A high-voltage direct-current power supply filter optimization design method

Abstract

The application provides a high-voltage direct-current power supply filter optimization design method, which sets multiple design constraint conditions about insertion loss, temperature rise and magnetic flux density for the comprehensive optimization target including filter product volume, mass and cost, and simultaneously considers source impedance and realizes automatic selection of filter topological structures of all levels through a genetic algorithm in the design, so that many defects existing in the prior filter design method are overcome, and the beneficial effects of sufficiently reducing cost and reducing volume on the basis of improving filter design performance are achieved.

Description

Technical Field

[0001] This invention belongs to the field of electromagnetic interference filter technology, and in particular relates to a filter design method for electromagnetic interference from high-voltage DC power supply in motor controllers of new energy vehicles. Background Technology

[0002] Because the power semiconductor devices used in the motor controller have high current change rates di / dt and voltage change rates du / dt during rapid switching, they generate unwanted electromagnetic noise. This noise not only affects radio receiving equipment inside and outside the vehicle but also impacts other high- and low-voltage components via the high-voltage power lines. Furthermore, this electromagnetic noise generated by the motor drive system can cause the device itself to fail to meet EMC standard limits and can also cause the entire vehicle to fail to meet EMC standard limits.

[0003] To overcome the effects of high-frequency noise, specialized filters need to be designed. The design goal of these filters is to achieve maximum impedance mismatch; however, existing design methods often fail to consider the varying source impedances of actual systems, sometimes leading to insufficient or negative insertion loss, or even amplifying electromagnetic noise. To compensate for this discrepancy, engineers leave a large margin when calculating the target insertion loss of the filter, but this can result in over-design, increasing the filter's size and reducing its power density. Currently, filter design methods that consider source impedance mainly include calculating component parameters based on source impedance and using optimization algorithms. However, calculating component parameters based on source impedance only qualitatively selects the filter topology based on the source and load impedances, while optimization algorithms cannot automatically select the filter topology that considers source impedance. Therefore, existing filter design technologies have certain shortcomings and cannot meet the needs of the new energy vehicle industry. Summary of the Invention

[0004] To address the aforementioned technical problems in this field, the present invention provides an optimized design method for a high-voltage DC power supply filter, specifically comprising the following steps:

[0005] Step 1: Initially determine the basic topological units composed of circuit elements in each stage of the filter to be designed, as well as the total number of stages of the filter to be designed;

[0006] Step 2: Calculate and determine the minimum insertion loss, maximum temperature rise, and maximum magnetic flux density limits of the filter to be designed as design constraints;

[0007] Step 3: Set the optimization goal for the filter design, that is, to achieve the optimal weighted sum of the three indicators of the filter to be designed: volume, mass and cost.

[0008] Step 4: Using parameters such as voltage, current, ambient temperature, source impedance, and magnetic ring capacitance impedance as input parameters for the genetic algorithm, and based on the design constraints determined in Step 2, the genetic algorithm is used to solve the optimization objective problem determined in Step 3, and the optimal topology unit structure and corresponding circuit element specific indicators are calculated for each level.

[0009] Furthermore, step 2 involves calculating and determining the various design constraints, specifically including:

[0010] 1) Minimum insertion loss constraint:

[0011] For a filter to be designed with n LCL basic units, its actual insertion loss is calculated using T-parameters. The T-parameter matrix of the i-th series inductor and the j-th parallel capacitor in each stage of the circuit is defined as follows:

[0012]

[0013]

[0014] In the formula, Z Li and Z Cj The common-mode impedance and capacitive impedance of the magnetic ring are given below, representing the impedances of the inductor and capacitor, respectively.

[0015]

[0016]

[0017] In the formula, L C and R C These represent the equivalent parasitic inductance and equivalent parasitic capacitance of the capacitor, respectively; j is the imaginary unit; L is the inductance of the magnetic ring coil (H); and F is the cross-sectional area of ​​the magnetic ring (cm²). 2 Let l be the average length (cm) of the magnetic ring, μ be the relative permeability of the magnetic ring (a function of frequency f), and C be the capacitance. Then the T-parameter matrix of the filter to be designed can be calculated as follows:

[0018] The T-parameter matrix of the filter to be designed can then be calculated as follows:

[0019]

[0020] In the formula, A1, B1, C1, and D1 are the T-parameters of the two-port filter network.

