CN110968958B - Wind power plant equivalence modeling method based on single-machine equivalence and selection modal analysis - Google Patents

Abstract

The invention discloses a wind power plant equivalence modeling method based on single machine equivalence and selection modal analysis, which is characterized in that more than one double-fed fan in a wind power plant is subjected to single machine equivalent polymerization to form one double-fed fan; modeling a dynamic mathematical model of a doubly-fed fan of a wind power plant to obtain a full-order mathematical model; equating the full-order mathematical model to be an aggregation model; then, reducing the equivalent doubly-fed wind turbine by selecting a modal analysis order reduction method; the method solves the problems that the dynamic equivalence method for the wind power plant in the prior art has some limitations on the stability research of a fan grid-connected system, and the physical meaning of a variable cannot be guaranteed not to change; the technical problems that the calculation efficiency is low and the like are caused by the fact that the system order is possibly too high only by using the single equivalent polymerization method.

Description

Wind power plant equivalence modeling method based on single-machine equivalence and selection modal analysis

Technical Field

The invention belongs to the technical field of power systems, and particularly relates to a wind power plant equivalence modeling method based on single-machine equivalence and selection modal analysis.

Background

Due to the fact that the problem of energy shortage and the problem of environmental pollution are increasingly serious due to the steady increase of global energy consumption in recent decades, new energy power generation, particularly wind power generation, is more and more emphasized, and plays an increasingly important role in a power system. Due to the randomness of wind energy and the uncertainty of accessing the power grid, the research on the stability of the wind turbine accessing the power grid gradually becomes a focus. The method has important significance for reasonably modeling the wind power plant for researching the dynamic characteristics of the grid connection of the wind power plant. The dynamic equivalence method of the wind power plant is mainly divided into two types according to whether a single machine structure is reserved: one is a polymerization process and the other is a reduction process. The stability research on the fan grid-connected system has some limitations, and the physical meaning of the variable cannot be guaranteed not to change; the technical problems that the calculation efficiency is low and the like are caused by the fact that the system order is possibly too high only by using the single equivalent polymerization method.

Disclosure of Invention

The technical problem to be solved by the invention is as follows: the wind power plant equivalence modeling method based on single-machine equivalence and selection modal analysis is provided to solve the problem that a dynamic equivalence method of a wind power plant has some limitations for stability research of a fan grid-connected system, and the physical meaning of variables cannot be guaranteed not to change; the technical problems that the calculation efficiency is low and the like are caused by the fact that the system order is possibly too high only by using the single equivalent polymerization method.

The technical scheme of the invention is as follows:

the method comprises the steps that more than one double-fed fan in the wind power plant is subjected to single-machine equivalent polymerization to form one double-fed fan; modeling a dynamic mathematical model of a doubly-fed fan of a wind power plant to obtain a full-order mathematical model; equating the full-order mathematical model to be an aggregation model; and then reducing the equivalent doubly-fed wind turbine by selecting a modal analysis order reduction method.

The modeling of the dynamic mathematical model of the doubly-fed wind turbine of the wind power plant comprises a transmission system model, a generator model, a current converter model and an external network model;

the model of the wind turbine is the transmission relation between wind energy and mechanical energy:

in the formula, P_tMechanical power output by the wind turbine is kW; λ is tip speed ratio, θ is pitch angle; v. of_windIs the wind speed, in m/s; c_pIs a dimensionless wind energy utilization coefficient; a. the_wtIs the area swept by the blade in m²(ii) a ρ is the air density in kg/m³；

The transmission system is slowed down into a single mass model, and the dynamic equation of the single mass model is

In the formula: omega_s、ω_rThe synchronous rotation speed of the generator and the rotation speed of the rotor are respectively. H_DIs the wind turbine inertia time constant, T_mFor mechanical torque, T_eIs generator electrical torque, E'_qDAnd E'_dDTransient rotor voltages, I, of the q-axis and d-axis, respectively_qsAnd I_dsQ-axis current and d-axis current of the generator stator side, respectively;

the generator adopts a two-axis model, adopts a dq coordinate system with q axis leading d axis by 90 degrees, and defines the following variables under the coordinate system:

in formula (II)'₀Is the transient open-circuit time constant; r_rIs the rotor resistance; x'_sIs a transient reactance; x_mIs the mutual impedance between the stator and the rotor; x_sIs a stator reactance; x_rIs the rotor reactance; psi_drIs a rotor d-axis flux linkage; psi_qrA rotor q-axis flux linkage; omega_sIs the synchronous speed.

