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Wave energy plants Control strategies for avoiding the stalling behaviour

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Renewable Energy 35 (2010) 2639e2648 Contents lists available at ScienceDirect Renewable Energy journal homepage: www.elsevier.com/locate/renene Wave energy plants: Control strategies for avoiding the stalling behaviour in the Wells turbine Modesto Amundarain*, Mikel Alberdi, Aitor J. Garrido, Izaskun Garrido, Javier Maseda Dept. of Automatic Control and Systems Engineering, EUITI Bilbao, University of the Basque Country, Plaza de la Casilla 3, 48012 Bilbao, Spain article info Article history: Received 16 October 2009 Accepted 10 April 2010 Available online 6 May 2010 Keywords: Wave energy Oscillating water column Wells turbine Double-fed induction generator Control abstract This study analyzes the problem of the stalling behaviour in Wells turbines, one of the most widely used turbines in wave energy plants. For this purpose two different control strategies are presented and compared. In the first one, a rotational speed control system is employed to appropriately adapt the speed of the double-fed induction generator coupling to the turbine, according to the pressure drop entry. In the second control strategy, an airflow control regulates the power generated by the turbine generator module by means of the modulation valve avoiding the stalling behaviour. It is demonstrated that the proposed rotational speed control design adequately matches the desired relationship between the slip of the double-fed induction generator and the pressure drop input, whilst the valve control using a traditional PID controller successfully governs the flow that modulates the pressure drop across the turbine. Ó 2010 Elsevier Ltd. All rights reserved. 1. Introduction The use of distributed energy resources is increasingly being pursued as a supplement and an alternative to large conventional central power stations [1]. Therefore, the control of the power delivered to the grid is becoming an important topic, especially as the number of distributed power generation systems increases. In this context, the ocean composes an enormous and predictable source of renewable energy with the potential to satisfy an important percentage of the worldwide electricity supply. It has been estimated that 0.02% of the renewable energy available within the oceans would satisfy the present world demand for energy [2]. There exist different forms of renewable energy available in the oceans: waves, currents, thermal gradients, salinity gradients, tides and others. During the last years, there has been a worldwide resurgent interest for wave energy. Harnessing the immense wave power of the world’s oceans can be part of the solution to our energy problems. Conversion of the wave resource alone could supply a substantial part of electricity demand of several countries in Europe, such as Ireland, UK, Denmark, Portugal, Spain and others. The Electric Power Research Institute has estimated the wave energy along the U.S. coastline at 2100 Twh per year, which represents half the total U.S. consumption of electricity. Ocean * Corresponding author. Tel.: þ34 946014503; fax: þ34 946014300. E-mail address: molty.amundarain@ehu.es (M. Amundarain). 0960-1481/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.renene.2010.04.009 waves arise from the transfer of energy from the sun to the wind and then to the water. Solar energy creates wind which then blows over the ocean, converting wind energy to wave energy. Once this conversion has taken place, wave energy can travel thousands of miles with little energy loss. Most importantly, waves are a regular source of power with an intensity that can be accurately predicted several days before their arrival. There exist many different technologies to convert ocean wave power into electricity and, nowadays, it remains unclear what the winning technical approach is. This is reflected by several different technical approaches and different methods and systems for converting this power into electrical power, such as oscillating water columns (OWC), hinged contour devices such as the Pelamis, overtopping devices such as the wave dragon and the Archimedes wave [3]. However, the oscillating water column type wave energy harnessing method is considered as one of the best techniques to convert wave energy into electricity. As shown schematically in Fig. 1, the OWC consists of a partially submerged, hollow structure, which is open to the sea below the water line. This structure encloses a column of air on top of a column of water. As waves impinge upon the device, they cause the water column to