CN109446729B - Model-independent extremely-short-term wind prediction method - Google Patents
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Abstract
The invention discloses a model-independent extremely short-term wind forecastThe method, which actually converts the prediction problem into the trajectory tracking problem, comprises the following steps: 1) Designing a wind prediction control rate; 2) Discretizing a motion equation; 3) Obtaining upsilon through historical data according to wind prediction control rate * And theta * (ii) a 4) Upsilon obtained in the step 3) * And theta * And (5) carrying the formula (6) into the formula (6) to obtain the wind predicted value at the next sampling moment. The wind forecasting method can be used for forecasting the wind without depending on a wind model, and when the wind forecasting is carried out, multi-step historical data are used, so that the forecasting accuracy and reliability are improved. The method can not only carry out simulation verification, but also is simple and easy to implement, is convenient to be applied to practice, and can ensure the convergence of prediction errors.
Description
Technical Field
The invention relates to the technical field of wind power generation, in particular to a model-independent extremely short-term wind forecasting method.
Background
With fans becoming larger and larger, more flexible and more advanced controllers become more and more important to reduce fatigue damage and optimize wind energy capture. The literature indicates that predictive controllers using short-term wind prediction information can optimize wind turbine performance by compensating for measurement information and actuator delays. The existing wind forecasting method mainly comprises the following steps: autoregressive moving average model (ARMA), artificial Neural Network (ANN), support Vector Machine (SVM), and the like. Most of the existing main prediction methods belong to model-dependent methods, and they are only evaluated by simulation, and more importantly, the methods cannot guarantee convergence of prediction errors.
Therefore, there is a need for a wind prediction method that is independent of models, simple and easy to apply to practice, good in reliability and stability, and capable of ensuring convergence of prediction errors.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a model-independent extremely-short-term wind forecasting method, which is easy to be applied to practice, has good reliability and stability, and can ensure the convergence of forecasting errors, thereby providing technical support for the optimization of a fan controller.
In order to achieve the purpose, the technical scheme provided by the invention is as follows: a model-independent very short term wind prediction method that actually transforms the prediction problem into a trajectory tracking problem:
coordinate system with time t as horizontal axis and y axis as vertical axisThe wind information is recorded as a toy coordinate system, changes along an arbitrary curve C in the toy coordinate system, and at a certain moment, the wind information is a point P on the curve C a ＝(t,y a ) If the wind information prediction is a moving point P = (t, y) in the toy coordinate system, the prediction problem is converted into a point P to a point P a The tracking problem of (2);
the equation of motion of point P in the toy coordinate system is:
wherein y is a position variable of the moving point P in the coordinate system, upsilon is a linear velocity of the moving point P, theta is a direction angle of the moving point P, namely an included angle between the linear velocity and a time axis direction, and theta belongs to (-pi/2, pi/2),
is the angular velocity of the moving point P;
point P a The equation of motion of (a) is:
in the formula, y a Is a moving point P in the coordinate system a Is a position variable of a Is a moving point P a Linear velocity of (a), theta a Is a moving point P a Is the angle of the linear velocity with respect to the time axis, and theta a ∈(-π/2,π/2)，
Is the angular velocity of the moving point P;
considering the position control and the direction control of the trajectory tracking together, the tracking error ε is defined as follows:
in which e and s are each an edge P a Linear velocity ofTracking error in the direction of the degree and perpendicular thereto, theta e Is the azimuth angle error, δ y ＝y-y a Is the tracking error in the y-axis direction;