Neglecting the change process of the stator flux linkage, the simplified model of the doubly-fed induction fan is as follows:

in the formula: r_sIs a stator resistor; i is_drIs the rotor d-axis current; i is_qrIs the rotor q-axis current;

V_Dto be fixedA sub terminal voltage; v_drAnd V_qrRotor d-axis and q-axis voltages, respectively; p_genAnd Q_genRespectively active power and reactive power to the grid side.

The rotor side control design of the converter is based on active output and reactive output decoupling; voltage V on the stator side when the d-axis is oriented for stator flux linkage_qs＝V_D，V _ds0 and the control system uses the most common proportional-integral (P-I) control, the model is:

wherein x₁Is the active outer loop control integral state quantity, K_I1Is the active outer loop control integral coefficient, K_P1Is the active outer loop control proportionality coefficient, x₂Is the current inner loop controlling the integral state quantity, K_I2Is the current inner loop control integral coefficient, K_P2Is the current inner loop control proportionality coefficient, x₃Is a reactive outer loop control integral state quantity, K_I3Is the reactive outer loop control integral coefficient, K_P3Is the reactive outer loop control proportionality coefficient, x₄Is the current inner loop controlling the integral state quantity, K_I4Is the current inner loop control integral coefficient, K_P4Is the current inner loop control proportionality coefficient; p_refAs active power reference value, Q_refIs an active power reference value;

network equation between generator side and grid: the generator side is also connected with a load through impedance; the network side balance equation of the system is expressed as

In the formula R₁And X₁Respectively a resistor and a reactor of a transmission line connected with an infinite bus; r₂And X₂Respectively a resistance and a reactance of a transmission line connected with the load end; v is the voltage of the infinite bus, V_DAnd theta_DAre respectively generator machinesVoltage and phase angle of the terminal; v_LAnd theta_LRespectively a load end voltage and a phase angle; p_LAnd Q_LLoad active power and reactive power respectively; i is_aAnd I_bThe current of an infinite bus is injected into the lower machine end of the synchronous coordinate system; i is_pAnd I_qIs the current injected into the network at the lower end of the synchronous coordinate system and is expressed as follows

In the formula I_GFor current at the injector side of the grid-connected converter, P_rThe active power at the injector end of the grid-connected converter is obtained.

The method for equating the full order mathematical model to the aggregation model comprises the following steps:

in a wind farm, the total mechanical power is

Wherein ng is the number of wind generating sets in the wind power plant,

for the mechanical power of each fan it is necessary,

is the total equivalent mechanical power.

In a steady state, the wind energy utilization factor of each fan is the largest regardless of the wind speed, and therefore,

while assuming theta ⁱ0; by using the definition of the wind energy utilization factor,

the mechanical power is then

Considering that the blade length of an equivalent wind turbine is the same as that of a single wind turbine; meanwhile, it is assumed that there is an equivalent active controller, so that the equivalent active controller is in a steady state

When the equivalent wind energy is

Defining a new equivalent wind speed

Is composed of

Taking into account the equivalent angular velocity

Having the same speed range as the angular speed of the individual wind turbine units, the torque equation can be expressed as

In the formula: b is^e＝ng×B；

Obtaining the mechanical power and the torque of the polymerization model by using the equivalent wind speed; treating the equivalent power as the sum of the powers of the single fans; then keeping equivalent variables and parameters; the active and reactive power references correspond to the sum of all wind turbine reference values, expressed as

Wherein: c^eNg × C, an equivalent coefficient of a prescribed equivalent power reference value;

in the equation of motion of the rotor

And

is shown as

Equivalent stator current of

In the equivalent model, the equivalent voltage has the same order of magnitude as the voltage in each individual wind turbine, and the current is ng times; the total power injected into the rotor circuit is

