Modeling and simulation method of power electronic converter based on high-order numerical integration

Abstract

The invention discloses a modeling and simulation method of a power electronic converter based on high-order numerical integration. The modeling and simulation method comprises the following steps: constructing a three-point integration formula based on a differential quadrature method, and constructing a four-point integration formula based on a single-step block method; taking voltage at two ends of the switching device as a voltage source, and obtaining discrete model expressions of on and off states of the switching device according to the constructed four-point integral formula and the four-point integral formula; determining optimal parameters of the switch discrete model of the switch device; calculating a historical current source by adopting system steady-state values of the switching device in different states; a topological structure of the power electronic converter and an external circuit of the power electronic converter are subjected to simulation analysis, a simulation step length is set as delta t, and a node analysis method is adopted to obtain a time domain change waveform of a required system state variable. According to the invention, an improved L / C constant admittance switch model based on a high-order numerical integration algorithm is adopted, so that stable transition of admittance is realized; and a historical current source item is calculated by adopting a circuit constraint equation in a switching steady state, so that the stability and reliability of a simulation result as well as the calculation precision and efficiency are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of electromagnetic transient simulation of power systems, and particularly to a modeling and simulation method for power electronic converters based on high-order numerical integration. Background Art

[0002] With the wide application of power electronic technology in power systems, the selection of power electronic switch device models is very important for electromagnetic transient simulation of power systems. As the basis and prerequisite of electromagnetic transient simulation, the accuracy of power electronic switch device models plays a crucial role in simulation accuracy and efficiency.

[0003] In the current simulation research on modular multilevel converters (MMCs) and high voltage direct current (HVDC) systems at the system level, the selection of power electronic switch device models mainly focuses on the two-value resistance switch model and the L / C constant admittance switch model. Among them, the two-value resistance switch model is widely used due to its simple structure and high calculation efficiency. However, it has an obvious limitation, that is, it cannot ensure the consistency of the equivalent admittance before and after switching, which may lead to numerical instability or a decrease in accuracy in the simulation results at the moment of switch switching. The L / C constant admittance switch model, by introducing inductance L and capacitance C elements, can artificially ensure that the admittance of the switch is constant in the on and off states, thus effectively avoiding the numerical oscillation problem caused by admittance mutation. However, the L / C constant admittance switch model has a transient error during the state switching process, which will generate a virtual power loss much larger than the actual one, affecting the simulation accuracy. Summary of the Invention

[0004] Aiming at the deficiencies of the existing power electronic switch device models in accurately simulating the dynamic behavior of switches and simulation efficiency, the present invention provides a modeling and simulation method for power electronic converters based on high-order numerical integration. The present invention adopts an improved L / C constant admittance switch model based on a high-order numerical integration algorithm to achieve a smooth transition of admittance; and uses the circuit constraint equation at the switch steady state to calculate the historical current source term, improving the stability, reliability, calculation accuracy and efficiency of the simulation results. This design is not only applicable to MMC-HVDC system simulation, but also provides a reference for other power electronic system simulations.

[0005] The technical solution adopted by the present invention is as follows:

[0006] A modeling and simulation method for power electronic converters based on high-order numerical integration, comprising the following steps:

[0007] Step 1: Construct a three-point integration formula based on the differential quadrature method, and construct a four-point integration formula based on the single-step block method;

[0008] Step 2: Regarding the voltage across the switching device as a voltage source, obtain the discrete model expressions for the on and off states of the switching device according to the four-point integration formula and the four-point integration formula constructed in Step 1.

[0009] Step 3: Determine the optimal parameters of the switching discrete model of the switching device.

[0010] Step 4: Calculate the historical current source using the system steady-state values under different states of the switching device.

[0011] Step 5: Conduct a simulation analysis on the topology structure of the power electronic converter and its external circuit. Set the simulation step size as Δt, and use the nodal analysis method to obtain the time-domain variation waveforms of the required system state variables.

[0012] In the said Step 1, a single-step multi-stage implicit numerical integration method is adopted to construct a high-order numerical integration formula for discretizing different states of the switching device.

