Electric vehicle charging pile electromagnetic transient modeling method and system based on implicit trapezoidal integration

Abstract

The application discloses a kind of based on implicit trapezoidal integration electric vehicle charging pile electromagnetic transient modeling method and system, specifically for: the equivalent electromagnetic transient model of the dynamic behavior of the description charging pile converter is established, the state variables of the whole system are divided into multiple subsystems;The state equation of charging pile is discretized using implicit trapezoidal integration method, and dynamic circuit is converted into static resistance network;The central difference method is used to process the discretized state equation, form semi-implicit difference equation, and each subsystem is independently calculated;Based on linear interpolation method, the error correction of multiple switches is carried out, the zero point time of charging pile action switch function is found, the equivalent duty ratio of switch signal in a step is calculated, and is brought into switch function, to realize the accurate error compensation of charging pile switch action.The application reduces the electromagnetic transient modeling calculation complexity of electric vehicle charging pile, improves the simulation accuracy, reduces the simulation time, and improves the simulation efficiency.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic transient modeling technology for electric vehicle charging piles, and in particular to a method and system for electromagnetic transient modeling of electric vehicle charging piles based on implicit trapezoidal integral. Background Technology

[0002] With the rapid increase in the global adoption of new energy vehicles, 800V high-voltage fast charging platforms are rapidly becoming widespread. The large-scale operation of millions of electric vehicles and charging equipment has a significant impact on the power balance and power quality of the power grid, while also posing a great challenge to the simulation modeling technology of electric vehicle charging piles. Electromagnetic transient modeling of electric vehicle charging piles uses numerical simulation technology to analyze the electromagnetic dynamic processes of charging piles on a microsecond time scale. Its core lies in capturing transient phenomena in the interaction between power electronic equipment and the power grid, which is of great significance for improving power grid stability, optimizing fault response capabilities, accommodating multi-energy system coupling, and meeting electromagnetic compatibility requirements.

[0003] Traditional explicit integration methods, such as the Euler method and the Runge-Kutta method, are forced to use sub-microsecond step sizes due to numerical stability limitations when dealing with nanosecond-level switching transients of SiC MOSFETs, resulting in low simulation efficiency. Furthermore, the commercial software PLECS, which uses a rectangular integral pulse approximation, introduces DC bias errors as high as 8% in power electronic converters. Moreover, existing tools suffer from dynamic interaction distortion between the control loop and the power loop in multi-timescale coupled scenarios, leading to excessive simulation errors for constant current / constant voltage switching overshoot, which directly threatens the reliability of fast charging module designs above 30kW.

[0004] Currently, in the electromagnetic transient simulation of traditional charging piles, the electromagnetic transient simulation modeling method based on electric vehicle charging piles mainly uses the double interpolation method. However, the double interpolation algorithm is complex and requires interpolation backoff operations on state variables, resulting in a large amount of computation. When a large number of electric vehicles and the power grid interact, the simulation system is large in scale and has a large number of switches. Therefore, the double interpolation method will bring a large computational burden and seriously affect the simulation efficiency and accuracy. Summary of the Invention

[0005] The purpose of this invention is to provide a method and system for electromagnetic transient modeling of electric vehicle charging piles based on implicit trapezoidal integrals, which has high simulation accuracy and efficiency.

[0006] The technical solution to achieve the purpose of this invention is: a method for electromagnetic transient modeling of electric vehicle charging piles based on implicit trapezoidal integrals, comprising the following steps:

[0007] Step 1: Perform input impedance equivalence on the DC-DC converter of the electric vehicle charging pile, simplify the two-stage structure of the charging pile into a single system model, and use the state-space method to establish an equivalent electromagnetic transient model describing the dynamic behavior of the charging pile converter.

[0008] Step 2: Divide the state variables of the entire system into multiple subsystems, and split the system matrix accordingly.

[0009] Step 3: During the simulation time stepping process, the implicit trapezoidal integral method is used to discretize the state equation of the charging pile, and the dynamic circuit is transformed into a static resistor network.

[0010] Step 4: Process the discretized state equations using the central difference method, introducing... Delayed decoupling, where The simulation step size is represented, and the delay term is explicitly converted into a known quantity to form a semi-implicit difference equation, thereby achieving decoupling between the two sets of variables and allowing each subsystem to be calculated independently.

[0011] Step 5: Correct the error of multiple switches based on linear interpolation, find the zero point of the charging pile action switching function, calculate the equivalent duty cycle of the switching signal within a step, determine the average conduction state of the switching device within the step, substitute the equivalent duty cycle of the switching action into the switching function, return to step 3, and realize the error compensation of the charging pile switching action.

[0012] An electromagnetic transient modeling system for electric vehicle charging piles based on implicit trapezoidal integrals is disclosed. This system implements the aforementioned electromagnetic transient modeling method for electric vehicle charging piles based on implicit trapezoidal integrals. The system includes a model building module, a subsystem partitioning module, a discretization module, a central difference module, and an error correction module, wherein:

[0013] The model building module performs input impedance equivalence on the DC-DC converter of the electric vehicle charging pile, simplifies the two-stage structure of the charging pile into a single system model, and uses the state-space method to establish an equivalent electromagnetic transient model describing the dynamic behavior of the charging pile converter.

[0014] The subsystem partitioning module divides the state variables of the entire system into multiple subsystems, and also splits the system matrix accordingly.

[0015] The discrete module uses the implicit trapezoidal integral method to discretize the state equation of the charging pile during the simulation time step, transforming the dynamic circuit into a static resistor network.

