CN111022254B

CN111022254B - Time-lag control method for tracking maximum power point of singular perturbation wind power generation model

Info

Publication number: CN111022254B
Application number: CN201911354431.7A
Authority: CN
Inventors: 张艳; 余振中; 王逸之; 陈丽换; 杨忠
Original assignee: Jinling Institute of Technology
Current assignee: Guodian Power Hunan Langshan Wind Power Development Co ltd; Shenzhen Luchen Information Technology Service Co ltd
Priority date: 2019-12-25
Filing date: 2019-12-25
Publication date: 2021-02-26
Anticipated expiration: 2039-12-25
Also published as: CN111022254A

Abstract

The invention discloses a time-lag control method for tracking maximum power point of a singular perturbation wind power generation model, which considers the situation that the wind speed is lower than the rated wind speed, collects the related data of a wind power generator system and establishes a variable-speed variable-pitch wind power generatorThe nonlinear singular perturbation model is used for linearizing the wind power generation system model at a plurality of operating points aiming at the singular perturbation wind power generation model, then the nonlinear variable parameter model is adopted to approximate the nonlinear model of the wind power generation system, and the LPV technology and the H technology are adopted_∞And time lag control is carried out, so that the aim of tracking the maximum power point of the wind power generation system is fulfilled. The mathematical model created by the method is closer to the original physical system, more accords with the mechanism characteristics of the wind power generation system, improves the modeling precision, reduces the error caused by modeling, and greatly reduces the conservatism and the calculation complexity of the controller.

Description

Time-lag control method for tracking maximum power point of singular perturbation wind power generation model

Technical Field

The invention relates to the technical field of wind power generation, in particular to a time-lag control method for tracking the maximum power point of a singular perturbation wind power generation model, which is suitable for improving the wind energy capture efficiency.

Background

The singular perturbation model is a very common dynamic system model. The model is a main tool for describing the system behavior with multi-time scale dynamics, overcoming the rigid ill-condition problem brought by the multi-time scale and obtaining satisfactory control effect.

Since the wind power generation system contains both a mechanical part (i.e., a fan part) and an electromagnetic part (i.e., a motor part). The rate of change of the electromagnetic part is very rapid compared to the dynamically changing characteristics of the mechanical part, so the system has obvious double-time scale characteristics. The modeling of the wind power generation system ignores the electromagnetic dynamic characteristics of the motor part. Obviously, this inevitably leads to inaccurate modeling and difficulty in improving the control accuracy.

For a wind Power generation system, in order to improve the wind energy capture efficiency in a region lower than a rated wind speed, a variable-speed constant-frequency wind Power generator set generally adopts a Maximum Power Point Tracking (MPPT) control strategy. The MPPT adjusts the rotation speed of the wind wheel to track a certain function related to the wind speed, so that a high wind energy capture efficiency can be obtained. However, Zaiyu Chen et al have demonstrated thatThe article: chen Z, Yin M, Zou Y, et al. Maximum Wind Energy Extraction for Variable Speed Wind Turbines With narrow Dynamic Behavior [ J]IEEE Transactions on Power Systems,2016 (PP (99):1-2.), the wind turbine tracks slow dynamics in wind speed (namely low-frequency fluctuation components in the wind speed), and can further improve the capture efficiency of wind energy and reduce the mechanical load of the system. This conclusion provides a new concept and method for improving the efficiency of wind energy capture. According to this idea, the fast dynamics of the wind speed (i.e. the high frequency fluctuating components in the wind speed) can be used as external disturbances of the system. And H_∞The control method is an effective method for overcoming disturbance and improving the robustness of the system. In the current patent literature, the utilization of H does not exist_∞The control method and the singular perturbation theory are used for realizing the technical method for tracking the maximum power point of the wind power generation system.

