Stability evaluation method and system for converter grid-connected system considering periodic time variation

Abstract

The present invention discloses a method and system for evaluating the stability of a converter grid-connected system considering periodic time variation, comprising: establishing an LTP state space model of a modular multi-level converter grid-connected system; selecting N+1 discrete points θ on a periodic interval [0, T]; j As the configuration point, at each discrete point, the derivative value l′ i (θ j ) is the element (j, i) to form a Chebyshev differential matrix; the periodic time-varying differential equations of the LTP state space model are converted into a set of algebraic equations using the Chebyshev differential matrix, and then a single-valued matrix is ​​obtained; all or part of the key eigenvalues ​​of the single-valued matrix are solved, and the stability of the modular multi-level converter grid-connected system is determined based on the key eigenvalues. The present invention can accurately evaluate the stability of the converter system considering the periodic time-varying characteristics, and has high efficiency compared with numerical methods such as time domain integration and is suitable for large-scale complex systems.

Description

Technical Field

[0001] The present invention relates to the field of power electronics technology, and in particular to a method and system for evaluating the stability of a converter grid-connected system taking into account periodic time variation. Background Art

[0002] The statements in this section merely provide background information related to the present invention and do not necessarily constitute prior art.

[0003] As the application of modular multilevel converters (MMC) in power electronic power systems continues to increase, the related stability issues have become more prominent, posing challenges to the safe and stable operation of flexible DC interconnected power grids. In this regard, the periodic time-varying characteristics of the MMC dynamic characteristic model have received much attention in recent years. This is caused by the switch modulation process and the steady-state operation cycle trajectory of the AC system. The MMC grid-connected system mainly includes three parts: the main circuit and controller of the MMC and the AC network. Its small disturbance dynamics can be described by a set of nonlinear periodic time-varying differential equations. Then, the trajectory is linearized on the steady-state operation cycle trajectory, and the corresponding linear periodic time-varying system (LTP) state space model can be established:

[0004]

[0005] In the formula, is the system state variable, Enter variables for the system; and It is the system time-varying matrix with the industrial frequency period T = 0.02s as the minimum period.

[0006] For example, ignoring the switching dynamics and the difference between the voltages of the bridge arm submodules, considering that the dynamics of the capacitor voltage of each submodule is affected by the bridge arm current i u (t), the total capacitance voltage v of the MMC single-phase upper bridge arm cu The linearized state equation of (t) is

[0007]

[0008] Where n u (t) is the switching modulation function; the subscript “0” represents the steady-state periodic trajectory of each variable, and the prefix “Δ” represents a small disturbance; n u0 (t) and i u0 (t) can be expressed as a trigonometric function, with n u0 (t) as an example:

[0009]

[0010] Among them, ω 1 is the system base frequency; mk and θ k (k=1,2,…) are the modulation sequence number and the corresponding phase angle of the fundamental or harmonic modulation voltage.

[0011] If the submodule capacitor voltage is constant, the MMC bridge arm voltage v u (t) = v cu n u (t) is an ideal step wave; if the switching function is not considered further, then v u (t) is an ideal sine wave, and the system can be represented by a time-invariant model. In addition, under the condition of asymmetric AC grid voltage, the energy between the three phases of the MMC and between the upper and lower bridge arms of each phase is no longer balanced, and the MMC grid-connected system exhibits more complex time-varying characteristics and multi-frequency component coupling characteristics.

[0012] In recent years, more and more literatures have been based on LTP state space model to achieve strict evaluation of the stability of MMC grid-connected system considering periodic time-varying characteristics. Considering that the frequency domain model of LTP system cannot be directly obtained by Laplace transform, it is best to convert it into a stability equivalent linear periodic time-invariant (LTI) system when conducting small disturbance stability analysis.

[0013] According to this idea, the famous Floquet theory points out that the transition matrix Φ(t 0 +T,t 0 ), that is, a single-value matrix, is time-invariant, where t 0 is any time. The eigenvalues ​​of the single-value matrix are called Floquet eigenmultipliers, and their position with the unit circle on the z plane directly indicates whether the original LTP system is unstable. However, due to the time-varying nature, the analytical expression of the differential equation of the LTP system is difficult to determine except for extremely simple cases. In other words, for complex LTP systems, it is difficult to obtain an analytical expression of the closed form of its single-value matrix.

