CN109450310B - Wind generating set H for suppressing disturbance∞Robust control method - Google Patents

Wind generating set H for suppressing disturbance∞Robust control method Download PDF

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CN109450310B
CN109450310B CN201811462068.6A CN201811462068A CN109450310B CN 109450310 B CN109450310 B CN 109450310B CN 201811462068 A CN201811462068 A CN 201811462068A CN 109450310 B CN109450310 B CN 109450310B
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霍志红
许昌
赵振宙
王碧涛
史俊杰
李�根
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Hohai University HHU
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P9/00—Arrangements for controlling electric generators for the purpose of obtaining a desired output
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P2101/00—Special adaptation of control arrangements for generators
    • H02P2101/15—Special adaptation of control arrangements for generators for wind-driven turbines
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P2103/00—Controlling arrangements characterised by the type of generator
    • H02P2103/10—Controlling arrangements characterised by the type of generator of the asynchronous type

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Abstract

The invention proposes a suppressionDisturbed wind generating set H∞A robust control method, comprising the steps of: s1, obtaining a state space model of the wind generating set with disturbance by combining the uncertainty of system model parameters in the wind generating system and the uncertainty of external disturbance according to the state space model with uncertainty; s2, for the state space model of the wind generating set with disturbance, obtaining a parameter expression of the state feedback controller of the wind generating set based on a feasible solution of a linear matrix inequality of robust control; s3, the state feedback controller obtained from S2 analyzes the robust stability of the state space model of the wind generating set with disturbance. In the modeling, the interference, the measurement error, the parameter estimation error and the modeling error of wind power generation are considered, and a state space model with uncertainty of the wind generating set is established, so that the modeling precision is improved; a robust control theory is introduced to analyze the stability of the wind generating set and improve the anti-interference capability of the system.

