An effective wind farm modeling method based on transfer function and aggregation equivalence

Abstract

This invention discloses an effective wind farm modeling method based on transfer function and aggregate equivalence, belonging to the field of wind power, including the following steps: S1: Establish a mathematical model of the wind turbine grid-connected system; S2: Reduce the order of the mathematical model of the wind turbine grid-connected system according to the given reduction principle and based on the equivalent transfer function; S3: Analyze the connection mode of each wind turbine and the collection system in the wind farm, and simplify the collection line using an equivalent line loss model; then, based on the reduced-order mathematical model of the wind turbine grid-connected system, classify and aggregate the wind turbines in the wind farm according to the wake effect, and perform capacity-weighted equivalent calculation of the aggregate parameters of the wind turbines, thereby realizing the reduced-order equivalent modeling of the wind farm. This invention can improve the simulation speed of large-scale wind farms and facilitate the rapid analysis of the dynamic characteristics of wind power transient steady-state grid connection.

Description

Technical Field

[0001] This invention patent belongs to the field of wind power technology, specifically relating to an effective wind farm modeling method based on transfer function and aggregate equivalence. Background Technology

[0002] Permanent magnet synchronous motors (PMSGs), as high-performance motors, are widely used in wind power generation due to their advantages such as fast response speed, high power factor, and high operational reliability. However, in PMSG systems, because the generator is connected to the grid through a full-power converter, the generator's rotor speed is decoupled from the grid, resulting in asynchronous operation and a series of transient stability problems. Therefore, it is necessary to establish a grid-connected model of the wind power system based on a simulation platform to simulate and analyze wind power control. Currently, the main modeling and simulation platforms for wind turbines include Matlab / Simulink and PSCAD / EMTTDC.

[0003] The detailed model of the permanent magnet synchronous power generation system includes the wind turbine, drive shaft, PMSG, full-power converter and its corresponding control system. However, the detailed model includes different time scales such as electromagnetic, electromechanical and mechanical. The high model order leads to slow simulation speed, making it inefficient to use for analysis of wind power grid-connected systems and difficult to optimize system control strategies.

[0004] With the continuous growth of wind power installed capacity, the single-unit grid-connected system model is complex and has low capacity, which cannot meet the actual wind power grid connection analysis. Therefore, it is necessary to perform reasonable equivalent simplification of large-scale wind farm grid-connected systems to meet actual simulation requirements. At present, the equivalent simplification of new energy sources is mainly divided into two parts: clustering between different types of new energy sources and aggregation equivalence of the same type of energy. Wind farms are mainly composed of wind turbine units of the same type, and the aggregation equivalence method can be used to simplify them.

[0005] Currently, there is a lot of research on the simplification of wind turbine units and the equivalent method of wind farms, but there is very little literature on combining the two to further reduce the complexity of large wind farms, and the numerical values ​​of the simplified model and the actual model parameters differ greatly. Summary of the Invention

[0006] The purpose of this invention is to solve the problems mentioned in the background art and provide an effective wind farm modeling method based on transfer function and aggregation equivalence, which can improve the simulation speed and accuracy of large wind farms.

[0007] To achieve the above-mentioned technical objectives, the technical solution adopted by the present invention is as follows:

[0008] An efficient wind farm modeling method based on transfer function and aggregation equivalence includes the following steps:

[0009] S1: Establish a mathematical model for the wind turbine grid connection system;

[0010] S2: According to the given order reduction principle, the mathematical model of the wind turbine grid-connected system is reduced in order based on the equivalent transfer function;

[0011] S3: Analyze the connection methods of each wind turbine and the power collection system in the wind farm, and simplify the power collection line using an equivalent line loss model; then, based on the reduced-order mathematical model of the wind turbine grid connection system, classify and aggregate the wind turbines in the wind farm according to the wake effect, and perform capacity-weighted equivalent calculations on the aggregated parameters of the wind turbines, thereby realizing the reduced-order equivalent modeling of the wind farm.

