风力发电机故障诊断与容错控制研究

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"Fault Diagnosis and Fault-Tolerant Control of Wind Turbines by Thomas Esbensen and Christoffer Slot from Denmark focuses on enhancing the reliability and reducing repair costs in wind turbines through advanced fault diagnosis and fault-tolerant control strategies." 在风力发电领域，由于许多风力涡轮机安装在偏远地区，故障诊断和容错控制成为提升设备可靠性和降低维修成本的有效途径。该项目由Thomas Esbensen和Christoffer Slot两位学者进行，他们隶属于丹麦的电子系统系自动化与控制科。研究中，他们采用了一个4.8兆瓦的虚构但具有现实性的风力涡轮机模型，以此为基础建立动态模型。首先，进行了故障分析，旨在识别可能的组件故障的发生频率及其对最终效果的严重性。接着，针对最具影响力的重大故障，应用了诊断和补偿方法。这些方法的实施有助于提前发现和应对潜在的问题，从而提高系统的稳定性和效率。诊断算法基于一个可重构的扩展卡尔曼滤波器结构，这使得能够同时诊断多个故障。对于突发性故障，通常采用假设测试为基础的方法进行诊断；而对于渐进型故障，可能会运用状态监测和数据融合技术来逐步识别其发展过程。在容错控制方面，设计了能够在检测到故障后调整控制策略的机制，以确保系统能在部分组件出现故障时仍能保持一定程度的功能。这可能包括切换到备用系统、调整控制参数或采用补偿算法来抵消故障影响。这项工作深入探讨了风力涡轮机的故障诊断和容错控制技术，为实际风能产业提供了理论支持和解决方案，有望改善风力发电系统的性能和经济性。通过这样的方法，不仅可以减少因故障停机带来的损失，还能延长风力涡轮机的使用寿命，进一步推动可再生能源领域的可持续发展。

System Description



Anemometer is used to measure the wind speed. The wind turbine is started when the wind

speed reaches a lower limit, while operation is cut-out when wind speeds become too high.



Brakes can be applied mechanically, electrically, or hydraulically and function as parking

brakes.



Gearbox connects the low-speed shaft to the high-speed shaft, thus increasing the rotational

speed to a level required by the generator to produce electric energy.



Generator converts rotational energy into electric energy. On a modern wind turbine the

maximum power output is typically from a few and up to ﬁve megawatts.



High-speed shaft drives the generator.



Hub and rotor blades together make up the rotor of the wind turbine. The hub connects

the rotor blades to the low-speed shaft. Pitching the blades is used to maximize the eﬃciency

in low winds and reduce eﬃciency in high winds to protect the wind turbine from structural

damage.



Low-speed shaft connects the rotor to the gearbox.



Nacelle is located atop the tower and contains the gearbox, low- and high-speed shafts,

generator, and brakes.



Tower carries the nacelle and the rotor. Since the wind speed increases with the height, a

taller tower generally enables a wind turbine to generate more electric energy.



Wind vane is used to measure the direction of the wind. The wind direction is used by the

yaw mechanism to orient the wind turbine perpendicular to the wind.



Yaw mechanism uses electrical motors to orient the wind turbine rotor perpendicular to

the direction of the wind.

Having introduced the main components of a wind turbine, the next section describes how a

variable-pitch, variable-speed wind turbine is typically controlled.

2.2 General Control Strategy

The purpose of this section is to explain how a variable-speed, variable-pitch wind turbine is con-

trolled along a typical operating trajectory, and also to explain the variables that are involved in

the control. This is relevant since the fault diagnosis and fault-tolerant control systems are subject

to the conditions in the closed-loop system.

When controlling a wind turbine, the overall target is to minimize the operational cost while

maximizing the generated power. This cost depends on the conditions under which the wind turbine

produces the power, and implies that wind turbines operate along a certain trajectory, as the one

shown in Figure 2.2. This trajectory is obtained using a strategy of control shown in Figure 2.3,

which illustrates the control signals and rotor speed for obtaining the desired output power.