[0016] The central difference module processes the discretized state equations using the central difference method, introducing... Delayed decoupling, where The simulation step size is represented, and the delay term is explicitly converted into a known quantity to form a semi-implicit difference equation, thereby achieving decoupling between the two sets of variables and allowing each subsystem to be calculated independently.

[0017] The error correction module performs error correction for multiple switches based on linear interpolation. It finds the zero point of the charging pile's action switching function, calculates the equivalent duty cycle of the switching signal within a step, determines the average conduction state of the switching device within that step, substitutes the equivalent duty cycle of the switching action into the switching function, and returns it to the discrete module to achieve error compensation for the charging pile's switching action.

[0018] A mobile terminal includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the electromagnetic transient modeling method for electric vehicle charging piles based on implicit trapezoidal integrals.

[0019] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps in the electromagnetic transient modeling method for electric vehicle charging piles based on implicit trapezoidal integrals.

[0020] Compared with the prior art, the significant advantages of this invention are: (1) This invention uses the implicit trapezoidal integral method to discretize the state equation and then uses the central difference method to approximate it. It introduces a Δt / 2 delay decoupling to form a semi-implicit difference equation, thereby achieving decoupling between the two sets of variables, supporting independent and efficient parallel computation of each subsystem, and significantly reducing computational complexity; (2) This invention accurately finds the zero point of the actual switching function through the formula, calculates the equivalent duty cycle of the switching state action, and substitutes it into the switching function to update each parameter matrix, thereby achieving error compensation for the switching action, ensuring the accuracy of the simulation, and significantly reducing the simulation time, providing a new idea for solving the electromagnetic transient modeling problem of charging piles. Attached Figure Description

[0021] Figure 1 This is a flowchart of the electromagnetic transient modeling method for electric vehicle charging piles based on implicit trapezoidal integrals according to the present invention.

[0022] Figure 2 This is a topology diagram of the charging pile converter in an embodiment of the present invention.

[0023] Figure 3 This is a schematic diagram illustrating the implicit trapezoidal integral and central integral in an embodiment of the present invention.

[0024] Figure 4 This is a timing diagram for parallel computing in an embodiment of the present invention.

[0025] Figure 5 This is a schematic diagram of the linear interpolation principle within the simulation step size in an embodiment of the present invention.

[0026] Figure 6 This is a schematic diagram illustrating the error compensation principle under multiple switching actions in an embodiment of the present invention.

[0027] Figure 7 This is a comparison chart of the accuracy of the equivalent model and the reference model at 1µs in an embodiment of the present invention.

[0028] Figure 8 This is a comparison chart of the accuracy of the equivalent model and the reference model at 10µs in this invention. Detailed Implementation

[0029] like Figure 1 As shown, the present invention provides an electromagnetic transient modeling method for electric vehicle charging piles based on implicit trapezoidal integrals, comprising the following steps:

[0030] Step 1: Perform input impedance equivalence on the DC-DC converter of the electric vehicle charging pile, simplify the two-stage structure of the charging pile into a single system model, and use the state-space method to establish an equivalent electromagnetic transient model describing the dynamic behavior of the charging pile converter.

[0031] Step 2: Divide the state variables of the entire system into multiple subsystems, and split the system matrix accordingly.

[0032] Step 3: During the simulation time stepping process, the implicit trapezoidal integral method is used to discretize the state equation of the charging pile, and the dynamic circuit is transformed into a static resistor network.

[0033] Step 4: Process the discretized state equations using the central difference method, introducing... Delayed decoupling, where The simulation step size is represented, and the delay term is explicitly converted into a known quantity to form a semi-implicit difference equation, thereby achieving decoupling between the two sets of variables and allowing each subsystem to be calculated independently.

[0034] Step 5: Correct the error of multiple switches based on linear interpolation, find the zero point of the charging pile action switching function, calculate the equivalent duty cycle of the switching signal within a step, determine the average conduction state of the switching device within the step, substitute the equivalent duty cycle of the switching action into the switching function, return to step 3, and realize the error compensation of the charging pile switching action.

[0035] As a specific example, in step 1, the electric vehicle charging pile has a two-stage structure including a front-stage AC-DC converter and a rear-stage DC-DC converter; the dynamic behavior of the charging pile converter specifically refers to the dynamic behavior of the 30kW fast charging pile converter.

[0036] As a specific example, step 1 involves performing an equivalent input impedance analysis on the downstream DC-DC converter of the electric vehicle charging pile, simplifying the two-stage structure of the charging pile into a single system model, and using the state-space method to establish an equivalent electromagnetic transient model describing the dynamic behavior of the charging pile converter, as detailed below:

[0037] Step 1.1: Equivalently represent the DC-DC converter of the electric vehicle charging station as a variable resistor. The impedance is shown in the following formula:

[0038]

[0039] in, This is the input impedance of the subsequent DC-DC converter; , These are the input impedances of the subsequent DC-DC converter. The corresponding equivalent voltage and current For the input power of the subsequent DC-DC converter, Charging power for electric vehicles, For efficiency;

[0040] Step 1.2: Map the battery voltage and current under different charging stages to a simplified power control model to obtain the power expression for the electric vehicle charging station:

[0041]

[0042] in, and The active and reactive power of the charging pile. This represents the rated power of the charging station. and This corresponds to the battery's starting and rated voltage. It is the moment when the voltage reaches the rated value. This represents the current attenuation coefficient during the constant voltage stage. express time;

[0043] A charging pile with a rated power of 30kW has a DC-DC efficiency of =0.97, DC bus voltage =800V, The input impedance of the DC-DC converter is calculated as the product of the battery voltage and battery current. During the constant current phase, the current remains constant at approximately 65A, the voltage at 800V, and the charging power at 5.36kW. It is approximately 12Ω.