[0013] The three-point integration formula (New Three-Point Formula) constructed based on the differential quadrature method, denoted as NTPF, is shown in Equation (1);

[0014]

[0015] The four-point integration formula (New Four-Point Formula) constructed based on the single-step block method, denoted as NFPF, is shown in Equation (2);

[0016]

[0017] In the above formula, [t, t + nh] represents the integration interval; f(x) represents the integrand; t represents the time variable; h represents the integration step size; n represents the number of integration steps.

[0018] In the said Step 2, the circuit dynamic equations when the switching device is on and off are as follows:

[0019]

[0020] In Equation (3), u on (t) represents the transient voltage when the switch is on; L on represents the on-state inductance when the switch is on; u off (t) represents the transient voltage when the switch is off; i on (t) represents the transient current when the switch is on; R off The analog resistance when the switch is off; represents the voltage across the capacitor when the switch is off; i offRepresents the current when the switch is off; C off Represents the blocking capacitance when the switch is off; u Coff (t) represents the transient voltage across the capacitor when the switch is off.

[0021] 1) The single-step block method is a numerical method for directly solving differential equations within one time step. By selecting multiple nodes within this step to construct a high-order integration formula, the solution at the next moment is calculated;

[0022] For the initial value problem:

[0023] y′(t) = f(t, y(t)), y(t0) = y0 (4);

[0024] In equation (4), t0 represents the initial moment; y0 represents the initial value of the function; y(t) represents the state quantity of the system at time t; y′(t) represents the first derivative of y(t) with respect to t;

[0025] The general form of the single-step block method is:

[0026]

[0027] In equation (5), y n+1 represents the numerical approximation at time t n +1; y n represents the numerical approximation at time t n ; h represents the step size; s represents the order; b i represents the coefficient for weighting the derivatives at each stage; k i represents the derivative at the i-th stage; c i represents the stage node; a ij represents the weighting coefficient for the previous stage value k i when calculating stage k j ; f(t, y) represents the function on the right side of the given differential equation, describing the dynamic changes of the system.

[0028] 2) The differential quadrature rule approximates the derivative or integral of a function as a weighted sum of function values at discrete nodes to achieve high-precision numerical solution.

[0029]

[0030] In equation (6), f (q) (x i ) represents the q-th derivative of the function f(x) at the node x i ; x i represents the i-th discrete node, i = 1, 2,..., N, and N represents the total number of nodes; represents the weight coefficient used to approximate the q-th derivative; f(xj ) represents the value of the function f(x) at the node x j ;

[0031] Higher-order numerical integration formulas are derived through the single-step block method and the differential quadrature method: Equations (1) and (2). Regarding the voltage across the switching device as a voltage source, based on the NTPF and NFPF constructed in Step 1, the discrete model expressions (7) to (10) for the on and off states of the switching device can be obtained;

[0032] (1). The discrete model of the switching device in the on state is as follows:

[0033]

[0034]

[0035] In the above formula, Y m represents the admittance when the switching device is off, m = 3, 4; i h_on (t) represents the historical current source when the switch is on; i on (t - 4Δt), i on (t - 3Δt), i on (t - 2Δt), i on (t - Δt) represent the historical current values of the switching device at the t - nΔt moment when it is on, n = (1 to 4); Δt represents the simulation step size; u h_on (t) represents the historical voltage source term u on (t - 3Δt), u on (t - 2Δt), u on (t - Δt) represent the historical current values of the switching device at the t - nΔt moment when it is on, n = (1 to 3); γ3, γ5 represent the coefficients of the discrete model of the switching device in the on state.

[0036] (2). The discrete model of the switching device in the off state is as follows:

[0037]

[0038] In the above formula, Y m ' represents the admittance when the switching device is off, m = 3, 4; i off (t) represents the transient current when the switch is off; u off (t) represents the transient voltage when the switch is off; i h_off (t) represents the historical current source in the off state of the switch; i off (t - 4Δt), i off (t - 3Δt), i off (t - 2Δt) and i off(t - Δt) represents the historical current value at the moment of t - nΔt when the switching device is turned off, where n = (1 to 4); Δt represents the simulation step size; u h_off (t) represents the historical voltage source term when the switch is turned off; u off (t - 4Δt) represents the historical voltage value at the moment of t - 4Δt when the switching device is turned off; R off represents the resistance in the off - state of the switch; C off represents the capacitance in the off - state of the switch; γ3' and γ5' represent the coefficients of the discrete model of the switching device in the off - state.

