CN109327043A - A method and system for modeling the inner loop control analytical transfer function of a grid-connected voltage source converter system - Google Patents

Abstract

The invention discloses a kind of voltage source converter grid-connected system inner loop controls to parse transfer function modeling method, and method includes: to establish to consider grid strength and the dynamic voltage source converter grid-connected system mathematical model of phaselocked loop based on the first assumed condition；Voltage source converter grid-connected system mathematical model is subjected to linearization process；Based on the second assumed condition, the simplification transmission function of the inner loop control of electric current is obtained；According to transmission function is simplified, the dynamic output phase expression formula of phaselocked loop is embodied, the inner loop control for establishing the voltage source converter grid-connected current for considering phaselocked loop dynamic effects parses transmission function；Parameter designing is and guided based on inner loop control parsing transfer function analysis voltage source converter grid-connected system inner loop control instability Mechanism.

Description

An analytical transfer function modeling method for the inner loop control of a grid-connected voltage source converter system law and system

technical field

The invention relates to the field of electric power technology, and more particularly, to a method and system for modeling an analytical transfer function of an inner loop control of a grid-connected system of a voltage source converter.

Background technique

Voltage source converters (Voltage Source Converters, VSCs) such as wind turbine converters, photovoltaic inverters, and flexible DCs have the risk of instability when they are connected to weak AC power grids. A set of voltage source converters VSC grid-connected systems are required. Modeling and stability analysis methods as tools for analysis and problem solving. At present, the modeling methods of voltage source converter VSC grid-connected system mainly include state space modeling method, input impedance method and complex torque method. These models are used to analyze the stability of voltage source converter VSC grid-connected system. The problems existing in the mechanism are as follows: the state space modeling method is too detailed, and can only use the characteristic root analysis and participation factor analysis to calculate the main participating variables of the instability mode, which cannot accurately explain the instability mechanism; the input impedance method model is too simplified, The instability of the system can only be judged by calculating the equivalent input impedance, but the instability mechanism cannot be revealed intuitively; the complex torque method model is too simplified, and the VSC system of the voltage source converter can only be divided into two subsystems, and the calculation of equivalent Synchronization and damping torque reveal the instability mechanism, but cannot intuitively explain the instability mechanism. The prior art cannot explain the instability mechanism of the voltage source converter VSC grid-connected system.

Therefore, there is a need for a technique to implement an analytical transfer function modeling method for the inner loop control of a grid-connected system of voltage source converters.

SUMMARY OF THE INVENTION

The technical solution of the present invention provides an analytical transfer function modeling method and system for the inner loop control of a grid-connected system of voltage source converters, so as to solve the problem of how to control the instability of the grid-connected system of voltage source converters, and how to guide the voltage The problem of designing the inner loop control parameters of the grid-connected system of source converters.

In order to solve the above problems, the present invention provides an analytical transfer function modeling method for the inner loop control of a grid-connected system of a voltage source converter, the method comprising:

Based on the first assumption, a mathematical model of the grid-connected system of voltage source converters considering grid strength and phase-locked loop dynamics is established;

Linearizing the mathematical model of the grid-connected system of the voltage source converter;

Based on the second assumption, the simplified transfer function of the inner loop control of the current is obtained; according to the simplified transfer function, the dynamic output phase expression of the phase-locked loop is embodied, and the voltage source commutation considering the dynamic influence of the phase-locked loop is established. Analytical transfer function of inner loop control of grid-connected current;

Based on the inner-loop control analytical transfer function, the instability mechanism of the inner-loop control of the grid-connected voltage source converter system is analyzed and the parameter design is guided.

Preferably, the first assumption condition is:

Only considering the strength of the electrical connection, the inner loop current feedback value can track the inner loop current reference value in real time, ignoring the filter capacitor of the common connection point, ignoring the modulation process delay and sampling delay, and ignoring the loss.

Preferably, the mathematical model of the grid-connected system includes:

Main circuit mathematical model, phase-locked loop dynamic mathematical model, inner loop control mathematical model.

Preferably, the main circuit mathematical model is:

The mathematical model of the main circuit part in the dq coordinate system is

Wherein, L _eq =L _t +L _arm /2, Re _eq =R _t +R _arm /2, L _ac =L _eq +L _g , R _ac =R _eq +R _g , s represents a differential operator, Re _eq is the equivalent resistance between the PCC bus and the valve side of the converter, L _eq is the equivalent inductance between the PCC bus and the valve side of the converter, L _t is the equivalent inductance of the AC grid transformer, and L _arm is the MMC bridge Arm inductance, R _t is the equivalent resistance of the AC grid transformer, L _ac is the equivalent inductance from the converter to the infinite system (ideal power supply), R _ac is the distance from the converter to the infinite system (ideal power supply) The equivalent resistance of , i _cd is the d-axis component of the inverter output current, i _cq is the q-axis component of the inverter output current, u _cd is the d-axis component of the equivalent output voltage of the inverter, and u _sd is the PCC bus voltage d shaft component, ω ₁ is the rated angular frequency, u _cq is the q-axis component of the equivalent output voltage of the converter, u _sq is the q-axis component of the PCC bus voltage, L _g is the equivalent inductance of the AC grid, and R _g is the q-axis component of the AC grid. Equivalent resistance, _ugd is the d-axis component of the voltage of the infinite system (ideal power supply), and _ugq is the d-axis component of the voltage of the infinite system (ideal power supply).

Preferably, the dynamic mathematical model of the phase-locked loop is:

in,

Among them, θ _PLL is the dynamic output phase of the phase-locked loop, θ _pll is the difference between the output phase of the phase-locked loop θ _PLL and ω ₁ t, ω ₁ t is the phase of the dq coordinate system whose initial phase is 0 and rotates at a constant angular velocity ω ₁ , k _{p_pll} is the proportional coefficient of the PLL dynamic proportional-integral controller, T _{i_pll} is the integral time constant of the PLL dynamic proportional-integral controller, u _sq is the q-axis component of the PCC bus voltage, ω1 is the rated angular velocity of the dq coordinate system, s is the pull Plass operator, G _pll is the phase-locked loop proportional-integral controller, is the q-axis component of the equivalent output voltage of the converter in the dq coordinate system of the control system.

Preferably, the dynamic mathematical model of the phase-locked loop is designed so that the parameter calculation formula of the second-order response characteristic is:

Among them, ω _pll is the dynamic design bandwidth of the phase-locked loop, the damping ratio ξ is 0.707, and u _sd0 is the steady-state value of the d-axis component of the PCC bus voltage.

