ac and dc aggregation effects

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AC and DC aggregation effects of small-scalewind generators

N. Stannard, J.R. Bumby, P. Taylor and L.M. Cipcigan

Abstract: Small-scale embedded generation (SSEG) has the potential to play an important part inthe future UK generation mix. If a single SSEG is considered, its environmental, commercial and network operational value is low, but if a cluster of SSEGs are considered and their outputsaggregated they have the potential to be significantly more valuable. The aggregation of small-scale wind generators is considered. Each turbine is driven by a wind that is turbulent innature and varies from location to location. The output from an individual turbine can be veryvariable, but when aggregated together with the power output from a number of turbines in thesame locality, can produce a power output that is much less variable. The authors examine, bysimulation, how the output from a number of small turbines can aggregate together to form amore consistent power output. Aggregation of the turbine outputs both after the power inverter,at alternating current (AC), and before the inverter, at direct current (DC), are examined. In

both cases power variations are shown to reduce as the number of turbines connected increases.Aggregation at DC can lead to non-optimum performance of the turbine itself, if passive rectifiers

are used, but can also lead to savings in the cost of the power conversion equipment required.

List of symbols

A Turbine swept area, m2

C p Coefficient of performance

E phase Induced emf per phase, V

h Tower height, m

I c

DC capacitor current, A

I d DC inverter current, A

J r Turbine and generator inertia, kg m2

k Generator emf constant

K F Gain of the Nichita filter

L phase Generator phase inductance, H

p Number of pole pairs

Pturbine Turbine mechanical power, W

P Power transfer through the inverter, W

Plimit Inverter rated power, W

R Turbine radius, m

RDC Generator resistance referred to the DC side of the converter, V

Rover Overlap resistance, V

R ph Generator resistance per phase, V

s Laplace operator

t Time, s

T elect Turbine electrical torque, Nm

T F Time constant of Nichita filter, s

T mech Turbine mechanical torque, Nm

U Average wind speed, m/s

V 1 Inverter DC cut-in voltage, V

V 2 DC voltage for maximum inverter power, V

V d DC voltage, V

V do Open circuit DC voltage, V

h WB Inverter efficiencyl Tip speed ratio

r Density of air, kg/m3

s u Standard deviation of wind turbulence

v m Turbine rotational speed, rad /s

1 Introduction

Micro-generation or small-scale embedded generation(SSEG), has a significant part to play in the future UK energy system and its importance has been recognised by

the UK government in its Energy White Paper [1]. TheUK government’s policy on renewable energy and com-

bined heat and power (CHP) is expected to lead to a con-tinuous increase in distributed generation (DG). TheGovernment have set a target that 10% of UK electricityshould be sourced from renewable energy by 2010 and 20% by 2020 [2]. In order to meet the 2010 target, approxi-mately 10 GW of additional DG will have to be connected to distribution networks. The DTI suggest that up to half of this 10% renewables target could be provided by wind energy [3]. A recent study focussing on SSEG investigated a number of potential penetration scenarios. Table 1 sum-marises the capacity (GW) and energy (TWh) which

could be provided by micro-generation to 2020 [4].SSEG includes small-scale wind turbines, solar photo-voltaics, micro-hydro generators, micro-CHP along withhydrogen fuel cells and bio-energy and is defined in

# The Institution of Engineering and Technology 2007

doi:10.1049/iet-rpg:20070001

Paper first received 17th January and in revised form 2nd April 2007The author are with the School of Engineering, Durham University, Science

Site, South Road, Durham, DH1 3LE, UK

E-mail: [email protected]