[0039] In step 3, determine the optimal parameters of the discrete model of the switching device:

[0040] Determine the value of the resistance R off of the switching device. According to the final - value theorem of the discrete - time system, R on can be taken as 10 -3 Ω; Discretize the on - state of the switching device using the four - point Newton - Cotes formula, and discretize the off - state of the switching device using the four - point integral formula (2). To ensure that the admittance remains unchanged before and after the switching of the switching device, let the discrete admittance in the on - state of the switch be equal to the discrete admittance in the off - state. Then there is:

[0041]

[0042] In formula (11), Δt represents the simulation step size, which is used to unify the discrete admittance in the on - and off - states of the switch; R on represents the simulated resistance when the switch is on; L on represents the simulated inductance in the on - state of the switch; C off represents the simulated capacitance in the off - state of the switch; R off represents the simulated resistance in the off - state of the switch;

[0043]

[0044] In formula (12), R off ' represents the resistance in the off - state of the switch; Δt' represents the simulation step size, which is used to calculate the resistance in the off - state of the switch; R on ' represents the resistance when the switch is on; L on ' represents the inductance in the on - state of the switch; C off ' represents the capacitance in the off - state of the switch.

[0045] According to the topology structure of the power - electronic converter and its external circuit, the state - space expression of the discrete - time system is sorted out as follows:

[0046]

[0047] X = CI h + Dr(14);

[0048] In the above formula, t represents the current moment in the simulation process; Δt represents the step size; A1, A2, A3, and A4 represent state sub - matrices, B i represents the input sub - matrix, (i = 1~4); I h (t) represents the transient value of the historical current source; I h (t - Δt), I h (t - 2Δt), I h (t - 3Δt) and I h (t + Δt) represent the historical current values of the switching device at the t - nΔt moment, n = (-1, 2, 3, 4); r i (t-(i - 1)Δt) represents the discrete values of the DC - side voltage and output current at different historical sampling points; i represents the sampling point during simulation; X represents the state vector of the switched discrete - time system; C represents the output matrix; I h represents the historical current source term; D represents the feed - forward matrix; r represents the system state variable vector;

[0049] After averaging the right - hand side of Equation (13), we get:

[0050]

[0051] In Equation (15), represents the average state matrix; represents the average historical current source term; represents the average input sub - matrix; r' represents the steady - state value vector of the system state variables.

[0052] Calculate the spectral radius of the average state matrix

[0053]

[0054] In Equation (16), represents the average state matrix; A i represents the discrete state matrix under different switch states; N is the total number of state matrices;

[0055] Spectral radius is the maximum value of the modulus of all eigenvalues of the matrix,

[0056]

[0057] In Equation (17), represents the average state matrix of the spectral radius; λ i represents the eigenvalue of the state matrix of; λi Denote the eigenvalue as λ i and its absolute value; max represents the maximum value among the absolute values of the eigenvalues;

[0058] Generally, the smaller the spectral radius of the average state matrix, the faster the convergence speed of the transient response of the switch. According to As L on and C off vary, select the parameter values of the dynamic elements of the appropriate switch device model. From Figure 6 the distribution of the system spectral radius, it can be seen that by observing how the system spectral radius changes with the dynamic element parameters L on and C off in the switch model, the smaller the spectral radius, the faster the convergence speed of the discrete system. However, the larger the dynamic element parameters of the switch, the slower the transient response speed of the system. Based on this, an optimal selection scheme for the parameter of the dynamic element of the appropriate switch model is L on = 0.701 mH, C off = 0.891 mF. Ensure that is smaller.

