风电控制算法：提高能源产出与减缓疲劳载荷

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"风电控制算法相关的英文教材，深入探讨了风机控制的各种算法，旨在最大化能量产出和减少风力机疲劳载荷，优化海上运行。教材重点关注主动失速调节和变速度概念。" 风电控制算法是风力发电领域的重要组成部分，其目的是通过精确调控风力发电机的运行状态来提高能效和减少机械应力。本教材"ECN-C--03-111 Wind turbine control algorithms"由E.L.vander Hooft, P.Schaak和T.G.van Engelen撰写，主要研究和开发了2003年DOWEC（欧洲风能合作）任务3的工作包1中的内容，目标是优化风力发电机的功率控制算法。在风力发电中，控制算法通常包括但不限于以下几方面： 1. **主动失速控制**：这是一种用于调整风轮叶片角度的技术，以控制风力机的功率输出。当风速超过一定的阈值时，通过让叶片失速（即叶片迎风面后退，降低攻角），可以防止过快的转速增长，从而保护风力机免受过大的机械载荷。 2. **变速度控制**：与传统的固定速度风力机不同，变速度风力机允许发电机的转速随着风速的变化而变化，从而更有效地捕获风能。这种控制策略可以显著提高能量产出，并降低塔筒和机械部件的疲劳载荷。 3. **模态控制结构**：教材中提到建立了一个基于理论分析和工业需求的模块化控制结构。这意味着控制算法可以根据不同的运行条件和风况进行调整和优化，提高了系统的灵活性和适应性。 4. **性能提升**：通过添加额外的控制功能和动作，例如涡流发生器控制、湍流抑制等，可以进一步提升风力机的功率输出和负载减轻效果。 5. **比较与验证**：教材中的独立比较表明，采用先进控制结构的DOWEC风力机在塔筒前后的弯曲矩、扭转载荷等方面都有显著改善。这证明了所研究的控制算法相对于传统的比例微分（PD）反馈控制具有优越性。 6. **海上优化**：由于海上风力机面临的环境条件更为复杂，如更大的风速波动、盐雾腐蚀和海浪冲击等，控制算法的优化对提高海上风电场的可靠性至关重要。总结来说，"风电控制算法"这一主题涵盖的内容广泛且深入，涉及了风力发电机的核心控制策略及其在实际应用中的优化方法。通过学习和理解这些算法，工程师能够设计出更高效、更耐用的风力发电系统，推动可再生能源技术的发展。

2 MODELLING THE DOWEC TURBINE

The nodding excitation force, F

top

, eq.(2.17), consists of tower top equivalent components

caused by the turbine thrust force F

, eq.(2.2), and the external (hydrodynamic) fore-aft forces

hyd

. From bending theory of slender beams [8] , it has been derived that the exitation force

components of F

top

appear as given in eq.(2.20)

top

= F

+ F

hyd

= F

t,wave

k=1



d − z



· F

hyd,k

(2.20)

The variables d and z

are related to the tower part below the water surface and deﬁned as the

waterdepth and the distance to the water surface at element k, respectively (see 2.3.2).

The naying excitation force, F

top

,eq.(2.18), consists of a nacelle force caused by the drive

train reaction torque on the tower F

top

nac

and the external sideward (hydrodynamic) forces F

hyd

. From bending theory of slender beams [8] , it has been derived that the exitation force

components of F

top

appear as given in eq.(2.21)

top

= F

top

nac

+ F

hyd

nac

t,wave

k=1



d − z



· F

hyd,k

(2.21)

The deﬁnitions of d and z

are equal as in eq.(2.20), T

nac

is the reaction torque of the drive

train as given in eq.(2.14)

Rotation effects in sideward direction will disturb the (measured) rotor speed. A rough (linear)

approximation of this rotation angle is given in eq.(2.22).

2 · x

(2.22)

Both in eq.(2.20) and eq.(2.21), simple addition is allowed, because the tower is assumed to

have a cilindrical shape and the angle of attack of the waves is assumed to be in line with the

axial force.

2.2.4 Electric conversion

The electric conversion part of the DOWEC turbine consists of a voltage source back-to-back

converter, which controls the rotor voltages of a doubly fed asynchronous generator using a

dedicated ’ﬁeld oriented control’ algorithm. The stator of the generator is directly connected

to the grid. This topology is able to realise cost-effective variable speed control for a limited

speed range (+/- 30%), determined by the capacity of the inverter. High speed switching power

electronics are able to set electric generator torque almost instantaneously with respect to the

mechanical dynamics. For the proposed control design purposes, only the generator side in-

verter of the converter is relevant and dynamic behaviour above 5-10Hz (suppression of shaft

torsion resonance 2-3Hz) are neglected. Therefore, a well ﬁtted second order torque-servo ap-

proach as given in eq.(2.23), represents the overall dynamic behaviour from setpoint to actual

torque, sufﬁciently.