IET Renew. Power Gener., 2007, 1 , (2), pp. 123–130 123



a passive rectifier and mains side IGBT inverter.Aggregation of the outputs of a number of such systemscan be achieved either on the AC side or DC side of themains connect inverter as shown in Fig. 2. Aggregation atthe AC side represents the normal situation where anumber of customers install a single wind turbine, eachwith a dedicated power electronic interface. It is generallyacknowledged that the aggregation of the output fromseveral wind turbines in this way is less variable than thatof a single wind turbine, and that the variability decreases

as the number of wind turbines aggregated increases [13].However, the effect of aggregating several small-scalewind turbines on the DC side of the inverter, so as toshare the same inverter and hence reduce power conversioncost, is much less clear. Such an approach to aggregationcould well appear attractive where, for example, a commer-cial building or block of flats installs a number of wind tur-

bines which share the same inverter.The paper begins by describing the model of the wind

turbine system used to investigate the AC and DC sideaggregation. Aggregation case studies at AC and DC arethen compared to evaluate the impact of aggregation on

both the net power generated and the performance of thewind turbine itself.

2 Small-scale wind turbine models

To examine aggregation effects, detailed models of theturbine and generator have been constructed in Matlab/Simulink. Most importantly, the model must account for the turbulence effects that exist in real winds. Such amodel has been developed previously [14] and brief detailsabout the models are given in Section 8. The impact thataggregation has on both the quality of the power supplied to the system and the operation of the turbines themselvesis evaluated. Fundamental to the model is the assumptionthat the injection of the generated power will have negligible

effect on the AC system voltage; that is a stiff AC system isassumed. Such an assumption is valid for normal operationin that the injected powers are relatively small, typicallyless than 20 kW, and that the turbines within the sameSSEZ will be electrically close together.

The wind model uses a spectral density function derived from real wind data to generate typical wind profiles around a mean wind speed as described in detail in [14] and summarised in Section 8.1. As the simulation is primarilyconcerned with second by second variations, the wind turbine is modelled by its C p/l performance curve such

as that shown in Fig. 3 for a Savonius wind turbine. The per-manent magnet generator and associated rectifier are mod-elled by an equivalent circuit viewed from the DC side of the rectifier as shown in Fig. 4 [14–16]. In all the simu-lations, the use of a permanent magnet generator isassumed. With this model the turbine speed is computed from

v m ¼1

J r

ð (T mech T elect) d t (1)

The turbine’s mechanical (or aerodynamic) torque isfound from the turbine performance characteristics, whilstthe generator torque is determined by the power transfer characteristics of the mains-connect inverter. The outputfrom the generator is rectified typically through a standard six-pulse rectifier before being connected to the power inverter. A widely used inverter that meets the G83 mainsconnect standard is the SMA Windy Boy [17]. This inverter transfers an amount of power to the mains depending on thevalue of the DC link voltage (Fig. 5).

Fig. 5a shows the power transfer characteristic of a500 W inverter used in the AC aggregation study and Fig. 5b the characteristic of the 2500 W inverter used inthe DC aggregation study. Each of the inverter power trans-fer profiles is similar and, for a mains voltage of 230 V, theinverter cuts-in at a DC voltage V 1 of about 250 V. Theinverter then transfers power as a linear function of the

Fig. 3 Savonius turbine C pl performance characteristics

Fig. 4 Generator equivalent circuit

Fig. 5 Windy Boy power-DC voltage characteristic

a For AC aggregation of 500 W turbinesb For DC aggregation of five, 500 W turbines

IET Renew. Power Gener., Vol. 1, No. 2, June 2007 125



DC link voltage until the maximum power, Plimit, of theinverter is reached; in this case 500 W or 2500 W, atvoltage V 2. This DC voltage V 2 must be,600 V (the inverter limit) and can be programmed by the user. Values used in thestudy are shown in Fig. 5. For a single turbine with a PM gen-

erator, the DC voltage is approximately proportional to theturbine rotational speed, v m, so that Fig. 5 is essentially anelectrical power –speed characteristic. This electricalcharacteristic can be combined with the turbine character-istic of Fig. 3 to give the power curves of Fig. 6; in thiscase for a small 500 W Savonius vertical axis wind turbine(VAWT). Where the two characteristics cross determinesthe system operating point and power transfer to the mainsfor any given wind speed. Dimensions of the Savoniuswind turbine are given in Table 2.

