Linear optimal output regulation control method for variable speed wind turbine in low wind speed region

Abstract

The application belongs to the field of control and energy, and particularly discloses a linear optimal output regulation control algorithm for a variable-speed wind turbine in a low wind speed area, which comprises the following steps: linearizing a nonlinear system of a transmission shaft model and a tower model of a wind turbine in a low wind speed area at an equilibrium operating point; constructing an external dynamic system capable of generating a disturbance wind speed signal and a linear wind turbine system controlled output tracking signal by using wind speed measurement data of a continuous wave laser radar; defining a controlled output tracking error, and designing an output regulation control rate containing feedforward and feedback control for the linear wind turbine system based on asymptotic convergence of the tracking error to zero; and obtaining a linear optimal output regulation control rate on the basis of the linear output regulation control rate by using coordinate transformation and minimizing a performance index function containing fatigue load.

Description

Technical Field

[0001] This invention belongs to the field of control and energy, and specifically relates to a linear optimal output regulation control algorithm for variable speed wind turbines in low wind speed areas. Background Technology

[0002] In recent years, the gradual depletion of fossil fuels (coal, oil, and natural gas) and the environmental problems caused by their overconsumption have become apparent. To alleviate the energy crisis and environmental pollution caused by fossil fuels, wind energy, with its characteristics of large quantity, wide distribution, renewability, and pollution-free operation, has attracted widespread attention from academic and engineering scholars.

[0003] To meet the ever-increasing demand for wind energy, the trend in wind turbine manufacturing is to increase their size and rated power. However, this, in turn, leads to increased structural fatigue loads and maintenance costs, and shortens the service life of the mechanical equipment. Due to the inherent flexibility of large wind turbines, components such as towers, drive shafts, and rotor blades are particularly susceptible to fatigue damage. Therefore, when operating under non-uniform turbulent conditions, their structural components will suffer more severe fatigue damage. To reduce the levelized cost of wind energy, from a control engineering perspective, the controller design objective should be dual: to maximize wind energy utilization to increase output power while minimizing maintenance costs by reducing fatigue loads on the turbine. Based on this, the applicant proposes a linear optimal output regulation control algorithm for variable-speed wind turbines in low wind speed areas. Summary of the Invention

[0004] This invention overcomes the shortcomings of existing technologies and addresses the technical problem of providing a linear optimal output regulation control algorithm for variable-speed wind turbines in low-wind-speed areas. For the controller design purpose, the nonlinear models of the wind turbine's drive shaft and tower are first linearized at the equilibrium operating point. Then, an external dynamic system is proposed that can generate disturbance wind speed signals and track the controlled output of the linear wind turbine system. Simultaneously, wind speed measurement data from a continuous-wave lidar is fitted using an autoregressive model, and the dynamics of the external system are constructed using this wind speed measurement data. Next, the system's controlled output tracking error is defined, and an output regulation control law incorporating feedforward and feedback control is designed for the linear wind turbine system, causing the tracking error to converge asymptotically to zero. The optimal output regulation controller is generated by minimizing a performance index function that includes fatigue load indicators. This invention reduces the fatigue load on the wind turbine's tower and drive shaft while sacrificing only a small portion of power generation.

[0005] The objective of this invention is achieved through the following technical solution:

[0006] A linear optimal output regulation control algorithm for variable-speed wind turbines in low-wind-speed areas, comprising the following steps:

[0007] (1) Linearize the nonlinear systems of the drive shaft model and tower model of wind turbine in low wind speed area at the equilibrium operating point;

[0008] (2) An external dynamic system that can generate disturbance wind speed signals and controlled output tracking signals of linear wind turbine systems can be constructed using wind speed measurement data from continuous wave lidar.

[0009] (3) Define the controlled output tracking error. Based on the asymptotic convergence of the tracking error to zero, design an output regulation control law that includes feedforward and feedback control for a linear wind turbine system.

[0010] (4) By minimizing the performance index function containing fatigue load, and using coordinate transformation, the linear optimal output regulation control rate is obtained based on the linear output regulation control rate.