For MPPT control problems, many scholars design controllers by linearizing the nonlinear system at some point. However, since the natural wind speed changes in real time, the method for linearizing the system and designing the controller under the condition of fixed wind speed has great conservatism, and the controller has a small application range. In addition, intelligent control algorithms, such as neural network control, genetic control algorithms, fuzzy control algorithms, etc., may be employed. The intelligent control algorithm can better process the nonlinear characteristics of the system, only the calculation amount is large, the requirement on a computer is high, the calculation time consumption is large, the calculation error accumulation is easily caused in the computer, and finally the control effect of the system is not good enough.

Disclosure of Invention

The invention aims to provide a time-lag control method for tracking the maximum power point of a singular perturbation wind power generation model, wherein a mechanical part (a fan part) and an electromagnetic part (a motor part) of a wind power generation system are subjected to unified modeling, so that a mathematical model is closer to an original physical system and better accords with the mechanism characteristics of the wind power generation system, the modeling precision is improved, and errors caused by modeling are reduced; in addition, aiming at the singular perturbation wind power generation model, the LPV technology and the H are adopted_∞Time lag control, the goal of realizing maximum power point tracking of the wind power generation system。

In order to achieve the above purpose, with reference to fig. 1, the present invention provides a time lag control method for tracking a maximum power point of a singular perturbation wind power generation model, where the time lag control method includes:

s1: the method comprises the steps of taking the situation that the wind speed is lower than the rated wind speed into consideration, collecting relevant data of a wind driven generator system, and establishing a nonlinear singular perturbation model for a variable-speed variable-pitch type wind driven generator;

s2: select 5 operating points θ_jJ is 1,2, …,5, so that a set of vertices with the operation point constitutes a convex hull Θ, and Θ is Co { θ {₁,θ₂,θ₃,θ₄,θ₅There is a set of non-negative numbers α for any point θ, θ ∈ Θ, within the convex hull Θ _j0, j ≧ 1,2, …,5, such that:

and is

S3: by at a plurality of operating points theta_jLinearizing the nonlinear singular shooting model to obtain 5 linear time invariant singular shooting models;

s4: combining a given gamma and each operating point theta for 5 linear time invariant singular perturbation models_jH is obtained by solving the matrix inequality through design_∞Robust time lag controller K_j(θ_j) The closed-loop linear time invariant singular perturbation model is robust and stable, gamma is an index requirement on infinite norm of a system transfer function, namely infinite norm | G(s) | Y of the system transfer function is required_∞＜γ；

S5: at t_kAt the moment, θ (t) is measured_k) And calculating a weight coefficient alpha_jSuch that it satisfies:

s6: at t_kAt the moment, the controller of the original system is designed as follows:

s7: calculating a control input u (t) according to the following formula_k)：u(t_k)＝K(θ(t_k) X (t-h), where K (θ (t)_k) X (t-h) is the state variable of the singular perturbation model, t is time, h is time lag, the control input u (t) is calculated_k) The method is applied to the original nonlinear wind power generation system;

s8: let t_k＝t_k+1And repeating the steps S5-S8 to control the wind power generation system in real time.

Compared with the prior art, the technical proposal of the invention has the obvious beneficial effects that,

(1) the double-time scale characteristics of the wind power generation system are fully considered, a singular perturbation method is adopted, the electromagnetic part and the mechanical part are modeled uniformly, and the modeling precision is improved.

(2) The method is characterized in that the wind power generation system model is linearized at a plurality of operating points, and then a Linear Parameter Varying (LPV) model is adopted to approximate to a nonlinear model of the wind power generation system, so that the conservatism of a controller can be greatly reduced, and the method is simple, convenient and effective and has limited calculation complexity; meanwhile, the LPV technology is essentially that flexible switching is realized by a weighted summation method in convex hulls formed by a plurality of operation points and surrounded by the operation points, so that the jitter problem caused by switching control is effectively avoided.

(3) Design H_∞The robust time-lag controller effectively improves the wind energy capture efficiency of the fan and makes full use of wind energy.

It should be understood that all combinations of the foregoing concepts and additional concepts described in greater detail below can be considered as part of the inventive subject matter of this disclosure unless such concepts are mutually inconsistent. In addition, all combinations of claimed subject matter are considered a part of the presently disclosed subject matter.

