Investigating the Performance of a Hydraulic Power Take-Off

Transcription

1 Investigating the Performane of a Hydrauli Power Take-Off A.R. Plummer and M. Shlotter Centre for Power Transmission and Control, University of Bath, Bath, BA 7AY, UK A.R.Plummer@bath.a.uk M.Shlotter@bath.a.uk Abstrat Many wave energy onverter (WEC) develoers are in the roess of saling u revious oint absorber onets to kw+ devies. As sizes inrease, serious hallenges in ower take off (PTO) design are being enountered. Hydrauli transmissions are favoured as gearing u to give high seed rotary motion is easily ahieved, and ower density is high. They are also highly ontrollable, for examle allowing take-off ylinders to be loked or free-running as onditions require via simle valve ontrol. Theoretial onets for extrating the maximum ower from waves already exist, using reative or lathing ontrol for examle, but these do not aount for the real engineering limitations or losses in ratial PTO systems. The onets assume that the PTO an generate any given fore/motion relationshi with equal effiieny. This aer resents the results of a simulation study on the design and ontrol of a hydrauli PTO. The ontrol strategies for maximum ower extration are omared with and without onsideration of the harateristis (losses) in the PTO. It is shown that effiieny an be surrisingly low. It is also shown that using omonents (motor and um in this ase) sized for smaller wave onditions may be referable as their effiieny is better. Keywords: wave energy onverters, ower take-off, hydraulis. Nomenlature s differential oerator M buoy mass C, K linearised resistane (drag), buoyany stiffness C, K PTO daming, stiffness f e, f exitation fore, PTO fore r ratio PTO daming / hydrodynami daming P av ower absorbed from buoy v, z fore, veloity, dislaement H, T wave height, wave eriod D um/motor dislaement Proeedings of the 8th Euroean Wave and Tidal Energy Conferene, Usala, Sweden, 9 Introdution This aer is onerned with the design and ontrol of hydrauli ower take offs (PTOs) for oint absorber wave energy onverters (WECs). Many revious aers have addressed the modelling and ontrol of oint absorbers [,], and large sale (kw+) oint absorbers are urrently being develoed by a number of omanies, e.g. [3]. However hardly any theoretial investigations have roerly aounted for PTO losses, and the aim here is to show that these losses an have a dramati effet on erformane. Although foused on oint absorbers, the results shown are of relevane to any design requiring onversion of reiroating to high seed rotary motion. Hydrauli ower transmissions are normally hosen for high ower WECs as they are easily ontrolled and have a high ower density [4]. The hydrauli PTO shown here is used for illustrative uroses; it is not roosed as neessarily the best design. It uses a single reiroating ylinder attahed between a buoy and a stationary reation oint, driving flow through a fixed aaity hydrauli motor. This is ouled to a variable aaity um delivering flow to a large aumulator at nominally onstant ressure. One or more onstant seed hydrauli motors and synhronous generator units an then be driven from the onstant ressure suly (or disabled when insuffiient ower is available). This art of the system is not modelled and not within the soe of the urrent analysis it should be relatively effiient if otimised for the orret steady state onditions. The variable aaity um allows the PTO to be ontrolled to vary the fore between ylinder and buoy. Varying the fore allow strategies suh as reative ontrol to be imlemented, where the PTO imedane is varied to maximise ower absortion (in theory) by ahieving resonane and an otimal level of daming. Alternative methods for ontrolling fore inlude: relaing the variable aaity um with a torque-ontrolled asynhronous generator; having several ylinders of different iston area whih an be swithed into the hydrauli iruit onneted to the (nominally) onstant ressure aumulator. Simler, unontrolled, systems use a bridge of four hek valves to retify the flow from a ylinder to harge an aumulator. 79