Also shown in Fig. 6 are experimental results for the per-manent magnet generator described in [15] connected to themains through a SMA inverter. This data is compared with

predicted results using the wind turbine data given inTable 2. Good agreement between measured and predicted results is achieved, giving confidence in the simulationmodel.

The Windy Boy inverter’s default operating mode is atunity power factor. However, reactive power controlwould be possible through modulation of the amplitude

and phase of the Windy Boy inverter voltage with respectto the network voltage. It is also possible that further reac-tive power control could be provided by the invertersassociated with distributed energy storage devices withinthe SSEZ. Reactive power control, however, would be of limited value since the reactance/resistance, X / R, ratio of typical LV distribution networks is less than one.

The key to operating a wind turbine system efficiently isin the careful matching of the different components and howthe whole system is controlled. Wind turbines only work efficiently in a narrow band of speeds, which vary accordingto the strength of the wind. Thus, the power extracted fromthe generator must be carefully controlled in order to main-tain the turbine’s optimal rotational speed.

3 Aggregation study

In this study, data for a 500 W Savonius wind turbine isused (Table 2). Such sized machines naturally lend them-selves to the use of a number of turbines aggregated atDC and connected to the mains through a single inverter.With such a connection, and the use of a passive rectifier,the inverter will control the power transfer from the groupof turbines rather than from each individual turbine.Larger turbines, of a few kW rating, would tend to be con-nected through a dedicated inverter allowing control of indi-vidual turbines. However, in order to obtain a direct

comparison between the two connection systems, thesame 500 W turbine system is used to study aggregationeffects on both the AC and DC side of the mains connectinverter. It is recognised that AC aggregation is moresuited to larger power turbines, but not exclusively so.

The study is carried out assuming each wind turbine isspaced far enough apart for the turbulence at each turbineto be independent from its neighbour so that a separateturbulent wind, but with the same mean wind speed, can

be used as the input for each turbine; an average wind speed of 10 m/s is used. The turbulent wind for eachturbine is therefore different, but by using the same ‘seed’in the turbulent wind model [14], can be repeated to allowan effective performance comparison.

The aggregation of five wind turbines is shown inFig. 7; Fig. 7a, c and e shows the power output, speed and DC link voltage of individual turbines, whilst Fig. 7b,d and f shows the same but for DC aggregation. Fig. 7 g shows the effect of aggregating the outputs of the fiveturbines. In both cases aggregation is seen to have asignificant effect on power smoothing. At time zero all theturbines are at rest and take about 15 s to reach operatingspeed. Power is not produced until about 10 s after thestart as the turbine speed, and hence DC link voltage, isless than the minimum required for the inverter to operate(Fig. 5).

The results show that with AC aggregation the turbines

operate at a lower speed, approximately 300 rpm, compared to DC aggregation, approximately 350 rpm. Speed vari-ations are also greater with AC aggregation. Similarly,DC link voltage is higher with DC aggregation than AC

Fig. 6 Windy Boy load characteristic showing Savonius power curves

Table 2: Parameters of the 500 W Savonius VAWT and

generator

Symbol Value Units

Savonius Turbine

Rotor height h 2.438 m

Rotor diameter d 0.780 m

Swept area A 1.902 m2

Rotor inertia J r 5.292 Kg m2

Cut-in wind speed V cut-in 2.5 m/s

Rated wind speed V rated 12.5 m/s

Cut-out wind speed V cut-out N/A

Energy capture

coefficient (max)