Preferably, the inner loop control mathematical model is:

in,

in, is the reference value of the d-axis component of the inverter output voltage in the control system coordinate system, is the reference value of the q-axis component of the inverter output voltage in the control system coordinate system, is the value of the d-axis component of the inverter output voltage in the control system coordinate system, is the value of the q-axis component of the converter output voltage in the control system coordinate system, ω _f is the voltage filter bandwidth, T _f is the voltage filter time constant, ω _CL is the inner loop bandwidth, and k _{p_cl} is the inner loop PI controller ratio coefficient, T _{i_cl} inner loop controller proportional coefficient, integral time constant, G _f is PCC bus voltage filter, G _CL is inner loop proportional integral controller, is the reference value of the d-axis component of the converter output current in the control system coordinate system, is the reference value of the q-axis component of the inverter output current in the control system coordinate system, is the value of the d-axis component of the converter output current in the control system coordinate system, is the value of the q-axis component of the converter output current in the control system coordinate system, ω ₁ is the rated angular frequency, L _eq is the equivalent inductance between the PCC busbar and the valve side of the converter, and s is the Laplace operator , _Req is the equivalent resistance between the PCC busbar and the valve side of the converter.

Preferably, the mathematical model of the modulation process is:

Among them, G _d =e ^-sTd , T _d is the equivalent delay of the flexible direct control system, uc _cd is the d-axis component of the equivalent output voltage on the AC side of the converter, and u _cq is the equivalent output voltage q on the AC side of the converter shaft component, u _dc is the DC side voltage, U _dc0 is the steady-state value of the DC side voltage, θ _pll is the difference between the phase-locked loop output phase θ _PLL and ω ₁ t, is the reference value of the d-axis component of the inverter output voltage in the control system coordinate system, is the reference value of the q-axis component of the inverter output voltage in the coordinate system of the control system, and G _d is the delay simulation link.

Based on another aspect of the present invention, an analytical transfer function modeling system for inner loop control of a grid-connected voltage source converter is provided, the system comprising:

a first establishment unit, configured to establish a mathematical model of the grid-connected system of the voltage source converter that considers the grid strength and the dynamics of the phase-locked loop based on the first assumption;

a processing unit for linearizing the mathematical model of the grid-connected system of the voltage source converter;

The second establishment unit is configured to obtain a simplified transfer function of the inner loop control of the current based on the second assumption; The inner loop control analytical transfer function of the grid-connected current of the voltage source converter affected;

The design unit is used for analyzing the instability mechanism of the inner-loop control of the grid-connected system of the voltage source type converter based on the inner-loop control analytical transfer function and guiding parameter design.

Preferably, the first assumption condition is:

Only considering the strength of the electrical connection, the inner loop current feedback value can track the inner loop current reference value in real time, ignoring the filter capacitor of the common connection point, ignoring the modulation process delay and sampling delay, and ignoring the loss.

Preferably, the mathematical model of the grid-connected system includes:

Main circuit mathematical model, phase-locked loop dynamic mathematical model, inner loop control mathematical model.

Preferably, the main circuit mathematical model is:

The mathematical model of the main circuit part in the dq coordinate system is

Wherein, L _eq =L _t +L _arm /2, Re _eq =R _t +R _arm /2, L _ac =L _eq +L _g , R _ac =R _eq +R _g , s represents a differential operator, Re _eq is the equivalent resistance between the PCC bus and the valve side of the converter, L _eq is the equivalent inductance between the PCC bus and the valve side of the converter, L _t is the equivalent inductance of the AC grid transformer, and L _arm is the MMC bridge Arm inductance, R _t is the equivalent resistance of the AC grid transformer, L _ac is the equivalent inductance from the converter to the infinite system (ideal power supply), R _ac is the distance from the converter to the infinite system (ideal power supply) The equivalent resistance of , i _cd is the d-axis component of the inverter output current, i _cq is the q-axis component of the inverter output current, u _cd is the d-axis component of the equivalent output voltage of the inverter, and u _sd is the PCC bus voltage d shaft component, ω ₁ is the rated angular frequency, u _cq is the q-axis component of the equivalent output voltage of the converter, u _sq is the q-axis component of the PCC bus voltage, L _g is the equivalent inductance of the AC grid, and R _g is the q-axis component of the AC grid. Equivalent resistance, _ugd is the d-axis component of the voltage of the infinite system (ideal power supply), and _ugq is the d-axis component of the voltage of the infinite system (ideal power supply). Preferably, the dynamic mathematical model of the phase-locked loop is:

in,

Among them, θ _PLL is the dynamic output phase of the phase-locked loop, θ _pll is the difference between the phase-locked loop output phase θ _PLL and ω ₁ t, ω ₁ t is the phase of the dq coordinate system with the initial phase of 0 rotating at a constant angular velocity ω ₁ , k _{p_pll} is the proportional coefficient of the PLL dynamic proportional-integral controller, T _{i_pll} is the integral time constant of the PLL dynamic proportional-integral controller, u _sq is the q-axis component of the PCC bus voltage, ω ₁ is the rated angular velocity of the dq coordinate system, s is the Laplace operator, G _pll is the phase-locked loop proportional-integral controller, is the q-axis component of the equivalent output voltage of the converter in the dq coordinate system of the control system.

Preferably, the dynamic mathematical model of the phase-locked loop is designed so that the parameter calculation formula of the second-order response characteristic is:

Among them, ω _pll is the dynamic design bandwidth of the phase-locked loop, the damping ratio ξ is 0.707, and u _sd0 is the steady-state value of the d-axis component of the PCC bus voltage.

Preferably, the inner loop control mathematical model is:

in,

in, is the reference value of the d-axis component of the inverter output voltage in the control system coordinate system, is the reference value of the q-axis component of the inverter output voltage in the control system coordinate system, is the value of the d-axis component of the inverter output voltage in the control system coordinate system, is the value of the q-axis component of the converter output voltage in the control system coordinate system, ω _f is the voltage filter bandwidth, T _f is the voltage filter time constant, ω _CL is the inner loop bandwidth, and k _{p_cl} is the inner loop PI controller ratio coefficient, T _{i_cl} inner loop controller proportional coefficient, integral time constant, G _f is PCC bus voltage filter, G _CL is inner loop proportional integral controller, is the reference value of the d-axis component of the converter output current in the control system coordinate system, is the reference value of the q-axis component of the inverter output current in the control system coordinate system, is the value of the d-axis component of the converter output current in the control system coordinate system, is the value of the q-axis component of the converter output current in the control system coordinate system, ω ₁ is the rated angular frequency, L _eq is the equivalent inductance between the PCC busbar and the valve side of the converter, and s is the Laplace operator , _Req is the equivalent resistance between the PCC busbar and the valve side of the converter.