[0059] In step 4, according to the topology of the power electronic converter and its external circuit, combined with the action timing of the switch device, give the circuit equation at the steady state of the switch according to the ideal switch characteristics, and substitute it into the four-point Newton-Cotes formula (2) for the discrete expressions (8) and (10) when the switch device is on, to obtain the calculation expressions of the corresponding historical current sources, as follows:

[0060] When the switch device switch S1 is on and the switch device S2 is off, according to the ideal switch characteristics, it can be known that:

[0061]

[0062] In Equation (18), u1(t) represents the voltage across switch S1; U d1 (t) represents the voltage across the upper arm of the DC side; u load (t) represents the transient voltage value of the load; i1(t) represents the current flowing through switch S1; i load (t) represents the current flowing through the load; u2(t) represents the voltage across switch S2; U d2 (t) represents the voltage across the lower arm of the DC side; i2(t) represents the current flowing through switch S2;

[0063] Substitute Equation (18) into the four-point Newton-Cotes formula (2) for the on-state discrete models (8) and (10) of the switch device, and the following can be obtained:

[0064]

[0065] In Equation (19), i h1 (t) is the historical current source of the upper bridge arm of the discrete circuit; Y sw represents the equivalent admittance of the switching device; R on represents the resistance when the switch is on; i load (t - 3Δt), i load (t - Δt), i load (t - 2Δt) represent the transient currents of the load when the simulation step nΔt, where n=(1 - 3); r represents the dynamic decay coefficient in the on state of the switch; Δt represents the step size;

[0066] i h2 (t)= - Y sw 'U d (t - 4Δt)(20);

[0067] In Equation (20), i h2 (t) is the historical current source of the lower bridge arm of the discrete circuit; Y sw ' represents the equivalent admittance of the switching device; U d (t - 4Δt) represents the transient voltage on the DC side at the moment of t - 4Δt.

[0068] In step 5, the node analysis method is adopted to obtain the time - domain variation waveforms of the required system state variables:

[0069] Firstly, establish the node admittance matrix Y of the circuit network to be solved. According to the different on - and off - state of the switching device, each element in the circuit is expressed in the form of constant admittance.

[0070] Y = U·I (21);

[0071] In Equation (21), Y represents the node admittance matrix; U represents the node voltage vector; I represents the Norton equivalent current vector.

[0072] By solving the equations composed of Equation (13) and Equation (14), the state variables such as node voltage and switch current can be obtained. Carry out simulation analysis on the above - mentioned process, set the simulation parameters as shown in Table 1, and obtain the time - domain waveforms as shown in Figure 7(a) and Figure 7(b).

[0073] For the modeling and simulation method of a power electronic converter based on high - order numerical integration of the present invention, the technical effects are as follows: 1) By discretizing the switching device using the high - order numerical integration formula, the present invention effectively improves the accuracy of the switching device model, enabling it to more accurately simulate the dynamic characteristics of the switching device, thereby improving the accuracy of the electromagnetic transient simulation of the power system containing power electronic switches.

[0074] 2) By introducing an improved constant admittance model, the present invention ensures a smooth transition of admittance when the switching device switches between the on and off states, avoiding the limitations of the traditional two-value resistance model, thereby improving the stability of the simulation results.

[0075] 3) By optimizing the parameter configuration, the present invention reduces the additional computational burden in the L / C constant admittance model, taking into account both the simulation accuracy and the computational efficiency, and improving the simulation efficiency.

[0076] 4) The switching device model design scheme proposed by the present invention is not only applicable to the simulation research of the MMC-HVDC system, but also can provide a reference for the simulation modeling of other power electronic systems, and has good application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] The present invention will be further described below in conjunction with the drawings and examples;

[0078] Fig. 1(a) is a conduction structure diagram;

[0079] Fig. 1(b) is a turn-off structure diagram.

[0080] Figure 2 is the switch conduction loop diagram.

[0081] Figure 3 is the switch turn-off loop diagram.

[0082] Figure 4 is the topology structure diagram of the two-level converter.

[0083] Figure 5 is the adjoint discrete circuit diagram of the half-bridge circuit.

[0084] Figure 6 is the curve of the spectral radius distribution of the discrete system.