Description

Wind generating set H for suppressing disturbance∞Robust control method
Technical Field
The invention belongs to the field of control of wind generating sets, and particularly relates to a robust control method for a wind generating set for suppressing disturbance.
Background
With the high importance of environmental pollution and energy crisis in all countries of the world, energy and environment become urgent problems to be solved for the survival and development of human beings at present. Wind power generation is an important renewable energy source, provides an energy production mode which is environment-friendly, economic and beneficial to social sustainable development, improves the operation efficiency of a unit, and utilizes wind energy to the maximum extent to become a main direction for researching the wind energy.
The robust control is not applied to a wind power generation system, the robust control can directly solve the control problems of modeling errors, uncertain parameters and unknown interference systems, and the algorithm has better intuitiveness and strict mathematical basis. Because the wind energy conversion system has the characteristics of randomness, time-varying property, uncertainty, strong nonlinearity and the like, a mathematical model of the system is difficult to accurately establish, and the system is effectively controlled. How to research a controller with simple design algorithm and strong robustness of an uncertain system in a wind energy conversion system.
Disclosure of Invention
In order to solve the problems, the invention provides a wind generating set robust control method for suppressing disturbance, which improves the dynamic response speed of the wind generating set and suppresses the disturbance, improves the reliability of a system, and improves the dynamic performance of the system.
The technical scheme is as follows: the invention provides a wind generating set H for inhibiting disturbance∞A robust control method, comprising the steps of: s1, obtaining a state space model of the wind generating set with disturbance by combining the uncertainty of system model parameters in the wind generating system and the uncertainty of external disturbance according to the state space model with uncertainty;
s2, for the state space model of the wind generating set with disturbance, obtaining a parameter expression of the state feedback controller of the wind generating set based on a feasible solution of a linear matrix inequality of robust control;
s3, the state feedback controller obtained from S2 analyzes the robust stability of the state space model of the wind generating set with disturbance.
Further, the state space model of the wind turbine generator system with disturbance of S1 is
Figure BDA0001887777490000021
y(t)＝(C+ΔC)x(t)+(D+ΔD)u(t)+Hw(t) (2)
Wherein
Figure BDA0001887777490000023
uT＝[βr],wT＝[v ui],yT＝[ωgm ωr Tm Pe]TWherein x ∈ RNIs the state vector, u ∈ RMControl input vector, w ∈ ROInterference input vector y ∈ RPControlling or measuring an output vector;
beta is the pitch angle, xi is the angular velocity,
Figure BDA0001887777490000022
is the derivative of angular velocity, ωgIs the angular velocity, omega, of the asynchronous generatorgmIs an asynchronous generator measuring angular velocity, betarIs the blade pitch angle reference, uiIs the voltage, TmIs the torque, PeIs the electric power, v is the wind speed, ωrIs the angular velocity of the blade;
a is a system constant matrix, B is an input constant matrix, C is an observation constant matrix, D is a feedback constant matrix, G is an external state uncertainty constant matrix, and H is a control or measurement output external uncertainty constant matrix; Δ A is a system internal uncertainty matrix, Δ B is an input internal uncertainty matrix, Δ C is an observation internal uncertainty matrix, Δ D is a feedback internal uncertainty matrix, and
[ΔA ΔB ΔC ΔD]＝MF[NA NB NC ND]
wherein F ∈ Ri×jIs an uncertain matrix function of a state space model of the wind generating set with disturbance and meets FFTI, where I is the identity matrix, M is the constancy matrix, NAIs a matrix of uncertainty constants, N, within the systemBIs input to an internal uncertainty constant matrix, NCIs to observe the internal uncertainty constant matrix, NDIs a feedback internal uncertainty constant matrix.
Further, for the wind turbine state space model with disturbance described in S2, the feasible solution of the linear matrix inequality based on robust control is that for a given desired gain value constant γ > 0, for all uncertainties of the allowed parameters, systems (3) - (4) are and only exist one positive symmetric matrix X and matrix W, so that the following inequalities hold, and X and W are solved;
Figure BDA0001887777490000031
systems (3) - (4) exist with a gamma-suboptimal H∞A state feedback controller u ═ Kx (t), where K is a coefficient matrix of the state feedback controller, and a parametric expression for the state feedback controller K ═ W (X)-1From this formula, K is solved.
Further, the state feedback controller u ═ kx (t) described in S2 derives the equations (1) and (2) as
Figure BDA0001887777490000032
y(t)＝((C+ΔC)+(D+ΔD)K)x(t)+Hw(t) (4)
By the formulas (3) and (4), for
Figure BDA0001887777490000033
uT＝[βr],wT＝[v ui], yT＝[ωgmωr Tm Pe]TThe parameters in (1) are controlled to keep the pitch angle beta stable.
Has the advantages that: the invention considers that wind power generation is a multivariable, strong coupling and nonlinear complex system, and considers interference, measurement error, parameter estimation error and modeling error in modeling, thereby establishing a state space model of the wind generating set with uncertainty to improve modeling precision; a robust control theory is introduced to analyze the stability of the wind generating set and improve the anti-interference capability of the system.
Drawings
FIG. 1 is a parameter logic structure diagram of a wind turbine generator set with disturbances;
FIG. 2 is a graph of input wind speed for simulated control of a wind turbine generator set with disturbances using the present invention;
FIG. 3 is a graph of pitch angle coordinates when using the present invention for simulated control of a wind turbine generator set with disturbances;