[0044] Step 1.3: Use the state-space method to establish an equivalent electromagnetic transient model describing the dynamic behavior of the charging pile converter. The dynamic behavior of the charging pile converter is described by the following differential equations:

[0045]

[0046] in, For state variables, They represent shaft current, Shaft current and DC-side capacitor voltage; For input variables, They represent shaft voltage, Shaft voltage and DC-side capacitor current; The system state parameter matrix, The coefficients of the system input parameter matrix;

[0047] The influence of the switching function is combined with state equations using algebraic equations. The algebraic equations reflect the constraints of the switching function and duty cycle, and describe the relationship between the switching state and the AC side voltage and DC side current. The algebraic equations are as follows:

[0048]

[0049] The algebraic-differential expression for the charging pile converter is:

[0050]

[0051] in The parameter matrix representing the state variables in the initial state. This represents the coefficients of the system input parameter matrix in the initial state. , All are determined by circuit parameters and switch states.

[0052] Step 1.4: Establish a three-phase voltage source rectifier charging station in The equation of state in the coordinate system is:

[0053]

[0054]

[0055] in, , They are respectively coordinate system shaft and The duty cycle represented by the axis For AC side inductance, For DC side capacitors, The rotor angular velocity, For AC side resistance, , It is the AC output voltage of the charging pile. , The component, in relation to the DC-side voltage and duty cycle, is as follows:

[0056]

[0057] Substituting the above equation into the state equation and rearranging it into state-space form, we obtain the parameter matrix. and :

[0058]

[0059] As a specific example, step 2 involves dividing the state variables of the entire system into multiple subsystems and simultaneously splitting the system matrix accordingly, as follows:

[0060] Step 2.1: Based on the circuit topology and component characteristics, and assuming the initial system values ​​are known, the system is finely divided into AC subsystems to achieve parallel computation. and DC subsystem Two parts, matrix It also splits into strongly coupled parts of the subsystem accordingly. and weakly coupled parts :

[0061]

[0062] Step 2.2: Split the coupling terms in the state equation multiple times to decompose the entire system into... The first subsystem, then the second... The state equations of the subsystem are:

[0063]

[0064] By splitting the matrix, the system of differential-algebraic equations for each subsystem can be written as:

[0065]

[0066] in, , They are the first , The state variables corresponding to each subsystem It is the first Local matrices of each subsystem Is with the first Input variables related to each subsystem For the first Strongly coupled parts of the subsystem In the The first subsystem The weakly coupled parts of the subsystem and The first The coefficients of the state parameter matrix and input parameter matrix corresponding to each subsystem. It is a positive integer.

[0067] As a specific example, in step 3, during the simulation time stepping process, the implicit trapezoidal integral method is used to discretize the state equation of the charging pile, transforming the dynamic circuit into a static resistor network, as detailed below:

[0068] Step 2.1: Integrating both sides of the system state equation in the time domain yields:

[0069]

[0070] Step 2.2: Differencing the above equation over a simulation step size. The time periods are:

[0071]

[0072] in, for The system state variables at time t. for The system state variables at time t. for The system input parameter matrix at time t.

[0073] As a specific example, step 4 involves processing the discretized state equation using the central difference method, introducing... Delayed decoupling, where The simulation step size is represented, and the delay term is explicitly expressed as a known quantity, forming a semi-implicit difference equation to decouple the two sets of variables. Each subsystem is calculated independently, as detailed below:

[0074] Since the area of ​​the trapezoidal integral can be approximated as The rectangular area is such that, in microsecond-level simulations, the central difference method is used to perform equivalent processing on the electromagnetic transient simulation, that is:

[0075]

[0076] in, , , They are respectively in , , The system input parameter matrix at time t;

[0077] Midpoint of the central integral Actual corresponding time The trapezoidal endpoints of the implicit trapezoidal integral method , Located respectively and When the rectangular area of ​​the central difference method is embedded into the implicit trapezoidal integral method framework using the area equivalence property, time alignment deviations cause problems in the discrete equations. The phase lag, which manifests as a half-step delay in the frequency domain, results in the following difference equation:

[0078]

[0079] in for The state parameter coefficient matrix at time t, for The state parameter coefficient matrix at time t, In order to be in Time and The common coefficients of the input parameter matrix at time 1. For the input parameter matrix in The coefficient at time.

[0080] As a specific example, step 5 involves error correction based on linear interpolation for multiple switches. This involves finding the zero point of the charging pile's switching function, calculating the equivalent duty cycle of the switching signal within a step, determining the average conduction state of the switching device within that step, substituting the equivalent duty cycle of the switching action into the switching function, and returning to step 3 to achieve error compensation for the charging pile's switching action. The details are as follows:

[0081] Step 5.1, Set the first Step size control function for:

[0082]

[0083] in, It is a triangular carrier wave. It is a modulated wave;

[0084] The control function is linearized. General and Piecewise linear approximation yields:

[0085]

[0086] in, In the first The value of the modulated wave at the step size, In the first The value of the modulated wave at the step size, In the first The specific time for step size, In the first The value of the triangular carrier wave at the step size. In the first The value of the triangular carrier wave at the step size.

