the current is in one phase, which accounts for the phase shift. The electrical period is 84.4 ms for a frequency of 11.8 Hz, which corresponds to a rotational speed of 12.7 r.p.m. The water speed at the same time is shown in Fig. 3.7. Results are plotted from the two vertically oriented ADCPs, upstream and downstream of the turbine. Due to the geometry of the riverbed, the undisturbed flow speed is slightly lower at the downstream ADCP than at the upstream one. When the turbine is operated, a wake develops and the downstream flow speed goes down dramatically, which is clearly seen in the diagram. The point in time when the electrical data of Fig. 3.6 was captured is also marked in the plot. Taken by themselves, these results really only show that turbine, generator and measuring instruments work. From the point of view of the Söderfors Project, they are extremely significant in that they mark the first actual operation of the test station at Söderfors.

3.3.2 Power coefﬁcient The performance of a turbine is often described in terms of the power coefﬁ- cient as a function of tip speed ratio, CP = CP(λ) (cf. Section 2.3). Published data on actual turbines is however very scarce.

35 36 aver- half-hour a represents IX. sample Paper Each from curve. 3 fitted Fig. a age. with together plotted m/s, 1.4 3.8. Figure V. Paper from current 2.5 load at AC phase measurement an during and captured line) line) (dashed (solid voltage 3.6. Figure Voltage (V) -200 -150 -100 100 150 200 -50 50 0 04 08 0 2 4 160 140 120 100 80 60 40 20 0 oe ofcetmaueet rmflwsed nteitra 1.2– interval the in speeds flow from measurements coefficient Power Power coefficient line-to-line of periods Two 0.05 0.15 0.25 0.1 0.2 0.3 0 Time (ms) ...... 4.6 4.4 4.2 4 3.8 3.6 3.4 3.2 3 2.8 Ω e hs.Fg 6 Fig. phase. per Current Voltage -40 -30 -20 -10 0 10 20 30 40 Ti

p Current (A) s ue.Fg rmPprV. cap- Paper from were 7 Fig. 3.6 tured. Figure in wave- displayed the when forms time the marks vertical line solid black The operated. was the machine which ar- during shaded periods time The indicate eas locations. two the undisturbed at time- the flow for the speed The show mean averaged lines 2013. dashed April 29 horizontal on line) energy unit the conversion (black of line) (grey upstream downstream and ADCP by sured 3.7. Figure p eed ratio Water speed (m/s) 0.5 1.5 0 1 33 34 40 41 14:30 14:15 14:00 13:45 13:30 Downstream Upstream enwtrpe mea- waterspeed Mean Time ofda y Paper IX reports measurements of output power from the Söderfors turbine under different operational conditions, recomputed as power coefficients. Measurements were made in water flow speeds of 1.2–1.4 m/s and with different resistive AC-configured loads connected. Compensation was made for mechanical losses in bearings and seals and for electrical losses in the generator. Results from half-hour runs were averaged to produce the plot in Fig. 3.8. A curve was fitted to the measured data points through least-squares min- imization, based on the expression for power coefficient given in Eq. (2.22). The curve-fit indicated that the maximum power coefficient of the Söderfors turbine was CPmax = 0.26 at λopt = 3.1. As discussed in Paper IX, this is comparable to the power coefficients reported for turbines operating in considerably higher flow speeds. This result shows that it is possible to build turbines that operate in slow moving currents with associated slow rotational speed and still capture the power available in the water as efficiently as turbines in faster flow. Obviously, the faster the flow the more available power, but the fraction of power captured does not have to be less in slower flow.

3.3.3 Load control methods As described in Section 1.3.2, the generator can be connected to a resistive load either directly (AC configuration) or via a rectifier (DC configuration). If the DC load setup is selected, active load control is possible. This can be done either as a constant pulse width modulation (PWM) setting, effectively creating a constant load, or by letting the control system continuously alter the PWM to maintain a specified DC voltage level. Since the voltage is proportional to rotational speed, this latter option effectively means keeping the turbine and generator at constant speed. In Paper VI, these three control methods – fixed AC load, fixed pulse width modulated DC load and constant DC bus voltage – are investigated and compared. The choice of load control method influences the variation in rotational speed. Table 3.2 summarises rotational speed data from the three control methods, based on measurements during 30 min for each case. The water

Table 3.2. Mean rotational speed and variance of the three load cases. Calculated average λ from average water speed and average rotational speed. Table 2 from Paper VI, prepared by J. Forslund.

