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Analysis of Wind Power Data for Optimising DFIGs

Wenping Cao1, Zheng Tan1, Ying Xie2, Bashar Zahawi1, Andrew Smith1, and Milutin Jovanovic3

1: School of Electrical & Electronic Engineering University of Newcastle upon Tyne

Newcastle upon Tyne, UK [email protected]

2: School of Electrical Engineering Harbin University of Science and Technology

Harbin, China [email protected]

3: School of Computing, Engineering & Information Sciences Northumbria University

Newcastle upon Tyne, UK [email protected]

Abstract—This paper evaluates various wind power estimation models to represent the wind energy for machine design and control purposes. Traditionally, linear, quadratic and cubic formulas have been used for interpolating wind power curves but have their limitations. Due to the fluctuating nature of wind power, they may not be accurate to model the actual wind speed profile and nor convenient for wind turbine generator design and control which demands a representative site-specific wind speed profile. On the basis of the DFIG equivalent circuit, loss components and maximum efficiency of DFIGs are derived and these are taken into account when optimising DFIGs to match the specific site of development.

Keywords—capacity factor; generator design; parameter estimation; power curve; power generation; wind power; wind speeds.

I. INTRODUCTION Wind energy is playing a critical role in the establishment

of an environmentally sustainable low carbon economy. In the latest proposal of Horizon 2020, wind energy is placed as one of the priority areas for development with a target to reduce the cost of electricity production of onshore and offshore wind by up to about 20% by 2020 compared to 2010 [1]. Given sufficient support, wind energy is estimated to be capable of providing up to 34% of EU electricity by 2030 [2]. In order to achieve these goals, the European Wind Energy Technology Platform (TPWind) has been established to support collaborative research between EU member states via the European Wind Initiative (EWI) [3]. Among all the EU nations, the UK is the richest country in terms of wind resource. For example, its offshore wind energy accounts for more than a third of the total European potential. In fact, the UK's offshore wind resource alone is approximately three times the UK's annual electricity consumption. In 2009, the UK completed its full Strategic Environmental Assessment of offshore energy [4] and concluded that 25GW of new

offshore wind farm development (Round 3) would be permissible in addition to existing plans for 8GW of offshore development (Rounds 1 & 2). This suggests several thousand more wind turbines will be needed requiring significant investment in the wind power manufacture, assembly and installation. However, operating the offshore wind turbines efficiently whilst maintaining them in healthy operation are particularly challenging technically and economically. For instance, electrical generators operate much less than their optimised efficiency with respect to their designed operating condition. This is often overlooked in estimating the wind power yield. Furthermore, offshore environments are corrosive and harsh so that the reliability of wind turbine components is compromised. In order to conduct maintenance work, maintenance personnel need to travel to the offshore tower by a ship or a helicopter, both subject to the weather conditions. In general, maintenance involves visual inspection, regular replacement and sometimes simple tests despite that fact there are some online condition monitoring techniques proposed in literature [5][6]. If a wind turbine fails between the scheduled visits, the downtime may be significant as well as the economic loss. These conventional methods are costly and unreliable. As a result, energy efficiency and reliability are the two key issues in wind power utilisation. This paper considers the former issue and focuses on techniques to maximising wind power generation.

When developing wind turbine systems, it is of prime importance to obtain knowledge about the meteorological regime and environmental aspects specific to the site of the development since they have a major impact on the design, viability and operation of the wind power system. With regard to wind profile, the specific sites can experience wind speeds more than double those measured at standard weather or climatic stations in the vicinity [7]. Wind speed information may be converted into available wind power by

2012 2nd International Symposium on Environment-Friendly Energies and Applications (EFEA)

Northumbria University

452978-1-4673-2911-8/12/$31.00 ©2012 IEEE

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various methods. Generally speaking, climatic wind data have mainly been used to rank potential sites on the basis of mean speeds, turbulence and direction classes. The wind turbine, generator, and associated components are selected from commercially available products so that they may not be optimised for a specific site.

Because over 70% of installed wind turbines utilise doubly-fed induction generators (DFIGs) [8], we will analyse the wind speed data and wind turbine performance based on the DFIG machines.

II. WIND POWER EVALUATION METHODS Wind data are available from the national weather

service. The standard anemometer height for collecting wind data is at 10m. Data on frequency of occurrence by wind direction sectors and wind speed classes are often required for the evaluation of wind power profile. In the literature, wind speed models fall into two types: the probability distribution and the time series models. Three commonly used probability density functions are Pearson, Rayleigh and Weibull functions [9][10]. The wind variation, for feasibility studies and turbine design optimization, is described by the Weibull distribution. This probability distribution includes all of the wind directions and all time scales present. However, the probability distribution models do not contain the information of the wind speed variations which can be used for machine design. On the other hand, time series models have periodic properties to represent distinct features on a large time scale. The different time scales may be classified according to Table I [11].

