Equivalent circuit modeling and parameter calculation method for post-arc sheath stage of vacuum circuit breaker

Abstract

The invention relates to the technical field of simulation modeling of power equipment, in particular to an equivalent circuit modeling and parameter calculation method for a sheath stage after arc of a vacuum circuit breaker. The invention provides a technical path for extracting instantaneous microcosmic parameters through PIC-MCC simulation and calculating time-varying circuit parameters in real time according to the instantaneous microcosmic parameters. Therefore, the equivalent circuit model is not a static'black box 'any more, but is a'transparent model' capable of accurately reproducing a post-arc complex dynamic process, and the problem that a traditional model is insufficient in precision is fundamentally solved. According to the method, a direct and computable mathematical relationship is established between the microscopic ion density and speed and the macroscopic circuit parameter conductance and capacitance, the physical image is clear, and the theoretical preciseness and engineering interpretation of the model are greatly enhanced. Through sufficient experimental verification, the reliability and practicability of the method and the model thereof are powerfully proved, and a solid foundation is laid for direct application of the method and the model thereof to product research and development.

Description

Technical Field

[0001] This invention relates to the field of power equipment simulation modeling technology, specifically to a method for equivalent circuit modeling and parameter calculation of the post-arc sheath stage of a vacuum circuit breaker. Background Technology

[0002] Vacuum circuit breakers are widely used in modern power systems due to their compact structure, environmentally friendly arc-extinguishing medium, and long service life. The core of their breaking capacity lies in whether the contact gap can quickly restore insulation strength after the current crosses zero, i.e., the "post-arc dielectric recovery process." This process is extremely complex, involving microscopic physical phenomena such as the movement of residual plasma, the formation and expansion of the sheath, and charge recombination.

[0003] For ease of engineering analysis, researchers have attempted to simplify complex physical processes into equivalent circuit models. Existing equivalent circuit models (ECMs) of the back-arc sheath treat the back-arc sheath as a variable resistor (R0). sh ) and a variable capacitor (C) sh The parallel circuit of the plasma region is modeled as a variable resistor (R). p ),like Figure 1 This model provides an intuitive perspective for understanding the electrical characteristics of the post-arc phase.

[0004] However, existing technologies have significant limitations. In the aforementioned models and most related studies, the resistance and capacitance parameters in the equivalent circuit are usually treated as fixed values ​​or simple empirical functions. This is seriously detached from physical reality. The post-arc process is a violent, dynamic, and transient process: the sheath thickness grows rapidly from zero, and the ion density and velocity are spatially and temporally unevenly distributed and evolve rapidly. Using fixed parameters cannot accurately describe this dynamic characteristic, resulting in insufficient accuracy in simulation results based on such models. This makes it difficult to use them for quantitative and high-precision prediction and evaluation of post-arc current (PAC) waveforms and dielectric recovery strength, thus limiting their application in the refined design of high-end vacuum switch products.

[0005] Therefore, there is an urgent need in this field for an equivalent circuit modeling method that can accurately reflect the dynamic physical nature of the post-arc process. This method needs to establish a real-time mapping from microscopic time-varying parameters to macroscopic circuit parameters in order to significantly improve the reliability of simulation and its practical engineering value. Summary of the Invention

[0006] This invention aims to overcome the technical shortcomings of existing post-arc equivalent circuit models, which use static or semi-static parameters and cannot accurately describe the dynamic process, resulting in low simulation accuracy. It provides a high-precision equivalent circuit modeling and parameter calculation method that can achieve dynamic coupling between microscopic physical parameters and macroscopic circuit parameters.

