Simulation of a wind turbine

MODELLING AND SIMULATION OF A WIND TURBINE

Project Report

P.G.S.R.WIJETUNGA;K.G.R.M.Jayathilake

11/17/2014

TABLE OF CONTENT

1.1 WIND TURBINE AERODYNAMICS.................................................................................................................21.2 POWER CURVE AND ROTOR SPEED CURVE...................................................................................................2

2.0 PROBLEM STATEMENT.................................................................................................................... 3

2.1 DESIGN PARAMETERS..................................................................................................................................42.1.1 Cut in wind speed (uci).......................................................................................................................42.1.2 Rotor speed (ωrot ).............................................................................................................................42.1.3 Rated wind speed (ur).........................................................................................................................4

3.0 GEAR BOX DESIGN............................................................................................................................ 5

4.0 CONTROL STRATEGY....................................................................................................................... 6

4.1 TORQUE CONTROLLER.................................................................................................................................64.2 PITCH CONTROLLER.....................................................................................................................................7

5.0 RESULTS.............................................................................................................................................. 8

5.1 RAMP WIND PROFILE....................................................................................................................................85.2 STEP WISE WIND PROFILE...........................................................................................................................105.3 IMPULSE WIND PROFILE.............................................................................................................................12

TABLE OF FIGURES

FIGURE 1: POWER VS. WIND SPEED CURVE............................................................................................................2FIGURE 2: ROTOR SPEED VS WIND SPEED..............................................................................................................3FIGURE 3: SIMULATIONX 2D MODEL.....................................................................................................................6FIGURE 4: SIMULATIONX 3D ANIMATION MODEL..................................................................................................6FIGURE 5: BLOCK DIAGRAM OF THE TORQUE CONTROLLER...................................................................................7FIGURE 6: BLOCK DIAGRAM OF THE PITCH CONTROLLER.......................................................................................8FIGURE 7: WIND SPEED VS TIME............................................................................................................................8FIGURE 8: GENERATOR POWER VS. TIME...............................................................................................................8FIGURE 9: GENERATOR SPEED VS. TIME.................................................................................................................9FIGURE 10: PITCH ANGLE VS. TIME.......................................................................................................................9FIGURE 11: GENERATOR TORQUE VS. TIME...........................................................................................................9FIGURE 12: WIND POWER VS. TIME.....................................................................................................................10FIGURE 13: WIND SPEED VS. TIME.......................................................................................................................10FIGURE 14: GENERATOR POWER VS. TIME...........................................................................................................10FIGURE 15: WIND SPEED VS TIME........................................................................................................................11FIGURE 16: GENERATOR TORQUE VS. TIME.........................................................................................................11FIGURE 17: PITCH ANGLE VS. TIME.....................................................................................................................11FIGURE 18: WIND POWER VS. TIME.....................................................................................................................12FIGURE 19: WIND SPEED VS. TIME......................................................................................................................12FIGURE 20: GENERATOR POWER VS. TIME...........................................................................................................12FIGURE 21: GENERATOR SPEED VS. TIME............................................................................................................13FIGURE 22: GENERATOR TORQUE VS. TIME.........................................................................................................13FIGURE 23: PITCH ANGLE VS. TIME.....................................................................................................................13FIGURE 24: WIND POWER VS. TIME.....................................................................................................................14

1.0 Introduction

Nowadays, the world is looking forward to various renewable energy forms. Among those, wind energy is more popular and the wind turbine farms construction is now a common fact. As the wind turbine technology getting advanced, design of powerful control systems is required to improve wind turbines behavior. There are mainly two types of wind turbines namely fixed speed and variable speed. Those two types can divided into two sub categories as fixed pitch and variable pitch. Here in this project the interest is on variable speed variable pitch wind turbines.

1.1 Wind turbine Aerodynamics

The power extracted by the rotor is,

Pair=0.5 ρπu3 R2 Cp (1)

C p=(0.44−0.012 θ ) sinπλ

(12−0.3 θ )−0.0015 λθ (2)

λ=V t

u (3)

V t=ωR (4)

R- Radius of the rotor

θ- Pitch angle of the blades

λ- tip speed ratio

ω- Rotor speed

Vt- tip speed

u- Wind speed

ρ- Density of air

Cp- power coefficient or wind turbine efficiency

1.2 Power Curve and rotor speed curve

Power curve specifies how much power can be extracted from the incoming wind. Figure 1 contains an ideal wind turbine power curve. Figure 2 contains the rotor speed curve.