[0014] Therefore, the time domain integration method is often used to numerically calculate the single-value matrix to analyze the stability of the MMC grid-connected system. First, it is assumed that the n initial states of the system are the column vectors of the unit matrix, and then the original state differential equation is integrated in the time domain to numerically construct the single-value matrix, that is, Φ(T,0)=[r 1 (T),r 2 (T),…,r n (T), where r k(T)(k=1,2,...,n) are n independent solutions obtained according to each initial condition. However, the time domain integration numerical method inevitably requires a lot of calculations, resulting in low computational efficiency, especially when applied to large-scale modular multilevel converter grid-connected systems, it cannot meet the requirements of the system. Summary of the invention

[0015] In order to solve the above problems, the present invention proposes a method and system for evaluating the stability of a converter grid-connected system considering periodic time variation. The method can accurately evaluate the stability of a modular multilevel converter grid-connected system.

[0016] In some embodiments, the following technical solutions are adopted:

[0017] A method for evaluating the stability of a converter grid-connected system considering periodic time variation, comprising:

[0018] Establish the LTP state space model of modular multilevel converter grid-connected system;

[0019] In the period interval [0, T] of the LTP state space model, select N+1 discrete points θ j As the configuration point, at each discrete point, the discrete values ​​of the system state Δx and its derivative z(t) of the LTP state space model are defined as Δx j and z j ; Assume that the only Lagrange interpolation polynomial that exists and does not exceed N is used as the collocation polynomial, satisfying t∈[0,T], where l j (·) is the discrete point θ j The relevant Lagrange interpolation coefficients, j = 0, 1, ..., N; N is a positive integer;

[0020] Take the derivative value l′ i (θ j )(i,j=0,1,...,N) forms the Chebyshev differential matrix D for element (j,i);

[0021] The periodic time-varying differential equations of the LTP state space model are transformed into a set of algebraic equations using the Chebyshev differential matrix D, and then the expression of the system state value at time t=T with respect to the initial state is obtained, and the coefficient matrix of the expression is a single-value matrix;

[0022] All or part of the key eigenvalues ​​of the single value matrix are solved, and the stability of the modular multilevel converter grid-connected system is determined based on the key eigenvalues.

[0023] If all the key eigenvalues ​​are within the unit circle of the z-plane, that is, the modulus values ​​are all less than 1, then the system is asymptotically stable; otherwise, the system is unstable.

[0024] In other embodiments, the following technical solutions are adopted:

[0025] A stability evaluation system for a converter grid-connected system considering periodic time variation, comprising:

[0026] A model building module for building an LTP state space model of a modular multilevel converter grid-connected system;

[0027] A configuration point selection module is used to select N+1 discrete points θ on the period interval [0, T] of the LTP state space model. j As a configuration point;

[0028] A polynomial definition module is configured to define the discrete values ​​of the system state Δx and its derivative z(t) of the LTP state space model at each discrete point as Δx j and z j ; Assume that the only Lagrange interpolation polynomial that exists and does not exceed N is used as the collocation polynomial, satisfying t∈[0,T], where l j (·) is the discrete point θ j The relevant Lagrange interpolation coefficients, j = 0, 1, ..., N; N is a positive integer;

[0029] Chebyshev differential matrix building block for the derivative value l′ i (θ j )(i,j=0,1,...,N) forms the Chebyshev differential matrix D for element (j,i);

[0030] The single-value matrix analytical solution module uses the Chebyshev differential matrix D to transform the periodic time-varying differential equations of the LTP state space model into a set of algebraic equations, and then obtains the expression of the system state value at time t=T with respect to the initial state, and the coefficient matrix of the expression is the single-value matrix;

[0031] The system stability analysis module is used to solve all or part of the key eigenvalues ​​of the single value matrix and perform stability determination of the modular multilevel converter grid-connected system based on the key eigenvalues.

