modeling and control of wind turbines including aerodynamics

8/14/2019 MODELING AND CONTROL OF WIND TURBINES INCLUDING AERODYNAMICS

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Scientific Bulletin - Faculty of Engineering - Ain Shams Uni.Vol. 41, No. 2, June 30, 2006.

MODELING AND CONTROL OF WIND TURBINES INCLUDING

AERODYNAMICS

M.EL-SHIMY

Electrical Power and Machines Department

Faculty of Engineering

Ain Shams University, Cairo, Egypt

ABSTRACT

Wind has proven to be one of the most successful of all available sources of renewable

energy offering relatively high capacity, with generation costs competitive with

conventional energy sources. Therefore, the technologies for generation of electrical

energy from renewable energy sources, especially wind energy, have evolved in recent

years. Most of available wind farm models in literature neither include aerodynamic

torque models nor model for mechanical parts. Therefore, this paper presents a model

for a variable-pitch, constant-speed horizontal-axis wind turbines including

aerodynamics and mechanical parts. Moreover, two techniques of control of the

considered wind turbine are applied. Both techniques objected to keep wind turbinespeed constant for wide range of wind speed variations. Both PID and neural network

NARMA-L2 controllers are used to control rotor blade pitch angle of the wind turbine.

Results show that both controllers are capable to keep wind turbine speed and output

power for various types of disturbances by controlling rotor blade pitch angle.

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INTRODUCTION

For thousands of years, man has harnessed energy from wind to sail ships, grind grain

and pump water. Windmills were in use in ancient Egypt fifty centuries ago for

grinding flour. Water pumping windmills have been recorded in Kautalyas

Arthashastra, indicating their existence in India from 400 BC. But it was only asrecently as the late 20

thCentury, that windmills were developed in Europe to generate

electricity.

Wind results from the differential heating of the earth and its atmosphere by Sun. It is

the kinetic energy in the wind that windmills convert into mechanical or electricalenergy. Wind energy is free, there is no cartel that controls its distribution and no

sanction or blockade on wind is possible. Since it is unlimited, renewable and a

pollution free source, there has been a movement the world over to develop highly

sophisticated technology to convert kinetic energy in wind to electrical energy.

Wind has proven to be one of the most successful of all available sources of renewable

energy offering relatively high capacity, with generation costs competitive with

conventional energy sources. Therefore, the technologies for generation of electrical

energy from renewable energy sources, especially wind energy, have evolved in recent

years [1, 2]. In 2002, the total installed capacity of Wind Energy allover the world

reached 27.257 GW [3]. It is predicted that 12% of the total world electricity demands

will be supplied from wind energy by 2020 [4].

In recent years, the cost associated with electric energy derived from fossil and nuclear

fuel, and the increase in environmental regulations continue to constraint the planning

and operation of electric utilities. Furthermore, the global economic and politicalconditions that tend to make countries more dependent on their own energy resources

have caused growing interest in the development and use of renewable energy [5, 6].

In terms of its environmental advantages, wind turbines generates electricity with no

contribution of carbon dioxide (CO2) or other greenhouse gases to the atmosphere and

they produce no pollutant discharge on water or soil. In terms of economics, the

improvements in technology and the acquired experience with wind power plants have

shown reliability and durability, and their operation and maintenance costs predictable

[5].

Wind farm modeling is very important to investigate the performance of the farm

either with grid connection or as a stand-alone system. During the last decade several

models have been introduced for the wind farm depending on the purpose of the study.

Most of available wind farm models in literature neither include aerodynamic torque

models nor model for mechanical parts.

A third-order dynamic model of induction machine is used in [7] neglectingaerodynamics and the turbines mechanical coupling on the performance of wind

farms.


