Numerical simulation method for power electronic power system in multi-scale time-frequency spectrum

Abstract

The application discloses a multi-scale time-frequency spectrum numerical simulation method for a power electronic power system, and the method comprises the following steps: a high-order state space model of a first-order DQ dynamic phase form of the power electronic power system is established in real number space by adopting a DQ unified frequency transformation method; for a numerical simulation sub-period n, state variables and algebraic variables are projected into a Haar wavelet multi-resolution analysis coefficient space to obtain a multi-scale numerical integral format of the state variables and a multi-scale wavelet coefficient format of the algebraic variables; the L 2 (R) characteristics, the multi-scale numerical integral format of the state variables is integrated to obtain the multi-scale wavelet coefficient format of the state variables; and the multi-scale wavelet coefficient formats of the state variables and the algebraic variables are substituted into the high-dimensional state space model of the power electronic power system. The application can better adapt to the multi-time scale characteristics of the power electronic power system, has high simulation precision, and can significantly reduce simulation time consumption and memory occupation.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of power electronic power system simulation method, in particular to a kind of power electronic power system multiscale time-frequency spectrum numerical simulation method. BACKGROUND

[0002] In recent years, with the development of energy transformation strategy and the deepening of low-carbon green concept, microgrid, new energy and the like are connected to power grid on a large scale, high-voltage direct-current transmission, flexible alternating current transmission and the like are developed and applied rapidly, and power system gradually evolves into a complex system with new energy as the main body and alternating current-dc hybrid connection. Power electronic devices are widely used in source-load-network and other links of the system, and their inherent low inertia and rapidity change the characteristics of long response time and large inertia of the traditional power system with synchronous machine as the core, and introduce new time scale characteristics. The dynamic process of power electronic power system is essentially a process of coupling between multiple time scales, but due to the large span of these time scales, the system is more rigid, and higher stability, accuracy and rapidity are required for the simulation algorithm. SUMMARY

[0003] The technical problem to be solved by the present application is to provide a kind of power electronic power system multiscale time-frequency spectrum numerical simulation method, which can well adapt to the multiscale characteristics of power electronic power system and realize efficient and rapid simulation.

[0004] To solve the above technical problems, the technical solution adopted by the present application is:

[0005] A kind of power electronic power system multiscale time-frequency spectrum numerical simulation method, the method steps are as follows:

[0006] S101: a DQ unified frequency transformation method is used to establish a high-order state space model of first-order DQ dynamic phasor form of power electronic power system in real number space;

[0007] S102: for numerical simulation sub-period n, the state variable and the algebraic variable are projected into the Haar wavelet multi-resolution analysis coefficient space, and the multiscale numerical integration format of the state variable and the multiscale wavelet coefficient format of the algebraic variable are obtained respectively;

[0008] S103: using the L2 (R) characteristics of Haar wavelet multi-resolution analysis, the multiscale numerical integration format of the state variable is integrated to obtain the multiscale wavelet coefficient format of the state variable;

[0009] S104: the multi-scale wavelet coefficient format of the state variable and the algebraic variable is substituted into the high-order state space model of the power electronic power system in the first-order DQ dynamic phasor form, to obtain a multi-scale wavelet algebraic model of the power electronic power system in the Haar wavelet multi-resolution analysis wavelet coefficient space;

[0010] S105: the wavelet collocation method is used to obtain a collocation format of the multi-scale wavelet algebraic model of the power electronic power system, the Haar wavelet coefficients are solved by using the Newton-Raphson method, and wavelet numerical results of the state variable and the algebraic variable based on the Haar wavelet collocation method are obtained;

[0011] S106: a simulation strategy of multi-interval self-adaptation and multi-level self-adaptation is used to simulate the multi-scale wavelet algebraic model of the power electronic power system;

[0012] S107: simulation of the n+1th sub-interval period is performed, and the step S105 and the step S106 are repeated, and the cycle is repeated until the simulation is completed.

[0013] The power electronic power system multi-scale time-frequency spectrum numerical simulation method, the step S101 is as follows:

[0014] (I) an electric power electronic power system composed of new energy, power transmission network and synchronous generator is established, and a formula one of a high-order state space model in a first-order DQ dynamic phasor form under respective reference frequency coordinate system is obtained:

[0015]

[0016] 0=g(x,y,t) (Formula One)

[0017] Wherein: x is a state variable, y is an algebraic variable, and t is a time variable; x=[x G-d ,x G-q ,y N-d ,y N-q ,y W-d ,y W-q ] T ; y=[y G ,y N ,y W ] T ; x G-d , x N-d , x W-d are state variables d-axis phasor of synchronous generator, power transmission network and new energy equipment respectively, x G-q , x N-q , x W-q are state variables q-axis phasor of synchronous generator, power transmission network and new energy equipment respectively;

[0018] (I) the steady-state operating frequency ω of the power electronic power system s As the DQ unified frequency coordinate system of the system multi-device, a homogenous group algebra structure of DQ unified frequency transformation is established, and Park transformation is used to convert the interface algebra variables under independent frequency of each module into unified frequency variables;

[0019] (III) the transformed unified frequency variables are brought into each device model to obtain a high-order state space model of the power electronic power system in the form of first-order DQ dynamic phasor.

[0020] The above-mentioned multi-scale time-frequency spectrum numerical simulation method of the power electronic power system, the numerical simulation sub-period n is a simulation sub-interval [t n ,t n+1 ].