[0032] If all the key eigenvalues ​​are within the unit circle of the z-plane, that is, the modulus values ​​are all less than 1, then the system is asymptotically stable; otherwise, the system is unstable.

[0033] In other embodiments, the following technical solutions are adopted:

[0034] A terminal device comprises a processor and a memory, wherein the processor is used to implement instructions; the memory is used to store a plurality of instructions, wherein the instructions are suitable for being loaded by the processor and executing the above-mentioned converter grid-connected system stability assessment method considering periodic time variation.

[0035] In other embodiments, the following technical solutions are adopted:

[0036] A computer-readable storage medium stores a plurality of instructions, wherein the instructions are suitable for being loaded by a processor of a terminal device and executing the above-mentioned converter grid-connected system stability assessment method considering periodic time variation.

[0037] Compared with the prior art, the present invention has the following beneficial effects:

[0038] (1) The present invention adopts a configuration method in the process of constructing a single-value matrix of an MMC grid-connected system considering periodic time-varying characteristics, including selecting a set of configuration points on a periodic interval and defining a configuration polynomial. Considering the superiority of the configuration method itself, the Floquet characteristic multiplier calculated by the method proposed in the present invention has a high accuracy, and its accuracy is related to the number of configuration points N.

[0039] (2) The analytical expression of the single-value matrix of the MMC grid-connected system constructed by the present invention considering the periodic time-varying characteristics is composed of the unit matrix, the discrete values ​​of the system time-varying state matrix, and the sub-matrix of the Chebyshev differential matrix D, where D is only related to the number of configuration points N. In other words, when analyzing different systems, it is only necessary to replace the corresponding discrete values ​​of the system state matrix, which is conducive to the application of the method proposed by the present invention in large systems.

[0040] (3) Compared with traditional numerical methods such as time domain simulation, the analytical solution method of the single-value matrix of the MMC grid-connected system considering the periodic time-varying characteristics proposed in the present invention has better computer computing performance, can accurately evaluate the system stability considering the periodic time-varying characteristics, and is suitable for larger-scale complex MMC grid-connected systems.

[0041] (4) The analytical solution method for the single-value matrix of the MMC grid-connected system considering the periodic time-varying characteristics proposed in the present invention is generalized and universal, and can essentially be used to process all systems whose dynamics are described by differential equations with periodic time-varying coefficients.

[0042] Other features and advantages of additional aspects of the present invention will be given in part in the following description, and in part will become obvious from the following description, or will be learned through the practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 It is a flow chart of a method for evaluating the stability of a converter grid-connected system considering periodic time variation in an embodiment of the present invention;

[0044] Figure 2 Schematic diagram of configuration points on a periodic interval and corresponding system states and their derivative discrete values ​​in an embodiment of the present invention. DETAILED DESCRIPTION

[0045] It should be noted that the following detailed descriptions are illustrative and are intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used in the present invention have the same meanings as those commonly understood by those skilled in the art to which the present application belongs.

[0046] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0047] Embodiment 1

[0048] In order to accurately evaluate the stability of the MMC grid-connected system considering the periodic time-varying characteristics, in one or more embodiments, a stability evaluation method for the converter grid-connected system considering the periodic time-varying characteristics is disclosed, by defining a set of Chebyshev configuration points and Lagrange configuration polynomials, constructing the transfer matrix of the system state before and after one cycle, that is, the analytical expression of the single-value matrix. On the one hand, due to the use of the configuration method, its eigenvalue, that is, the Floquet eigenmultiplier, has high precision and can accurately evaluate the stability of the MMC grid-connected system; on the other hand, compared with traditional numerical methods such as time domain simulation, this method can obtain efficient computer performance.

[0049] Combination Figure 1 The method of this embodiment specifically includes the following process:

[0050] Step 1: Establish the LTP state space model of the modular multilevel converter grid-connected system;

[0051] Specifically, the small disturbance dynamics of the MMC grid-connected system is described by a set of nonlinear periodic time-varying differential equations;

[0052] Then the trajectory is linearized on the steady-state operation cycle trajectory to obtain:

[0053]

[0054] in, are system state variables, such as the differential-mode and common-mode components of the output voltages of the upper and lower bridge arms, the differential-mode and common-mode components of the output currents of the upper and lower bridge arms, etc.; Input variables for the system, such as DC side voltage, command reference values ​​for active current controller and circulating current suppression controller, etc. and They are respectively the system time-varying matrices with the power frequency period T = 0.02s as the minimum period.