[0087] make Export about The linear equation:

[0088]

[0089] Solving for:

[0090]

[0091] Then the zero-point crossing moment for:

[0092]

[0093] in, This refers to the ratio of the specific action moment of the control signal within a step size to the step size itself. In the first The value of the control function at the step size. In the first The value of the control function at the step size.

[0094] Step 5.2: Determine the zero-crossing time of the charging pile converter switch operation. Then, the duty cycle and Represented as:

[0095]

[0096] in It is the ratio of the time spent conducting within the switch action step to the total step length. This is the ratio of the area turned off within the total step length of the switch action step, but when the switch changes multiple times within one step length... and All are equivalent duty cycles accumulated over the corresponding time periods. The switching signals of the charging pile converter model are represented by 0 and 1. and They are respectively in and The time value at any given moment and These are the on and off times of the switch, respectively.

[0097] Step 5.3: Substitute the equivalent duty cycle of the switch state action into the switch function, return to step 3, and use it for the state update of the charging pile converter.

[0098] This invention also provides an electromagnetic transient modeling system for electric vehicle charging piles based on implicit trapezoidal integrals. This system is used to implement the aforementioned electromagnetic transient modeling method for electric vehicle charging piles based on implicit trapezoidal integrals. The system includes a model building module, a subsystem partitioning module, a discretization module, a central difference module, and an error correction module, wherein:

[0099] The model building module performs input impedance equivalence on the DC-DC converter of the electric vehicle charging pile, simplifies the two-stage structure of the charging pile into a single system model, and uses the state-space method to establish an equivalent electromagnetic transient model describing the dynamic behavior of the charging pile converter.

[0100] The subsystem partitioning module divides the state variables of the entire system into multiple subsystems, and also splits the system matrix accordingly.

[0101] The discrete module uses the implicit trapezoidal integral method to discretize the state equation of the charging pile during the simulation time step, transforming the dynamic circuit into a static resistor network.

[0102] The central difference module processes the discretized state equations using the central difference method, introducing... Delayed decoupling, where The simulation step size is represented, and the delay term is explicitly converted into a known quantity to form a semi-implicit difference equation, thereby achieving decoupling between the two sets of variables and allowing each subsystem to be calculated independently.

[0103] The error correction module performs error correction for multiple switches based on linear interpolation. It finds the zero point of the charging pile's action switching function, calculates the equivalent duty cycle of the switching signal within a step, determines the average conduction state of the switching device within that step, substitutes the equivalent duty cycle of the switching action into the switching function, and returns it to the discrete module to achieve error compensation for the charging pile's switching action.

[0104] The present invention also provides a mobile terminal, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the electromagnetic transient modeling method for electric vehicle charging piles based on implicit trapezoidal integrals.

[0105] The present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein the program, when executed by a processor, implements the steps in the electromagnetic transient modeling method for electric vehicle charging piles based on implicit trapezoidal integrals.

[0106] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0107] Example

[0108] To verify the effectiveness of this invention in improving the accuracy and efficiency of simulation models in the field of electromagnetic transient modeling of charging piles, this invention conducted relevant simulation modeling analysis on a commercially available charging pile. The electromagnetic transient modeling of the car charging pile proposed in this invention was implemented using Matlab programming. A detailed model of the charging pile was built in PSCAD / EMTD as a reference model, and the simulation results were compared with those of the method of this invention. The structural topology diagram of the charging pile is shown below. Figure 2 As shown, its simulation parameters are shown in Table 1.

[0109] Table 1 Simulation parameters of charging piles

[0110]

[0111] like Figure 1 As shown in the figure, the electromagnetic transient modeling method for electric vehicle charging piles based on implicit trapezoidal integrals provided in this embodiment includes the following steps:

[0112] Step 1: Perform input impedance equivalence on the subsequent DC-DC converter to simplify the two-stage charging pile structure into a single system model. Then, use the state-space method to establish an equivalent electromagnetic transient model describing the dynamic behavior of the charging pile converter, as follows:

[0113] Step 1.1: Equivalently convert the charging pile's downstream DC-DC converter to a variable resistor. The impedance is shown in the following formula:

[0114]

[0115] in, This is the input impedance of the subsequent DC-DC converter; , These are the input impedances of the subsequent DC-DC converter. The corresponding equivalent voltage and current For the input power of the subsequent DC-DC converter, Charging power for electric vehicles, For efficiency;

[0116] Step 1.2: Map the battery voltage and current under different charging stages to a simplified power control model to obtain the power expression for the electric vehicle charging station:

[0117]

[0118] in, and The active and reactive power of the charging pile. This represents the rated power of the charging station. and This corresponds to the battery's starting and rated voltage. It is the moment when the voltage reaches the rated value. This represents the current attenuation coefficient during the constant voltage stage. express time;

[0119] Step 1.3: Considering that the charging pile basically operates at rated power during the constant current phase, the focus is on refining the model of the charging pile in constant current mode. First, it is necessary to perform a variable resistance equivalent model of the converter in the front stage of the simplified model of the charging pile. The topology diagram of the charging pile converter is as follows: Figure 2 As shown, an equivalent electromagnetic transient model describing the dynamic behavior of the charging pile is established using the state-space method. The dynamic behavior of the charging pile converter is described by the following differential equations:

[0120]

[0121] in, For state variables, They represent shaft current, Shaft current and DC-side capacitor voltage; For input variables, They represent shaft voltage, Shaft voltage and DC-side capacitor current; The system state parameter matrix, The coefficients of the system input parameter matrix;

[0122] The influence of the switching function is combined with state equations using algebraic equations. The algebraic equations reflect constraints such as the switching function and duty cycle, and describe the relationship between the switching state and the AC side voltage and DC side current.