The foregoing and other aspects, embodiments and features of the present teachings can be more fully understood from the following description taken in conjunction with the accompanying drawings. Additional aspects of the present invention, such as features and/or advantages of exemplary embodiments, will be apparent from the description which follows, or may be learned by practice of specific embodiments in accordance with the teachings of the present invention.

Drawings

The drawings are not intended to be drawn to scale. In the drawings, each identical or nearly identical component that is illustrated in various figures may be represented by a like numeral. For purposes of clarity, not every component may be labeled in every drawing. Embodiments of various aspects of the present invention will now be described, by way of example, with reference to the accompanying drawings, in which:

fig. 1 is a flowchart of a method for MPPT control of a wind power system based on a singular perturbation modeling theory and a robust time lag control method of the present invention.

Fig. 2 is a schematic diagram comparing the tracking effect of the wind wheel rotating speed under the control of the robust time-lag control method and the optimal torque method of the invention.

Fig. 3 is a schematic diagram comparing the tracking effect of the wind wheel rotating speed under the control of the robust time-lag control method and the optimal torque method of the invention.

Detailed Description

In order to better understand the technical content of the present invention, specific embodiments are described below with reference to the accompanying drawings.

Example one

With reference to fig. 1, the invention provides a time lag control method for tracking a maximum power point of a singular perturbation wind power generation model, which specifically includes the following steps:

step 1: considering the situation that the wind speed is lower than the rated wind speed, determining numerical values of system parameters (a reduction ratio of a gearbox, the efficiency of the gearbox, the inertia moment of a fan, the inertia moment of a motor, the electromagnetic torque of a generator, the rigidity coefficient of a high-speed transmission shaft, the damping coefficient of the high-speed transmission shaft, the resistance of a stator, the stator inductance of d-axis and q-axis components, the number of pole pairs and magnetic flux), and establishing a singular perturbation model for the variable-speed variable-pitch type wind driven generator, wherein the singular perturbation model comprises the following steps:

wherein, ω is_r(t) wind wheel speed, i represents gearbox reduction ratio, η represents gearbox efficiency, J_rIs the fan moment of inertia, T_rIs an air dynamic moment, omega_g(t) motor speed, J_gIs the moment of inertia of the motor, T_H(T) is the high-speed shaft torque, T_g(t) is the electromagnetic torque of the generator, K_gIs the rigidity coefficient of high-speed transmission shaft, B_gIs the damping coefficient of high-speed drive shaft, and is a singular perturbation parameter, i ═ 0.01_d(t)、L_d、u_d(t) and i_q(t)、L_q、u_q(t) stator currents, inductances and voltages, respectively d-and q-axis components, R_sIs the resistance of the stator and is,

p is the number of pole pairs, phi_mIs the magnetic flux.

Air dynamic moment T_rIs described as

Where ρ is the air density, V (t) is the wind speed, R is the fan plane radius, the power coefficient C_Q(λ) is approximated by a quadratic polynomial of the tip speed ratio λ (t): c_Q(λ)＝C_Qmax-k_Q(λ(t)-λ_Qmax)²，C_QmaxIs the maximum moment coefficient, λ_QmaxRepresenting tip speed ratio, k, corresponding to the maximum moment coefficient_QAre approximated coefficients.

Tip speed ratio λ (t) defines:

electromagnetic torque T of generator_g(T) is T_g(t)＝pφ_mi_q(t)。

Step 2: properly selecting 5 operating points

So that the set of vertices with the operation point constitutes a convex hull Θ, i.e., Θ ═ Co { θ }₁,θ₂,θ₃,θ₄,θ₅}. Then any one point in the convex hull may be represented by the operating point theta_jIs shown, i.e. any theta e theta exists in a set of nonnegative numbers alpha_jNot less than 0, j is not less than 1,2, …,5, so that

And step 3: at the operating point

Calculating the electromagnetic torque of the corresponding generator

And air dynamic moment

So that the operating point θ can be obtained by the calculation of equation (3)_jCorresponding to