through the design of the trajectory tracking control rates upsilon and omega, the moving point P (t) can stably track the actual trajectory P a (t), namely, the tracking error is consistent and finally bounded or finally converged to 0 after a certain time, so that the wind information is predicted;
the extremely short-term wind forecasting method comprises the following steps:
1) Design wind predictive control rate
Predicted point P (t) tracks actual point P a (t) if v and ω are updated according to the following control rate:
it is possible to realize the predicted point P (t) versus the actual point P a (t) consistent final bounded tracking, i.e. making predictions of wind information, where η 1 And η 2 Are all positive constants;
and (3) proving that: defining a non-negative Lyapunov function
Determining the derivative of V with respect to time>
And the control rates of upsilon and omega are introduced, and finally the following results are obtained:
because V is more than or equal to 0,
Get V bounded according to Lyapunov's stability theory, and then get e and s bounded, θ e ＝θ-θ a E (-pi, pi) is also bounded; due to>
Is bounded and therefore->
And &>
Bounded and combined with>
And &>
Bounded, as derived from the Barbalt theorem, when time t tends to infinity, δ y sin theta and sin theta e Tends to zero, so when time t tends to infinity, e tends to zero, s tends to zero, θ e Tends to zero;
2) Discretization of equation of motion
Will be that in the above formula (1)
Discretizing to obtain:
y((k+1)T)＝y(kT)+Tυ * sinθ * (6)
where k is a positive integer, T is a sampling period, y ((k + 1) T) and y (kT) are values of the wind predicted value at the next sampling time and the current sampling time, respectively, upsilon * And theta * Respectively the desired linear velocity and the direction angle at the next sampling moment;
3) Obtaining upsilon through historical data according to wind prediction control rate * And theta * The specific process comprises the following steps:
according to the formula (4), after discretization, the desired angular velocity ω is expected at the next sampling moment * The control rate of (c) is as follows:
in the formula, delta y (kT) is the tracking error in the y-axis direction at the present time, δ y (kT)＝y(kT)-y a (kT); y ((k-1) T) is a predicted value at the previous time; y is a (kT)、y a ((k-1)T)、y a (k-2) T is a current sampling time value, a previous sampling time value, and a previous sampling time value of the actual wind information, respectively; theta a (kT)、θ a (k-1) T is the actual direction angle at the present time, the actual direction angle at the previous time, and θ a (kT)＝arctan((y a (kT)-y a ((k-1)T))/T)，θ a ((k-1)T)＝arctan((y a ((k-1)T)-y a ((k-2)T))/T)；ω a (kT) is the actual angular velocity at the present moment, ω a (kT)＝(θ a (kT)-θ a ((k-1) T))/T; θ (kT) is a direction angle of a predicted value at the current sampling time, and θ (kT) = arctan ((y (kT) -y ((k-1) T))/T); upsilon is a (kT) is the actual linear velocity at the current sampling instant,
k is a positive integer greater than 2;
due to theta * Is unknown according to
And & ->
By T omega * + θ (kT) to obtain θ * ；
According to the formula (4), after discretization, the expected linear velocity upsilon at the next sampling moment * The control rate of (c) is as follows:
4) Upsilon obtained in the step 3) * And theta * And (5) substituting the formula (6) to obtain the wind predicted value at the next sampling moment.
Compared with the prior art, the invention has the following advantages and beneficial effects:
1. wind prediction can be carried out without depending on a wind model, and when wind prediction is carried out, multi-step historical data are used, so that the prediction accuracy and reliability are improved.
2. The method can not only carry out simulation verification, but also is simple and easy to implement, is convenient to be applied in practice, and can ensure the convergence of prediction errors.
Drawings
FIG. 1 is a graph of the relationship between the actual wind direction profile and the predicted wind direction profile of an example.
FIG. 2 is a schematic illustration of an example stroke prediction error.
Detailed Description
The present invention will be further described with reference to the following specific examples.
