CN107294372A - The high ferro low-frequency oscillation suppression method of Model Predictive Control based on disturbance estimation - Google Patents

Abstract

The invention discloses a kind of high ferro low-frequency oscillation suppression method of the Model Predictive Control based on disturbance estimation, comprise the following steps：A, structured‑qThe EMUs net-side rectifier dynamic characteristic equation of meter and parameter error amount under rotating coordinate system；B, definition disturbance quantity, are obtained according to dynamic characteristic equationd‑qMeter and the EMUs net-side rectifier current forecasting model of disturbance quantity under rotating coordinate system；C, using electric current, disturbance quantity as state variable, obtain disturbing the state-space model of estimator, build disturbance estimator；D, the current forecasting model for substituting into disturbance quantity estimate in step B obtain current forecasting value, and obtained current forecasting value is substituted into cost function obtains next sampling period control voltage；E, control voltage obtained by coordinate transformα‑βCoordinate system component, by sinusoidal pulse width modulation output control pulse, completes high ferro low-frequency oscillation and suppresses；The present invention improves the antijamming capability and robust performance of control system, and voltage variety floats minimum within the cycle, insensitive to Parameters variation.

Description

High-speed rail low-frequency oscillation suppression method based on model predictive control of disturbance estimation

Technical Field

The invention relates to a control method of a grid-side rectifier of a motor train unit, in particular to a high-speed rail low-frequency oscillation suppression method based on model predictive control of disturbance estimation.

Background

With the rapid development of high-speed railways, novel 'AC-DC-AC' electric locomotives are widely applied to electrified railway systems due to the advantages of high power factor, high power, high traction and the like; the traditional control method of the 'AC-DC-AC' locomotive is mainly divided into two types, namely indirect current control and direct current control; the indirect current control is represented by 'phase amplitude control', and the direct current control comprises hysteresis current control, prediction current control, transient current control and the like; the transient direct current control adopts more control strategies in the electric locomotive and the high-speed motor train unit at present; the control effect of the traditional linear control method is difficult to be improved, so that a nonlinear control method, such as predictive control, passive control and the like, is necessary to be introduced into the control of the converter; the predictive control is a control algorithm which is proposed along with a complex actual production process, and is widely applied due to good robustness and good control performance of a complex system; the conventional model prediction control includes prediction current control, prediction direct power control and the like, only the prediction current obtained by a prediction model is considered to track a set value to improve the control effect, but the problem that the parameters of a model parameter actually controlled object cannot be completely matched is not considered.

Disclosure of Invention

The invention provides a high-speed and low-frequency oscillation suppression method for model predictive control based on disturbance estimation, which can improve the robustness of the model predictive control.

The technical scheme adopted by the invention is as follows: a high-speed rail low-frequency oscillation suppression method based on model predictive control of disturbance estimation comprises the following steps:

A. constructing a dynamic characteristic equation of the motor train unit network side rectifier considering the parameter error amount under a d-q rotating coordinate system;

B. b, defining a disturbance amount, and obtaining a current prediction value of a motor train unit grid-side rectifier current prediction model considering the disturbance amount under a d-q rotating coordinate system according to the dynamic characteristic equation obtained in the step A;

C. taking the current and the disturbance quantity as state variables to obtain a state space model of a disturbance estimator, and constructing the disturbance estimator to obtain a disturbance quantity estimated value;

D. substituting the disturbance quantity estimation value into the current prediction model in the step B to obtain a current prediction value, and substituting the obtained current prediction value into a cost function to obtain the control voltage of the next sampling period;

E. and D, carrying out coordinate transformation on the control voltage of the next sampling period obtained in the step D to obtain an alpha-beta coordinate system component, and outputting a control pulse through sine pulse width modulation to finish the suppression of the low-frequency oscillation of the high-speed rail.

Further, the dynamic characteristic equation of the grid-side rectifier of the motor train unit, which takes the parameter error amount into account in the step a, is as follows:

defining a resistance rating parameter R_NORated parameter L of inductor_NOActual resistance parameter and rated parameter error amount delta R_NAnd the error amount Delta R between the actual parameter and the rated parameter of the inductor_NObtaining:

in the formula: r_NActual parameter of resistance, L_NActual parameters of the inductor are obtained;

according to an alternating-current side Hall voltage law equation, obtaining a dynamic characteristic equation of the motor train unit grid side rectifier considering parameter error under a d-q rotating coordinate system:

in the formula: u. of_Nd、u_NqFor an input voltage u on the AC side_NA dq direct current component on a two-phase rotating coordinate system; i.e. i_Nd、i_NqRespectively, an input current i on the AC side_NA dq direct current component on a two-phase rotating coordinate system; u. of_abd、u_abqAre respectively the rectifier input voltage u_abA dq direct current component on a two-phase rotating coordinate system; ω is the angular velocity of rotation and t is a time variable.

Further, the motor train unit grid-side rectifier current prediction model for calculating the disturbance amount in the step B is as follows:

defining the disturbance quantity, obtaining:

in the formula: f. of_d、f_qThe disturbance component on the two-phase rotating coordinate system;

then, the dynamic characteristic equation of the grid-side rectifier of the motor train unit can be changed into:

for the discretization of the above formula, a current prediction model considering the disturbance quantity can be obtained:

in the formula: k represents a discrete quantity corresponding to the time t and is the current sampling moment; k +1 is the next sampling moment; t is_sIs a sampling period; u. of_Nd(k)、u_Nq(k) Are respectively an AC side input voltage u_NDiscretizing dq direct current components at the current moment; i.e. i_Nd(k)、i_Nq(k) Respectively, an input current i on the AC side_NDiscretizing dq direct current components at the current moment; u. of_abd(k)、u_abq(k) Are respectively the rectifier input voltage u_abDiscretizing dq direct current components at the current moment; f. of_d(k)、f_q(k) Respectively, the disturbance dq direct current components at the current sampling moment.

Further, the method also comprises the following steps:

defining a control output voltage value u at a current sampling instant_abd(k)、u_abq(k) Comprises the following steps:

in the formula: u. of_abd(k-1)、u_abq(k-1) are respectively the rectifier input voltage u_abDiscretizing a dq direct current component at the previous sampling moment; Δ u_abd(k) And Δ u_abq(k) Respectively representing the variation of the dq component of the control voltage from the moment k-1 to the moment k;

substituting the current prediction model can obtain:

in the formula i_Nd0(k+1)、i_Nq0(k +1) are respectively neglected control voltage variation amount Deltau_abd(k) And Δ u_abq(k) The current prediction value dq component at time k-1.