Order to

δV(t)＝V(t)-V^j，

Linearizing the nonlinear singular shooting model to obtain:

where δ v (t) is taken as a perturbation, the coefficient matrix is as follows:

wherein the content of the first and second substances,

then the LPV singular perturbation model can be written:

marking

Then

Wherein

B(θ_j)＝[B₁(θ_j) B₂]。

Known from step 2

And because of B_gq(θ_j)、B_qg(θ_j)、B_gd(θ_j)、B_dg(θ_j)、B_r(θ_j)、K_rv(θ_j) Is theta_jSo for any theta e theta, there is a set of positive numbers alpha_j> 0, j-1, 2, … 5 so that

Therefore, at any operation point theta epsilon theta, a linear variable parameter singular perturbation model can be obtained:

and 4, step 4: for a given gamma and operating point theta_jJ-1, 2, … 5, design H_∞Robust skew controller

Substituted into the system (8) to obtain

Wherein the content of the first and second substances,

to simplify notation, the coefficient matrix A (θ) is conditioned and proved in the matrix inequality_j) Abbreviated as a.

For known ε > 0, h > 0, if a 5 × 5 dimensional matrix P exists_εSo that E_εP_εGreater than 0 true, 2 x 2 dimensional matrix Q,2 x 2 dimensional matrix R₁Greater than 0,2 x 2 dimensional matrix R₂The > 0 and 5 x 5 dimensional matrix H make the matrix inequality (13) true:

wherein

The closed-loop linear time invariant singular perturbation model (12) is robust and stable, and the gain coefficient of the controller is

Wherein

Is composed of

The generalized inverse matrix of (2).

Next, robust stability verification is performed to verify the reasonable effectiveness of the proposed control scheme.

(1) It was first demonstrated that the closed loop system is asymptotically stable with zero disturbance.

Let δ v (t) be 0

Defining the Lyapunov function (for simplification of notation, labeled X)_t＝X(t))：

Wherein the content of the first and second substances,

for Lyapunov function

Along the system (12) the time t is derived

It is known that

For both side integrals, one can derive

So that there are

(21) Can be obtained by substituting into the formula (17)

Because for any α, β ∈ RⁿAnd any symmetric positive definite n x n dimensional matrix H has

-2α^Tβ≤α^TH^-1α+β^THβ

Then the matrix R is positively determined for an arbitrary 2 x 2 dimensional symmetry₁And a 2 x 2-dimensional symmetric positive definite matrix R₂All are provided with

It is known that

Then

Substituting into formula (22) to obtain

Removing the underlined part of the above formula to obtain

Further arranging the underline part out for recording

Then can be collated to obtain

According to Schur's theorem, the matrix inequality (13) can be used to know

In combination with the inequality (25), it is easy to know

It follows that the equilibrium point of the system (12) is asymptotically stable when the disturbance δ v (t) is 0.

(2) Next, it is proved that the system is robust under the condition of the matrix inequality (13) when δ v (t) ≠ 0.

Also using the Lyapunov function as (16)

For a function

Derivation of time t along the system (26)

Then there is a change in the number of,

by using Schur supplement theory, it can be seen from the condition (13)

The above inequality is equivalent to

The above inequality can be further converted into

Substituted into formula (27)

As is also known, the amount of oxygen present,

therefore, the first and second electrodes are formed on the substrate,

based on the demonstration of asymptotic stability, X can be known_t(∞) is 0. Now suppose X_t(0) When the inequality (29) is integrated on both sides, 0 is obtained:

namely, it is

It is apparent from this that

I.e., | | C (sE)_ε-A(θ))^-1B₁(θ)||_∞< gamma. The syndrome is two

By solving the matrix inequality (13), the gain factor of the controller can be obtained as

Wherein

Is composed of

The generalized inverse matrix of (2).