TABLE I: LIST OF TIME SERIES MODELS

Time scale Timespan Effect

Long term Years Pay-back time calculationsSeasons Production forecast

Intermediate Days Production forecast Hours Production forecast

Short term Minutes Stability analysis Seconds Power quality

Local, regional and national codes specify what wind

speeds are to be assumed. Wind data can be described on three timescales or in any time series format. Alternatively, they can also be described in a summary format such as the following forms [7]:

Mean wind speed Wind speed as a function of wind direction Wind speed frequency distribution (a function of

wind speed class) Joint wind speed frequency distribution (a function of

wind direction and class) Weibull parameters of wind speed frequency

distribution Weibull parameters as a function wind direction Wind speed time series for periods of hours to days.

The long-term wind profile provides fundamental information for evaluation of available wind energy which is particularly useful when calculating pay-back time of a wind farm. In this paper, annual wind speed data with an hourly interval for a site in the Northwest of England have been obtained through the UK Meteorological Office. As shown in Figure 1, wind speeds for this site varied significantly from time to time, with an annual mean wind speed of 7m/s.

Figure 1. Annual wind speed data for the site.

A. Simplied Interpolation Methods Wind speed data are commonly analysed using statistical

methods (e.g. probability density function). Wind speeds can then be characterised as arithmetic mean, root mean and cubic mean values [3][12][13][14]. These are presented in Figure 2.

Figure 2. Curves of conventional formulas compared with a

real wind power curve [15]. From this figure, the linear, quadratic, and cubic

formulas have been used to approximate the real wind power curve in the interval of the cut-in and rated wind speeds. It is reported that the cubic mean wind speed is more realistic compared to the arithmetic and root mean values for wind turbine applications [16].

The cubic mean wind speed is calculated using the equation [17],



453

3

31

1

3

1

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

=∑

=

N

VV

N

ii

m

(1)

where Vm1 is the mean wind speed, N is the number of wind speed observations, and Vi is the observed speed sample.

After the mean wind speed is derived, it needs to be

corrected to the hub height at the given site, using the equation [12],

α

⎟⎟⎠

⎞⎜⎜⎝

⎛=

rmm H

HVV 1 (2)

where α is the fractional coefficient.

These methods may provide certain guidance on estimating wind energy resource. Ideally, the output wind power would be smooth and constant while the actual wind speed is in excess of the rated speed. Without doubt, fluctuating wind speeds call for sophisticated control of the wind turbine, the generator and the related power electronics. In theory, the rotor speed can be controlled with adjustable pitch angle actuators to shed the aerodynamic power for the high wind speed region and the rotor-side converter.

The mean wind speeds shown in Figure 1 at the anemometer height and hub height are calculated to be 7m/s and 11m/s, respectively. The latter is corrected with an estimated at the hub height of 100m and a fractional coefficient of 0.2. Nonetheless, these are not suited for optimising machine design since the actual wind power is the cubic function of wind speed. By this adjustment, the normalised mean wind speed is estimated to be 11m/s.

From the design and control perspectives, the wind characteristics must match up with the wind turbine generator’s characteristics through drive train systems. These features are illustrated in Figure 3.

Figure 3. The wind turbine load characteristics [18].

B. Correlated Prediction Methods Correlated prediction methods are used to estimate the

wind profile at a given wind farm site correlating to a neighbouring test station.

The long-term mean wind speed is given by [7],

s

srs

VVCVV

σσ −

−= (3)

where sV is the observed mean wind speed at the

measurement station, C is the spatial cross-correlation of daily wind speeds between the reference and wind farm sites, σ and sσ are the standard derivations of daily average wind speeds at the site and the reference station, respectively.

III. DFIG MODELS AND THEIR CONTROL Wind speeds may apply for various time periods such as

annual, monthly, daily or hourly. It would be ideal to obtain wind speed data with a good resolution such as a 10 min interval which may reflect the actual wind turbine operation at a farm. However, such wind data may not always be available.

A schematic diagram of the DFIG wind turbine system is given in Figure 4(a). As shown in this figure, the rotor is connected to the wind turbine through a drive train system, which contains high and low speed shafts, bearings and a gearbox. The DFIG is constructed from a wound rotor induction machine where its stator is directly connected to the grid and its rotor is fed by bi-directional voltage-source converters. The speed and torque of the DFIG can be regulated by controlling the rotor side converter (RSC). In the simulation model, three main components: the wind turbine, DFIG, and drive train need to developed and modelled for the system analysis.