The model-independent extremely short-term wind prediction method provided by the embodiment actually converts the prediction problem into the trajectory tracking problem:
a coordinate system with the horizontal axis as time t and the vertical axis as the y axis is taken as a toy coordinate system, wind information changes along an arbitrary curve C in the toy coordinate system, and at a certain moment, the wind information is a point P on the curve C a ＝(t,y a ) If the wind information prediction is a moving point P = (t, y) in the toy coordinate system, the prediction problem is converted into a point P to a point P a The tracking problem of (2);
the equation of motion of point P in the toy coordinate system is:
wherein y is a position variable of the moving point P in the coordinate system, upsilon is a linear velocity of the moving point P, theta is a direction angle of the moving point P, namely an included angle between the linear velocity and a time axis direction, and theta belongs to (-pi/2, pi/2),
is the angular velocity of the moving point P;
point P a The equation of motion of (a) is:
in the formula, y a Is a moving point P in the coordinate system a Is a position variable of a Is a moving point P a Linear velocity of (a), theta a Is a moving point P a I.e. the angle between the linear velocity and the direction of the time axis, and theta a ∈(-π/2,π/2)，
Is the angular velocity of the moving point P;
considering the position control and the direction control of the trajectory tracking together, the tracking error ε is defined as follows:
in which e and s are each an edge P a Of the linear velocity direction and the tracking error in the vertical direction, theta e Is the azimuth angle error, δ y ＝y-y a Is the tracking error in the y-axis direction;
the invention aims to ensure that a moving point P (t) can stably track an actual track P through the design of track tracking control rates upsilon and omega a (t), namely, the tracking errors are consistent after a certain time and are finally bounded or finally converged to 0, and the wind information is predicted.
The extremely short-term wind forecasting method comprises the following steps:
1) Design wind predictive control rate
Predicted point P (t) tracks actual point P a (t) if v and ω are updated according to the following control rate:
it is possible to realize the predicted point P (t) versus the actual point P a Consistent final bounded tracking of (t), i.e. enabling prediction of wind information, where η 1 And η 2 Are all positive constants;
and (3) proving that: defining a non-negative Lyapunov function
Determining the time derivative of V>
And the control rates of upsilon and omega are brought in, and finally the following can be obtained:
because V is more than or equal to 0,
The V bounded value is obtained according to the Lyapunov stability theory, and then e and s are bounded, theta e ＝θ-θ a E (-pi, pi) is also bounded; due to->
Is bounded and therefore->
And &>
Has a bounded area and also has->
And &>
Bounded, as derived from the Barbalt theorem, when time t tends to infinity, δ y sin theta and sin theta e Tends to zero, so when time t tends to infinity, e tends to zero, s tends to zero, θ e Tends to zero;
2) Discretization of equation of motion
Will be given in the above formula (1)
Discretization yields:
y((k+1)T)＝y(kT)+Tυ * sinθ * (6)
where k is a positive integer, T is a sampling period, y ((k + 1) T) and y (kT) are values of the wind predicted value at the next sampling time and the current sampling time, respectively, upsilon * And theta * Respectively the desired linear velocity and the direction angle at the next sampling moment;
3) Obtaining upsilon through historical data according to wind prediction control rate * And theta * The specific process is as follows:
after discretization, the desired angular velocity ω is the next sampling instant, according to equation (4) * The control rate of (c) is as follows:
in the formula, delta y (kT) is the tracking error in the y-axis direction at the present time, δ y (kT)＝y(kT)-y a (kT); y ((k-1) T) is a predicted value at the previous time; y is a (kT)、y a ((k-1)T)、y a (k-2) T is a current sampling time value, a previous sampling time value, and a previous sampling time value of the actual wind information, respectively; theta a (kT)、θ a (k-1) T is the actual direction angle at the present time, the actual direction angle at the previous time, and θ a (kT)＝arctan((y a (kT)-y a ((k-1)T))/T)，θ a ((k-1)T)＝arctan((y a ((k-1)T)-y a ((k-2)T))/T)；ω a (kT) is the actual angular velocity at the present moment, ω a (kT)＝(θ a (kT)-θ a ((k-1) T))/T; θ (kT) is a direction angle of a predicted value at the current sampling time, and θ (kT) = arctan ((y (kT) -y ((k-1) T))/T); v is a cell a (kT) is the actual linear velocity at the current sampling instant,
k is a positive integer greater than 2;
due to theta * Is unknown according to
And & ->
By T omega * + θ (kT) to obtain θ * ；
According to the formula (4), after discretization, the expected linear velocity upsilon at the next sampling moment * The control rate of (c) is as follows:
4) Upsilon obtained in the step 3) * And theta * And (5) carrying the formula (6) into the formula (6) to obtain the wind predicted value at the next sampling moment.