rise and fall, which alternatively compresses and depressurises the air column. If this trapped air is allowed to flow to and from the atmosphere via a turbine generator, energy can be extracted from the system and used to generate electricity. As indicated in Ref. [4], two different turbines are currently in use; the Wells turbine [5e8] and the impulse turbine [9]. Both 2640 M. Amundarain et al. / Renewable Energy 35 (2010) 2639e2648 2. Theoretical analysis and modelling In this section we will present the necessary theoretical analysis to model the different components of the systems, i.e.: wave model, oscillating water column, Wells turbine, and the induction generator. Fig. 1. Scheme of OWC. these turbines are currently in operation in different power plants in Europe, India, Japan, Korea, and so forth [10]. The Wells turbine, which was developed by Prof. Alan Wells in 1976, has been extensively researched over the last 30 years. This turbine, converts the bi-directional airflow into mechanical energy in the form of unidirectional shaft power, which is in turn used to move the wound rotor induction machine. The use of double-fed induction generator, DFIG, has a huge potential in the development of distributed renewable energy sources [11,12]. DFIG is essentially an asynchronous machine, but instead of the rotor windings being shorted (as in a “squirrel-cage” induction machine), it is arranged to allow an AC current to be injected into the rotor, via the power converter. By varying the phase and frequency of the rotor excitation it is possible to optimise the energy conversion [13]. The frequency converter only has to process the generator’s slip power fraction, which is generally no more than 30% of the generator rated power. This reduced rating for the frequency converter implies an important cost saving, compared to a fully rated converter. Several prototypes of OWCs have been built, such as, Toftstalen, Norway, 1985; Trivandrum, India, 1990; Pico, Portugal, 1999; Limpet, UK, 2000; Port Kembla, Australia, 2005 [14]. The Basque Energy Board (EVE) was created by the Basque Government in 1982 and has been the main agent of energy policy in the Basque Country. The NEREIDA MOWC project is intended to demonstrate the successful incorporation of the OWC technology with Wells turbine power take-off into a newly constructed rubble mound breakwater in the Basque location of Mutriku, in the northern coast of Spain. This demo project aims to demonstrate the viability of this technology for future commercial projects. In this context, the objectives of the present work are twofold: on one hand, to present and compare two different control strategies for avoiding the stalling behaviour in the Wells turbine and, on the other hand, to particularize these results to the case of Mutriku. The paper is organized as follows: in Section 2 is presented a theoretical analysis and modelling of the waves, OWC, Wells turbine, and DFIG. In Section 3, the problem of the stalling behaviour in the Wells turbine and the uncontrolled case drawbacks are described. Section 4 presents the control strategies for avoiding the stalling behaviour in Wells turbine in two different ways. Results and discussions comparing the uncontrolled and controlled cases are presented in Section 5. Finally, concluding remarks are given in Section 6. 2.1. Wave theories. Power per meter of wave front The first objective of our analysis is to find the power per meter of wave front (or wave crest) to model the input to the system. The mathematical description of periodic progressive waves is not a trivial issue. Some well-known works of authors, such as Muir Wood (1969), Le Mahaute (1969) and Korma (1976) recommended ranges of application for the various wave theories [15]. Therefore, a number of regular wave theories of diverse degree of complexity have been developed to describe the water particle kinematics associated with ocean waves. These would include linear or Airy wave theory, Stokes second order and other higher order theories, stream-function and cnoidal wave theories, amongst others. Fortunately, the earliest (and simplest) description, attributed to Airy in 1845, is generally accurate enough for many engineering purposes and specifically for control design purposes [16]. Linear (or Airy) wave theory describes ocean waves as simple sinusoidal waves. Surfaces waves can be classified according to the ratio of the wavelength (L) to the water depth (h), as follows:  Deep-water: h/L > 0.25.  Transitional water: 0.25 ! h/L > 0.05.  