Preferably, the mathematical model of the modulation process is:

Among them, G _d =e ^-sTd , T _d is the equivalent delay of the flexible direct control system, uc _cd is the d-axis component of the equivalent output voltage on the AC side of the converter, and u _cq is the equivalent output voltage q on the AC side of the converter shaft component, u _dc is the DC side voltage, U _dc0 is the steady-state value of the DC side voltage, θ _pll is the difference between the phase-locked loop output phase θ _PLL and ω ₁ t, is the reference value of the d-axis component of the inverter output voltage in the control system coordinate system, is the reference value of the q-axis component of the inverter output voltage in the coordinate system of the control system, and G _d is the delay simulation link.

The technical scheme of the present invention provides a method and system for modeling the inner loop control analytical transfer function of a grid-connected system of a voltage source type converter. The mathematical model of the grid-connected system of the converter; the mathematical model of the grid-connected system of the voltage source converter is linearized; based on the second assumption, the simplified transfer function of the inner loop control of the current is obtained; according to the simplified transfer function, the The output phase expression of the phase loop dynamics is embodied, and the inner loop control analytical transfer function of the grid-connected current of the voltage source converter is established considering the dynamic influence of the phase locked loop; the voltage source converter is analyzed based on the inner loop control analytical transfer function. The inner loop of the grid-connected system controls the instability mechanism and guides the parameter design. A voltage source converter VSC grid-connected system analytical transfer function model with an appropriate degree of simplification established by the technical solution of the present invention can intuitively explain the instability mechanism of the voltage source converter VSC grid-connected system, and can also guide the voltage source converter VSC grid-connected system. The design of the inner loop control parameters of the inverter VSC grid-connected system has positive significance for guiding the design of the control strategy. The voltage source converter VSC grid-connected system mainly includes inner loop control and outer loop control. The inner loop control is more than ten times faster than the outer loop control. When studying the inner loop control, it can be assumed that the outer loop is in a steady state. The inner loop can be ignored to control the dynamic process.

Description of drawings

Exemplary embodiments of the present invention may be more fully understood by reference to the following drawings:

1 is a flowchart of a method for modeling an analytical transfer function of an inner loop control of a grid-connected system of a voltage source converter according to a preferred embodiment of the present invention;

2 is a structural diagram of a main circuit and a control system of a voltage source converter VSC grid-connected system according to a preferred embodiment of the present invention;

3 is a schematic diagram of the coordinate system of the main circuit and the control system according to the preferred embodiment of the present invention;

4 is a schematic diagram of a phase-locked loop dynamic PLL according to a preferred embodiment of the present invention;

5 is a schematic diagram of an inner loop current control block diagram according to a preferred embodiment of the present invention;

6 is a schematic block diagram of an analytical transfer function model for inner loop current control according to a preferred embodiment of the present invention;

7 is a schematic block diagram of an analytical transfer function model for inner loop current control according to a preferred embodiment of the present invention;

FIG. 8 is a structural diagram of an analytical transfer function modeling system for inner-loop control of a grid-connected voltage source converter system according to a preferred embodiment of the present invention.

Detailed ways

Exemplary embodiments of the present invention will now be described with reference to the accompanying drawings, however, the present invention may be embodied in many different forms and is not limited to the embodiments described herein, which are provided for this thorough and complete disclosure invention, and fully convey the scope of the invention to those skilled in the art. The terms used in the exemplary embodiments shown in the drawings are not intended to limit the invention. In the drawings, the same elements/elements are given the same reference numerals.

Unless otherwise defined, terms (including scientific and technical terms) used herein have the commonly understood meanings to those skilled in the art. In addition, it is to be understood that terms defined in commonly used dictionaries should be construed as having meanings consistent with the context in the related art, and should not be construed as idealized or overly formal meanings.

FIG. 1 is a flowchart of an analytical transfer function modeling method for inner-loop control of a grid-connected system of a voltage source converter according to a preferred embodiment of the present invention. Embodiments of the present invention provide a method for modeling an analytical transfer function of the inner loop control of a grid-connected system of a voltage source converter. The method includes four steps: establishing a power grid strength and a Phase Locked Loop (PLL) dynamic based on assumptions. The mathematical model of the voltage source converter VSC grid-connected system, linearizes the mathematical model of the voltage source converter VSC grid-connected system, and solves the inner loop control analytical transfer function model, based on the inner loop control analytical transfer function model analysis The instability mechanism of the inner loop control of the voltage source converter VSC grid-connected system and the guidance of the control parameter selection. As shown in Figure 1, a voltage source converter grid-connected system inner loop control analytical transfer function modeling method, the method includes:

Preferably, in step 101 : establishing a mathematical model of the grid-connected system of the voltage source converter that considers the grid strength and the dynamics of the phase-locked loop based on the first assumption. Preferably, the first assumption condition is: only consider the strength of the electrical connection, the inner loop current feedback value can track the inner loop current reference value in real time, ignore the filter capacitor of the common connection point, ignore the modulation process delay and sampling delay, ignore loss. Preferably, the mathematical model of the grid-connected system includes: a main circuit mathematical model, a phase-locked loop dynamic mathematical model, and an inner-loop control mathematical model.

The assumptions for establishing the mathematical model of the voltage source converter VSC grid-connected system in this application are that only the strength of the electrical connection is considered, the inner loop current feedback value can track the inner loop current reference value in real time, and the filter capacitor at the common connection point is ignored. The modulation process delay and sampling delay are ignored, and the loss is ignored. The power and current reference directions are shown in Figure 2.

The mathematical model of the VSC grid-connected system includes: the main circuit mathematical model, the PLL mathematical model, and the inner loop control mathematical model.

