US 2025/0146470 A1 · METHOD FOR OPTIMIZING WIND FARM ELECTRIC POWER GENERATION USING MULTIVARIABLE SYSTEM IDENTIFICATION

Abstract

A method for optimizing wind farm electric power generation using multivariable system identification, which reduces energy loss caused by the wind turbine wake effect by optimizing and adjusting the yaw angle and axial induction factor of each wind turbine, so as to maximize the total power generation of the wind farm. According to the method, accurate optimization gradient estimates are obtained by using the experimental data and the identification model, and then a gradient-ascend optimization with large initial step size and variable step size iteration is carried out, so that the problems of large model errors and of high computation cost of mechanism modeling are avoided. The method is easy to implement and has a high modeling accuracy and efficiency, and thus is suitable for solving the electric power generation optimization problem of large-scale real-life wind farms.

A method for optimizing wind farm power generation using multivariable system identification, comprising the following steps:

constructing an optimization model by taking yaw angles and axial induction factors of all wind turbines in a wind farm as optimization variables and a total power generation of the wind farm as objective function, wherein the optimization model is a dynamic nonlinear function Pout(t)=f(θ, υ, β, t), where
θ
=
[
γ
a
]
,
is a vector of optimization variables, γ is a yaw angle vector of the wind turbines, a is an axial induction factor vector of the wind turbines, υ is wind speed of the wind farm, β is the wind direction angle of the wind farm, and t is the sampling time;
carrying out linear approximation on the dynamic nonlinear function at current working point θ*:
P
out
(
t
)
-
P
out
*
≈
G
⁡
(
q
-
1
,
θ
*
)
⁢
[
θ
⁡
(
t
)
υ
⁡
(
t
)
β
⁡
(
t
)
]
︸
u
⁡
(
t
)
+
v
⁡
(
t
)
(
1
)
where Pout* is a constant, with a value being the total power generation of the wind farm at the current working point θ*;
Pout(t) is the total power generation of the wind farm near the current working point θ* at time t;
G(q−1,θ*) is a dynamic linear model of the current working point θ*, q−1 is the unit delay operator, and v(t) is an unmeasured stochastic disturbance of the system;
wherein the gradients of Pout(t) for θ(t) at the current working point θ* are the static gains of the dynamic linear model G(q−1,θ*), namely:
∂
P
out
(
t
)
∂
θ
⁡
(
t
)
=
G
⁡
(
q
-
1
,
θ
*
)
T
❘
"\[LeftBracketingBar]"
q
=
1
=
G
⁡
(
1
,
θ
*
)
T
(
2
)
obtaining a local optimum through iterative optimization using a gradient ascent method;
and
applying an excitation signal to the setpoints of the yaw angles and axial induction factors of all wind turbines, collecting experimental data, obtaining a dynamic linear model of the optimization model by using a system identification method, taking the static model gains between the yaw angles and axial induction factors of wind turbines and the total power generation in the dynamic linear model as optimization gradients, performing optimization iteration using a gradient ascent method, and optimally adjusting the yaw angle and axial induction factor of the wind turbines;
wherein obtaining the dynamic linear model and the optimization gradients by using the system identification method further comprises the following substeps:
(i) identification experiment:
simultaneously applying independent random excitation signals to all optimization variables;
(ii) model identification:
collecting the optimization variables where excitation signals are added, measurable disturbance variables and power generation data of the wind farm, and using the following method for the model identification:
parameterizing the dynamic linear model as follows:
P
out
(
t
)
⁢
P
out
*
≈
G
⁡
(
q
-
1
,
θ
*
)
[
θ
⁡
(
t
)
υ
⁡
(
t
)
β
⁡
(
t
)
]
+
v
⁡
(
t
)
=
1
A
⁡
(
q
-
1
)
[
B
1
(
q
-
1
)
,
B
2
(
q
-
1
)
,
…
⁢
B
2
⁢
n
+
2
(
q
-
1
)
]
[
θ
⁡
(
t
)
υ
⁡
(
t
)
β
⁡
(
t
)
]
+
C
⁡
(
q
-
1
)
D
⁡
(
q
-
1
)
⁢
e
⁡
(
t
)
(
3
)
where A(q−1), B1(q−1), B2(q−1), . . . B2n+2(q−1), C(q−1), D(q−1) are polynomials of q−1, with unknown coefficients to be determined, and e(t) is an unknown white noise signal with a mean value of zero;
and
determining the unknown coefficients of each polynomial in equation (3) by minimizing the following loss function:
V
=
1
N
⁢
∑
t
=
1
N
(
D
⁡
(
q
-
1
)
C
⁡
(
q
-
1
)
⁢
{
P
out
(
t
)
-
P
out
*
-
1
A
⁡
(
q
-
1
)
[
B
1
(
q
-
1
)
,
B
2
(
q
-
1
)
,
…
⁢
B
2
⁢
n
+
2
(
q
-
1
)
]
⁢
u
⁡
(
t
)
}
)
2
(
4
)
where N is the number of data samples;
and
(iii) model gain error estimation, comprising:
calculating an upper error bound of a frequency of each dynamic linear model according to an asymptotic identification method, wherein a frequency response of the dynamic linear model at zero frequency is the model gain, and
obtaining an upper error bound of the model gain, and
when all the optimization gradients become smaller than their upper error bounds, stopping the optimization iteration, and controlling each wind turbine to operate using the obtained optimal yaw angles and axial induction factors.

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Method for optimizing wind farm electric power generation using multivariable system identification

Life of this patent

Method for optimizing wind farm electric power generation using multivariable system identification

Life of this patent

Abstract

Claims8