Equivalent rotor current of

Model relating to equivalent controllers

By the polymerization of the monomer(s) in the presence of a catalyst,

are all amplified by ng times;

therefore, the temperature of the molten metal is controlled,

at the time of the steady-state,

the polymerization model has the same order of magnitude as a single fan;

all fans are connected in parallel and equivalent resistance and equivalent reactance parameters are calculated; obtaining equivalent impedance Z of wind power plant at PCC point when wind turbine is short-circuited_equiv(ii) a The equivalent fan model is connected with an external network through an equivalent circuit; series impedance of equivalent circuit equal to Z_equiv。

The method for reducing the equivalent doubly-fed wind turbine by selecting the order reduction method of modal analysis comprises the following steps:

selecting dominant mode

The first step is to select a dominant mode, namely a dominant pole or a dominant characteristic value, and select a mode which is closest to an imaginary axis in the left half plane of the complex plane as the dominant mode;

② determining the relevant status

The participation matrix P is used to reflect the relationship between modalities and state variables, which is defined as follows:

element P in the participation matrix P_ki＝u_kiv_kiAs an engagement factor, it can be used to measure the degree of mutual engagement between the ith modality and the kth state variable;

structure order reducing system

Let R be equal to R^r×1In order to be a function of the relevant state variable,

in order to be an irrelevant state variable,

thus linearizing the system

Can be expressed as

The irrelevant state subsystem can be expressed as

Wherein y is_zAn output of the subsystem for an unrelated state; the relevant state subsystem is represented as

The states and inputs of the uncorrelated state subsystems are z and r, respectively; for t ≧ t₀The analytical solution for z is:

the correlation state r can be represented as:

wherein λ is_iIs the ith dominant mode, v_iIs its corresponding feature vector; l_iIs a constant; then there are:

output y of uncorrelated state subsystems_zThe analytic solution of (c) is:

wherein, H (lambda)_i)＝A₁₂(λ_iI-A₂₂)-¹A₂₁Is the transfer function of the uncorrelated state subsystems;

the dynamic response of the uncorrelated state subsystems to the correlated state r is represented as:

y_z＝M₀r

M₀a sufficient condition exists that rank (V)_h) H; if and only if rank (V)_h) When h is r, M₀There is a unique solution; finally, the following reduced order system is obtained:

in the formula, A_r＝A₁₁+M₀；

For an input-output system, the following division is made

Obtaining a reduced order model (A)_r,B_r,C_r,D_r)。

The invention has the beneficial effects that:

the invention establishes a full-order model of the wind turbine, the drive train, the generator, the inverter and their external network. Firstly, a polymerization model differential-algebraic equation set is established according to a full-order mathematical model of the whole system. The aggregation model is based on the idea of wind power plant single machine equivalence. Then, further performing order reduction analysis on the polymerization model by using a method of selecting modal analysis, and enabling the order reduction analysis to be equivalent to a first-order model, wherein the method not only retains the physical meaning of the original variable, but also has strong applicability and flexibility; and finally, on the premise of not losing precision, by carrying out aggregation and order reduction analysis on the wind power plant, the method can greatly reduce the model order of the system and improve the calculation efficiency.

The invention has the advantages that: the method has the advantages that the wind power plant is subjected to single-machine equivalence and equivalent single-machine reduction, the physical meaning of the original variable is reserved, and the method has strong applicability and flexibility. Compared with a full-order model, the order of the model is greatly reduced, and the calculation efficiency is improved. And the aggregation model can restore the dynamic characteristics of the wind power plant with certain precision.

The method solves the problems that the dynamic equivalence method for the wind power plant in the prior art has some limitations on the stability research of a fan grid-connected system, and the physical meaning of a variable cannot be guaranteed not to change; the technical problems that the calculation efficiency is low and the like are caused by the fact that the system order is possibly too high only by using the single equivalent polymerization method.

Drawings

FIG. 1 is a graph of wind speed and equivalent speed for each fan in an embodiment;

FIG. 2 is a graph illustrating the output power of each fan in an exemplary embodiment;

FIG. 3 is a sum of active power of an equivalent fan and actual 10 fan outputs in an embodiment;

FIG. 4 is a diagram illustrating a comparison of model orders in an embodiment;

FIG. 5 illustrates exemplary system feature values in accordance with certain embodiments.