[0021] The insertion loss of the filter is expressed as follows:

[0022]

[0023] In the formula, Z S Z is the noise source impedance of the system.L The load impedance of the system;

[0024] To meet the target insertion loss requirement of the filter, both the common-mode insertion loss and the differential-mode insertion loss of the filter should not be less than the target insertion loss. Therefore, the minimum insertion loss constraint is expressed as follows:

[0025]

[0026] In the formula, IL CM and IL DM These are common-mode insertion loss and differential-mode insertion loss, respectively. CMX and IL DMX These are common-mode target insertion loss and differential-mode target insertion loss, respectively.

[0027] 2) Maximum temperature rise constraint:

[0028] Utilizing the heat loss P of the filter loss Characterizing temperature rise, including the loss P of the common-mode magnetic ring. ring and copper busbar loss P copper Two parts, namely:

[0029] P loss =P ring +P copper

[0030] Among them, the core loss of magnetic cores with small or no air gap comes from the harmonics of the switching frequency current and the order of the switching frequency current harmonics, while the loss P of the common-mode magnetic ring is... ring The following formula can be used to calculate:

[0031] P ring (W / kg)=Kf(kHz) N B(T) M

[0032] In the formula, B is the magnetic flux density, and K, N and M are coefficients related to the magnetic core material, which can be calculated from the temperature rise curve in the magnetic core material data table;

[0033] copper busbar loss P copper The following formula can be used for calculation:

[0034] P copper =I 2 R copper

[0035] In the formula, I is the working current flowing through the copper bar, and R... copper The resistance of the copper busbar can be calculated by measurement or using the following formula:

[0036]

[0037] In the formula, ρ is the resistivity of the copper strip, and l copper Let S be the length of the copper strip and S be the cross-sectional area of ​​the copper strip.

[0038] Temperature rise T of magnetic core and copper busbar rise-ring and T rise-copper It can be calculated using the following formula:

[0039] T rise-ring =M ring ×P ring ×R th-ring

[0040] T rise-copper =P copper ×R th-copper

[0041] In the formula R th-ring and R th-copper The thermal resistances of the magnetic ring and copper busbar are respectively, which can be found in datasheets or relevant manuals.

[0042] A corresponding threshold is set for the sum of the above two temperature rises. At the same time, the maximum allowable temperature rise ΔT is determined by considering the impact of temperature rise on the filter capacitor performance. Together, these factors determine the maximum temperature rise constraint t. rise ;

[0043] 3) Maximum magnetic flux density constraint:

[0044] Magnetic flux density B caused by common-mode current and differential-mode current CM and B DM It can be calculated using the following formula:

[0045]

[0046]

[0047] In the formula, L CM and L DM These are the common-mode inductance and differential-mode inductance of the magnetic ring, respectively. For a common-mode magnetic ring, the common-mode inductance is the self-inductance of the magnetic ring, and the differential-mode inductance is the leakage inductance of the magnetic ring.

[0048] The total magnetic flux density of the magnetic core can be calculated using the following formula:

[0049]

[0050] To prevent the magnetic ring from saturating under both common-mode and differential-mode currents, the maximum magnetic flux density constraint shown in the following formula must be satisfied:

[0051] B total ≤B S

[0052] Among them, B Sdenoted as saturation magnetic flux density of the magnetic material.

[0053] Furthermore, the optimization objective in step 3 specifically involves solving the following problem: min(J)

[0054] J = q1V filter +q2M filter +q3P filter

[0055] In the formula, q1, q2, and q3 are weighting factors for volume, mass, and cost, with values ​​ranging from (0 to 1), and can be selected according to actual needs;

[0056] Define V filter M filter P filter The volume, mass, and cost of the filter to be designed are respectively expressed by the following formula:

[0057]

[0058]

[0059]

[0060] In the formula, i, j, and k represent the number of magnetic rings, X capacitors, and Y capacitors, respectively, and M... CX-n and M CY-n The masses of capacitor X and capacitor Y are V, respectively. ring-n V is the volume of the magnetic ring. CX-n and V Y-n The volumes of capacitor X and capacitor Y are given by P. ring-n P CX-n and P CY-n The costs of the magnetic ring, X capacitor, and Y capacitor are respectively, ρ ring-n p ring-n These are the density and unit volume cost of the magnetic ring, respectively.

[0061] The volume, mass, cost, voltage level, and capacitance of a capacitor are all related to its specific parameters. A fitting function can be established to calculate these parameters based on the parameters in the capacitor's datasheet.