[0021] The above-mentioned multi-scale time-frequency spectrum numerical simulation method of the power electronic power system, the steps of step S102 are as follows:

[0022] (I) the state variable differential term and the algebraic variable are projected into the wavelet multi-resolution analysis coefficient space to obtain an approximation polynomial based on the wavelet form:

[0023]

[0024]

[0025] Wherein: P j is the orthogonal projection on the space V j , corresponding to the slow scale information in the state variable differential term and the algebraic variable, expressed by the low-resolution scale function , corresponding to the faster scale information in the state variable differential term and the algebraic variable, expressed by the high-resolution wavelet function ψ j,k (t);

[0026] (II) the i-th order Haar wavelet scale function in a simulation sub-period n is expressed as:

[0027]

[0028] Wherein: ξ1(i)=t n +2kμ△x, ξ2(i)=t n +(2k+1)μ△x, ξ3(i)=t n +2(k+1)μ△x, μ=M / m, M=2 J , m=2 j(j = 0, 1...J), k = 0, 1,...m-1, i = j+k+1, j and k represent the coefficients of stretching and translation respectively, J represents the maximum resolution corresponding to the number of wavelet layers;

[0029] (III) using the orthogonality of Haar wavelet function , the state variables and algebraic variables in the high-order state space model of the first-order DQ dynamic phasor form of the power electronic power system are projected into the Haar wavelet multi-resolution analysis coefficient space, to obtain the multi-scale wavelet coefficient format of the differential items of the state variables and the algebraic variables:

[0030]

[0031]

[0032] wherein, is the i-th coefficient of the approximation expression of the differential items of the state variables and the algebraic variables on the simulation sub-time period [t n , t n+1 ];

[0033] (IV) integrating the differential items of the system state variables to obtain the multi-scale numerical integration format of the state variables x(t):

[0034]

[0035] wherein: x(t n ) is the value of the state variable x at t n .

[0036] The multi-scale time-frequency spectrum numerical simulation method of the power electronic power system, the formula of the multi-scale wavelet coefficient format of the state variables in step S103 is as follows:

[0037]

[0038] wherein: x(t n ) is the value of the state variable x at t n ; p i (t) is the integral item based on the analytical expression of the Haar wavelet scale function.

[0039] The multi-scale time-frequency spectrum numerical simulation method of the power electronic power system, the formula of the multi-scale wavelet algebraic model in step S104 is as follows:

[0040]

[0041]

[0042] wherein:

[0043] F = [F G ,F N ,F W ], G = [G G ,G N ,G W ],

[0044] The above-mentioned multi-scale time-frequency spectrum numerical simulation method of the power electronic power system, the wavelet collocation method in step S105 is used to obtain the multi-scale wavelet algebraic model of the power electronic power system, and the collocation format of the multi-scale wavelet algebraic model of the power electronic power system is obtained as follows:

[0045] (I) Constructing the interpolation wavelet collocation points on the simulation sub-interval [t n ,t n+1 ], the formula is used to solve each collocation point value.

[0046] Wherein: the wavelet layer number is J, the interpolation wavelet collocation point number is 2 J+1 , △t = (t n+1 -t n ) / 2 J+1 ;

[0047] (II) The calculated wavelet collocation point is substituted into the multi-scale wavelet format of each variable to obtain the multi-scale wavelet collocation format of the related variable, the scale stretching coefficient j is obtained to a certain upper limit J, and the resolution is 2 J+1 , and the multi-scale wavelet collocation format of each variable is approximately expressed as:

[0048]

[0049] Wherein: H, P are Haar wavelet transform matrices, H(i, l) = h i (x l ), P(i, l) = p i (x l ),

[0050] (III) The multi-scale wavelet format based on the Haar wavelet collocation is substituted into the multi-scale wavelet algebraic model of the power electronic power system in the Haar wavelet multi-resolution analysis wavelet coefficient space, and the formula of the collocation format of the multi-scale wavelet algebraic model of the power electronic power system is obtained:

[0051]

[0052] ​The multi-scale time-frequency spectrum numerical simulation method of the power electronic power system, the step S105 adopts Newton-Raphson method to solve the Haar wavelet coefficient, and the steps are as follows:

[0053] (I) calculating the initial value of the Haar wavelet coefficient under low resolution; by calculating the Haar wavelet matrix P, H under a small number of collocation points J=1 or 2, and then substituting the approximation polynomial in the wavelet form into the system differential algebraic model to solve simultaneously;

[0054] (II) recursively calculating the high-resolution Haar wavelet coefficient; the low-resolution Haar wavelet coefficient is used as part of the initial value of the wavelet coefficient under the next level resolution J+1, that is, if the wavelet coefficient value under a certain resolution J is obtained , then the initial value of the wavelet coefficient under the next level resolution J+1 is:

[0055]

[0056]

[0057] The multi-scale time-frequency spectrum numerical simulation method of the power electronic power system, the step S105 obtains the wavelet numerical result of the state variable and the algebraic variable based on the Haar wavelet collocation method, and the steps are as follows:

[0058] In a simulation sub-interval [t n , t n+1 ], the wavelet coefficients a, b obtained by Newton-Raphson method are substituted into formula eight to obtain the wavelet numerical result of the state variable and the algebraic variable based on the Haar wavelet collocation method in the simulation sub-interval [t n , t n+1 ].