[0055] Since the system stability determination is independent of the input variable △u(t), △u(t) is usually set to 0; thus establishing the corresponding LTP state space model:

[0056] △z(t)=A(t)△x(t)

[0057] in, is the system state variable, △z(t) is the derivative of the system state variable, It is the system time-varying matrix with the industrial frequency period T = 0.02s as the minimum period.

[0058] Step 2: On the interval [-1,1], the first kind N-order Chebyshev polynomial is defined as:

[0059] T N (t)=cos(Nθ)=cos(Narccos(t))(t∈[-1,1]), and has N+1 poles t j =cos(jπ / N)(j=0,1,...,N).

[0060] Accordingly, select N+1 discrete points θ on the periodic interval [0,T] j =T(t j +1) / 2(j=0,1,...,N) as the collocation point, such as Figure 2 shown.

[0061] Step 3: At N+1 discrete points θ j At (j=0,1,...,N), the discrete values ​​of the system state Δx and its derivative z(t) are defined as Δx j and z j Assume that the only Lagrange interpolation polynomial that exists and does not exceed N is used as the collocation polynomial, satisfying:

[0062]

[0063] Among them, l j (·) is the discrete point θ j The associated Lagrange interpolation coefficients, j = 0, 1, ..., N;

[0064]

[0065] θ j and θk Both refer to discrete points, k≠j.

[0066] Step 4: Take the derivative value l′ i (θ j )(i,j=0,1,...,N) forms the Chebyshev differential matrix for element (j,i) Its explicit expression is:

[0067]

[0068]

[0069] Step 5: At a non-zero configuration point θ j (j=0,1,...,N-1), we have:

[0070]

[0071] Among them, l′ i (θ j ) is shown below, i = 0, 1, ..., N; j = 1, 2, ..., N.

[0072]

[0073] θ i ,θ j and θ k All refer to discrete points, k≠i,j.

[0074] In this way, the periodic time-varying differential equations are transformed into a set of algebraic equations. Then, they are rewritten into vector form and the appropriate terms are transposed to obtain the expression of the system state value at time t = T with respect to the initial state △x N =Σ△x 0 , whose coefficient matrix is ​​the analytical expression of the single-value matrix

[0075]

[0076] In the formula, and A is a submatrix of the Chebyshev differential matrix D. j (j=0,1,…N-1) is N non-zero discrete points θ j The discrete value of the system time-varying state matrix A(t) at (j=0,1,...,N-1), that is, A j =A(θ j )(j=0,1,…N-1).

[0077] It should be noted that the single-value matrix Σ is composed of the unit matrix, the discrete value A of the system time-varying state matrixj (j=0,1,…N-1) and the submatrix of the Chebyshev differential matrix D, where D is only related to the number of configuration points N. In other words, when analyzing different systems, it is only necessary to replace the corresponding system state matrix discrete value A j (j=0,1,…N-1). It should also be pointed out that due to the superiority of the collocation method, the matrix Σ is an approximate analytical solution of the system single-value matrix with high accuracy, and its accuracy is related to the number of collocation points N.

[0078] Step 6: Using the QR or Krylov subspace eigenvalue solution method, all or part of the key eigenvalues ​​of the single-value matrix, namely the Floquet characteristic multipliers, can be efficiently solved to quickly determine the stability of the system. If all Floquet characteristic multipliers are within the unit circle of the z plane, that is, the modulus values ​​are all less than 1, then the system is asymptotically stable.