[0012] Preferably, in step S1, the mathematical model of the wind turbine grid-connected system adopts the permanent magnet synchronous power generation system model. The permanent magnet synchronous power generation system model includes: wind turbine, drive shaft, permanent magnet synchronous motor (PMSG), full-power converter, and corresponding control system model; the wind turbine captures wind energy and converts it into rotor kinetic energy, and the wind turbine rotor converts the kinetic energy into electrical energy through the drive shaft to the PMSG. The three-phase current output by the PMSG is connected to the grid and outputs power through the full-power converter.

[0013] Preferably, step S1 requires deriving the mechanical power and mechanical torque of the wind turbine, as well as the rotor dynamic equation expression of the permanent magnet synchronous motor; the mechanical power obtained by the wind turbine from capturing wind energy is:

[0014] P m =ρSC p (λ,β)v 3 / 2=T m ω m ①

[0015] In the formula, ρ is the air density; S = πR 2 R is the scanning area of ​​the wind turbine; R is the radius of the wind turbine blades; v is the wind speed; C p The wind energy utilization coefficient is a function of the tip speed ratio λ and the pitch angle β; T m For the mechanical torque of the wind turbine, ω m This refers to the wind turbine's rotational speed.

[0016] The expression for λ is:

[0017]

[0018] From equations ① and ②, the mechanical torque of the wind turbine can be obtained as follows:

[0019]

[0020] Among them, C p It can be represented as:

[0021]

[0022] In the formula, α is an intermediate variable;

[0023] When the wind turbine is operating under maximum power point tracking (MPPT) control, the output power can be expressed as:

[0024]

[0025] C p,opt For the optimal wind energy utilization coefficient, k opt These are parameters related to the characteristics of the wind turbine itself;

[0026] From equations ②, ③, and ④, the optimal output mechanical torque of the wind turbine can be obtained as follows:

[0027]

[0028] The function of the PMSG is to convert the wind energy captured by the wind turbine into electrical energy through electromagnetic effects. Ignoring its shaft dynamic effects, the rotor dynamic equation expression is:

[0029]

[0030] In the formula T e denoted as the electromagnetic torque of the permanent magnet synchronous motor, and D as the mechanical damping coefficient of the PMSG.

[0031] Preferably, the order reduction principle in step S2 includes:

[0032] A. Ignore the dynamic response of the dq-axis current in the PMSG, that is, ignore the dynamic response of the PMSG under the electromagnetic time scale;

[0033] B. Ignore mechanical damping and electromagnetic losses in PMSG;

[0034] C. Ignore the dynamic response of the switches, the dynamic response of each flux linkage, the dynamic response of the phase-locked loop, and the dynamic response of the inner current loop in the full-power converter.

[0035] D. The full-power converter adopts dq-axis decoupled control, so active power control and reactive power control are separated, and DC side voltage control is ignored.

[0036] Preferably, in step S2, the output variable of the simplified equivalent model of the wind turbine is the mechanical torque T. m The input variables are wind speed v and rotor speed ω. m And the pitch angle β; based on the reduction principles A and B, the rotor dynamic equation expression in PMSG can be simplified to:

[0037]

[0038] The equivalent simplified model of PMSG is designed with rotor speed ω as the output variable. m The input variable is the mechanical torque T. m and electromagnetic torque T e ;

[0039] Based on the equivalent transfer function, the transfer function between speed and torque is:

[0040]

[0041] In the formula, H is the inertial time constant of the PMSG; s is the complex frequency.

[0042] In the simplified model of the full-power converter, based on the order reduction principles C and D, a first-order inertial element is used to replace both the machine-side converter and the grid-side converter; the simplified wind turbine output power is:

[0043]

[0044] In the formula, P wind P is the output power of the wind turbine generator; wind_ref This is a reference value for the output power of the wind turbine; T w The power control time constant is related to the generator-side converter and the grid-side converter; s is the complex frequency;

[0045] To achieve the aforementioned power output while keeping the rotor speed below the rated value, a pitch angle control system is required to assist in control. Based on the transfer function, the pitch angle control system can be equivalent to a first-order inertial element.

[0046]

[0047] In the formula, G(s) is the transfer function of the pitch servo; T β is the time constant; s is the complex frequency.

