Quantitative description method for transient synchronous stability boundary of multi-converter system

Abstract

The invention discloses a quantitative description method for a transient synchronous stability boundary of a multi-converter system, and belongs to the technical field of power electronic control. Aiming at the challenges that the relative power angle motion between the converters in the multi-converter system is difficult to accurately describe and a multi-group relative power angle coupling action mechanism is difficult to analyze, the input-output stability of a relative power angle motion subsystem between every two converters in the multi-converter system is analyzed; and constructing a dissipation matrix for describing the motion stability property of each power angle of the multi-converter system and the interconnection relationship of the power angle motion, and realizing quantitative description of the dissipation property of the multi-power-angle synchronous motion of the multi-converter system. Furthermore, a Lyapunov function for describing the power angle motion of the multi-converter system is constructed, so that the quantitative estimation of the transient synchronous stability boundary of the multi-converter system is realized.

Description

Technical Field

[0001] This invention belongs to the field of power electronic control technology, specifically relating to a method for quantitative characterization of transient synchronous stability boundary of a multi-converter system. Background Technology

[0002] Grid-connected converters primarily employ two synchronization strategies: grid-following control and grid-building control. Grid-following control achieves synchronization with the grid through a phase-locked loop (PLL) structure, possessing precise power injection capabilities and typically exhibiting controlled current source characteristics. Grid-building converters achieve grid connection through power synchronization, possessing autonomous voltage and frequency support capabilities and exhibiting controlled voltage source characteristics. In future renewable energy power systems with a higher proportion of renewable energy, both grid-following and grid-building converters will coexist extensively and for a long period, jointly influencing the behavioral characteristics and stability boundaries of future power systems.

[0003] The transient dynamic characteristics of grid-connected and grid-connected converters are primarily determined by their control strategies. When a transient fault occurs in the system, the grid-connected converter may lose synchronization with the grid due to power imbalance; simultaneously, the power injection behavior of the grid-connected converter is also affected by changes in the port voltage of the grid-connected converter. Therefore, there are complex coupling relationships between the converter power angle dynamics during transient processes, resulting in an unclear transient synchronization stability mechanism for multi-converter systems containing both grid-connected and grid-connected converters. This poses a significant challenge to transient synchronization stability analysis and system relay protection settings.

[0004] Traditional quantitative analysis methods are mainly based on the energy function method, which can intuitively and quantitatively analyze the conversion process of kinetic and potential energy in rotor-like transient motion in converter grid-connected systems. However, this method is difficult to apply to the converter power angle behavior defined by various synchronization control strategies, resulting in unclear transient synchronization stability boundaries for multi-converter systems and an inability to quickly calculate the critical fault clearing time of multi-converter systems. Summary of the Invention

[0005] To quantitatively analyze the transient synchronous stability boundary of a multi-converter system, this invention proposes a method for quantitative analysis of transient interactive power between converters in a hybrid grid-connected system.

[0006] The multi-converter system described in this invention comprises a plurality of grid-connected converters and at least two grid-connected converters; the method for quantitatively characterizing the transient synchronous stability boundary includes the following steps: 1) Establish the transient motion equations of each converter in the multi-converter system; 2) Based on the transient motion equations and the admittance matrix of the multi-converter system, the relative power angle motion equations between each pair of converters in the system are obtained; 3) Based on the relative power angle motion equation, construct a dissipation matrix describing the relative power angle motion stability and interconnection relationship of the converter; 4) Determine the rectangular stability region of the system's relative work angle under the condition that the dissipation matrix is ​​a non-singular M-matrix; 5) Construct the global Lyapunov function of the system within the rectangular stability domain and calculate the critical energy value; based on the critical energy value, determine the elliptical power angle domain of the transient synchronous stability boundary of the system as the transient synchronous stability boundary of the multi-converter system.