[0062] When the material is constant, the mass and cost of the magnetic ring are linearly related to its volume. The volume of the magnetic ring is related to the inductance, the size of the copper busbar, and the arrangement of the filter, and can be calculated based on the following factors:

[0063] ① Determine the dimensions of the copper busbar based on the operating voltage and current;

[0064] ②Establish the relationship between inductance and inductance volume.

[0065] Furthermore, step 4 utilizes a genetic algorithm to solve the optimization objective problem, including combining the various design constraints into the following nonlinear constraint Φ:

[0066] Φ = max(0, b1, b2, b3, b4)

[0067]

[0068] In the formula, b1 and b2 are the criteria for whether the common-mode insertion loss and differential-mode insertion loss meet the constraints. Since the insertion loss is a function of frequency, when making comparisons, m frequency points are selected within the frequency range as needed, and the insertion loss at these frequency points is compared and calculated.

[0069] The genetic algorithm solves the problem by obtaining the available topologies for each stage. For example, for a filter to be designed with an initial set of n LCL basic topology units, the algorithm can replace each stage with a more suitable LC, CL, or CLC topology, thus achieving automatic topology selection in filter design. Theoretically, the larger the value of n, the more filter topology options are available, but this comes with a large computational burden. Therefore, the value of n should be selected according to the actual insertion loss requirements of the filter.

[0070] The high-voltage DC power supply filter optimization design method provided by the present invention sets various design constraints such as insertion loss, temperature rise, and magnetic flux density to comprehensively optimize the product's size, weight, and cost. At the same time, the design considers both the source impedance and uses a genetic algorithm to automatically select the filter's topology at each stage, thereby overcoming many defects in existing filter design methods. It has the beneficial effect of significantly reducing costs and shrinking size while improving filter design performance. Attached Figure Description

[0071] Figure 1 This is the initial topology circuit of the filter in the method provided by the present invention;

[0072] Figure 2 The flowchart shows the filter program design of the method provided by this invention.

[0073] Figure 3 This is the filter program output interface of the method provided by the present invention;

[0074] Figure 4 This is a diagram of the filter topology implemented in this invention;

[0075] Figure 5 This is a three-dimensional model diagram of the filter implemented in this invention;

[0076] Figure 6 Experimental results of conducted disturbance voltage before and after the filter designed using the method of the present invention were installed;

[0077] Figure 7 Time-domain curves of conducted disturbance current before and after the filter designed using the method of this invention are shown.

[0078] Figure 8 Frequency domain curves of conducted disturbance current before and after the filter designed using the method of this invention is installed. Detailed Implementation

[0079] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0080] This invention provides an optimized design method for a high-voltage DC power supply filter, which specifically includes the following steps:

[0081] Step 1: Initially determine the basic topological units composed of circuit elements in each stage of the filter to be designed, as well as the total number of stages of the filter to be designed;

[0082] Step 2: Calculate and determine the minimum insertion loss, maximum temperature rise, and maximum magnetic flux density limits of the filter to be designed as design constraints;

[0083] Step 3: Set the optimization goal for the filter design, that is, to achieve the optimal weighted sum of the three indicators of the filter to be designed: volume, mass and cost.

[0084] Step 4: Using parameters such as voltage, current, ambient temperature, source impedance, and magnetic ring capacitance impedance as input parameters for the genetic algorithm, and based on the design constraints determined in Step 2, the genetic algorithm is used to solve the optimization objective problem determined in Step 3, and the optimal topology unit structure and corresponding circuit element specific indicators are calculated for each level.

[0085] In a preferred embodiment of the present invention, step 2, calculating and determining the various design constraints, specifically includes:

[0086] 1) Minimum insertion loss constraint:

[0087] For a filter to be designed with n LCL basic units, its actual insertion loss is calculated using T-parameters. The T-parameter matrix of the i-th series inductor and the j-th parallel capacitor in each stage of the circuit is defined as follows:

[0088]

[0089]

[0090] In the formula, ZLi and Z Cj The common-mode impedance and capacitive impedance of the magnetic ring are given below, representing the impedances of the inductor and capacitor, respectively.

[0091]

[0092]

[0093] In the formula, L C and R C These represent the equivalent parasitic inductance and equivalent parasitic capacitance of the capacitor, respectively; j is the imaginary unit; L is the inductance of the magnetic ring coil (H); and F is the cross-sectional area of ​​the magnetic ring (cm²). 2 Let l be the average length (cm) of the magnetic ring, μ be the relative permeability of the magnetic ring (a function of frequency f), and C be the capacitance. Then the T-parameter matrix of the filter to be designed can be calculated as follows:

[0094]

[0095] In the formula, A1, B1, C1, and D1 are the T-parameters of the two-port filter network.