[0048] Preferably, the process of simplifying the collector line using an equivalent line loss model in step S3 includes:

[0049] Let S1, S2, ..., S n These represent the output power of each wind turbine; U1, U2, ..., U n Z1, Z2, ..., Zn are the terminal voltages of each wind turbine; the collector line impedances between two adjacent wind turbines are Z1, Z2, ..., Zn. n ;

[0050] When performing equivalent calculations on the collector lines, the wind turbine and its transformer are simplified as a single current source. Assuming each wind turbine has the same output, the current phasors they inject into the collector lines are equal. Therefore, the losses on each section of the collector lines in the wind turbine group are as follows:

[0051]

[0052] The total loss of the collector line can be expressed as:

[0053]

[0054] The equivalent wind turbine capacity is:

[0055] S eq =S1+S2+...+S n

[0056] The current injected into the transmission line by the equivalent wind turbine generator is expressed as:

[0057] I eq =I1+I2+...+I n =nI

[0058] The impedance of the equivalent transmission line of the wind turbine generator is represented by Zeq. The loss along this line is:

[0059]

[0060] For the equivalent value of the transmission line-to-ground capacitance, assuming the transmission line voltage remains stable during normal operation of the wind farm, the equivalent value of the transmission line-to-ground capacitance is calculated as follows:

[0061]

[0062] In the formula: B eq This is the equivalent capacitance to ground; B i Let be the capacitance to ground of the i-th line in the wind farm.

[0063] Preferably, in step S3, the wind turbines within the wind farm are classified and aggregated according to the wake effect. The Jensen wake model is used to calculate the input wind speed of each turbine. Based on this assumption, the wind speed in both regions is constant at a certain distance from the wind turbine. According to the momentum theorem, the dimensionless axial velocity v in the wake region of the wind turbine can be obtained. c 'for:

[0064]

[0065] In the formula, v C The axial velocity along the wake's rotation axis is v; the initial wind speed is C. T denoted as axial thrust coefficient of the wind turbine; k is the wake attenuation coefficient, where the wake attenuation coefficient of the upstream wind turbine is 0.075 and that of the downstream wind turbine is 0.11 when two wind turbines are arranged in series; X is the axial distance from a point downstream to the wind turbine plane; R XThe radius of the wake is X, which is the radius of the wind turbine blade R when X is 0.

[0066] Based on the connection status and geographical location of each wind turbine, the initial wind speed and wind direction are first collected, the groups are divided according to the connection method, the number of wind turbines in each group is determined, and then the input wind speed of each turbine is calculated according to the wake model mentioned above.

[0067] Then, the capacity-weighted method was used to perform equivalent calculations on the parameters of each loop.

[0068] Preferably, the capacity-weighted method calculates the wind turbine parameters and generator parameters proportionally based on the proportion of each wind turbine's capacity in the total wind turbine capacity.

[0069] The proportion of each wind turbine's capacity in the total wind turbine capacity is represented by the weight δ. i Its calculation equation is

[0070]

[0071] Where: δ i S represents the weighting coefficients of the capacity-weighted method; i Let be the capacity of the i-th wind turbine in the wind farm; n is the total number of wind turbines in the wind farm.

[0072] According to the weight δ i The equivalent parameters of the wind turbine can be calculated as follows:

[0073]

[0074] In the formula: A i C p_i and V i Let A represent the swept area, wind energy utilization rate, and wind speed captured by the i-th wind turbine in the wind farm, respectively; eq C p_eq and V eq These represent the equivalent swept area, wind energy utilization rate, and equivalent wind speed, respectively.

[0075] The equivalent calculations for the generator parameters are as follows:

[0076]

[0077] In the formula: P i S i R i X i and H i Let P represent the active power, rated capacity, stator resistance, stator reactance, and inertial time constant of the i-th generator in the wind farm, respectively; eq S eq Req X eq and H eq These represent the equivalent active power, rated capacity, stator resistance, stator reactance, and inertial time constant, respectively; once the equivalent parameters are obtained, the equivalent modeling of the wind farm is complete.