[0007] According to a preferred embodiment of the present invention, step 1) further includes: the transient power angle motion of the grid converter in the multi-converter system is expressed as follows: in, , These are the first in the multi-converter system The power angle and speed of grid-type converters. For the first The proportional gain of the first-order phase-locked loop in the grid-type converter. For the first The phase-locked loop of the grid-type converter detects the q-axis quadrature component of the converter port voltage.

[0008] The transient power angle motion of a grid-type converter in a multi-converter system is expressed as follows: in, , These are the first in the multi-converter system The power angle and speed of a grid-type converter. For the first The droop coefficient of power synchronization control for a grid-type converter. For the first The output active power of the grid-type converter For the first Active power reference for Taiwan-type grid converter.

[0009] According to a preferred embodiment of the present invention, step 2) further includes: 21) For a one containing Taiwan-type grid converter and For a multi-converter system with a grid-type converter, the port voltage-current relationship can be described by the system admittance matrix, and its expression is as follows: in and They are respectively The current vector and voltage vector of the grid-type converter are defined by the first... The output current and port voltage of the grid-type converter are respectively and , and Written as ; and They are respectively The current vector and voltage vector of the grid-type converter are defined by the first... The output current and port voltage of the grid-connected converter are respectively and , and Written as ; This is the admittance matrix of the multi-current converter system, which can be directly obtained from the specific circuit relationships. , , , for The corresponding submatrix.

[0010] 22) Based on the circuit relationships of the multi-converter system, and It can be expressed by the output current of the grid-connected converter, the port voltage of the grid-connected converter, and the circuit impedance: Furthermore, the first The phase-locked loop of the grid-connected converter detects the q-axis quadrature component of the converter port voltage. and the Output active power of the grid-type converter It can be expressed by the output current of the grid-connected converter, the port voltage of the grid-connected converter, and the circuit impedance: in, and The first The amplitude and current angle of the output current of the grid-connected converter. For the first The terminal voltage amplitude of the grid-type converter, and the definitions of other related physical quantities in the circuit are as follows: 23) Based on this, the first [number] in the multi-converter system is obtained. Taiwan-connected grid converter and the first The transient motion expression of the relative power angle of a grid-type converter is written as: in, For the first Taiwan-connected grid converter and the first The relative power angle between the transformer and the grid converter. For the first Taiwan-connected grid converter and the first The relative power angle between grid-type converters. For the first Taiwan-type grid converter and the first The relative power angle between grid-type converters. For the first Taiwan-connected grid converter and the first The relative speed between the grid-type converters.

[0011] Similarly, the first [unit / type] in the multi-converter system is obtained. Taiwan-type grid converter and the first The transient motion expression of the relative power angle of a grid-type converter is written as: in For the first Taiwan-type grid converter and the first The relative speed between the grid-type converters.

[0012] According to a preferred embodiment of the present invention, step 3) further includes: 31) For those containing Taiwan-type grid converter and Multi-converter systems using grid-type converters are selected. The relative power angle motion of the grid-type converter with respect to the network-type converter, and The relative power angle motion between two grid-connected converters fully describes the power angle dynamics of a multi-converter system, with each converter being included in at least one selected set. In the relative power angle motion of the group, the power angle dynamics of the multi-converter system can be determined by a single... A nonlinear system description of a subsystem, wherein the state variables of the nonlinear system are those selected above. The relative angle of work is expressed as follows: in, For selection Relative power angle of grid-type converter - network-type converter and their respective steady-state values ​​at their stable equilibrium points Difference between , For selection Network converter - Relative power angle of network converter and their respective steady-state values ​​at their stable equilibrium points Difference between .

[0013] 32) Based on the transient equations of motion of relative work angle, the multi-converter system can be... The dynamic unified expression of each subsystem is as follows: Where the function Let be the dynamic function of each subsystem, whose detailed expression can be obtained from the previous expression for the transient motion of the relative work angle.