Further, the construction process of the estimation perturber is as follows:

disturbance amount f_d(k) And f_q(k) Equal in one sampling period, namely:

in the formula: f. of_d(k) And f_q(k) Respectively representing disturbance components on the two-phase rotating coordinate system at the current sampling moment; f. of_d(k +1) and f_q(k +1) are disturbance components on the two-phase rotating coordinate system at the next sampling moment respectively;

the state quantity and the input quantity are defined as follows:

in the formula:are respectively i_Nd0(k+1)、i_Nq0An estimated value of (k + 1); i.e. i_Nd0(k)、i_Nq0(k) To ignore the current prediction value dq component at the time k-1 of the control voltage variation,are respectively i_Nd0(k)、i_Nq0(k) An estimated value of (d);are respectively f_d(k)、f_q(k) Is determined by the estimated value of (c),are respectively f_d(k+1)、f_qAn estimated value of (k + 1); x (k +1) is a state component at the moment k +1, x (k) is a state component at the moment k, and u (k) is an input component at the moment k; u. of_Nd(k)、u_Nq(k) Are respectively an AC side input voltage u_NDiscretizing dq direct current components at the current moment;

obtaining a state space model of the disturbance estimator:

x(k+1)＝Ax(k)+Bu(k)

in the formula:

in the formula: r_NOTo define the rated resistance parameter, L_NOIs a rated parameter of the inductor, omega is a rotation angular velocity, T_sIs a sampling period;

constructing a disturbance estimator based on the state space model:

in the formula:are respectively i_Nd0(k+1)、i_Nq0An estimated value of (k + 1);are respectively f_d(k +1) and f_qAn estimated value of (k + 1);are respectively i_Nd0(k)、i_Nq0(k) An estimated value of (d); are respectively f_d(k)、f_q(k) In the following equation:

in the formula I₁、l₂Feedback coefficients of a state observer gain matrix L; from the above formula, one can obtain:

x(k+1)＝(A-LC)x(k)+Bu(k)

and completing the construction of the disturbance estimator.

Further, the cost function in step D is:

in the formula: g_rIn order to be a function of the cost,setting a value for a q-axis component of the alternating-current side current of the rectifier;setting value i for d-axis component of AC side current of rectifier_Nd(k+1)、i_Nq(k +1) are input currents i on the AC side_NDiscretizing a dq direct current component in the next sampling period;

in the formula:is a DC side voltage reference value, U_dAs a measured value of the DC side voltage, K_pIs the ratio of PI controllersExample coefficient, T_iIs the PI controller integration coefficient.

Substituting the disturbance quantity estimated value into the current prediction model to obtain

Substituting the obtained current predicted value into a cost function to obtain the control voltage of the next sampling period;

further, the method for calculating the control voltage in the next sampling period is as follows:

partial derivatives of the voltage variation are obtained from the cost function to obtain the voltage variation delta u which can make the cost function obtain minimum value_abd(k) And Δ u_abq(k)：

In the formula: i.e. i_Nd0(k+1)、i_Nq0(k +1) is the neglect of the control voltage variation Δ u_abd(k) And Δ u_abq(k) The current prediction value dq component at the k-1 moment; l is_NOThe inductance rated parameter; t is_sIs a sampling period;

the next sampling period control voltage is:

in the formula: u. of_abd(k+1)、u_abq(k +1) is the rectifier input voltage u_abAn input value at a next sampling period; u. of_abd(k)、u_abq(k) Is a rectifier input voltage u_abDiscretizing dq direct current components at the current sampling moment; Δ u_abd(k)、Δu_abq(k) The voltage variation from the time k-1 to the time k-1 is controlled.

The invention has the beneficial effects that:

(1) according to the invention, the disturbance quantity is considered, the anti-interference capability and the robustness of the control system are improved, and the problem of electric quantity oscillation of the traction network-motor train unit can be damped;

(2) according to the invention, the control voltage variable which enables the cost function to obtain a minimum value is obtained by solving the partial derivative of the cost function, the predicted current value can track the current setting value by stepping, and the voltage variable is enabled to float minimum in a period;

(3) the invention needs less parameters to be set, the control system is insensitive to parameter change, and the control has better robustness and dynamic performance in an effective range.

Drawings

Fig. 1 is a control structure diagram of the present invention.

FIG. 2 is an equivalent circuit diagram of a rectifier according to the present invention.

FIG. 3 is a partial block diagram of a predictive model of the invention.

FIG. 4 is a diagram of a portion of the disturbance estimation of the present invention.

FIG. 5 is a diagram of a simulation model according to the present invention.

FIG. 6 is a graph showing the waveforms of the road side voltage, the AC side current and the AC side voltage according to the present invention.

Fig. 7 is a waveform diagram of the net side voltage and the net side current in the embodiment of the invention.

Detailed Description

The invention is further described with reference to the following figures and specific embodiments.

A high-speed rail low-frequency oscillation suppression method based on model predictive control of disturbance estimation comprises the following steps:

A. constructing a dynamic characteristic equation of the motor train unit network side rectifier considering the parameter error amount under a d-q rotating coordinate system;

assuming that a four-quadrant pulse rectifier is adopted by a motor train unit grid-side rectifier, the following model aims at a single-phase two-level topological structure; the pantograph is used for taking current from a contact network, the current is reduced by a vehicle-mounted transformer and then is used as the input of a rectifier, and the rectifier converts the input single-phase alternating-current voltage into stable direct-current voltage;

defining a resistance rated parameter R by considering the uncertainty of the circuit parameter at the AC side_NORated parameter L of inductor_NOActual resistance parameter and rated parameter error amount delta R_NAnd the error amount Delta R between the actual parameter and the rated parameter of the inductor_NObtaining:

in the formula: r_NActual parameter of resistance, L_NActual parameters of the inductor are obtained;

according to an alternating-current side Hall voltage law equation, obtaining a dynamic characteristic equation of the motor train unit grid side rectifier considering parameter error under a d-q rotating coordinate system:

in the formula: u. of_Nd、u_NqFor an input voltage u on the AC side_NA dq direct current component on a two-phase rotating coordinate system; i.e. i_Nd、i_NqRespectively, an input current i on the AC side_NA dq direct current component on a two-phase rotating coordinate system; u. of_abd、u_abqAre respectively the rectifier input voltage u_abA dq direct current component on a two-phase rotating coordinate system; ω is the angular velocity of rotation and t is a time variable.

B. B, defining a disturbance amount, and obtaining a current prediction value of a motor train unit grid-side rectifier current prediction model considering the disturbance amount under a d-q rotating coordinate system according to the dynamic characteristic equation obtained in the step A;

defining the disturbance quantity, obtaining:

in the formula: f. of_d、f_qThe disturbance component on the two-phase rotating coordinate system;

then, the dynamic characteristic equation of the grid-side rectifier of the motor train unit can be changed into:

for the discretization of the above formula, a current prediction model considering the disturbance quantity can be obtained:

in the formula: k represents a discrete quantity corresponding to the time t and is the current sampling moment; k +1 is the next sampling moment; t is_sIs a sampling period; u. of_Nd(k)、u_Nq(k) Are respectively an AC side input voltage u_NDiscretizing dq direct current components at the current moment; i.e. i_Nd(k)、i_Nq(k) Respectively, an input current i on the AC side_NDiscretizing dq direct current components at the current moment; u. of_abd(k)、u_abq(k) Are respectively the rectifier input voltage u_abDiscretizing dq direct current components at the current moment; f. of_d(k)、f_q(k) Respectively, the disturbance dq direct current components at the current sampling moment.

Defining a control output voltage value u at a current sampling instant_abd(k)、u_abq(k) Comprises the following steps:

in the formula: u. of_abd(k-1)、u_abq(k-1) are respectively the rectifier input voltage u_abDiscretizing a dq direct current component at the previous sampling moment; Δ u_abd(k) And Δ u_abq(k) Respectively representing the variation of the dq component of the control voltage from the moment k-1 to the moment k;

substituting the current prediction model can obtain:

in the formula i_Nd0(k+1)、i_Nq0(k +1) are respectively neglected control voltage variation amount Deltau_abd(k) And Δ u_abq(k) The current prediction value dq component at time k-1.