C p(max) 0.2

Savonius generator

Rated power P elec 500 W

Rated speed N 300 rpm

Rated frequency f 40 Hz

Rated EMF (per coil) E coil 33.6 V

Number of phases 3

Number of pole pairs p 8

Number of armature coils 12

Machine constant K 0.11 V/rpm/coil

Coil resistance R coil 1.205 V

Coil inductance Lcoil 4.74 mH

DC efficiency h dc 92 %

Generator diameter D gen 0.462 m




(there is only one DC link voltage with DC aggregation because of the use of a common DC bus). It is alsonotable from Fig. 7 g that although in both cases aggregationleads to substantially smoother power delivery, the power

delivered using DC aggregation is substantially less thanwhen AC aggregation is used.Connecting multiple turbines to a single inverter creates a

more complicated power transfer system than using a

Fig. 7 Effect of aggregation at AC and DC

a Individual speeds at ACb Individual speeds at DCc Individual power outputs at ACd Individual power outputs at DCe DC link voltage at AC f DC link voltage at DC

g Total output power for turbines aggregated at AC and DC




dedicated inverter for each individual turbine. When asingle turbine is connected to a single inverter the power output follows the Windy Boy’s load line according to theinstantaneous turbine speed, as shown in Fig. 5, sinceturbine speed and the DC link voltage are tightly linked.With several turbines connected to the inverter, the tur-

bine’s power output becomes decoupled from the WindyBoy’s operating line, since the individual turbine speedsand DC link voltage are set by the group. Consider Fig. 8,which shows the power transfer as a function of the DC link

voltage. If all five turbines were producing the same power P then the power converter must transfer 5 P to the mains.This can only be achieved if the DC link voltage rises to ahigher DC voltage, V 5. This in turn corresponds to a higher turbine speed so that each turbine will operate at a higher speed than if it were transferring power individually throughits own dedicated power converter. This has the effect of shift-ing the turbine operating curve to the right (Fig. 9a).

The impact of this behaviour is well demonstrated inFig. 9a by simulating each of the five wind turbines operatingat constant wind speeds of 9, 10, 11, 12 and 14 m/s, respect-ively; this is shown as ‘operating line 1’ in Fig. 9a. (Theoperating line in Fig. 9a would be vertical if each generator was ideal; that is it had no armature resistance or inductance,

and all five generators would run at exactly the same speed.)As the DC voltage is set by the total power transfer, all fiveturbines operate at higher rotational speeds than if theywere controlled separately. This new common operatingline intersects the operating points of the five individualturbines, shown as circles in the figure. The power transfer mechanism is further complicated as the common operatingline shifts along the x-axis depending on the average wind speed across the group of turbines. This can be seen by mod-ifying the five wind speeds to 9.5, 10, 10.5, 11 and 12 m/srespectively, and is shown as ‘operating line 2’ on Fig. 9a.

When turbulent wind inputs are used, the average wind speed fluctuates with time, and has the effect of shifting

the common operating line back and forth along the x-axis. The power output of a single turbine moves up and down the common operating line as the wind speed at theindividual turbine fluctuates due to turbulence, while thecommon operating line moves back and forth along the

x-axis as the average wind speed fluctuates. This behaviour is shown in Fig. 9b where the output power and speed of oneSavonius turbine from the model has been plotted during the100 s simulation run.

4 Discussion

Aggregation of a number of wind turbines rapidly smoothesthe net power output compared to the power output from an

individual turbine. This is true regardless of whether the

aggregation is performed at AC or DC. However, in DCaggregation the power transfer is determined by the beha-viour of the group of turbines so that each turbine operatessub-optimally and power transfer is not as great as with ACaggregation. However, there are cost savings by using asingle inverter. Current costs for mains connect invertersare tabulated in Table 3 [18]. The cost of a 2500 W inverter is about twice the cost of a 700 W inverter so that aggregat-ing 5 500 W turbines through one 2500 W inverter

reduces the cost from 5 £686 to 1 £1244; a costsaving of £2186. Further, by aggregating at DC the power variation the inverter must now cope with has beenreduced; in the case of dedicated inverters each inverter may be called upon to transfer 500 W (Fig. 7c), whilst theDC aggregated maximum is under 1000 W (even the ACaggregated is less than 1500 W). This means that either more turbines could be connected to the inverter or theinverter rating could be reduced to, say 1700 W, further reducing cost (Table 3).

