Where: I T = moment of inertia of turbine rotor. T = angular shaft speed. T E = mechanical torque...
1
Where: • I T = moment of inertia of turbine rotor. • T = angular shaft speed. • T E = mechanical torque necessary to turn the generator. • T A = aerodynamic torque, is expressed in terms of the variable torque coefficient C q (,) which is dependent on the tip speed ratio () and blade pitch angle () and wind speed v. • C = 0.5AR; is air density, A is rotor swept area, R is rotor radius. Electrical and Computer Systems Engineering Electrical and Computer Systems Engineering Postgraduate Student Research Forum 2001 Postgraduate Student Research Forum 2001 Variable-Speed Wind Turbine Controller Nolan D. Caliao Supervisor: Dr. A. Zahedi T E n gear T A K High speed shaft Gear box Low speed shaft Aero dynamic I T Figure 2: Physical model of drive train, I = turbine and generator inertias, K = spring stiffness 3 2 1 w T T T v I op q op w T T T C v R C I 1 op q op op q op w op T T T C C v C I 2 2 op q op w op T T C v C I 2 2 The Operating and Linearised Points Figure 3: C q under the normal and stall regions. Regions belonging to below crit and above crit represent the normal and the stall regions respectively. Figure 4: Reference and linearised operating points. Figure 6: Wind speed data at 1 Hz. • high wind, mean = 15.7 m/s; standard deviation = 6.9 m/s • low wind, mean = 9.5 m/s; standard deviation = 4.2 m/s) Figure 5: Block diagram of the simulation model Conclusion Figure 9: Comparison of the rotor speed and blade pitch angle traces for the PID and the PI controllers of the linear model A. Figure 8: Performance Under High Wind of the linear model A for PI controller E A T T T T I Figure 1: Significant parts of a wind turbine The Mathematical Model The Physical Model 1st order model linearised model Rotor speed + Controller (PI/PID) + + Pitch Angle Limit Actuator Wind Turbine Wind Speed Ref. Rotor Speed Reference Pitch (ref) (error) Figure 7: Wind turbine disturbance response (13 m/s – 14 m/s wind speed step change) • Step disturbances are the simplest to model and analyze yet they represent the most severe disturbances a wind turbine is likely to encounter. • operating tip speed ratio ( op ) maximum C p • the objective of the controller is to set the blade pitch ( op ) at a certain operating value so as to attain and maintain maximum C p as possible during operation. Linearised coefficients Table 2:Average tip speed ratio and w ind turbine pow erunderhigh w ind. Ave.tip speed ratio ( ) Std.deviation oftip speed ratio ( ) Ave.pow er(W ) M odel PID PI PID PI PID PI R eference Point 6.87 6.76 2.62 2.83 8.9580 10 4 9.4669 10 4 LinearA 7.07 6.86 2.71 2.83 1.7798 10 6 1.7886 10 6 LinearB 6.79 6.79 2.61 2.82 1.5864 10 5 1.6157 10 5 LinearC 6.80 6.72 2.53 2.79 1.3495 10 5 1.3972 10 5 Table 1:R M S and AD C values foreach m odel High wind M odel Perform anc e check PID PI RMS 0.0325 0.0464 R eference Point ADC 0.6599 0.7000 RMS 0.0308 0.0457 LinearA ADC 0.5042 0.5638 RMS 0.0314 0.0467 LinearB ADC 0.4258 0.4859 RMS 0.0304 0.0451 LinearC ADC 0.3741 0.4452 2 ) )( , ( w q A v C C T The Simulation Model The Performance Outputs The Performance Indicators Since life of most of the wind turbine components is determined by its capacity to withstand high wind speed, a highly turbulent wind speed data was used as an input to the first-order nonlinear wind turbine model. RMS and ADC of linear model C are considered the preffered values however linear model A has better power output. Generally, the PID controller has better performance in terms of the RMS and ADC measures. If the power generation output is however the important criteria in the design, the PI controller should be the preferrence controller. Abstr act Two metrics determines the performance of the controller. • The root mean square (RMS) of the error between the actual rotational speed and the desired fluctuations is minimised • The actuator duty cycle (ADC) was used to measure the actuator motion during the simulation. ADC is the total number of degrees pitched over the period of the simulation. Uncontrolled wind turbine configuration such as stall- regulation captures energy relative to the amount of wind speed. This configuration requires constant turbine speed because the generator that is being directly coupled is also connected to a fixed-frequency utility grid. In extremely strong wind, only a fraction of available energy is captured. Plants designed in such configuration are not economically feasible to run at this occasion. Thus, wind turbines operating at variable speed are better alternatives. A controller design methodology applied to a variable- speed, horizontal axis wind turbine was developed. A simple but rigid wind turbine model was used and linearised to some operating points to meet the desired objectives. From a reference value; by using blade pitch control the deviation of the actual rotor speed is minimised. The performances of PI and PID controllers were compared relative to a step wind disturbance. Results show comparative responses between these two controllers. With the present methodology, despite the erratic wind data, the wind turbine still manages to operate at the stable region 88% most of the time.