C. Taking the current and the disturbance quantity as state variables to obtain a state space model of a disturbance estimator, and constructing the disturbance estimator to obtain a disturbance quantity estimated value;

the construction process of the estimation perturber is as follows:

assuming disturbance quantity f_d(k) And f_q(k) Equal in one sampling period, namely:

in the formula: f. of_d(k) And f_q(k) Respectively representing disturbance components on the two-phase rotating coordinate system at the current sampling moment; f. of_d(k +1) and f_q(k +1) is the disturbance component on the two-phase rotating coordinate system at the next sampling momentAn amount;

the state quantity and the input quantity are defined as follows:

in the formula:are respectively i_Nd0(k+1)、i_Nq0An estimated value of (k + 1); i.e. i_Nd0(k)、i_Nq0(k) To ignore the current prediction value dq component at the time k-1 of the control voltage variation,are respectively i_Nd0(k)、i_Nq0(k) An estimated value of (d);are respectively f_d(k)、f_q(k) Is determined by the estimated value of (c),are respectively f_d(k+1)、f_qAn estimated value of (k + 1); x (k +1) is a state component at the moment k +1, x (k) is a state component at the moment k, and u (k) is an input component at the moment k; u. of_Nd(k)、u_Nq(k) Are respectively an AC side input voltage u_NThe dq dc component is discretized at the current time.

Obtaining a state space model of the disturbance estimator:

x(k+1)＝Ax(k)+Bu(k)

in the formula:

in the formula: r_NOTo define the rated resistance parameter, L_NOIs a rated parameter of the inductor, and omega is a rotation angular velocityDegree, T_sIs a sampling period;

constructing a disturbance estimator based on the state space model:

in the formula:are respectively i_Nd0(k+1)、i_Nq0An estimated value of (k + 1);are respectively f_d(k +1) and f_qAn estimated value of (k + 1);are respectively i_Nd0(k)、i_Nq0(k) An estimated value of (d); are respectively f_d(k)、f_q(k) An estimated value of (d);

in the formula: l₁、l₂Feedback coefficients of a state observer gain matrix L;

from the above formula, one can obtain:

x(k+1)＝(A-LC)x(k)+Bu(k)

in the closed-loop discrete system, the dynamic characteristic of the state reconstruction error depends on a coefficient matrix A-LC; and determining a feedback coefficient of a gain matrix of the disturbance estimator for stabilizing the discrete system through a pole distribution diagram according to the principle that all closed-loop poles are required to be located in a unit circle with the origin as the origin to ensure the stability of the disturbance interference device, and completing the construction of the disturbance estimator.

D. Substituting the disturbance quantity estimation value into the current prediction model in the step B to obtain a current prediction value, substituting the obtained current prediction value into a cost function, solving the partial derivative about the voltage variation of the cost function to obtain the voltage variation which can enable the cost function to obtain a minimum value, and adding the voltage variation to the current time voltage to obtain the control voltage of the next sampling period;

the cost function is:

in the formula: g_rIn order to be a function of the cost,setting a value for a q-axis component of the alternating-current side current of the rectifier;setting value i for d-axis component of AC side current of rectifier_Nd(k+1)、i_Nq(k +1) are input currents i on the AC side_NDiscretizing a dq direct current component in the next sampling period;

in the formula:the reference value of the direct-current side voltage is different according to different motor train unit models, and for the CRH3 motor train unit,for the CRH 5-type vehicle,U_dis a direct current side voltage measurement value; k_pProportional coefficient of PI controller; t is_iIs the PI controller integration coefficient.

Further, the method for calculating the control voltage in the next sampling period is as follows:

partial derivatives of the voltage variation are obtained from the cost function to obtain the voltage variation delta u which can make the cost function obtain minimum value_abd(k) And Δ u_abq(k)：

In the formula: i.e. i_Nd0(k+1)、i_Nq0(k +1) is the neglect of the control voltage variation Δ u_abd(k) And Δ u_abq(k) The current prediction value dq component at the k-1 moment; l is_NOThe inductance rated parameter; t is_sIs a sampling period;

the next sampling period control voltage is:

in the formula: u. of_abd(k+1)、u_abq(k +1) is the rectifier input voltage u_abAn input value at a next sampling period; u. of_abd(k)、u_abq(k) Is a rectifier input voltage u_abDiscretizing dq direct current components at the current sampling moment; Δ u_abd(k)、Δu_abq(k) The voltage variation from the time k-1 to the time k-1 is controlled.

E. And D, converting the control voltage obtained in the step D through coordinates to obtain an alpha-beta coordinate system component, and outputting a control pulse through sine pulse width modulation to finish the suppression of the low-frequency oscillation of the high-speed rail.

Examples

Taking a CRH3 motor train unit as an example, the method comprises the following steps:

A. constructing a dynamic characteristic equation of the motor train unit network side rectifier considering the parameter error amount under a d-q rotating coordinate system;

as shown in fig. 2, a motor train unit grid-side rectifier dynamic characteristic equation considering parameter error amount under a d-q rotating coordinate system can be obtained by writing a KVL equation to an alternating-current side column;

in the motor train unit network rectifier, the values of the corresponding quantities are R respectively_NO＝0.06Ω，L_NO＝2.3mH，L₂＝0.603mH，C₂＝4.56mF，C_d＝4mF，R_d＝10Ω，u_N＝2192sin(ωt)V。

B. B, defining a disturbance amount, and obtaining a current prediction value of a motor train unit grid-side rectifier current prediction model considering the disturbance amount under a d-q rotating coordinate system according to the dynamic characteristic equation obtained in the step A;

the dynamic characteristic equation of the grid-side rectifier of the motor train unit is expressed as follows:

a discretized prediction model that accounts for disturbance variables can be obtained:

get T_sFor controlling the sampling period of the system, set to T_s＝5e-5s；

According to the current sampling timeTo control the output voltage value u_abd(k)、u_abq(k) The definition of (a) can be given as:

wherein,

C. taking the current and the disturbance quantity as state variables to obtain a state space model of a disturbance estimator, and constructing the disturbance estimator to obtain a disturbance quantity estimated value;

state space model of disturbance estimator:

x(k+1)＝Ax(k)+Bu(k)

wherein,

constructing a disturbance estimator based on the state space model:

wherein,

can be obtained from the above formula

x(k+1)＝(A-LC)x(k)+Bu(k)

In the closed-loop discrete system, the dynamic characteristic of the state reconstruction error depends on a coefficient matrix A-LC; determining a discrete system through a pole distribution diagram according to the principle that all closed-loop poles are required to be located in a unit circle with the origin as the origin if the stability of the disturbance interference device is required to be ensuredFeedback coefficient of gain matrix of disturbance estimator for system stabilization₁＝1.5，l₂＝-24。

D. B, substituting the disturbance quantity estimated value into a current prediction model, and substituting the current predicted value obtained in the step B into a cost function; obtaining the voltage variation which can make the cost function obtain the minimum value by calculating the partial derivative of the voltage variation on the cost function, adding the voltage variation to the current time voltage to obtain the control voltage of the next sampling period

Cost function g_rComprises the following steps:

in the formula:is generally set to 0;the calculation is as follows:wherein, K_p＝9，T_i0.1, dc side voltage reference U_d ^*According to the different models of motor train units, for the CRH3 model,

calculating a partial derivative related to the voltage variation of the cost function to obtain the voltage variation which can enable the cost function to obtain a minimum value:

the control voltage amount at the next sampling time is:

E. and D, converting the control voltage obtained in the step D through coordinates to obtain an alpha-beta coordinate system component, and outputting a control pulse through sine pulse width modulation.