[0096] The insertion loss of the filter is expressed as follows:

[0097]

[0098] In the formula, Z S Z is the noise source impedance of the system. L The load impedance of the system;

[0099] To meet the target insertion loss requirement of the filter, both the common-mode insertion loss and the differential-mode insertion loss of the filter should not be less than the target insertion loss. Therefore, the minimum insertion loss constraint is expressed as follows:

[0100]

[0101] In the formula, IL CM and IL DM These are common-mode insertion loss and differential-mode insertion loss, respectively. CMX and IL DMX These are common-mode target insertion loss and differential-mode target insertion loss, respectively.

[0102] 2) Maximum temperature rise constraint:

[0103] Utilizing the heat loss P of the filter loss Characterizing temperature rise, including the loss P of the common-mode magnetic ring. ring and copper busbar loss P copper Two parts, namely:

[0104] P loss =P ring +Pcopper

[0105] Among them, the core loss of magnetic cores with small or no air gap comes from the harmonics of the switching frequency current and the order of the switching frequency current harmonics, while the loss P of the common-mode magnetic ring is... ring The following formula can be used to calculate:

[0106] P ring (W / kg)=Kf(kHz) N B(T) M

[0107] In the formula, B is the magnetic flux density, and K, N and M are coefficients related to the magnetic core material, which can be calculated from the temperature rise curve in the magnetic core material data table;

[0108] copper busbar loss P copper The following formula can be used for calculation:

[0109] P copper =I 2 R copper

[0110] In the formula, I is the working current flowing through the copper bar, and R... copper The resistance of the copper busbar can be calculated by measurement or using the following formula:

[0111]

[0112] In the formula, ρ is the resistivity of the copper strip, and l copper Let S be the length of the copper strip and S be the cross-sectional area of ​​the copper strip.

[0113] Temperature rise T of magnetic ring and copper busbar rise-ring and T rise-copper It can be calculated using the following formula:

[0114] T rise-ring =M ring ×P ring ×R th-ring

[0115] T rise-copper =P copper ×R th-copper

[0116] In the formula R th-ring and R th-copper The thermal resistances of the magnetic ring and copper busbar are respectively, which can be found in datasheets or relevant manuals.

[0117] A corresponding threshold is set for the sum of the above two temperature rises. At the same time, the maximum allowable temperature rise ΔT is determined by considering the impact of temperature rise on the filter capacitor performance. Together, these factors determine the maximum temperature rise constraint t. rise ;

[0118] 3) Maximum magnetic flux density constraint:

[0119] Magnetic flux density B caused by common-mode current and differential-mode current CM and B DM It can be calculated using the following formula:

[0120]

[0121]

[0122] In the formula, L CM and L DM These are the common-mode inductance and differential-mode inductance of the magnetic ring, respectively. For a common-mode magnetic ring, the common-mode inductance is the self-inductance of the magnetic ring, and the differential-mode inductance is the leakage inductance of the magnetic ring.

[0123] The total magnetic flux density of the magnetic core can be calculated using the following formula:

[0124]

[0125] To prevent the magnetic ring from saturating under both common-mode and differential-mode currents, the maximum magnetic flux density constraint shown in the following formula must be satisfied:

[0126] B total ≤B S

[0127] Among them, B S denoted as saturation magnetic flux density of the magnetic material.

[0128] Considering the filter length limitation, this embodiment selects as follows: Figure 1 The 5th-order LCLCL filter topology circuit shown is used for filter optimization design considering source impedance and high-frequency parameters. The optimization objective of the filter is to minimize its size, and the design constraints are an insertion loss of 50dB across the entire frequency band of 100kHz-108MHz, an operating voltage of 1000V, and an operating current of 300A.

[0129] The genetic algorithm is implemented using the Genetic Algorithm Toolbox in Matlab. The parameter settings are shown in Table 1, and the program flowchart is as follows. Figure 2 As shown, the program output interface is as follows: Figure 3 As shown, the optimal filter topology is LCLC, with L1 = 12.9 μH, L2 = 15.3 μH, C1 = 1.7 μF, C2 = 1.8 μF, and volume V = 119.3 cm3.