Load Case AC Fixed PWM Constant DC Average speed (r.p.m.) 15.35 15.68 15.65 Variance 2.34 2.11 0.65 Average λ 3.61 3.65 3.67

37 speed during these measurements was approximately 1.4 m/s at the upstream ADCP. The mean rotational speed is roughly the same for the two DC load cases and slightly lower for the AC case. The variance is considerably smaller for the fixed DC case than for the other two, confirming that the active load control method results in a more even rotational speed over time. Paper VI also reports overall system efficiencies (from water to load) of slightly less than 19 % with small variations among the control methods at tip speed ratios of about 3.6. Considering that the generator efficiency is on the order of 80 % [79], this result seems consistent with the power coefficient results reported in Paper IX.

3.3.4 Step response To be able to study the test station’s behaviour under various discharge scenar- ios, a numerical model was developed that couples the hydrodynamic vortex model used for simulating the turbine [60] with a Matlab SIMULINK model of the station’s electrical system (generator, control system and load). Paper X reports the validation of this model against experimental data from Söderfors. Fig. 3.9 shows an example of the station’s response to a step change in the prescribed (or target) DC bus voltage level. In Fig. 3.9 (a), the machine is operated with a target DC bus voltage of 128 V, corresponding to a rotational speed of approximately 12.5 r.p.m. At time t = 0, the target DC voltage is changed to 147 V. As can be seen from the plot, the experimental values show that the machine adapts the DC bus voltage to the new target level in just less than 20 ms, and the simulation is able to recreate the process closely. The plot does not show the development of rotational speed. Speed also increases to adapt to the new target voltage level, but the response is slower; on the order of a second as can be seen in Fig. 8 in Paper X. The turbine wake also develops to the new situation. Fig. 3.9 (b) shows the behaviour when the target DC voltage is lowered. At this point the machine has been operating at the 147 V level for a few minutes, long enough that the wake has developed fully. The target voltage is decreased to 110 V and the station responds. In less than 10 ms the DC bus voltage is brought down to the new level. Again, there is a lag in rotational speed adaptation, not shown in the plot. Paper X shows that the coupled model can predict the response of the test station to step changes in the control parameters.

3.4 Wake measurements Wake characteristics of marine current turbines are important for the development of the marine current energy resource. Spacing of turbines in arrays de- pends on wake recovery, and environmental impact on e.g. the riverbed is also

38 150

145

140 ( ) a 135

Voltage (V) Target DC voltage 130 Experimental voltage Simulated DC bus voltage 125 -30 -20 -10 0 10 20 30 40 50 60 70 Time (ms)

150 Target DC voltage 140 Experimental voltage Simulated DC bus voltage

130 (b)

Voltage (V) 120

110

-10-50 5 101520 Time (ms) Figure 3.9. Simulated and experimental step response close to optimal tip speed ratio. (a) Increasing tip speed ratio. (b) Decreasing tip speed ratio. Similar to Fig. 5 from Paper X; diagrams by J. Forslund. influenced by wake behaviour. Most wake studies have been performed on horizontal axis turbines and mainly carried out as scale model experiments or numerical simulations. Paper VII describes wake measurements at the Söder- fors test site, carried out in an attempt to develop a method for wake characterization. For this study, a vertically oriented ADCP was mounted upside down on small floating vessel towed by an open boat. A high accuracy GNSS receiver was mounted on top of the ADCP to record the locations of measurements. The boat was then driven across the river while the turbine was running, the ADCP recording the water speed on the way. In post-processing, GNSS posi- tions were associated with ADCP readings based on data time stamps, and the plots of the velocity field could be made. Leading lines were established to aid in navigation. These were approximately, but not entirely, oriented along or perpendicular to the main direction of flow. It was not possible to follow the lines perfectly with the boat. Fig. 3.10 shows depth-mean speeds, normalised by the average undisturbed free-stream speed, plotted on a flow-aligned grid with the x-axis in the main flow direction. Grid squares are one turbine diameter by one turbine diameter in size. The structure of the measurement runs can be seen, with several cross-flow runs and a few along-flow. The turbine wake can be quite clearly