Finally, a simulation model is built in Matlab/Simulink as shown in FIG. 5, and the obtained voltage and current waveforms are shown in FIG. 6; 0-0.5s is a pre-charging stage; 0.5s-1s is a light load stage, and the equivalent resistance is 100 omega; 1s-1.5s is rated load, and the equivalent load resistance is 10 omega; the waveform shows that the overshoot of the direct-current side voltage under light load is 11.7%, the peak time is 0.08s, the adjusting time is 0.25s, and the voltage fluctuation is +/-5V; the overshoot of the direct-current side voltage under a rated load is 15.6%, the peak time is 0.035s, the regulation time is 0.135s, and the voltage fluctuation is +/-5V; compared with the common transient direct current control, the performance index is better improved, only one cycle is needed from starting to stabilizing of the alternating current, and the harmonic distortion THD is obviously reduced.

The control algorithm is applied to a traction network-motor train unit cascade simulation model, the number of motor train units connected into the traction network is sequentially increased, and under the traditional transient direct current control, when the number of the connected motor train units reaches 7, the voltage and the current of the motor train units and the traction network are obviously shifted, and the low-frequency oscillation phenomenon of the motor train network is generated; under the control of the robust model prediction control high-speed rail low-frequency oscillation overvoltage damping method based on disturbance estimation, when the number of connected motor train units reaches or exceeds 7, the electric quantity is basically stable, and as shown in fig. 7, the problem of low-frequency oscillation does not occur.

The invention controls the current voltage i except the alternating current side_N，u_NAnd a DC side voltage u_dIn addition, disturbance quantity is also considered, the anti-interference capability and the robustness of a control system are improved, and the problem of electric quantity oscillation of a traction network-motor train unit can be damped; the control voltage variation quantity which enables the quality function to obtain a minimum value is obtained by solving the partial derivative of the cost function, so that the predicted current value can be ensured to track the current setting value, and the voltage variation quantity is enabled to beThe chemical quantity floats minimum in the period; the invention needs less parameters to be set, controls the system and is insensitive to parameter change, and the control has better robustness and dynamic performance in an effective range.

Claims (7)

1. A high-speed rail low-frequency oscillation suppression method based on model predictive control of disturbance estimation is characterized by comprising the following steps:

A. constructing a dynamic characteristic equation of the motor train unit network side rectifier considering the parameter error amount under a d-q rotating coordinate system;

B. b, defining a disturbance amount, and obtaining a current prediction value of a motor train unit grid-side rectifier current prediction model considering the disturbance amount under a d-q rotating coordinate system according to the dynamic characteristic equation obtained in the step A;

C. taking the current and the disturbance quantity as state variables to obtain a state space model of a disturbance estimator, and constructing the disturbance estimator to obtain a disturbance quantity estimated value;

D. substituting the disturbance quantity estimation value into the current prediction model in the step B to obtain a current prediction value, and substituting the obtained current prediction value into a cost function to obtain the control voltage of the next sampling period;

E. and D, carrying out coordinate transformation on the control voltage of the next sampling period obtained in the step D to obtain an alpha-beta coordinate system component, and outputting a control pulse through sine pulse width modulation to finish the suppression of the low-frequency oscillation of the high-speed rail.

2. The method for suppressing the high-speed and low-frequency oscillation of the motor train unit grid-side rectifier based on the model predictive control of the disturbance estimation as claimed in claim 1, wherein the motor train unit grid-side rectifier dynamic characteristic equation considering the parameter error amount in the step a is as follows:

defining a resistance rating parameter R_NORated parameter L of inductor_NOActual resistance parameter and rated parameter error amount delta R_NAnd the error amount Delta R between the actual parameter and the rated parameter of the inductor_NObtaining:

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in the formula: r_NActual parameter of resistance, L_NActual parameters of the inductor are obtained;

according to an alternating-current side Hall voltage law equation, obtaining a dynamic characteristic equation of the motor train unit grid side rectifier considering parameter error under a d-q rotating coordinate system:

<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mrow> <mo>(</mo> <mrow> <msub> <mi>L</mi> <mrow> <mi>N</mi> <mi>O</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;Delta;L</mi> <mi>N</mi> </msub> </mrow> <mo>)</mo> </mrow> <mfrac> <mrow> <msub> <mi>di</mi> <mrow> <mi>N</mi> <mi>d</mi> </mrow> </msub> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> <mo>=</mo> <msub> <mi>u</mi> <mrow> <mi>N</mi> <mi>d</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>u</mi> <mrow> <mi>a</mi> <mi>b</mi> <mi>d</mi> </mrow> </msub> <mo>-</mo> <mrow> <mo>(</mo> <mrow> <msub> <mi>R</mi> <mrow> <mi>N</mi> <mi>O</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;Delta;R</mi> <mi>N</mi> </msub> </mrow> <mo>)</mo> </mrow> <msub> <mi>i</mi> <mrow> <mi>N</mi> <mi>d</mi> </mrow> </msub> <mo>+</mo> <mi>&amp;omega;</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>L</mi> <mrow> <mi>N</mi> <mi>O</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;Delta;L</mi> <mi>N</mi> </msub> </mrow> <mo>)</mo> </mrow> <msub> <mi>i</mi> <mrow> <mi>N</mi> <mi>q</mi> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mrow> <mo>(</mo> <mrow> <msub> <mi>L</mi> <mrow> <mi>N</mi> <mi>O</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;Delta;L</mi> <mi>N</mi> </msub> </mrow> <mo>)</mo> </mrow> <mfrac> <mrow> <msub> <mi>di</mi> <mrow> <mi>N</mi> <mi>q</mi> </mrow> </msub> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> <mo>=</mo> <msub> <mi>u</mi> <mrow> <mi>N</mi> <mi>q</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>u</mi> <mrow> <mi>a</mi> <mi>b</mi> <mi>q</mi> </mrow> </msub> <mo>-</mo> <mrow> <mo>(</mo> <mrow> <msub> <mi>R</mi> <mrow> <mi>N</mi> <mi>O</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;Delta;R</mi> <mi>N</mi> </msub> </mrow> <mo>)</mo> </mrow> <msub> <mi>i</mi> <mrow> <mi>N</mi> <mi>q</mi> </mrow> </msub> <mo>-</mo> <mi>&amp;omega;</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>L</mi> <mrow> <mi>N</mi> <mi>O</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;Delta;L</mi> <mi>N</mi> </msub> </mrow> <mo>)</mo> </mrow> <msub> <mi>i</mi> <mrow> <mi>N</mi> <mi>d</mi> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced>

in the formula: u. of_Nd、u_NqFor an input voltage u on the AC side_NA dq direct current component on a two-phase rotating coordinate system; i.e. i_Nd、i_NqRespectively, an input current i on the AC side_NA dq direct current component on a two-phase rotating coordinate system; u. of_abd、u_abqAre respectively integralInput voltage u of current transformer_abA dq direct current component on a two-phase rotating coordinate system; ω is the angular velocity of rotation and t is a time variable.