Detailed Description

A wind power plant equivalence modeling method based on single machine equivalence and selection modal analysis is characterized in that a plurality of double-fed fans in a wind power plant are subjected to single machine equivalent aggregation to form one double-fed fan, and then the equivalence double-fed fan is subjected to order reduction through an order reduction method of the selection modal analysis.

A double-fed-fan wind power plant-based aggregation reduced-order analysis method is characterized by comprising the following steps:

(A) the dynamic mathematical model modeling of the doubly-fed wind turbine of the wind power plant comprises a transmission system model, a generator model, a current converter model and an external network model.

The model of the wind turbine is the transmission relationship between wind energy and mechanical energy, and the transmission relationship comprises the following steps:

in the formula, P_tIs the mechanical power output by the wind turbine in kW. λ is tip speed ratio, θ is pitch angle; v. of_windIs the wind speed in m/s. C_pIs a dimensionless wind energy utilization coefficient. A. the_wtIs the area swept by the blade in m². ρ is the air density in kg/m³。

② the driveline is typically slowed down to a single mass model. The dynamic equation of the single mass model is

In the formula: omega_s、ω_rThe synchronous rotation speed of the generator and the rotation speed of the rotor are respectively. H_DIs the wind turbine inertia time constant, T_mFor mechanical torque, T_eIs generator electrical torque, E'_qDAnd E'_dDTransient rotor voltages, I, of the q-axis and d-axis, respectively_qsAnd I_dsQ-axis current and d-axis current of the generator stator side, respectively;

thirdly, the generator adopts a two-axis model, adopts a dq coordinate system with q axis leading d axis by 90 degrees, and defines the following variables under the coordinate system:

in formula (II)'₀Is the transient open-circuit time constant; r_rIs the rotor resistance; x'_sIs a transient reactance; x_mIs the mutual impedance between the stator and the rotor; x_sIs a stator reactance; x_rIs the rotor reactance; psi_drIs a rotor d-axis flux linkage; psi_qrA rotor q-axis flux linkage; omega_sIs the synchronous speed.

Neglecting the change process of the stator flux linkage, the simplified model of the doubly-fed induction fan is as follows:

in the formula: r_sIs a stator resistor; i is_drIs the rotor d-axis current; i is_qrIs the rotor q-axis current; v_DIs the stator terminal voltage; v_drAnd V_qrRotor d-axis and q-axis voltages, respectively; p_genAnd Q_genRespectively active power and reactive power to the grid side.

And fourthly, decoupling based on active output and reactive output in the control design of the rotor side of the converter. When the d axis isStator side voltage V when stator flux linkage is oriented_qs＝V_D，V _ds0 and the control system uses the most common proportional-integral (P-I) control, which is modeled as:

wherein x₁Is the active outer loop control integral state quantity, K_I1Is the active outer loop control integral coefficient, K_P1Is the active outer loop control proportionality coefficient, x₂Is the current inner loop controlling the integral state quantity, K_I2Is the current inner loop control integral coefficient, K_P2Is the current inner loop control proportionality coefficient, x₃Is a reactive outer loop control integral state quantity, K_I3Is the reactive outer loop control integral coefficient, K_P3Is the reactive outer loop control proportionality coefficient, x₄Is the current inner loop controlling the integral state quantity, K_I4Is the current inner loop control integral coefficient, K_P4Is the current inner loop control proportionality coefficient; p_refAs active power reference value, Q_refIs an active power reference value.

A network equation between the generator side and the power grid: the generator side is also connected to a load via an impedance. The network side balance equation of the system can be expressed as

In the formula R₁And X₁Respectively a resistor and a reactor of a transmission line connected with an infinite bus; r₂And X₂Respectively a resistance and a reactance of a transmission line connected with the load end; v is the voltage of the infinite bus, V_DAnd theta_DThe voltage and the phase angle of the generator terminal are respectively; v_LAnd theta_LRespectively a load end voltage and a phase angle; p_LAnd Q_LLoad active power and reactive power respectively; i is_aAnd I_bThe current of an infinite bus is injected into the lower machine end of the synchronous coordinate system; i is_pAnd I_qIs the current injected into the network at the lower end of the synchronous coordinate system and is expressed as follows

In the formula I_GCurrent at the injector end of the grid-connected converter; p_rThe active power at the injector end of the grid-connected converter is obtained.