39 discerned as a region of slow-speed flow in the centre, downstream of the turbine. Regions of slower flow can also be observed approximately three turbine diameters to either side of the turbine. These are the wakes from the bridge pillars (cf. Fig. 1.3). Fig. 3.11 shows speed transects across the flow at different downstream distances from the turbine. The wake is strong at 1.3 turbine diameters downstream from the turbine, still distinctly visible at 5.4 diameters and all but gone at 9.7 diameters. The bridge pillar wakes are also clearly visible at close range. The black areas at the bottom of the plot indicate measurement bins where the ADCP did not get a good reading due to signal interference close to the riverbed. The actual riverbed lies a little deeper than the disturbed measurement bins. One along-flow transect is shown in Fig. 3.12. The wake is very clear as far as 6 turbine diameters downstream. The wake does not however recover quickly within the space of a single turbine diameter, as it might seem from this figure. As discussed in Paper VII, the boat run was not perfectly straight and in all probability the measurements at more than 7 diameters in this plot were taken to the side of the actual wake. The measurements reported in this paper were carried out in the autumn of 2013, when the discharge in the river was at too low levels to run the turbine. In order to create a wake, the generator was run as a motor since the water speed was insufficient to drive the turbine. Consequently, the tip speed ratio was very high, approximately 5.6, and so few conclusions can probably be drawn from these results regarding the wake in normal operation. However, the fact that the wake can be detected by this method was established.

3.5 Turbine runaway behaviour If a fault occurs during operation of a marine current turbine and the connexion to the load is lost for any reason, the electrical torque will disappear. The hydrodynamic torque will accelerate the turbine to the speed at which the net torque is zero, known as the runaway speed. However, due to the delay in wake build-up, the turbine will momentarily rotate faster than the runaway speed, before it slows back down and settles at that speed. The forces that the turbine is subjected to are dependent on rotational speed, and so the peak rotational speed during runaway speed overshoot is important to know when dimensioning a turbine [89]. In Paper VIII, two one-dimensional models of turbine runaway behaviour in terms of rotational speed are developed. The output from the models is compared to experimental results.

40 y x 2

D normalized speed 0 Figure 3.10. Normalised depth-mean speeds plotted where they were collected. Fig. 7 from Paper VII.

0 2

C1 -0.5 1 z/D

-1 0 normalized speed -3 -2 -1 0 1 23 y/D 0 2

C2 -0.5 1 z/D

-1 0 normalized speed -3 -2 -1 0 1 23 y/D 0 2

C3 -0.5 1 z/D

-1 0 normalized speed -3 -2 -1 0 1 23 y/D Figure 3.11. Velocity proﬁles across the direction of ﬂow. Projections are made 1.3, 5.4 and 9.7 turbine diameters, respectively, downstream of the turbine. The solid black lines at the centre indicate the turbine frontal area. Fig. 9 from Paper VII.

0 2

A1 -0.5 1 z/D

-1 0 normalized speed 0 1 2345678910 x/D Figure 3.12. A velocity proﬁle along the direction of ﬂow. Offset from centreline is 0.3 turbine diameters. Fig. 10 from Paper VII.

41 One model is analytical. If the ﬂow speed u is constant, Eq. (2.14) is a separable differential equation with solution − 2 2 4k2k3 k1u 4k k − k2u2 tan C − t + k u 2 3 1 int 2J 1 ω(t)= , (3.1) 2k2 where Cint is a constant of integration. With the initial condition that angular velocity is ω = ω0 at time t = 0, the constant becomes 2k2ω0 − k1u Cint = arctan . − 2 2 4k2k3 k1u

The constants k1, k2 and k3, as well as the inertia of the rotating system J, are determined by properties of the actual turbine being modelled. This analytical model does not capture the runaway speed overshoot phenomenon. This is due to the assumption stated initially that the flow speed seen by the turbine runner is constant. The overshoot phenomenon is caused by the relative difference in inertia between the turbine (the rotating system) and the medium (here, water) in which it operates. As the rotational speed increases, the apparent water speed goes down; however, the turbine changes speed quicker than the water adapts, leading to the overshoot. A model that does not take the change in flow speed into account, will not recreate the overshoot. The second model of Paper VIII is numerical and takes the changing apparent speed into account. Supposing that the turbine can be regarded as operating in a volume V whose kinetic energy is EV and where the apparent flow speed is uapp, ω and uapp are modelled in terms of rotational and kinetic energy. The system of equations is ∂E rot = P(ω,u ) (3.2) ∂t app ∂E V = P (λ) − P(ω,u ) (3.3) ∂t std app where ω and uapp are retrieved by the relations 2E 2E ω = rot and u = V . (3.4) J app ρV

The idea behind the model is that the turbine captures power P at a rate decided by its rotational speed and the apparent ﬂow speed. Some ‘steady component’ Pstd, corresponding to the power captured in steady operation at the current tip speed ratio, of this captured power always comes from the freestream ﬂow, while the balance P − Pstd comes from the operational volume V.