From examining the power curve it is obvious that the wind turbine only produces power in a

limited range of wind speeds, which is further divided into two distinct regions, I and II; denoted

the partial load region and the full load region. At wind speeds below the cut-in speed, V

w,cut-in

the wind turbine does not produce any energy since the operational cost exceeds the value of the

produced power. Similarly, no energy is produced when wind speeds exceed the cut-out wind speed,

w,cut-out

, where the wind turbine is shut down to protect it from structural overloads. To explain

what happens in the two regions of power production, these are explained separately in the following

numbered list:

Page 6

2.2 General Control Strategy

g,N

w,cut-out

w,N

w,cut-in

Cut-in

Cut-out

12.3

v [m/s]

P [W]

3 25

Partial load region

Full load region

Figure 2.2: Ideal power curve for the wind turbine limiting the output power at high wind speeds to

the rated value of 4.8 MW. The interval of the wind speed is divided into two regions, I and II, in

which diﬀerent control objectives exist.

[m/s]

0.5

[rad/s]

1.5

1.6

3.2

4.8

6.6

13.2

19.8

10.7

21.4

32.1

[MW]

β [

◦

]

[kNm]

Figure 2.3: Typical control strategy for following the ideal power curve. The plots of the pitch angle

(green) and the generator torque (red) show how the control signals are manipulated to obtain the

desired output power (blue) as function of the wind speed v

I. The partial load region is located between the cut-in wind speed, V

w,cut-in

, and the rated wind

speed, V

w,N

. In this region the wind turbine is controlled to generate as much power as pos-

sible. This is achieved by adjusting the generator torque to obtain an optimum ratio between

the tip speed of the blades and the wind speed. Hereby, the eﬃciency of the aerodynamics is

maximized.

II. The full load region is located between the rated wind speed, V

w,N

, and the cut-out wind speed,

w,cut-out

. Operation in the full load region involves that the produced power is kept at a

rated value to minimize structural loads and thereby reduce fatigue damages. Additionally,

the rotor speed is ﬁxed to reduce acoustic noise emission from the wind turbine, which depends

on the speed of the rotor.

Due to the existence of two distinct regions of control, the usual approach is to apply two

diﬀerent sets of controllers and interconnect these using a bumpless transfer mechanism. This is

illustrated in Figure 2.4, which shows a block diagram of a reference controller that is based on

classical methods and is introduced to establish a frame of reference. Notice that the structure of

the reference controller is set up in compliance with kk-electronic a/s.

The strategy of the reference controller is to use two diﬀerent controllers for the partial load

region and the full load region. When the wind speed is below the rated value, the control system

should maintain the pitch angle at its optimal value and control the generator torque in order

to achieve the optimal tip-speed ratio. This behavior is achieved by setting the two switches in

Figure 2.4 to be in Position I.

Page 7

Wind Turbine Modeling

The purpose of this chapter is to set up a mathematical model of the considered wind turbine. The

model should be detailed enough to be used as simulation model. From the non-linear model a

linear model is derived to be used in the linear design methods presented throughout the thesis.

Notice that the chapter is inspired by

[

Esbensen et al., 2008, pp. 23-38

]

, and that the sections:

Model Structure, Aerodynamic Model, and Drive Train Model are only slightly modiﬁed.

In the following section the structure of the wind turbine model is presented in a block diagram.

Afterwards, each sub-model of the wind turbine is presented and combined to obtain a complete

model of the wind turbine. To enable the further design, the model is linearized in Appendix B

and rewritten on state space form.

3.1 Model Structure

The ﬁrst stage of the modeling procedure is to divide the overall wind turbine system model into

appropriate sub-models suitable of being modeled separately. These sub-models are shown in Fig-

ure 3.1.