3. The method for suppressing the high-speed rail low-frequency oscillation based on the disturbance estimation model predictive control of claim 2, wherein the motor train unit grid-side rectifier current predictive model for calculating the disturbance quantity in the step B is as follows:

defining the disturbance quantity, obtaining:

<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>f</mi> <mi>d</mi> </msub> <mo>=</mo> <msub> <mi>&amp;Delta;L</mi> <mi>N</mi> </msub> <mfrac> <mrow> <msub> <mi>di</mi> <mrow> <mi>N</mi> <mi>d</mi> </mrow> </msub> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> <mo>-</mo> <msub> <mi>&amp;omega;&amp;Delta;L</mi> <mi>N</mi> </msub> <msub> <mi>i</mi> <mrow> <mi>N</mi> <mi>q</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;Delta;R</mi> <mi>N</mi> </msub> <msub> <mi>i</mi> <mrow> <mi>N</mi> <mi>d</mi> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>f</mi> <mi>q</mi> </msub> <mo>=</mo> <msub> <mi>&amp;Delta;L</mi> <mi>N</mi> </msub> <mfrac> <mrow> <msub> <mi>di</mi> <mrow> <mi>N</mi> <mi>q</mi> </mrow> </msub> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> <mo>+</mo> <msub> <mi>&amp;omega;&amp;Delta;L</mi> <mi>N</mi> </msub> <msub> <mi>i</mi> <mrow> <mi>N</mi> <mi>d</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;Delta;R</mi> <mi>N</mi> </msub> <msub> <mi>i</mi> <mrow> <mi>N</mi> <mi>q</mi> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced>

in the formula: f. of_d、f_qThe disturbance component on the two-phase rotating coordinate system;

then, the dynamic characteristic equation of the grid-side rectifier of the motor train unit can be changed into:

<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>L</mi> <mrow> <mi>N</mi> <mi>O</mi> </mrow> </msub> <mfrac> <mrow> <msub> <mi>di</mi> <mrow> <mi>N</mi> <mi>d</mi> </mrow> </msub> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> <mo>=</mo> <msub> <mi>u</mi> <mrow> <mi>N</mi> <mi>d</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>u</mi> <mrow> <mi>a</mi> <mi>b</mi> <mi>d</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>R</mi> <mrow> <mi>N</mi> <mi>O</mi> </mrow> </msub> <msub> <mi>i</mi> <mrow> <mi>N</mi> <mi>d</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;omega;L</mi> <mrow> <mi>N</mi> <mi>O</mi> </mrow> </msub> <msub> <mi>i</mi> <mrow> <mi>N</mi> <mi>q</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>f</mi> <mi>d</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>L</mi> <mrow> <mi>N</mi> <mi>O</mi> </mrow> </msub> <mfrac> <mrow> <msub> <mi>di</mi> <mrow> <mi>N</mi> <mi>q</mi> </mrow> </msub> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> <mo>=</mo> <msub> <mi>u</mi> <mrow> <mi>N</mi> <mi>q</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>u</mi> <mrow> <mi>a</mi> <mi>b</mi> <mi>q</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>R</mi> <mrow> <mi>N</mi> <mi>O</mi> </mrow> </msub> <msub> <mi>i</mi> <mrow> <mi>N</mi> <mi>q</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>&amp;omega;L</mi> <mrow> <mi>N</mi> <mi>O</mi> </mrow> </msub> <msub> <mi>i</mi> <mrow> <mi>N</mi> <mi>d</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>f</mi> <mi>q</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced>

for the discretization of the above formula, a current prediction model considering the disturbance quantity can be obtained:

<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>i</mi> <mrow> <mi>N</mi> <mi>d</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <msub> <mi>T</mi> <mi>s</mi> </msub> <msub> <mi>L</mi> <mrow> <mi>N</mi> <mi>O</mi> </mrow> </msub> </mfrac> <mrow> <mo>(</mo> <mrow> <msub> <mi>u</mi> <mrow> <mi>N</mi> <mi>d</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>u</mi> <mrow> <mi>a</mi> <mi>b</mi> <mi>d</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>-</mo> <mfrac> <mrow> <msub> <mi>R</mi> <mrow> <mi>N</mi> <mi>O</mi> </mrow> </msub> <msub> <mi>T</mi> <mi>s</mi> </msub> </mrow> <msub> <mi>L</mi> <mrow> <mi>N</mi> <mi>O</mi> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> <msub> <mi>i</mi> <mrow> <mi>N</mi> <mi>d</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>&amp;omega;T</mi> <mi>s</mi> </msub> <msub> <mi>i</mi> <mrow> <mi>N</mi> <mi>q</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <mfrac> <msub> <mi>T</mi> <mi>s</mi> </msub> <msub> <mi>L</mi> <mrow> <mi>N</mi> <mi>O</mi> </mrow> </msub> </mfrac> <msub> <mi>f</mi> <mi>d</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>i</mi> <mrow> <mi>N</mi> <mi>q</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <msub> <mi>T</mi> <mi>s</mi> </msub> <msub> <mi>L</mi> <mrow> <mi>N</mi> <mi>O</mi> </mrow> </msub> </mfrac> <mrow> <mo>(</mo> <mrow> <msub> <mi>u</mi> <mrow> <mi>N</mi> <mi>q</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>u</mi> <mrow> <mi>a</mi> <mi>b</mi> <mi>q</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>-</mo> <mfrac> <mrow> <msub> <mi>R</mi> <mrow> <mi>N</mi> <mi>O</mi> </mrow> </msub> <msub> <mi>T</mi> <mi>s</mi> </msub> </mrow> <msub> <mi>L</mi> <mrow> <mi>N</mi> <mi>O</mi> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> <msub> <mi>i</mi> <mrow> <mi>N</mi> <mi>q</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>&amp;omega;T</mi> <mi>s</mi> </msub> <msub> <mi>i</mi> <mrow> <mi>N</mi> <mi>d</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <mfrac> <msub> <mi>T</mi> <mi>s</mi> </msub> <msub> <mi>L</mi> <mrow> <mi>N</mi> <mi>O</mi> </mrow> </msub> </mfrac> <msub> <mi>f</mi> <mi>q</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced>

in the formula: k represents a discrete quantity corresponding to the time t and is the current sampling moment; k +1 is the next sampling moment; t is_sIs a sampling period; u. of_Nd(k)、u_Nq(k) Are respectively an AC side input voltage u_NDiscretizing dq direct current components at the current moment; i.e. i_Nd(k)、i_Nq(k) Respectively, an input current i on the AC side_NDiscretizing dq direct current components at the current moment; u. of_abd(k)、u_abq(k) Are respectively the rectifier input voltage u_abDiscretizing dq direct current components at the current moment; f. of_d(k)、f_q(k) Respectively, the disturbance dq direct current components at the current sampling moment.

4. The method for suppressing the low-frequency oscillation of the high-speed rail based on the model predictive control of the disturbance estimation as claimed in claim 3, characterized by further comprising the following steps:

defining a control output voltage value u at a current sampling instant_abd(k)、u_abq(k) Comprises the following steps:

<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <msub> <mi>u</mi> <mrow> <mi>a</mi> <mi>b</mi> <mi>d</mi> </mrow> </msub> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mo>=</mo> <msub> <mi>u</mi> <mrow> <mi>a</mi> <mi>b</mi> <mi>d</mi> </mrow> </msub> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> <mo>+</mo> <mi>&amp;Delta;</mi> <msub> <mi>u</mi> <mrow> <mi>a</mi> <mi>b</mi> <mi>d</mi> </mrow> </msub> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>u</mi> <mrow> <mi>a</mi> <mi>b</mi> <mi>q</mi> </mrow> </msub> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mo>=</mo> <msub> <mi>u</mi> <mrow> <mi>a</mi> <mi>b</mi> <mi>q</mi> </mrow> </msub> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> <mo>+</mo> <mi>&amp;Delta;</mi> <msub> <mi>u</mi> <mrow> <mi>a</mi> <mi>b</mi> <mi>q</mi> </mrow> </msub> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mtd> </mtr> </mtable> </mfenced>

in the formula: u. of_abd(k-1)、u_abq(k-1) are respectively the rectifier input voltage u_abDiscretizing a dq direct current component at the previous sampling moment; Δ u_abd(k) And Δ u_abq(k) Respectively representing the variation of the dq component of the control voltage from the moment k-1 to the moment k;

substituting the current prediction model can obtain:

<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>i</mi> <mrow> <mi>N</mi> <mi>d</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>i</mi> <mrow> <mi>N</mi> <mi>d</mi> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>-</mo> <mfrac> <msub> <mi>T</mi> <mi>s</mi> </msub> <msub> <mi>L</mi> <mrow> <mi>N</mi> <mi>O</mi> </mrow> </msub> </mfrac> <msub> <mi>&amp;Delta;u</mi> <mrow> <mi>a</mi> <mi>b</mi> <mi>d</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>i</mi> <mrow> <mi>N</mi> <mi>q</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>i</mi> <mrow> <mi>N</mi> <mi>q</mi> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>-</mo> <mfrac> <msub> <mi>T</mi> <mi>s</mi> </msub> <msub> <mi>L</mi> <mrow> <mi>N</mi> <mi>O</mi> </mrow> </msub> </mfrac> <msub> <mi>&amp;Delta;u</mi> <mrow> <mi>a</mi> <mi>b</mi> <mi>q</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced>

<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>i</mi> <mrow> <mi>N</mi> <mi>d</mi> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mfrac> <mrow> <msub> <mi>R</mi> <mrow> <mi>N</mi> <mi>O</mi> </mrow> </msub> <msub> <mi>T</mi> <mi>s</mi> </msub> </mrow> <msub> <mi>L</mi> <mrow> <mi>N</mi> <mi>O</mi> </mrow> </msub> </mfrac> <mo>)</mo> </mrow> <msub> <mi>i</mi> <mrow> <mi>N</mi> <mi>d</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>&amp;omega;T</mi> <mi>s</mi> </msub> <msub> <mi>i</mi> <mrow> <mi>N</mi> <mi>q</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <msub> <mi>T</mi> <mi>s</mi> </msub> <msub> <mi>L</mi> <mrow> <mi>N</mi> <mi>O</mi> </mrow> </msub> </mfrac> <msub> <mi>u</mi> <mrow> <mi>N</mi> <mi>d</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <mfrac> <msub> <mi>T</mi> <mi>s</mi> </msub> <msub> <mi>L</mi> <mrow> <mi>N</mi> <mi>O</mi> </mrow> </msub> </mfrac> <msub> <mi>u</mi> <mrow> <mi>a</mi> <mi>b</mi> <mi>d</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>-</mo> <mfrac> <msub> <mi>T</mi> <mi>s</mi> </msub> <msub> <mi>L</mi> <mrow> <mi>N</mi> <mi>O</mi> </mrow> </msub> </mfrac> <msub> <mi>f</mi> <mi>d</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>i</mi> <mrow> <mi>N</mi> <mi>q</mi> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mfrac> <mrow> <msub> <mi>R</mi> <mrow> <mi>N</mi> <mi>O</mi> </mrow> </msub> <msub> <mi>T</mi> <mi>s</mi> </msub> </mrow> <msub> <mi>L</mi> <mrow> <mi>N</mi> <mi>O</mi> </mrow> </msub> </mfrac> <mo>)</mo> </mrow> <msub> <mi>i</mi> <mrow> <mi>N</mi> <mi>q</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>&amp;omega;T</mi> <mi>s</mi> </msub> <msub> <mi>i</mi> <mrow> <mi>N</mi> <mi>d</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <msub> <mi>T</mi> <mi>s</mi> </msub> <msub> <mi>L</mi> <mrow> <mi>N</mi> <mi>O</mi> </mrow> </msub> </mfrac> <msub> <mi>u</mi> <mrow> <mi>N</mi> <mi>q</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <mfrac> <msub> <mi>T</mi> <mi>s</mi> </msub> <msub> <mi>L</mi> <mrow> <mi>N</mi> <mi>O</mi> </mrow> </msub> </mfrac> <msub> <mi>u</mi> <mrow> <mi>a</mi> <mi>b</mi> <mi>q</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>-</mo> <mfrac> <msub> <mi>T</mi> <mi>s</mi> </msub> <msub> <mi>L</mi> <mrow> <mi>N</mi> <mi>O</mi> </mrow> </msub> </mfrac> <msub> <mi>f</mi> <mi>q</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced>

in the formula i_Nd0(k+1)、i_Nq0(k +1) are respectively neglected control voltage variation amount Deltau_abd(k) And Δ u_abq(k) The current prediction value dq component at time k-1.

5. The method for suppressing the low-frequency oscillation of the high-speed rail based on the model predictive control of the disturbance estimation as claimed in claim 1, wherein the estimation disturber is constructed by the following process:

disturbance amount f at current sampling time_d(k) And f_q(k) Equal in one sampling period, namely:

<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <msub> <mi>f</mi> <mi>d</mi> </msub> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> <mo>=</mo> <msub> <mi>f</mi> <mi>d</mi> </msub> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>f</mi> <mi>q</mi> </msub> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> <mo>=</mo> <msub> <mi>f</mi> <mi>q</mi> </msub> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mtd> </mtr> </mtable> </mfenced>

in the formula: f. of_d(k) And f_q(k) Respectively representing disturbance components on the two-phase rotating coordinate system at the current sampling moment; f. of_d(k +1) and f_q(k +1) are disturbance components on the two-phase rotating coordinate system at the next sampling moment respectively;

the state quantity and the input quantity are defined as follows:

<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>x</mi> <mrow> <mo>(</mo> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mrow> <mo>&amp;lsqb;</mo> <mrow> <msub> <mover> <mi>i</mi> <mo>^</mo> </mover> <mrow> <mi>N</mi> <mi>d</mi> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mover> <mi>i</mi> <mo>^</mo> </mover> <mrow> <mi>N</mi> <mi>q</mi> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mover> <mi>f</mi> <mo>^</mo> </mover> <mi>d</mi> </msub> <mrow> <mo>(</mo> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mover> <mi>f</mi> <mo>^</mo> </mover> <mi>q</mi> </msub> <mrow> <mo>(</mo> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mi>T</mi> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mrow> <mo>&amp;lsqb;</mo> <mrow> <msub> <mover> <mi>i</mi> <mo>^</mo> </mover> <mrow> <mi>N</mi> <mi>d</mi> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mover> <mi>i</mi> <mo>^</mo> </mover> <mrow> <mi>N</mi> <mi>q</mi> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mover> <mi>f</mi> <mo>^</mo> </mover> <mi>d</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mover> <mi>f</mi> <mo>^</mo> </mover> <mi>q</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mi>T</mi> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>u</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mrow> <mo>&amp;lsqb;</mo> <msub> <mi>u</mi> <mrow> <mi>N</mi> <mi>d</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>u</mi> <mrow> <mi>a</mi> <mi>b</mi> <mi>d</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>u</mi> <mrow> <mi>N</mi> <mi>q</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>u</mi> <mrow> <mi>a</mi> <mi>b</mi> <mi>q</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mi>T</mi> </msup> </mrow> </mtd> </mtr> </mtable> </mfenced>

in the formula:are respectively i_Nd0(k+1)、i_Nq0An estimated value of (k + 1); i.e. i_Nd0(k)、i_Nq0(k) To ignore the current prediction value dq component at the time k-1 of the control voltage variation,are respectively i_Nd0(k)、i_Nq0(k) An estimated value of (d);are respectively f_d(k)、f_q(k) Is determined by the estimated value of (c),are respectively f_d(k+1)、f_qAn estimated value of (k + 1); x (k +1) is a state component at the moment k +1, x (k) is a state component at the moment k, and u (k) is an input component at the moment k; u. of_Nd(k)、u_Nq(k) Are respectively an AC side input voltage u_NDiscretizing dq direct current components at the current moment;

obtaining a state space model of the disturbance estimator:

x(k+1)＝Ax(k)+Bu(k)

in the formula:

<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>A</mi> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mn>1</mn> <mo>-</mo> <mfrac> <mrow> <msub> <mi>R</mi> <mrow> <mi>N</mi> <mi>O</mi> </mrow> </msub> <msub> <mi>T</mi> <mi>s</mi> </msub> </mrow> <msub> <mi>L</mi> <mrow> <mi>N</mi> <mi>O</mi> </mrow> </msub> </mfrac> </mrow> </mtd> <mtd> <mrow> <msub> <mi>&amp;omega;T</mi> <mi>s</mi> </msub> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <mfrac> <msub> <mi>T</mi> <mi>s</mi> </msub> <msub> <mi>L</mi> <mrow> <mi>N</mi> <mi>O</mi> </mrow> </msub> </mfrac> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <msub> <mi>&amp;omega;T</mi> <mi>s</mi> </msub> </mrow> </mtd> <mtd> <mrow> <mn>1</mn> <mo>-</mo> <mfrac> <mrow> <msub> <mi>R</mi> <mrow> <mi>N</mi> <mi>O</mi> </mrow> </msub> <msub> <mi>T</mi> <mi>s</mi> </msub> </mrow> <msub> <mi>L</mi> <mrow> <mi>N</mi> <mi>O</mi> </mrow> </msub> </mfrac> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mfrac> <msub> <mi>T</mi> <mi>s</mi> </msub> <msub> <mi>L</mi> <mrow> <mi>N</mi> <mi>O</mi> </mrow> </msub> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> </mrow> </mtd> <mtd> <mrow> <mi>B</mi> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mfrac> <msub> <mi>T</mi> <mi>s</mi> </msub> <msub> <mi>L</mi> <mrow> <mi>N</mi> <mi>O</mi> </mrow> </msub> </mfrac> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mfrac> <msub> <mi>T</mi> <mi>s</mi> </msub> <msub> <mi>L</mi> <mrow> <mi>N</mi> <mi>O</mi> </mrow> </msub> </mfrac> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> </mrow> </mtd> </mtr> </mtable> </mfenced>

in the formula: r_NOTo define the rated resistance parameter, L_NOIs a rated parameter of the inductor, omega is a rotation angular velocity, T_sIs a sampling period;

constructing a disturbance estimator based on the state space model:

<mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mover> <mi>i</mi> <mo>^</mo> </mover> <mrow> <mi>N</mi> <mi>d</mi> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mover> <mi>i</mi> <mo>^</mo> </mover> <mrow> <mi>N</mi> <mi>q</mi> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mover> <mi>f</mi> <mo>^</mo> </mover> <mi>d</mi> </msub> <mrow> <mo>(</mo> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mover> <mi>f</mi> <mo>^</mo> </mover> <mi>q</mi> </msub> <mrow> <mo>(</mo> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mi>A</mi> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mover> <mi>i</mi> <mo>^</mo> </mover> <mrow> <mi>N</mi> <mi>d</mi> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mover> <mi>i</mi> <mo>^</mo> </mover> <mrow> <mi>N</mi> <mi>q</mi> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mover> <mi>f</mi> <mo>^</mo> </mover> <mi>d</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mover> <mi>f</mi> <mo>^</mo> </mover> <mi>q</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>+</mo> <mi>B</mi> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>u</mi> <mrow> <mi>N</mi> <mi>d</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>u</mi> <mrow> <mi>a</mi> <mi>b</mi> <mi>d</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>u</mi> <mrow> <mi>N</mi> <mi>q</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>u</mi> <mrow> <mi>a</mi> <mi>b</mi> <mi>q</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>+</mo> <mi>L</mi> <mrow> <mo>(</mo> <mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>i</mi> <mrow> <mi>N</mi> <mi>d</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>i</mi> <mrow> <mi>N</mi> <mi>q</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>i</mi> <mrow> <mi>N</mi> <mi>d</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>i</mi> <mrow> <mi>N</mi> <mi>q</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mi>C</mi> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mover> <mi>i</mi> <mo>^</mo> </mover> <mrow> <mi>N</mi> <mi>d</mi> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mover> <mi>i</mi> <mo>^</mo> </mover> <mrow> <mi>N</mi> <mi>q</mi> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mover> <mi>f</mi> <mo>^</mo> </mover> <mi>d</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mover> <mi>f</mi> <mo>^</mo> </mover> <mi>q</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow> <mo>)</mo> </mrow> </mrow>

in the formula:are respectively i_Nd0(k+1)、i_Nq0An estimated value of (k + 1);are respectively f_d(k +1) and f_qAn estimated value of (k + 1);are respectively i_Nd0(k)、i_Nq0(k) An estimated value of (d); are respectively f_d(k)、f_q(k) An estimated value of (d);

<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>L</mi> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>l</mi> <mn>1</mn> </msub> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <msub> <mi>l</mi> <mn>1</mn> </msub> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <msub> <mi>l</mi> <mn>2</mn> </msub> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <msub> <mi>l</mi> <mn>2</mn> </msub> </mtd> </mtr> </mtable> </mfenced> </mrow> </mtd> <mtd> <mrow> <mi>C</mi> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> </mrow> </mtd> </mtr> </mtable> </mfenced>

in the formula I₁、l₂Feedback coefficients of a state observer gain matrix L; from the above formula, one can obtain:

x(k+1)＝(A-LC)x(k)+Bu(k)

and completing the construction of the disturbance estimator.

6. The method for suppressing the low-frequency oscillation of the high-speed rail based on the model predictive control of the disturbance estimation as claimed in claim 1, wherein the cost function in the step D is:

<mrow> <msub> <mi>g</mi> <mi>r</mi> </msub> <mo>=</mo> <msup> <mrow> <mo>&amp;lsqb;</mo> <msubsup> <mi>i</mi> <mrow> <mi>N</mi> <mi>d</mi> </mrow> <mo>*</mo> </msubsup> <mo>-</mo> <msub> <mi>i</mi> <mrow> <mi>N</mi> <mi>d</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>&amp;lsqb;</mo> <msubsup> <mi>i</mi> <mrow> <mi>N</mi> <mi>q</mi> </mrow> <mo>*</mo> </msubsup> <mo>-</mo> <msub> <mi>i</mi> <mrow> <mi>N</mi> <mi>q</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mn>2</mn> </msup> </mrow>

in the formula: g_rIn order to be a function of the cost,setting a value for a q-axis component of the alternating-current side current of the rectifier;setting value i for d-axis component of AC side current of rectifier_Nd(k+1)、i_Nq(k +1) are input currents i on the AC side_NDiscretizing a dq direct current component in the next sampling period;

<mrow> <msubsup> <mi>i</mi> <mrow> <mi>N</mi> <mi>d</mi> </mrow> <mo>*</mo> </msubsup> <mo>=</mo> <msub> <mi>K</mi> <mi>P</mi> </msub> <mrow> <mo>(</mo> <msubsup> <mi>U</mi> <mi>d</mi> <mo>*</mo> </msubsup> <mo>-</mo> <msub> <mi>U</mi> <mi>d</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <mn>1</mn> <mo>/</mo> <msub> <mi>T</mi> <mi>i</mi> </msub> <mo>&amp;Integral;</mo> <mrow> <mo>(</mo> <msubsup> <mi>U</mi> <mi>d</mi> <mo>*</mo> </msubsup> <mo>-</mo> <msub> <mi>U</mi> <mi>d</mi> </msub> <mo>)</mo> </mrow> <mi>d</mi> <mi>t</mi> </mrow>

in the formula:is a DC side voltage reference value, U_dAs a measured value of the DC side voltage, K_pProportional coefficient of PI controller, T_iIs the PI controller integration coefficient.

