Methods and systems to operate a wind turbine system using a non-linear damping model
A wind turbine system is presented. The wind turbine system includes a tower, a plurality of blades, a rotor supported by the tower and rotatably coupled to the plurality of blades, a control unit programmed to predict a net energy of the tower at one or more future points in time, and if the predicted net energy is within a design limit, then continue with baseline operating control models for normal operation of the wind turbine system, if the predicted net energy exceeds the design limit, then use a non-linear tower damping model to generate tower damping commands to control tower damping of the wind turbine system.
1. A wind turbine system, comprising:
a tower having at least one sensor mounted thereon;
a plurality of blades;
a rotor supported by the tower and rotatably coupled to the plurality of blades;
a control unit programmed to:
determine a current deflection of the tower, a current fore-aft velocity of the tower, and a current acceleration of the tower based on information sensed by the at least one sensor;
determine a predicted deflection of the tower as a function of the current deflection of the tower, the current fore-aft velocity of the tower and the current acceleration of the tower;
determine a predicted tower-load-moment indicative parameter of the tower, wherein the predicted tower-load-moment indicative parameter comprises a predicted net energy of the tower, where a net energy of the tower includes a net potential energy of the tower, a net kinetic energy of the tower, or a total of the net potential energy of the tower and the net kinetic energy of the tower; and
compare the predicted tower-load-moment indicative parameter of the tower to a design limit,
wherein, if the predicted tower-load-moment indicative parameter is within the design limit, then a baseline operating control model is used by the control unit for normal operation of the wind turbine system; and
wherein, if the predicted tower-load-moment indicative parameter exceeds the design limit, then a non-linear tower damping model is used by the control unit to determine a non-linear variable damping coefficient to prevent damage to the tower; and
wherein the non-linear damping model is configured to generate a tower damping command in phase with the current fore-aft velocity of the tower; and
wherein the tower damping command comprises a blade pitch angle alteration command.
2. The wind turbine system of claim 1 , wherein the blade pitch angle alteration command is determined by the following equation:
θ
add
=
Ϛ
*
ω
*
X
.
0
*
M
/
(
∂
Fz
Aero
∂
θ
)
where,
θ add is the blade pitch angle alteration command;
ζ is the non-linear variable damping coefficient;
φ is a natural frequency of the tower;
{dot over (X)} 0 is the current fore-aft velocity of the tower;
M is a modal mass of the tower;
Fz Aero is an aerodynamic rotor thrust; and
∂
Fz
Aero
∂
θ
is a sensitivity of the aerodynamic rotor thrust with respect to a pitch angle, θ, of the plurality of blades.
3. The wind turbine system of claim 2 , wherein the blade pitch angle alteration command comprises a collective pitch angle alteration command for all of the plurality of blades.
4. The wind turbine system of claim 2 , wherein the blade pitch angle alteration command comprises an individual pitch angle alteration command for each of the plurality of blades.
5. The wind turbine system of claim 1 , wherein the blade pitch angle alteration command is determined by the following equation:
θ
add
=
θ
rate
T
left
where,
θ add is the blade pitch angle alteration command;
θ rate is a pitch rate to prevent damage to the tower; and
T left is a remaining amount of time before damage occurs to the tower.
6. A wind turbine system, comprising:
a tower having at least one sensor mounted thereon;
a plurality of blades;
a rotor supported by the tower and rotatably coupled to the plurality of blades;
a control unit programmed to:
determine a current fore-aft deflection of the tower, a current fore-aft velocity of the tower, and a current fore-aft acceleration of the tower based on information sensed by the at least one sensor;
determine a predicted deflection of the tower as a function of the current fore-aft deflection of the tower, the current fore-aft velocity of the tower and the current acceleration of the tower;
determine a predicted net energy of the tower, wherein a net energy of the tower comprises a net potential energy of the tower, a net kinetic energy of the tower, or a total of the net potential energy of the tower and the net kinetic energy of the tower; and
compare the predicted net energy of the tower to a design limit,
wherein, if the predicted net energy is within the design limit, then a baseline operating control model is used by the control unit for normal operation of the wind turbine system; and
wherein, if the predicted net energy exceeds the design limit, then a non-linear tower damping model is used by the control unit to determine a non-linear variable damping coefficient to prevent damage to the tower,
wherein the non-linear variable damping coefficient is a function of an energy reduction factor and a remaining amount of time before damage occurs to the tower,
wherein the energy reduction factor is determined using the following equation:
E ratio =R predicted /R max
where,
E ratio is the energy reduction factor;
R predicted is the predicted net energy of the tower; and
R max is the design limit.
7. The wind turbine system of claim 6 , wherein the design limit, R max , comprises a maximum potential energy of the tower at a maximum tower deflection limit of the tower.
8. The wind turbine system of claim 6 , wherein the predicted net energy is determined by the following equation:
R predicted =√{square root over ((ω Y dim ) 2 +X dim 2 )}
where,
R predicted is the predicted net energy of the tower;
ω is a natural frequency of the tower;
Y dim is a first dimensionless parameter; and
X dim is a second dimensionless parameter.