[0059] The multi-scale time-frequency spectrum numerical simulation method of the power electronic power system, the content and steps of the step S106 are as follows:

[0060] (I) limiting a certain error threshold ε (ε>0) of the wavelet coefficient, and dividing the multi-scale wavelet format of each variable into two parts, taking the state variable as an example, to obtain the following form:

[0061]

[0062]

[0063]

[0064] (II) for a given wavelet coefficient error threshold ε, when max|a i |>ε, the number of wavelet subspaces W j is increased to become WJ1 , This provides a new approximate solution in the multi-resolution coefficient space of the Haar wavelet;

[0065] (III) The wavelet multi-interval adaptive simulation strategy described herein is to simulate sub-time periods [t] n ,t n+1 The interval length t n+1 -t n denoted as △t n The intervals are divided according to the accuracy requirements of each sub-interval, where the left endpoint of the next sub-interval is the right endpoint of the previous sub-interval; when the obtained Haar wavelet coefficients meet the conditions... When the system is considered to be in a transient response process, the length of the next subinterval is appropriately increased, and adaptively selected as . Otherwise, assuming the system is in a steady-state response process, the length of the compressed subinterval is calculated using the formula:

[0066] The beneficial effects of adopting the above technical solution are as follows: the Haar wavelet collocation method has relatively flexible high-order accuracy, and the accuracy requirements can be achieved by changing the simulation step size and the number of wavelet decomposition layers. Moreover, the simulation results are relatively reliable and accurate, and it has good adaptability to the dynamic simulation of power electronic power systems.

[0067] Under the premise of meeting certain accuracy requirements, based on the sparsity characteristics of the Haar wavelet matrix, the simulation speed of the Haar wavelet collocation method is significantly better than that of the trapezoidal integral method and the Runge-Kutta method. Moreover, compared with the trapezoidal integral method and the Runge-Kutta method, which cannot achieve large step size simulation, the simulation results of the Haar wavelet collocation method are stable and reliable under large step size, and the simulation efficiency is significantly improved.

[0068] The Haar wavelet collocation method has significant advantages in adaptive simulation, and can further improve the simulation efficiency of multi-timescale power electronic power systems through multi-interval adaptive and multi-level adaptive simulation techniques. Attached Figure Description

[0069] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0070] Figure 1 This is a schematic diagram of the simulation process of the virtual synchronous power grid system based on the adaptive Haar wavelet point allocation method according to an embodiment of the present invention;

[0071] Figure 2 This is a model structure diagram of the virtual synchronous power grid system according to an embodiment of the present invention;

[0072] Figure 3 This is a control structure diagram of a single-machine virtual synchronous power grid system according to an embodiment of the present invention;

[0073] Figure 4 A simulation curve diagram of filter q-axis voltage ufq of a single-machine infinite virtual synchronous machine system;

[0074] Figure 5 A simulation curve comparison diagram of filter q-axis voltage ufq of a single-machine infinite virtual synchronous machine system based on three simulation methods;

[0075] Figure 6 A filter voltage ufq error convergence characteristic curve diagram of a single-machine example system;

[0076] Figure 7 A model structure diagram of a two-region four-machine system of a virtual synchronous power grid according to an embodiment of the application;

[0077] Figure 8 A simulation comparison diagram of filter voltage ufq of G1-4 virtual synchronous machines in a two-region four-machine system;

[0078] Figure 9 A simulation curve comparison diagram of filter voltage ufq of G1 in a two-region four-machine system based on three simulation methods;

[0079] Figure 10 A filter voltage ufq error convergence characteristic curve diagram of G1 in a two-region four-machine system; DETAILED DESCRIPTION

[0080] The embodiments of the present application will be described in further detail below with reference to the drawings. Obviously, the described embodiments are only part of the embodiments of the present application, but not all the embodiments. Based on the embodiments of the present application, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the scope of the present application.

[0081] Referring to Figure 1 , the method comprises the following steps:

[0082] S101: A high-order state space model of a first-order DQ dynamic phasor form of a power electronic power system is established in real number space by using a DQ unified frequency transformation method.

[0083] The specific steps are as follows:

[0084] (I) A power electronic power system including new energy equipment, a power transmission network and a synchronous generator is established, and a high-order state space model of a first-order DQ dynamic phasor form of the new energy equipment, the power transmission network and the synchronous generator in respective reference frequency coordinate systems is established:

[0085]

[0086] 0=g(x,y,t) (Formula One)

[0087] where: x is state variable, y is algebraic variable, t is time variable; x = [x G-d ,x G-q ,y N-d ,y N-q ,y W-d ,y W-q ] T , y = [y G ,y N ,y W ] T , x G-d , x N-d , x W-d are the state variable d-axis phasor form of synchronous generator, power transmission network, new energy equipment respectively, x G-q , x N-q , x W-q are the state variable q-axis phasor form of synchronous generator, power transmission network, new energy equipment respectively.

[0088] (II): taking the steady-state operation frequency ω s of the power electronic power system as the DQ unified frequency coordinate system of synchronous generator, power transmission network, new energy equipment, establishing the isomorphic group algebraic structure of DQ unified frequency transformation, and converting the interface algebraic variables under independent frequency of each module into unified frequency variables by Park transformation;

[0089] (III): bringing the transformed unified frequency variables into the device model of synchronous generator, power transmission network, new energy equipment, obtaining the high-order state space model of the first-order DQ dynamic phasor form of the power electronic power system, and realizing the interconnection and intercommunication among each device.

[0090] S102: for a numerical simulation sub-period n, n is a simulation sub-interval [t n ,t n+1 ]. Project the state variable and the algebraic variable into the Haar wavelet multi-resolution analysis coefficient space, respectively obtaining the multi-scale numerical integral format of the state variable and the multi-scale wavelet coefficient format of the algebraic variable; the specific steps are as follows:

[0091] (I) project the differential term of the state variable and the algebraic variable into the wavelet multi-resolution analysis coefficient space, and obtain the analytical polynomial based on the wavelet form:

[0092]

[0093]

[0094] where: P j is the orthogonal projection in the space V j , The slow scale information in the differential terms of state variables and algebraic variables is expressed by low resolution scaling functions , The faster scale information in the differential terms of state variables and algebraic variables is expressed by high resolution wavelet functions j,k (t).