2 Fore Control Strategy To test the effiieny of the PTO, a ontrol strategy is required. This will be based on reative ontrol, but with limits on buoy dislaement and veloity for ratial reasons (PTO stroke and flow limits). Using a linear hydrodynami model, ( Ms + Cs + K) z = f e f () where M is the buoy mass and added mass, C is a linearised radiation resistane/drag term, and K is the buoyany stiffness. The buoy uward dislaement is z, uward wave exitation fore is f e, and downward PTO fore is f. The fore ontrol algorithm is hosen as: f = ( C s K )z () + From Eq. () and (), the buoy veloity is: v = Ms + ( C + C s )s + ( K + K f ) e (3) A method for hoosing C and K is required. Consider a regular (sinusoidal) wave of frequeny ω. In the frequeny domain, the amlitude of veloity and exitation fore are related by: V = (4) K K Mω (C C ) ω or V = (5) C K K Mω ( r ) Cω where C = r C (thus PTO daming is hosen as a multile r of hydrodynami daming). The average ower absorbed from the buoy by the PTO is the averaged rodut of the daming fore v and veloity v, whih for a sinusoid is: P P av = av so = r CV ( + r ) 4r K + K Mω + Cω 8C C (6) It an be shown that to maximise the ower from the buoy (i.e. maximise P av ): r = This is reative ontrol: K (whih is usually negative) alters the natural frequeny to math the wave frequeny i.e. the buoy is in resonane. The reative term the seond term in the denominator of Eq. (6) disaears beause the inertia and stiffness fores anel. However this hoie for K and r may give too large a motion amlitude (from Eq. 6). To redue the amlitude K or r an be inreased, but it is lear from Eq. (6) that the latter is best as r also aears in the numerator and ower will not be so greatly affeted. In summary, the desired PTO fore is given by Eq. () with K = K Mω (7) and r = max(,r,r ) (8) v where (from Eq. 5): lim z rv = (9) CV r z F = CωZ e lim () and where V lim is the veloity limit, and Z lim is the dislaement limit (tyially half the ylinder s working stroke). Power from the buoy (Eq. 6) redues to: P av 4r = ( + r ) 8C () Suh a ontrol strategy requires an estimation of the dominant wave exitation fore amlitude and frequeny; how this might be done is not addressed here. 3 Ideal PTO Simulation Results The arameters of Table were used to test the ontrol strategy. The values of r whih are greater than result from the veloity limit; the stroke is not a onstraint in this ase. The wave fore is aroximated by the rodut of buoyany stiffness and wave osition: H F e = K () Figures to 3 show the behaviour for the three wave onditions. The average owers are alulated numerially aording to Eq. (). As exeted, the ontroller works well to maximise the ower absorbed within the hysial onstraints. K = K Mω 73

3 Hydrodynami arameters Constraints Mass+added mass, M Daming, C Buoyany stiffness, K 8 tonne 6 kn/(m/s) 77 kn/m Veloity limit, V lim.6m/s Dislaement limit, Z lim. m Wave onditions (sinusoidal: amlitude H/, eriod T) a) H = m, T = 6s r =. b) H = m, T = 8s r = 3. ) H = 3m, T = s r = 5. - Table : Parameters for ideal PTO testing. Wave: height m, eriod 6 s Average PTO ower: 4. kw PTO -5 Figure : Ideal PTO with m wave, T = 6s, r =. 4 - Wave: height m, eriod 8 s Average PTO ower: 9.9 kw PTO - Figure : Ideal PTO with m wave, T = 8s, r = Wave: height 3 m, eriod s - - PTO - 6 Average PTO ower:. kw 4 - Figure 3: Ideal PTO with 3m wave, T = s, r =