[0079] Embodiment 2

[0080] In one or more embodiments, a system for evaluating the stability of a grid-connected converter system considering periodic time variation is disclosed, comprising:

[0081] A model building module for building an LTP state space model of a modular multilevel converter grid-connected system;

[0082] A configuration point selection module is used to select N+1 discrete points θ on the period interval [0, T] of the LTP state space model. j As a configuration point;

[0083] A polynomial definition module is configured to define the discrete values ​​of the system state Δx and its derivative z(t) of the LTP state space model at each discrete point as Δx j and z j ; Assume that the only Lagrange interpolation polynomial that exists and does not exceed N is used as the collocation polynomial, satisfying t∈[0,T], where l j (·) is the discrete point θ j The relevant Lagrange interpolation coefficients, j = 0, 1, ..., N; N is a positive integer.

[0084] Chebyshev differential matrix building block for the derivative value l′ i (θ j )(i,j=0,1,...,N) forms the Chebyshev differential matrix D for element (j,i);

[0085] The single-value matrix analytical solution module uses the Chebyshev differential matrix D to transform the periodic time-varying differential equations of the LTP state space model into a set of algebraic equations, and then obtains the expression of the system state value at time t=T with respect to the initial state, and the coefficient matrix of the expression is the single-value matrix;

[0086] The system stability analysis module is used to solve all or part of the key eigenvalues ​​of the single value matrix and perform stability determination of the modular multilevel converter grid-connected system based on the key eigenvalues.

[0087] If all the key eigenvalues ​​are within the unit circle of the z-plane, that is, the modulus values ​​are all less than 1, then the system is asymptotically stable; otherwise, the system is unstable.

[0088] In this embodiment, the specific implementation of each module can refer to the description in the above embodiment 1 and will not be repeated here.

[0089] Embodiment 3

[0090] In one or more embodiments, a terminal device is disclosed, including a server, the server including a memory, a processor, and a computer program stored in the memory and executable on the processor, and the processor implements the method for evaluating the stability of a grid-connected converter system considering periodic time variation in Embodiment 1 when executing the program. For the sake of brevity, it will not be described in detail here.

[0091] It should be understood that in this embodiment, the processor may be a central processing unit CPU, and the processor may also be other general-purpose processors, digital signal processors DSP, application-specific integrated circuits ASIC, off-the-shelf programmable gate arrays FPGA or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc.

[0092] The memory may include a read-only memory and a random access memory, and provide instructions and data to the processor. A portion of the memory may also include a non-volatile random access memory. For example, the memory may also store information about the device type.

[0093] In the implementation process, each step of the above method can be completed by an integrated logic circuit of hardware in a processor or an instruction in the form of software.

[0094] Embodiment 4

[0095] In one or more embodiments, a computer-readable storage medium is disclosed, in which a plurality of instructions are stored, wherein the instructions are suitable for being loaded by a processor of a terminal device and executing the method for evaluating the stability of a converter grid-connected system considering periodic time variation described in Example 1.

[0096] Although the above describes the specific implementation mode of the present invention in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art on the basis of the technical solution of the present invention without creative work are still within the scope of protection of the present invention.

Claims

1. A method for evaluating the stability of a grid-connected converter system considering periodic time variation, characterized in that: include: Establish the LTP state space model of modular multilevel converter grid-connected system; In the period interval [0, T] of the LTP state space model, select N+1 discrete points θ j As the configuration point, at each discrete point, the discrete values ​​of the system state Δx and its derivative z(t) of the LTP state space model are defined as Δx j and z j ; Assume that the only Lagrange interpolation polynomial that exists and does not exceed N is used as the collocation polynomial, satisfying in is the discrete point θ j The relevant Lagrange interpolation coefficients, j = 0, 1, ..., N; N is a positive integer; Take the derivative value (i,j=0,1,...,N) forms the Chebyshev differential matrix D for element (j,i); The periodic time-varying differential equations of the LTP state space model are transformed into a set of algebraic equations using the Chebyshev differential matrix D, and then the expression of the system state value at time t=T with respect to the initial state is obtained, and the coefficient matrix of the expression is a single-value matrix; All or part of the key eigenvalues ​​of the single value matrix are solved, and the stability of the modular multilevel converter grid-connected system is determined based on the key eigenvalues.

