Simulation design method for alternating-current resistance of large-section cable under non-sinusoidal harmonic

Abstract

The invention relates to the technical field of power transmission, in particular to a large-section cable alternating-current resistance simulation design method under non-sinusoidal harmonics, and the method comprises the steps: building a finite element simulation model capable of reflecting the skin effect of a cable; performing eddy current field simulation analysis on the finite element simulation model to obtain a finite element simulation model in which an eddy current field is introduced; a fundamental wave and a harmonic wave are applied to the finite element simulation model with the eddy current field introduced, a preliminary reference result is obtained, and the preliminary reference result comprises electromagnetic power loss and an alternating current resistance value; according to the preliminary reference result, fundamental waves and harmonic waves are applied to the finite element simulation model with the introduced eddy current field at the same time, a final reference result is obtained, and the final reference result comprises the influence of the harmonic content and the harmonic number on the electromagnetic power loss and the alternating-current resistance value; and carrying out cable design according to the final reference result. The invention aims to solve the problem that the electromagnetic loss and alternating-current resistance of a cable cannot be accurately measured in a complex harmonic environment in the prior art.

Description

Technical Field

[0001] The invention relates to the technical field of power transmission, and in particular to a simulation design method for AC resistance of a large-section cable under non-sinusoidal harmonics. Background Art

[0002] With the rapid development of new energy technology and power electronics technology, a large number of distributed energy and nonlinear loads have been introduced into the power grid, making the harmonic problem increasingly serious. When high-order harmonic current flows in the cable, the apparent resistance of the cable increases significantly due to the skin effect and proximity effect, which leads to additional losses. At high-order harmonic frequencies, a significant eddy current effect will be generated inside the conductor of a large-section cable, which will not only increase the loss of the cable, but may also cause overheating problems, thereby affecting the service life and safe operation of the cable. Therefore, it is particularly important to calculate the AC resistance of large-section cables under non-sinusoidal conditions.

[0003] The measurement methods of conductor AC resistance are mainly divided into thermal measurement method and electrical measurement method. However, since the thermal measurement method requires a long preparation time and has large errors, its application is subject to certain restrictions. In contrast, the electrical measurement method calculates the AC resistance by measuring the phase difference between voltage and current. It has the advantages of simple operation and high accuracy, so it is widely used. However, traditional electrical measurement methods usually require that the collected voltage and current waveforms are sinusoidal, which limits its application under non-sinusoidal conditions. Since the excitation source (current source) cannot guarantee a complete sine wave, the current and voltage waveform data obtained in the actual measurement have non-sinusoidal distortion, so it is necessary to improve the existing method to adapt to the AC resistance measurement of large-section cables under non-sinusoidal conditions. Summary of the invention

[0004] The present invention provides a simulation design method for the AC resistance of large-section cables under non-sinusoidal harmonics, aiming to solve the problem that the prior art cannot accurately measure the electromagnetic loss and AC resistance of cables under complex harmonic environments, and provides an important theoretical basis for the optimal design of cable lines under harmonic environments.

[0005] To achieve the above object, the present invention provides the following technical solutions:

[0006] A method for simulating and designing AC resistance of large-section cables under non-sinusoidal harmonics comprises the following steps:

[0007] Establish a finite element simulation model that can reflect the skin effect of cables;

[0008] Performing eddy current field simulation analysis on the finite element simulation model to obtain a finite element simulation model with eddy current field introduced;

[0009] Apply fundamental wave and harmonic wave to the finite element simulation model with eddy current field introduced, respectively, to obtain preliminary reference results, wherein the preliminary reference results include electromagnetic power loss and AC resistance value;

[0010] According to the preliminary reference results, the fundamental wave and the harmonic wave are simultaneously applied to the finite element simulation model introducing the eddy current field to obtain the final reference results, wherein the final reference results include the influence of the harmonic content and the harmonic order on the electromagnetic power loss and the AC resistance value;

[0011] The cable design is performed according to the final reference result.

[0012] The method for simulating and designing AC resistance of large-section cables under non-sinusoidal harmonics as described above, further, the finite element simulation model is a two-dimensional finite element simulation model of the single-core cable body.

[0013] The method for simulating and designing AC resistance of a large cross-section cable under non-sinusoidal harmonics as described above, further includes performing simulation analysis of the eddy current field on the finite element simulation model to obtain a finite element simulation model that introduces the eddy current field, specifically comprising:

[0014] The finite element simulation model that introduces the eddy current field includes the skin depth.

[0015] The skin depth δ is obtained according to the following preset formula:

[0016]

[0017] Among them, δ is the skin depth, ρ is the resistivity, ω is the angular frequency, μ is the magnetic permeability, the unit is H / m, and σ is the electrical conductivity, the unit is S / m.