42 Furthermore, expressions for P and Pstd are needed. They are 3 2 P(ω,uapp)=−k2ω + k1uappω − k3ω (3.5) and 3 2 u∞ u∞ u∞ P (λ)=−k λ 3 + k u (λ) λ 2 − k λ. (3.6) std 2 R3 1 std R2 3 R To complete the model, the apparent speed in steady operation ustd must be determined. Based on momentum theory and experimental results, it is postulated that the apparent speed seen by the runner in steady operation can be written as k4 (λ)= ∞ , ustd u 2 (3.7) k4 + λ where the constant k4 will have to be experimentally determined. Lastly, the size of the operational volume is given as

V = k5DAt, (3.8) where k5 is a constant. In all, five constants k1–k5 have to be determined for the numerical model as opposed to three for the analytical model. For the Söderfors turbine, the first four were determined directly or indirectly by measurements, while the last one k5 had to be calibrated against experimental results. Further details of the derivation of the models are in Paper VIII. In Fig. 3.13 the model predictions are compared to experimental results. The turbine was operated in 1.4 m/s freestream flow speed at approximately 1.5 rad/s (just below 15 r.p.m.), i.e. nominal operational conditions, when the load was removed and the turbine spun free. Angular velocity increased rapidly and reached a maximum of nearly 2.5 rad/s (24 r.p.m.) before slowing down and settling at the runaway speed of 2.15 rad/s (20.6 r.p.m.). The real turbine has five blades, which means there is a small torque ripple in the experimental measurements which does not occur in the numerical model results. Apart from that, the numerical predictions follow the experimental values remarkably well, catching both the timing and magnitude of the peak angular velocity. The analytical model, as expected, does not exhibit any runaway speed overshoot. Looking at the time derivatives to get an idea of the accelerations involved, differentiation of the experimental results clearly amplify the ripple effect. That said, both the numerical model and the analytical get the order of magnitude of the initial accelerations right. Fig. 3.14 shows initial and maximum accelerations ω predicted by the models compared to initial experimental values. The numerical and analytical models essentially agree on the magnitude of initial accelerations. If the turbine is released from an initial angular velocity ω0 close to or above nominal speed ωnom, the initial acceleration is also the highest acceleration. In this

43 3

2 (rad/s) ω 1 measured analytical numerical 0 024681012 Time (s)

3 measured

) analytical

2 2 numerical 1

/dt (rad/s 0 ω d -1

024681012 Time (s) Figure 3.13. Comparison of overshoot model predictions with measured results. At the top rotational speed, below numerically computed time derivatives. Fig. 3 (c) and 4 (c) from Paper VIII.

regime, the experimental initial accelerations follow roughly the same trend as the model accelerations, although magnitudes are as a rule slightly below predicted values. The maximum runaway speed overshoot, normalised by the runaway speed, as a function of normalised release speed is plotted in Fig. 3.15. Predictions of the numerical model follow the trend set by the experimental values very well. With a different turbine-to-medium inertia relationship, the overshoot will be more or less pronounced. In the case of wind power, the size of the turbine runner and the mass density of air make the phenomenon all but negligible. As an example, Fig. 3.16 shows the runaway behaviour of a 12 kW vertical axis wind turbine, predicted by the two models. The wind turbine is an experimental unit located at Marsta and operated by the Division of Electricity at Uppsala University [90]. The model constants k1, k2 and k3 could be estimated from known properties of the turbine. However, there were no experimental runaway measurements available. Since the turbine type is the same, and since the constants k4 and k5 are associated with wake properties, the values from the Söderfors turbine were used for the Marsta turbine. As expected, there is no noticable overshoot of the runaway speed. Ini- tially, both models agree well with each other. The numerical model reaches

44 3 2.5 num init anal init ) 2 2 num max anal max 1.5

(rad/s exper init 0 '

ω 1 0.5 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 ω /ω 0 nom Figure 3.14. Initial and maximum accelerations predicted analytically and numerically. Fig. 5 from Paper VIII.

1.4 numerical 1.3 experimental rwy ω

./ 1.2 max ω 1.1

1 0 0.2 0.4 0.6 0.8 1 1.2 1.4 ω /ω 0 nom Figure 3.15. Maximum angular velocity overshoot normalised by runaway angular velocity. Fig. 6 from Paper VIII.