2. A method for evaluating the stability of a converter grid-connected system considering periodic time variation according to claim 1, characterized in that: The LTP state space model of the modular multilevel converter grid-connected system is established, specifically: The small disturbance dynamics of the modular multilevel converter grid-connected system is described by a set of nonlinear periodic time-varying differential equations, and the trajectory is linearized on the steady-state operation cycle trajectory to establish the corresponding LTP state space model, i.e., △z(t)=A(t)△x(t); in, is the system state variable, △z(t) is the derivative of the system state variable, It is the system time-varying matrix with the industrial frequency period T = 0.02s as the minimum period.

3. A method for evaluating the stability of a converter grid-connected system considering periodic time variation according to claim 1, characterized in that: With discrete points θ j The relevant Lagrange interpolation coefficients Specifically: Among them, θ j and θ k Both refer to discrete points, k≠j.

4. A method for evaluating the stability of a converter grid-connected system considering periodic time variation according to claim 1, characterized in that: The single value matrix is ​​specifically: in, and is a submatrix of the Chebyshev differential matrix D; A j (j=0,1,…N-1) is N non-zero discrete points θ j The discrete value of the system time-varying state matrix A(t) at (j=0,1,...,N-1), that is, A j =A(θ j )(j=0,1,…N-1).

5. The method for evaluating the stability of a converter grid-connected system considering periodic time variation according to claim 1, characterized in that: Solve all or part of the key eigenvalues ​​of the single value matrix, specifically: The QR or Krylov subspace eigenvalue solving method is used to solve all or part of the key eigenvalues ​​of the single-valued matrix.

6. A method for evaluating the stability of a converter grid-connected system considering periodic time variation according to claim 1, characterized in that: The stability of the modular multilevel converter grid-connected system is determined based on the key characteristic values, specifically: If all the key eigenvalues ​​are within the unit circle of the z-plane, that is, the modulus values ​​are all less than 1, then the system is asymptotically stable; otherwise, the system is unstable.

7. A stability assessment system for a converter grid-connected system considering periodic time variation, characterized in that: include: A model building module for building an LTP state space model of a modular multilevel converter grid-connected system; A configuration point selection module is used to select N+1 discrete points θ on the period interval [0, T] of the LTP state space model. j As a configuration point; A polynomial definition module is configured to define the discrete values ​​of the system state Δx and its derivative z(t) of the LTP state space model at each discrete point as Δx j and z j ; Assume that the only Lagrange interpolation polynomial that exists and does not exceed N is used as the collocation polynomial, satisfying in is the discrete point θ j The relevant Lagrange interpolation coefficients, j = 0, 1, ..., N; N is a positive integer; Chebyshev differential matrix building block for using derivative values (i,j=0,1,...,N) forms the Chebyshev differential matrix D for element (j,i); The single-value matrix analytical solution module uses the Chebyshev differential matrix D to transform the periodic time-varying differential equations of the LTP state space model into a set of algebraic equations, and then obtains the expression of the system state value at time t=T with respect to the initial state, and the coefficient matrix of the expression is the single-value matrix; The system stability analysis module is used to solve all or part of the key eigenvalues ​​of the single value matrix and perform stability determination of the modular multilevel converter grid-connected system based on the key eigenvalues.

8. A converter grid-connected system stability assessment system considering periodic time variation as claimed in claim 7, characterized in that: The stability of the modular multilevel converter grid-connected system is determined based on the key characteristic values, specifically: If all the key eigenvalues ​​are within the unit circle of the z-plane, that is, the modulus values ​​are all less than 1, then the system is asymptotically stable; otherwise, the system is unstable.

9. A terminal device, comprising a processor and a memory, wherein the processor is used to implement instructions; and the memory is used to store multiple instructions, characterized in that: The instructions are suitable for being loaded by a processor and executing the method for evaluating the stability of a converter grid-connected system taking into account periodic time variation as described in any one of claims 1 to 6.

10. A computer-readable storage medium storing a plurality of instructions, characterized in that: The instructions are suitable for being loaded by a processor of a terminal device and executing the method for evaluating the stability of a converter grid-connected system taking into account periodic time variation as described in any one of claims 1 to 6.

Images