Shallow-water: 0.05 ! h/L. NEREIDA MOWC is a project involving the integration of an OWC system with Wells turbines in the new rockfill breakwater at the harbour in Mutriku, located in the Basque coast of Spain. The technical solution adopted in this case consists of 16 OWCs, to give an active collector length of close to 100 m. The breakwater is located in 7 m (h) of MWL or SWL (mean water level or still water level) [17]. The average height of waves in the Cantabrian coast is less than 2 m with a period between 8 and 12 s [18]. According to these data, the most suitable approach in our case is to use the linear wave theory for transitional water. In Fig. 2 is shown a wave with its characteristic parameters. The part of the wave profile with the maximum elevation above the still water level (SWL) is called the wave crest and the part of the wave Fig. 2. Ocean wave. M. Amundarain et al. / Renewable Energy 35 (2010) 2639e2648 2641 profile with the lowest depression is the wave trough. The distance from the SWL to the crest or the trough is the amplitude of the wave and the wave height (H) is defined as the total distance from the trough to the crest. The wavelength of a regular wave at any depth is the horizontal distance between successive points of equal amplitude and phase for example from crest to crest or trough to trough and is defined according to the linear theory as: L ¼ gT 2 2p tanhð2ph=LÞ (1) where: L: wavelength (m). g: gravitational constant (9.81 m/s2). T: wave period (s). h: water depth (distance from ocean floor to SWL) (m). The equation describing the free surface as a function of time t and horizontal distance x for a simple sinusoidal wave can be shown to be: h ¼ ðH=2Þ cosðð2px=LÞ À ð2pt=TÞÞ (2) where: h: elevation of the water surface relative to the SWL (m). H: wave height (m). The propagation speed or celerity of a regular wave is given by: C ¼ L=T ¼ gT 2p tanhð2ph=LÞ (3) The total average wave energy per unit surface area is called the specific energy or energy density and is given by: Edensity ¼ E L ¼ rwgH2 8 (4) The energy density of a wave, shown in Eq. (4), is defined as the mean energy flux crossing a vertical plane parallel to a wave’s crest. The energy per wave period represents the wave’s power density. Eq. (5) shows how the wave power density can be found by dividing the energy density by the wave period. Pdensity ¼ Edensity T ¼ rwgH2 8T (5) where: Edensity: wave energy density (J/m2). Pdensity: wave power density (W/m2). The rate at which wave energy propagates is directly dependent on the group velocity of the wave. The group velocity is given by: Cg ¼ nC (6) where: Cg: celerity (wave front velocity) (m/s). C: wave celerity (m/s). n: constant determined by: n ¼  11 2 þ 4ph=L  sinhð4ph=LÞ (7) Therefore, since a wave resource is typically described in terms of power per meter of wave front, it can be computed by multiplying the energy density by the wave front velocity as expressed in Eq. (8) [19]. L Pwavefront ¼ nCEdensity ¼ CgEdensity; with C ¼ T (8) Pwavefront ¼ rwgH2L1 16T þ 4ph=L  sinhð4ph=LÞ ðW=mÞ (9) 2.2. Oscillating water column The OWC energy equations are similar to those used for wind turbines. Eq. (10) expresses the power available from the airflow in the OWC’s chamber.   Pin ¼ p þ rVx2=2 Vxa (10) where: Pin: pneumatic incident power (W). p: pressure at the turbine duct (Pa). r: air density (kg/m3). Vx: airflow speed at the turbine (m/s). a: area of turbine duct (m2). 2.3. Turbo-generation equipment The equation for the system turbo-generator can be written as: Jvvut  ¼ Tt À Tg (11) where: J: moment of inertia of the system (kg m2). u: angular velocity of rotor (rad/s). Tt: torque produced by the turbine (N m), calculated below. Tg: torque imposed by the generator (N m), calculated below. 2.3.1. Wells turbine The input to the Wells turbine is the pulsating pressure drop across the turbine rotor which is generated due to the airflow from the OWC chamber. The equations for the turbine are: h i dP ¼ CaKð1=aÞ Vx2 þ ðrutÞ2 (12) h i Tt ¼ CtKr Vx2 þ ðrutÞ2 (13) Tt ¼ dPCtCaÀ1ra f ¼ VxðrutÞÀ1 (14) (15) Q ¼ Vxa (16) hturbine ¼ TtutðdPQ ÞÀ1 ¼ CtðCaphyÞÀ1 (17) K ¼ rb ln=2 (18) 2642 M. Amundarain et al. / Renewable Energy 35 (2010) 2639e2648 14 12 Ca (Power Coefficient) 10 8 6 Fig. 3. Dynamic d-q equivalent circuit of DFIG d axis circuit. 4 where: dP: pressure drop across the rotor (Pa). Ca: power coefficient. K: constants (kg/m). a: cross sectional area (m2). Vx: airflow velocity (m/s). r: mean radius (m). ut: turbine angular velocity (rad/s). Ct: torque coefficient. f: flow coefficient (can be expressed as angle). b: blade height (m). l: blade chord length (m). n: number of blades. 