(a)

(b)

Figure 4. (a) Schematic of a DFIG-based wind turbine; (b) Per-phase equivalent circuit of the DFIG.

Wind speed

Load

pro

file

1

00%

Power

Torque

Vin Vrated Vout

Wind speed



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In Figure 4(b), the DFIG equivalent circuit differs from the conventional one in the rotor circuit where a voltage source is added to inject into to the rotor windings. The actual d-q control of the DFIG is similar to the magnitude and phase control of the injected voltage in the circuit.

In order to optimise the DFIG machine design, its losses and efficiency need to derive analytically or numerically. This paper uses an analytical model based on the steady state equivalent circuit extended from Figure 4(b).

The input power Pin can be summarised from the output power Pout and the total loss Ploss. The latter includes stator conductor loss Pcu1, rotor conductor loss Pcu2, core loss Pcore, windage and friction losses Pwf and stray load loss Pstray. Among these losses, Pcu1 is assumed to vary with the square of the stator current Is while Pcu2 varies with the square of the rotor current Ir. The stray load loss could be split into two parts: the fundamental component Pfun occurring at the stator side and Phar at the rotor side. Thus Pfun is proportional to Is

2 while Phar is proportional to Ir2.

The total loss is then given by

wfcoreharrrfunssloss PPRRIRRIP +++++= )'(3)(3 22 (4) The efficiency of the DFIG is

routharrfunss

rout

in

out

VRRRRIV

PP

φφη

cos3)'(6cos3

++++== (5)

The efficiency can be expressed as a function of the load current Is and this function is continuous and monotonic, consequently the maximum efficiency ηmax can be found when

0=∂∂

sIη (6)

As a result, the condition of maximum efficiency for DFIGs is

straycucuwfcore PPPPP ++=+ 21 (7) This condition of the maximum efficiency occurrence

indicates: when the load-dependent losses equalise the load-invariant losses, the machine efficiency peaks. In the design and operation of DFIGs, it is beneficial to match the generator with the site-specific wind speed by moving this maximum efficiency point close to the rated load.

The DFIG and wind turbine’s specifications are listed in Table II. Their mathematical models are introduced as follows whilst power converters and controllers are excluded for clarity.

A. Wind Turbine Aerodynamic Model The wind turbine is a nonlinear system whose total

output power extracted from the wind is given as 2 31( ) ( , )

2w w w w pP R Cυ ρπ υ λ β=

(8)

where ρ is the air density in kg/m2, wR is the rotor radius in m, and wυ is the wind speed in m/s. ( , )pC λ β is the power

coefficient, which is a function of the tip-speed ratio λ and the blade pitch angle β .

Tip-speed ratio λ is defined as

w w

w

Rωλυ

= (9)

where wω is the wind turbine rotor speed in rad/sec. Its

relation with the rotor speed of DFIG gω in rad/sec is

by g wGω ω= , where G is the gearbox ratio.

TABLE II: SPECIFICATIONS OF A 2-MW DFIG-BASED WIND TURNBINE

Wind Turbine Rotor radius 35m Air density 1.25kg/m2

Cut-in wind speed 4m/s Cut-out wind speed 25m/s Rated wind speed 12m/s Pitch angle 0o

Gearbox ratio 120 Total inertia constant 53.036kg.m2

DFIG Rated power 2MW Rated voltage 575V Frequency 60Hz Pole pairs 3 Stator/rotor turns ratio 1 Stator resistance 1.4Χ10-3Ω Stator leakage inductance 8.998 Χ 10-5H Rotor resistance 9.9187 Χ 10-4Ω Rotor leakage inductance 8.2088 Χ 10-5H Magnetizing inductance 1.526 Χ 10-3H

In this simulation model, ( , )pC λ β is given as

21116( , ) 0.5176( 0.4 5) 0.0068i

pi

C e λλ β β λλ

−

= − − +

(10)

3

1 1 0.0350.08 1iλ λ β β

= −+ +

(11)

For o=0β , the maximum power efficient is max 0.48pC = (12)

Therefore, the maximum power extracted from the wind at o=0β is

max 2 3 max12w w w pP R Cρπ υ=

(13)

The output power of the wind turbine on different regions of wind speed is given by:

_ _

_ _

_ _

;

= ( ) ;

0 ; and

rated w rat w w cout

wt w w w cin w w rat

w w cin w w cout

P

P P

υ υ υυ υ υ υ

υ υ υ υ

⎧ ≤ ≤⎪

≤ ≤⎨⎪ ≤ ≥⎩

(14)



455

5

where ratedP , _w ratυ , _w cinυ and _w coutυ are the rated power, rated wind speed, cut-in wind speed and cut-out wind speed, respectively.