[0123]

[0124] Where C and N are determined by circuit parameters and switching states, the algebraic-differential expression of the charging pile converter is:

[0125]

[0126] Step 1.4: For a three-phase voltage source rectifier charging pile, based on the state-average law, the switching function is equivalent to the duty cycle, and the system's state equation is:

[0127]

[0128] Applying the Clarke transform to the state-averaged equations first, followed by a rotational coordinate transformation, yields the dq coordinate coefficient mathematical model:

[0129]

[0130] After simplification, the differential equation for the three-phase converter of the charging pile is:

[0131]

[0132] in, , They are respectively coordinate system shaft and The duty cycle represented by the axis For AC side inductance, For DC side capacitors, The rotor angular velocity, For AC side resistance, , It is the AC output voltage of the charging pile. , The component, in relation to the DC-side voltage and duty cycle, is as follows:

[0133]

[0134] Substituting the above equation into the state equation and rearranging it into state-space form, we obtain the parameter matrix. and :

[0135]

[0136] Step 2: Divide the state variables of the entire system into N subsystems, and simultaneously split the system matrix G accordingly, as follows:

[0137] Step 2.1: Based on the circuit topology and component characteristics, and assuming the initial system values ​​are known, the system is finely divided into AC subsystems to achieve parallel computation. and DC subsystem Two parts, matrix It also splits into strongly coupled parts of the subsystem accordingly. and weakly coupled parts :

[0138]

[0139] Step 2.2: Following this pattern, the coupling terms in the state equations are split multiple times to decompose the entire system into... The first subsystem, then the second... The state equations of the subsystem are:

[0140]

[0141] By splitting the matrix, the system of differential-algebraic equations for each subsystem can be written as:

[0142]

[0143] in, , They are the first , The state variables corresponding to each subsystem It is the first Local matrices of each subsystem Is with the first Input variables related to each subsystem For the first Strongly coupled parts of the subsystem In the The first subsystem The weakly coupled parts of the subsystem and The first The coefficients of the state parameter matrix and input parameter matrix corresponding to each subsystem. It is a positive integer.

[0144] Step 3: During the simulation time stepping process, the implicit trapezoidal integration method is used to discretize the state equation of the charging pile, transforming the dynamic circuit into a static resistor network, as follows:

[0145] Step 2.1: Integrating both sides of the system state equation in the time domain yields:

[0146]

[0147] Step 2.2: Apply the implicit trapezoidal rule to the set of state variables associated with the split matrices H and B / M. The specific principle is as follows: Figure 3 As shown, numerical stability is ensured, allowing for a larger simulation step size, but the calculation utilizes information from the previous time step, thus achieving decoupling between the two sets of variables. Difference is applied to the above equation within a simulation step. The time periods are:

[0148]

[0149] in, for The system state variables at time t. for The system state variables at time t. for The system input parameter matrix at time t.

[0150] Step 4: Process the discretized state equations using the central difference method, introducing... Delayed decoupling, where The simulation step size is represented, and the delay term is explicitly expressed as a known quantity, forming a semi-implicit difference equation to decouple the two sets of variables. Each subsystem is calculated independently, as detailed below:

[0151] Since the area of ​​the trapezoidal integral can be approximated as... The rectangular area is determined by the central difference method, which is computationally efficient and supports decoupling. Therefore, in microsecond-level simulations, the central difference method is used to perform equivalent processing on electromagnetic transient simulations. The specific principle is as follows: Figure 3 As shown, the equivalent effect has almost no impact on the accuracy of the system compared to the original effect, that is:

[0152]

[0153] in, , , They are respectively in , , The system input parameter matrix at time t;

[0154] Midpoint of the central integral Actual corresponding time The trapezoidal endpoints of the implicit trapezoidal integral method , Located respectively and When the rectangular area of ​​the central difference method is embedded into the implicit trapezoidal integral method framework using the area equivalence property, time alignment deviations cause problems in the discrete equations. The phase lag, which manifests as a half-step delay in the frequency domain, results in the following difference equation:

[0155]

[0156] in for The state parameter coefficient matrix at time t, for The state parameter coefficient matrix at time t, In order to be in Time and The common coefficients of the input parameter matrix at time 1. For the input parameter matrix in The coefficient at time.

[0157] First, integrating the state equations of the split system, we can obtain:

[0158]

[0159] Discretizing using the implicit trapezoidal rule and replacing the right-hand integral with the central integral, we get:

[0160]

[0161] Phase shift simplification yields:

[0162]

[0163] in,

[0164] From the above formula, we can see that and , There is a delay of half a step between them, so this equation is a semi-implicit difference equation, and the right-hand side consists of known terms. Substituting the data into the difference equation, we get:

[0165]

[0166] in for The dq-axis current and DC-side voltage values; for The dq-axis current and DC-side voltage values; Let dq-axis current and DC-side voltage values ​​be at time t. Let be the dq-axis voltage and DC-side current values ​​at time t.

[0167] After decoupling and grouping the system, parallel computation can be achieved directly without solving a system of simultaneous equations, such as... Figure 4 As shown.