2.3.2. Double-fed induction generator (DFIG) Figs. 3 and 4 show the d-q dynamic model equivalent circuits. As it is well-known, the main advantage of the d-q dynamic model of the machine, also know as vector control or field oriented control is that all the sinusoidal variables in stationary frame appear as DC quantities referred to the synchronous rotating frame [13]. Hence, the equations for the generator are simplified to: vqs ¼ Rsiqs þ ddtjqs þ uejds (19) vds ¼ Rsids þ ddtjds À uejqs (20) vqr ¼ Rriqr þ ddtjqr þ ðue À urÞjdr (21) vdr ¼ Rridr þ ddtjdr À ðue À urÞjqr Te ¼ 32P2jdsiqs À  jqsids (22) (23) 2 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Flow Coefficient Fig. 5. Power coefficient vs flow coefficient. and the flux linkage expressions in terms of the currents can be written as follows: jqs ¼ Lsiqs þ Lmiqr; jqr ¼ Lriqr þ Lmiqs (24) jds ¼ Lsids þ Lmidr; jdr ¼ Lridr þ Lmids (25) Ls ¼ Lls þ Lm; Lr ¼ Llr þ Lm where: (26) Rs, Lls: stator resistance and leakage inductance (U). Rr, Llr: rotor resistance and leakage inductance (U). Lm: magnetizing inductance (H). Ls, Lr: total stator and rotor inductances (H). vqs, iqs: q axis stator voltage and current (V, A). vqr, iqr: q axis rotor voltage and current (V, A). vds, ids: d axis stator voltage and current (V, A). vdr, idr: d axis rotor voltage and current (V, A). jqs, jds: stator q and d axes fluxes (Wb). jqr, jdr: rotor q and d axes fluxes (Wb). 0.6 0.5 0.4 X: 0.3 Y: 0.34 0.3 Ct (Torque Coefficient) 0.2 0.1 0 Fig. 4. Dynamic d-q equivalent circuit of DFIG q axis circuit. -0.1 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Flow Coefficient Fig. 6. Torque coefficient vs flow coefficient. M. Amundarain et al. / Renewable Energy 35 (2010) 2639e2648 2643 Pressure drop (Pa) Turbine power (W) 7000 6000 5000 4000 3000 2000 1000 0 0 10 20 30 40 50 60 70 80 90 100 time (s) Fig. 7. dP ¼ j7000 sinð0:1ptÞj Pa: ue: stator supply frequency (rad/s). P: number of poles of the machine. ur: rotor electrical speed ¼ u (P/2) (rad/s). Te: electromagnetic torque (N m). 3. Problem formulation: stalling behaviour in the Wells turbine The performance of the Wells turbine is limited by the onset of the stalling phenomenon on the turbine blades. In order to explain the nature of the stalling behaviour it is recommendable to introduce some previous concepts regarding the operation of the system. The torque and power developed by the turbine can be computed based on the behaviour of the power coefficient and the torque coefficient with respect to the flow coefficient [20]. These are the characteristic curves of the turbine under study and their shape may be seen in Figs. 5 and 6. From Eq. (15), it may be observed that when the airflow velocity increases, the flow coefficient also increases provoking the so-called stalling behaviour in the turbine. This behaviour is also clearly observable in Fig. 6 when f approaches 0.3 (this value may change depending on the characteristic curve of each turbine). In order to x 104 6 5 Stalling behabior 4 3 2 1 0 Average value (21.554kw) -1 0 10 20 30 40 50 60 70 80 90 100 time (s) Fig. 9. Pt vs time for dP ¼ j7000 sinð0:1ptÞj Pa: model the waves, it is necessary to take into account the spectrum of the wave climate, which indicates the amount of wave energy at different wave frequencies. Considering this data and the value T ¼ 10 s [17] for the standard input pressure drop in our case, the turbine may be experimentally modelled as j7000 sinð0:1ptÞj Pa; as it may be seen in Fig. 7. With this input, the variation of the flow coefficient for the uncontrolled system may be seen in Fig. 8. It can be observed that its value is higher than 0.3, which corresponds to the stalling behaviour threshold value for our turbine. In this sense, Figs. 9 and 10 show the power extracted from the turbine and generator respectively. Please note that the negative sign of the generator power in Fig. 10 is due to the sign convention used, and it just means that this power is provided to the grid. As indicated before, it may be clearly observed that the power to be extracted by the turbine and generator is limited by its stalling behaviour. In conclusion, the power to be extracted by the OWC-turbine generator module is limited by the stalling behaviour in the Wells turbine, composing therefore the main problem to resolve. 0.6 x 105 3 Flow Coefficient Power generated (W) 0.5 2.5 2 0.4 Stalling behavior 1.5 0.3 Averaga value (-20.053kw) 1 0.2 0.5 0.1 0 0 0 10 20 30 40 50 60 70 80 90 100 time (s) Fig. 8. Flow coefficient vs time for dP ¼ j7000 sinð0:1ptÞj Pa: -0.5 0 10 20 30 40 50 60 70 80 90 100 time (s) Fig. 10. Pg vs time for dP ¼ j7000 sinð0:1ptÞj Pa: 2644 M. Amundarain et al. / Renewable Energy 35 (2010) 2639e2648 Fig. 11. Rotational speed control scheme. 