Figure 1: Power vs. wind speed curve

Figure 2: Rotor speed vs Wind speed

Region I is the max-Cp region where the pitch angle is set to zero & the tip speed ratio is maintained at constant by varying the rotor speed. Cut in wind speed (uci) the wind speed where wind can’t generate a reasonable torque to rotate the turbine. Below that the turbine is at rest. Here torque is controlled to obtain the rated air power by varying the rotor speed.

Region III is the maximum power region where turbine output power is kept at rated power. Cut out wind speed (uco) is the maximum wind speed the turbine can generate power without any damage to the structure. Beyond that speed rotor is locked. In this region pitch is controlled to keep the turbine at rated power by maintaining a constant torque.

Region II is the transition region between other two; here the maximum allowable tip speed is maintained. Region transits when the obtainable air power reaches rated value at rated wind speed (ur).

2.0 Problem statement

A wind turbine drive train has to be designed with some given parameters and it has to fulfill certain performance requirements according to the problem. Some of the main parameters are been given. The wind turbine has a nominal power of 2 MW and has a blade radius of 35m. The maximum allowable tip speed is 60 ms-1. The generator has a nominal power of 2.1 MW at a nominal speed of 1550 revmin-1.

With the above details and the requirements the turbine drive train should be able to respond according to the following conditions with various performance indices.

Interval A: If the wind speed is so small that the available power is less than 10% of the nominal power then the wind turbine should be at rest.

Interval B: Otherwise the power factor should be kept at its optimum value, i.e., keep λ= 6 and θ= 0. This interval is valid until the optimal tip speed ratio cannot be fulfilled without violating the maximum allowable tip speed.

Interval C: Otherwise, maintain maximum allowable tip speed. This interval is valid until the obtainable air power reaches the nominal value. Interval D: Otherwise, maintain maximum allowable tip speed and nominal air power, i.e., constant generator torque. This interval is valid until the maximum acceptable wind speed is reached, u max =25 ms-1.

Interval E: Finally, with the wind speed larger than its maximum acceptable value the wind turbine should be at rest.

In order to obtain the required results a wind turbine drive train has been modeled using |SimulationX software and the required results are obtained using that model.

2.1 Design parametersIn order to achieve the given task, certain wind speed values, control systems and |simulation results has to be obtained. Below, in the following section, some important wind speeds related to the three regions of figure 2, are calculated.

2.1.1 Cut in wind speed (uci)

Below this speed, the wind power extracted is less than 10% of the nominal value.

Here pitch angle (θ) is 0 (zero) and tip speed ratio (λ) should be kept at 6.

Pair is 0.2 MW at this wind speed.

Rotor radius R = 35 m and Air density ρ=1.2 kgm−3 at 20℃.

By substituting the values in equation (2),

C p=0.44

Then by equation (1),

2 X 105=0.5∗1.2∗π∗uci3∗352∗0.44

uci=5.811m s−1

2.1.2 Rotor speed (ωrot)

Maximum allowable tip speed is 6 0m s−1 , pitch angle (θ) is 0 (zero) and tip speed ratio (λ) should be kept at 6.

According to the equation (3)

un=606

=10 ms−1

Then by equation (4) ωrot=6 u35

Maximum rotor speed is at maximum tip speed and it is equal to 1.714 rads-1

2.1.3 Rated wind speed (ur)

At this speed the maximum allowable air power is extracted and maximum allowable tip speed is maintained. The pitch angle remains in zero at this speed.

From equation (3) λ=60u

Substituting the value in equation (2)

C p=0.44 sin5πur

Then by equation (1),

2 X 106=0.5∗1.2∗π∗ur3∗352∗0.44 sin

5 πu

ur=¿12.79 ms−1¿

Cut off wind speed

uco = 25ms-1.

3.0 Gear box design

A gear is consisting with one planetary gear stage and two regular stages. The gear ratio was identified to satisfy the following requirement. When the tip speed is at its maximum value, the generator should operate close to its nominal speed. The main shaft of the rotor is connected to the planet carrier of the planetary gear stage and the sun shaft connected to the regular gear stage and output from the second regular stage is connected to the generator rotor shaft.