Preferably, after considering the first assumption, the mathematical model of the main circuit is:

The mathematical model of the main circuit part in the dq coordinate system is

Wherein, L _eq =L _t +L _arm /2, Re _eq =R _t +R _arm /2, L _ac =L _eq +L _g , R _ac =R _eq +R _g , s represents a differential operator, Re _eq is the equivalent resistance between the PCC bus and the valve side of the converter, L _eq is the equivalent inductance between the PCC bus and the valve side of the converter, L _t is the equivalent inductance of the AC grid transformer, and L _arm is the MMC bridge Arm inductance, R _t is the equivalent resistance of the AC grid transformer, L _ac is the equivalent inductance from the converter to the infinite system (ideal power supply), R _ac is the distance from the converter to the infinite system (ideal power supply) The equivalent resistance of , i _cd is the d-axis component of the inverter output current, i _cq is the q-axis component of the inverter output current, u _cd is the d-axis component of the equivalent output voltage of the inverter, and u _sd is the PCC bus voltage d shaft component, ω ₁ is the rated angular frequency, u _cq is the q-axis component of the equivalent output voltage of the converter, u _sq is the q-axis component of the PCC bus voltage, L _g is the equivalent inductance of the AC grid, and R _g is the q-axis component of the AC grid. Equivalent resistance, _ugd is the d-axis component of the voltage of the infinite system (ideal power supply), and _ugq is the d-axis component of the voltage of the infinite system (ideal power supply). The control system coordinate system and the main circuit coordinate system oriented by the PCC point voltage U _s ∠θ _s are shown in Figure 3. The coordinate system determined by the d axis and the q axis is the main circuit coordinate system, which is determined by d ^cf and q ^cf. The coordinate system of is the control system coordinate system, f _d , f _q are the components of the vector F in the main circuit coordinate system, is the component of the vector F in the control system coordinate system. The position of the control system coordinate system is determined by the PLL output. This application adopts the orientation of U _s ∠ θ _s . In the steady state, the d-axis of the control system coordinate system coincides with U _s ∠ θ _s , θ _pll = θ _s , and the transient process after disturbance θ _pll ≠ θ _s . The relationship between the projected components of the voltage and current vectors in the two coordinate systems is:

Among them, _f is the variable u _s , uc , _ug , _ic and so on.

Preferably, the dynamic mathematical model of the phase-locked loop is:

in,

Among them, θ _PLL is the dynamic output phase of the phase-locked loop, θ _pll is the difference between the phase-locked loop output phase θ _PLL and ω ₁ t, ω ₁ t is the phase of the dq coordinate system with the initial phase of 0 rotating at a constant angular velocity ω ₁ , k _{p_pll} is the proportional coefficient of the PLL dynamic proportional-integral controller, T _{i_pll} is the integral time constant of the PLL dynamic proportional-integral controller, u _sq is the q-axis component of the PCC bus voltage, ω1 is the rated angular velocity of the dq coordinate system, and s is Laplace operator, G _pll is the phase-locked loop proportional-integral controller, is the q-axis component of the equivalent output voltage of the converter in the dq coordinate system of the control system.

Preferably, the dynamic mathematical model of the phase-locked loop is designed so that the parameter calculation formula of the second-order response characteristic is:

Among them, ω _pll is the dynamic design bandwidth of the phase-locked loop, the damping ratio ξ is 0.707, and u _sd0 is the steady-state value of the d-axis component of the PCC bus voltage.

Preferably, the inner loop control mathematical model is:

in,

in, is the reference value of the d-axis component of the inverter output voltage in the control system coordinate system, is the reference value of the q-axis component of the inverter output voltage in the control system coordinate system, is the value of the d-axis component of the inverter output voltage in the control system coordinate system, is the value of the q-axis component of the converter output voltage in the control system coordinate system, ω _f is the voltage filter bandwidth, T _f is the voltage filter time constant, ω _CL is the inner loop bandwidth, and k _{p_cl} is the inner loop PI controller ratio coefficient, T _{i_cl} inner loop controller proportional coefficient, integral time constant, G _f is PCC bus voltage filter, G _CL is inner loop proportional integral controller, is the reference value of the d-axis component of the converter output current in the control system coordinate system, is the reference value of the q-axis component of the inverter output current in the control system coordinate system, is the value of the d-axis component of the converter output current in the control system coordinate system, is the value of the q-axis component of the converter output current in the control system coordinate system, ω ₁ is the rated angular frequency, L _eq is the equivalent inductance between the PCC busbar and the valve side of the converter, and s is the Laplace operator , _Req is the equivalent resistance between the PCC busbar and the valve side of the converter. In this application, T _f is generally 300us.

Preferably, the mathematical model of the modulation process is:

Among them, G _d =e ^-sTd , T _d is the equivalent delay of the flexible direct control system, uc _cd is the d-axis component of the equivalent output voltage on the AC side of the converter, and u _cq is the equivalent output voltage q on the AC side of the converter shaft component, u _dc is the DC side voltage, U _dc0 is the steady-state value of the DC side voltage, θ _pll is the difference between the phase-locked loop output phase θ _PLL and ω ₁ t, is the reference value of the d-axis component of the inverter output voltage in the control system coordinate system, is the reference value of the q-axis component of the inverter output voltage in the coordinate system of the control system, and G _d is the delay simulation link. T _d is the equivalent delay of the flexible straight control system, generally 400 ~ 500us.

Preferably, in step 102: linearize the mathematical model of the grid-connected system of the voltage source converter.

The mathematical model of the VSC grid-connected system of the voltage source converter is a typical nonlinear model. In order to study the stability of the grid-connected system, it needs to be linearized. Each variable f in equations (41)-(52) is a small disturbance f = After substituting in the form of f ₀ +Δf to eliminate the steady-state quantity, the linearized model can be obtained.

In order to obtain the detailed expression of the VSC grid-connected current, the linearization model of the simultaneous equations (41)-(52) can be obtained after sorting out the inner loop current control linearity considering the influence of PLL, delay, voltage filter, and DC voltage disturbance. The closed-loop expression is as follows:

Ignoring secondary factors, the second assumption is made as follows:

(1) Since the delay of the entire converter system is very small, generally 400-500us, assuming that T _d ≈ 0, then G _d =1;

(2) The delay of the voltage sampling filter is very small. Generally, the value is 300us, and T _f ≈ 0, then G _f =1;

(3) The DC voltage maintains a constant value, Δu _dc =0;

Considering the above second assumption, the simplified transfer function of the available current inner loop control is:

In the formula, Z _ic =sL _eq +R _eq +G _CL , it can be seen from formula (54) that the d and q-axis current disturbances of the grid-connected VSC are mainly affected by the current reference value disturbance and the PLL output disturbance, respectively representing the outer loop control , The influence of PLL on current inner loop control.