And 5: for the LPV singular perturbation model, at t_kAt the moment, the parameter θ (t) is measured_k)＝[ω_r V ω_g i_di_q]And calculating a weight coefficient alpha_jSuch that it satisfies:

step 6: at t_kAnd (3) calculating the controller gain of the original wind power generation system:

and 7: calculating a control input u (t)_k)＝K(θ_k) X (t-h), using u (t)_k) To the original nonlinear wind power generation system;

and 8: at t_k+1And (5) repeating the steps 5-8 at any time.

Example two

In the embodiment, a CART3 blade wind turbine built by renewable energy laboratories (NREL) of the national department of energy is adopted as a research object. The parameters of the wind turbine are shown in table 1.

TABLE 1 aerogenerator parameters

Name (R)

Symbol

Numerical value

Name (R)

Symbol

Numerical value

Optimum tip speed ratio

λ_opt

5.8

Radius of fan

R

20m

Optimum coefficient of wind energy utilization

C_Pmax

0.467

Density of air

ρ

0.98Kg/m³

Coefficient of gearbox

η

1

Inertia of fan

J_r

3.88Kg·m²

Inertia of motor

J_g

0.22Kg·m²

Number of pole pairs

P

3

Gear ratio

i

43.165

Magnetic flux

φ_m

0.4382wb

Damping coefficient of motor

B_g

0.3Kg·m²/s

Coefficient of stiffness of motor

K_g

75Nm/rad

Stator d-axis inductor

L_d

41.56mH

Stator q-axis inductor

L_q

41.56mH

Stator damping

R_s

3.3Ω

With the parameter values in table 1, a nonlinear singular perturbation model can be established as follows:

then, the control method provided by the invention is used for controlling the wind power generation system, and compared with an optimal torque method, a tracking effect comparison graph of the rotating speed of the wind wheel can be obtained. As can be seen from FIG. 1, the tracking effect of the robust time-lag control method provided by the invention based on the singular perturbation method is more accurate. FIG. 2 is a tracking error contrast diagram, the tracking error of the wind wheel rotating speed obtained by the robust time-lag control method is smaller than the error of the optimal torque method, and the effectiveness and superiority of the method provided by the invention are further verified.

The robust time-lag control method and the optimal torque control are applied to control the wind driven generator, the simulation time is 500 seconds, the average wind energy capture efficiency of the two methods is calculated, and the result is shown in table 2. It is obvious from table 2 that, compared with the optimal torque control method, the robust time lag control method can achieve higher wind energy capture efficiency and has superiority.

TABLE 2 control effect comparison

Method of producing a composite material	Mean windEfficiency of energy capture
		Robust skew control	0.4496
Optimal torque control	0.4455

In this disclosure, aspects of the present invention are described with reference to the accompanying drawings, in which a number of illustrative embodiments are shown. Embodiments of the present disclosure are not necessarily defined to include all aspects of the invention. It should be appreciated that the various concepts and embodiments described above, as well as those described in greater detail below, may be implemented in any of numerous ways, as the disclosed concepts and embodiments are not limited to any one implementation. In addition, some aspects of the present disclosure may be used alone, or in any suitable combination with other aspects of the present disclosure.

Although the present invention has been described with reference to the preferred embodiments, it is not intended to be limited thereto. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the invention. Therefore, the protection scope of the present invention should be determined by the appended claims.

Claims

1. A singular perturbation wind power generation model maximum power point tracking time lag control method is characterized by comprising the following steps:

s2: select 5 operating points θ_jJ is 1,2, …,5, so that a set of vertices with the operation point constitutes a convex hull Θ, and Θ is Co { θ {₁,θ₂,θ₃,θ₄,θ₅There is a set of non-negative numbers α for any point θ, θ ∈ Θ, within the convex hull Θ_j0, j ≧ 1,2, …,5, such that:

and is

s4: combining a given gamma and each operating point theta for 5 linear time invariant singular perturbation models_jH is obtained by solving the matrix inequality through design_∞Robust time lag controller K_j(θ_j) The closed-loop linear time invariant singular perturbation model is robust and stable, and gamma is an index requirement on infinite norm of a system transfer function;

s7: calculating a control input u (t) according to the following formula_k)：u(t_k)＝K(θ(t_k) X (t-h), where K (θ (t)_k) X (t-h) is the state variable of the singular perturbation model, t is time, h is time lag; will calculate the control input u (t)_k) The method is applied to the original nonlinear wind power generation system;

s8: let t_k＝t_k+1Repeating the steps S5-S8 to control the wind power generation system in real time;

in step S1, the nonlinear singular perturbation model is:

p is the number of pole pairs, phi_mIs the magnetic flux; air dynamic moment T_rIs described as