4. Control strategies for avoiding the stalling behaviour The input power to any wave energy generator must be variable when considering both short and long terms, since each wave cycle produces two power cycles giving a short-term variation, and a fluctuation in the medium and long-term wave environment that produces the corresponding change in the output of the induction generator [21]. Therefore, it is necessary to establish a control strategy to accommodate establish a control strategy to accommodate these fluctuations subject to the local conditions. Two control strategies have been considered. 4.1. Rotational speed control The undesired stalling behaviour can be avoided or delayed if the turbine accelerates fast enough in response to the incoming airflow which can be accomplished by increasing the permissible slip of the generator, allowing the system to reach higher speeds [22e25]. Thus, the control system for the flow coefficient is achieved by varying the slip of the DFIG. This type of generator has an ACeDCeAC converter connected to the rotor windings instead of the stator windings. The advantage is that variable speed operation of the turbine is possible whereas the converter can be much smaller, allowing also to achieve cost reduction. The power rating of the converter is often chosen to be about 1/3 of the generator rating, which is the rate that has been implemented, as shown schematically in Fig. 11. Our purpose is to calculate the maximum pressure drop across the rotor of the turbine without stalling behaviour. To do so, numerous simulations have been carried out in order to study the variation of the flow coefficient for different pressure drops and slip Table 1 Flow coefficient vs pressure drop and slip. P0 ðdP ¼ jP0 sinð0:1ptÞj PaÞ 0e5500 5500e5790 5790e5975 5975e6175 6175e6375 6375e6600 6600e6850 6850e7100 7100e7375 7375e7670 f 0e0.2987 0e0.2999 0e0.2995 0e0.2999 0e0.2995 0e0.2995 0e0.2999 0e0.2998 0e0.2998 0e0.2999 slipAVER À0.0056 À0.0234 À0.0413 À0.0600 À0.0790 À0.0986 À0.1194 À0.1406 À0.1628 À0.1860 of the generator rotor. The results may be observed in Table 1 which shows the variation of flow coefficient for different values of pressure drop (dP) and slip of the DFIG. Using this table, it is possible to derive an optimum range for the slip as a function of the pressure drop avoiding stalling in the turbine. The control block of Fig. 11 changes the value of the slip of the induction generator according to the parameters studied in Section 3 and the optimal values of slip for each specific range of pressure drop presented in Table 1. This study may be extended to other Wells turbines, since all of them present similar behaviour. In this way, our control allows to vary the higher velocities of the system and avoid the stalling behaviour. The control scheme functioning is detailed in what follows. The DFIG is attached to the Wells turbine by means of the gearbox. As indicated before, the DFIG stator windings are connected directly to the grid while the rotor windings are connected to the back to back (AC/DC/AC) converter. The converter is composed of a grid side converter (GSC) connected to the grid, and a rotor side converter (RSC) connected to the wound rotor windings. The RSC controls the active power and reactive power of the DFIG independently, while the GSC controls the DC voltage and grid side reactive power. The RSC is expected to achieve the following objective: to regulate the DFIG rotor speed for maximum wave power generation without stalling behaviour in the Wells turbine. In order to achieve independent control of the stator active power (by means of the speed controller) and reactive power (by means of rotor current regulation), Turbine speed (rad/s) 78 77 a 76 75 740 50 100 150 200 250 300 350 Turbine speed (rad/s) 95 90 b 85 80 75 0 Average value 50 100 150 200 250 300 350 time (s) Fig. 12. ut vs time for dP ¼ j7000 sinð0:1ptÞj Pa: (a) Uncontrolled case, (b) rotational speed control. M. Amundarain et al. / Renewable Energy 35 (2010) 2639e2648 2645 Pgref OWC TURBINE GENERATOR PID e dP dP Wt J(dw/dt)=Tt-Tg Wt Tt Wg Tg Pg Tt Wg Tg Fig. 13. Air valve control scheme. the instantaneous three-phase rotor currents ir,abc are sampled and transformed to d-q components iqr and idr in the stator-flux oriented reference frame. A detailed study about DFIG control devices by means of RSC and GSC has been conducted in Refs. [26,27]. The reaction of the system to the controller may clearly be observed in Fig. 12, where it is shown how the stalling phenomenon is eliminated by increasing the turbine speed due to the generator slip increment in response to the incoming airflow. 