The smoothing effect of aggregation at both AC and DCis shown in Fig. 10, where the variation in power output as afraction of the average power output is plotted. Thevariation is calculated using (2) with the analysis performed

for a single turbine and for the aggregated outputs of 2, 3, 4,5, 6 and 7 turbines. As the variation in power output isdependant on the exact nature of the turbulent wind

Fig. 9 Output of Savonius VAWT

a Multiple Savonius operating characteristicb Output of one Savonius turbine

Fig. 8 Windy Boy characteristic showing how DC voltage deter-mines total exported power




profile (Fig. 7c and d ), the model was run over ten differentrandom turbulent wind profiles and the results are averaged in order to obtain a meaningful result. In all cases the samemean wind speed was used.

Power variation¼(Maximum power Minimum power)=2

Average power

(2)

Fig. 10 shows that the variations in power decrease, fromapproximately 90% to about 20% of the average power, asthe number of turbines aggregated increases to 7. It is clear that aggregation quickly smoothes the power output. Fig. 10also suggests that better power smoothing is achieved with

DC aggregation as the turbines are constrained to operate ina much narrower speed range for reasons described above. Itis reasonable to assume that the reduction in variability willincrease as more and more turbines are aggregated.Therefore significant smoothing can be expected within asmall-scale energy zone (Fig. 1), where anything up to 50or 100 turbines could be present and available for aggregation.

As explained above, if aggregation is performed onthe DC side, and a single common inverter used, thenthe optimum power transfer from each turbine may becompromised if the turbines are connected to a commonDC link through conventional passive rectifiers as has

been assumed here. This issue can be solved by modifyingthe operation of the power electronic interface so that thediode rectifier is replaced by a more intelligent converter system that allows each turbine to be controlled indepen-dently. Such a converter system using a standard six-pulserectifier and DC/DC boost converter is described in [19].This modification is worthy of further investigation as thecost of G83 compliant power electronic interfaces is asignificant proportion of the overall costs for small-scalewind generation systems; typically 50% of the turbine and generator cost (or 15–20% of the installed cost).

This work represents the first step in aggregation in theSSEZ concept as only wind generation was considered

here and with only five wind turbines. Nevertheless, thestudy has demonstrated the benefits of aggregation and raised some of the issues faced in the aggregation process.It must also be realised that the aggregation effect examined is due to turbulent wind and as such is limited to a relativelyshort period that is a few minutes. It does not examine theimpact of diurnal variations nor does it account for longer term weather fluctuations. In order to realise the benefitsof aggregation on these longer time scales, aggregationmust be applied to zones that contain a mix of a large

number of SSEG technologies, controllable loads and energy storage devices. Multiple zones must also be con-sidered to reap the full potential of this idea.

5 Conclusions

This paper has presented the aggregation of small-scale wind turbines and has shown that the aggregated output issmoothed as a result of the aggregation even for a smallnumber of wind turbines. It is clear that aggregation at ACis straightforward but problems can be experienced with

basic power electronic interfaces if aggregation takes placeon the DC side. With a passive rectifier, aggregation at DC

can lead to sub-optimal operation of the turbine system butcan also lead to a saving in power conversion cost.The value of small-scale wind aggregation can be quanti-

fied in the following ways:

1. For the distribution network operator (DNO).† If the DNO can treat a number of small-scale wind tur-

bines as one lumped generator which has a smoother and more predictable power output profile this can assist withnetwork operational tasks.2. Revenue streams from the sale of electricity.† If the SSEG owners can secure power purchase agree-ments with supply companies as an aggregated block, theincreased capacity and greater predictability achieved

should allow improved contractual terms to be negotiated.3. Environmental benefits.† If the aggregated SSEGs output is more predictable thiswill provide more confidence that fossil fuel generating

plant can be displaced by the growth of SSEGs. Thiswill therefore translate into significant environmental

benefits.