[0085] Fig. 7(a) is the current simulation diagram of switch S1;

[0086] Fig. 7(b) is the voltage simulation diagram of switch S1. DETAILED DESCRIPTION OF THE INVENTION

[0087] Modeling and simulation method for power electronic converters based on high-order numerical integration. By discretizing switching devices using high-order numerical integration formulas, the accuracy of the switching device model is effectively improved, enabling it to more accurately simulate the dynamic characteristics of switching devices, thereby enhancing the accuracy of electromagnetic transient simulation of power electronic converters. At the same time, this model can ensure the constancy of admittance when the switching device switches between the on and off states, avoiding the limitations of the traditional two-value resistance model, and thus improving the stability of simulation results. In addition, the present invention calculates the historical current source by using the circuit constraint equation in the steady state of the switching device, reducing the additional computational burden and taking into account both the accuracy and computational efficiency of power electronic converter simulation.

[0088] The modeling and simulation method for power electronic converters based on high-order numerical integration performs the selection and calculation of relevant circuit parameters according to the following steps:

[0089] (1): Adopt a single-step multi-stage implicit numerical integration formula to construct a new high-precision numerical integration formula and discretize Equation (22).

[0090]

[0091] Use two common single-step multi-stage implicit numerical integration methods, namely the differential quadrature method and the single-step block method, to solve the analytical integral of the following unknown function. For the following definite integral I(f), the numerical integration formula with 4th-order algebraic accuracy adopted by the present invention is as follows:

[0092]

[0093] In the formula, [t, t + nh] represents the integration interval; f(t) represents the integrand; t represents the time variable; h represents the integration step size, and n represents the number of integration steps, where n = 4.

[0094] (2): Regarding the switching device voltage as a voltage source, according to the 4th-order algebraic accuracy differential quadrature method and single-step block method, the discrete model expressions (7) and (8) of the switching device when it is conducting can be obtained.

[0095]

[0096] Among them, u on and i on represent the voltage and current when the switching device is in the on state; Y m (m = 3, 4) represents the admittance of the switching device; i h_on represents the historical current source of the switching device discrete model; γ4 represents the coefficient of the switching device discrete model.

[0097] Similarly, the discrete model of the switching device in the off state is as follows:

[0098]

[0099] Among them, u off and i off represent the voltage and current when the switching device is turned off; Y m (m = 3, 4) represents the admittance when the switching device is turned off; i h_off represents the historical current source of the discrete model of the switching device; γ3' and γ5' represent the coefficients of the discrete model of the switching device in the off state.

[0100] (III): Determine the optimal parameters of the switching model:

[0101] According to the final value theorem, R on = 10 -3 Ω can be taken. To determine the value of R off , the four-point Newton-Cotes formula is used to discretize the on-state of the switching device, and the new four-point integral formula NFPF is used to discretize the off-state of the switching device. To ensure that the admittance of the switching device remains unchanged before and after switching, the discrete switching admittances of the two are made equal, so there is:

[0102]

[0103] Combined with the two-level converter shown in Figure 4 , the state-space expression of the discrete-time system after closing the switching device S1 and opening the switching device S2 is sorted out as follows:

[0104]

[0105] After averaging the right side of Equation (10), we get:

[0106]

[0107] Calculate the spectral radius of the average state matrix As L on and C off An optimal selection scheme for choosing the parameters of the dynamic elements of the appropriate switching device model is L on = 0.701 mH, C off = 0.891 mF.

[0108] (IV): Calculate the historical current source using the steady-state values of the system in different states of the switching device. When the switching device S1 is conducting and the switching device S2 is off, according to the ideal switch characteristics, we know that:

[0109]

[0110] Substitute Equation (26) into the discrete models of the on-state of the switching device, Equations (7) and (8), using the four-point Newton-Cotes formula, and we can get:

[0111]

[0112] i h2 (t) = -Y sw U d (t - 4Δt)(28)

[0113] (5): The half - bridge inverter circuit in Figure 1 is simulated and analyzed. The simulation step size is taken as 2 μs. In one power frequency cycle, S1 conducts in the positive half - axis and S2 conducts in the negative half - axis, conducting alternately in this way. The simulation parameters are shown in Table 1. The simulation results are shown in Figure 7(a) and Figure 7(b).

[0114] Table 1 Simulation parameter settings

[0115]

[0116] It can be seen from Figure 7(a) and Figure 7(b) that the current of switch S1 shows a rapid rise at the moment of conduction, then tends to the steady - state value, and rapidly drops to zero when turned off. The voltage of switch S1 rapidly drops to 0 at the moment of conduction, then tends to the steady - state value, and rapidly rises to the bus voltage when turned off. The rising and falling processes of the current / voltage of the switching device do not complete instantaneously, but have a certain short delay and smooth transition.