[0011] Furthermore, the steps specifically include:

[0012] The nonlinear system expressions for the drive shaft model and tower model of a wind turbine in low wind speed areas are as follows:

[0013]

[0014]

[0015]

[0016]

[0017]

[0018] Where ω r and ω g These are the rotor speed and generator speed, δ is the drive shaft torsion, and N is the torque. g It refers to the gearbox ratio, T. a and T g It refers to pneumatic torque and generator torque, J r and J g It refers to the rotor inertia and the generator inertia, D. s and K s These are the damping coefficient and elastic coefficient of the low-speed shaft, ξ and F. t It is the displacement of the tower and the thrust it experiences, M t D t and K t These are the tower's mass, damping coefficient, and elastic modulus, τ. T and T g,ref These are the time constant and the required generator torque;

[0019] Define a nonlinear system model containing six system states. The control input is u = T g,ref d = v is an uncontrollable input disturbance. For a given average wind speed v0, the equilibrium operating point (x * ,u * ,d * The following conditions must be met:

[0020]

[0021]

[0022] in It is a compact form of nonlinear wind turbine system, λ * This represents the optimal tip speed ratio, where R is the rotor radius;

[0023] After obtaining the Jacobian system matrix at the equilibrium point, the linearized wind turbine model can be expressed as:

[0024]

[0025]

[0026]

[0027] in and and These are the measured output and controlled output of the linear fan system, represented by matrices A, B, H, and C. y and C z These are the system's state matrix, control input matrix, external disturbance matrix, measurement output matrix, and controlled output matrix, respectively.

[0028] Furthermore, in step (2), the external dynamic system is defined as having the following form:

[0029]

[0030]

[0031]

[0032] Where w and E is the state vector of the external dynamic system and the controlled output reference signal, E is the state matrix of the external dynamic system, and E1 and E2 represent the output matrix of the disturbance signal and the output matrix of the reference signal of the external dynamic system, respectively.

[0033] Considering zero-order hold and sampling period T, the external dynamic system is discretized; then, an autoregressive model is used to fit the wind speed signal measured by the continuous-wave lidar. The external dynamic system then has the following form:

[0034]

[0035]

[0036] in It is the cumulative average wind speed measured by a continuous wave lidar over a period of time. Let a represent the wind speed measured by the continuous wave lidar at sampling time k. k ,k∈1,2,...,N are the model coefficients, and N is the order of the external dynamic system;

[0037] A larger value for N will make the external dynamic system model more accurate, thereby increasing power generation, but it will also increase the fatigue load on the wind turbine. Therefore, based on experience, the order N = 3 is chosen, and the dynamics of the external dynamic system are as follows:

[0038] w k+1 =E d w k

[0039] in Optimal model coefficients 1≤k≤3 is obtained by recursive least squares method;

[0040] The output matrices E1 and E2 of the external dynamic system are:

[0041] E1 = [1 0 0]

[0042]

[0043] Furthermore, in step (3), considering the zero-order hold and the sampling period T, the linear fan system is discretized and combined with the external dynamic system dynamics to obtain the following form:

[0044]

[0045] w k+1 =E d w k

[0046]

[0047]

[0048] in w k =[w(t)]t＝kT , A d =e AT , and D = HE1;

[0049] Define the controlled output tracking error as but

[0050]

[0051] Where F = -E², when the linear fan system satisfies the following regulation equation...

[0052] XE d =A d X+B d U+D d

[0053] 0 = C z X+F

[0054] The controlled output tracking error asymptotically converges to 0, where (X,U) is the solution to the regulation equation, and a linear output regulation control law of the following form can be obtained:

[0055]

[0056] Where K is an arbitrary feedback gain matrix that makes the system stable, and L is a feedforward gain matrix of the following form:

[0057] L = U + KX.

[0058] Furthermore, in step (4), the following coordinate transformation is considered:

[0059]

[0060]

[0061] The linear fan system can then be rewritten in the following form:

[0062]

[0063] The optimal feedback controller can be designed as follows:

[0064]

[0065] Where K * Let the optimal feedback gain be expressed as the sum of its parts, and the optimal feedback gain is obtained by solving the following optimization problem:

[0066]

[0067] Where Q = QT ≥0, R=R T >0 represents the weight matrices of the system state and control input, respectively. It is observable;

[0068] The optimal output regulation control rate of the linear fan system is:

[0069]

[0070] Where the feedforward gain L * We obtain it through the following formula:

[0071] L * =U+K * X.