[0095] (II) In a simulation sub-interval l = [t n ,t n+1 ], the i-th order Haar wavelet scaling function is expressed as:

[0096]

[0097] wherein: ξ1(i) = t n + 2kμ△x, ξ2(i) = t n +(2k+1)μ△x, ξ3(i) = t n +2(k+1)μ△x, μ = M / m, M = 2 J , m = 2 j (j = 0, 1...J), k = 0, 1...m-1, i = j+k+1 j and k represent the scaling and translation coefficients respectively, and J represents the maximum resolution corresponding to the wavelet layer number.

[0098] (III) Using the orthogonality of Haar wavelet function , the state variables and algebraic variables in the high order state space model of the first order DQ dynamic phasor form of the power electronic power system are further projected into the Haar wavelet multi-resolution analysis coefficient space, and the multi-scale wavelet format of the differential terms of state variables and algebraic variables is further simplified as:

[0099]

[0100]

[0101] wherein, is the i-th coefficient of the approximation expression of the differential terms of state variables and algebraic variables in the simulation sub-interval [t n ,t n+1 ].

[0102] (IV) Integrating the differential terms of state variables corresponding to the state variables in formula four, the multi-scale numerical integration format of the state variables x(t) is as follows:

[0103]

[0104] wherein: x(t n ) is the value of the state variable x at t n . ​

[0105] S103: L 2 (R) characteristics, the multi-scale numerical integration format of the state variable is integrated to obtain the multi-scale wavelet coefficient format of the state variable;

[0106] Based on the analytical expression of the Haar wavelet scaling function, numerical integration is performed to obtain:

[0107]

[0108] The differential term corresponding to the system state variable is integrated, and the integral result of the Haar wavelet scaling function is substituted to obtain the multi-scale wavelet coefficient format of the state variable x(t) as follows:

[0109]

[0110] Where: x(t n ) is the value of the state variable x at time t n .

[0111] S104: Substitute the multi-scale wavelet coefficient format of the state variable and the algebraic variable into the high-dimensional state space model of the power electronic power system to obtain the multi-scale wavelet algebraic model of the power electronic power system in the Haar wavelet multi-resolution analysis wavelet coefficient space;

[0112]

[0113]

[0114] Where:

[0115] F = [F G , F N , F W ], G = [G G , G N , G W ],

[0116] Using multi-resolution analysis of wavelets, the differential term and the algebraic quantity of the system are mapped to the wavelet coefficient space, converted to an approximation polynomial based on the Haar wavelet form, and the system differential algebraic equation model is converted to an algebraic equation model. The essence of system simulation is converted to solving a set of nonlinear algebraic equations.

[0117] S105:

[0118] (I) The wavelet collocation method is used to obtain the collocation format of the multi-scale wavelet algebraic model of the power electronic power system, as follows:

[0119] Construct a simulation sub-period [tn t n+1 ] on the interpolation wavelet collocation, using the formula to solve each collocation point value.

[0120] Where: the wavelet layer is J, the interpolation wavelet collocation point is 2 J+1 , △t = (t n+1 -t n ) / 2 J+1 .

[0121] Using the calculated wavelet collocation point into the multi-scale wavelet format of each variable, the multi-scale wavelet collocation point format of the related variable is obtained, and the scale stretching coefficient j is obtained in the solving process. A certain upper limit J is obtained, so that the resolution reaches 2 J+1 , and the multi-scale wavelet collocation point format of each variable is approximately expressed as:

[0122]

[0123] Where: H, P is the Haar wavelet transform matrix, H(i, l) = h i (x l ), P(i, l) = p i (x l ),

[0124] (II) The multi-scale wavelet format based on the Haar wavelet collocation is substituted into the multi-scale wavelet algebraic model of the system, and the collocation format of the multi-scale wavelet algebraic model of the power electronic power system is obtained:

[0125]

[0126] (III) Newton-Raphson method is used to solve the Haar wavelet coefficient, and recursive calculation method is used to select the initial value of the Haar wavelet coefficient. First, calculate the initial value of the Haar wavelet coefficient at low resolution. By calculating the Haar wavelet matrix P, H under a small number of collocation points (J = 1 or 2), the approximation polynomial in wavelet form is substituted into the system differential algebraic model to solve. Then recursively calculate the high-resolution Haar wavelet coefficient. The low-resolution Haar wavelet coefficient is used as part of the initial value of the wavelet coefficient at the next level of resolution J+1, that is, if the wavelet coefficient value at a certain resolution J is obtained , then the initial value of the wavelet coefficient at the next level of resolution J+1 is:

[0127]

[0128]

[0129] (IV) The wavelet numerical results of the state variables and algebraic variables based on the Haar wavelet collocation method are as follows:

[0130] In one simulation sub-interval [t n ,t n+1 ], the wavelet coefficients a, b obtained by Newton-Raphson method are substituted into the formula The result is the wavelet numerical result of state variables and algebraic variables in the simulation sub-interval [t n ,t n+1 ] based on the Hal wavelet collocation method.

[0131] S106: simulate the multi-scale wavelet algebraic model of the power electronic power system by using the multi-interval adaptive and multi-level adaptive simulation strategy;

[0132] In step S106, the multi-interval adaptive and multi-level adaptive simulation strategy specifically includes: (I) limiting the error threshold ε (ε>0) of the wavelet coefficients, dividing the multi-scale wavelet format of each variable into two parts, and taking the state variable as an example to obtain the following form:

[0133]

[0134]

[0135]

[0136] (II) for a given wavelet coefficient error threshold ε, when max|a i |>ε, increase the number of wavelet subspaces W j to become W J1 , which is the new approximate solution in the Hal wavelet multi-resolution coefficient space. In this way, as long as the error ε of a certain sub-interval is controlled, the size of the wavelet expansion level can be automatically determined according to the requirement.