Knowing historical wind direction measurement information y of a certain position a (T)，y a (2T),...,y a ((N-1)T),y a (NT), where N is a positive integer greater than 3, the sampling period is 6 seconds, the method for predicting very short-term wind direction in 6 seconds according to the present embodiment is used, and the sequence of prediction values is y (T), y (2T),.., y ((N-1) T), y (NT), and further verifies the validity and reliability of the method, which is specifically as follows:
the first step is as follows: a sequence of predictor values is initialized.
The second step is that: let k =3 predict the wind direction at the next sampling instant, i.e. calculate y ((k + 1) T), as follows:
1) Using the current time and the wind direction measurement value and the wind direction prediction initialization value before the current time, ω shown by equation (7) * Controlling the rate to obtain the desired angular velocity ω at the next sampling instant * A value of (d);
2) By T omega * + theta (kT) to obtain theta * ；
3) Using the measured value of the wind direction and the initialized value of the wind direction prediction at and before the current time, v is shown by formula (8) * Controlling the rate to obtain the next sampling time upsilon * A value of (d);
4) Using the resultant v * And theta * Using equation (6), the next sampling instant can be obtainedThe predicted value y (k + 1) of the wind direction of (1);
5) And updating the wind direction prediction sequence.
The third step: let k = k +1 and repeat the second step until k = N-1.
In this example, pass test η 1 ＝0.988，η 2 The effect is better when the wind direction curve is =0.851, the actual wind direction curve and the predicted wind direction curve are shown in fig. 1, the correlation coefficient between the actual wind direction curve and the predicted wind direction curve is 0.9096, the wind direction prediction error is shown in fig. 2, and the wind direction prediction is more accurate.
The above-mentioned embodiments are merely preferred embodiments of the present invention, and the scope of the present invention is not limited thereto, so that the changes in the shape and principle of the present invention should be covered within the protection scope of the present invention.
Claims (1)
1. A model-independent method for extremely short-term wind prediction, characterized in that it essentially transforms the prediction problem into a trajectory tracking problem:
the coordinate system with the horizontal axis as time t and the vertical axis as y axis is recorded as a toy coordinate system, wind information changes along any curve C in the toy coordinate system, and at a certain moment, the wind information is a point P on the curve C a ＝(t,y a ) If the wind information prediction is a moving point P = (t, y) in the toy coordinate system, the prediction problem is converted into a point P to a point P a The tracking problem of (2);
the equation of motion of point P in the toy coordinate system is:
wherein y is a position variable of a moving point P in a coordinate system, upsilon is a linear velocity of the moving point P, theta is a direction angle of the moving point P, namely an included angle between the linear velocity and a time axis direction, and theta belongs to (-pi/2, pi/2),
is the angular velocity of the moving point P;
point P a The equation of motion of (a) is:
in the formula, y a Is a moving point P in the coordinate system a Is a position variable of a Is a moving point P a Linear velocity of (a), theta a Is a moving point P a Is the angle of the linear velocity with respect to the time axis, and theta a ∈(-π/2,π/2)，
Is the angular velocity of the moving point P;
considering the position control and the direction control of the trajectory tracking together, the tracking error ε is defined as follows:
in which e and s are each an edge P a Linear velocity direction of (a) and tracking error in the perpendicular direction of (b), theta e Is the azimuth angle error, δ y ＝y-y a Is the tracking error in the y-axis direction;
through the design of the trajectory tracking control rates upsilon and omega, the moving point P (t) can stably track the actual trajectory P a (t), namely, the tracking error is consistent and finally bounded or finally converged to 0 after a certain time, so that the wind information is predicted;