Preferably, in step 103: based on the second assumption condition, a simplified transfer function of the inner loop control of the current is obtained; according to the simplified transfer function, the dynamic output phase of the phase-locked loop is embodied, and a voltage source considering the dynamic influence of the phase-locked loop is established Analytic transfer function of inner loop control of grid-connected current of type converter.

In order to obtain the analytic transfer function model of the current inner loop control considering the influence of the PLL and the strength of the AC power grid, the PLL output phase disturbance expression in Eq. (54) needs to be specified, Δθ _pll is eliminated, and a closed loop from the control system to the main circuit is established.

From equation (54) and u _gd =0, u _gq =0 can be obtained:

tidy up

Figure 5 shows a block diagram of equation (56), which can intuitively represent the influence of the PLL on the inner loop current control.

Solving Equation (56), we can obtain the analytical expression of the grid-connected VSC current inner loop control considering the influence of PLL as:

in

The block diagram of the small-signal analytical transfer function expression for the current inner loop control of the grid-connected VSC system is shown in Figure 6. It can be seen from equations (57) and (59) that the equivalent inductance Lg, which reflects the strength of the AC power grid, plays a decisive role in the interaction between the PLL and the current inner loop control, and the size of _Lg determines the severity of the interaction between the two. . When the AC grid is an infinite system, R _g ≈ 0, L _g ≈ 0, G _dd = G _qq = 0, G _dq = G _qd = 0, B = C = 0, there is no influence between the PLL and the current inner loop control, There is no influence between the current inner loop control d and q axis control. When the strength of the AC power grid is small, L _g ≠ 0, and the interaction between the PLL and the current inner loop is strengthened, and it can be seen from equation (59) that the larger I _cd0 and I _cq0 , which characterize the magnitude of active and reactive power, the more obvious the interaction is. .

Preferably, in step 104: based on the inner-loop control analytical transfer function, analyze the instability mechanism of the inner-loop control of the grid-connected voltage source converter system and guide the parameter design.

From equation (61), it can be known that the characteristic equation that determines the stability of the inner loop current control is:

G ₀ is composed of three parts, G _CL /Z _ic reflects the role of inner loop control under ideal conditions without considering PLL and grid strength, G _PLL reflects the influence of PLL, and the remaining part reflects grid strength, active current (active power) power) and reactive current (reactive power). Under the assumption of unity power factor:

Using equation (61) combined with the stability criteria on the Bode diagram or Nyquist diagram shown in Figure 7, the influence of power grid strength, active power, PLL bandwidth and other factors on the stability of the inner loop control can be analyzed, and the PLL bandwidth and inner loop control can be guided. Bandwidth parameter design. The grid equivalent reactance determines the initial position of the Bode diagram, the phase-locked loop bandwidth determines the position of the maximum amplitude value, and the inner loop bandwidth does not affect the maximum amplitude value. According to the strength of the power grid and the bandwidth of the inner loop, the bandwidth parameters of the phase-locked loop can be reasonably selected to ensure that the stability criterion that the maximum value of the Bode graph amplitude is less than 0 is satisfied.

2 is a structural diagram of a main circuit and a control system of a voltage source converter VSC grid-connected system according to a preferred embodiment of the present invention. The meaning of each variable in Figure 2 is explained in Table 1.

Table 1 VSC grid-connected system variables

The present application provides a method for modeling and analyzing the analytic transfer function of the inner-loop control of a VSC grid-connected system in a weak grid, which can be used to analyze the instability mechanism of the inner-loop control of a VSC grid-connected system in a weak grid, and guide the selection of control parameters. The analytical modeling method for the inner loop control of the VSC grid-connected system proposed in this application can intuitively explain the influence of various factors on the stability, locate the main influencing factors, and the model has strong explanatory power because the transfer function is used for analytical modeling. The instability mechanism analysis method based on the inner-loop control analytical model of the VSC grid-connected system proposed in this application can intuitively reveal the influence of various influencing factors on the inner-loop control stability of the VSC grid-connected system, and guide the wind turbine converter and photovoltaic inverter. The control parameter design of the inner loop control of the VSC grid-connected system can create obvious economic benefits.

FIG. 8 is a structural diagram of an analytical transfer function modeling system for inner-loop control of a grid-connected voltage source converter system according to a preferred embodiment of the present invention. As shown in Figure 8, a voltage source converter grid-connected system inner loop control analytical transfer function modeling system, the system includes:

The first establishing unit 801 is configured to establish, based on the first assumption, a mathematical model of the grid-connected system of the voltage source converter that considers the grid strength and the dynamics of the phase-locked loop. Preferably, the first assumption condition is: only consider the strength of the electrical connection, the inner loop current feedback value can track the inner loop current reference value in real time, ignore the filter capacitor of the common connection point, ignore the modulation process delay and sampling delay, ignore loss. Preferably, the mathematical model of the grid-connected system includes: a main circuit mathematical model, a phase-locked loop dynamic mathematical model, and an inner-loop control mathematical model.

Preferably, the mathematical model of the main circuit is:

The mathematical model of the main circuit part in the dq coordinate system is

Wherein, L _eq =L _t +L _arm /2, Re _eq =R _t +R _arm /2, L _ac =L _eq +L _g , R _ac =R _eq +R _g , s represents a differential operator, Re _eq is the equivalent resistance between the PCC bus and the valve side of the converter, L _eq is the equivalent inductance between the PCC bus and the valve side of the converter, L _t is the equivalent inductance of the AC grid transformer, and L _arm is the MMC bridge Arm inductance, R _t is the equivalent resistance of the AC grid transformer, L _ac is the equivalent inductance from the converter to the infinite system (ideal power supply), R _ac is the distance from the converter to the infinite system (ideal power supply) The equivalent resistance of , i _cd is the d-axis component of the inverter output current, i _cq is the q-axis component of the inverter output current, u _cd is the d-axis component of the equivalent output voltage of the inverter, and u _sd is the PCC bus voltage d shaft component, ω1 is the rated angular frequency, u _cq is the q-axis component of the equivalent output voltage of the converter, u _sq is the q-axis component of the PCC bus voltage, L _g is the equivalent inductance of the AC power grid, R _g is the AC power grid, etc. Effective resistance, _ugd is the d-axis component of the infinite system (ideal power supply) voltage, and _ugq is the d-axis component of the infinite system (ideal power supply) voltage. Preferably, the dynamic mathematical model of the phase-locked loop is:

in,

Among them, θ _PLL is the dynamic output phase of the phase-locked loop, θ _pll is the difference between the phase-locked loop output phase θ _PLL and ω ₁ t, ω ₁ t is the phase of the dq coordinate system with the initial phase of 0 rotating at a constant angular velocity ω ₁ , k _{p_pll} is the proportional coefficient of the PLL dynamic proportional-integral controller, T _{i_pll} is the integral time constant of the PLL dynamic proportional-integral controller, u _sq is the q-axis component of the PCC bus voltage, ω1 is the rated angular velocity of the dq coordinate system, and s is Laplace operator, G _pll is the phase-locked loop proportional-integral controller, is the q-axis component of the equivalent output voltage of the converter in the dq coordinate system of the control system. Preferably, the dynamic mathematical model of the phase-locked loop is designed so that the parameter calculation formula of the second-order response characteristic is:

Among them, ω _pll is the dynamic design bandwidth of the phase-locked loop, the damping ratio ξ is 0.707, and u _sd0 is the steady-state value of the d-axis component of the PCC bus voltage.