4.2. Air valve control In order to implement this second strategy we have opted for an airflow control to regulate the power generated by the turbine generator module by means of a modulation valve. The choice of control has been determined by the fact that despite all the advances in science and technology in recent decades in the field of automatic control, the truth is that the PID remains the most widely used controller in industrial process control. Based on a survey of over 11,000 controllers in the refining, chemicals and pulp and paper industries, 97% of regulatory controllers utilize PID feedback [28]. Most of the feedback loops are controlled using this algorithm or some variant thereof. There is therefore an unquestionable acceptability within the industry and despite its longevity this trend is unlikely to change in the immediate future. The control scheme is shown schematically in Fig. 13. In this sense, the control system implemented in the turbine generator module is composed of a modified anti-windup PID type controller, where the output of the generator is the controlled variable (the generated power) and the pressure drop across the rotor (dP) is the manipulated variable. It must be taken into account that, in our case, the applied control fully accomplishes the desired control requirements. At this point, the authors would like to remark that, as indicated before, the OWC control system presented in this work represents a real application that will be implemented in the near future in the NEREIDA project of the Basque Energy Board (EVE), so that one of the requisites is to maintain the air valve control as simple as possible while meeting the system performance Table 2 Turbine and generator parameters. Turbine n¼8 K ¼ 0.7079 r ¼ 0.7285 a ¼ 1.1763 Pam ¼ 760 Tamb ¼ 30 b ¼ 0.4 Generator P¼4 Rs ¼ 0.0181 Lls ¼ 0.13 Lm ¼ 7.413 Rm ¼ 107.303 Rr ¼ 0.0334 Llr ¼ 0.16 Flow Coefficient Flow Coefficient Flow Coefficient 0.3 a 0.2 0.1 0 0 0.3 b 0.2 0.1 0 0 0.3 c 0,2 0,1 0 0 50 100 150 200 250 300 350 50 100 150 200 250 300 350 50 100 150 200 250 300 350 time(s) Fig. 14. Flow coefficient vs time for dP ¼ j5000 sinð0:1ptÞj Pa: (a) Uncontrolled case, (b) rotational speed control, (c) air valve control. requirements. This is the case of the PID-based control law used for the second control method. Of course, other control schemes were initially considered and developed within the research group, as ANN-based controllers or robust sliding-mode controllers [29], but they were finally discarded for the sake of implementation reliability. On the other hand, the obtained results showed that the tuning procedure was easily performed and provided an adequate response of the system within the operation range. A ZieglereNichols-based experimental procedure has been used to tune the controller. As it is well-known, the ZieglereNichols rule is a heuristic PID tuning rule that attempts to produce reasonable values for the three PID gain parameters. Due to the presence of an integrative model, the first method is not suitable and tuning has been performed with the ZieglereNichols second method [30]. The steps for tuning a PID controller via this method are as follows (using only proportional feedback control): 1. Reduce the integrator and derivative gains to 0. 2. Increase Kp from 0 to some critical value Kp ¼ Kcr at which sustained oscillations occur. If it does not occur then another method has to be applied. Turbine power (w) x 10 4 a2 Average value 0 0 50 5 x 10 Turbine power (w) 4 b3 2 1 0 0 50 x 10 4 c2 100 150 200 250 300 100 150 200 250 300 Turbine power (w) 0 0 50 100 150 200 250 300 time(s) Fig. 15. Pt vs time for dP ¼ j5000 sinð0:1ptÞj Pa: (a) Uncontrolled case, (b) rotational speed control, (c) air valve control. 2646 M. Amundarain et al. / Renewable Energy 35 (2010) 2639e2648 Power generated (w) Power generated (w) Power generated (w) x 10 20 a 10 0 Average value (-20.060 Kw) 0 50 x 10 20 b 10 0 100 150 200 250 300 0 50 x 10 20 c 10 0 0 50 100 150 200 250 300 100 150 200 250 300 time(s) Fig. 16. Pg vs time for dP ¼ j5000 sinð0:1ptÞj Pa: (a) Uncontrolled case, (b) rotational speed control, (c) air valve control. 3. Note the value of Kcr and the corresponding period of sustained oscillation, Pcr. Please note that proportional action is just used during the tuning process to achieve adequate gain and frequency that define the proportional, integral and derivative constants accordingly with this ZieglereNichols method. But once it has been tuned, all three PID actions are employed. Using this procedure some initial values for the controller gains were obtained, and afterwards refined in an experimental trial and error basis over the controlled system, obtaining the following controller parameters: Kp ¼ 0.82; Ti ¼ 1.58 and Td ¼ 1.2. As usual, reference and feedback generate the error signal, which serves as input to the controller. As the valve