[0072] The beneficial effects of this invention compared to the prior art are:

[0073] This invention first employs an output regulation control algorithm to enable the controlled output (rotor speed) of the wind turbine's linear system to asymptotically track its optimal value in low-wind-speed regions, thereby maximizing power generation. Simultaneously, it asymptotically suppresses external wind speed disturbances within the linear system. Then, through coordinate transformation, based on the output regulation control law, an optimal output regulation controller is designed by minimizing a performance index function that includes fatigue load parameters. This theoretically explains why the designed controller can reduce fatigue loads. Furthermore, this invention uses an external dynamic system to generate the controlled output reference signal and wind speed disturbance signal, utilizing wind speed measurements from a continuous-wave lidar to construct the dynamics of the external dynamic system. This invention reduces fatigue loads on the tower and drive shaft while sacrificing only a small portion of power generation. Attached Figure Description

[0074] Figure 1 This is a flowchart of the present invention;

[0075] Figure 2 This is a block diagram of the optimal output regulation and control method in this invention;

[0076] Figure 3 This is a model diagram of the drive shaft of the wind turbine in this invention;

[0077] Figure 4 This is a comparison chart of turbulent wind speed and wind speed measured by continuous wave lidar in this invention;

[0078] Figure 5 This is a comparison diagram of the drive shaft torsion of LOORC and Baseline in this invention;

[0079] Figure 6 This is a comparison diagram of the low-speed shaft torque between LOORC and Baseline in this invention;

[0080] Figure 7 This is a comparison chart of the tower displacement change rates between LOORC and Baseline in this invention;

[0081] Figure 8 This is a comparison chart of the power generation of LOORC and Baseline in this invention. Detailed Implementation

[0082] To more clearly illustrate the embodiments of the present invention, specific implementation methods will be described below with reference to the accompanying drawings. The following examples are only used to more clearly illustrate the technical solutions of the present invention and should not be construed as limiting the scope of protection of the present invention.

[0083] Please see Figure 1 This invention provides a linear optimal output regulation control algorithm for a variable-speed wind turbine in low-wind-speed areas. The wind turbine type selected is a three-bladed horizontal-axis variable-speed wind turbine with a rated power of 5MW. The block diagram of the optimal output regulation control method proposed in this invention is shown below. Figure 2 As shown, the specific implementation of this method includes the following steps:

[0084] (1) Linearization of the nonlinear systems of the drive shaft model and tower model of wind turbines in low wind speed areas at the equilibrium operating point is performed, specifically including:

[0085] First, some parameters of a three-bladed horizontal axis variable speed wind turbine with a rated power of 5MW are given, as shown in Table 1:

[0086] Table 1 Parameter Table of 5MW Horizontal Axis Wind Turbine

[0087] <![CDATA[J r ]]> <![CDATA[5.9×10 7 kgm 2 ]]> <![CDATA[J g ]]> <![CDATA[500kgm 2 ]]> <![CDATA[D s ]]> <![CDATA[8.3×10 7 kgm 2 / rad / s]]> <![CDATA[K s ]]> <![CDATA[8.7×10 8 Nm / rad]]> <![CDATA[M t ]]> <![CDATA[4.2×10 5 kg]]> <![CDATA[D t ]]> <![CDATA[2×10 3 kgm 2 / rad / s]]> <![CDATA[K t ]]> <![CDATA[1.7×10 6 Nm / rad]]> <![CDATA[λ * ]]> 7.55 <![CDATA[N g ]]> 97 R 63m

[0088] The nonlinear system expressions for the drive shaft model and tower model of a wind turbine in low wind speed areas are as follows:

[0089]

[0090]

[0091]

[0092]

[0093]

[0094] Where ω r and ω g These are the rotor speed and generator speed, δ is the drive shaft torsion, and N is the torque. g It refers to the gearbox ratio, T. a and Tg It refers to pneumatic torque and generator torque, J r and J g It refers to the rotor inertia and the generator inertia, D. s and K s These are the damping coefficient and elastic coefficient of the low-speed shaft, ξ and F. t It is the displacement of the tower and the thrust it experiences, M t D t and K t These are the tower's mass, damping coefficient, and elastic modulus, τ. T and T g,ref These are the time constant and the required generator torque. In this invention, τ T =0.1s. The drive shaft model of the wind turbine in this invention is as follows: Figure 3 As shown;

[0095] Define a nonlinear system model containing six system states. The control input is u = T g,ref d = v is an uncontrollable input disturbance. For a given average wind speed v0, the equilibrium operating point (x * ,u * ,d * The following conditions must be met:

[0096]

[0097]

[0098] in It is a compact form of nonlinear wind turbine system, λ * This represents the optimal tip speed ratio, where R is the rotor radius;

[0099] After obtaining the Jacobian system matrix at the equilibrium point, the linearized wind turbine model can be expressed as:

[0100]

[0101]

[0102]

[0103] in and and These are the measured output and controlled output of the linear fan system, respectively. Furthermore, the system's state matrix, control input matrix, and external disturbance matrix are as follows:

[0104]

[0105] in and

[0106] The measurement output and controlled output matrices of the linear fan system are as follows:

[0107]

[0108] C z =[1 0 0 0 0 0].