[0014] 33) Further, the dynamic functions of each subsystem are decomposed into the sum of the action functions of each state variable of the system, written as: Where the coefficient function From the following formula, we get 34) Define the Lyapunov function of each subsystem as follows: Based on the dynamic equations of the subsystem, the input-output inequality of the subsystem is further obtained, written as: in, is the coefficient of Young's inequality, which can take any positive value; and Defined as 35) Based on the input-output inequalities of the obtained subsystem, the input-output inequalities of the multi-converter system are further expressed using the dissipation matrix. Representation, dissipation matrix The definition of Therefore, the input-output inequality of the multi-converter system is expressed as follows: in, , .

[0015] According to a preferred embodiment of the present invention, step 4) further includes: 41) Based on the input-output stability inequalities of each subsystem in a multivariator system, construct the global Lyapunov function of the multivariator system, which is defined as follows: Where the weighting coefficient vector is .

[0016] To ensure that the overall Lyapunov function can characterize the transient stability of the multivariator system, the following inequality must be satisfied. Based on this inequality, it can be deduced that the dissipation matrix... When the M-matrix is ​​non-singular, the weighted coefficient vector can be constructed based on the following formula. : in The elements in the set are any values ​​greater than zero, and the overall Lyapunov function satisfies the following dissipation relation: Therefore, within the power angle region corresponding to a non-singular M-matrix dissipation matrix, the global Lyapunov function is constructed. It can be used to characterize the transient synchronization stability properties of multi-converter systems.

[0017] 42) Therefore, based on the dissipation matrix Given the existence condition of the global Lyapunov function of the nonsingular M matrix, a series of rectangular power angle domains can be obtained. Within these rectangular power angle domains, the global Lyapunov function of the multivariator system can be obtained using the above construction method. The expression for the rectangular power angle domain is: The boundary of this functional angle domain is defined by vectors. Definition, vector The boundary dissipation matrix satisfies its definition. It is a non-singular M matrix.

[0018] According to a preferred embodiment of the present invention, step 5) further includes: The minimum energy of the global Lyapunov function on the boundary of the rectangular work angle domain is defined as the critical energy value of the system, written as: Based on this, a certain value can be obtained within the aforementioned rectangular power angle domain. The elliptic transient synchronous stability region of the work angle is written as Based on the above analysis, it can be seen that in the elliptical work angle domain For any angle of work within the range, the global Lyapunov function satisfies Therefore, it can be deduced that the initial state of the power angle of a multi-converter system defined at any point within the elliptical power angle domain gradually converges to the system's stable equilibrium point during the transient process. Thus, the elliptical power angle domain... The boundary can be used as a conservative estimate of the transient synchronous stability boundary of the multi-converter system.

[0019] Based on the above technical solution, the present invention has the following beneficial technical effects: This invention proposes an input-output stability quantification method for the transient motion of relative power angles among converters in a multi-converter system, solving the problem that existing transient analysis tools are unable to characterize the stability characteristics between the power angles of converters using different control strategies and parameters in a multi-converter system.

[0020] This invention proposes a quantitative description method for the dissipative properties of multi-converter systems based on the input-output stability analysis of the relative work angle motion subsystem. Based on this, a global Lyapunov function construction method for multi-converter systems is proposed, which realizes the quantitative estimation of the transient synchronous stability boundary of multi-converter systems. It has the advantages of fast solution speed and high accuracy, and can realize the online calculation of the critical fault clearing time of multi-converter systems. Attached Figure Description

[0021] Figure 1 This is a schematic diagram of the circuit structure of a grid-connected control structure, a grid-connected control structure, and a grid-connected converter hybrid grid-connected system. Detailed Implementation

[0022] To explain the present invention in more detail, the following example is a grid-connected system of a grid-connected converter with constant current control and constant terminal voltage control under a three-phase-to-ground short-circuit fault, in conjunction with the accompanying drawings and embodiments, to further illustrate the present invention.