4 4 PTO Design Inluding Loss Model Figure 4 shows the PTO onet. The aumulator is assumed to be suffiiently large so that its ressure an be assumed onstant, and thus the um (and motor) torque is roortional to the um dislaement. Losses aside, the ylinder fore is roortional to motor torque, so the um dislaement is the ontrol inut used to alter the PTO fore. An over-entre um is used, meaning that the flow an reverse diretion with unidiretional shaft rotation; this ours when the um dislaement is negative. The art of the system whih draws oil off to drive the generator is not shown, and losses for this art are not aounted for. In reality both um and motor an transmit ower in the oosite diretion, i.e. the um an at as a motor, and the motor as a um. Buoy Note that ressure loss and omliane are really distributed effets, but a lumed arameter model is used here. Pum and motor losses onform to the well established Wilson model [5] exet that omressibility loss is negleted. 5 Realisti PTO Simulation Results Table shows a set of PTO arameters. The same tye of unit is used for both um and motor (albeit the former is a variable aaity version), so the arameters are the same for eah. The values are for a Denison Hydraulis Gold Cu Series 3 unit [6]. The losses (leakage, oulomb frition and visous frition) aroximate the loss harateristis measured by the manufaturer and shown as art of the erformane urves rerodued in Fig. 6. Note that the ideal relationshis are: flow rate = D angular veloity torque = D ressure differene Figure 4: Hydrauli PTO onet. To fixed seed hydrauli motor & synhronous generator where D is the um (or motor) dislaement. The oil/hose stiffness value is based on the aroximate volume of traed oil, a bulk modulus of.9 GN/m and a.5m length of hose at eah ylinder ort with effetive bulk modulus of.3 GN/m. Cylinder fition and ressure loss values are the best exeted for a well designed system. Buoy Comliane Pie/manifold ressure loss Motor Pum Leakage Inertia Visous & oulomb frition Pum & motor arameters Maximum ressure 35 bar Maximum seed 8 rev/min (Maximum) aaity (D).5 L/rev Inertia.86 kgm Leakage.67 L/min/bar 7 Nm Visous frition.6 Nm/(rev/min) Cylinder arameters Area (A).3 m 5 kn Stroke 4.m Figure 5: Hydrauli PTO with non-ideal harateristis. Figure 5 indiates the main non-ideal harateristis whih our in this PTO. The losses are: oulomb frition in the ylinder visous and oulomb frition in the um and motor leakage in um and motor (laminar) ie and manifold ressure loss (turbulent) Other unwanted harateristis, but ones whih do not dissiate energy, are: oil and hose omliane um and motor inertia Lumed model arameters Oil/hose stiffness (referred to ylinder) Pie/manifold ressure loss (roortional to square of flow) Derived arameters Cylinder stall fore Veloity limit (V lim ) Dislaement limit (Z lim ).89 kn/mm 9 L/min 455 kn.6 m/s. m Table : PTO arameters (Series 3 um & motor). 73 4

5 from Eqs. (8) and (9), r =.3, 5.5 and 8.8 for waves a), b) and ) resetively (refer to Table ). The average owers transmitted by the PTO in the ideal ase (no losses) are 34kW, 83kW, 3kW resetively (smaller than the revious values 4kW, kw and kw due to the larger r values). With the realisti PTO simulation, Figs. to 3, there is an imrovement for the two smaller waves omared with using the larger um/motor units. Wave dislaement K Exitation fore Veloity Fore Position Buoy / hydro dynamis Produt buoy _ower PTO fore Pos PTO ower Vel Fore md Position real PTO Fore md Veloity PTO _ower ideal PTO Figure 7: Simulink model of the PTO system. PRESSURE - bar Figure 6: Pum erformane urves (Denison Hydraulis Gold Cu Series 3) [6]. The system has been designed to work in waves of u to 3m, and the iston area has been hosen to give a stall fore equal to the 3m wave exitation fore amlitude. Results are resented for the same hydrodynami and wave arameters as before (Table ), and as the veloity and dislaement limits have not hanged, the ontroller arameters are also the same. The desired PTO fore is now used to adjust the um dislaement, and the ahieved fore will deviate from the desired due to various losses. The simulation model is imlemented in Simulink; Fig. 7 shows the to level blok diagram. Figures 8- show the results equivalent to Figs. -3. As the iston fore needs to overome the oulomb, visous and ie frition fores, the PTO fore tends to be higher than desired, and buoy movement is less. Leakage losses throughout the yle add to the roblem. Clearly the devie should be deativated in the smallest waves, and shows about 3% effiieny in 3m waves (or about % of the theoretial maximum ower generation with no veloity limit, i.e. r = ). In an attemt to imrove effiieny for smaller waves, smaller um and motor units ould be used. The new um/motor arameters are shown in Table 3, together with the new veloity limit; other arameters are the same. The same tests are erformed, but due to the lower V lim, the PTO daming needs to inrease; Wave: height m, eriod 6 s Average PTO ower: -4.6 kw -5 Figure 8: PTO with losses, m wave. T = 6s, r =