FIG. 4 is a graph of output power when using the present invention to simulate control of a wind turbine generator set with disturbances.
Detailed Description
The invention provides a wind generating set H for inhibiting disturbance∞A robust control method, comprising the steps of: s1, obtaining a state space model of the wind generating set with disturbance by combining the uncertainty of system model parameters in the wind generating system and the uncertainty of external disturbance according to the state space model with uncertainty;
the state space model of the wind generating set with disturbance is
Figure BDA0001887777490000041
y(t)＝(C+ΔC)x(t)+(D+ΔD)u(t)+Hw(t) (2)
Wherein
Figure BDA0001887777490000042
uT＝[βr],wT＝[v ui],yT＝[ωgm ωr Tm Pe]TWherein x ∈ RNIs the state vector, u ∈ RMControl input vector, w ∈ ROInterference input vector y ∈ RPControlling or measuring an output vector;
as shown in fig. 1, β is the pitch angle, ξ is the angular velocity,
Figure BDA0001887777490000043
is the derivative of angular velocity, ωgIs the angular velocity, omega, of the asynchronous generatorgmIs an asynchronous generator measuring angular velocity, betarIs the blade pitch angle reference, uiIs the voltage, TmIs the torque, PeIs the electric power, v is the wind speed, ωrIs the angular velocity of the blade;
a is a system constant matrix, B is an input constant matrix, C is an observation constant matrix, D is a feedback constant matrix, G is an external state uncertainty constant matrix, and H is a control or measurement output external uncertainty constant matrix; Δ A is a system internal uncertainty matrix, Δ B is an input internal uncertainty matrix, Δ C is an observation internal uncertainty matrix, Δ D is a feedback internal uncertainty matrix, and
[ΔA ΔB ΔC ΔD]＝MF[NA NB NC ND]
wherein F ∈ Ri×jIs an uncertain matrix function of a state space model of the wind generating set with disturbance and meets FFTI, where I is the identity matrix, M is the constancy matrix, NAIs a matrix of uncertainty constants, N, within the systemBIs input to an internal uncertainty constant matrix, NCIs to observe the internal uncertainty constant matrix, NDIs a feedback internal uncertainty constant matrix.
S2, for the state space model of the wind generating set with disturbance, obtaining a parameter expression of the state feedback controller of the wind generating set based on a feasible solution of a linear matrix inequality of robust control;
for a wind generating set state space model with disturbances, a feasible solution of the linear matrix inequality based on robust control is that for a given gain expectation value constant γ > 0, for all uncertainties of the allowed parameters, systems (3) - (4) are and only if there is one positive definite symmetric matrix X and matrix W, so that the following inequalities hold, and X and W are solved;
Figure BDA0001887777490000051
systems (3) - (4) exist with a gamma-suboptimal H∞A state feedback controller u ═ Kx (t), where K is a coefficient matrix of the state feedback controller, and a parametric expression for the state feedback controller K ═ W (X)-1From this formula, K is solved.
S3, analyzing the robust stability of the state space model of the wind generating set with disturbance by the state feedback controller obtained in the S2;
the state feedback controller u ═ kx (t) described in S2, and equation (1) or (2) is derived as
Figure BDA0001887777490000052
y(t)＝((C+ΔC)+(D+ΔD)K)x(t)+Hw(t) (4)
By the formulas (3) and (4), for
Figure BDA0001887777490000053
uT＝[βr],wT＝[v ui], yT＝[ωgmωr Tm Pe]TThe parameters in the process are operated and controlled, and the pitch angle beta is kept stable, so that the output power of the unit in the running state is stable, the influence of disturbance on the wind generating set is inhibited, and the robust stability of the system is improved.
1.5MW wind generating set state space model based on laboratory digital simulation
Figure BDA0001887777490000054
Figure BDA0001887777490000055
Figure BDA0001887777490000061
Figure BDA0001887777490000062
γ＝0.3。
Based on linear matrix inequality of a state space model of a wind generating set with disturbance and a parameterized expression of a state feedback controller, MATLAB simulation software is provided
Figure BDA0001887777490000063
W＝[23.3112 2.7163 -11.0380 -11.2457 0.0002]
Thus, K ═ 0.00001.545 e 51.2e 32.4728e 60.0000 ] was obtained.
Substituting the numerical values into formulas (3) and (4) to obtain the wind generating set H∞Simulating the robust control model, such as randomly inputting the wind speed v in fig. 2, and as can be seen from simulating fig. 3 and 4, compared with the conventional PID control, H∞The robust control method reduces the jitter amplitude in the pitch variation process, the change of the pitch angle is more stable, the influence of disturbance on the wind generating set is inhibited, the robustness and the reliability of the system are improved, and the output power of the wind generating set is more stable.
The method is characterized in that the following method is adopted to prove that the linear matrix inequality based on the state space model of the wind generating set with disturbance and the parameterized expression of the state feedback controller:
first, for a system state space model with uncertainty
Figure BDA0001887777490000064
Figure BDA0001887777490000065
Wherein
Figure BDA0001887777490000071
For the time-varying coefficient matrix, there are theorems 1 and 2 as follows:
theorem 1: for equations (5) - (6), γ > 0 is a given constant, and the following expressions are equivalent
(1) The system is progressively stabilized, andee＜γ；
(2) the existence of a positive definite symmetric matrix P > 0
Figure BDA0001887777490000072
Theorem 2: for a given symmetric matrix
Figure BDA0001887777490000073
The following three conditions are equivalent:
(1)S＜0
(2)
Figure BDA0001887777490000074
(3)
Figure BDA0001887777490000075
from theorem 1, if the equations (1) and (2) are gradually stable, the following matrix inequality is satisfied
Figure BDA0001887777490000076
Wherein
Figure BDA0001887777490000077
To obtain
Figure BDA0001887777490000078
From theorem 2, the linear matrix inequality based on the state space model of the wind generating set with disturbance and the parameterized expression of the state feedback controller can be obtained and proved.