Where ρ is the air density, V (t) is the wind speed, R is the fan plane radius, the power coefficient C_Q(λ) is approximated by a quadratic polynomial of the tip speed ratio λ (t):

C_Q(λ)＝C_Qmax-k_Q(λ(t)-λ_Qmax)²，C_Qmaxis the maximum moment coefficient, λ_QmaxRepresenting tip speed ratio, k, corresponding to the maximum moment coefficient_QIs an approximation coefficient; the tip speed ratio λ (t) is defined as:

electromagnetic torque T of generator_g(T) is T_g(t)＝pφ_mi_q(t)；

In step S2, the 5 operation points θ_jExpressed as:

in step S3, the passing is at a plurality of operating points theta_jThe method for linearizing the nonlinear singular shooting model to obtain 5 linear time invariant singular shooting models comprises the following steps:

s31: at the operating point

Calculating the electromagnetic torque of the corresponding generator

And air dynamic moment

Thereby calculating the operation point theta_jCorresponding to

S32: order to

δV(t)＝V(t)-V^j，

Linearizing the nonlinear singular shooting model to obtain:

in the formula, B_gq(θ_j)、B_qg(θ_j)、B_gd(θ_j)、B_dg(θ_j)、B_r(θ_j)、K_rv(θ_j) Is theta_jThe affine function of (a) is,

s33: obtaining a linear variable parameter singular perturbation model:

s331: marking

z(t)＝[δi_d(t) δi_q(t)]^T，u(t)＝[δu_d(t) δu_q(t)]^TThen, then

Wherein

B(θ_j)＝[B₁(θ_j) B₂]；

S332: let there be a set of positive numbers α for any θ ∈ Θ_j> 0, j ═ 1,2, … 5 such that:

then at any operation point theta epsilon theta, the linear variable parameter singular perturbation model is transformed into:

in step S4, the method combines a given γ and each operation point θ for 5 linear time-invariant singular perturbation models_jH is obtained by solving the matrix inequality through design_∞Robust time lag controller K_j(θ_j) The process for making the closed-loop linear time-invariant singular perturbation model robust and stable comprises the following steps:

s41: for a given gamma and operating point theta_jJ-1, 2, … 5, design H_∞The robust time lag controller is as follows:

substituting the linear variable parameter into the singular perturbation model to obtain

Wherein the content of the first and second substances,

s42: setting matrix inequality conditions and coefficient matrix A (theta) in the proving process_j) Abbreviated as a;

for known ε > 0, h > 0, if a 5 × 5 dimensional matrix P exists_εSo that E_εP_εGreater than 0 true, 2 x 2 dimensional matrix Q,2 x 2 dimensional matrix R₁Greater than 0,2 x 2 dimensional matrix R₂The following matrix inequality is established when the dimension H of the matrix is more than 0 and 5 multiplied by 5, the closed loop linear time invariant singular perturbation model is determined to be robust and stable, and the gain coefficient of the controller is

Wherein

Is composed of

Generalized inverse matrix of (1):

wherein:

2. the singularity perturbation wind power generation model maximum power point tracking time lag control method according to claim 1, wherein the related data of the wind power generator system comprise a gearbox reduction ratio, gearbox efficiency, fan inertia moment, motor inertia moment, electromagnetic torque of a generator, a rigidity coefficient of a high-speed transmission shaft, a damping coefficient of the high-speed transmission shaft, resistance of a stator, stator inductance of d-axis and q-axis components, the number of pole pairs and magnetic flux.