[0117] It can be known that the proposed discrete model of high - order numerical integration of the switch has good steady - state characteristics. Due to the large dynamic element parameters in the switching device model, there is a certain delay in both the rising and falling processes of the voltage / current of the switching device. This model realizes the improvement of the accuracy of the switching device model and the enhancement of the stability of the simulation results by adopting the high - order numerical integration formula and the improved constant admittance model.

[0118] The present invention proposes a modeling and simulation method for the field of power electronic power system simulation, that is, improving the traditional L / C model of power electronic switches to accurately characterize the behavior of switching devices while improving the calculation efficiency. In view of the system topology complexity and uncertainty brought about by the popularization of new power electronic devices such as new energy power generation and flexible DC transmission, the present invention puts forward new design requirements for the adaptability and robustness of the switching device model. In addition, the research on the power electronic switch model will strive to achieve higher accuracy, efficiency and adaptability to meet the complexity of the electromagnetic transient simulation requirements of the power system. In order to meet the stability requirements of the switch model in simulation and the consistency requirements of admittance switching, the present invention proposes an optimized design scheme for the switching device model. This scheme improves the limitations of the traditional two - value resistance model by optimizing key parameters such as resistance, inductance, and capacitance in the switch model and introducing an improved constant admittance model. In addition, by adjusting the relevant parameters of the L / C constant admittance model, the simulation accuracy and calculation efficiency are balanced.

Claims

1. A modeling and simulation method for a power electronic converter based on high-order numerical integration, characterized in that It includes the following steps: Step 1: Construct a three-point integral formula based on the differential quadrature method and a four-point integral formula based on the single-step block method; Step 2: Regard the voltage across the switching device as a voltage source, and according to the four-point integral formula and the four-point integral formula constructed in Step 1, obtain the discrete model expressions for the on and off states of the switching device; Step 3: Determine the optimal parameters of the switching discrete model of the switching device; Step 4: Calculate the historical current source by using the system steady-state values under different states of the switching device; Step 5: Conduct a simulation analysis on the topology structure of the power electronic converter and its external circuit, set the simulation step size as Δt, and use the nodal analysis method to obtain the time-domain variation waveforms of the required system state variables.

2. The modeling and simulation method of the power electronic converter based on high-order numerical integration according to claim 3, characterized in that: In Step 1, the single-step block method constructs a high-order integral formula by selecting multiple nodes within this step, so as to calculate the solution at the next moment; For the initial value problem: y′(t)=f(t,y(t)), y(t0)=y0 (4); In Equation (4), t0 represents the initial moment; y0 represents the initial value of the function; y(t) represents the state quantity of the system at time t; y′(t) represents the first derivative of y(t) with respect to t; The form of the single-step block method is: In Equation (5), y n+1 represents the numerical approximate solution at time t n +1; y n represents the numerical approximate solution at time t n ; h represents the step size; s represents the order; b i represents the coefficient for weighting each stage derivative; k i represents the stage derivative of the i-th order; c i represents the stage node; a ij represents the weighting coefficient for the previous stage value k i when calculating stage k j . The differential quadrature method approximates the derivative or integral of a function as a weighted sum of function values at discrete nodes to achieve high-precision numerical solution; In Equation (6), f (q) (x i ) represents the q-th order derivative of the function f(x) at the node x i ; x i represents the i-th discrete node, where i = 1, 2, ..., N, and N represents the total number of nodes; represents the weight coefficient used to approximate the q-th order derivative; f(x j ) represents the value of the function f(x) at the node x j .

3. The modeling and simulation method of a power electronic converter based on high-order numerical integration according to claim 2, wherein: In the said Step 1, Denote the three-point integral formula constructed based on the differential quadrature method as NTPF, as shown in Equation (1); Denote the four-point integral formula constructed based on the single-step block method as NFPF, as shown in Equation (2); In the above formula, [t,t+nh] represents the integral interval; f(x) represents the integrand; t represents the time variable; h represents the integral step size; n represents the number of integral steps.