(rad/s) 16 ω

14 analytical numerical 13 0246810 Time (s) Figure 3.16. Runaway development of a 12 kW vertical axis wind turbine. Fig. 9 from Paper VIII.

45 runaway speed a little before the analytical model, since the latter does not take into account the time lag in wake development. On the whole, both models give a very similar account of the runaway behaviour, which it would be very interesting to compare with experimental data. In summary, both models derived in Paper VIII yield reasonable estimates of peak accelerations to which a runaway turbine is subjected. The numerical model furthermore captures the whole runaway process very well. The point of predicting accelerations and peak rotational speeds is to estimate the forces acting on the turbine. Calculation of these forces was beyond the scope of Paper VIII.

46 4. Future work

Marine current energy conversion is still in its infancy as a scientific field. There are infinite possibilities for continued research. Limiting the discussion to the Söderfors experimental station, there are still many openings available. A few examples: • The possibilities to study the wake of the turbine should be exploited. Paper VII showed that it is possible to study the wake with available equipment, even though the methodology needs further refinement. The Söderfors site offers (nearly) steady flow conditions – as opposed to a tidal site, where flow conditions are always changing – which makes wake studies very doable, and there is little published material on real- world wake measurements available. Development of numerical tools to model the wake would also be of interest. • The phenomenon of runaway speed overshoot considered in Paper VIII should be studied further. In addidtion to characterizing the runaway behaviour, the forces involved must be studied. This will require further and more advanced numerical modelling. Experimental measurement of forces on the turbine would be highly desirable, but would require further development of the turbine with the addition of appropriate sen- sors etc. In this particular area, prior publications are also very scarce. • Modifications to the turbine, such as changing the fixed pitch of the turbine blades, might be considered. Comparison with results from the original zero-pitch setting would be very interesting. Such results would also be very useful for numerical model development and validation. • Work on connecting the test station to the electrical grid is already un- derway. • The Söderfors location provides for the possibility to actively change the flow conditions (through cooperation with the hydro power plant operator). Such experiments require due planning and coordination, but would make for interesting tests of the control system.

5. Concluding remarks

Marine current energy conversion is a subject of research which has been around for a long time but has seen an increased and intensified interest in recent years. In that sense, it could be said to be relatively young or even new, or at least filled with new topics that evolve and develop. This thesis has considered some limited parts of a few of these topics. If a single, overall conclusion should be drawn from the results of the papers on which this thesis is based, it would have to be that the Söderfors Project has shown that it is possible to build small energy conversion units for low flow speeds with reasonable system efficiency. There are numerous ways in which the design of the unit at Söderfors could be optimised and improved, and so a second-generation machine might be expected to perform significantly better in the same conditions. Engineering is an iterative business. Another conclusion which might be said to be supported by the material in the thesis is that real-world experiments have an important role to fill in engineering sciences. Looking at published results in the field of marine current energy conversion, one will find a lot of numerical studies and quite a few scale-model experiments. Out-of-laboratory experiments are relatively unusual. There is an experience bank being built within the emerging marine current power industry, but for commercial reasons a lot of that experience does not get published. Provided that these conclusions are valid, there is a future for the Söder- fors experimental marine current power station. That is good news for the development of marine current energy conversion.

6. Summary of papers

Paper I A review of the tidal current energy resource in Norway The paper reviews the potential of tidal energy exploitation in Norway, looking at the oceanography of the Norwegian coast, various numerical models for tidal current calculation and three different resource assessments, one of which is made speciﬁcally for this paper. The conclusion is that tidal energy should be an interesting option for Norway in terms of renewable ocean energy. The thesis author wrote the section on numerical models, contributed to the text of the introduction and discussion sections and made the ﬁgures showing maps. Published in Renewable & Sustainable Energy Reviews, 13(8):1898–1909, 2009.

Paper II A design study of marine current turbine-generator combinations The paper discusses three different turbine-generator combinations to achieve a certain power output at a particular water ﬂow speed. Advantages and dis- advantages with the different designs are considered. The thesis author made the turbine simulations, did the majority of the writing of the paper and presented it orally at the OMAE 2009 conference. Published in Proceedings of the 28th International Conference on Offshore Mechanics and Arctic Engineering, OMAE 2009, paper OMAE2009-79350, pages 1–7, June 2009. Reviewed conference paper.

