A method for modeling high-frequency parameter frequency variation characteristics of a four-core long-line cable
Patent Information
- Application Number
- CN202611543548.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-10-08
- Publication Date
- 2026-11-03
AI Technical Summary
Existing cable modeling methods cannot accurately describe the high-frequency frequency variation characteristics of four-core long cables exceeding 100 meters in length. In particular, in motor speed control systems, traditional lumped parameter modeling methods fail in the high-frequency band and lack systematic methods for extracting high-frequency parameters and constructing circuit models.
Using transmission line theory, by measuring the open-circuit and short-circuit impedances of a four-core cable, and combining the RL ladder network model and the GC parallel circuit model, a suitable circuit model is directly constructed to characterize the frequency-varying characteristics of the cable. This model is suitable for impedance and transmission characteristic analysis over a wide frequency range.
It achieves accurate characterization of the frequency-varying characteristics of long cables, and is applicable to cables longer than 100 meters, especially in the conducted electromagnetic interference band of 150kHz to 30MHz. It provides an accurate model basis for overvoltage and EMI prediction of long cables in motor drive systems.
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Abstract
Description
Technical Field
[0001] This invention relates to the field of high-frequency modeling technology for cables, specifically to a method for modeling the frequency-varying characteristics of high-frequency parameters of four-core long cables, applicable to the high-frequency characteristic characterization and electromagnetic compatibility analysis of long cables in motor speed control systems such as elevators and wind power generation. Background Technology
[0002] In practical engineering applications such as elevators and wind power generation, the distance between the motor and the converter in a motor speed control system often exceeds 100 meters, requiring a long cable connection. Long cables significantly impact overvoltage and electromagnetic interference (EMI) in the motor speed control system. The peak overvoltage of the motor can reach up to twice the pulse voltage, seriously threatening the insulation of the motor and cable and affecting the motor's lifespan.
[0003] Existing cable modeling methods typically employ impedance analyzers to measure the open-circuit and short-circuit impedances of cables, thereby establishing a lumped parameter model of the cable's RLGC (Restricted Linear GC) structure. However, this method is only suitable for short cables a few meters long. As cables lengthen, their internal RLGC parameters exhibit significant frequency-dependent characteristics, rendering traditional lumped parameter modeling methods completely ineffective at high frequencies. Specifically, due to the skin effect and proximity effect, the resistance and inductance of conductors change with frequency; simultaneously, the frequency-dependent dielectric constant of the insulating material causes capacitance and conductance to also change with frequency. For cables exceeding 100 meters in length, their input impedance resonates at relatively low frequencies (on the order of MHz), and traditional methods combining open-circuit / short-circuit impedance measurements with simple lumped parameter extraction cannot accurately describe this frequency-dependent behavior.
[0004] In addition, existing modeling methods are mostly for two-core or coaxial cables. For four-core cables (three-phase power lines plus ground wire), due to the complex mutual coupling relationship between the cores and the existence of multiple differential and common mode propagation paths, there is a lack of systematic methods for extracting high-frequency parameters and constructing circuit models.
[0005] Therefore, establishing a high-frequency modeling method applicable to four-core long cables and capable of accurately characterizing their frequency-varying characteristics is of great significance for overvoltage and noise prediction in electric drive systems. Summary of the Invention
[0006] This invention provides a method for modeling the frequency-varying characteristics of high-frequency parameters of four-core long cables. This method can characterize the frequency-varying characteristics of long cables without analyzing the cable structure from a physical perspective. It starts directly from transmission line theory, incorporates frequency-varying factors, and establishes a suitable circuit model, which can accurately predict the impedance and transmission characteristics of long cables over a wide frequency range.
[0007] To achieve the above objectives, the present invention adopts the following technical solution.
[0008] A method for modeling the frequency-varying characteristics of high-frequency parameters of a four-core long cable includes the following steps:
[0009] Step 1: In the electromagnetic shielding room, use an impedance analyzer to measure the open-circuit input impedance and short-circuit input impedance of the four-core cable under different core combinations, and obtain the impedance curve as a function of frequency.