[0109] (2) An external dynamic system was constructed using wind speed measurement data from a continuous wave lidar system. This system can generate disturbed wind speed signals and controlled output tracking signals for linear wind turbine systems. Specifically, it includes:

[0110] An external dynamic system can be defined in the following form:

[0111]

[0112]

[0113]

[0114] Where w and E is the state vector of the external dynamic system and the controlled output reference signal, E is the state matrix of the external dynamic system, and E1 and E2 represent the output matrices of the external dynamic system's disturbance signal and reference signal.

[0115] To construct the external dynamic system dynamics based on wind speed measurement data from a continuous-wave lidar, the external dynamic system is discretized, considering zero-order hold and a sampling period T. Then, an autoregressive model is used to fit the wind speed signal measured by the continuous-wave lidar. The external dynamic system then has the following form:

[0116]

[0117]

[0118] in It is the cumulative average wind speed measured by a continuous wave lidar over a period of time. Let a represent the wind speed measured by the continuous wave lidar at sampling time k. k ,k∈1,2,...,N are the model coefficients, and N is the order of the external dynamic system;

[0119] A larger value for N will make the external dynamic system model more accurate, thereby increasing power generation, but it will also increase the fatigue load on the wind turbine. Therefore, based on experience, the order N = 3 is chosen, and the dynamics of the external dynamic system are as follows:

[0120]

[0121] in Optimal model coefficients The following can be obtained using the recursive least squares method:

[0122]

[0123]

[0124]

[0125] Furthermore, since the input disturbance is the deviation between the wind speed and its mean, and the target of the controlled output of the system is the optimal rotor speed, the output matrices E1 and E2 of the external dynamic system are:

[0126] E1 = [1 0 0]

[0127] E2 = [0.1198 0 0]

[0128] This invention considers turbulent wind speed with an average wind speed of 8 m / s. A comparison of the turbulent wind speed and the wind speed measured by continuous wave lidar is shown in the figure below. Figure 4 As shown.

[0129] (3) Define the controlled output tracking error. Based on the asymptotic convergence of the tracking error to zero, design an output regulation control law that includes feedforward and feedback control for a linear wind turbine system. Specifically, this includes:

[0130] Considering zero-order hold and sampling period T = 0.006, the linear fan system is discretized and combined with the external dynamic system dynamics, resulting in the following form:

[0131]

[0132] w k+1 =E d w k

[0133]

[0134]

[0135] in w k =[w(t)] t＝kT , A d =e AT , and D = HE1;

[0136] Define the controlled output tracking error as but

[0137]

[0138] Where F = -E² = [-0.1198 0 0]. When the linear fan system satisfies the regulation equation of the following form,

[0139] XE d =A d X+B d U+D d

[0140] 0 = C z X+F

[0141] The controlled output tracking error asymptotically converges to 0, where (X,U) is the solution to the regulation equation, resulting in a linear output regulation controller of the following form:

[0142]

[0143] Where K is an arbitrary feedback gain matrix that makes the system stable, and L is a feedforward gain matrix of the following form:

[0144] L = U + KX.

[0145] (4) By minimizing the performance index function containing fatigue load, and using coordinate transformation, the linear optimal output regulation control rate is obtained based on the linear output regulation control rate. Specifically, this includes:

[0146] Consider the following coordinate transformation:

[0147]

[0148]

[0149] The linear fan system can then be rewritten in the following form:

[0150]

[0151] Therefore, the optimal feedback controller can be designed as follows:

[0152]

[0153] Where K * Let the optimal feedback gain be expressed as the sum of its parts, and the optimal feedback gain is obtained by solving the following optimization problem:

[0154]

[0155] Where Q = Q T ≥0, R=R T>0 represents the weight matrices of the system state and control input, respectively. It is observable; in this invention, the values ​​of Q and R are respectively:

[0156]

[0157] R = 0.00001

[0158] Therefore, the optimal control law for the linear fan system is:

[0159]

[0160] Where the feedforward gain L * It can be obtained through the following formula:

[0161] L * =U+K * X

[0162] Since the first 50 seconds are necessary for the initialization of the Linear Optimal Output Regulator (LOORC), this period was excluded from the simulation comparison. The drive shaft torsion comparison graph between the Linear Optimal Output Regulator (LOORC) and the Baseline Generator Torque Controller (Baseline) is shown below. Figure 5 As shown in the figure. Low-speed shaft torque can be used to quantitatively describe the fatigue load on the drive shaft. The comparison chart of low-speed shaft torque between LOORC and Baseline is shown in the figure. Figure 6 As shown. (Through) Figure 5 and Figure 6 It can be concluded that the LOORC algorithm in this invention can reduce the fatigue load on the wind turbine drive shaft. A comparison of the tower displacement change rate between LOORC and the baseline is shown in the figure below. Figure 7 As shown. (Through) Figure 7 It can be concluded that the LOORC algorithm in this invention can reduce the fatigue load on the wind turbine drive shaft. A comparison of power generation between LOORC and the baseline is shown in the figure below. Figure 8 As shown in Table 2, the average power generation is compared with that in Table 2. As can be seen from Table 2, the LOORC algorithm in this invention reduces fatigue load while sacrificing only a small portion of power generation.