Aerodynamics

Drive train

Generator

Tower

Pitch

system

v (t)

ù (t)

â(t)

T (t)

ù (t)

F (t)

x (t)

â (t)

ref

Converter

T (t)

P (t)

T (t)

g,ref

P (t)

Wind model

v (t)

Figure 3.1: Relationship between sub-models of the wind turbine system model. The wind speed,

(t), is the exogenous input and the generator power, P

(t), is the system output. The controllable

inputs are the pitch angle reference, β

ref

(t), and the generator torque reference, T

g,ref

(t). The rotor

speed is fed to the wind model to create wind shear and tower shadow eﬀects.

The wind speed is the driving force of the system. Due to the swaying of the tower, the wind

speed seen at the rotor is obtained by subtracting the speed of the nacelle from the speed of the

wind.

The aerodynamic properties of the wind turbine are aﬀected by the pitch angles of the blades,

the speed of the rotor, and the wind speed. On this basis, an aerodynamic torque is transferred

from the rotor to the generator through the drive train, and an aerodynamic thrust aﬀects the rotor

and thereby the tower.

The output of the wind turbine is electric power which comes from the converter. To operate

the wind turbine according to the set of operating requirements, the pitch angles of the blades and

the generator torque are adjusted. A pitch system controls the pitch angles of the blades, while a

converter controls the generator torque.

In this section the wind turbine model has been divided into seven sub-models, in order to be

individually modeled and combined afterwards. The purpose of the next section is to model the

wind speed, being the exogenous input to the wind turbine.

Page 9

Wind Turbine Modeling

3.2 Wind Model

The purpose of this section is to design a wind model, by determining and modeling the components

that inﬂuence the wind speed applied to each blade. The model must generate the input to the

wind turbine model; hence, an eﬀective wind speed on each blade must be calculated. Additionally,

the wind model should provide an output resembling the input to the anemometer, which is a point

wind speed, contrary to the remaining considered wind speeds.

Generally, the wind speed is inﬂuenced by several components, which depend on the environment

where the wind turbine is located. An equation giving an overview of the components is shown

below.

(t) = ¯v

(t) + v

(t) [m/s] (3.1)

where:

(t) is the wind speed tower shadow component [m/s]

(t) is the wind speed turbulence component [m/s]

(t) is the wind speed including tower shadow, turbulence, and wind shear [m/s]

¯v

(t) is the mean wind speed [m/s]

(t) is the wind shear component [m/s]

This general model is utilized in the designed wind model. The output from the wind model

is wind speeds averaged over an area, instead of point wind speeds. Therefore, these are called

eﬀective wind speeds.

The next subsections describe the components, which form the basis for modeling the wind

speed.

Wind Shear

The ground and other obstacles in the path of the wind cause frictional forces to act on the wind.

The frictional forces imply that the mean wind speed becomes dependent on the height above

ground level. This eﬀect is called wind shear and can be calculated from the equation shown below

[

Dolan and Lehn, 2006

]

. The equation integrates the wind speed components from the beginning

to the end of the blade proﬁle and sums the components for the three blades obtaining the wind

shear eﬀect for the rotor plane. Figure 3.2 illustrates some of the parameters used in the equation.

(t) =

hub

(t)

3qR

i=1



cos (ψ

(t)) +

α (α − 1)

cos

(ψ

(t))

α (α − 1) (α − 2)

cos

(ψ

(t))



(t) =

hub

(t)

3qR

i=1



cos (ψ

(t)) +

α (α − 1)

cos

(ψ

(t))

α (α − 1) (α − 2)

30h

cos

(ψ

(t))



−



cos (ψ

(t)) +

α (α − 1)

cos

(ψ

(t)) +

α (α − 1) (α − 2)

30h

cos

(ψ

(t))



[m/s]

(3.2)

∆

= 1 −





where:

h is the height of the tower [m]

R is the radius of the rotor [m]

is the radius at which the blade proﬁle begins [m]

hub

(t) is the wind speed at hub height [m/s]

α is the empirical wind shear exponent [·]

(t) is the azimuth angle of Blade i [rad]

Page 10

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