[0010] Step 2: Based on transmission line theory, calculate the characteristic impedance and propagation coefficient of the cable from the measured open-circuit input impedance and short-circuit input impedance at the termination.
[0011] Step 3: Based on the characteristic impedance and propagation coefficient, calculate the distributed resistance, distributed inductance, distributed capacitance and distributed conductance per unit length of the cable, and obtain the curves of each distributed parameter as a function of frequency;
[0012] Step 4: For distributed resistance and distributed inductance, use the RL ladder network model for fitting to determine the resistance and inductance values in the ladder network; for distributed capacitance and distributed conductance, use the GC parallel circuit model for fitting to determine the resistance and capacitance values in the parallel circuit.
[0013] Step 5: Combine the RL ladder network model and the GC parallel circuit model into a cable unit model, and cascade N cable unit models to obtain the high-frequency parameter frequency-varying model of a four-core long cable.
[0014] Based on the above, in the second step, the characteristic impedance Z c The propagation coefficient γ is calculated using the following formula when total internal reflection occurs at the cable termination:
[0015]
[0016] Among them, Z sc Z is the short-circuit input impedance at the termination. oc is the open-circuit input impedance at the terminal, and l is the cable length.
[0017] Based on the above, in the fourth step, the RL ladder network model is composed of resistor R s1 Resistance R s2 Inductor L s1 and inductor L s2 constitute;
[0018] Based on the impedance expression of the RL ladder network model, and combining the curves of distributed resistance and distributed inductance as a function of frequency, we obtain R... s1 R s2 L s1 and L s2 The parameter value.
[0019] Based on the above, the RL ladder network model consists of a resistor Rs1 Inductor L s1 Then connected in series with resistor R s2 Inductor L s2 The series branches are connected in parallel.
[0020] Based on the above, in the fourth step, the GC parallel circuit model is composed of the conductance G. p1 Conductivity G p2 Capacitor C p1 and capacitor C p2 constitute;
[0021] Based on the admittance expression of the GC parallel circuit model, and combined with the curves of distributed capacitance and distributed conductance as a function of frequency, we obtain G p1 G p2 C p1 and C p2 The parameter value.
[0022] Based on the above, the GC parallel circuit model is composed of conductance G p1 Capacitor C p1 After parallel connection, then with conductance G p2 Capacitor C p2 The parallel branches are connected in series.
[0023] Based on the above, in step five, the RL ladder network model and the GC parallel circuit model are combined into a cable unit model. The specific combination method is as follows:
[0024] Using the RL ladder network model as the self-impedance and the GC parallel circuit model as the mutual impedance, the self-impedance is connected in series on each core wire, and the mutual impedance is connected in parallel between the core wires, thus forming a cable unit model.
[0025] Based on the above, in the fifth step, the number N of the cable unit models is determined according to the cable length and the highest modeling frequency, such that the unit length is less than 1 / 10 of the wavelength corresponding to the highest frequency.
[0026] Compared with the prior art, the present invention has the following beneficial effects:
[0027] (1) It can accurately characterize the frequency-varying characteristics of long cables. Based on transmission line theory, this invention directly extracts the distributed parameters that vary with frequency by measuring the open-circuit and short-circuit impedances at the terminals, and uses the RL ladder network model and GC parallel circuit model for fitting, overcoming the defect of traditional lumped parameter models failing at high frequencies. It is especially suitable for long cables with a length greater than 100 meters, as well as the 150kHz to 30MHz conducted electromagnetic interference frequency band.
[0028] (2) No need to analyze the physical structure of the cable. This invention does not rely on the geometric dimensions and material parameters of the cable, but is based entirely on measurement data modeling. It is applicable to various complex multi-core shielded or unshielded cables and has strong versatility.
[0029] (3) Complete modeling applicable to four-core cables. The present invention designs a systematic measurement scheme that covers all possible transmission paths between four cores, and can fully consider differential mode and common mode propagation characteristics, providing an accurate model basis for overvoltage and EMI prediction of long cables in motor drive systems.