[0130] Table 1. Specific parameter settings for the genetic algorithm

[0131]

[0132] The filter topology and parameters were calculated based on the optimization algorithm program, and the calculated dimensions of the copper busbar and magnetic ring are shown in Table 2. Since the inductance values ​​of L1 and L2 are not significantly different, both inductors were chosen to have an inductance of 15μH in the actual design, and the Y capacitors were both chosen to have a capacitance of 1μF. Furthermore, to improve the filter's suppression of differential-mode noise, three 10μF X capacitors were added between the filter's input port, output port, and between L1 and L2. The final filter topology is shown in Table 2. Figure 4 As shown, the 3D layout diagram is as follows: Figure 5 As shown.

[0133] Table 2 Dimensions of Filter Copper Busbars and Magnetic Rings

[0134]

[0135] In a specific embodiment of this invention, an experimental platform for suppressing conducted electromagnetic interference on the high-voltage DC power line of a motor drive system was constructed according to GB / T18655-2018. After designing a filter based on the method provided by this invention, it was installed between the high-voltage LISN and the DC input port of the motor controller via a high-voltage DC shielded cable, and securely connected to the input / output cables. Under the conditions of a motor controller DC input voltage of 336V, an input current of 32A, a motor speed of 1900rpm, and an output torque of 53Nm, the conducted interference voltage on the high-voltage positive power line of the motor controller after the filter was installed was measured using a receiver. Figure 6 As shown, after installing this filter, the conduction voltage of the high-voltage positive power line of the motor controller meets the level 3 limit requirements of GB / T 18655-2018, with a margin of 30dB. This filter allows the motor drive system to pass the most stringent level 5 standard limit of GB / T 18655-2018.

[0136] A conducted disturbance current test platform was built according to GB / T18655-2018. Time-domain and frequency-domain current probes were attached to the high-voltage positive power supply line. At a motor operating condition of 1900 rpm and 10⁶ Nm, the time-domain waveform and frequency-domain curve of the conducted disturbance current on the high-voltage positive power supply line were measured before and after the installation of the optimized filter. The results are shown below. Figure 7 and Figure 8 As shown. From Figure 7 As can be seen, before the filter was installed, the high-voltage positive current would oscillate momentarily when the IGBT switching state changed, with the peak-to-peak value of the oscillating current reaching over 100A. This oscillating current could impact and even damage the internal components of the motor controller. However, after installing the filter designed based on this invention, the oscillation in the high-voltage positive current was eliminated, and the fluctuation amplitude when the current stabilized was reduced from 20A to 10A. Figure 8It can be seen that before the filter was installed, the average conducted interference current of the system exceeded the level 3 limit requirements of GB / T 18655-2018 standard at 150kHz-180kHz, 530kHz-1.8MHz, and 46MHz, with a maximum exceedance of 10dB. After the filter was installed, the amplitude of the conducted interference current of the system decreased significantly and met the level 3 limit requirements of the standard.

[0137] It should be understood that the sequence number of each step in the embodiments of the present invention does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention.

[0138] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for optimizing the design of a high-voltage DC power supply filter, characterized in that: Specifically, the following steps are included: Step 1: Initially determine the basic topological units composed of circuit elements in each stage of the filter to be designed, as well as the total number of stages of the filter to be designed; Step 2: Calculate and determine the minimum insertion loss, maximum temperature rise, and maximum magnetic flux density limits of the filter to be designed as design constraints; Step 3: Set the optimization objective for the filter design, which is to achieve the optimal weighted sum of the three indicators of the filter to be designed: volume, mass, and cost. Specifically, this involves solving the following min(J) problem: J = q1V filter + q2M filter + q3P filter In the formula, q1, q2, and q3 are weighting factors for volume, mass, and cost, with values ​​ranging from (0 to 1), and can be selected according to actual needs; Definition V filter , M filter , P filter are the volume, mass and cost of the filter to be designed, respectively, and are expressed by the following equations: In the formula, i, j, and k represent the number of magnetic rings, X capacitors, and Y capacitors, respectively, and M... CX-n and M CY-n The masses of capacitor X and capacitor Y are V, respectively. ring-n V is the volume of the magnetic ring. CX-n and V CY-n The volumes of capacitor X and capacitor Y are given by P. CX-n and P CY-n The costs of capacitors X and Y are respectively, ρ ring-n p ring-n These are the density and unit volume cost of the magnetic ring, respectively. Step 4: Using voltage, current, ambient temperature, source impedance, and magnetic ring capacitance impedance parameters as input parameters for the genetic algorithm, and based on the design constraints determined in Step 2, the genetic algorithm solves the optimization objective problem determined in Step 3, including combining the design constraints into the following nonlinear constraint Φ: Φ = max(0, b1, b2, b3, b4) In the formula, b1 and b2 are the criteria for whether the common-mode insertion loss and differential-mode insertion loss satisfy the constraint conditions, and IL CM and IL DM These are common-mode insertion loss and differential-mode insertion loss, respectively. CMX and IL DMX These are common-mode target insertion loss and differential-mode target insertion loss, respectively. k For the k-th frequency point, since insertion loss is a function of frequency, when making comparisons, m frequency points are selected within the frequency range as needed, and the insertion loss at these frequency points is compared and calculated; t rise For the maximum temperature rise constraint, ΔT is the maximum temperature rise, B total B is the total magnetic flux density of the magnetic core. S The saturation magnetic flux density of the magnetic material is used as the basis for calculations. Finally, the optimal topological unit structure for each level and the specific specifications of the corresponding circuit elements are obtained.