[0023] Figure 1 This is a schematic diagram of a grid-connected system containing two converters. The grid-connected converter achieves synchronization with the grid through a phase-locked loop (PLL) structure and regulates active power output by adjusting its output current. The grid-connected converter regulates active power output by adjusting the phase of its output voltage. The output current of the grid-connected converter is... ,in and To determine the amplitude and phase angle of the injected current to the grid-connected converter, To determine the power angle of the phase-locked loop output of the grid converter, its transient motion equation is as follows: in, , These refer to the power angle and speed of the grid converter, respectively. The proportional gain is the same as that of the first-order phase-locked loop of the grid converter. The phase-locked loop of the grid converter detects the q-axis orthogonal component of the converter port voltage.

[0024] The terminal voltage amplitude of a grid-type converter is its reference value. The power angle generated by its power synchronization control loop is Therefore, the port voltage of the grid-type converter is written as The transient motion equations of a grid-type converter are as follows: in, , These refer to the power angle and speed of the grid-type converter in a multi-converter system. The droop coefficient for power synchronization control of grid-type converters. For the output active power of the grid-type converter, Use it as a reference for its active power.

[0025] Furthermore, the amplitude and phase of the power grid in the hybrid grid-connected system are respectively and Due to its frequency For a given value, an infinitely large power grid can be equivalently represented as a grid-type converter with an equivalent droop coefficient approaching infinity, i.e. The voltage at the grid port can be written as .

[0026] also, Figure 1 The structure of the hybrid grid-connected circuit is also given, in which , , These are the line impedances between the grid-connected converter and its common coupling point, between the grid-connected converter and its common coupling point, and between the two converters, respectively. Therefore, defining the grid-connected port of the grid-connected converter, the grid-connected port of the grid-connected converter, and the grid port as ports 1 to 3, the system admittance matrix of the hybrid grid-connected system is then obtained. Can be written as in .

[0027] Define the output current vector and port voltage vector of the grid converter in the system as follows: in Let the port voltages of the grid-connected converter be defined. The output current vector and port voltage vector of the generalized grid-connected converter are defined as follows: in and These are the port currents of the grid-connected converter and the power grid, respectively.

[0028] Therefore, the phase-locked loop detection voltage of the grid-connected converter can be characterized based on the system admittance matrix, the output current of the grid-connected converter, and the port voltage of the generalized grid-connected converter. The output active power of the grid-type converter , written as The circuit-related physical quantities are obtained from the admittance matrix, and its specific expression is as follows: | and ∠ represent taking the magnitude and phase angle of the corresponding complex number, respectively; The phase-locked loop detection voltage of the grid converter will be used. The output active power of the grid-type converter Substituting the corresponding transient motion equations of the converter, we obtain the relative power angles of the grid-connected converter and the grid-connected converter in the hybrid grid-connected system. And the relative power angle of the grid-connected converter relative to the power grid. The transient equations of motion are respectively in , and Relative work angles and The difference between the steady-state values ​​at their corresponding stable equilibrium points, and The detailed expression is function and Defined as In the above transient motion equations, the coefficient function The detailed expression is written as Where the function and Defined as Based on this, the dissipation matrix used to characterize the relative power angle input-output stability and its interconnection relationship in a hybrid grid system can be obtained. , written as in Furthermore, the coefficients of Young's inequality are chosen as... Then, when the following relationship is satisfied, the dissipation matrix is... For non-singular M-matrices: Based on the above constraints, a series of rectangular energy angle domains were calculated. in Within this rectangular power angle domain, the global Lyapunov function of the hybrid grid-connected system can be constructed, written as: The coefficients in the function can be obtained from get, The elements in the middle can be any value greater than zero.

[0029] The minimum energy of the global Lyapunov function on the boundary of the rectangular work angle domain is defined as the critical energy value of the system, written as: Based on this, an elliptical transient synchronous stability domain can be obtained within the aforementioned rectangular power angle domain, written as: In the elliptic work angle domain For any angle of work within the range, the global Lyapunov function satisfies Therefore, it can be deduced that the initial state of the power angle of a multi-converter system defined at any point within the elliptical power angle domain gradually converges to the system's stable equilibrium point during the transient process. Thus, the elliptical power angle domain... The boundary can be used as a conservative estimate of the transient synchronous stability boundary of the multi-converter system.