Paper III A parameter study of the influence of struts on the performance of a vertical-axis marine current turbine The paper reports a numerical study of how the level of acceptable stress on a turbine blade influences turbine efficiency through the requirement of supporting struts for the blade. The thesis author made some of the numerical calculations and contributed to the writing of the paper. Published in Proceedings of the 8th European Wave and Tidal Energy Con- ference, EWTEC09, Uppsala, Sweden, pages 477–483, September 2009. Re- viewed conference paper.

51 Paper IV The Söderfors Project: Construction of an experimental hydrokinetic power station The paper describes the current state and short term plans concerning the Söderfors Project. Some design choices, site selection and other aspects of the project are also discussed. The thesis author made some of the ﬁgures and contributed to the writing of the paper. Published in Proceedings of the 9th European Wave and Tidal Energy Con- ference, EWTEC11, Southampton, UK, 5 pages, September 2011. Reviewed conference paper.

Paper V The Söderfors project: Experimental hydrokinetic power station deployment and ﬁrst results The paper reports the deployment of the turbine at Söderfors and some initial measurements made shortly after deployment. The thesis author planned and coordinated the deployment activities, participated in making the reported measurements and did the majority of the writing of the paper. Published in Proceedings of the 10th European Wave and Tidal Energy Conference, EWTEC13, Aalborg, Denmark, 5 pages, September 2013. Re- viewed conference paper.

Paper VI Experimental results of a DC bus voltage level control for a load controlled Marine Current Energy Converter The paper discusses different load control methods for a marine current energy converter based on experiments carried out at the Söderfors test site. The thesis author participated in measurements and contributed to the parts of the text on turbine theory and test site description. Published in Energies, 8:4572–4586, 2015.

Paper VII Studying the wake of a marine current turbine using an acoustic doppler current proﬁler The paper describes a method for measuring the wake of the Söderfors turbine using mobile acoustic doppler current proﬁlers and high-accuracy satel- lite navigation systems. Examples of measurement results are given and various aspects of the chosen methodology are discussed.

52 The thesis author participated in the measurements, wrote most of the paper and presented it orally at the EWTEC 2015 conference. Published in Proceedings of the 11th European Wave and Tidal Energy Conference, EWTEC15, Nantes, France, pages 09A2-3-1–8, September 2015. Reviewed conference paper.

Paper VIII One-dimensional modelling of marine current turbine runaway behaviour The paper derives two models, one analytical and one numerical, to describe turbine runaway behaviour. Model results are compared to experimental results from the Söderfors experimental station. The thesis author conceived of, derived and implemented the models, participated in the measurements and wrote the manuscript. Submitted to Energies, February 2016.

Paper IX Experimental demonstration of performance of a vertical axis marine current turbine in a river This paper reports the performance of the Söderfors turbine in terms of its power coefﬁcient in comparison to published values for other turbines. The thesis author participated in the design, construction and deployment of the experimental station, took part in making the reported measurements and wrote the manuscript. In manuscript, March 2016.

Paper X Validation of a coupled electrical and hydrodynamic simulation model for vertical axis marine current energy converters The paper describes a coupled electrical-hydrodynamic numerical model for vertical axis marine current energy converters and the validation of the model against experimental results from Söderfors. The thesis author participated in the measurements and contributed to the analysis of the experimental results. In manuscript, March 2016.