[0168] Step 5: Based on linear interpolation, perform error correction for multiple switches, find the zero point of the charging pile's action switching function, calculate the equivalent duty cycle of the switching signal within one step, determine the average conduction state of the switching device within that step, substitute the equivalent duty cycle of the switching action into the switching function, and pass it to Step 3 to achieve accurate error compensation for the charging pile's switching action, as detailed below:

[0169] Step 5.1: In the real-time simulation of power electronic devices, the simulation step size Δt must be set strictly less than the controller switching cycle T. sw This is an engineering practice principle determined by both the Nyquist sampling theorem and numerical stability. In some typical scenarios, T swThe step size is approximately 50-100 μs, while real-time simulation step sizes are typically compressed to the order of 1-10 μs. This difference in step size means that the precise timing of the switching event often falls between two simulation step size points, such as... Figure 5 As shown. To accurately reconstruct continuous control behavior in the discrete-time domain, it is necessary to find the actual action moments using formulas. After linearizing the control signal, it is equivalently represented within a simulation step according to the occupied area, thereby accurately finding the zero points of the switching function, such as... Figure 6 As shown, in SPWM, the control function for the k-th step is set as follows:

[0170]

[0171] in, It is a triangular carrier wave. It is a modulated wave;

[0172] By linearizing the control function and approximating m(t) and c(t) piecewise linearly over Δt, we can obtain:

[0173]

[0174] in, In the first The value of the modulated wave at the step size, In the first The value of the modulated wave at the step size, In the first The specific time for step size, In the first The value of the triangular carrier wave at the step size. In the first The value of the triangular carrier wave at the step size.

[0175] make Export about The linear equation:

[0176]

[0177] Solving for:

[0178]

[0179] Then the zero-point crossing moment for:

[0180]

[0181] in, This refers to the ratio of the specific action moment of the control signal within a step size to the step size itself. In the first The value of the control function at the step size. In the first The value of the control function at the step size.

[0182] Step 5.2: Determine the zero-crossing time of the charging pile converter switch operation. Then, the duty cycle and It can be represented as:

[0183]

[0184] in It is the ratio of the time spent conducting within the switch action step to the total step length. This is the ratio of the area turned off within the total step length of the switch action step, but when the switch changes multiple times within one step length... and All are equivalent duty cycles accumulated over the corresponding time periods. The switching signals of the charging pile converter model are represented by 0 and 1. and They are respectively in and The time value at any given moment and These are the on and off times of the switch, respectively.

[0185] Step 5.3: Substitute the equivalent duty cycle of the switch state action into the switch function and pass it to step 3 for the state update of the charging pile converter.

[0186] The specific precision quantification standard is expressed in the form of root mean square:

[0187]

[0188] Where x represents the simulation data from PSCAD. The simulation data for the method presented in this paper are given, where n is the number of simulation data sets.

[0189] By comparing with the dual interpolation method of PSCAD / EMTDC, the total simulation time was 1 second, and the integration step sizes were 1 microsecond and 10 microseconds, respectively. Simulation results under different integration step sizes were compared, such as... Figure 7 and Figure 8 As shown, Figure 7 This is a magnified comparison of the equivalent model of this invention and the reference model in terms of AC phase A voltage, AC phase A current, and AC active power of the charging pile at a step size of 1 microsecond. Figure 8The figure shows a magnified comparison of the equivalent model and the reference model of the present invention in terms of AC phase A voltage, AC phase A current and AC active power of the charging pile when the step size is 10 microseconds. As the simulation step size increases, the simulation error increases slightly, but the simulation accuracy is guaranteed to a certain extent and the simulation time is greatly reduced. The following is a detailed analysis.

[0190] This embodiment simulates a specific working scenario of a charging station, where the charging station is charging an electric vehicle, such as... Figure 7 , Figure 8 As shown in Table 2, the simulation accuracy is calculated using the above-mentioned root mean square formula.

[0191] Table 2 Simulation accuracy of charging piles at the same step size

[0192]

[0193] Table 3 Simulation schedule of charging piles at different step sizes

[0194]

[0195] It can be seen that, compared with the detailed model of the reference model constructed by the method of the present invention at the same integration step size, the detailed reference model of PSCAD has an accuracy of 100%. At 1µs, the accuracy of phase A voltage, phase A current, and active power is 99.34%, 99.17%, and 99.42% of the reference model, respectively; at 10µs, the accuracy of phase A voltage, phase A current, and active power is 98.85%, 98.36%, and 98.62% of the reference model, respectively. This means that the method of the present invention can... The simulation accurately simulates the actual behavior of charging piles and has high simulation accuracy. Regarding simulation time, the simulation step sizes for the PSCAD model and the model of this invention are 1 microsecond and 10 microseconds, respectively. By adopting an equivalent model and increasing the simulation step size, as shown in Table 3, with a step size of 1 microsecond, the simulation time for the reference model is 65.391s, and the simulation time for the equivalent model of this invention is 24.479s; with a step size of 10 microseconds, the simulation time for the reference model is 8.106s, and the simulation time for the equivalent model of this invention is 3.225s. The simulation time is significantly reduced, and the simulation efficiency is improved by approximately 2.6 times.

[0196] Experimental results show that the refined charging pile model proposed in this method has high simulation accuracy. Although there is a slight error compared with the detailed model, it is within the acceptable range. Furthermore, it can significantly improve the simulation efficiency of the model, proving that the modeling method is effective and can effectively solve the problem that the simulation system is large in scale and seriously affects the simulation efficiency and accuracy when a large number of electric vehicles and the power grid interact.