4. The modeling and simulation method of the power electronic converter based on high-order numerical integration according to claim 3, characterized in that: In the said Step 2, the circuit dynamic equations when the switching device is on and off are as follows: In Equation (3), u on (t) represents the transient voltage when the switch is on; L on represents the on-state inductance when the switch is on; u off (t) represents the transient voltage when the switch is off; i on (t) represents the transient current when the switch is on; R off is the simulated resistance when the switch is off; represents the voltage across the capacitor when the switch is off; i off represents the current when the switch is off; C off represents the blocking capacitance when the switch is off; u Coff (t) represents the transient voltage across the capacitor when the switch is off.

5. The modeling and simulation method of a power electronic converter based on high-order numerical integration according to claim 4, characterized in that: Derive the high-order numerical integral formulas (1) and (2) through the single-step block method and the differential quadrature method. Regard the voltage across the switching device as a voltage source. According to the NTPF and NFPF constructed in Step 1, the discrete model expressions (7) to (10) for the on and off states of the switching device can be obtained; The discrete model of the switching device in the on state is as follows: In the above formula, Y m represents the admittance when the switching device is turned off, m = 3, 4; i h_on (t) represents the historical current source when the switch is on; i on (t - 4Δt), i on (t - 3Δt), i on (t - 2Δt), i on (t - Δt) represent the historical current values at the moment of t - nΔt when the switching device is on, n = (1 to 4); Δt represents the simulation step size; u h_on (t) represents the historical voltage source term u on (t - 3Δt), u on (t - 2Δt), u on (t - Δt) represent the historical current values at the moment of t - nΔt when the switching device is on, n = (1 to 3); γ3, γ5 represent the coefficients of the discrete model of the switching device in the on state; The discrete model of the switching device in the off state is as follows: In the above formula, Y m ' represents the admittance when the switching device is turned off, m = 3, 4; i off (t) represents the transient current when the switch is turned off; u off (t) represents the transient voltage when the switch is turned off; i h_off (t) represents the historical current source in the off state of the switch; i off (t - 4Δt), i off (t - 3Δt), i off (t - 2Δt) and i off (t - Δt) represent the historical current values at the moment of t - nΔt when the switching device is turned off, n = (1 to 4); Δt represents the simulation step size; u h_off (t) represents the historical voltage source term when the switch is turned off; u off (t - 4Δt) represents the historical voltage value at the moment of t - 4Δt when the switching device is turned off; R off represents the resistance in the off state of the switch; C off represents the capacitance in the off state of the switch; γ'3, γ'5 represent the coefficients of the discrete model of the switching device in the off state.

6. The modeling and simulation method of the power electronic converter based on high-order numerical integration according to claim 5, characterized in that: In the said Step 3, determine the optimal parameters of the switching discrete model: Determine the value of the switching device R off The value is determined as follows. The on-state of the switching device is discretized using the four-point Newton-Cotes formula, and the off-state of the switching device is discretized using the four-point integral formula (2). To ensure that the admittance remains unchanged before and after the switching of the switching device, the discrete admittance in the on-state of the switch is made equal to the discrete admittance in the off-state, so we have: In Equation (11), Δt represents the simulation step size, which is used to unify the discrete admittance in the on and off states of the switch; R on represents the simulated resistance when the switch is on; L on represents the simulated inductance in the on state of the switch; C off represents the simulated capacitance in the off state of the switch; R off represents the simulated resistance in the off state of the switch; In formula (12), R' off represents the resistance in the switch-off state; Δt' represents the simulation step size used to calculate the resistance in the switch-off state; R' on represents the resistance when the switch is on; L' on represents the inductance in the switch-on state; C' off represents the capacitance in the switch-off state.