6 Acknowledgments

This work has been carried out as part of a project on‘Intelligent active energy management for small scaleenergy zones’ and the authors gratefully acknowledge the

financial support from EPSRC.

7 References

1 DTI Energy White Paper: ‘Our energy future – creating a low carboneconomy.’ DTI, February 2003

2 Carbon Trust Report: ‘Mott McDonald, capacity mapping and marketscenarios for 2010 and 2020’, November 2003.

3 Milborrow, D.: ‘Assimilating wind, wind energy contribution to UK energy needs’, IEE Rev., 2002, 48, (1), pp. 9–13

4 DTI’s Distributed Generation Programme: ‘System integration for additional microgeneration (SIAM)’. DTI, 2004.

5 Engineering Recommendation G83/1: ‘Recommendations for theconnection of small-scale embedded generators (up to 16 A per phase) in parallel with public low-voltage distribution networks’

(Energy Networks Association, London, September 2003), availableat http://www.energynetworks.org.uk

6 Dutton, A.G., Halliday, J.A., and Blanch, M.J.: ‘The feasibility of building mounted integrated wind turbines (BUWTs): achieving

Table 3: Cost of Windy Boy inverters [18]

Rating

(W)

Cost

(£)

Cost/W

(£/W)

700 686 0.98

1700 943 0.56

2500 1244 0.50

Fig. 10 Power output variations for different numbers of wind turbines aggregated




their potential for carbon emissions reduction’. Report for the CarbonTrust, 2002-07-028-1-6, May 2005

7 ‘Ancillary service provision from distributed generation’, DTI, Contractnumber DG/CG/00030/00/00,DTI Technology Programme: Newand Renewable Energy, 2004

8 Gordijn, J., and Akkermans, H.: ‘Business models for distributed energy resources in a liberalized market environment’, Electr. Power Syst. Res. J., 2007 (in press)

9 Franke, M., Rolli, D., Kamper, A., Dietrich, A., Geyer-Schulz, A.,Lockemann, P., Schmeck, H., and Weinhardt, C.: ‘Impacts of distributed generation from virtual power plants’. Proc. Annual Int.Sustainable Development Research Conf., June 2005, vol. 11, pp. 1– 12

10 Taylor, P.: ‘Active network management as an enabler for the proliferation of domestic combined heat and power’. 12th Int.Stirling Engine Conf., Durham, September 2005

11 Taylor, P., and Cipcigan, L.: ‘Small scale energy zones for theeffective participation of SSEGs in energy markets’. WEC RegionalEnergy Forum – FOREN 2006, 11–15 June 2006, Neptun,Romania, s4–27

12 Ingram, S., and Probert, S.: ‘The impact of small scale embedded generation on the operating parameters of distribution networks’.P B Power, DTI New and Renewable Energy Programme, June 2003

13 Manwell, J., and Hunter, R.: ‘Wind diesel systems’ (CambridgeUniversity Press, UK, 1994)

14 Bumby, J.R., and Stannard, N.: ‘Performance aspects of mainsconnected small scale wind turbines’, IET Gener., Transm. Distrib.,2007, 1 , (2), pp. 348–356

15 Bumby, J.R., and Martin, R.: ‘An axial flux, permanent magnet,

air-cored generator for small scale wind turbines’, Proc. IEE Electr. Power Appl., 2005, 152, (5), pp. 1065–107516 El Mokadem, M., Nichita, C., Dakyo, B., and Koczara, W.:

‘Maximum wind power control using torque characteristic in a wind diesel system with battery storage’. 16th Int. Conf. on ElectricalMachines, Cracow, Poland, 5–8 September 2004