[0197] This invention, by accurately locating the action points of the switch state and applying the principle of area equivalence, can effectively eliminate the transient errors caused by updating state variables within the action step size. It establishes a refined simulation model of electric vehicle charging piles that considers error compensation, and can achieve results similar to those of small step size simulations even with larger simulation step sizes. This effectively ensures simulation accuracy and significantly improves simulation efficiency, providing a new approach to improving the accuracy and efficiency of simulation systems when solving large-scale vehicle-network interaction.

[0198] The above are merely preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for electromagnetic transient modeling of electric vehicle charging piles based on implicit trapezoidal integrals, characterized in that, The steps include the following: Step 1: Perform input impedance equivalence on the DC-DC converter of the electric vehicle charging pile, simplify the two-stage structure of the charging pile into a single system model, and use the state-space method to establish an equivalent electromagnetic transient model describing the dynamic behavior of the charging pile converter. The two-stage structure of the charging pile is simplified into a single system model, as follows: Step 1.1: Equivalently represent the DC-DC converter of the electric vehicle charging station as a variable resistor. The impedance is shown in the following formula: ； in, This is the input impedance of the subsequent DC-DC converter; , These are the input impedances of the subsequent DC-DC converter. The corresponding equivalent voltage and current For the input power of the subsequent DC-DC converter, Charging power for electric vehicles, For efficiency; Step 1.2: Map the battery voltage and current under different charging stages to a simplified power control model to obtain the power expression for the electric vehicle charging station: ； in, and The active and reactive power of the charging pile. This represents the rated power of the charging station. and This corresponds to the battery's starting and rated voltage. It is the moment when the voltage reaches the rated value. This represents the current attenuation coefficient during the constant voltage stage. express time; Step 2: Divide the state variables of the entire system into multiple subsystems, and split the system matrix accordingly. Step 3: During the simulation time stepping process, the implicit trapezoidal integral method is used to discretize the state equation of the charging pile, and the dynamic circuit is transformed into a static resistor network. Step 4: Process the discretized state equations using the central difference method, introducing... Delayed decoupling, where The simulation step size is represented, and the delay term is explicitly converted into a known quantity to form a semi-implicit difference equation, thereby achieving decoupling between the two sets of variables and allowing each subsystem to be calculated independently. Step 5: Correct the error of multiple switches based on linear interpolation, find the zero point of the charging pile action switching function, calculate the equivalent duty cycle of the switching signal within a step, determine the average conduction state of the switching device within the step, substitute the equivalent duty cycle of the switching action into the switching function, return to step 3, and realize the error compensation of the charging pile switching action.

2. The electromagnetic transient modeling method for electric vehicle charging piles based on implicit trapezoidal integrals according to claim 1, characterized in that, In step 1, the electric vehicle charging pile has a two-stage structure including a front-stage AC-DC converter and a rear-stage DC-DC converter; the dynamic behavior of the charging pile converter specifically refers to the dynamic behavior of the 30kW fast charging pile converter.

3. The electromagnetic transient modeling method for electric vehicle charging piles based on implicit trapezoidal integrals according to claim 2, characterized in that, Step 1 describes the use of the state-space method to establish an equivalent electromagnetic transient model describing the dynamic behavior of the charging pile converter, as follows: Step 1.3: The dynamic behavior of the charging pile converter is described by the following differential equation: ； in, For state variables, They represent shaft current, Shaft current and DC-side capacitor voltage; For input variables, They represent shaft voltage, Shaft voltage and DC-side capacitor current; The system state parameter matrix, The coefficients of the system input parameter matrix; The influence of the switching function is combined with state equations using algebraic equations. The algebraic equations reflect the constraints of the switching function and duty cycle, and describe the relationship between the switching state and the AC side voltage and DC side current. The algebraic equations are as follows: ； The algebraic-differential expression for the charging pile converter is: ； in The parameter matrix representing the state variables in the initial state. This represents the coefficients of the system input parameter matrix in the initial state. , All are determined by circuit parameters and switch states; Step 1.4: Establish a three-phase voltage source rectifier charging station in The equation of state in the coordinate system is: ； ； in, , They are respectively coordinate system shaft and The duty cycle represented by the axis For AC side inductance, For DC side capacitors, The rotor angular velocity, For AC side resistance, , It is the AC output voltage of the charging pile. , The component, in relation to the DC-side voltage and duty cycle, is as follows: ； Substituting the above equation into the state equation and rearranging it into state-space form, we obtain the parameter matrix. and : 。 4. The electromagnetic transient modeling method for electric vehicle charging piles based on implicit trapezoidal integrals according to claim 3, characterized in that, Step 2 involves dividing the state variables of the entire system into multiple subsystems and simultaneously splitting the system matrix accordingly, as detailed below: Step 2.1: Based on the circuit topology and component characteristics, and assuming the initial system values ​​are known, the system is finely divided into AC subsystems to achieve parallel computation. and DC subsystem Two parts, matrix It also splits into strongly coupled parts of the subsystem accordingly. and weakly coupled parts : ； Step 2.2: Split the coupling terms in the state equation multiple times to decompose the entire system into... The first subsystem, then the second... The state equations of the subsystem are: ； By splitting the matrix, the system of differential-algebraic equations for each subsystem can be written as: ； in, , They are the first , The state variables corresponding to each subsystem It is the first Local matrices of each subsystem Is with the first Input variables related to each subsystem For the first Strongly coupled parts of the subsystem In the The first subsystem The weakly coupled parts of the subsystem and The first The coefficients of the state parameter matrix and input parameter matrix corresponding to each subsystem. It is a positive integer.