Preferably, the inner loop control mathematical model is:

in,

in, is the reference value of the d-axis component of the inverter output voltage in the control system coordinate system, is the reference value of the q-axis component of the inverter output voltage in the control system coordinate system, is the value of the d-axis component of the inverter output voltage in the control system coordinate system, is the value of the q-axis component of the converter output voltage in the control system coordinate system, ω _f is the voltage filter bandwidth, T _f is the voltage filter time constant, ω _CL is the inner loop bandwidth, and k _{p_cl} is the inner loop PI controller ratio coefficient, T _{i_cl} inner loop controller proportional coefficient, integral time constant, G _f is PCC bus voltage filter, G _CL is inner loop proportional integral controller, is the reference value of the d-axis component of the converter output current in the control system coordinate system, is the reference value of the q-axis component of the inverter output current in the control system coordinate system, is the value of the d-axis component of the converter output current in the control system coordinate system, is the value of the q-axis component of the converter output current in the control system coordinate system, ω ₁ is the rated angular frequency, L _eq is the equivalent inductance between the PCC busbar and the valve side of the converter, and s is the Laplace operator , _Req is the equivalent resistance between the PCC busbar and the valve side of the converter.

Preferably, the mathematical model of the modulation process is:

Among them, G _d =e ^-sTd , T _d is the equivalent delay of the flexible direct control system, uc _cd is the d-axis component of the equivalent output voltage on the AC side of the converter, and u _cq is the equivalent output voltage q on the AC side of the converter shaft component, u _dc is the DC side voltage, U _dc0 is the steady-state value of the DC side voltage, θ _pll is the difference between the phase-locked loop output phase θ _PLL and ω ₁ t, is the reference value of the d-axis component of the inverter output voltage in the control system coordinate system, is the reference value of the q-axis component of the inverter output voltage in the coordinate system of the control system, and G _d is the delay simulation link.

The processing unit 802 is used for linearizing the mathematical model of the grid-connected system of the voltage source converter. The mathematical model of the VSC grid-connected system of the voltage source converter is a typical nonlinear model, and it needs to be linearized in order to study the stability of the grid-connected system. After substituting in the form of f ₀ +Δf to eliminate the steady-state quantity, the linearized model can be obtained.

In order to obtain the detailed expression of the VSC grid-connected current, the linearization model of the simultaneous equations (62)-(71) can be obtained by sorting out the inner loop current control linearity considering the influence of PLL, delay, voltage filter, and DC voltage disturbance. The closed-loop expression is as follows:

Ignoring secondary factors, the second assumption is made as follows:

(1) Since the delay of the entire converter system is very small, generally 400-500us, assuming that T _d ≈ 0, then G _d =1;

(2) The delay of the voltage sampling filter is very small. Generally, the value is 300us, and T _f ≈ 0, then G _f =1;

(3) The DC voltage maintains a constant value, Δu _dc =0;

Considering the above second assumption, the simplified transfer function of the available current inner loop control is:

In the formula, Z _ic =sL _eq +R _eq +G _CL , it can be seen from equation (73) that the d and q-axis current disturbances of the grid-connected VSC are mainly affected by the PLL output disturbance and the current reference value disturbance, which represent the PLL, external The effect of loop control on current inner loop control.

The second establishment unit 803 is configured to obtain the simplified transfer function of the inner loop control of the current based on the second assumption condition; according to the simplified transfer function, specify the dynamic output phase expression of the phase-locked loop, and establish the dynamic influence of the phase-locked loop into consideration. The inner loop control of the grid-connected current of a voltage source converter is an analytical transfer function. In order to obtain the analytic transfer function model of the current inner loop control considering the influence of the PLL and the strength of the AC power grid, the PLL output phase disturbance expression in Eq. (73) needs to be specified, Δθ _pll is eliminated, and a closed loop from the control system to the main circuit is constructed.

From formula (73) and u _gd =0, u _gq =0 can be obtained:

Arrange to get:

Figure 5 shows a block diagram of equation (75), which can intuitively represent the influence of the PLL on the inner loop current control.

Solving Equation (75), the analytical expression for the inner loop control of grid-connected VSC current considering the influence of PLL can be obtained as:

in,

The block diagram of the small-signal analytical transfer function expression for the current inner loop control of the grid-connected VSC system is shown in Figure 6. It can be seen from equations (76) and (78) that the equivalent inductance Lg, which reflects the strength of the AC power grid, plays a decisive role in the interaction between the PLL and the current inner loop control, and the magnitude of _Lg determines the severity of the interaction between the two. . When the AC grid is an infinite system, R _g ≈ 0, L _g ≈ 0, G _dd = G _qq = 0, G _dq = G _qd = 0, B = C = 0, there is no influence between the PLL and the current inner loop control, There is no influence between the current inner loop control d and q axis control. When the strength of the AC power grid is small, L _g ≠ 0, the interaction between the PLL and the current inner loop is strengthened, and it can be seen from equation (78) that the larger I _cd0 and I _cq0 , which characterize the magnitude of active and reactive power, the more obvious the interaction is. .

The design unit 804 is configured to analyze the instability mechanism of the inner-loop control of the grid-connected system of the voltage source converter based on the inner-loop control analytical transfer function and guide the parameter design.