[0137] (III) the wavelet multi-interval adaptive simulation strategy specifically divides the interval length t n -t n+1 of the simulation sub-interval [t n+1 ,t n ] into △t n according to the accuracy requirement of each sub-interval, wherein the left end point value of the next sub-interval is the right end point value of the previous sub-interval. When the obtained Hal wavelet coefficients satisfy the condition , it is considered that the system is in a transient response process, and the length of the next sub-interval is appropriately increased to adaptively take Otherwise, it is considered that the system is in a steady-state response process, and the length of the sub-interval is compressed, and the length formula is The multi-interval adaptation is realized within the range of accuracy requirements, and the simulation efficiency is further improved.

[0138] S107: when the nth+1 sub-interval period is simulated, return to step S105, repeat steps S105 and S106, and cycle in this way until the simulation is completed.

[0139] For different sub-intervals, the multi-interval self-adaption and multi-level self-adaption simulation technology can automatically select the number of wavelet levels according to specific precision requirements, the number of wavelet levels J corresponding to different sub-intervals can be different, and through the control of the self-adaption algorithm on the selection of the sub-interval and the number of wavelet levels, the simulation efficiency can be improved and the memory used for calculation can be saved.

[0140] The simulation of the power electronic power system described in the method adopts a traditional collocation numerical algorithm with the following solving form:

[0141]

[0142] In the formula, a ij and b i are integral weight coefficients, c i is called an internal node, is the approximate value of the state variable at the internal node c i , and is called an internal point, when l=2 and b i =1 / 2, it is the expression form of the trapezoidal integral method.

[0143] In the sub-interval [t n , t n+1 ], the error of the collocation point will be transmitted to the collocation point , and the simulation error will continuously increase with the increase of the simulation time, and the simulation is relatively inefficient.

[0144] The overall truncation error calculation formula of the multi-scale time-frequency spectrum numerical simulation method of the power electronic power system is:

[0145]

[0146]

[0147] Wherein: * represents the accurate value, which is assumed to be known, R n is the local truncation error.

[0148] The overall truncation error depends on the value x n of the previous iteration and the local truncation error R n , there is no error transmission between adjacent collocation points, the overall error is low, the simulation precision and stability can be improved, and the simulation effect in a long time process is relatively superior to that of the traditional numerical method.

[0149] The method of the embodiment is further described below in combination with the legends in the drawings and examples in the description. The present application is analyzed and described based on a virtual synchronous grid example system. The virtual synchronous grid system is connected in parallel by multiple VSGs, transmits and exchanges power through a power transmission network, and is integrated into a power grid. Figure 2 A structural diagram of the virtual synchronous grid system is given. The parameters in the diagram are given in the dq rotating coordinate system, V d-qg ,i d-qg are the output voltage and output current of the gth VSG, respectively; V fd-qg ,i fd-qg are the port voltage and port current of the gth VSG, respectively, L fg ,C fg are the inductance and capacitance of the LC filter of the gth VSG. For the virtual synchronous grid system, the synchronous control loop simulates the inertia and damping characteristics of the synchronous generator, the voltage and current closed-loop controller reflects the dynamic characteristics of the inverter, and the LC filter embodies the voltage and current dynamic process of the grid system, and the control diagram is as shown in Figure 3 .

[0150] From the perspective of single-machine and multi-machine synchronous grid example systems, the dynamic simulation effects of the simulation method provided by the present application and the traditional simulation method are compared and analyzed. The structural diagram of the single-machine virtual synchronous grid example system is as shown in Figure 3 , and the specific parameter settings are as shown in Table 1.

[0151] Table 1 Parameter setting table of single-machine example system

[0152]

[0153] (1) Analysis of multi-time scale characteristics of single-machine system

[0154] Based on the established single-machine virtual synchronous grid model, the small disturbance model of the system is obtained after linearization at the equilibrium point, and the distribution of the characteristic roots of the system is given in Table 2.

[0155] Table 2 Distribution of characteristic roots of small disturbance model of system

[0156]

[0157] The characteristic roots of the system in Table 2 are all distributed in the left half of the complex plane, indicating that the system is small disturbance stable at the operating point. Since the essence of multi-time scale is a rigid system, from the distribution of the characteristic roots, according to the definition of the rigidity ratio, the rigidity ratio of the system is calculated as From the oscillation frequency, the characteristic roots λ 1,2 , λ 3,4 , λ 5,6The corresponding frequencies are 6689.6 Hz, 56.2938 Hz and 10.619 Hz, respectively, which include high frequency oscillation, super-synchronous oscillation and sub-synchronous oscillation, and reflect the wide frequency domain characteristics of the multi-time scale system. From the main relevant state variables, the dq-axis voltage and current u fd 、u fq 、i fd 、i fq of the LC filter are coupled by multiple oscillation modes, and the multi-time scale characteristics are obvious.

[0158] Based on the established single-machine virtual synchronous grid system model, time domain simulation is carried out, and the simulation curve of the filter voltage u fq is obtained, as shown in Figure 4 . The simulation time is 2s. As shown in Figure 4 , in the initial stage of disturbance, the system has more oscillation modes, which is reflected in the simulation waveform as short oscillation period and obvious superposition effect. After 0.2s, the fast scale mode is basically attenuated, the oscillation period gradually becomes longer, and the amplitude of oscillation relatively becomes smaller, until the system returns to steady state operation. In order to more accurately describe the multi-scale characteristics of the system, prony identification is carried out on the filter voltage ufq, and the results are shown in Table 3, which are basically consistent with the results of small disturbance in Table 2.