is electrically actuated through a gearbox, the output control drives the valve into the demanded position. Once in position, it is held steady by an electromagnetic brake. In the event of a control failure or in case the grid connection is lost or an emergency closure is demanded, the brake supply is interrupted and the valve closes by means of the influence of the return weight. In this way, the modulation of the valve aims to adjust the pressure drop across the Wells turbine Turbine power (w) 6 x 10 4 a2 0 0 50 8 x 10 100 150 200 250 300 350 Turbine power (w) 6 b4 2 0 0 50 6 x 10 100 150 200 250 300 350 Turbine power (w) 4 c2 0 0 50 100 150 200 250 300 350 400 450 500 time(s) Fig. 18. Pt vs time for dP ¼ j7000 sinð0:1ptÞj Pa: (a) Uncontrolled case, (b) rotational speed control, (c) air valve control. rotor. A detailed mechanical arrangement and functioning of the used valve can be found in Ref. [31]. 5. Results and discussion In order to improve the stability of the generated power, a comparative study for both uncontrolled and controlled cases has been performed. Three different sea conditions have been considered. The parameters used for the turbine generator module are shown in Table 2. The first case study considers a scenario where waves produce a typical variation in pressure drop of j5000 sinð0:1ptÞj Pa: This pressure drop does not produce the stalling behaviour neither in the uncontrolled case nor in controlled cases, as can be seen in Fig. 14, where the flow coefficient does not exceed the stalling threshold value 0.3. The power generated by the turbine and the induction generator is shown in Figs. 15 and 16 respectively for the uncontrolled case (a), rotational speed control (b) and air valve control (c). As shown in Fig. 16, the generated power is the same in both cases [Fig. 16 (a) and (b)], with an average value of 20.060 kw. In the case where the Flow Coefficient Flow Coefficient Flow Coefficient 0,4 0.3 a 0.2 0.1 00 0.4 0.3 b 0.2 0.1 00 0.4 0.3 c 0.2 0.1 00 50 100 150 200 250 300 350 50 100 150 200 250 300 350 50 100 150 200 250 300 350 time(s) Fig. 17. Flow coefficient vs time for dP ¼ j7000 sinð0:1ptÞj Pa: (a) Uncontrolled case, (b) rotational speed control, (c) air valve control. Power generated (w) Power generated (w) Power generated (w) 5 x 104 a0 Average value (-20.053 kw) -5 50x 104 50 100 150 200 250 300 350 b0 Average value (-27.560 kw) -5 50x 104 50 c0 100 150 200 250 300 350 Average value (-21 kw) -5 0 100 200 300 400 500 time(s) Fig. 19. Pg vs time for dP ¼ j7000 sinð0:1ptÞj Pa: (a) Uncontrolled case, (b) rotational speed control, (c) air valve control. Pressure drop (Pa) Power generated (w) Power generated (w) Power generated (w) 8000 7000 6000 5000 4000 M. Amundarain et al. / Renewable Energy 35 (2010) 2639e2648 2647 5 x 10 a0 -5 0 50 5 x 10 100 150 200 250 300 350 400 450 500 b0 3000 2000 1000 0 0 5 10 15 20 25 30 35 40 45 50 time(s) Fig. 20. Irregular waves generated in a realistic sea scenario. -5 0 50 5 x 10 c0 100 150 200 250 300 350 400 450 500 -5 0 50 100 150 200 250 300 350 400 450 500 time(s) Fig. 22. Pg vs time for irregular waves. (a) Uncontrolled case, (b) rotational speed control, (c) air valve control. control is through a valve (c), the power output takes lower values depending on the generated power reference. This is interesting since, given the case, it may be necessary to reduce the production of energy to the grid for different reasons. The second case study considers waves producing pressure drop variations of j7000 sinð0:1ptÞj Pa; which provoke the stalling behaviour in the uncontrolled system. Fig. 17 shows the variation of the flow coefficient for this case. As it may be observed, the flow coefficient reaches the stalling threshold value, as shown in Fig. 17 (a). In contrast, the rotational speed control and the air valve control avoid this stalling behaviour, as shown in Fig. 17 (b) and (c). As it may be seen, now the flow coefficient does not exceed the stalling threshold value 0.3. The rotational speed control [Fig. 17 (b)] is faster than the air valve control [Fig. 17 (c)]. The PID transitory regime is not relevant because of the systems time constant. The power generated by the turbine and induction generator is shown in Figs. 18 and 19 respectively for the uncontrolled case (a), rotational speed control (b) and air valve control (c). As shown in Fig. 19 (a), the average generated power in the uncontrolled case is 20.053 kw, while the power generated in the controlled case using rotational speed control, increases up to 27.560 kw, as shown in Fig. 19 (b). This represents an increment on the generated power Fig. 21. Flow coefficient vs time for irregular waves. (a) Uncontrolled case, (b) rotational