Maximum rotor speed ωrot , max = 1.714 rads–1

Generator nominal speed ωg , nom=1550*2π/60 rads-1

Overall gear ratio = ωg , nom/ωrot ,max

= 94.699

Hence the following gear ratios have been selected.

Overall gear ratio as 96

Planetary gear ratio as 6

Each of other stages having a gear ratio of 4.

The annular gear (or the ring gear) is held stationary and the sun gear is driven by the power supplied to the planet carrier.

Gear ratio of the planetary stage = Teeth on the driven gear / Teeth on driving gear

6 = Tsun / Tplanetcarrier

6 = Tsun / (Tring+Tsun)

Tring / Tsun = 5

So number of teeth on the ring gear, sun gear and planet gear is selected as 150, 30 and 60 respectively.

For both the regular gear stages, teeth of the driven gears and drive gears are selected as 18 and 72 respectively to make gear ratio of 4 for each stage.

Figure 3: SimulationX 2D model

Figure 4: SimulationX 3D animation model

4.0 Control Strategy

When power production is below the rated power of the machine, the turbine operates at variable rotor speeds to capture the maximum amount of energy available in the wind. Generator torque provides the control input to vary the rotor speed, and the blade pitch angle is held constant in this period. In above-rated power conditions, the primary objective is to maintain a constant power output. This is generally achieved by varying the blade pitch angle while holding the generator torque constant. So here two types of controllers have been used to achieve maximum power output as much as possible.

4.1 Torque controller

Figure 4 shows the designed torque controller which uses a pid controller. Feedback controls the speed of the generator while Set point (ωref ) for the PID block is set by calculating the generator speed according to the wind speed in different regions as below.

If the wind speed is less than uci ωref=0

If else wind speed is less than un then ωref = 6*u*gear ratio/35

If else wind speed is less than uco wind speed then ωref = 155π/3(rated value)

Else ωref=0

Torque controller transfer function (TTF) =

1

( 116 π

)2

S2+( 110 π ) S+1

PID block transfer function = G(1+ 1T i S

+Td S)

Where G,T i and T d are gain integral time and derivative time respectively. Limiter function make sure torque is within -1.8 T g ,nomand 1.8T g ,nom where

T g , nom={Pg ,nom

ωg ,nom

Pg ,nom

ωg

ωg ≤ ωg ,nom

ωg>ωg ,nom

Figure 5: Block diagram of the torque controller

4.2 Pitch controller

For the pitch controller we used a feed forward controller with a PID feedback controller. We have calculated the pitch angle for the maximum power output corresponding to the wind speed and it is summed with the output of the feedback controller and fed to the pitch control device.

Torque controller is the feedback input while reference point is set according to the following conditions.

If the wind speed is less than ur reference torque is equal to generator torque

If it is less than cut off wind speed it is equal to Pg , nom

ωref

Pitch controller transfer function (TTF) =

1

( 12 π

)2

S2+( 1π )S+1

PID block transfer function = G(1+ 1T i S

+Td S)

Where G,T i and T d are gain integral time and derivative time respectively. Limiter function make sure pitch is within 00 300.

Figure 6: Block diagram of the pitch controller

5.0 Results

Following results were obtained for different wind profiles

5.1 Ramp wind profile

Figure 7: Wind speed vs Time

Figure 8: Generator power vs. Time

Figure 9: generator speed vs. Time

Figure 10: Pitch angle vs. Time

Figure 11: Generator torque vs. Time

Figure 12: Wind power vs. Time

5.2 Step wise wind profile

Figure 13: Wind speed vs. Time

Figure 14: Generator power vs. Time

Figure 15: Wind speed vs Time

Figure 16: Generator torque vs. Time

Figure 17: Pitch angle vs. Time

Figure 18: Wind Power vs. Time

5.3 Impulse wind profile

Figure 19: Wind Speed vs. Time

Figure 20: Generator Power vs. Time

Figure 21: Generator Speed vs. Time

Figure 22: Generator Torque vs. Time

Figure 23: Pitch Angle vs. Time

Figure 24: Wind Power vs. Time