7. Sammanfattning på svenska

Marina strömmar, d.v.s. strömmar i hav och älvar, utgör en stor energiresurs. Vidare är denna resurs förnybar, och givet att sätt att utnyttja den kan tänkas ut som i sig själva är rena (i någon miljömässig mening) kan den komma att lämna ett betydelsefullt bidrag till världens energimix. Denna avhandling redogör för forskning om energiomvandling ur marina strömmar i vid mening. Forskningen har bedrivits vid avdelningen för elek- triciteslära vid Uppsala universitet och har kretsat kring eller varit kopplad till avdelningens försöksanläggning för marin strömkraft i Söderfors. Avhand- lingen bygger på de bilagda uppsatserna, på engelska ’Paper’, som hänvisas till med romerska siffror. Hav och älvar har utgjort en kraftkälla för mänskliga samhällen under lång tid. Elkraftstationer som utnyttjar tidvatten anlades på olika håll i världen på 1960-talet. På senare år har, i ljuset av risken för klimatförändringar till följd av det omfattande bruket av fossila bränslen, intresset för utvinning av el ur marina strömmar vaknat till liv. Särskilt stort är intresset för tidvattenström- mar, som på vissa platser har goda förutsättningar att täcka en stor andel av det lokala eller regionala elbehovet. Energiresursen marina strömmar karakte- riseras av att vara förnybar och intermittent men förutsägbar, varav sistnämnda egenskap (som i särskild grad gäller tidvattenströmmar) särskiljer den från de ﬂesta andra förnybara energikällor. Marin strömkraft som forskningsfält är på stark tillväxt. Vid avdelningen för elektricitetslära har forskning om marin strömkraft bedrivits under många år. Tidiga numeriska och teoretiska studier följdes av konstruktion och bygge i laboratoriemiljö av en generatorprototyp för ström- kraft. Generatorn var permanentmagnetiserad och utmärktes av att vara ex- tremt långsamtgående, vilket är en förutsättning för effektiv energiomvandling i låga strömningshastigheter utan växellåda melan turbin och generator. På dessa erfarenheter byggdes sedan Söderforsprojektet med målet att kon- struera, bygga, sätta ut och driva en försöksanläggning för marin strömkraft i Dalälven vid Söderfors. Platsen, som givit projektet dess namn, valdes efter en omfattande inventering av tänkbara platser runt om i Sverige. Valet föll till slut på Söderfors p.g.a. de lämpliga nivåerna på vattenhastigheter och vattendjup, gynnsamma bottenförhållanden, möjligheten till samverkan med operatören av den konventionella vattenkraftstationen på platsen samt den relativa närhe- ten till Uppsala. Maskinen sattes i älven den 7 mars 2013. Söderforsprojektet ﬁnns beskrivet i Paper IV och Paper V. I Paper I redogörs för en studie av förutsättningarna för tidvattenkraft i Nor- ge. Längs norska kusten förekommer starka tidvattenströmmar på åtskilliga

55 ställen till följd av de många fjordarna. Vidare finns i Norge en stark offshore- industriell tradition att bygga på och en uttalad politisk vilja att öka den för- nybara andelen i landets energiförsörjning. Avancerade numeriska modeller för beräkning av havsströmmar som utvecklats vid norska universitet visar på den akademiska styrkan inom landet på detta område, och modellerna torde gå att vidareutveckla för tidvattenkraftsändamål. Slutsatsen av studien är att tidvattenkraft borde vara av stort intresse för Norge att utveckla. Två uppsatser handlar om olika designöverväganden vid konstruktion av ett strömkraftverk. Paper II behandlar kombinationen av turbin och generator. Huvudtesen är att man inte kan betrakta turbin och generator var för sig, utan för bästa resultat måste de båda huvudkomponenterna optimeras tillsammans utifrån de förutsättningar som råder på platsen där kraftverket skall sättas ut. Långa turbinblad är som regel gynnsamt ur effektivitetssynpunkt, men ju mer långsmalt ett blad blir desto fler stöttor måste till vilket ger hydrodynamiska förluster som måste tas hänsyn till. Om detta handlar Paper III, som studerar stöttornas påverkan på turbinens effektivitet utifrån dess geometri. Mätningar gjorda vid Söderforsanläggningen ligger till grund för flera uppsatser. Paper V beskriver sjösättningen av maskinen men redovisar också de första mätningarna av vattenfart samt elektrisk ström och spänning. Mätning- arna visade att försöksanläggningen var tagen i drift och fungerade, vilket ut- gjorde en betydelsefull milstolpe i projektet. Mer omfattande mätningar av turbinens effektkoefficient, ett mått på hur effektivt den fångar effekt ur vattnet, redovisas i Paper IX. Resultatet visar att det går att bygga turbiner för låg strömningshastighet med god effektivitet (jämförbar med betydligt snabbare turbiners). Tillämpningen av olika styrstrategier för generatorn studeras i Pa- per VI. Beroende på vilket last som kopplas in och hur den styrs, uppträder turbin och generator olika i termer av varvtalsvariation, effektförluster m.m. I Paper X studeras en simuleringsmodell för turbin och generator och dess för- måga att förutse maskinens beteende vid stegvis ändring av löptal (rotations- hastigheten i förhållande till vattenfarten). Jämförelser med mätningar från Söderfors visar att modellen väl förutser beteendet vid förändringar i närheten av optimalt löptal. Nedströms om turbinen bildas när den roterar ett turbulent område med läg- re genomsnittsfart är friströmsfarten, till följd av turbinens växelverkan med vattnet. Området kallas vak och har stor betydelse, bl.a. vid utplacering av flera turbiner i en s.k. park då dessa kan komma att hamna ”i skuggan” av varandra med nedsatt effektivitet som följd. Turbinvaksstudier är därför in- tressanta. Paper VII beskriver försök med vakmätningsmetodik som bedrivits från båt i Söderfors med ADCP (mätinstrument för vattenfart som utnyttjar ultraljud) och satellitnavigeringsutrustning. Ett antal erfarenheter som dragits av försöken redovisas, liksom erhållna mätresultat. Slutsatsen är att metoden, med vissa begränsningar, går att använda för vakmätning. Paper IX redovisar enkla modeller för beskrivning av turbinens beteende vid rusning samt jämförelser av modellernas utfall med mätningar från Sö-