[0159] Table 3 prony identification of filter q-axis voltage

[0160]

[0161] (2) Comparison between Hal wavelet collocation method and traditional simulation algorithm

[0162] Based on the single-machine virtual synchronous grid system model, trapezoidal integration method (2nd order), implicit Runge-Kutta method (6th order) and wavelet collocation method are used for solving, respectively. The results of solving the q-axis component of filter voltage u fq are shown in Figure 5 .

[0163] Figure 5 The simulation step length of trapezoidal integration method and Runge-Kutta method is 1x10 -5 s, and the traditional simulation method can obtain relatively accurate numerical solution. The step length of wavelet collocation method is 1x10 -5 s, and the wavelet layer number is J=4, as shown in Figure 5It can be seen that the wavelet collocation method can obtain more accurate numerical solution. Taking the sixth-order Runge-Kutta method as a reference, it can be seen from the local enlarged view that the trapezoidal integration method has obvious phase lag, while the wavelet collocation method can well coincide with the simulation curve of the sixth-order Runge-Kutta method. In addition, compared with the Runge-Kutta method and the trapezoidal integration method, the wavelet collocation method takes enough collocation points in each integration step, so that the numerical simulation curve is smoother and closer to the actual analytical solution. It can be seen that the Haar wavelet collocation method is more reliable and accurate, which can solve the phase lag problem caused by low-order methods, and can obtain more accurate and smooth simulation effect than the high-order method at the same step.

[0164] Further, the concept of base solution matrix is introduced, the analytical solution of the linearized model of the virtual synchronous machine system is obtained after linearization, and the logarithmic error order is cited. By taking the logarithm of the relative error, the error convergence order of the system is obtained. Figure 6 The error convergence of the filter voltage ufd in the first integration step is given, the horizontal coordinate is the wavelet decomposition layer J, and the vertical coordinate represents the error convergence order. Different curves mean different simulation step lengths. When the step length is constant, the error order of the system increases with the increase of the wavelet layer, and when the simulation step length is further reduced, the error of the system will also be further reduced. When the step length is 10 -2 s, only the wavelet layer number needs to be taken as 4, and the convergence order of the system can reach about 3 orders, which exceeds the 2-order accuracy of the trapezoidal integration method. For a single-machine virtual synchronous power grid system, the limit step length of the traditional numerical integration is 10 -4 s, and when the wavelet collocation method step length is 10 -4 s, the error order of the system can reach about eight orders or even higher, and the simulation effect is obviously higher than that of the traditional numerical integration method. With the gradual increase of the wavelet layer number and the gradual reduction of the simulation step length, the accuracy convergence order of the system can increase by 1-2 orders, the error decay rate is faster and faster, and the simulation accuracy is higher and higher.

[0165] Table 4 Comparison of simulation time consumption of single-machine system

[0166]

[0167] Table 4 lists the simulation time consumption of trapezoidal integration method, Runge-Kutta method and Haar wavelet collocation method. The simulation time consumption of Haar wavelet collocation method is obviously less than that of the other two simulation methods under the condition of meeting the simulation accuracy requirement. The main reason is that the sparsity of Haar wavelet matrix greatly reduces the calculation amount, and the sufficient number of collocation points in each integration step also ensures the adaptation to large step simulation. If the Runge-Kutta method (sixth order) is taken as the reference, under the same accuracy, the step length and decomposition level of the wavelet collocation method are h = 0.1 ms and J = 5, and the simulation acceleration efficiency can be improved to 83.32%. When the simulation step length is increased to 1 ms, the trapezoidal integration method cannot accurately simulate the actual dynamic process of the system due to the insufficient numerical accuracy, so it is meaningless to evaluate the simulation time. The Runge-Kutta method also has the problem of large cumulative error due to the increase of step length, resulting in the result of iteration not converging, and it no longer has the advantage of large step simulation.

[0168] It can be seen that the Haar wavelet collocation method meets the requirements of simulation accuracy and simulation speed in single-machine virtual synchronous grid system simulation, and has sufficient reliability and accuracy.

[0169] The multi-machine virtual synchronous grid example system adopts a VSG two-area four-machine system, and the topology is shown in Figure 7 The control mode of VSG is consistent, and is a double closed-loop control of voltage outer loop and current inner loop. The specific parameter configuration is shown in Table 5.

[0170] Table 5 Parameter setting table of multi-machine example system

[0171]

[0172]

[0173] (1) Analysis of multi-time scale characteristics of two-area four-machine system

[0174] From the perspective of the model, after adding VSG control in the traditional two-area four-machine system, the multi-time scale characteristics are more obvious while increasing the order of the system model. Taking the filter voltage ufq which reflects the obvious multi-scale characteristics as an example, Figure 8 The filter voltage simulation diagram of G1-G4 is given, and it can be seen from the local enlarged diagram that there are many oscillation modes caused by the disturbance at the initial stage. The simulation curve presents the effect of mixed superposition of multiple modes, and with the passage of time, many faster modes decay, and the period of system oscillation increases obviously in the later stage of simulation until the system returns to steady state operation.

[0175] The prony identification is performed on the filter voltage ufq simulation curve of the first generator G1, and the identification result is compared with the small disturbance result, as shown in Table 6.

[0176] Table 6 Prony identification and small signal results comparison table

[0177]

[0178]

[0179] It can be seen from Table 6 that the oscillation frequency of the system at the initial disturbance stage presents a wide frequency domain distribution trend, including super high frequency oscillation, high frequency oscillation, super synchronous oscillation, sub synchronous oscillation and other oscillation types, and the multi-time scale coupling effect is very complex. In addition, the results of small disturbance and Prony identification are basically consistent, which shows the unity of multi-scale in time domain and frequency domain.