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A PQ-model was used to investigate the operation of a wind farm consisting of parallel

connected doubly fed induction machines [8] and used in calculating the output active

and reactive power of each generator unit. The variation of the wind speed experienced

by each generator was simulated in two different ways; a constant wind speed and a

sinusoidal type wind speed. The conventional PQ-model for the wind farmwhere the

generators active power and the power factors were assumed and the reactive powerwas calculatedwas modified by considering the steady state model of induction-type

generators that assumed to be identical [9] [12]. Moreover, an RX-model wasdeveloped. In these models, the real power was calculated from the wind speed using

the power curves in the first iteration then it was assumed constant during the iterative

simulation. This made the simulation easier as the reactive power will be dependentonly on the buses voltages. Both PQ-models and RX-models are suitable for load flow

studies. Therefore, these models are not sufficient for studies involving dynamic

operation under various operating conditions. This because the lake of the effect of the

mechanical construction of the turbines as well as the models for the turbine

interconnections.

A state variable model for wind turbines was developed to investigate the transient

stability analysis of the Cyprus power system with small wind farm connection [13].

Aggregate models of wind farms considering aerodynamics and mechanical coupling

were developed in [14, 15] consisting of aggregated models for wind speed, wind

turbines, and a wind farm layout. A Model suitable for transient stability studies was

developed [16]. Each equivalent wind turbine model consisted of the aerodynamic

torque, drive train, and induction generator model. This model was used to investigate

the effect of short circuit power at bus connection, reactive power compensation, rotor

inertia, and wind speed on the transient stability of the system. It was shown that the

effect of the short circuit power and the variation in the rotor speed is very significanton the stability, while the reactive power compensation has only a slight effect.

Detailed modeling of wind farms [17, 18] suitable for wide range of studies were

developed consisted of; a model for electric generators, a model for the mechanical

parts of the wind turbine, an aerodynamic model represented by the aerodynamic

power equation, and a wind model.

Several schemes and techniques have been developed to control the active and reactive

power flow to and from the wind farm by controlling each individual unit or a group of

units in order to insure that the reactive power demand by the farm is within the

required limits. While others were devoted to regulate the output voltage of each unit.

In addition to the maximum power tracking control by which each unit was equipped

[19-25].

This paper presents a model for a variable-pitch, constant-speed horizontal-axis wind

turbines including aerodynamics and mechanical parts. Moreover, two techniques ofcontrol of the considered wind turbine are applied. Both techniques objected to keep

wind turbine speed constant for various disturbances. Both PID and neural networkNARMA-L2 controllers are used to control rotor blade pitch angle of the wind turbine.


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Results show that both controllers are capable to keep wind turbine speed and output

power for various types of disturbances by controlling rotor blade pitch angle.

DESCRIPTION OF WIND TURBINE

The wind turbine rotor is connected to a generator. The generator output can becontrolled to follow the commanded voltage. The wind turbine has pitchable blades to

control the aerodynamic power extracted from the wind. Also there is a mechanicalcomponent (gearbox) between the low-speed rotor shaft and the high-speed generator

shaft. The low-speed shaft is driven by the turbine blades, which generates

aerodynamic power. The high-speed shaft is loaded by the electric generator in theform of an electrical load. As the wind speed fluctuates, the wind turbine is controlled

by changing the pitch angle to avoid the rotor speed following the variation of the

wind speed. Therefore, the wind-turbine-generator (WTG) system converts rotational

energy to electrical energy, which is usually supplied to the utility grid at the

distribution level.

WIND POWER AVAILABLE

The kinetic energy, Uof a packet of wind of mass mflowing at upstream speed u in

the axial direction of the wind turbine is given by [26]:

22

2

1

2

1uAxmuU )( (1)

where Ais the cross-sectional (swept) area of the wind turbine, is the air density and

xis the thickness of the wind packet.

The wind power, Pw in the wind, which represents the total power available for

extraction, is given by:

dt

dUPw (2)

Therefore,

32

2

1

2

1Au

dt

dxAuPw (3)

The mechanical power, Pm extracted from the available power in the wind Pw is

expressed by the turbine power coefficient of performance CP which is a nonlinear

function of tip speed ratio and pitch angle . Therefore,

wpm PCP , (4)

In ideal conditions [26], the turbine cannot extract more than 59% of the total power ofundisturbed tube of air with cross sectional area equals to wind turbine swept area.