(B) The full-order mathematical model is equivalent to the aggregate model. In a wind farm, the total mechanical power is

Wherein ng is the number of wind generating sets in the wind power plant,

for the mechanical power of each fan it is necessary,

is the total equivalent mechanical power.

To obtain an equivalent or aggregate model, this total power is defined as the mechanical power applied to the shaft of the equivalent generator or to the equivalent generator. Generally, the aggregate model technique is based on the idea of increasing the power of a single wind turbine.

All wind power plants are considered to have the same parameters and they do not necessarily operate at the same wind speed. Since the speed control maximizes the penetration of wind energy, the wind energy utilization coefficient is also maximized. In a steady state, the wind energy utilization factor of each wind turbine is the largest regardless of the wind speed. Therefore, the temperature of the molten metal is controlled,

while assuming thetaⁱ0 (wind speed remains within its limits, no tilt angle control is needed). By using the definition of the wind energy utilization factor,

the mechanical power is then

Consider that the blade length of an equivalent wind turbine is the same as a single wind turbine. Meanwhile, it is assumed that there is an equivalent active controller, so that the equivalent active controller is in a steady state

When the equivalent wind energy is

Defining a new equivalent wind speed

Is composed of

Therefore, the temperature of the molten metal is controlled,

furthermore, the equivalent angular velocity is taken into account

Having the same speed range as the angular speed of the individual wind turbine units, e.g.

The torque equation can be expressed as

Wherein: b is^e＝ng×B。

Currently, with equivalent wind speed, the mechanical power and torque of the aggregate model have been derived. To determine all the parameters of the aggregate model, the equivalent power is considered as the sum of the powers of the individual fans in the same way as before. Then, equivalent variables and parameters are kept equal. The polymerization process chosen is similar to that used for the mixed speed fan. The active and reactive power references correspond to the sum of all wind turbine reference values, expressed as

Wherein: c^eNg × C is an equivalent coefficient of a prescribed equivalent power reference value.

Then in the equation of motion of the rotor

And

can be expressed as

Wherein the equivalent stator current is

In the equivalent model, the equivalent voltage is of the same order of magnitude as the voltage in each individual wind turbine, and the current is approximately ng times. Total power injected into the rotor circuit is

Wherein the equivalent rotor current is

A model associated with an equivalent controller is studied.

In the formula: by the polymerization of the monomer(s) in the presence of a catalyst,

are all amplified by ng times. Therefore, the temperature of the molten metal is controlled,

it is worth noting that, at steady state,

the polymerization model is of the same order of magnitude as a single fan.

Finally, by observing an algebraic equation, all fans need to be connected in parallel and the equivalent resistance and equivalent reactance parameters need to be calculated. Considering an external network connected with wind power, and obtaining equivalent impedance Z of the wind power plant at a PCC point when a fan is in short circuit_equiv. And then, the equivalent fan model is connected with an external network through an equivalent line. Series impedance of equivalent circuit equal to Z_equiv。

In summary, the following parameters need to be scaled:

all other parameters are equal to a single fan parameter.

(C) And carrying out SMA (shape memory alloy) order reduction treatment on the wind power plant aggregation model.

SMA is a set of comprehensive algorithms for modeling, analyzing and controlling a linear dynamics system. In this context, SMA is used to reduce the order of the aggregated fan stand-alone model, and its core idea is to select the state variables most relevant to the system dominant mode, and intercept these as the reserved state variables, thereby reducing the order of the system. This is briefly described below.

Selecting dominant mode

The first step of SMA is to select the so-called dominant mode, i.e. the dominant pole or dominant eigenvalue, here the mode in the left half-plane of the complex plane closest to the imaginary axis is selected as the dominant mode.

② determining the relevant status

The participation matrix P is used to reflect the relationship between modalities and state variables, which is defined as follows:

element P in the participation matrix P_ki＝u_kiv_kiCan be used to measure the participation factorThe degree of mutual engagement between the ith modality and the kth state variable.