[0030] (4) The model is simple and easy to implement in engineering. The equivalent circuit is composed of conventional RLC components and can be directly imported into circuit simulation software such as SPICE for time-domain and frequency-domain analysis, which is convenient for engineering technicians to use. Attached Figure Description
[0031] Figure 1 This is a schematic diagram of the structure of a four-core cable in an embodiment of the present invention;
[0032] Figure 2 This is a circuit structure diagram of the cable transmission line unit model in an embodiment of the present invention;
[0033] Figure 3 This is a schematic diagram of the wiring method corresponding to number 3 in the embodiment of the present invention;
[0034] Figure 4 This is a schematic diagram of the wiring method corresponding to number 4 in the embodiment of the present invention;
[0035] Figure 5 In this embodiment of the invention, the distributed resistance R0 varies with frequency. f A schematic diagram of the changing curve;
[0036] Figure 6 In this embodiment of the invention, the distributed inductance L0 varies with frequency. f A schematic diagram of the changing curve;
[0037] Figure 7 In this embodiment of the invention, the distributed capacitance C0 varies with frequency. f A schematic diagram of the changing curve;
[0038] Figure 8 In this embodiment of the invention, the distributed conductance G0 varies with frequency. f A schematic diagram of the changing curve;
[0039] Figure 9 This is a circuit diagram of the RL ladder network model in an embodiment of the present invention;
[0040] Figure 10 This is a circuit diagram of the GC parallel circuit model in an embodiment of the present invention;
[0041] Figure 11 This is a circuit diagram of a cable unit model in an embodiment of the present invention;
[0042] Figure 12 for Figure 11 China Z p A schematic diagram representing the circuit of the RL ladder network model;
[0043] Figure 13 for Figure 11 China Z vp A schematic diagram representing the circuit represented by the GC parallel circuit model;
[0044] Figure 14 This is a schematic diagram of a cascaded cable unit model in an embodiment of the present invention;
[0045] Figure 15 This is a comparison chart of the measured short-circuit input impedance and the model fitting results in an embodiment of the present invention. Detailed Implementation
[0046] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments.
[0047] like Figures 1 to 14 As shown, a method for modeling the frequency-varying characteristics of high-frequency parameters of a four-core long cable includes the following steps:
[0048] Step 1: Measure the open-circuit and short-circuit input impedance of the four-core cable.
[0049] In an electromagnetic shielding room, an impedance analyzer 10 was used to measure the four-core cable. The four-core cable includes... U , V , W Three-phase power lines and PE ground wire, U The two ends of the line are respectively U 1 and U 2, V The two ends of the line are respectively V 1 and V 2, W The two ends of the line are respectively W 1 and W 2, PE The two ends of the ground wire are respectively PE 1 and PE 2.
[0050] Since the impedance analyzer 10 has only two measurement ports (measurement point 1 and measurement point 2 respectively), it can only measure one transmission path at a time. Therefore, it is necessary to design 12 measurement schemes according to Table 1 to measure the terminal short-circuit input impedance and terminal open-circuit input impedance under different core wire combinations.
[0051] During measurement, the impedance analyzer 10 is connected to two measuring points at the beginning of the cable. The core wires at the cable termination are connected in a short-circuit or open-circuit state according to Table 1. Taking numbers 3 and 4 in Table 1 as examples: number 3 is for terminal short-circuit measurement, and number 4 is for terminal open-circuit measurement. Both correspond to the same transmission path (between measuring point 1 and measuring point 2, via...). U and W (e.g., connection methods), respectively obtain the terminal short-circuit input impedance Z. sc and open circuit impedance Z oc , obtain frequency f The changing impedance curve (the impedance curve is obtained by measuring the open-circuit input impedance and short-circuit input impedance of the cable termination using an impedance analyzer 10; the measured curve is the impedance curve that changes with frequency) f (Changeable).
[0052] Table 1 Measurement Table of Parameters for Four-Core Cables
[0053]
[0054] Step 2: Calculate the characteristic impedance and propagation coefficient of the cable.