[0007] To solve the above-mentioned technical problems, the present invention adopts the following technical solution: The equivalent circuit modeling and parameter calculation method for the post-arc sheath stage of a vacuum circuit breaker includes the following steps: Step S1: Constructing a simplified physical model. Ignoring the plasma region with extremely low resistivity in the post-arc stage, the electrical characteristics of the post-arc contact gap of the vacuum circuit breaker are concentratedly characterized by the contribution of the post-arc sheath, thus establishing a simplified equivalent circuit model: This model abstracts the post-arc sheath as a variable resistor (R0). sh ) and a variable capacitor (C) sh Parallel circuits; externally applied transient recovery voltage (TRV, denoted as U) trv The load is directly applied across the two ends of this parallel circuit. Step S2: Dynamic physical parameter acquisition. Based on the Particle-in-Cell Monte Carlo Collision (PIC-MCC) numerical simulation method, the back-arc sheath development process under specific interruption conditions is simulated with high precision, and the key physical parameters of the sheath evolution over time during the expansion process are extracted in real time; the key physical parameters include at least: instantaneous sheath thickness (l), average ion density (n) within the sheath region. i ), average ion velocity (v i The average electric field strength (E) is also calculated. Step S3: Calculation of time-varying circuit parameters. Based on the instantaneous physical parameters obtained in step S2, the variable resistance (R) in the simplified equivalent circuit model is calculated in real time and dynamically using a set of mathematical formulas with clear physical definitions. sh The resistance value of the variable capacitor (C) and the variable capacitor (C) sh The capacitance value is obtained, thus yielding a series of circuit parameters R that vary with time. sh (t) and C sh (t). Step S4: Post-arc current synthesis calculation. The known or predefined transient recovery voltage waveform U... trv (t) is applied to the simplified equivalent circuit model constructed in step S1, and the time-varying parameter R calculated in step S3 is substituted into it. sh (t) and C sh (t), calculate the conduction current I through the resistor branch respectively. c (t) and the displacement current I through the capacitor branch d (t), summing the two yields the simulated total waveform of the post-arc current (PAC) I. PAC (t).

[0008] In step S3, the variable resistance (R) is calculated. sh The method for determining the resistance value specifically includes the following sub-steps: First, based on the principle of current continuity and the plasma conductivity formula, from the formula σ=n i×q i ×μ i Calculate the equivalent conductivity (σ) of the sheath at a certain moment; where q i The value μ represents the charge carried by an ion (for monovalent ions, this is the elementary charge e). i This represents ion mobility. Secondly, according to the definition of mobility, it is expressed by the formula μ. i =v i / E calculates the ion mobility at that moment (μ). i Finally, based on Ohm's law and geometric relationships, the formula R... sh =l / (σ×S) is used to calculate the instantaneous resistance value of the variable resistor at that moment; where S is the effective cross-sectional area of ​​the vacuum circuit breaker contact.

[0009] In step S3, the variable capacitor (C) is calculated. sh The method for determining the capacitance value is as follows: based on the principle of parallel plate capacitors and considering the sheath collision effect, it is calculated using formula C. sh =K cap The calculation is performed using ×ε0×S / l; where ε0 is the vacuum permittivity (its value is 8.85×10). (-12) F / m), K cap This is a constant factor used for correction; for sheaths with collisions, a recommended value of 0.751 is given.

[0010] The method further includes a model verification step S5: verifying the simulated post-arc current waveform I obtained in step S4. PAC The simplified equivalent circuit model and its dynamic parameter calculation method are verified by comparing (t) with the arc current waveform obtained by actual experimental measurement under the same interruption conditions, and evaluating the degree of agreement between the two in terms of peak value, rate of rise, and decay trend.

[0011] In step S2, the initial conditions necessary to start the PIC-MCC simulation are determined based on the specific experimental data or design parameters of the target vacuum circuit breaker. The initial conditions include, but are not limited to, the plasma density, electron temperature, ion temperature, and overall initial drift velocity of the residual plasma at the moment the current crosses zero.

[0012] The method also includes a parameter influence analysis step S6: systematically changing a key initial condition in the PIC-MCC simulation (especially the initial drift velocity of the residual plasma), repeating steps S2 to S4, and studying the effect of the change in the initial condition on the calculated time-varying circuit parameter R. sh (t), C sh (t) and the influence of the peak value and shape of the final post-arc current simulation waveform, thereby deepening the understanding of the physical mechanism and providing guidance for performance optimization.

[0013] A non-transitory computer-readable storage medium storing a computer program, which, when executed by a processor, enables a method for equivalent circuit modeling and parameter calculation in the post-arc sheath stage of a vacuum circuit breaker.

[0014] Compared with the prior art, the technical solution provided by the present invention has the following significant advantages: Achieving true dynamic simulation: This invention creatively proposes a technical approach to extract instantaneous microscopic parameters through PIC-MCC simulation and calculate time-varying circuit parameters in real time based on these parameters. This transforms the equivalent circuit model from a static "black box" into a "transparent model" capable of accurately reproducing complex post-arc dynamic processes, fundamentally solving the problem of insufficient accuracy in traditional models.

[0015] A clear cross-scale mapping was established: through the formula σ=n i ×q i ×(v i / E) and C sh =K cap ×ε0×S / l, etc., the present invention focuses on the microscopic ion density (n i ), speed (v) i ) and macroscopic circuit parameters conductance (σ), capacitance (C) sh A direct, computable mathematical connection was established between them, providing a clear physical picture and greatly enhancing the theoretical rigor and engineering interpretability of the model.