[0018] The above-mentioned large cross-section cable AC resistance simulation design method under non-sinusoidal harmonics is further:

[0019] The finite element simulation model that introduces the eddy current field includes the eddy current density,

[0020] The eddy current density is obtained according to the following preset formula:

[0021]

[0022] in, is the electric field strength, is the magnetic induction intensity, is the magnetic field strength, is the current density, is the electric displacement;

[0023] According to the above-mentioned non-sinusoidal harmonic large cross-section cable AC resistance simulation design method, further, the electromagnetic power loss is obtained according to the following preset formula:

[0024]

[0025] The above-mentioned large cross-section cable AC resistance simulation design method under non-sinusoidal harmonics is further:

[0026] The AC resistance value is obtained according to the following preset formula:

[0027]

[0028] Where P is the heating power, U(t) is the voltage across the resistor, I(t) is the current through the resistor, T is the cycle time, R AC is the AC resistance of the conductor.

[0029] Compared with the prior art, the present invention has the following beneficial effects:

[0030] 1. In a complex harmonic environment, the present invention significantly reduces the error caused by the skin effect by introducing the simulation analysis of the eddy current field, can accurately measure the AC resistance of cables with large cross-sections, and solves the shortcomings of the prior art in a complex harmonic environment.

[0031] 2. The present invention can reduce the cable loss caused by skin effect and proximity effect, and help improve the efficiency of the power system. The influence of harmonics on the cable body loss is analyzed by using the established cable body finite element model, and all sequence harmonics are considered.

[0032] 3. The present invention can predict the loss and AC resistance of the cable under different harmonic conditions through simulation calculation, which can provide reliable technical reference and data support for the design of the cable body under harmonic environment, and help optimize the design of the cable line.

[0033] 4. The present invention can evaluate the thermal performance and life of the cable by simulating and calculating the loss and AC resistance of the cable under different conditions, which can provide an important basis for the prediction of the operating temperature of the cable and the evaluation of the thermal aging life, and help to ensure the safe operation of the cable. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings required for use in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0035] Figure 1 This is a schematic diagram of the structure of a single-core power cable according to an embodiment of the present invention;

[0036] Figure 2 : is the eddy current loss diagram of a single-core cable under different excitation currents according to an embodiment of the present invention; wherein, Figure 2The horizontal axis is the frequency of different applied currents, and the vertical axis is the eddy current loss of the single-core cable. Different curves correspond to different loads.

[0037] Figure 3 : is an AC resistance diagram of a single-core cable under different excitation currents according to an embodiment of the present invention; wherein, Figure 3 The horizontal axis is the frequency of different applied currents, and the vertical axis is the AC resistance of the single-core cable. Different curves correspond to different loads.

[0038] Figure 4 is a load waveform diagram of an embodiment of the present invention; wherein, Figure 4 The horizontal axis is time, the vertical axis is the AC resistance of the load, and different curves correspond to different loads;

[0039] Figure 5 : is a graph of eddy current loss and AC resistance value of different loads of an embodiment of the present invention; wherein, Figure 5 In Figures (a) and (b), the horizontal axis is temperature, the vertical axis of Figure (a) is eddy current loss at different loads, and Figure (b) is the AC resistance value at different loads. Different curves correspond to different loads.

[0040] Figure 6 The figure is a flow chart of a simulation design method according to an embodiment of the present invention. DETAILED DESCRIPTION

[0041] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0042] Example:

[0043] It should be noted that the terms "including" and "having" and any variations of the embodiments of the present invention are intended to cover non-exclusive inclusions. For example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0044] See also Figures 1 to 5 The embodiment of the present invention provides a method for simulating and designing the AC resistance of a large-section cable under non-sinusoidal harmonics, which may specifically include the following steps:

[0045] Step 1: Establish a finite element simulation model that can reflect the skin effect of the cable.

[0046] In this step, a two-dimensional finite element simulation model of the single-core cable body is established by ANSYS. In the specific implementation, because the single-core compressed circular power cable structure can better reflect the skin effect, the model selected in the embodiment is YJLW03-64 / 110-1X630mm 2 The single-core compressed round power cable is taken as the research object, and a two-dimensional finite element simulation model of the single-core cable body is established through ANSYS. The cable body structure is as follows Figure 1 As shown, Table 1 gives the structure and material parameters of each layer of the cable body.

[0047] Table 1 Structure and material parameters of YJLW03-64 / 110-1X630mm

[0048]

[0049] Step 2: Perform eddy current field simulation analysis on the finite element simulation model to obtain a finite element simulation model with eddy current field introduced.