From equation (80), it can be known that the characteristic equation that determines the stability of the inner loop current control is:

G ₀ consists of three parts, G _CL /Z _ic reflects the role of the inner loop control under ideal conditions without considering PLL and grid strength, GPLL reflects the influence of PLL, and the remaining part reflects grid strength, active current (active power ), the influence of reactive current (reactive power). Under the assumption of unity power factor:

Using equation (80) combined with the stability criteria on the Bode diagram or Nyquist diagram shown in Figure 7, the influence of power grid strength, active power, PLL bandwidth and other factors on the stability of the inner loop control can be analyzed, and the PLL bandwidth and inner loop control can be guided. Bandwidth parameter design. The grid equivalent reactance determines the initial position of the Bode diagram, the phase-locked loop bandwidth determines the position of the maximum amplitude value, and the inner loop bandwidth does not affect the maximum amplitude value. According to the strength of the power grid and the bandwidth of the inner loop, the bandwidth parameters of the phase-locked loop can be reasonably selected to ensure that the stability criterion that the maximum value of the Bode graph amplitude is less than 0 is satisfied.

An analytical transfer function modeling system 800 for inner-loop control of a grid-connected voltage source converter system according to an embodiment of the present invention and a method for modeling the inner-loop control analytical transfer function of a grid-connected voltage source converter system according to another embodiment of the present invention 100 corresponds to, and will not be repeated here.

The present invention has been described with reference to a few embodiments. However, as is known to those skilled in the art, other embodiments than the above disclosed invention are equally within the scope of the invention, as defined by the appended patent claims.

Generally, all terms used in the claims are to be interpreted according to their ordinary meaning in the technical field, unless explicitly defined otherwise herein. All references to "a/the/the [means, component, etc.]" are open to interpretation as at least one instance of said means, component, etc., unless expressly stated otherwise. The steps of any method disclosed herein do not have to be performed in the exact order disclosed, unless explicitly stated.

Claims (16)

1. A method for modeling an inner ring control analytic transfer function of a grid-connected system of a voltage source converter comprises the following steps:

establishing a voltage source type converter grid-connected system mathematical model considering the power grid strength and the phase-locked loop dynamics based on a first assumed condition;

carrying out linearization processing on the voltage source type converter grid-connected system mathematical model;

acquiring a simplified transfer function of inner loop control of the current based on a second assumed condition; according to the simplified transfer function, the dynamic output phase expression of the phase-locked loop is specified, and an inner loop control analysis transfer function of the grid-connected current of the voltage source type converter considering the dynamic influence of the phase-locked loop is established;

and analyzing an inner ring control instability mechanism of the voltage source type converter grid-connected system and guiding parameter design based on the inner ring control analytic transfer function.

2. The method of claim 1, the first hypothetical condition being:

only the strength of the electrical connection is considered, the inner loop current feedback value can track the inner loop current reference value in real time, the filter capacitor of the common connection point is ignored, the delay in the modulation process and the sampling delay are ignored, and the loss is ignored.

3. The method of claim 1, the grid tie system mathematical model comprising:

a main circuit mathematical model, a phase-locked loop dynamic mathematical model and an inner loop control mathematical model.

4. The method of claim 3, the primary circuit mathematical model being:

the mathematical model of the main circuit part is as follows under dq coordinate system

Wherein L is_eq＝L_t+L_arm/2，R_eq＝R_t+R_arm/2，L_ac＝L_eq+L_g，R_ac＝R_eq+R_gS denotes a differential operator, R_eqIs the equivalent resistance between the PCC bus and the converter valve side, L_eqIs the equivalent inductance between the PCC bus and the converter valve side, L_tIs the equivalent inductance, L, of an AC mains transformer_armIs an MMC bridge arm inductor, R_tIs an equivalent resistance of an AC network transformer, L_acIs equivalent inductance between the converter and the infinite system, R_acIs the equivalent resistance from the converter to the infinite system, i_cdFor the d-axis component of the converter output current i_cqFor the converter output current q-axis component, u_cdIs d-axis component, u, of the converter equivalent output voltage_sdIs the d-axis component, ω, of the PCC bus voltage₁At a nominal angular frequency, u_cqFor the q-axis component of the converter equivalent output voltage, u_sqIs the q-axis component of the PCC bus voltage, L_gIs an equivalent inductance of an AC network, R_gIs the equivalent resistance of the AC network, u_gdD-axis component, u, of infinite system voltage_gqThe d-axis component of the infinite system voltage.

5. The method of claim 3, the phase-locked loop dynamic mathematical model being:

wherein,

wherein, theta_PLLFor dynamically outputting phase, theta, to a phase-locked loop_pllFor phase-locked loop output phase theta_PLLAnd omega₁Difference of t, ω₁t is an initial phase of 0 at a constant angular velocity ω₁Phase of rotating dq coordinate system, k_{p_pll}For phase-locked loop dynamic proportional integral controller proportionality coefficient, T_{i_pll}Integrating time constant, u, for a phase locked loop dynamic proportional integral controller_sqIs the q-axis component, ω, of the PCC bus voltage₁Is the rated angular velocity of dq coordinate system, s is LaplacaOperator of sj, G_pllIs a proportional-integral controller for a phase-locked loop,the q-axis component of the equivalent output voltage of the converter in the dq coordinate system of the control system.

6. The method of claim 5, wherein the dynamic mathematical model of the phase-locked loop is designed to have a second-order response characteristic with a parameter calculation formula as follows:

wherein, ω is_pllFor dynamically designing the bandwidth of the phase-locked loop, the damping ratio ξ is 0.707 u_sd0Is a steady-state value of the d-axis component of the PCC bus voltage.

7. The method of claim 3, the inner loop control mathematical model being:

wherein,

wherein,for reference values of the d-axis component of the inverter output voltage in the control system coordinate system,for controlling inverter output in the system coordinate systemA reference value of the q-axis component of the voltage,to control the value of the d-axis component of the inverter output voltage in the system coordinate system,for controlling the value of the q-axis component of the converter output voltage in the system coordinate system, omega_fIs the voltage filter bandwidth, T_fIs the time constant of the voltage filter, omega_CLIs the inner loop bandwidth, k_{p_cl}Is the inner loop PI controller proportionality coefficient, T_{i_cl}Proportional coefficient, integral time constant, G, of inner loop controller_fIs a PCC bus voltage filter, G_CLIs an inner ring proportional-integral controller,for reference values of the d-axis component of the inverter output current in the control system coordinate system,for reference values of the q-axis component of the inverter output current in the control system coordinate system,to control the value of the d-axis component of the inverter output current in the system coordinate system,for controlling the value of the q-axis component of the converter output current in the system coordinate system, omega₁At a nominal angular frequency, L_eqIs the equivalent inductance between the PCC bus and the converter valve side, s is the Laplace operator, R_eqIs the equivalent resistance between the PCC bus and the converter valve side.