[0163] Table 2 Comparison of Average Power Generation

[0164] LOORC 1.67MW Baseline 1.73MW LOORC compared to Baseline -3.47％

[0165] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A linear optimal output regulation control method for variable speed wind turbine in low wind speed region, characterized in that, The method includes the following steps: (1) Linearization of the nonlinear systems of the drive shaft model and tower model of wind turbines in low wind speed areas at the equilibrium operating point, specifically including: The nonlinear system expressions for the drive shaft model and tower model of a wind turbine in low wind speed areas are as follows: in and These are the rotor speed and the generator speed. It's the drive shaft twisting. It refers to the gearbox ratio. and It refers to pneumatic torque and generator torque. and These are the rotor inertia and the generator inertia. and These are the damping coefficient and elastic modulus of the low-speed shaft. and It refers to the displacement of the tower and the thrust it experiences. , and These are the tower's mass, damping coefficient, and elastic modulus. and These are the time constant and the required generator torque; The nonlinear system model is defined to contain six system states , the control input is , is an uncontrollable input disturbance, for a given average wind speed , the equilibrium operating point satisfies the following conditions: wherein is a compact form of the nonlinear fan system, denotes the optimal tip speed ratio, is the rotor radius; After obtaining the Jacobian system matrix at the equilibrium point, the linearized wind turbine model is expressed as: wherein , and , and are the measured outputs and controlled outputs of the linear fan system, respectively, and matrices A, B, H, C y and C z are the state matrix, control input matrix, external disturbance matrix, measured output matrix and controlled output matrix of the system, respectively. (2) Construct an external dynamic system that can generate disturbance wind speed signals and controlled output tracking signals of linear wind turbine systems using wind speed measurement data from continuous wave lidar; (3) Define the controlled output tracking error. Based on the asymptotic convergence of the tracking error to zero, design the output regulation control law including feedforward and feedback control for the linear wind turbine system. (4) By minimizing the performance index function containing fatigue load, and using coordinate transformation, the linear optimal output regulation control rate is obtained based on the linear output regulation control rate.

2. The linear optimal output regulation control method of a variable-speed wind generator in low wind speed region according to claim 1, characterized in that, In step (2), the external dynamic system is defined in the following form: in and These are the state vector of the external dynamic system and the controlled output reference signal. It is the state matrix of the external dynamic system. and This represents the output matrix of the external dynamic system disturbance signal and the output matrix of the reference signal; Consider zeroth order hold and sampling period Discretize the external dynamic system; then, use an autoregressive model to fit the wind speed signal measured by a continuous-wave lidar The external dynamic system then has the form: wherein is the cumulative average of the wind speed measured by the continuous wave lidar over a period of time, denotes the sampling time is the wind speed measured by the continuous wave lidar, is a model coefficient, is the order of the external dynamic system; order of selection The dynamics of the external dynamic system are then: wherein , optimal model coefficients are obtained by recursive least squares Output matrix of an external dynamic system and is: 。 3. The linear optimal output regulation control method of a variable-speed wind generator in low wind speed region according to claim 1, characterized in that, In step (3), zero-order hold and sampling period are considered The linear blower system is discretized and combined with the external dynamic system dynamics to obtain the following form: wherein , , , , , , , and ; Define the controlled output tracking error as then wherein When the linear blower system satisfies a regulation equation having the form The controlled output tracking error asymptotically converges to 0, where is the solution of the regulation equation, resulting in a linear output regulation control rate of the form wherein is an arbitrary feedback gain matrix that stabilizes the system, is a feedforward gain matrix of the form 。 4. The linear optimal output regulation control method of a variable-speed wind generator in low wind speed region according to claim 3, characterized in that, In step (4), the following coordinate transformation is considered: The linear fan system is then rewritten in the following form: The optimal feedback controller is designed as follows: wherein is denoted the optimal feedback gain and is obtained by solving the following optimization problem: wherein , are weight matrices for system states and control inputs, respectively, and is observable; The optimal output regulation control rate of the linear fan system is: where the feedforward gain is obtained by the equation: 。

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