[0016] Extensive experimental verification has been conducted: as shown in the specific implementation, the post-arc current waveform calculated using the method of this invention closely matches the measured waveform. This verification based on real experimental data strongly demonstrates the reliability and practicality of the method and model of this invention, laying a solid foundation for its direct application in product development.

[0017] This invention expands the analytical dimensions and application scenarios: The method not only outputs the final post-arc current, but also provides detailed curves of resistance and capacitance changes over time (see...). Figure 7 This provides a completely new perspective for understanding the strength and variation of post-arc medium recovery.

[0018] Attached Figure Description Figure 1 This is a schematic diagram of a typical post-arc gap equivalent circuit model in the prior art.

[0019] Figure 2 This is a schematic diagram of the simplified equivalent circuit model (ECM) proposed in this invention.

[0020] Figure 3 This is a voltage potential distribution curve in the contact gap at different times after the arc, obtained through PIC-MCC simulation.

[0021] Figure 4 This is an ion velocity distribution map along the contact gap direction extracted from the PIC-MCC simulation results at a specific moment.

[0022] Figure 5 To and Figure 4 Electric field intensity distribution along the contact gap at the same time.

[0023] Figure 6 To and Figure 4 Ion density distribution along the contact gap at the same time.

[0024] Figure 7 This is a typical curve showing the change of equivalent resistance (R~sh~(t)) and equivalent capacitance (C~sh~(t)) over time, calculated using the method of this invention.

[0025] Figure 8 This is a comparison chart of the simulated waveform and the experimentally measured waveform of the final calculated arc current (I~PAC~(t)) when applying the method of the present invention to a specific interruption case. Detailed Implementation

[0026] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be described in detail below with reference to the accompanying drawings and a specific DC interruption simulation embodiment. It should be noted that this embodiment is only for explaining the invention and not for limiting it.

[0027] Example: High-precision simulation of post-arc current based on DC interruption experiment This embodiment is based on a set of DC vacuum circuit breaker breaking experimental data recorded in the literature (contact material is copper, gap length is 2 mm, breaking current is 600 A), and demonstrates the whole process of applying the method of the present invention to simulate the post-arc current.

[0028] Step 1: Determine initial conditions and build the model First, based on the measurement report of the experiment, the initial parameters for the PIC-MCC simulation were determined: the gap length was set to 2 mm; the applied transient recovery voltage (TRV) rise rate was set to -1.756 kV / μs; and by integrating the experimentally measured post-arc current waveform over time, the initial plasma density at the current zero-crossing moment was estimated to be approximately 8.17 × 10⁻⁶. 17 m -3 Based on relevant research, the atomic density was set to 1×10⁻⁶. 19 m-3, with electron and ion temperatures set to 3 eV and 2 eV respectively; initial ion drift velocity set to 3000 m / s, pointing towards the back-arc cathode.

[0029] Subsequently, according to the present invention, a structure is constructed as follows: Figure 2 The simplified equivalent circuit model shown serves as the circuit framework for subsequent calculations.

[0030] Step 2: Perform PIC-MCC simulation and extract dynamic parameters Using the initial parameters described above, a one-dimensional PIC-MCC simulation program was run to simulate the entire process of the sheath expanding from the cathode to the anode. During the simulation, the system automatically recorded the physical field data at each time step.

[0031] Let's take t=0.04μs and t=0.2μs as examples for illustration: Depend on Figure 3 As can be seen from the potential distribution diagram, the voltage is mainly applied to the sheath region, and the plasma region has a flat potential, which verifies the rationality of ignoring the resistance of the plasma region.

[0032] The process of extracting key physical parameters from simulation results is as follows: At any given time, the sheath thickness l(t) can be determined based on the electron density distribution at that time, i.e., the distance between the cathode and the position where the electron density drops to approximately zero. For example, at t=0.04μs, from the electron density distribution map (such as...) Figure 4 From the simulation results, the sheath thickness l(0.04μs) ≈ 0.105mm can be determined; at t=0.2μs, the corresponding thickness expands to l(0.2μs) ≈ 0.33mm. Simultaneously, the PIC-MCC simulation directly outputs the spatial distribution of physical quantities along the gap direction at each moment. Taking t=0.2μs as an example, the ion velocity distribution vi(x) (similar to...) can be obtained from the simulation results. Figure 4 ), electric field intensity distribution E(x) (like Figure 5 ), ion density distribution ni(x) (like Figure 6 To facilitate subsequent calculation of equivalent circuit parameters, the above physical quantities are usually spatially averaged within the sheath region [0, l(t)] to obtain the average ion velocity vi(avg), average electric field intensity E(avg), and average ion density ni(avg) within the sheath at that moment, which are then substituted into the calculation formula as representative values.