7. The modeling and simulation method of the power electronic converter based on high-order numerical integration according to claim 6, characterized in that: The state-space expression of the discrete-time system is as follows: X = CI h + Dr (14); In the above formula, t represents the current moment during the simulation process; Δt represents the step size; A1, A2, A3, and A4 represent state sub-matrices, B i represents the input sub-matrix, (i = 1 to 4); I h (t) represents the transient value of the historical current source; I h (t - Δt), I h (t - 2Δt), I h (t - 3Δt) and I h (t + Δt) represent the historical current values of the switching device at the t - nΔt moment, n = (-1, 2, 3, 4); r i (t - (i - 1)Δt) represents the discrete values of the DC-side voltage and output current at different historical sampling points; i represents the sampling point during the simulation; X represents the state vector of the switched discrete-time system; C represents the output matrix; I h represents the historical current source term; D represents the feedforward matrix; r represents the system state variable vector; After averaging the right side of Equation (13), we get: In Equation (15), represents the average state matrix; represents the average historical current source term; represents the average input submatrix; r' represents the steady-state value vector of the system state variables.

8. The modeling and simulation method of the power electronic converter based on high-order numerical integration according to claim 7, characterized in that: Calculate the spectral radius of the average state matrix In formula (16), represents the average state matrix; A i represents the discrete state matrix under different switch states; N is the total number of state matrices; Spectral radius is the maximum of the moduli of all the eigenvalues of the matrix, In formula (17), represents the spectral radius of the average state matrix ; λ i represents the eigenvalue of the state matrix ; |λ i | represents the absolute value of the eigenvalue λ i ; max represents the maximum value among the absolute values of the eigenvalues; The smaller the spectral radius of the average state matrix, the faster the convergence rate of the transient response of the switch. According to As L on and C off vary, select the parameter values of the dynamic elements of the appropriate switch device model. From the distribution of the system spectral radius, it can be seen that by observing the variation of the system spectral radius with the dynamic element parameters L on and C off in the switch model, the smaller the spectral radius, the faster the convergence rate of the discrete system. However, the larger the parameters of the switch dynamic elements, the slower the transient response speed of the system. Based on this, select the parameters of the dynamic elements of the appropriate switch model.

9. The modeling and simulation method of the power electronic converter based on high-order numerical integration according to claim 1, characterized in that: In the said Step 4, combining the action timing of the switching device, give the circuit equation at the switch steady state according to the switch characteristics, and substitute it into the four-point Newton-Cotes formula (2) for the discrete expressions (8) and (10) when the switching device is on, to obtain the calculation expressions for the corresponding historical current source, specifically as follows: When the switch S1 of the switching device is on and the switch S2 is off, according to the ideal switch characteristics, we know: In Equation (18), u1(t) represents the voltage across switch S1; U d1 (t) represents the voltage across the upper arm of the DC side; u load (t) represents the transient voltage value of the load; i1(t) represents the current flowing through switch S1; i load (t) represents the current flowing through the load; u2(t) represents the voltage across switch S2; U d2 (t) represents the voltage across the lower arm of the DC side; i2(t) represents the current flowing through switch S2; Substitute Equation (18) into the four-point Newton-Cotes formula (2) for the discrete models (8) and (10) of the on state of the switching device, and we can get: In Equation (19), i h1 is the historical current source of the upper bridge arm of the discrete circuit; Y sw represents the equivalent admittance of the switching device; R on represents the resistance when the switch is on; i load (t - 3Δt), i load (t - Δt), i load (t - 2Δt) represent the transient currents of the load when the simulation step nΔt, where n = (1 to 3); r represents the dynamic attenuation coefficient in the on state of the switch; Δt represents the step size; i h2 i(t) = -Y' sw U d U(t - 4Δt)(20); In formula (20), i h2 (t) is the historical current source of the lower arm of the discrete circuit; Y' sw represents the equivalent admittance of the switching device; U d (t - 4Δt) represents the DC-side transient voltage at the moment of t - 4Δt.

10. The modeling and simulation method of the power electronic converter based on high-order numerical integration according to claim 7, characterized in that: In the said Step 5, use the nodal analysis method to obtain the time-domain variation waveforms of the required system state variables: First, establish the nodal admittance matrix Y of the circuit network to be solved. According to the different on and off states of the switching devices, each element in the circuit is expressed in the form of constant admittance; Y = U·I (21); In Equation (21), Y represents the nodal admittance matrix; U represents the nodal voltage vector; I represents the Norton equivalent current vector; By solving the system of equations formed by Equations (13) and (14), state variables such as nodal voltages and switching currents can be obtained. Perform simulation analysis on the above process, set the simulation parameters, and obtain the time-domain waveforms.

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