6 4 - Wave: height m, eriod 8 s Average PTO ower: 6. kw - Figure 9: PTO with losses, m wave. T = 8s, r = 3. 5 Wave: height 3 m, eriod s 6 Conlusions and Disussion Simulating system behaviour inluding PTO losses an reveal that the ower generated might be muh lower than exeted only about 3% of the ideal value for 3m waves in this ase. For m waves no ower is generated. For m waves, the smaller um and motor units investigated give better ower absortion due to imroved effiieny. In fat, as the smaller waves are likely to be more ommon, the smaller um/motor is robably referable. Both the design and ontrol of PTO s must be based on an understanding of real-life harateristis and realisti loss models. The PTO simulated here is only one ossible design, but other designs will exhibit similar roblems. The fundamental issue is that ower transmissions (both hydrauli and eletrial) an be designed to be fairly effiient around one oerating ondition, but the extremely variable quantity of ower available from waves means that for most of the time the oerating ondition will be far from the otimum. This variability ours both within one wave and between sea states. Systems designed to extrat ower from large (high ower) waves, are likely to be unable to generate any ower in more revalent almer onditions. Oen loo PTO ontrol is used here it is a ommon assumtion that this is suffiient. However it is lear that due to omliane, inertia, and various losses the desired fore is not aurately ahieved. A losed-loo fore ontrol method would be better, enabling the PTO behaviour to be muh loser to the ideal imedane harateristi. Note also that the alulation of the fore ommand deends on redominant wave frequeny, thus this needs to be estimated Average PTO ower: 66.4 kw Pum & motor arameters Maximum ressure 35 bar Maximum seed 4 rev/min (Maximum) aaity (D).3 L/rev Inertia.85 kgm Leakage. L/min/bar Nm Visous frition.6 Nm/(rev/min) Derived arameters Veloity limit (V lim ).7 m/s Table 3: Alternative PTO arameters (Series 4 um & motor). - Figure : PTO with losses, m wave. T = s, r =

7 Wave: height m, eriod 6 s Wave: height 3 m, eriod s Average PTO ower: -9. kw 3 Average PTO ower: 59.3 kw -5 - Figure : PTO with smaller um and motor, m wave. T = 6s, r =.3. Figure 3: PTO with smaller um and motor, 3m wave. T = s, r = Wave: height m, eriod 8 s Average PTO ower: 3. kw -5 Figure : PTO with smaller um and motor, m wave. T = 8s, r = 5.5. Referenes [] A. Clement, P. MCullen, A. Falao, A. Fiorentino, F. Gardner, K. Hammarlund, G. Lemonis, T. Lewis, K. Nielsen, S. Petronini, M.-T. Pontes, B.- O. Shild, P. Sjostrom, H.C. S, and T. Thore. Wave energy in Euroe: urrent status and ersetives. Renewable and Sustainable Energy Reviews, 6(5):45 43,. [] J. Falnes. A review of wave-energy extration. Marine Strutures, :85, 7. [3] Anon. OPT - Oean Power Tehnology. Obtained from: htt:// on /7/8. [4] R. Henderson. Design, simulation, and testing of a novel hydrauli ower take-off system for the Pelamis wave energy onverter. Renewable Energy, 3():7 83, bruary 6. [5] W. E. Wilson, Performane riteria for ositivedislaement ums and fluid motors Trans. Am. So. Meh. Eng, 7(), 949. [6] Denison Hydraulis - Gold Cu Series: iston ums for oen & losed iruits. Publiation: LT3- --A,