Structure order reducing system

Let R be equal to R^r×1In order to be a function of the relevant state variable,

in order to be an irrelevant state variable,

thus linearizing the system

Can be expressed as

The irrelevant state subsystem can be expressed as

Wherein y is_zIs the output of the uncorrelated state subsystems. The associated state subsystem may be represented as

The states and inputs of the uncorrelated state subsystems are z and r, respectively. For t ≧ t₀The analytical solution for z is:

the correlation state r can be represented as:

wherein λ is_iIs the ith dominant mode, v_iIs it corresponds toThe feature vector of (2). Note that v_iOnly this part of the relevant state is considered. l_iIs a constant. Substituting equation 72 into equation 71, there are:

output y of uncorrelated state subsystems_zThe analytic solution of (c) is:

wherein, H (lambda)_i)＝A₁₂(λ_iI-A₂₂)^-1A₂₁Is the transfer function of the uncorrelated state subsystems.

The above constructively demonstrates that the dynamic response of an irrelevant state subsystem to a relevant state r can be expressed as:

y_z＝M₀r (38)

here, M₀A sufficient condition exists that rank (V)_h) H; if and only if rank (V)_h) When h is r, M₀There is a unique solution. The following reduced order system is finally obtained:

in the formula, A_r＝A₁₁+M₀；

The above results in a reduced order model of the autonomous system, for which the following divisions can be made.

Similar to A in autonomous system_rBy the method of construction of (A), a reduced order model (A) can be obtained_r,B_r,C_r,D_r). Wherein,

the working principle of the invention is as follows: a full-order model of the wind turbine, the drive train, the generator, the converter and its external network is considered. Firstly, a polymerization model differential-algebraic equation set is established according to a full-order mathematical model of the whole system. The aggregation model is based on the idea of wind power plant single machine equivalence. And then, further carrying out reduced order analysis on the polymerization model by using a method of selecting modal analysis, and enabling the polymerization model to be equivalent to a first-order model. . And finally, on the premise of not losing precision, by carrying out aggregation and order reduction analysis on the wind power plant, the method can greatly reduce the model order of the system and improve the calculation efficiency.

Firstly, equating the parameters of the fans, and equating 10 fans of the wind power plant to be a single fan, wherein the wind speed accepted by the 10 fans is as follows

As shown, the dotted line is equivalent wind speed, and the output active power of each fan is as shown.

After the wind power plant is subjected to equivalence single-machine analysis, the order reduction analysis is carried out on the single-machine model by adopting the selected mode analysis method, the equivalent wind speed is used as an input variable of the system, the emitted active power is used as an output variable of the system, and the following linearized model can be obtained by using a Jacobian matrix J of the system at a balance point:

the system is subjected to small interference stability analysis at a given specific working point, and the solution of the characteristic value is shown in figure 5

By analyzing 7 characteristic values, the lambda can be obviously seen₅The absolute value is the smallest compared to the other 6 eigenvalues, which are closer to the imaginary axis, for which purpose λ is chosen when the order reduction is performed₅As the dominant mode.

For lambda₅Is analyzed to obtain the state variable omega most relevant to the factor_rThus, the characteristic value of the correlation is λ₅And the associated state variable is ω_rConstructing a reduced order system by rearranging the state variables, wherein the reserved state variables are arranged to the top

Wherein Z ═ E'_qD，E′_dD，Δx₁，Δx₂，Δx₃，Δx₄]^TAre uncorrelated state variables. Consider z (t) ═ λ₅I-A₂₂)^-1A₂₁Δω_rReducing the model

ΔP_gen＝α_PΔω_r (47)

Wherein

Further obtain

Wherein

At steady state, the output success can be expressed as

When the input wind speed of the system is as shown in fig. 1, fig. 3 shows the active power output by the system by adopting a full-order model, an aggregation model and a reduced-order model of a wind farm, and it can be seen that the aggregation model and the reduced-order model basically restore the dynamic behavior of the original system with a certain precision.

Fig. 4 is a comparison graph of orders of three models, in this example, a full-order model of a wind farm composed of 10 fans is 70 orders, after an aggregation equivalence is a single-machine model, the model order is reduced to 7 orders, and then the order reduction is performed by a method of selecting modal analysis, and the model order after the order reduction is 1 order, so that the model order is greatly reduced and the complexity of analysis problems is simplified while the steady-state and transient-state behaviors of the system are reduced with a certain precision.