∗

(ω

)

2β

+ T

(2.23)

The used bandwidth amounted to 6Hz (ω

= ± 38 rad/s), which is quite conservative, the

damping rate β

was set to 0.7 which implicates a just critical damped system. The electric

torque servo controlequuipment will certainly be capable to achieve these requirements.

Further simpliﬁcation can be achieved by ignoring second order dynamics and take only a ﬁrst

order dynamics into consideration:

∗

= τ

+ T

(2.24)

ECN-C--03-111 15

Wind turbine control algorithms

A conservative value for the time constant τ

will be 0.1s.

Basically the electric torque setpoint consists of the stationary relation for power produc-

tion (subsection 3.4.1). Sideward tower movements (‘naying’) will slightly affect the electric

torque. Additional (dynamic) torque setpoint components T

∗

e,ctrl

can be added to achieve im-

proved turbine control (subsection 3.4.2 and 3.4.3) or reduction of resonances (section 5.1,

section 5.3).

∗

= T

∗

(Ω

− 2

˙x

) + T

∗

e,ctrl

(2.25)

2.2.5 Pitch actuation system

The calculated pitch speed setpoint of the control algorithm will be applied to the blades by

pitch actuation. For the DOWEC turbine, three independent but simultaneous acting electric

pitch actuators will change the pitch angle of the blades each control step.

The speed control equipment of the electric drive system usually acts as a servo system with

respect to its commanded (pitch)speed, by separation of ﬁeld and torque control. The dynamics

of electric components are usually small with respect to the mechanical loading behaviour.

The pitch motor load is determined by the pitch system inertia and a (disturbing) torque due

to friction of the blade bearing. This friction consists of a component which is proportional to

the pitch speed and a constant component (Coulomb friction), which changes of sign at pitch

speed reversal. Bending of the blades are mainly responsible for the friction behaviour of pitch

bearings.

In [8] it has been proved that a delayed second order system ﬁts the pitch actuator dynamics

sufﬁciently for control analysis purposes and that the Coulomb friction behaviour can be mod-

elled by adding additional actuation delay in case of pitch speed reversal (in Laplace domain):

θ(s) = H

(s) ·

∗

(s)

(s) =

−(T

ptv

ptx

)·s



(ω

)

· s

2·β

· s + 1



∗

(s), (2.26)

in which T

ptx

is deﬁned as the conditional delay time to overcome Coulomb friction. T

ptv

, β

, are equivalent system parameters which represent the overall pitch actuation delay

during normal operation: pitch delay time, pitch system eigen frequency, damping rate.

Usual values for T

ptv

, ω

and β

are respectively: 1-3 ms, 80-100 rad/s and 0.3-0.5. The

representive delay for Coulomb friction is relative large, ± 100 ms. This means well damped

dynamic behaviour with a bandwidth of approximately 10-15 Hz and a dominating conditional

delay.

2.3 External phenomena

As mentioned before in ﬁg.(2.1), two external disturbing inﬂuences are relevant for an offshore

turbine: wind speed and wave forces. Both comprises stochastic properties. In subsection

2.3.1, wind speed will be modelled ‘rotor wide’; on the one hand side as a driving quantity

(to produce power from aerodynamic torque) and on the other hand side as a disturbing quan-

tity (ﬂuctuations by turbulences). In subsection 2.3.2, wave forces will be modelled as force

effective wave accellerations, which excite the tower (disturbing quantity).

2.3.1 Rotor effective windspeed

To verify the performance of a control algorithm by time domain simulations, a representative

wind speed signal is necessary. Therefore, ‘rotor effective wind speed’ is deﬁned as [8]:

‘a single point wind speed signal which will cause wind torque variations through rotor power

and thrust coefﬁcients, that will be stochastically equivalent to those calculated with blade

element momentum theory in a turbulent wind ﬁeld’.