[0055] According to transmission line theory, when total internal reflection occurs in a cable, the short-circuit input impedance Z at the termination of a uniform transmission line is... sc and the open-circuit input impedance Z oc With characteristic impedance Z c The propagation coefficient γ and the cable length l have the following relationship:
[0056]
[0057]
[0058] Therefore, we can conclude that:
[0059]
[0060] The Z-axis of the same transmission path measured in the first step sc and Z oc Substituting into the above equation, the characteristic impedance Z of this path can be obtained. c and the propagation coefficient γ.
[0061] Step 3: Calculate the distribution parameters per unit length.
[0062] Based on characteristic impedance Z c And the propagation coefficient γ, calculate the distributed resistance R0, distributed inductance L0, distributed capacitance C0 and distributed conductance G0 per unit length using the following formula:
[0063]
[0064] in, wLet ω be the angular frequency, and ω = 2πf.
[0065] Therefore, the distributed resistance R0, distributed inductance L0, distributed capacitance C0, and distributed conductance G0 as a function of frequency are obtained. f A changing curve.
[0066] Step 4: Construct an equivalent circuit model with frequency-varying parameters.
[0067] For the distributed resistance R0 and distributed inductance L0, an RL ladder network model is used for fitting, such as... Figure 9 As shown, the model consists of resistor R s1 Inductor L s1 Then connected in series with resistor R s2 Inductor L s2 The series branches are connected in parallel, and its impedance expression is:
[0068]
[0069] Where j is an imaginary number, w ω is the angular frequency.
[0070] By substituting the curves of distributed resistance R0 and distributed inductance L0 as a function of frequency into the impedance expression and solving the system of equations, R can be obtained. s1 R s2 L s1 L s2 The parameter value.
[0071] For the distributed capacitance C0 and distributed conductance G0, a parallel circuit model of GC is used for fitting. For example... Figure 10 As shown, this model consists of the conductivity G. p1 Capacitor C p1 After parallel connection, then with conductance G p2 Capacitor C p2 The parallel branches are connected in series, and its admittance expression is:
[0072]
[0073] Where j is an imaginary number, w ω is the angular frequency.
[0074] The distributed capacitance C0 and distributed conductance G0 as a function of frequency f By substituting the changing curve into the admittance expression and solving, we can obtain G. p1 G p2 C p1 C p2 The parameter value.
[0075] Step 5: Cascade to form a long cable model.
[0076] Using the RL ladder network model as the self-impedance and the GC parallel circuit model as the mutual impedance, the self-impedances are connected in series on each core wire, and the mutual impedances are connected in parallel between the core wires, thus forming a cable unit model, such as... Figure 11 As shown.
[0077] This unit model also includes series branches (Z) u Z v Z w Z p ) and parallel branches (Z) uv Z uw Z up Z vw Z vp Z wp ), Z u Z v Z w Z p These are the self-impedances of the cable, characterized by the previously calculated RL ladder network model circuit; Z uv Z uw Z up Z vw Z vp Z wp These are the mutual impedances of the cables, characterized by the GC parallel circuit model calculated earlier.
[0078] like Figure 14 As shown, cascading N identical cable unit models can characterize the frequency-varying characteristics of distributed parameters in long cables. The number of units N should be chosen such that the unit length is much smaller than the wavelength corresponding to the highest modeling frequency (usually less than 1 / 10 of the wavelength) to ensure model accuracy.
[0079] For the transmission path between each pair of cores in a four-core cable, a corresponding frequency variation model is established according to the above steps, and finally a complete high-frequency parameter frequency variation model of a four-core long cable is obtained.
[0080] Experimental example:
[0081] This experimental example uses a four-core long cable (length l = 100m) as an example to verify and illustrate the method of the present invention. The structure of the four-core cable is as follows: Figure 1 As shown, Figure 1 In the middle section: 1 is the outer sheath (PVC), 2 is the plastic insulation layer, 3 is the copper core wire, and 4 is the wool filling material.