Claims (2)

1. A wind power plant equivalence modeling method based on single-machine equivalence and selection modal analysis is characterized by comprising the following steps: the method comprises the steps that more than one double-fed fan in the wind power plant is subjected to single-machine equivalent polymerization to form one double-fed fan; modeling a dynamic mathematical model of a doubly-fed fan of a wind power plant to obtain a full-order mathematical model; equating the full-order mathematical model to be an aggregation model; then, reducing the equivalent doubly-fed wind turbine by selecting a modal analysis order reduction method;

the modeling of the dynamic mathematical model of the doubly-fed wind turbine of the wind power plant comprises a transmission system model, a generator model, a current converter model and an external network model;

the model of the wind turbine is the transmission relation between wind energy and mechanical energy:

in the formula, P_tMechanical power output by the wind turbine is kW; λ is tip speed ratio, θ is pitch angle; v. of_windIs the wind speed, in m/s; c_pIs a dimensionless wind energy utilization coefficient; a. the_wtIs the area swept by the blade in m²(ii) a ρ is the air density in kg/m³(ii) a The transmission system is slowed down into a single mass model, and the dynamic equation of the single mass model is

In the formula: omega_s、ω_rThe synchronous rotating speed of the generator and the rotating speed of the rotor are respectively set; h_DIs the wind turbine inertia time constant, T_mFor mechanical torque, T_eIs generator electrical torque, E'_qDAnd E'_dDTransient rotor voltages, I, of the q-axis and d-axis, respectively_qsAnd I_dsQ-axis current and d-axis current of the generator stator side, respectively;

the generator adopts a two-axis model, adopts a dq coordinate system with q axis leading d axis by 90 degrees, and defines the following variables under the coordinate system:

in formula (II)'₀Is the transient open-circuit time constant; r_rIs the rotor resistance; x'_sIs a transient reactance; x_mIs the mutual impedance between the stator and the rotor; x_sIs a stator reactance; x_rIs the rotor reactance; psi_drIs a rotor d-axis flux linkage; psi_qrA rotor q-axis flux linkage; omega_sThe synchronous rotating speed is adopted;

neglecting the change process of the stator flux linkage, the simplified model of the doubly-fed induction fan is as follows:

in the formula: r_sIs a stator resistor; i is_drIs the rotor d-axis current; i is_qrIs the rotor q-axis current; v_DIs the stator terminal voltage; v_drAnd V_qrRotor d-axis and q-axis voltages, respectively; p_genAnd Q_genRespectively the active power and the reactive power transmitted to the power grid side;

the rotor side control design of the converter is based on active output and reactive output decoupling; voltage V on the stator side when the d-axis is oriented for stator flux linkage_qs＝V_D，V_ds0 and the control system uses the most common proportional-integral (P-I) control, the model is:

wherein x₁Is the active outer loop control integral state quantity, K_I1Is the active outer loop control integral coefficient, K_P1Is the active outer loop control proportionality coefficient, x₂Is the current inner loop controlling the integral state quantity, K_I2Is the current inner loop control integral coefficient, K_P2Is the current inner loop control proportionality coefficient, x₃Is a reactive outer loop controlIntegrating the state quantity, K_I3Is the reactive outer loop control integral coefficient, K_P3Is the reactive outer loop control proportionality coefficient, x₄Is the current inner loop controlling the integral state quantity, K_I4Is the current inner loop control integral coefficient, K_P4Is the current inner loop control proportionality coefficient; p_refAs active power reference value, Q_refAs active power reference value

Network equation between generator side and grid: the generator side is also connected with a load through impedance; the network side balance equation of the system is expressed as

In the formula R₁And X₁Respectively a resistor and a reactor of a transmission line connected with an infinite bus; r₂And X₂Respectively a resistance and a reactance of a transmission line connected with the load end; v is the voltage of the infinite bus, V_DAnd theta_DThe voltage and the phase angle of the generator terminal are respectively; v_LAnd theta_LRespectively a load end voltage and a phase angle; p_LAnd Q_LLoad active power and reactive power respectively; i is_aAnd I_bThe current of an infinite bus is injected into the lower machine end of the synchronous coordinate system; i is_pAnd I_qIs the current injected into the network at the lower end of the synchronous coordinate system and is expressed as follows