the extremely short-term wind forecasting method comprises the following steps:
1) Design wind predictive control rate
Predicted point P (t) tracks actual point P a (t) if v and ω are updated according to the following control rate:
then prediction can be achievedPoint P (t) to actual point P a (t) consistent final bounded tracking, i.e. making predictions of wind information, where η 1 And η 2 Are all positive constants;
and (3) proving that: defining non-negative Lyapunov functions
Determining the derivative of V with respect to time>
And the control rates of upsilon and omega are introduced, and finally the following results are obtained:
because V is more than or equal to 0,
According to Lyapunov's stability theory, V is bounded, and then e and s are bounded, theta e ＝θ-θ a E (-pi, pi) is also bounded; due to->
Is bounded and therefore->
And &>
Has a bounded area and also has->
And &>
Bounded, as derived from the Barbalt theorem, when time t tends to infinity, δ y sin theta and sin theta e And the flow rate of the water tends to zero,therefore, when the time t tends to infinity, e tends to zero, s tends to zero, and θ e Tends to zero;
2) Discretization of equation of motion
Will be that in the above formula (1)
Discretization yields:
y((k+1)T)＝y(kT)+Tυ * sinθ * (6)
where k is a positive integer, T is a sampling period, y ((k + 1) T) and y (kT) are values of the wind predicted value at the next sampling time and the current sampling time, respectively, upsilon * And theta * Respectively the desired linear velocity and the direction angle at the next sampling moment;
3) Obtaining upsilon through historical data according to wind prediction control rate * And theta * The specific process is as follows:
after discretization, the desired angular velocity ω is the next sampling instant, according to equation (4) * The control rate of (c) is as follows:
in the formula, delta y (kT) is the tracking error in the y-axis direction at the present time, δ y (kT)＝y(kT)-y a (kT); y ((k-1) T) is a predicted value at the previous time; y is a (kT)、y a ((k-1)T)、y a (k-2) T is a current sampling time value, a previous sampling time value, and a previous sampling time value of the actual wind information, respectively; theta a (kT)、θ a (k-1) T is the actual direction angle at the present time, the actual direction angle at the previous time, and θ a (kT)＝arctan((y a (kT)-y a ((k-1)T))/T)，θ a ((k-1)T)＝arctan((y a ((k-1)T)-y a ((k-2)T))/T)；ω a (kT) is the actual angular velocity at the present moment, ω a (kT)＝(θ a (kT)-θ a ((k-1) T))/T; θ (kT) is a direction angle of a predicted value at the current sampling time, and θ (kT) = arctan ((y (kT) -y ((k-1) T))/T); upsilon is a (kT) Is the actual linear velocity at the current sampling instant,
k is a positive integer greater than 2;
due to theta * Is unknown according to
And & ->
By T omega * + theta (kT) to obtain theta * ；
According to the formula (4), after discretization, the expected linear velocity upsilon at the next sampling moment * The control rate of (c) is as follows:
4) V obtained in step 3) * And theta * And (5) substituting the formula (6) to obtain the wind predicted value at the next sampling moment.
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| JP2000241539A (en) * | 1999-02-17 | 2000-09-08 | Mitsubishi Electric Corp | Target-tracking device |
| CN103279810A (en) * | 2013-06-09 | 2013-09-04 | 重庆大学 | Short-term load predication method based on predication error convergence test and track correction |
| CN104102957A (en) * | 2014-08-07 | 2014-10-15 | 重庆大学 | Load predicting method based on trajectory tracking control |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| JP2000241539A (en) * | 1999-02-17 | 2000-09-08 | Mitsubishi Electric Corp | Target-tracking device |
| CN103279810A (en) * | 2013-06-09 | 2013-09-04 | 重庆大学 | Short-term load predication method based on predication error convergence test and track correction |
| CN104102957A (en) * | 2014-08-07 | 2014-10-15 | 重庆大学 | Load predicting method based on trajectory tracking control |
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