[0078] The beneficial effects of this invention are:

[0079] This invention is based on a wind turbine reduced-order model with an equivalent transfer function. It calculates equivalent parameters according to the wake model and uses a capacity-weighted method to perform equivalent calculations on the wind farm. This can improve the simulation speed of large-scale wind farms and facilitate rapid analysis of the dynamic characteristics of wind power transient steady-state grid connection. Attached Figure Description

[0080] Figure 1 This is a schematic diagram of the connection structure of a permanent magnet synchronous power generation system;

[0081] Figure 2 This is a simplified model structure diagram of a wind turbine generator based on the equivalent transfer function for order reduction.

[0082] Figure 3 This is a comparison chart of the captured power of the simplified model and the detailed model under wind speed variations;

[0083] Figure 4 Comparison of rotor speeds between the simplified and detailed models under varying wind speeds;

[0084] Figure 5 Comparison of grid-connected power between simplified and detailed models under varying wind speeds. Detailed Implementation

[0085] The embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0086] It should be noted that the terms such as "upper", "lower", "left", "right", "front", and "back" used in the invention are only for clarity of description and are not intended to limit the scope of the invention. Changes or adjustments to their relative relationships, without substantially altering the technical content, should also be considered within the scope of the invention.

[0087] This specific implementation discloses an efficient wind farm modeling method based on transfer function and aggregate equivalence, including the following steps:

[0088] S1: Establish a mathematical model for the wind turbine grid connection system;

[0089] S2: According to the given order reduction principle, the mathematical model of the wind turbine grid-connected system is reduced in order based on the equivalent transfer function;

[0090] S3: Analyze the connection methods of each wind turbine and the power collection system in the wind farm, and simplify the power collection line using an equivalent line loss model; then, based on the reduced-order mathematical model of the wind turbine grid connection system, classify and aggregate the wind turbines in the wind farm according to the wake effect, and perform capacity-weighted equivalent calculations on the aggregated parameters of the wind turbines, thereby realizing the reduced-order equivalent modeling of the wind farm.

[0091] In step S1, the mathematical model of the wind turbine grid-connected system is mainly based on the permanent magnet synchronous power generation system model, including the wind turbine, drive shaft, permanent magnet synchronous motor (PMSG), full-power converter, and its corresponding control system model. The wind turbine captures wind energy and converts it into rotor kinetic energy. The wind turbine rotor converts the kinetic energy into electrical energy through the drive shaft to the PMSG. The three-phase current output by the PMSG is connected to the grid and outputs power through the full-power converter. Its structure is as follows: Figure 1 As shown.

[0092] The mechanical power obtained by the wind turbine in capturing wind energy is:

[0093] P m =ρSC p (λ,β)v 3 / 2=T m ω m ①

[0094] In the formula, ρ is the air density; S = πR 2 R is the scanning area of ​​the wind turbine; R is the radius of the wind turbine blades; v is the wind speed; C p Let be the wind energy utilization coefficient, which is a function of the tip speed ratio λ and the blade pitch angle β. The expression for λ is:

[0095]

[0096] In the formula, ω m This refers to the rotational speed of the wind turbine.

[0097] From equations ① and ②, the mechanical torque of the wind turbine can be obtained as follows:

[0098]

[0099] Among them, C p It can be represented as:

[0100]

[0101] In the formula, α is an intermediate variable.

[0102] When the wind turbine is operating under maximum power point tracking (MPPT) control, the output power can be expressed as:

[0103]

[0104] Cp,opt For the optimal wind energy utilization coefficient, k opt These are parameters related to the characteristics of the wind turbine itself.

[0105] From equations ②, ③, and ④, the optimal output torque of the wind turbine can be obtained as follows:

[0106]

[0107] The function of the PMSG is to convert the wind energy captured by the wind turbine into electrical energy through electromagnetic effects. If the dynamic effects of its shaft system are ignored, the expression for the rotor dynamic equation is:

[0108]

[0109] In the formula T e denoted as the electromagnetic torque of the permanent magnet synchronous motor, and D as the mechanical damping coefficient of the PMSG.