B. Drive Train Model One mass model is used to represent the dynamic of

drive train, which is given as

1= ( )g w eT TJ

ω −

(15)

where J is the total inertia constant in kgm2. wT is the transferred wind turbine torque on the generator side in Nm.

C. DFIG Mathmetical Model The DFIG model in the synchronous reference frame is

given by sd

sd s sd s sq

sqsq s sq s sd

dv r idt

dv r i

dt

ψ ω ψ

ψω ψ

⎧ = + −⎪⎪⎨⎪ = + +⎪⎩

(16)

( )

( )

rdrd r rd s r rq

rqrq r rq s r rd

dv r idt

dv r i

dt

ψ ω ω ψ

ψω ω ψ

⎧ = + − −⎪⎪⎨⎪ = + + −⎪⎩

(17)

( )( )

sd ls m sd m rd

sq ls m sq m rq

L L i L iL L i L i

ψψ

= + +⎧⎪⎨ = + +⎪⎩

(18)

( )( )

rd lr m rd m sd

rq lr m rq m sq

L L i L iL L i L i

ψψ

= + +⎧⎪⎨ = + +⎪⎩

(19)

where sr and rr are the stator and rotor resistances in Ω, lsL and lrL are the stator and rotor leakage inductances in H,

mL is the magnetizing inductance in H. sω is the

synchronous electrical speed in rad/sec. rω is the rotor electrical speed of the DFIG and its relation with rotor mechanical speed gω is r gPω ω= , where P is pole pairs.

The electromagnetic torque is 3 ( )2e m sq rd sd rqT PL i i i i= −

(20)

The simulation is conducted in Matlab environment with the DIG model shown in Figure 5.

IV. SITE-MATCHING MACHINE DESIGN When designing the wind turbine generators, some

difficulties arise in interpretation of the wind data for reliable statistics under the desired conditions. At a good wind turbine site, the wind turbine’s long term average power output may only be equal to 30% of the generator’s rating [7]. Owing to the intermittent nature of wind energy, it is difficult to optimise the machines for wind turbine applications taking account of actual wind speeds at a site.

Figure 5. The DFIG Model.

Matching machine characteristics of the wind turbine

generators with site-specific wind profiles have been attempted previously [16][19][20][21]. In terms of machine design, little progress has been made to match machine characteristics with the site wind profile. In this paper, site matching is achieved by predicting the maximum efficiency from selected standard machines and matching this with the normalised mean wind speed obtained from annual wind profile.

This study incorporates site-specific wind profiles into the machine characteristics at the design stage by balancing the load-dependent and load-invariant loss components. By doing so, the maximum efficiency point on the efficiency-torque characteristic can be moved close to the most likely operating point which corresponds to the cubic-mean wind speed of the particular site. This is particularly relevant to the wind power generation because the wind turbine operation changes with the wind speed from time to time.

The DFIG is modeled in Finite Element (FE) software MagNet (see Figure 6) and loss balancing is performed in Matlab/Simulink environments. The total energy production is used as a key criterion to refine the machine design considering various arrangements for stator and rotor windings, slot shapes, length-diameter ratio, slot pitch ratio, and other design issues. As a result, complete losses and efficiency can be obtained for the whole load range. Power loss balance is then input to the Matlab/Simulink so as to provide guidelines on which loss component needed to modify in order to shift the maximum efficiency in relation to the actual wind speed. Through this iterative procedure, a range of good designs are generated and a best design is selected for the specific site. A downsized prototype machine is being produced and experimental validation will be followed.

V. CONCLUSIONS It is essential to match the available wind power specific

to a development site to the wind turbine generator. A good assessment of the potential site’s wind regime for the



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purpose of predicting wind energy yield is thus desired as well as its cubic-mean wind speed. These are used for site-matching DFIG machine design and its control. From theoretical analysis, the machine’s maximum efficiency occurs when the losses are balanced. This provides a new refinement criterion for the machine design, in addition to traditional design tools.

In the further work, experimental tests will be conducted on a standard 30kW DFIG and its modified 30kW DFIG (prototype machine) to validate the concept proposed in this paper.

Figure 6. Flux distribution of the DFIG.

ACKNOWLEDGMENT The authors would like to thank the financial support

from the European Commission seventh framework programme (FP7) under the grant FP7-PEOPLE-2012-IRSES/318925.

REFERENCES [1] European Commission Research and Innovation, Horizon 2020,

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