7. The method as claimed in claim 6, wherein the disturbance estimation value is substituted into the current prediction model to obtain the disturbance estimation value

<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>i</mi> <mrow> <mi>N</mi> <mi>d</mi> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mfrac> <mrow> <msub> <mi>R</mi> <mrow> <mi>N</mi> <mi>O</mi> </mrow> </msub> <msub> <mi>T</mi> <mi>s</mi> </msub> </mrow> <msub> <mi>L</mi> <mrow> <mi>N</mi> <mi>O</mi> </mrow> </msub> </mfrac> <mo>)</mo> </mrow> <msub> <mi>i</mi> <mrow> <mi>N</mi> <mi>d</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>&amp;omega;T</mi> <mi>s</mi> </msub> <msub> <mi>i</mi> <mrow> <mi>N</mi> <mi>q</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <msub> <mi>T</mi> <mi>s</mi> </msub> <msub> <mi>L</mi> <mrow> <mi>N</mi> <mi>O</mi> </mrow> </msub> </mfrac> <msub> <mi>u</mi> <mrow> <mi>N</mi> <mi>d</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <mfrac> <msub> <mi>T</mi> <mi>s</mi> </msub> <msub> <mi>L</mi> <mrow> <mi>N</mi> <mi>O</mi> </mrow> </msub> </mfrac> <msub> <mi>u</mi> <mrow> <mi>a</mi> <mi>b</mi> <mi>d</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>-</mo> <mfrac> <msub> <mi>T</mi> <mi>s</mi> </msub> <msub> <mi>L</mi> <mrow> <mi>N</mi> <mi>O</mi> </mrow> </msub> </mfrac> <msub> <mover> <mi>f</mi> <mo>^</mo> </mover> <mi>d</mi> </msub> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>i</mi> <mrow> <mi>N</mi> <mi>q</mi> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mfrac> <mrow> <msub> <mi>R</mi> <mrow> <mi>N</mi> <mi>O</mi> </mrow> </msub> <msub> <mi>T</mi> <mi>s</mi> </msub> </mrow> <msub> <mi>L</mi> <mrow> <mi>N</mi> <mi>O</mi> </mrow> </msub> </mfrac> <mo>)</mo> </mrow> <msub> <mi>i</mi> <mrow> <mi>N</mi> <mi>q</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>&amp;omega;T</mi> <mi>s</mi> </msub> <msub> <mi>i</mi> <mrow> <mi>N</mi> <mi>d</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <msub> <mi>T</mi> <mi>s</mi> </msub> <msub> <mi>L</mi> <mrow> <mi>N</mi> <mi>O</mi> </mrow> </msub> </mfrac> <msub> <mi>u</mi> <mrow> <mi>N</mi> <mi>q</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <mfrac> <msub> <mi>T</mi> <mi>s</mi> </msub> <msub> <mi>L</mi> <mrow> <mi>N</mi> <mi>O</mi> </mrow> </msub> </mfrac> <msub> <mi>u</mi> <mrow> <mi>a</mi> <mi>b</mi> <mi>q</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>-</mo> <mfrac> <msub> <mi>T</mi> <mi>s</mi> </msub> <msub> <mi>L</mi> <mrow> <mi>N</mi> <mi>O</mi> </mrow> </msub> </mfrac> <msub> <mover> <mi>f</mi> <mo>^</mo> </mover> <mi>q</mi> </msub> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced>

Substituting the obtained current predicted value into a cost function to obtain the control voltage of the next sampling period;

the method for calculating the control voltage in the next sampling period comprises the following steps:

partial derivatives of the voltage variation are obtained from the cost function to obtain the voltage variation delta u which can make the cost function obtain minimum value_abd(k) And Δ u_abq(k)：

<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>&amp;Delta;u</mi> <mrow> <mi>a</mi> <mi>b</mi> <mi>d</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <msub> <mi>L</mi> <mrow> <mi>N</mi> <mi>O</mi> </mrow> </msub> <msub> <mi>T</mi> <mi>s</mi> </msub> </mfrac> <mo>&amp;lsqb;</mo> <msubsup> <mi>i</mi> <mrow> <mi>N</mi> <mi>d</mi> </mrow> <mo>*</mo> </msubsup> <mo>-</mo> <msub> <mi>i</mi> <mrow> <mi>N</mi> <mi>d</mi> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>&amp;Delta;u</mi> <mrow> <mi>a</mi> <mi>b</mi> <mi>q</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <msub> <mi>L</mi> <mrow> <mi>N</mi> <mi>O</mi> </mrow> </msub> <msub> <mi>T</mi> <mi>s</mi> </msub> </mfrac> <mo>&amp;lsqb;</mo> <msubsup> <mi>i</mi> <mrow> <mi>N</mi> <mi>q</mi> </mrow> <mo>*</mo> </msubsup> <mo>-</mo> <msub> <mi>i</mi> <mrow> <mi>N</mi> <mi>q</mi> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> </mtable> </mfenced>

In the formula: i.e. i_Nd0(k+1)、i_Nq0(k +1) is the neglect of the control voltage variation Δ u_abd(k) And Δ u_abq(k) The current prediction value dq component at the k-1 moment; l is_NOThe inductance rated parameter; t is_sIs a sampling period;

the next sampling period control voltage is:

<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <msub> <mi>u</mi> <mrow> <mi>a</mi> <mi>b</mi> <mi>d</mi> </mrow> </msub> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> <mo>=</mo> <msub> <mi>u</mi> <mrow> <mi>a</mi> <mi>b</mi> <mi>d</mi> </mrow> </msub> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mo>+</mo> <mi>&amp;Delta;</mi> <msub> <mi>u</mi> <mrow> <mi>a</mi> <mi>b</mi> <mi>d</mi> </mrow> </msub> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>u</mi> <mrow> <mi>a</mi> <mi>b</mi> <mi>q</mi> </mrow> </msub> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> <mo>=</mo> <msub> <mi>u</mi> <mrow> <mi>a</mi> <mi>b</mi> <mi>q</mi> </mrow> </msub> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mo>+</mo> <mi>&amp;Delta;</mi> <msub> <mi>u</mi> <mrow> <mi>a</mi> <mi>b</mi> <mi>q</mi> </mrow> </msub> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mtd> </mtr> </mtable> </mfenced>

in the formula: u. of_abd(k+1)、u_abq(k +1) is the rectifier input voltage u_abAn input value at a next sampling period; u. of_abd(k)、u_abq(k) Is a rectifier input voltage u_abDiscretizing dq direct current components at the current sampling moment; Δ u_abd(k)、Δu_abq(k) The voltage variation from the time k-1 to the time k-1 is controlled.