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The tip speed ratio is a variable that combines effect of rotational speed of the

turbine and wind speed. It is defined as the ratio between the rectilinear speed of the

turbine tip (R) and the wind speed (u).

uR (5)

where R is the maximum radius of the wind turbine swept area.

The following equation can be used to approximate the CP(, ) curve [27]:

Kp eKC 512

540116220 ...),( (6)

where

1

0350

080

1

3 .

.K (7)

Variation of CPwith tip speed ratio at constant pitch angle and variation of CPwith

pitch angle at constant tip speed ratio are shown in Fig. 1 and Fig. 2 respectively.

In addition to the turbine power coefficient of performance CP, the wind turbine rotor

performance can also be evaluated as function of the coefficient of torque Cq. As the

wind power Pw is equal to the product of the aerodynamic torque TA and the rotor

rotational speed , the torque coefficient can be related to the power coefficient by:

),(),( qp CC (8)

Using (3), (4), (5), and (8), the aerodynamic torque that turns the rotor shaft takes the

form:

2

2

1uCART qA ),(

(9)

WIND TURBINE PLANT MATHEMATICAL MODELING

The most special feature about wind turbines is the fact that, unlike other generation

systems, the power inflow rate is not controllable. In most power generation systems,

the fuel flow rate, or the amount of energy, applied to the generator controls the output

voltage and frequency. However, wind speed varies with time and so does the power

demand. Therefore, other generation systems can be referred to as controlled energy

sources, whereas the wind is an uncontrolled energy resource and the power demand is

an uncontrolled energy sink.On occasion, the wind speed can be very high resulting in power generation that

exceeds the demand of the load. This might lead to the turbine exceeding its rotational


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speed rating and subsequent damage to the turbine. On the other hand, the wind speed

can be too low for any power production and therefore alternative energy sources

should be used.

The fact that one has no control over the energy source input, the unpredictability of

wind and the varying power demand are more than enough concerns to justify the needfor a controller, which will regulate all the parameters that need to be controlled for a

matched operation of the wind turbine.

The wind-turbine-generator (WTG) model is divided into two main parts. The first

part is the wind turbine, which included a turbine rotor on a low-speed shaft, a gearboxand high-speed shaft. The inputs for this part of the plant are the wind speed and the

blade pitch angle while the outputs are the high-speed shaft angular rotation and the

mechanical power, Pm. The second part is the electric generator whose input is

constant angular rotation from the turbine plant and whose output is electrical power.

Fig. 3 shows a block diagram of the wind turbine system.

The equation of motion of wind turbine system is given by:

LAT TTdt

dJ

(10)

where JTis the equivalent combined moment of inertia of the rotor, gear reducer and

both the low-speed and high-speed shafts, TL is the wind turbine load torque

representing the input torque to the electrical generator and opposed by its electricaltorque.

For the purpose of dynamic analysis and for designing a linear controller, such as PID

controller, equation (10) is linearized around an initial operating point (uo, o, o).Substituting for TAin (10) using (9), the linearized form of (10) takes the form:

T

L

J

Tu

dt

d

(11)

The parameters , and are calculated at the initial operating conditions (uo, o)

and are given by:

o

q

oqoo

T d

dCCARu

J 2

2

1 (12)

o

q

o

T

d

dCuAR

J 2

2

1 (13)


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o

q

o

T d

dCARu

J 2

2

1 (14)

The magnitude of and respectively show the relative weight of the effect of windspeed and pitch angle on the wind turbine dynamics.

In s-space, (11) takes the form:

T

L

J

Tssu

ss )()()(

1 (15)

Equation (15) represents the linearized form of the wind turbine transfer function.

However, the turbine power output is given by:

Am TP (16)

The linearized form of output power equation (16) takes the form:

AoAom TTP (17)

Based on (11) and (17), the block diagram of wind turbine plant is given in Fig. 4.

Wind Turbine Control

A general block diagram for wind turbine control system is shown in Fig. 5.