[0050] In this step, the current distribution unevenness caused by the skin effect can be measured by the skin depth. Skin depth refers to the penetration depth when the current density drops to 1 / e, which is closely related to the frequency of the alternating current and the electrical conductivity and magnetic permeability of the conductor. Under the action of the alternating current field, the AC resistance of the conductor will be significantly affected by the skin effect. The skin depth δ is defined as the depth range where the current is mainly concentrated on the surface of the conductor, and its calculation formula is as follows:

[0051]

[0052] Where, δ is the skin depth, ρ is the resistivity, ω is the angular frequency, μ is the magnetic permeability, and the unit is H / m; σ is the electrical conductivity, and the unit is S / m.

[0053] The skin depth is related to the electromagnetic properties of the material and the frequency of the excitation source. In order to accurately calculate the AC resistance of a large-section conductor, this embodiment introduces a simulation analysis method for the eddy current field. The generation of eddy currents originates from the alternating magnetic field inducing closed current loops inside the conductor, which in turn generate new magnetic fields. According to Lenz's law, the direction of this newly generated magnetic field is opposite to the original magnetic field, which in turn causes energy loss. By solving Maxwell's equations, the eddy current density can be calculated:

[0054]

[0055]

[0056] in is the electric field strength, is the magnetic induction intensity, is the magnetic field strength, is the current density, is the electric displacement. This embodiment realizes the simulation analysis of the eddy current field by adopting the finite element simulation model of the eddy current field. In the process of constructing the finite element simulation model, the model is used to effectively introduce the eddy current field.

[0057] According to Maxwell's equations, the electromagnetic power loss is calculated by formulas (4)-(5) as follows:

[0058]

[0059] The AC resistance can be determined by various experimental methods such as the electrical measurement method. Among them, the calculation principle of the AC resistance by the electrical measurement method is shown in formulas (6)-(7).

[0060]

[0061] Where J0 is the current density, I is the instantaneous current, r is the cable radius, δ is the skin depth, P is the heating power, U(t) is the voltage across the resistor, I(t) is the current through the resistor, and T is the cycle time. is the average current in one cycle, R AC is the AC resistance of the conductor.

[0062] Step 3: Apply fundamental wave and harmonic wave to the finite element simulation model with eddy current field introduced respectively to obtain preliminary reference results, which include electromagnetic power loss and AC resistance value.

[0063] In this step, the established finite element simulation model with eddy current field is used to analyze the influence of harmonics on the cable body loss, and all sequence harmonics are considered to calculate the cable loss and AC resistance value in the non-sinusoidal voltage caused by the harmonic environment.

[0064] In specific implementation, the fundamental wave, low-order harmonics of the 3rd, 5th, 7th, 9th and 11th orders, and high-order harmonics of the 13th, 15th, 17th and 19th orders are applied to the single-core cable respectively, and the electromagnetic power loss (or cable core loss, cable loss for short) under each harmonic is calculated based on the finite element method, thereby obtaining the cable core AC resistance value under each harmonic.

[0065] Among them, under the action of different excitation currents (here refers to currents of different harmonic orders, where the higher the harmonic order, the higher the corresponding harmonic frequency), the influence of cable loss is as follows: Figure 2 As shown, the change of AC resistance value is as follows Figure 3 Observation Figure 3It can be found that with the increase of harmonic frequency, the loss of cable core conductor gradually increases and tends to saturation under the action of high-frequency harmonics. The reason for this phenomenon is that with the increase of harmonic frequency, the skin effect of the cable becomes more significant, which in turn increases the AC resistance of the cable, and ultimately leads to an increase in cable loss; since the cross-sectional area of ​​the conductor is limited, when it gradually approaches the upper limit of the skin depth function, the increase in its loss will also tend to be flat.

[0066] Step 4: Based on the preliminary reference results, the fundamental wave and harmonics are simultaneously applied to the finite element simulation model that introduces the eddy current field to obtain a final reference result, which includes the influence of the harmonic content and the harmonic order on the electromagnetic power loss and the AC resistance value.

[0067] In this step, based on the preliminary reference results described in step 3, the AC resistance value of the cable core and the cable loss under the influence of different harmonics are preliminarily obtained, which provides necessary data support for the analysis of applying fundamental and superimposed harmonic currents to the cable in step 4. By simultaneously applying fundamental and harmonic waves in the finite element simulation model that introduces the eddy current field, the final reference result is obtained, which describes in detail the influence of harmonic content and order on electromagnetic power loss and AC resistance value. Combined with the preliminary reference results of step 3, the present invention can conduct an in-depth analysis of the final reference result, thereby obtaining the relationship between harmonic content and order and electromagnetic power loss and AC resistance value.