17 SMA: ‘Windy Boy grid tied inverter – operators manual addendumfor the Sunny Boy 1800U/2500U’. SMA America, October 2003

18 Wind and Sun, Inverter costs, http://www.windandsun.demon.co.uk ,accessed March 2007

19 Parker, M.A., Tavner, P.J., Ran, L., and Wilson, A.: ‘A low cost power tracking controller for a small vertical axis wind turbine’. 40thUniversities Power Engineering Conf., Cork, Ireland, September 2005

20 Nichita, C., Luca, D., Dakyo, B., and Ceanga, E.: ‘Large band simulation of the wind speed for real time wind turbine simulators’, IEEE Trans. Energy Convers., 2002, 17, pp. 523–529

8 Appendix

8.1 Spectral turbulent wind model

A schematic representation of the turbulent wind model isshown in Fig. 11 and full details of this wind model can

be found in [14]. Central to the wind model is the randomnumber generator, which produces normally distributed white noise; this acts as the basis for the turbulent wind component. Since the wind speed cannot (for physicalreasons) change instantaneously, the white noise must be

smoothed using a carefully designed signal shaping filter in order to achieve the correct spectral distribution. Theshaping filter must be chosen to best characterise the truespectrum of the wind and there are a number of candidatesfor this task. This shaping filter is well represented by a VonKarmen filter, or as used here, a second order approximation

proposed by Nichita [20].

W Nichita( s) ¼ K Fm1T F s þ 1

T F s þ 1

m2T F s þ 1 (3)

with m1 ¼ 0.4 and m2 ¼ 0.2.The gain K F and time constant T F of the filter depend on

the turbulence length scale that is the typical length of eddies in the free stream wind and also on the mean wind speed and are carefully chosen so as to ensure that the stan-dard deviation of the filtered output is equal to 1. This nor-malised coloured noise is then be multiplied by therespective wind-speed dependent standard deviation, s u,to provide a turbulent wind component with the correctstandard deviation that is intensity. The standard deviations u increases in proportion to the wind average speed as

s u ¼ k s U (4)

where k s

, the proportionality constant depends on theterrain conditions. By adding the base wind speed, U , tothe turbulent component, a turbulent wind profile can then

be generated. This model produces a point wind speed; so before finally applying the wind speed to the turbinemodel it must be further filtered to take account of disc aver-

aging. The effects of wind shear and tower shadow are notincluded in the model.

This turbulent wind model accurately accounts for atmos- pheric disturbance and is valid for a time period of a fewminutes. It does not, and is not intended to, account for wind variations on a longer time scale than this.

8.2 Turbine model

The power produced by the turbine is related to the turbinedimensions and the wind speed by

Pturbine ¼1

2C Pr AU 3 (W) (5)

with the torque produced by the turbine given by

T mech ¼ Pturbine

v m(6)

The wind speed is obtained at each time instant from thespectral wind model [14] whilst the air density and sweptarea of the turbine are constant (or at least dictated by exter-nal factors such as the weather conditions and turbine geo-metry), so that only the energy capture coefficient, C p, need to be determined in order to calculate the turbine power (and hence torque).

C p is a function of the turbine blade pitch angle, u , and a

dimensionless group, the tip-speed ratio, l. For many smallturbines the turbine blades are fixed at a constant pitchangle, which constrains C p to be a function of l only. Thetip-speed ratio is defined as the tip speed of the turbine

blades divided by the oncoming wind speed, as

l ¼v m R

U (7)

The variation of C p as a function of l produces a perform-ance curve for the turbine and is a fundamental part of thespecification of any turbine, whether small or large. Atypical curve for a Savonius VAWT is shown in Fig. 3.

In modelling this system, l is calculated from (7), whichthen allows C p to be interpolated for a given value of l. The

turbine torque can then be computed from (5) and (6) for usein (1).Fig. 11 Schematic representation of the turbulent wind model


ac and dc aggregation effects

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