speed control, (c) air valve control. due to its stabilization by totally eliminating the losses associated with stalling behaviour. In the controlled case, using air valve control, the average generated power depends on the chosen reference for the output power. In this case, it was considered a power reference Pgref of 21 kw. The controller totally eliminates the losses associated with the stalling behaviour as can be observed in detail in Fig. 19 (c). The third case study considers a realistic scenario with irregular waves, which produces changes in the pressure drop input to the turbine as shown in Fig. 20. As it is shown in the uncontrolled case of Fig. 21 (a), the flow coefficient reaches the stalling threshold value. In contrast, the rotational speed control and the air valve control avoid this stalling behaviour, as shown in Fig. 21 (b) and (c). In particular, it may be observed how the rotational speed control is also faster than the air valve control in this case study. As it has been indicated before, the PID controlled module transitory regime is not relevant taking into account the time constant of the system. Nevertheless, it could be reduced by increasing the proportional action, if necessary. In this case the average power of the generator fed into the grid is significantly higher in the controlled cases than in the uncontrolled one as shown in Fig. 22. In the uncontrolled case, the turbine reaches repeatedly the stalling threshold value, generating an average power of 22.942 kw, as shown in Fig. 22 (a). In contrast, the controlled average generated power, using rotational speed control, is increased up to 27.036 kw, as shown in Fig. 22 (b). The air valve control tends to avoid the stalling behaviour, as shown in Fig. 22 (c), allowing an increment in the generated power. Finally, Table 3 shows the average power delivered by the generator for different pressure drop inputs (with Pgref (max)) in three different cases: the uncontrolled case (a), rotational speed control (b) and air valve control (c). It may be seen how the proposed control schemes highly improve the power generated by the turbine generator module. Table 3 Turbine and generator efficiency vs pressure drop. dP ¼ jP0 sinð0:1ptÞj P0 ðPaÞ 4000 5000 6000 7000 8000 Irregular wave (a) Pgenerator (kw) 11.920 20.060 25.202 20.053 15.012 22.942 (b) Pgenerator (kw) 11.920 20.060 25.570 27.560 29.480 27.036 (c) Pgenerator (kw) 11.920 20.060 25.275 22.562 18.565 25.328 2648 M. Amundarain et al. / Renewable Energy 35 (2010) 2639e2648 6. Conclusions In this work, two control strategies of an OWC-Wells turbine generator module are proposed and compared in order to study the stalling behaviour in the Wells turbine. In the first method, the control system does appropriately adapt the slip of the induction generator according to the pressure drop entry in order to maximize the generated power while in the second method a PID type control has been implemented in order to deal with the desired power reference tracking problem. It has been shown how the controllers avoid the stalling behaviour and that the average power of the generator fed into the grid in the controlled cases is significantly higher than in the uncontrolled one while providing the desired output power. The experiments suggest that while the rotational speed control behaves better with respect to the maximum power delivered to the grid, the air control valve is more adequate to regulate the generated power according to the demand of the grid. Therefore, the obtained results depicted the ability of both methods to control the generated active power fed to the grid in ways that may complement each other. Acknowledgements The authors are very grateful to UPV/EHU and the Science and Innovation Council MICINN for its support through research projects GIU07/08, and DPI2006-01677 and ENE2009-07200 respectively. They are also grateful to the Basque Government for its partial support through the research projects S-PE07UN04, S-PE08UN15 and S-PE09UN14. References [1] Carrasco JM, Franquelo LG, Bialasiewicz JT, Galvan E, Guisado RCP, Prats AM, et al. Power-electronic systems for the grid integration of renewable energy sources: a survey. IEEE Trans Ind Electron 2006;53(4):1002e16. [2] Dauncey G, Mazza P. Stormy weather. British Columbia, Canada: New Society Publishers; 2001. [3] Polinder H, Scuotto M. Wave energy converters and their impact on power systems. In: International conference on future power systems, Amsterdam, Nov 16e18, 2005. p. 62e70. [4] Thakker A, Abdulhadi R. The performance of Wells turbine under bi-directional air flow. Renew Energy 2008;33(11):2467e74. 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