[0082] I. Measuring Input Impedance
[0083] In the electromagnetic shielding room, connect the impedance analyzer 10 (such as Keysight E4991A) to two measuring points at the beginning of the cable. Follow the wiring diagram for number 3 in Table 1 (terminal short circuit, its wiring method is as follows). Figure 3 (as shown) and number 4 (terminal open circuit, its wiring method is as follows) Figure 4 (As shown) Connect the cable terminals and measure the short-circuit input impedance Z of the terminals for this transmission path. sc and the open-circuit input impedance Z oc The frequency range was set to 100Hz to 30MHz, and the results were obtained as a function of frequency. f The changing impedance curve.
[0084] Figure 7 In the diagram, the red solid line curve represents the measured terminal short-circuit input impedance as a function of frequency. f The impedance curve shows the measured open-circuit input impedance as a function of frequency. The solid blue line represents the measured open-circuit input impedance. f The changing impedance curve.
[0085] II. Calculation of Characteristic Impedance and Propagation Coefficient
[0086] Transmission line unit such as Figure 2 As shown, Figure 2 In the diagram: x represents the distance from a point on the cable to the starting point, t represents time, i represents current, and u(t) represents voltage as it changes over time.
[0087] According to the transmission line equation, the measured Z sc and Z oc Substituting into the formula, the characteristic impedance Z of this path can be obtained. c And the propagation coefficient γ:
[0088]
[0089] Due to the influence of resonance, the calculation results are distorted. Parameter fitting using a vector matching algorithm can avoid interference from the resonance region. The vector matching algorithm is existing technology in this field and will not be described in detail in this embodiment.
[0090] III. Calculation of Distribution Parameters
[0091] The distributed resistance R0, distributed inductance L0, distributed capacitance C0, and distributed conductance G0 are calculated according to the formula:
[0092]
[0093] The unit length distribution parameter as a function of frequency was calculated. f A curve showing the change in distributed resistance R0 with frequency. f The changing curve is as follows Figure 5 As shown, the distributed inductance L0 varies with frequency. f The changing curve is as follows Figure 6 As shown, the distributed capacitance C0 varies with frequency. f The changing curve is as follows Figure 7 As shown, the distributed conductance G0 varies with frequency.f The changing curve is as follows Figure 8 As shown.
[0094] The results show that R0 increases with increasing frequency (skin effect and proximity effect); G0 increases with increasing frequency (dielectric loss); L0 and C0 decrease with increasing frequency.
[0095] IV. Constructing an equivalent circuit model
[0096] For R0 and L0, select impedance data and substitute them into the impedance expression of the RL ladder network:
[0097]
[0098] Solving the system of equations yields: R s1 R s2 L s1 L s2 The specific value.
[0099] For C0 and G0, select admittance data at the same frequency point and substitute them into the admittance expression for the GC parallel circuit:
[0100]
[0101] Solving for G, we get: p1 G p2 C p1 C p2 The specific value.
[0102] V. Cascading to form the final model
[0103] The above RL network and GC network are combined into a frequency-varying cable unit model (e.g.) Figures 11 to 13 (As shown). Based on the highest modeling frequency (30MHz) and cable length (100m), the number of elements is selected as N=20 (each element is 5m long, much smaller than the wavelength). The 20 elements are cascaded, as shown. Figure 14 As shown, the high-frequency conversion model of the entire cable is obtained.
[0104] VI. Model Validation
[0105] The above cascaded model was built in circuit simulation software, and the input impedance was simulated under both short-circuit and open-circuit conditions, and compared with the measured impedance. The results are as follows: Figure 15 As shown, within the frequency band of 150kHz to 30MHz, the simulated values and measured values are in high agreement (error less than 5%), indicating that the established circuit model can reflect the transmission line characteristics of the cable, thus verifying the effectiveness of the invention.
[0106] The above embodiments are only used to illustrate and not limit the technical solutions of the present invention. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the present invention without departing from the spirit and scope of the present invention. Any modifications or partial substitutions should be covered within the scope of the claims of the present invention.
[0107] If the terms "first" or "second" are used in this document to define components, those skilled in the art should know that the use of "first" or "second" is merely for the convenience of describing the invention and simplifying the description, and unless otherwise stated, the above terms have no special meaning.