9. The wind turbine system of claim 8 , wherein the first dimensionless parameter, Y dim , is determined by the following equation:
Y
dim
=
ω
y
predicted
-
Fz
aero
/
K
y
max
-
Fz
aero
/
K
where,
y predicted is the predicted tower deflection;
K is a modal stiffness of the tower;
y max is a maximum deflection of the tower in a fore-aft direction; and
Fz aero is aerodynamic rotor thrust, and
wherein the second dimensionless parameter, X dim , is determined by the following equation:
X
dim
=
X
°
0
ω
(
y
max
-
Fz
aero
/
K
)
where
X 0 is the current fore-aft deflection of the tower;
{dot over (X)} 0 is the current fore-aft velocity of the tower; and
ω is the natural frequency of the tower.
10. The wind turbine system of claim 6 , wherein the predicted net energy is determined by the following equation:
Net
Energy
=
0.5
*
(
K
*
(
X
0
-
Fz
aero
K
)
2
)
+
0.5
*
M
*
X
°
0
2
where,
Net Energy is the predicted net energy;
K is a modal stiffness of the tower;
X 0 is the current fore-aft deflection of the tower;
{dot over (X)} 0 is the current fore-aft velocity of the tower;
Fz aero is an aerodynamic rotor thrust; and
M is a modal mass of the tower.
11. The wind turbine system of claim 6 , wherein the remaining amount of time before damage occurs to the tower is determined by the following equation:
T
left
=
θ
predicted
ω
where,
T left is the remaining amount of time before damage occurs to the tower;
θ predicted is an angular representation of the remaining amount of time before damage occurs to the tower; and
ω is a natural frequency of the tower.
12. The wind turbine system of claim 11 , wherein the angular representation of the remaining amount of time before damage occurs to the tower, θ predicted , is determined by the following equation:
θ
predicted
=
tan
-
1
(
ω
X
dim
Y
dim
)
where,
Y dim is a first dimensionless parameter; and
X dim is a second dimensionless parameter.
13. The wind turbine system of claim 12 , wherein the first dimensionless parameter, Y dim , is determined by the following equation:
Y
dim
=
ω
y
predicted
-
Fz
aero
/
K
y
max
-
Fz
aero
/
K
where,
y predicted is a predicted deflection of the tower;
K is a modal stiffness of the tower;
y max is a maximum deflection of the tower;
Fz aero is an aerodynamic thrust of the rotor, and
wherein the second dimensionless parameter, X dim , is determined by the following equation:
X
dim
=
X
°
0
ω
(
y
max
-
Fz
aero
/
K
)
where,
X 0 is the current fore-aft deflection of the tower; and
{dot over (X)} 0 is the current fore-aft velocity of the tower.
14. The wind turbine system of claim 13 , wherein the predicted deflection of the tower is determined by the following equation:
y
predicted
=
X
0
+
(
X
°
0
*
T
)
+
(
1
2
X
°°
0
*
T
2
)
where,
T is a future time (sec); and
is the current fore-aft acceleration of the tower.
15. The wind turbine system of claim 6 , wherein the non-linear damping coefficient, ζ, is determined by the following equation:
Ϛ
(
θ
predicted
,
E
ratio
)
=
max
(
0
,
min
(
1
,
(
Π
/
2
)
3
2
*
ln
(
E
ratio
)
(
θ
predicted
-
Π
/
2
)
3
)
)
where,
θ predicted is an angular representation of the remaining amount of time before damage occurs to the tower; and
E ratio is the energy reduction factor.
16. A method of operating a wind turbine system, the wind turbine system comprising a tower having at least one sensor mounted thereon, a plurality of blades, a rotor supported by the tower and rotatably coupled to the plurality of blades, and a control unit; the method comprising:
determining, in the control unit of the wind turbine system, a current fore-aft deflection of the tower, a current fore-aft velocity of the tower, and a current fore-aft acceleration of the tower based on information sensed by the at least one sensor of the wind turbine system;
determining, in the control unit of the wind turbine system, a predicted deflection of the tower as a function of the current fore-aft deflection of the tower, the current fore-aft velocity of the tower and the current fore-aft acceleration of the tower;
determining, in the control unit of the wind turbine system, a predicted tower-load-moment indicative parameter of the tower, wherein the predicted tower-load-moment indicative parameter comprises a predicted net energy of the tower, where a net energy of the tower includes a net potential energy of the tower, a net kinetic energy of the tower, or a total of the net potential energy of the tower and the net kinetic energy of the tower; and
comparing the predicted tower-load-moment indicative parameter of the tower to a design limit,
wherein, if the predicted tower-load-moment indicative parameter is within the design limit, then a baseline operating control model is used by the control unit for normal operation of the wind turbine system;
wherein, if the predicted tower-load-moment indicative parameter exceeds the design limit, then a non-linear tower damping model is used by the control unit to determine a non-linear variable damping coefficient to prevent damage to the tower;
wherein the non-linear damping model is configured to generate a tower damping command in phase with the current fore-aft velocity of the tower; and
wherein the tower damping command comprises a blade pitch angle alteration command.