5. The electromagnetic transient modeling method for electric vehicle charging piles based on implicit trapezoidal integrals according to claim 4, characterized in that, In step 3, during the simulation time stepping process, the implicit trapezoidal integral method is used to discretize the state equation of the charging pile, transforming the dynamic circuit into a static resistor network, as detailed below: Step 2.1: Integrating both sides of the system state equation in the time domain yields: ； Step 2.2: Differencing the above equation over a simulation step size. The time periods are: ； in, for The system state variables at time t. for The system state variables at time t. for The system input parameter matrix at time t.

6. The electromagnetic transient modeling method for electric vehicle charging piles based on implicit trapezoidal integrals according to claim 5, characterized in that, Step 4 describes processing the discretized state equations using the central difference method, introducing... Delayed decoupling, where The simulation step size is represented, and the delay term is explicitly expressed as a known quantity, forming a semi-implicit difference equation to decouple the two sets of variables. Each subsystem is calculated independently, as detailed below: Since the area of ​​the trapezoidal integral can be approximated as The rectangular area is such that, in microsecond-level simulations, the central difference method is used to perform equivalent processing on the electromagnetic transient simulation, that is: ； in, , , They are respectively in , , The system input parameter matrix at time t; Midpoint of the central integral Actual corresponding time The trapezoidal endpoints of the implicit trapezoidal integral method , Located respectively and When the rectangular area of ​​the central difference method is embedded into the implicit trapezoidal integral method framework using the area equivalence property, time alignment deviations cause problems in the discrete equations. The phase lag, which manifests as a half-step delay in the frequency domain, results in the following difference equation: ； in for The state parameter coefficient matrix at time t, for The state parameter coefficient matrix at time t, In order to be in Time and The common coefficients of the input parameter matrix at time 1. For the input parameter matrix in The coefficient at time.

7. The electromagnetic transient modeling method for electric vehicle charging piles based on implicit trapezoidal integrals according to claim 6, characterized in that, Step 5 describes the error correction of multiple switches based on linear interpolation. It involves finding the zero point of the charging pile's action switching function, calculating the equivalent duty cycle of the switching signal within a step size, determining the average conduction state of the switching device within that step size, substituting the equivalent duty cycle of the switching action into the switching function, and returning to step 3 to achieve error compensation for the charging pile's switching action. The details are as follows: Step 5.1, Set the first Step size control function for: ； in, It is a triangular carrier wave. It is a modulated wave; The control function is linearized. General and Piecewise linear approximation yields: ； in, In the first The value of the modulated wave at the step size, In the first The value of the modulated wave at the step size, In the first The specific time for step size, In the first The value of the triangular carrier wave at the step size. In the first The value of the triangular carrier wave at the step size; make Export about The linear equation: ； Solving for: ； Then the zero-point crossing moment for: ； in, This refers to the ratio of the specific action moment of the control signal within a step size to the step size itself. In the first The value of the control function at the step size. In the first The value of the control function at the step size; Step 5.2: Determine the zero-crossing time of the charging pile converter switch operation. Then, the duty cycle and Represented as: ； in It is the ratio of the time spent conducting within the switch action step to the total step length. This is the ratio of the area turned off within the total step length of the switch action step, but when the switch changes multiple times within one step length... and All are equivalent duty cycles accumulated over the corresponding time periods. The switching signals of the charging pile converter model are represented by 0 and 1. and They are respectively in and The time value at any given moment and These are the on and off times of the switch, respectively. Step 5.3: Substitute the equivalent duty cycle of the switch state action into the switch function, return to step 3, and use it for the state update of the charging pile converter.

8. A system for electromagnetic transient modeling of electric vehicle charging piles based on implicit trapezoidal integrals, characterized in that, This system is used to implement the electromagnetic transient modeling method for electric vehicle charging piles based on implicit trapezoidal integrals as described in any one of claims 1 to 7. The system includes a model building module, a subsystem partitioning module, a discretization module, a central difference module, and an error correction module, wherein: The model building module performs input impedance equivalence on the DC-DC converter of the electric vehicle charging pile, simplifies the two-stage structure of the charging pile into a single system model, and uses the state-space method to establish an equivalent electromagnetic transient model describing the dynamic behavior of the charging pile converter. The subsystem partitioning module divides the state variables of the entire system into multiple subsystems, and also splits the system matrix accordingly. The discrete module uses the implicit trapezoidal integral method to discretize the state equation of the charging pile during the simulation time step, transforming the dynamic circuit into a static resistor network. The central difference module processes the discretized state equations using the central difference method, introducing... Delayed decoupling, where The simulation step size is represented, and the delay term is explicitly converted into a known quantity to form a semi-implicit difference equation, thereby achieving decoupling between the two sets of variables and allowing each subsystem to be calculated independently. The error correction module performs error correction for multiple switches based on linear interpolation. It finds the zero point of the charging pile's action switching function, calculates the equivalent duty cycle of the switching signal within a step, determines the average conduction state of the switching device within that step, substitutes the equivalent duty cycle of the switching action into the switching function, and returns it to the discrete module to achieve error compensation for the charging pile's switching action.

9. A mobile terminal, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the electromagnetic transient modeling method for electric vehicle charging piles based on implicit trapezoidal integrals as described in any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps in the electromagnetic transient modeling method for electric vehicle charging piles based on implicit trapezoidal integrals as described in any one of claims 1 to 7.

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