In the formula I_GFor current at the injector side of the grid-connected converter, P_rActive power at the injector end of the grid-connected converter;

the method for equating the full order mathematical model to the aggregation model comprises the following steps:

in a wind farm, the total mechanical power is

Wherein ng is the number of wind generating sets in the wind power plant,

for the mechanical power of each fan it is necessary,

is the total equivalent mechanical power;

in a steady state, the wind energy utilization factor of each fan is the largest regardless of the wind speed, and therefore,

while assuming thetaⁱ0; by using the definition of the wind energy utilization factor,

the mechanical power is then

Considering that the blade length of an equivalent wind turbine is the same as that of a single wind turbine; meanwhile, it is assumed that there is an equivalent active controller, so that the equivalent active controller is in a steady state

When the equivalent wind energy is

Defining a new equivalent wind speed

Is composed of

Taking into account the equivalent angular velocity

Having the same speed range as the angular speed of the individual wind turbine units, the torque equation can be expressed as

In the formula: b is^e＝ng×B；

Obtaining the mechanical power and the torque of the polymerization model by using the equivalent wind speed; treating the equivalent power as the sum of the powers of the single fans; then keeping equivalent variables and parameters; the active and reactive power references correspond to the sum of all wind turbine reference values, expressed as

Wherein: c^eNg × C, an equivalent coefficient of a prescribed equivalent power reference value;

in the equation of motion of the rotor

And

is shown as

Equivalent stator current of

In the equivalent model, the equivalent voltage has the same order of magnitude as the voltage in each individual wind turbine, and the current is ng times; the total power injected into the rotor circuit is

Equivalent rotor current of

Model relating to equivalent controllers

By the polymerization of the monomer(s) in the presence of a catalyst,

are all amplified by ng times;

therefore, the temperature of the molten metal is controlled,

at the time of the steady-state,

the polymerization model has the same order of magnitude as a single fan;

all fans are connected in parallel and equivalent resistance and equivalent reactance parameters are calculated; obtaining equivalent impedance Z of wind power plant at PCC point when wind turbine is short-circuited_equiv(ii) a The equivalent fan model is connected with an external network through an equivalent circuit; series impedance of equivalent circuit equal to Z_equiv。

2. The wind power plant equivalence modeling method based on stand-alone equivalence and selection modal analysis according to claim 1, characterized in that: the method for reducing the equivalent doubly-fed wind turbine by selecting the order reduction method of modal analysis comprises the following steps:

selecting dominant mode

The first step is to select a dominant mode, namely a dominant pole or a dominant characteristic value, and select a mode which is closest to an imaginary axis in the left half plane of the complex plane as the dominant mode;

② determining the relevant status

The participation matrix P is used to reflect the relationship between modalities and state variables, which is defined as follows:

element P in the participation matrix P_ki＝u_kiv_kiAs an engagement factor, it can be used to measure the degree of mutual engagement between the ith modality and the kth state variable;

structure order reducing system

Let R be equal to R^r×1For the relevant state variable, z ∈ R^(n-r)×1Are uncorrelated state variables, thus linearizing the system

Can be expressed as

The irrelevant state subsystem can be expressed as

Wherein y is_zAn output of the subsystem for an unrelated state; the relevant state subsystem is represented as

The states and inputs of the uncorrelated state subsystems are z and r, respectively; for t ≧ t₀The analytical solution for z is:

the correlation state r can be represented as:

wherein λ is_iIs the ith dominant mode, v_iIs its corresponding feature vector; l_iIs a constant; then there are:

output y of uncorrelated state subsystems_zThe analytic solution of (c) is:

wherein, H (lambda)_i)＝A₁₂(λ_iI-A₂₂)-¹A₂₁Is the transfer function of the uncorrelated state subsystems;

the dynamic response of the uncorrelated state subsystems to the correlated state r is represented as:

y_z＝M₀r

M₀a sufficient condition exists that rank (V)_h) H; if and only if rank (V)_h) When h is r, M₀There is a unique solution; finally, the following reduced order system is obtained:

in the formula, A_r＝A₁₁+M₀；

For an input-output system, the following division is made

Obtaining a reduced order model (A)_r,B_r,C_r,D_r)

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