56 derfors. Vid normal drift balanseras det pådrivande hydrodynamiska vridmomentet på turbinen av det bromsande elektriska vridmomentet som uppstår då effekt tas ut ur generatorn. Om lasten plötsligt kopplas ur, t.ex. till följd av nå- got inträffat fel, försvinner också det bromsande vridmomentet och turbinens varvtal ökar tills ett nytt jämviktsläge uppnås vid ett varvtal där nettovrid- momentet är noll, det s.k. rusningsvarvtalet. Till följd av förhållandet mellan trögheten hos å ena sidan den roterande massan i löphjul och rotor och å den andra det omgivande vattnet, kommer en strömkraftsturbin att varva upp en god bit över det slutliga rusningsvarvtalet innan den saktar ner till det. Detta fenomen är inte alls lika tydligt förekommande hos t.ex. vindkraftsturbiner. Då de krafter som turbinbladen utsätts för beror av varvtalet, blir maximalt rus- ningsvarvtal av stort intresse vid dimensionering av bladen. I Paper IX härleds en analytisk och en numerisk modell för rusning, där den förstnämnda inte fångar övervarvningsfenomenet då den ej omfattar vattnets fartutveckling. Den numeriska modellen tar hänsyn till trögheten hos det roterande systemet såväl som hos vattnet. Resultaten stämmer anmärkningsvärt väl med experi- mentella värden vid en jämförelse. Avhandlingen avslutas med några förslag på fortsatt forskning. Inom ramen för Söderforsprojektet bör fortsatta vakstudier bedrivas, och rusningsfenome- net bör också undersökas vidare. Förändringar av turbinen, t.ex. ändring av inställd bladvinkel, bör övervägas för jämförelser med effektkoefficientvärden med dagens vinkelinställning. Arbete med nätanslutning av anläggningen har redan påbörjats. Möjligheten till styrning av vattenflödet, som finns genom samverkan med kraftstationen uppströms, bör utnyttjas för olika försök med styrsystemet.

Acknowledgements

My PhD candidate position was originally funded by Statkraft AS, which ﬁnancial support is hereby gratefully acknowledged. Further support for the Söderfors project is acknowledged in the included papers.

På det personliga planet vill jag tacka min handledare, professor Mats Leijon, och min biträdande handledare, professor emeritus Sven Israelsson, för tiden som doktorand. Ett tack för gott samarbete och medförfattarskap vill jag också rikta till kamraterna i strömkraftsgruppen genom åren – Karin Thomas, Katarina Yuen, Anders Goude (med särskilt omnämnande för gott rumskamratskap), Mårten Grabbe, Emilia Lalander, Johan Forslund och Nicole Carpman. Här måste jag också tacka Anders Nilsson, som ritade maskinen i Söderfors åt oss, och sända en tanke till alla ex-, sommar- och projektjobbare som hjälpte oss att bygga den. Jag vill vidare tacka den tekniska och administrativa personalen på avdelningen för elektricitetslära och institutionen för teknikvetenskaper för allt stöd genom åren. Samtliga på ellära förtjänar mitt tack för de många muntra stunder som förevarit i olika sammanhang. Om jag särskilt nämner medlemmarna i den lösligt sammansatta avdelningskören och dem, som brukar hänga i baren, är det ingalunda avsett att förringa min tacksamhet gentemot någon annan. Slutligen är jag ett sjusärdeles stort tack skyldig mina föräldrar och svärföräldrar samt sist men inte minst min hustru Kristina, vars fantastiska stöd med s.k. markservice möjliggjort det praktiska skrivandet av denna avhandling.

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