The transfer function of a hydraulic actuator that changes the blade pitch angle can be

represented by first-order transfer function:

A

A

c

A

ks

k

s

ssG

)(

)()(

(18)

In this paper two controllers are considered; a PID and a neural network NARMA-L2

controllers [28].

PID controllers regulate the error, or difference between the measured input and the

desired input. This error value along with its derivative and integral with respect to

time provides a signal to the actuator(s), which affects the controlled plant. The PID

controller is a linear, single-input single- output controller limited to three gains. The

transfer function of the PID controller is given by:


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sks

kk

s

ssG D

Ip

cC

)(

)()(

(19)

The central idea of the NARMA-L2 neurocontroller [28] is to transform nonlinear

system dynamics into linear dynamics by canceling the nonlinearities. There aretypically two stages involved when using neural networks for control. The first stage is

system identification in which a neural network model of the plant to be controlled isdeveloped by training a neural network to represent the forward dynamics of the

system. The second stage is control design in which the neural network plant model is

used to design (or train) the controller.

APPLICATIONS

The mathematical model in previous sections is applied to develop the response of

controlled and uncontrolled wind turbine plant. The wind turbine parameters [29] aregiven in Table 1.

UNCONTROLLED RESPONSE OF WIND TURBINE PLANT

With initial operating point is (uo= 7 m/s, o= 10.5 rad/s, o= 9 deg.) the parameters

, , and calculated using equations (12), (13), and (14) and given as 0.2071, -

0.0668, and 0.0298 respectively. With uncontrolled wind-turbine plant, the responseto a unit step in wind speed, a unit step in pitch angle, and a 10% step increase in load

torque are determined and shown in Fig. 6, Fig. 7, and Fig. 8 respectively. These

responses are mainly dependent on the rotational inertia of the wind turbine plant, thescaling factors and and the parameter . The parameter represents the wind

turbine aerodynamic characteristics and it does not affect the wind turbine plant inputs.

CONTROLLED RESPONSE OF WIND TURBINE PLANT

PID and neural network NARMA-L2 controllers are used to compensate the wind

turbine speed deviations by changing the pitch angle .

Based on Routh-analysis of the wind turbine transfer function and trial and error

approach, the gains of PID controller are selected to be (kP= 60, kI= 50, and kD= 20).The plant response to a unit step in wind speed, and a 10% step increase in load torque

are shown in Fig. 9, and Fig. 10 respectively. It is shown that PID controller succeededin keeping wind turbine speed and output power. In order to show the validity of the

PID controller, a variable wind speed is assumed as shown in Fig. 11, the plant

response to this variable wind speed is shown in Fig. 12. It is clear that plant response

suffers from a small amount of control errors.

Neural network NARMA-L2 controller with on-line training is used instead of PID

controller. The plant response to a unit step in wind speed, a 10% step increase in load

torque, and variable wind speed are shown in Fig. 13, Fig. 14 and Fig. 15 respectively.


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Although a small amount of control errors are obtained when using PID controllers,

high accuracy of plant response to follow the objective of zero speed deviation is

obtained with neural network NARMA-L2 controller.

CONCLUSION

In this paper a model for variable-pitch, a constant-speed horizontal-axis wind turbine

is given including aerodynamics. In order to control the wind turbine speed for variousdisturbances in wind speed and load torque two controllers are presented classical PID

controller and neural network NARMA-L2 controller. Although PID controllers are

considered as the industry standard for blade-pitch control, the neural networkNARMA-L2 controller gives better system response than the PID controller. However,

both controllers act well in keeping the wind turbine speed and output power.

REFERENCES

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Table 1: Wind turbine parameters

Rated Power (kW) 20

Radius (m) 5

Drive train inertia (kg.m ) 1270

Gear ratio 11.43

Operation angular speed (rpm) 105

Rated wind speed (m/s) 11.7

Cut-in speed (m/s) 6.5

Furling speed (m/s) 23
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modeling and control of wind turbines including aerodynamics

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