2. The method as described in claim 1, characterized in that: Step 2 involves calculating and determining the various design constraints, specifically including: 1) Minimum insertion loss constraint: The T-parameter matrix of the filter to be designed is calculated as follows: In the formula, A1, B1, C1, and D1 are the T-parameters of the two-port filter network; in the subscript n, n represents the filter stage number, and L and C represent the inductance and capacitance of each stage, respectively. The insertion loss IL of the filter is expressed as follows: In the formula, Z S Z is the noise source impedance of the system. L The load impedance of the system; To meet the target insertion loss requirement of the filter, both the common-mode insertion loss and the differential-mode insertion loss of the filter should not be less than the target insertion loss. Therefore, the minimum insertion loss constraint is expressed as follows: In the formula, IL CM and IL DM These are common-mode insertion loss and differential-mode insertion loss, respectively. CMX and IL DMX These are common-mode target insertion loss and differential-mode target insertion loss, respectively. 2) Maximum temperature rise constraint: Utilizing the heat loss P of the filter loss Characterizing temperature rise, including the loss P of the common-mode magnetic ring. ring and copper busbar loss P copper Two parts, namely: P loss =P ring +P copper Among them, the loss P of the common-mode magnetic ring ring Calculate using the following formula: P ring =Kf N B M In the formula, B is the magnetic flux density, K, N and M are coefficients related to the magnetic ring material, which are calculated from the temperature rise curve in the magnetic ring material data table, and f is the frequency; copper busbar loss P copper Calculate using the following formula: P copper =I 2 R copper In the formula, I is the working current flowing through the copper bar, and R... copper The resistance of the copper busbar can be obtained through direct measurement or by calculating using the following formula: In the formula, ρ is the resistivity of the copper strip, and l copper Let S be the length of the copper strip, and S be the cross-sectional area of ​​the copper strip. Temperature rise T of magnetic ring and copper busbar rise-ring and T rise-copper Calculated using the following formula: T rise-ring =M ring ×P ring ×R th-ring T rise-copper =P copper ×R th-copper In the formula, M ring R is the mass of the magnetic ring. th-ring and R th-copper These are the thermal resistances of the magnetic ring and the copper busbar, respectively. A corresponding threshold is set for the sum of the above two temperature rises. At the same time, the maximum allowable temperature rise ΔT is determined by considering the impact of temperature rise on the filter capacitor performance. Together, these factors determine the maximum temperature rise constraint t. rise ; 3) Maximum magnetic flux density constraint: Magnetic flux density B caused by common-mode current and differential-mode current CM and B DM It can be calculated using the following formula: In the formula, I CM and I DM These are the common-mode current and differential-mode current of the magnetic ring, respectively, L CM and L DM These are the common-mode inductance and differential-mode inductance of the magnetic ring, respectively, where F is the cross-sectional area of ​​the magnetic ring. For a common-mode magnetic ring, the common-mode inductance is the self-inductance of the magnetic ring, and the differential-mode inductance is the leakage inductance of the magnetic ring. The total magnetic flux density B of the magnetic core total Calculate using the following formula: To prevent the magnetic ring from saturating under both common-mode and differential-mode currents, the maximum magnetic flux density constraint shown in the following formula must be satisfied: B total ≤B S Among them, B S denoted as saturation magnetic flux density of the magnetic material.

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