[0068] Among them, the actual operating conditions of the cable in a harmonic environment are simulated, and the influence of harmonic content and harmonic number on cable loss is studied:

[0069] Table 2 Load types

[0070]

[0071]

[0072] Fundamental harmonic currents are applied to the cables to simulate the actual operating conditions of the cables in a harmonic environment, and the effects of harmonic content and harmonic order on cable losses are studied. In order to fit the actual project, four representative industrial loads and two office loads are selected. Considering that the low-order harmonic content in the actual power grid is much higher than the high-order harmonic content, the embodiment focuses on the analysis of the situation when the 3rd, 5th, 7th, 9th, and 11th harmonic currents are superimposed. Table 2 Load Type gives the harmonic synthesis of the load current and the total RMS value I d.rmsand total harmonic distortion (THD) as a percentage of the fundamental frequency current. Load A is a computer load, Load B is a typical AC-DC-AC drive with a large inductor on the DC side, Load C is a drive with capacitors on the DC side and no series choke, Load D is a drive with capacitors on the DC side and a 5% series choke, Load E is a drive with relatively high 11th harmonics, and Load F is a typical office load consisting of a computer and a fluorescent lamp with an inductive ballast.

[0073] The load current waveform is as follows: Figure 4 shown.

[0074] The AC resistance value under each load current is as follows Figure 5 (b) As shown. It can be observed that the AC resistance of load A is the highest, the AC resistance of load E is the lowest, and the AC resistance values ​​of other loads are between the two. This is because the harmonic content of load A is the highest, while the harmonic content of load E is the lowest. At the same time, the higher the harmonic order and the greater the proportion, the greater the AC resistance of the cable conductor. This shows that the presence of harmonics will significantly enhance the skin effect of large-section cable conductors, thereby increasing the AC resistance value.

[0075] Step 5: Design the cable based on the final reference result.

[0076] In this step, you can use Figure 4 and Figure 5 The conclusions provided a basis for the design of cable bodies, operating temperature prediction and thermal aging life in harmonic environments.

[0077] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples, without contradiction.

[0078] The above embodiments are only for illustrating the technical concept and features of the present invention, and their purpose is to enable ordinary technicians in the field to understand the content of the present invention and implement it accordingly, and they cannot be used to limit the protection scope of the present invention. Any equivalent changes or modifications made based on the essence of the content of the present invention should be included in the protection scope of the present invention.

Claims

1. A simulation design method for AC resistance of large-section cables under non-sinusoidal harmonics, characterized in that: Includes steps: Establish a finite element simulation model that can reflect the skin effect of cables; Performing eddy current field simulation analysis on the finite element simulation model to obtain a finite element simulation model with eddy current field introduced; Apply fundamental wave and harmonic wave to the finite element simulation model with eddy current field introduced, respectively, to obtain preliminary reference results, wherein the preliminary reference results include electromagnetic power loss and AC resistance value; According to the preliminary reference results, the fundamental wave and the harmonic wave are simultaneously applied to the finite element simulation model introducing the eddy current field to obtain the final reference results, wherein the final reference results include the influence of the harmonic content and the harmonic order on the electromagnetic power loss and the AC resistance value; The cable design is performed according to the final reference result.

2. The method for simulating and designing AC resistance of large-section cables under non-sinusoidal harmonics according to claim 1 is characterized in that: The finite element simulation model is a two-dimensional finite element simulation model of a single-core cable body.

3. The method for simulating and designing AC resistance of large-section cables under non-sinusoidal harmonics according to claim 2 is characterized in that: Performing simulation analysis of the eddy current field on the finite element simulation model to obtain a finite element simulation model introducing the eddy current field specifically includes: The finite element simulation model that introduces the eddy current field includes the skin depth. The skin depth δ is obtained according to the following preset formula: Among them, δ is the skin depth, ρ is the resistivity, ω is the angular frequency, μ is the magnetic permeability, the unit is H / m, and σ is the electrical conductivity, the unit is S / m.

4. The method for simulating and designing AC resistance of large-section cables under non-sinusoidal harmonics according to claim 3 is characterized in that: The finite element simulation model that introduces the eddy current field includes the eddy current density, The eddy current density is obtained according to the following preset formula: in, is the electric field strength, is the magnetic induction intensity, is the magnetic field strength, is the current density, is the electric displacement.

5. The method for simulating and designing AC resistance of large-section cables under non-sinusoidal harmonics according to claim 4 is characterized in that: The electromagnetic power loss is obtained according to the following preset formula:

6. The method for simulating and designing AC resistance of large-section cables under non-sinusoidal harmonics according to claim 5 is characterized in that: The AC resistance value is obtained according to the following preset formula: Where P is the heating power, U(t) is the voltage across the resistor, I(t) is the current through the resistor, T is the cycle time, R AC is the AC resistance of the conductor.

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