8. The method of claim 3, the mathematical model of the modulation process being:

wherein G is_d＝e^-sTd，T_dFor the equivalent delay of the flexible-straight control system, u_cdIs d-axis component, u, of the equivalent output voltage at the AC side of the converter_cqFor the q-axis component of the equivalent output voltage at the AC side of the converter, u_dcIs a DC side voltage, U_dc0Is a steady-state value of the DC side voltage, theta_pllFor phase-locked loop output phase theta_PLLAnd omega₁the difference between the values of t and t,for reference values of the d-axis component of the inverter output voltage in the control system coordinate system,for reference values of q-axis components of converter output voltage in a control system coordinate system, G_dIs a time delay simulation link.

9. An analytic transfer function modeling system of voltage source converter grid-connected system inner loop control, the system comprising:

the first establishing unit is used for establishing a voltage source type converter grid-connected system mathematical model considering the power grid strength and the phase-locked loop dynamic state based on a first assumed condition;

the processing unit is used for carrying out linearization processing on the voltage source type converter grid-connected system mathematical model;

a second establishing unit for acquiring a simplified transfer function of inner loop control of the current based on a second assumption condition; according to the simplified transfer function, the dynamic output phase expression of the phase-locked loop is specified, and an inner loop control analysis transfer function of the grid-connected current of the voltage source type converter considering the dynamic influence of the phase-locked loop is established;

and the design unit is used for analyzing the inner ring control instability mechanism of the voltage source type converter grid-connected system and guiding parameter design based on the inner ring control analytic transfer function.

10. The system of claim 9, the first assumption condition being:

only the strength of the electrical connection is considered, the inner loop current feedback value can track the inner loop current reference value in real time, the filter capacitor of the common connection point is ignored, the delay in the modulation process and the sampling delay are ignored, and the loss is ignored.

11. The system of claim 9, the grid tie system mathematical model comprising:

a main circuit mathematical model, a phase-locked loop dynamic mathematical model and an inner loop control mathematical model.

12. The system of claim 11, the primary circuit mathematical model being:

the mathematical model of the main circuit part is as follows under dq coordinate system

Wherein L is_eq＝L_t+L_arm/2，R_eq＝R_t+R_arm/2，L_ac＝L_eq+L_g，R_ac＝R_eq+R_gS denotes a differential operator, R_eqIs the equivalent resistance between the PCC bus and the converter valve side, L_eqIs the equivalent inductance between the PCC bus and the converter valve side, L_tIs the equivalent inductance, L, of an AC mains transformer_armIs an MMC bridge arm inductor, R_tIs an equivalent resistance of an AC network transformer, L_acFor the purpose of changing from one to anotherEquivalent inductance between the device and the infinite system, R_acIs the equivalent resistance from the converter to the infinite system, i_cdFor the d-axis component of the converter output current i_cqFor the converter output current q-axis component, u_cdIs d-axis component, u, of the converter equivalent output voltage_sdIs d-axis component of PCC bus voltage, omega 1 is rated angular frequency, u_cqFor the q-axis component of the converter equivalent output voltage, u_sqIs the q-axis component of the PCC bus voltage, L_gIs an equivalent inductance of an AC network, R_gIs the equivalent resistance of the AC network, u_gdD-axis component, u, of infinite system voltage_gqThe d-axis component of the infinite system voltage.

13. The method of claim 11, the phase-locked loop dynamic mathematical model being:

wherein,

wherein, theta_PLLFor dynamically outputting phase, theta, to a phase-locked loop_pllFor phase-locked loop output phase theta_PLLAnd omega₁Difference of t, ω₁t is an initial phase of 0 at a constant angular velocity ω₁Phase of rotating dq coordinate system, k_{p_pll}For phase-locked loop dynamic proportional integral controller proportionality coefficient, T_{i_pll}Integrating time constant, u, for a phase locked loop dynamic proportional integral controller_sqIs the q-axis component, ω, of the PCC bus voltage₁Is the nominal angular velocity of dq coordinate system, s is the Laplace operator, G_pllIs a proportional-integral controller for a phase-locked loop,the q-axis component of the equivalent output voltage of the converter in the dq coordinate system of the control system.

14. The system of claim 13, wherein the dynamic mathematical model of the phase-locked loop is designed to have a second-order response characteristic with a parameter calculation formula as follows:

wherein, ω is_pllFor dynamically designing the bandwidth of the phase-locked loop, the damping ratio ξ is 0.707 u_sd0Is a steady-state value of the d-axis component of the PCC bus voltage.

15. The system of claim 11, the inner loop control mathematical model being:

wherein,

wherein,for reference values of the d-axis component of the inverter output voltage in the control system coordinate system,to control the reference value of the q-axis component of the inverter output voltage in the system coordinate system,to control the value of the d-axis component of the inverter output voltage in the system coordinate system,for controlling the value of the q-axis component of the converter output voltage in the system coordinate system, omega_fIs the voltage filter bandwidth, T_fIs the time constant of the voltage filter, omega_CLIs the inner loop bandwidth, k_{p_cl}Is the inner loop PI controller proportionality coefficient, T_{i_cl}Proportional coefficient, integral time constant, G, of inner loop controller_fIs a PCC bus voltage filter, G_CLIs an inner ring proportional-integral controller,for reference values of the d-axis component of the inverter output current in the control system coordinate system,for reference values of the q-axis component of the inverter output current in the control system coordinate system,to control the value of the d-axis component of the inverter output current in the system coordinate system,for controlling the value of the q-axis component of the converter output current in the system coordinate system, omega₁At a nominal angular frequency, L_eqIs the equivalent inductance between the PCC bus and the converter valve side, s is the Laplace operator, R_eqIs the equivalent resistance between the PCC bus and the converter valve side.

16. The system of claim 11, the mathematical model of the modulation process being:

wherein G is_d＝e^-sTd，T_dFor the equivalent delay of the flexible-straight control system, u_cdFor the AC side equivalent output of the converterD-axis component of the output voltage u_cqFor the q-axis component of the equivalent output voltage at the AC side of the converter, u_dcIs a DC side voltage, U_dc0Is a steady-state value of the DC side voltage, theta_pllFor phase-locked loop output phase theta_PLLAnd omega₁the difference between the values of t and t,is a reference value of the d-axis component of the inverter output voltage,reference value, G, for q-axis component of converter output voltage_dIs a time delay simulation link.