[0108] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," "counterclockwise," "axial," "radial," and "circumferential" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing this invention and simplifying the description, and are not intended to indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.
[0109] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.
Claims
1. A method for modeling the frequency-varying characteristics of high-frequency parameters of a four-core long cable, characterized in that, Includes the following steps: Step 1: In the electromagnetic shielding room, use an impedance analyzer to measure the open-circuit input impedance and short-circuit input impedance of the four-core cable under different core combinations, and obtain the impedance curve as a function of frequency. Step 2: Based on transmission line theory, calculate the characteristic impedance and propagation coefficient of the cable from the measured open-circuit input impedance and short-circuit input impedance at the termination. Step 3: Based on the characteristic impedance and propagation coefficient, calculate the distributed resistance, distributed inductance, distributed capacitance and distributed conductance per unit length of the cable, and obtain the curves of each distributed parameter as a function of frequency; Step 4: For distributed resistance and distributed inductance, use the RL ladder network model for fitting to determine the resistance and inductance values in the ladder network; for distributed capacitance and distributed conductance, use the GC parallel circuit model for fitting to determine the resistance and capacitance values in the parallel circuit. Step 5: Combine the RL ladder network model and the GC parallel circuit model into a cable unit model, and cascade N cable unit models to obtain the high-frequency parameter frequency-varying model of a four-core long cable.
2. The method for modeling the frequency-varying characteristics of high-frequency parameters of a four-core long cable according to claim 1, characterized in that, In the second step, the characteristic impedance Z c The propagation coefficient γ is calculated using the following formula when total internal reflection occurs at the cable termination: Among them, Z sc Z is the short-circuit input impedance at the termination. oc is the open-circuit input impedance at the terminal, and l is the cable length.
3. The method for modeling the frequency-varying characteristics of high-frequency parameters of a four-core long cable according to claim 1, characterized in that, In the fourth step, the RL ladder network model is composed of resistor R s1 Resistance R s2 Inductor L s1 and inductor L s2 constitute; Based on the impedance expression of the RL ladder network model, and combining the curves of distributed resistance and distributed inductance as a function of frequency, we obtain R... s1 R s2 L s1 and L s2 The parameter value.
4. The method for modeling the frequency-varying characteristics of high-frequency parameters of a four-core long cable according to claim 3, characterized in that, The RL ladder network model consists of a resistor R. s1 Inductor L s1 Then connected in series with resistor R s2 Inductor L s2 The series branches are connected in parallel.
5. The method for modeling the frequency-varying characteristics of high-frequency parameters of a four-core long cable according to claim 1, characterized in that, In the fourth step, the GC parallel circuit model is composed of the conductance G. p1 Conductivity G p2 Capacitor C p1 and capacitor C p2 constitute; Based on the admittance expression of the GC parallel circuit model, and combined with the curves of distributed capacitance and distributed conductance as a function of frequency, we obtain G p1 G p2 C p1 and C p2 The parameter value.
6. The method for modeling the frequency-varying characteristics of high-frequency parameters of a four-core long cable according to claim 5, characterized in that, The GC parallel circuit model is based on the conductance G. p1 Capacitor C p1 After parallel connection, then with conductance G p2 Capacitor C p2 The parallel branches are connected in series.
7. The method for modeling the frequency-varying characteristics of high-frequency parameters of a four-core long cable according to claim 1, characterized in that, In the fifth step, the RL ladder network model and the GC parallel circuit model are combined into a cable unit model. The specific combination method is as follows: Using the RL ladder network model as the self-impedance and the GC parallel circuit model as the mutual impedance, the self-impedance is connected in series on each core wire, and the mutual impedance is connected in parallel between the core wires, thus forming a cable unit model.
8. The method for modeling the frequency-varying characteristics of high-frequency parameters of a four-core long cable according to claim 1, characterized in that, In the fifth step, the number N of the cable unit models is determined based on the cable length and the highest modeling frequency, such that the unit length is less than 1 / 10 of the wavelength corresponding to the highest frequency.