[0110] In permanent magnet direct-drive wind turbines, the role of the full-power converter is to transform and control the output power under the designed control strategy. It consists of a machine-side converter and a grid-side converter, both of which achieve the control target by generating PWM signals through PI control in a decoupled dq coordinate system. Generally, the wind turbine achieves MPPT control by controlling the machine-side converter, while the grid-side converter is used to maintain voltage stability on the DC side of the converter and provide reactive power support for the system.

[0111] In step S2, considering that the subsequent reduced-order models need to be superimposed and synthesized, the output variable of the equivalent simplified model of the wind turbine is designed as mechanical torque T. m The input variables are wind speed v and rotor speed ω. m And propeller pitch angle β.

[0112] In the PMSG equivalent simplification, the design follows the principle of order descent:

[0113] 1) Ignore the dynamic response of the dq axis current in the PMSG, that is, ignore the dynamic response of the PMSG under the electromagnetic time scale.

[0114] 2) Ignore mechanical damping and electromagnetic losses in PMSG.

[0115] Based on the above principle of order reduction, the expression for the rotor dynamic equation in PMSG can be simplified to:

[0116]

[0117] The equivalent simplified model of PMSG is designed with rotor speed ω as the output variable. m The input variable is the mechanical torque T. m and electromagnetic torque T e .

[0118] Based on the equivalent transfer function, the transfer function between speed and torque is:

[0119]

[0120] In the formula, H is the inertial time constant of the PMSG; s is the complex frequency.

[0121] In the simplified model of the converter, the design follows the principle of order reduction:

[0122] 1) Ignore the dynamic responses of the switches, flux linkages, phase-locked loop, and inner current loop in the converter.

[0123] 2) The full-power converter adopts qd-axis decoupled control, so active power control and reactive power control are separated, and DC side voltage control is ignored.

[0124] Based on the above order reduction principle, a first-order inertial element is used to replace both the machine-side converter and the grid-side converter. The simplified wind turbine output power is:

[0125]

[0126] In the formula, P wind P is the output power of the wind turbine generator; wind_ref This is a reference value for the output power of the wind turbine; T w is the power control time constant related to the generator and grid-side converters; s is the complex frequency.

[0127] In the decoupled dq coordinate system, the converter achieves its control objective by generating a PWM signal through PI control. After simplifying the converter to a first-order inertial element, the power control loop is simplified, and the electromagnetic power of the wind turbine can be determined by the output power reference value P. wind_ref The output power reference value is obtained directly, while the overall operating strategy of the wind turbine depends on the P. wind_ref According to the rotational speed ω m The values ​​are selected to achieve the maximum power capture of the wind turbine. Considering that the PMSG equivalent simplified model requires electromagnetic torque as an input variable, the input variable of the power control system model is the rotational speed ω. m The output variable is the output power reference value P. wind_ref With electromagnetic torque T e .

[0128] To achieve the aforementioned power output while keeping the rotor speed below the rated value, a pitch angle control system is required to assist in control. Based on the transfer function, the pitch angle control system can be equivalently represented as a first-order inertial element.

[0129]

[0130] In the formula, G(s) is the transfer function of the pitch servo; T β is the time constant; s is the complex frequency.

[0131] Wind turbine reduced-order models based on equivalent transfer functions can greatly reduce the complexity and time of simulation in wind farm modeling.

[0132] In step S3, the connection method of the wind farm's power collection system is analyzed, and the power collection lines are simplified using an equivalent line loss model.

[0133] Let S1, S2, ..., S n Let U1, U2, ..., U be the output power of n wind turbine units respectively; n Z1, Z2, ..., Zn are the terminal voltages of each wind turbine; the collector line impedances between two adjacent wind turbines are Z1, Z2, ..., Zn. n When performing equivalent calculations on the collector lines, the wind turbine and its transformer can be simplified as a single current source. Assuming each wind turbine has the same output, the current phasors they inject into the collector lines are equal. Therefore, the losses on each section of the collector lines in the wind turbine group are as follows:

[0134]

[0135] The total loss of the collector line can be expressed as:

[0136]

[0137] The equivalent wind turbine capacity is:

[0138] S eq =S1+S2+...+S n

[0139] The current injected into the transmission line by the equivalent wind turbine generator is expressed as:

[0140] I eq =I1+I2+...+I n =nI

[0141] The impedance of the equivalent transmission line of a wind turbine is represented by Z. eq Therefore, the loss on this line is:

[0142]

[0143] For the equivalent value of the transmission line-to-ground capacitance, since the reactive power of the ground capacitance is proportional to the square of the voltage applied across the capacitor, and assuming the transmission line voltage remains stable during normal operation of the wind farm, the equivalent value of the transmission line-to-ground capacitance is calculated as follows:

[0144]

[0145] In the formula: B eq This is the equivalent capacitance to ground; B i Let be the capacitance to ground of the i-th line in the wind farm.

[0146] After simplifying the power collection lines, and considering the wake effect, the wind turbines within the site are classified and aggregated.

[0147] This paper uses the Jensen wake model to calculate the input wind speed of each generator unit. This model assumes that the initial diameter of the wake region is equal to the rotor radius, and the radius of the wake region increases linearly with distance, with the growth rate being the only free parameter of the model. Using this geometric assumption, the airflow behind the rotor is divided into a conical wake region and a undisturbed flow region. At a certain distance from the wind turbine, the wind speed in both regions is constant. According to the momentum theorem, the dimensionless axial velocity v in the wind turbine wake region can be obtained. c 'for:

[0148]

[0149] In the formula, v c Let v be the axial velocity along the wake's rotation axis, v be the initial wind speed, and C be the axial velocity. T R is the axial thrust coefficient of the wind turbine, k is the wake attenuation coefficient. When two wind turbines are arranged in series, the wake attenuation coefficient of the upstream wind turbine is taken as 0.075, and the wake attenuation coefficient of the downstream wind turbine is taken as 0.11. X is the axial distance from a point downstream to the wind turbine plane; X The radius of the wake is X, which is the radius of the wind turbine blade R when X is 0.

[0150] Based on the connection status and geographical location of each wind turbine, the initial wind speed and direction are first collected, the groups are divided according to the connection method, the number of wind turbines in each group is determined, and then the input wind speed of each turbine is calculated according to the wake model mentioned above.

[0151] Then, the capacity-weighted method was used to perform equivalent calculations on the parameters of each loop.

[0152] The capacity-weighted method uses the proportion of each wind turbine's capacity in the total wind farm capacity as the weight δ. i The parameters of the wind turbine and generator are calculated proportionally based on weights. Weight δ i The calculation equation is as follows

[0153]

[0154] Where: δ i S represents the weighting coefficients of the capacity-weighted method; i Let be the capacity of the i-th wind turbine in the wind farm; n is the total number of wind turbines in the wind farm.

[0155] According to the weight δ i The equivalent parameters of the wind turbine can be calculated as follows:

[0156]

[0157] In the formula: A i C p_i and V i Let A represent the swept area, wind energy utilization rate, and wind speed captured by the i-th wind turbine in the wind farm, respectively; eq C p_eq and V eq These represent the equivalent swept area, wind energy utilization rate, and equivalent wind speed, respectively.

[0158] The equivalent calculations for the generator parameters are as follows:

[0159]

[0160] In the formula: P i S i R i X i and H i Let P represent the active power, rated capacity, stator resistance, stator reactance, and inertial time constant of the i-th generator in the wind farm, respectively; eq S eq R eq X eq and H eq The equivalent active power, rated capacity, stator resistance, stator reactance, and inertial time constant are represented respectively. Once the equivalent parameters are obtained, the equivalent modeling of the wind farm is completed.

[0161] The simplified model structure of the wind turbine based on the equivalent transfer function is as follows: Figure 2 As shown; the output power (captured power, rotor speed, grid-connected power) of the simplified model after equivalent modeling of the wind farm is compared with that of the detailed model. Figure 3-5 As shown.

[0162] The above are merely preferred embodiments of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principle of the present invention should be considered within the scope of protection of the present invention.