-
Upload
marlene-atkins -
Category
Documents
-
view
215 -
download
0
Transcript of Where: I T = moment of inertia of turbine rotor. T = angular shaft speed. T E = mechanical torque...
Where: • IT = moment of inertia of turbine rotor.• T = angular shaft speed.• TE = mechanical torque necessary to turn the generator.• TA = aerodynamic torque, is expressed in terms of the variable torque coefficient Cq(,) which is dependent on the tip speed ratio () and blade pitch angle () and wind speed v.• C = 0.5AR; is air density, A is rotor swept area, R is rotor radius.
Electrical and Computer Systems EngineeringElectrical and Computer Systems EngineeringPostgraduate Student Research Forum 2001Postgraduate Student Research Forum 2001
Variable-Speed Wind Turbine ControllerNolan D. Caliao Supervisor: Dr. A. Zahedi
TE
ngear
TA
K
High speed shaft
Gearbox
Lowspeedshaft
Aerodynamic
IT
Figure 2: Physical model of drive train, I = turbine and generator inertias, K = spring stiffness
321 wTTT vI
op
qopw
T
TT
CvRCI
1
op
qopopqopw
opT
TT
CCvCI
22
op
qopw
op
TT
CvCI
2
2
The Operating and Linearised Points
Figure 3: Cq under the normal and stall regions. Regions belonging to below crit and above crit represent the normal and the stall regions respectively.
Figure 4: Reference and linearised operating points.
Figure 6: Wind speed data at 1 Hz.
• high wind, mean = 15.7 m/s; standard deviation = 6.9 m/s• low wind, mean = 9.5 m/s; standard deviation = 4.2 m/s)
Figure 5: Block diagram of the simulation model
Conclusion
Figure 9: Comparison of the rotor speed and blade pitch angle traces for the PID and the PI controllers of the linear model A.
Figure 8: Performance Under High Wind of the linear model A for PI controller
EATT TTI
Figure 1: Significant parts of a wind turbine
The Mathematical Model
The Physical Model
1st order model
linearised model
Rotor speed
+
Controller(PI/PID)
+ +
Pitch Angle Limit
Actuator
Wind Turbine
WindSpeed
Ref. RotorSpeed
Reference Pitch (ref)
(error)
Figure 7: Wind turbine disturbance response (13 m/s – 14 m/s wind speed step change)
• Step disturbances are the simplest to model and analyze yet they represent the most severe disturbances a wind turbine is likely to encounter.
• operating tip speed ratio (op) maximum Cp
• the objective of the controller is to set the blade pitch (op) at a certain operating value so as to attain and maintain maximum Cp as possible during operation.
Linearised coefficients
Table 2: Average tip speed ratio and wind turbine power under high wind.Ave. tip speed ratio
()Std. deviation of tip speed
ratio ()Ave. power (W)
ModelPID PI PID PI PID PI
ReferencePoint
6.87 6.76 2.62 2.83 8.9580 104 9.4669 104
Linear A 7.07 6.86 2.71 2.83 1.7798 106 1.7886 106
Linear B 6.79 6.79 2.61 2.82 1.5864 105 1.6157 105
Linear C 6.80 6.72 2.53 2.79 1.3495 105 1.3972 105
Table 1: RMS and ADC values for each modelHigh wind
ModelPerformance check PID PI
RMS 0.0325 0.0464ReferencePoint ADC 0.6599 0.7000
RMS 0.0308 0.0457Linear A
ADC 0.5042 0.5638
RMS 0.0314 0.0467Linear B
ADC 0.4258 0.4859
RMS 0.0304 0.0451Linear C
ADC 0.3741 0.4452
2))(,( wqA vCCT
The Simulation Model
The Performance Outputs
The Performance Indicators
Since life of most of the wind turbine components is determined by its capacity to withstand high wind speed, a highly turbulent wind speed data was used as an input to the first-order nonlinear wind turbine model. RMS and ADC of linear model C are considered the preffered values however linear model A has better power output.
Generally, the PID controller has better performance in terms of the RMS and ADC measures. If the power generation output is however the important criteria in the design, the PI controller should be the preferrence controller.
Abstract
Two metrics determines the performance of the controller.
• The root mean square (RMS) of the error between the actual rotational speed and the desired fluctuations is minimised
• The actuator duty cycle (ADC) was used to measure the actuator motion during the simulation. ADC is the total number of degrees pitched over the period of the simulation.
Uncontrolled wind turbine configuration such as stall-regulation captures energy relative to the amount of wind speed. This configuration requires constant turbine speed because the generator that is being directly coupled is also connected to a fixed-frequency utility grid. In extremely strong wind, only a fraction of available energy is captured. Plants designed in such configuration are not economically feasible to run at this occasion. Thus, wind turbines operating at variable speed are better alternatives.
A controller design methodology applied to a variable-speed, horizontal axis wind turbine was developed. A simple but rigid wind turbine model was used and linearised to some operating points to meet the desired objectives. From a reference value; by using blade pitch control the deviation of the actual rotor speed is minimised. The performances of PI and PID controllers were compared relative to a step wind disturbance. Results show comparative responses between these two controllers. With the present methodology, despite the erratic wind data, the wind turbine still manages to operate at the stable region 88% most of the time.