16 ECN-C--03-111

2 MODELLING THE DOWEC TURBINE

The stochastic wind speed signal is derived from the autopower spectrum of the longitudinal

wind speed variations and lateral coherence in the rotor plane, according to IEC class IIB with

turbulence intensity 16% [1]. The rotor effective wind speed signal has been normalised by the

mean value of wind speed and comprises:

• tower shadow inﬂuences;

• wind shear variations;

• 0p mode of the turbulent windﬁeld;

• 3p- and 6p effects of the rotationally sampled wind ﬁeld.

Fig.(2.5) shows these components in detail during 20 seconds. In the upper plot of ﬁg.(2.5),

0 5 10 15 20 25 30 35 40

−1.5

−1

−0.5

0.5

wind speed variations at 1.63 r/s (15.6rpm) rotor speed and 12.3 m/s mean wind

tower+shear infl. [m/s]

0 5 10 15 20 25 30 35 40

−1

−0.5

0.5

turb.mode 3 6 [m/s]

0 5 10 15 20 25 30 35 40

−1

turb.mode 0 [m/s]

time [s]

file E:\schaak\...\SCOPE\PS\rot1\vwexcitm.ps 26−Feb−2003

by E:\schaak\...\SCOPE\M\scturbu.m

Figure 2.5: Details of contributions to rotor effective windspeed; tower and shear, rotational

sampling, 0p mode

tower shadow inﬂuences are clearly visible as 3p periodical notches. Wind shear is nearly

negligible. The middle plot shows the 3p and 6p rotational wind ﬁeld sampling effects of the

blades. Because these effects considerably affect the rotor acceleration, incorporating them is

signiﬁcant to verify ﬁltering performance during rotor speed control. The lower plot shows

‘low frequent’ wind speed variations (0p) determined by the stochastic properties of wind and

turbulence intensity.

For simulation purposes the actual wind speed is determined from a prior calculated wind ﬁle

comprising normalised periodic and turbulent components for actual rotor azimuth, Ψ

and

desired mean wind speed,

Ω

· dt

· [1 + v

tur

(Ψ

)]+

· [1 + v

tur

(Ψ

)] · [v

tow

(Ψ

mod2π) + v

shr

(Ψ

mod2π)]

(2.27)

In eq.(2.27), both tower shadow and wind shear variations are periodic effects in the range

[0, 2π] of the rotor azimuth, and scalable with ‘rotor uniform wind’, V

unif

. Turbulence is

approximately proportional with mean wind speed,

. In eq.(2.27), the components v

tur

tow

and v

shr

are normalised variations with respect to the mean windspeed V

ECN-C--03-111 17

Wind turbine control algorithms

Finally, ﬁg.(2.6) shows simulation time series of the rotor uniform wind speed and rotor effec-

tive wind speed, respectively.

0 100 200 300 400 500 600 700 800 900

Absolute wind speed time series at 15.6 rpm rotor speed and mean value 12.3 m/s

uniform wind speed [m/s]

0 100 200 300 400 500 600 700 800 900

rotor effective wind speed [m/s]

tijd [s]

file E:\vdhooft\...\SCOPE\PS\rot1\vwabs.ps 10−Dec−2003

by E:\vdhooft\...\SCOPE\M\scturbu.m

Figure 2.6: Time series of uniform wind speed and rotor effective wind speed signals

2.3.2 Towertop effective wave forces

The stochastic properties of linear waves are described by spectral density functions like the

one of Pierson-Moskowitz. Speciﬁcally, the model for wind turbine simulation should describe

the impacts on the tower base structure and its foundation. These wave disturbances (diffrac-

tion) are described by the MacCamy Fuchs correction. Modelling of waves has been restricted

by taking the following assumptions into account:

• the considered waves pertain to a speciﬁc mean wind speed value;

• the propagation of the waves are horizontal and uni-directional;

• ‘low waves’, which means that the wave heights are small with respect to their length

and depth;

Below the modelling approach of wave impact on the turbine tower is discussed shortly, more

detailed analysis can be found in [8] and fundamental theory in [10].

Horizontal wave velocity and acceleration: In case of ‘low waves’ it is allowed to use

theory for linear waves (Airy’s theory), which describes two important issues:

1. both the water velocity w and acceleration ˙w, for any arbitrary distance to the surface

of the water z, is fully determined by surface raisings (elevation, η) via a scaling factor,

which depends on the distance to the surface, the wave length λ and the wave frequency

ω;

2. the so called relation of dispersion, which unambigiously establishes the relationship

between wave length, water depth d and wave frequency ω

2πg

· tanh



2πd



. (2.28)

18 ECN-C--03-111

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