Claims

1. An efficient wind farm modeling method based on transfer function and aggregation equivalence, characterized in that, Includes the following steps: S1: Establish a mathematical model for the wind turbine grid connection system; S2: According to the given order reduction principle, the mathematical model of the wind turbine grid-connected system is reduced in order based on the equivalent transfer function; the order reduction principle includes: A. Ignore the dynamic response of the dq-axis current in the PMSG, that is, ignore the dynamic response of the PMSG under the electromagnetic time scale; B. Ignore mechanical damping and electromagnetic losses in PMSG; C. Ignore the dynamic response of the switches, the dynamic response of each flux linkage, the dynamic response of the phase-locked loop, and the dynamic response of the inner current loop in the full-power converter; D. The full-power converter adopts qd-axis decoupled control, so active power control and reactive power control are separated, and DC side voltage control is ignored. The output variable of the equivalent simplified model of the wind turbine is mechanical torque. T m The input variable is wind speed. v Rotor speed ω m and propeller pitch angle β Based on reduction principles A and B, the rotor dynamic equation expression in PMSG is simplified to: The output variable of the PMSG equivalent simplified model is the rotor speed. ω m The input variable is mechanical torque. T m and electromagnetic torque T e ; Based on the equivalent transfer function, the transfer function between speed and torque is: In the formula, H Let be the inertial time constant of the PMSG; s be the complex frequency. In the simplified model of the full-power converter, based on the order reduction principles C and D, a first-order inertial element is used to replace both the machine-side converter and the grid-side converter; the simplified wind turbine output power is: In the formula, P wind This refers to the output power of the wind turbine generator; P wind_ref This is a reference value for the output power of the wind turbine. T w The power control time constants associated with the generator-side converter and the grid-side converter; s It is a complex frequency; The above power is achieved by a pitch angle control system while ensuring the rotor speed does not exceed the rated value. The pitch angle control system is based on a transfer function that is equivalent to a first-order inertial element. In the formula, G(s) The transfer function for pitch servo; T β It is a time constant; s It is a complex frequency; S3: Analyze the connection methods of each wind turbine and the power collection system in the wind farm, and simplify the power collection line using an equivalent line loss model; then, based on the reduced-order mathematical model of the wind turbine grid connection system, classify and aggregate the wind turbines in the wind farm according to the wake effect, and perform capacity-weighted equivalent calculations on the aggregated parameters of the wind turbines, thereby realizing the reduced-order equivalent modeling of the wind farm.

2. The effective wind farm modeling method based on transfer function and aggregate equivalence as described in claim 1, characterized in that: In step S1, the mathematical model of the wind turbine grid-connected system adopts the permanent magnet synchronous power generation system model. The permanent magnet synchronous power generation system model includes: wind turbine, drive shaft, permanent magnet synchronous motor (PMSG), full-power converter and corresponding control system model; the wind turbine captures wind energy and converts it into rotor kinetic energy. The wind turbine rotor converts the kinetic energy into electrical energy through the drive shaft to the PMSG. The three-phase current output by the PMSG is connected to the grid and outputs power through the full-power converter.

3. The effective wind farm modeling method based on transfer function and aggregate equivalence according to claim 2, characterized in that: Step S1 requires deriving the mechanical power and mechanical torque of the wind turbine, as well as the rotor dynamic equation expression of the permanent magnet synchronous motor; the mechanical power obtained by the wind turbine from capturing wind energy is: ① In the formula, ρ air density; S=πR 2 It is the scanned area of ​​the wind turbine; R The radius of the wind turbine blade; v Wind speed; C p The wind energy utilization coefficient is the value of the tip speed ratio. λ With pitch angle β The function; For the mechanical torque of the wind turbine, This refers to the wind turbine's rotational speed. λ The expression is: ② From equations ① and ②, the mechanical torque of the wind turbine can be obtained as follows: ③ in, C p It can be represented as: In the formula, α As an intermediate variable; When the wind turbine is operating under maximum power point tracking (MPPT) control, the output power can be expressed as: ④ C p,opt To achieve the optimal wind energy utilization coefficient, k opt These are parameters related to the characteristics of the wind turbine itself; From equations ②, ③, and ④, the optimal output mechanical torque of the wind turbine can be obtained as follows: The function of the PMSG is to convert the wind energy captured by the wind turbine into electrical energy through electromagnetic effects. Ignoring its shaft dynamic effects, the rotor dynamic equation expression is: In the formula For the electromagnetic torque of a permanent magnet synchronous motor, D is the mechanical damping coefficient of PMSG.