[0180] (2) Comparison between Haar wavelet collocation method and traditional simulation algorithm

[0181] Referring to Figure 9 , the trapezoidal integration method and the Runge-Kutta method (sixth order) are also used for comparison. The step length of the two traditional simulation methods is taken as the limit step length 10 -4 s, and the Haar wavelet collocation method uses a variable step length simulation strategy. When the initial mode is more, the step length is taken as 10 -2 s, and after the fast mode is attenuated in the later stage, a larger step length is used. Compared with the sixth order Runge-Kutta method, the trapezoidal integration method has obvious phase lag, and the accuracy is obviously lower than that of the Haar wavelet collocation method. Compared with the Runge-Kutta method, the simulation curve of the wavelet collocation method is smoother and closer to the actual analytical solution. It can be seen that the Haar wavelet collocation method has obvious advantages in multi-machine system simulation.

[0182] The concept of basis solution matrix is further introduced, and the analytical solution of the linearized model of the two-area four-machine system model is obtained after linearization, which is taken as the reference. The simulation change graph of the convergence order of VSG1 filter voltage ufd with the decomposition layer number and the simulation step length is obtained, as shown in Figure 10 . The following conclusions can be drawn:

[0183] When the step length is 10 -3 s, compared with the second order accuracy of the trapezoidal integration method, the convergence order of the Haar wavelet collocation method has reached more than two orders. With the further increase of the wavelet layer number, the number of collocation points in an integral time step increases exponentially, and the simulation accuracy is further improved.

[0184] When the step length is constant, with the increase of the wavelet layer number, the convergence order of the system can generally be improved by 1-2 orders. If the wavelet layer number continues to increase, the error convergence order can be further increased on the basis of meeting the simulation speed.

[0185] Under the premise of meeting certain simulation accuracy threshold, Table 7 gives the simulation time consumption of three simulation algorithms in the multi-machine example system. The simulation time consumption of the wavelet collocation method is less than that of the traditional trapezoidal integral method and the Runge-Kutta method. If the Runge-Kutta method (sixth order) is taken as a reference, under the same accuracy, the wavelet collocation method step size and decomposition level are h = 0.1 ms and J = 5. At this time, the simulation speed efficiency can be improved by 82.37%. It can be seen from Table 7 that the greater the value of J, the longer the simulation time consumption of the Haar wavelet collocation method. In actual application process, the appropriate wavelet level can be selected according to the accuracy requirement of actual simulation.

[0186] It can be seen that the Haar wavelet collocation method still has good reliability and accuracy in the multi-scale simulation of the virtual synchronous multi-machine example system.

[0187] Table 7 Simulation time consumption table of multi-machine example system

[0188]

Claims

1. A multi-scale time-frequency spectrum numerical simulation method for power electronic power systems, characterized in that, The method comprises the following steps: S101: a DQ unified frequency transformation method is used to establish a high-order state space model of a power electronic power system in a first-order DQ dynamic phasor form in a real number space; S102: for a numerical simulation sub-period n, state variables and algebraic variables are projected into a Haar wavelet multi-resolution analysis coefficient space to obtain a multi-scale numerical integral format of the state variables and a multi-scale wavelet coefficient format of the algebraic variables, respectively; S103: L 2 (R) characteristics, the multi-scale numerical integration format of the state variable is integrated to obtain the multi-scale wavelet coefficient format of the state variable. S104: the multi-scale wavelet coefficient formats of the state variables and the algebraic variables are substituted into the high-order state space model of the power electronic power system in the first-order DQ dynamic phasor form to obtain a multi-scale wavelet algebraic model of the power electronic power system in the Haar wavelet multi-resolution analysis coefficient space; S105: a wavelet collocation method is used to obtain a collocation format of the multi-scale wavelet algebraic model of the power electronic power system, a Haar wavelet coefficient is solved by using a Newton-Raphson method, and a wavelet numerical result of the state variables and the algebraic variables based on the Haar wavelet collocation method is obtained; S106: a simulation strategy of multi-interval self-adaptation and multi-level self-adaptation is used to simulate the multi-scale wavelet algebraic model of the power electronic power system; (I) a certain error threshold ε (ε>0) of the wavelet coefficient is limited, the multi-scale wavelet format of each variable is divided into two parts, and the state variables are taken as an example to obtain the following form: (II) For a given wavelet coefficient error threshold ε, when max |a i | > ε, increase the number of wavelet subspaces W j to become W J1 , is the new approximate solution for the Haar wavelet multi-resolution coefficient space. (III) The wavelet multi-interval adaptive simulation strategy described herein is to simulate sub-time periods [t] n ,t n+1 The interval length t n+1 -t n Let it be Δt n The intervals are divided according to the accuracy requirements of each sub-interval, where the left endpoint of the next sub-interval is the right endpoint of the previous sub-interval; when the obtained Haar wavelet coefficients meet the conditions... When the system is considered to be in a transient response process, the length of the next subinterval is appropriately increased, and adaptively selected as . Otherwise, assuming the system is in a steady-state response process, the length of the compressed subinterval is calculated using the formula: S107: simulation of an n+1 sub-interval period is performed, and the step S105 and the step S106 are repeated, so that the simulation is ended.

2. The power electronics-based power system multi-scale time-frequency spectral numerical simulation method according to claim 1, characterized in that, The step S101 comprises the following steps: (I) an electric power electronic power system composed of new energy, a power transmission network and a synchronous generator is established to obtain a formula one of a high-order state space model in a first-order DQ dynamic phasor form in a respective reference frequency coordinate system; wherein: x is a state variable, y is an algebraic variable, t is a time variable; x = [x G-d ,x G-q ,x N-d ,x N-q ,x W-d ,x W-q ] T ; y = [y G ,y N ,y W ] T ; x G-d , x N-d , x W-d are state variables d-axis phasors of the synchronous generator, the power transmission network, and the new energy equipment respectively, x G-q , x N-q , x W-q are state variables q-axis phasors of the synchronous generator, the power transmission network, and the new energy equipment respectively; (II) The steady-state operating frequency ω of the power electronic power system s As the system multi-device DQ unified frequency coordinate system, the isomorphic group algebra structure of DQ unified frequency transformation is established, and the interface algebra variables under the independent frequency of each module are converted into unified frequency variables by Park transformation. (III) the transformed unified frequency variable is brought into each device model to obtain the high-order state space model of the power electronic power system in the first-order DQ dynamic phasor form.