[0030] for Figure 1 The grid-connected system of the grid-connected converter shown is verified using the following per-unit parameter settings: the reference current of the grid-connected converter. for pu, the reference voltage amplitude of the grid-type converter. Rated value is pu, the line impedances are respectively =j0.1 pu 、 =j0.05 pu、 =j1.0p.u., grid voltage amplitude It is 1.0 pu. This is the proportional gain of the phase-locked loop (PLL) of the grid converter. The equivalent damping coefficient of the grid-type converter is 0.2 pu. The active power reference value for a grid-type converter is 20 pu. It is -0.50 pu.

[0031] Using the critical fault clearing time as an indicator allows for a quantitative measurement of the accuracy of different critical stability criteria. The actual critical fault clearing time of the system is 338 ms. Based on the critical stability criterion obtained by approximating the transient damping energy after fault clearing using the proposed method, the critical fault clearing time is calculated to be 207 ms. This is close to the actual fault clearing time and conservatively estimates the impact of transient interaction power between converters on transient stability. Therefore, the result can be used to guide fault clearing in the system.

[0032] The above analysis results verify the effectiveness and advantages of the proposed quantitative analysis method for transient damping energy.

[0033] The above description of the embodiments is provided to enable those skilled in the art to understand and apply the present invention. It will be apparent to those skilled in the art that various modifications can be easily made to the above embodiments, and the general principles described herein can be applied to other embodiments without creative effort. Therefore, the present invention is not limited to the above embodiments, and any improvements and modifications made to the present invention by those skilled in the art based on the disclosure thereof should be within the scope of protection of the present invention. Figure 1 The control structure shown considers reactive power control, analysis using different fault types, and analysis of systems with multiple converters and different circuit structures. Therefore, the claims are intended to cover all variations within the true concept and scope of this invention.

Claims

1. A method for quantitatively characterizing the transient synchronous stability boundary of a multi-converter system, characterized in that, The multi-converter system comprises several grid-type converters and at least two network-type converters; the method for quantitatively characterizing the transient synchronous stability boundary includes the following steps: 1) Establish the transient power angle motion equations for each converter in the multi-converter system; 2) Based on the transient power angle motion equation and the admittance matrix of the multi-converter system, the relative power angle motion equation between each pair of converters in the system is obtained; 3) Based on the relative power angle motion equation, construct a dissipation matrix describing the relative power angle motion stability and interconnection relationship of the converter; 4) Determine the rectangular stability region of the system's relative work angle under the condition that the dissipation matrix is ​​a non-singular M-matrix; 5) Construct the global Lyapunov function of the system within the rectangular stability domain and calculate the critical energy value; based on the critical energy value, determine the elliptical power angle domain of the transient synchronous stability boundary of the system as the transient synchronous stability boundary of the multi-converter system.

2. The method according to claim 1, characterized in that, In step 1), the first The transient power angle motion of a grid-type converter is expressed as follows: ； in, , These are the power angle and speed of the grid converter, respectively. This refers to the proportional gain of the first-order phase-locked loop of the grid converter. The phase-locked loop of the grid converter detects the q-axis quadrature component of the converter port voltage; No. The transient power angle motion of a grid-type converter is expressed as follows: ； in, , These are the power angle and speed of the grid-type converter. This is the droop coefficient for power synchronization control of the grid-type converter. This refers to the output active power of the grid-type converter. This serves as the active power reference for the grid-type converter.

3. The method according to claim 1, characterized in that, Step 2) includes: 21) For those containing Taiwan-type grid converter and For a multi-converter system with a grid-type converter, the port voltage-current relationship is described by the system admittance matrix, and its expression is as follows: ； in and They are respectively The current vector and voltage vector of the grid-type converter. and They are respectively Current vector and voltage vector of a grid-type converter Here is the admittance matrix of the multi-converter system. , , , for The corresponding submatrix; 22) and Expressed by the output current of the grid-connected converter, the port voltage of the grid-connected converter, and the circuit impedance; and It is expressed by the output current of the grid-connected converter, the port voltage of the grid-connected converter, and the circuit impedance; 23) Obtain the first... in the multi-converter system Taiwan-connected grid converter and the first The relative power angle motion equations of a grid-type converter and the first in a multi-converter system. Taiwan-type grid converter and the first The relative power angle motion equation of a grid-type converter.