4. The effective wind farm modeling method based on transfer function and aggregate equivalence as described in claim 3, characterized in that: The process of simplifying the collector line using an equivalent line loss model in step S3 includes: set up S 1. S 2、…、 S n These represent the output power of each wind turbine unit; U 1. U 2、…、 U n These are the terminal voltages of each wind turbine; the collector line impedances between two adjacent wind turbines are respectively... Z 1. Z 2、…、 Z n ; When performing equivalent calculations on the collector lines, the wind turbine and its transformer are simplified as a single current source. Assuming each wind turbine has the same output, the current phasors they inject into the collector lines are equal. Therefore, the losses on each segment of the collector lines in the wind turbine group are as follows: The total loss of the collector line can be expressed as: The equivalent wind turbine capacity is: The current injected into the transmission line by the equivalent wind turbine generator is expressed as: The impedance of the equivalent transmission line of the wind turbine generator is used Z eq Therefore, the loss on this line is: For the equivalent value of the transmission line-to-ground capacitance, assuming the transmission line voltage remains stable during normal operation of the wind farm, the equivalent value of the transmission line-to-ground capacitance is calculated as follows: In the formula, B eq This is the equivalent capacitance to ground; B i For the first wind farm i The capacitance to ground of the line.

5. The effective wind farm modeling method based on transfer function and aggregate equivalence as described in claim 4, characterized in that: In step S3, the wind turbines within the wind farm are classified and aggregated based on the wake effect. The Jensen wake model is used to calculate the input wind speed of each turbine. Based on this assumption, the wind speed in both regions is constant at a certain distance from the wind turbine. According to the momentum theorem, the dimensionless axial velocity in the wake region of the wind turbine can be obtained. v c ’ for: In the formula, v c The axial velocity on the wake rotation axis; v Initial wind speed; C T This is the axial thrust coefficient of the wind turbine; k The wake attenuation coefficient is 0.075 for the upstream wind turbine and 0.11 for the downstream wind turbine when the two wind turbines are arranged in series. X This represents the axial distance from a point downstream to the wind turbine plane. R X Let be the wake radius, when X When it is 0, its value is the radius of the wind turbine blade. R ; Based on the connection status and geographical location of each wind turbine, the initial wind speed and wind direction are first collected, the groups are divided according to the connection method, the number of wind turbines in each group is determined, and then the input wind speed of each turbine is calculated according to the wake model mentioned above. Then, the capacity-weighted method was used to perform equivalent calculations on the parameters of each loop.

6. The effective wind farm modeling method based on transfer function and aggregate equivalence as described in claim 5, characterized in that: The capacity-weighted method calculates the wind turbine parameters and generator parameters proportionally based on the proportion of each wind turbine's capacity in the total wind turbine capacity. The proportion of each wind turbine's capacity in the total wind turbine capacity is a weight. δ i The calculation equation is as follows: In the formula, δ i These are the weighting coefficients for the capacity-weighted method; S i For the first wind farm i The capacity of the typhoon generator set; n This represents the total number of wind turbines in the wind farm. According to weights δ i The equivalent parameters of the wind turbine can be calculated as follows: In the formula, A i , C p_i and V i They represent the first in the wind farm. i The swept area, wind energy utilization rate, and captured wind speed of a typhoon turbine; A eq , C p_eq and V eq These represent the equivalent swept area, wind energy utilization rate, and equivalent wind speed, respectively. The equivalent calculations for the generator parameters are as follows: In the formula: P i , S i , R i , X i and H i They represent the first in the wind farm. i The active power, rated capacity, stator resistance, stator reactance, and inertial time constant of the generator; P eq , , R eq , X eq and H eq These represent the equivalent active power, rated capacity, stator resistance, stator reactance, and inertial time constant, respectively; once the equivalent parameters are obtained, the equivalent modeling of the wind farm is complete.

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