3. The power electronics-based power system multi-scale time-frequency spectral numerical simulation method of claim 1, wherein, The numerical simulation sub-period n is a simulation sub-interval [t n ,t n+1 ].

4. The power electronics-based power system multi-scale time-frequency spectral numerical simulation method of claim 1, wherein, The step S102 comprises the following steps: (I) the differential items of the state variables and the algebraic variables are projected into a wavelet multi-resolution analysis coefficient space to obtain an approximation polynomial based on a wavelet form: where: P j is the orthogonal projection onto the space V j , corresponding to slow scale information in the state variable differential terms and algebraic variables, is expressed by the low resolution scale function , corresponding to faster scale information in the state variable differential terms and algebraic variables, is expressed by the high resolution wavelet function ψ j,k (t) (II) an i-order Haar wavelet scale function in a simulation sub-period n is represented as: wherein: ξ1(i) = t n + 2kμΔx, ξ2(i) = t n + (2k + 1) μΔx, ξ3(i) = t n + 2(k + 1) μΔx, μ = M / m, M = 2 J , m = 2 j (j = 0, 1...J), k = 0, 1...m - 1, i = j + k + 1 j and k represent the coefficients of stretching and translation respectively, J represents the maximum resolution corresponding to the number of wavelet layers; (III) Using the orthogonality of Haar wavelet function The state variables and algebraic variables in the high-order state space model of the first-order DQ dynamic phasor form of the power electronic power system are projected into the Haar wavelet multi-resolution analysis coefficient space by using the orthogonality of Haar wavelet function, and a multi-scale wavelet format of the differential items of the state variables and the algebraic variables is obtained: wherein, is the i-th coefficient of the approximation expression of the state variable differential term and the algebraic variable on the simulation sub-period [t n ,t n+1 ] (IV) the differential term corresponding to the system state variable Integrating, the multi-scale numerical integration scheme of the state variable x(t) is obtained: where: x(t) is the value of the state variable x at time t. n n t.​ 5. The power electronics-based power system multi-scale time-frequency spectral numerical simulation method of claim 1, wherein, The formula of the multi-scale wavelet coefficient format of the state variables in the step S103 is as follows: where: x(t n ) is the value of the state variable x at time instant t n ; p i (t) is the integral term based on the analytical expression of the Haar wavelet scaling function.

6. The power electronics-based power system multi-scale time-frequency spectral numerical simulation method of claim 1, wherein, The formula of the multi-scale wavelet algebraic model in the step S104 is as follows: Wherein: F = [F G , F N , F W ], G = [G G , G N , G W ], 7. The power electronics-based power system multi-scale time-frequency spectral numerical simulation method of claim 1, wherein, The step S105 in the step S105 comprises the following steps: (I) Constructing the interpolation wavelet collocation points on the sub-interval [t n , t n+1 ] of the simulation interval, and solving each collocation point value by using the formula ; Wherein: the wavelet layer number is J, the interpolation wavelet collocation number is 2 J+1 , Delta t = (t n+1 -t n ) / 2 J+1 ; (II) Using the calculated wavelet collocation points to substitute into the multi-scale wavelet format of each variable, the multi-scale wavelet collocation format of the related variable is obtained, the scale stretching coefficient j is obtained to a certain upper limit J, and the resolution is reached to 2 J+1 , and the multi-scale wavelet collocation format of each variable is approximately expressed as: where: H, P are the Haar wavelet transform matrices, H(i,1) = h i (x l ), P(i,1) = p i (x l ), (III) the multi-scale wavelet format based on the Haar wavelet collocation is substituted into the multi-scale wavelet algebraic model of the power electronic power system in the Haar wavelet multi-resolution analysis coefficient space to obtain a formula of the collocation format of the multi-scale wavelet algebraic model of the power electronic power system:

8. The power electronics-based power system multi-scale time-frequency spectral numerical simulation method of claim 1, wherein, The step of solving the Haar wavelet coefficient by using the Newton-Raphson method in the step S105 comprises the following steps: (I) Calculate the initial value of the Haar wavelet coefficient under low resolution; through the calculation of a small number of Haar wavelet matrix P, H under J=1 or 2, the approximation polynomial in the form of wavelet is substituted into the system differential algebraic model to solve simultaneously; (II) recursively calculating the high resolution Haar wavelet coefficients; using the low resolution Haar wavelet coefficients as part of the initial values for the next level of resolution J+1 wavelet coefficients, i.e. if the wavelet coefficients for a certain resolution J are calculated then the initial values for the next level of resolution J+1 wavelet coefficients are:

9. The power electronics-based power system multi-scale time-frequency spectral numerical simulation method of claim 7, wherein, The step of obtaining the state variable and the algebraic variable based on the wavelet numerical result of the Haar wavelet collocation method in the step S105 is as follows: In a simulated sub-time interval [t] n ,t n+1 Substitute the wavelet coefficients a and b obtained by the Newton-Raphson method into formula eight. The simulation sub-time interval [t] is obtained n ,t n+1 Wavelet numerical results of internal state variables and algebraic variables based on the Haar wavelet collocation method.

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