4. The method according to claim 3, characterized in that, In step 22), and The expression is as follows: ； and The expression is as follows: ； in, k For each grid-type converter, the index number is... r For each grid-type converter; and The first The amplitude and current angle of the output current of the grid-connected converter. For the first The terminal voltage amplitude of the grid-type converter; the remaining parameters in the expression satisfy: Where | and ∠ represent the magnitude and phase angle of the corresponding complex number, respectively.

5. The method according to claim 4, characterized in that, In step 23), the first in the multi-converter system Taiwan-connected grid converter and the first The transient motion expression of the relative power angle of a grid-type converter is written as: ； in, For the first Taiwan-connected grid converter and the first The relative power angle between the transformer and the grid converter. For the first Taiwan-connected grid converter and the first The relative power angle between grid-type converters. For the first Taiwan-type grid converter and the first The relative power angle between grid-type converters. For the first Taiwan-connected grid converter and the first The relative speed between the grid-type converters.

6. The method according to claim 5, characterized in that, In step 23), the first in the multi-converter system Taiwan-type grid converter and the first The transient motion expression of the relative power angle of a grid-type converter is written as: ； in For the first Taiwan-type grid converter and the first The relative speed between the grid-type converters.

7. The method according to claim 1, characterized in that, Step 3) includes: 31) The power angle dynamics of a multi-converter system are determined by a single... A nonlinear system description of several subsystems, wherein The state variables of this nonlinear system are The relative angle of work is expressed as follows: ； in, For selection Relative power angle of grid-type converter - network-type converter and their respective steady-state values ​​at their stable equilibrium points Difference between , For selection Network converter - Relative power angle of network converter and their respective steady-state values ​​at their stable equilibrium points Difference between ,in The value is arrive ; 32) In the multi-variable converter system The dynamic unified expression of each subsystem is as follows: ； Where the function For each subsystem, there is a dynamic function; 33) Decompose the dynamic function of each subsystem into the sum of the action functions of each state variable of the system, written as: ； Where the coefficient function From the following formula, we get ； 34) Define the Lyapunov function of each subsystem as follows: Based on the dynamic equations of the subsystem, the input-output inequality of the subsystem is further obtained, written as: ； in, is the coefficient of Young's inequality, which can take any positive value; and Defined as ； 35) Further refine the input-output inequality of the multivariator system using the dissipation matrix. Representation, dissipation matrix The definition of 。 8. The method according to claim 1, characterized in that, Step 4) includes: Construct the global Lyapunov function of the multivariator system, which is defined as follows: ； Where the weighting coefficient vector is ; If and only if the dissipation matrix When the M matrix is ​​non-singular, the weighted coefficient vector can be constructed based on the following formula. : ； in The elements in the set are any values ​​greater than zero, and the overall Lyapunov function satisfies the following dissipation relation: ； Thus, a series of rectangular work angle domains are obtained, expressed as: ； The boundary of this functional angle domain is defined by vectors. Definition, vector The boundary dissipation matrix satisfies its definition. It is a non-singular M matrix.

9. The method according to claim 8, characterized in that, Step 5) includes: The minimum energy of the global Lyapunov function on the boundary of the rectangular work angle domain is defined as the critical energy value of the system, written as: Based on this, a... The elliptic transient synchronous stability region of the work angle is written as In the elliptic work angle domain For any angle of work within the range, the global Lyapunov function satisfies The initial state of the power angle of a multi-converter system defined at any point within the elliptical power angle domain gradually converges to the stable equilibrium point of the system during the transient process.

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