Claims (2)

1. Wind generating set H for suppressing disturbance∞The robust control method is characterized by comprising the following steps:
s1, obtaining a state space model of the wind generating set with disturbance by combining the uncertainty of system model parameters in the wind generating system and the uncertainty of external disturbance according to the state space model with uncertainty;
s2, for the state space model of the wind generating set with disturbance, obtaining a parameter expression of the state feedback controller of the wind generating set based on a feasible solution of a linear matrix inequality of robust control;
s3, analyzing the robust stability of the state space model of the wind generating set with disturbance by the state feedback controller obtained in the S2;
s1, the state space model of the wind generating set with disturbance is
Figure FDA0003458145270000011
y(t)＝(C+ΔC)x(t)+(D+ΔD)u(t)+Hw(t) (2)
Wherein
Figure FDA0003458145270000012
uT＝[βr],wT＝[v ui],yT＝[ωgm ωr Tm Pe]T
Wherein x ∈ RNIs the state vector, u ∈ RMControl input vector, w ∈ ROInterference input vector y ∈ RPControlling or measuring an output vector;
beta is the pitch angle, xi is the angular velocity,
Figure FDA0003458145270000013
is the derivative of angular velocity, ωgIs the angular velocity, omega, of the asynchronous generatorgmIs an asynchronous generator measuring angular velocity, betarIs the blade pitch angle reference, uiIs the voltage, TmIs the torque, PeIs the electric power, v is the wind speed, ωrIs the angular velocity of the blade;
a is a system constant matrix, B is an input constant matrix, C is an observation constant matrix, D is a feedback constant matrix, G is an external state uncertainty constant matrix, and H is a control or measurement output external uncertainty constant matrix; Δ A is a system internal uncertainty matrix, Δ B is an input internal uncertainty matrix, Δ C is an observation internal uncertainty matrix, Δ D is a feedback internal uncertainty matrix, and
[ΔA ΔB ΔC ΔD]＝MF[NA NB NC ND]
wherein F ∈ Ri×jIs an uncertain matrix function of a state space model of the wind generating set with disturbance and meets FFTI, where I is the identity matrix, M is the constancy matrix, NAIs a matrix of uncertainty constants, N, within the systemBIs input to an internal uncertainty constant matrix, NCIs to observe the internal uncertainty constant matrix, NDIs a feedback internal uncertainty constant matrix.
2. Disturbance-suppressing wind park H according to claim 1∞The robust control method is characterized in that: for the wind turbine state space model with disturbance described in S2, a feasible solution of the linear matrix inequality based on robust control is that for a given desired gain value constant γ > 0, for all uncertainties of the allowed parameters, systems (3) - (4) if and only if there is one positive definite symmetric matrix X and matrix W, so that the following inequality holds, and X and W are solved;
Figure FDA0003458145270000021
systems (3) - (4) exist with a gamma-suboptimal H∞A state feedback controller u ═ Kx (t), where K is a coefficient matrix of the state feedback controller, and a parametric expression for the state feedback controller K ═ W (X)-1Solving K by the formula;
the systems (3) to (4) are derived from the state feedback controller u ═ kx (t) described in S2 by deriving the equations (1) and (2)
Figure FDA0003458145270000022
y(t)＝((C+ΔC)+(D+ΔD)K)x(t)+Hw(t) (4)
By the formulas (3) and (4), for
Figure FDA0003458145270000023
uT＝[βr],wT＝[v ui],yT＝[ωgm ωrTm Pe]TThe parameters in (1) are controlled to keep the pitch angle beta stable.
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