[0033] Step 3: Calculate the parameters of the time-varying circuit The average value of the physical parameters extracted in the second step, together with the known contact area S (diameter 50.8 mm, S≈0.002 m²), is used to calculate the contact area. 2 The constants such as the elementary charge e are substituted into the formulas described in claims 2 and 3 for calculation. For the time t = 0.2 μs: Calculate ion mobility: μ i =v i (avg) / E(avg) Calculate the sheath conductivity: σ=n i (avg)×e×μ i Calculate instantaneous resistance: R sh (0.2μs)=l(0.2μs) / (σ×S) Calculate instantaneous capacitance: C sh (0.2μs)=0.751×(8.85×10 -12 )×S / l(0.2μs) Repeat this process to calculate for all times within the simulated time series to obtain the complete Ri. sh (t) and C sh (t) curve, such as Figure 7 As shown in the figure. The resistor R is clearly visible in the diagram. sh Starting from near zero, it monotonically increases to the order of several thousand ohms as the sheath thickens; capacitance C sh It then starts from the maximum value (approximately 126 pF) and decreases monotonically as the sheath thickens.

[0034] Step 4: Synthesize the post-arc current and compare it with the experimental results to verify that the known TRV waveform is U trv (t)=-(1.756×10 9 )×t (V). For each time t, the post-arc current is composed of two parts: Conduction current: I c (t)=U trv (t) / R sh (t) Displacement current: I d (t)=C_sh(t)×dU trv (t) / dt=C sh (t)×(-1.756×10 9 ) Total current: I PAC (t)=I c (t)+I d (t) Calculate I at all times using this formula. PAC (t) yields the complete simulated post-arc current waveform. This waveform is then compared with the measured post-arc current waveform provided in the experimental report on the same coordinate system. The results are as follows: Figure 8 As shown, the simulated waveform matches the experimental measurement results well in terms of the peak value, rising segment, and falling segment shape, thus verifying the effectiveness of the model and method of this invention.

[0035] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for equivalent circuit modeling and parameter calculation in the post-arc sheath stage of a vacuum circuit breaker, characterized in that, Includes the following steps: Step S1: Construct a simplified equivalent circuit model of the back-arc sheath of the vacuum circuit breaker, wherein the model equates the back-arc sheath to a variable resistor R. sh With a variable capacitor C sh Parallel circuit; Step S2: Based on particle cloud mesh-Monte Carlo collision (PIC-MCC) simulation, obtain the key physical parameters of the evolution of the back-arc sheath over time during its development stage. The key physical parameters include at least the sheath thickness and the average ion density n within the sheath. i Average ion velocity v i And the average electric field strength E; Step S3: Based on the key physical parameters obtained in step S2, dynamically calculate the variable resistance R in the equivalent circuit model using a preset calculation formula. sh The resistance value and the variable capacitor C sh The capacitance value; Step S4: Apply the transient recovery voltage to the simplified equivalent circuit model, and calculate the simulated waveform of the post-arc current by combining the calculated time-varying resistance and capacitance values.

2. The method for equivalent circuit modeling and parameter calculation of the post-arc sheath stage of a vacuum circuit breaker according to claim 1, characterized in that, In step S3, the variable resistor R is calculated. sh Methods for determining resistance values ​​include: According to the formula σ=n i ×q i ×μ i Calculate the equivalent conductivity σ of the sheath, where q i For ionic charge, μ i It represents ion mobility; According to the formula μ i =v i / E calculates the ion mobility µ i ; According to formula R sh =l / (σ×S) calculates the resistance value of the variable resistor, where S is the cross-sectional area of ​​the contact.

3. The method for equivalent circuit modeling and parameter calculation of the post-arc sheath stage of a vacuum circuit breaker according to claim 1, characterized in that, In step S3, the variable capacitor C is calculated. sh The method for determining the capacitance value is as follows: According to formula C sh =K cap The calculation is performed using ×ε0×S / l, where ε0 is the vacuum permittivity and K is the lattice permittivity. cap It is a constant related to the collision state of the sheath.

4. The method for equivalent circuit modeling and parameter calculation of the post-arc sheath stage of a vacuum circuit breaker according to claim 1, characterized in that, It also includes a verification step S5: comparing the simulated waveform of the post-arc current calculated in step S4 with the experimentally measured waveform of the post-arc current under the corresponding interruption conditions to verify the effectiveness of the simplified equivalent circuit model and parameter calculation method.

5. The method for equivalent circuit modeling and parameter calculation of the post-arc sheath stage of a vacuum circuit breaker according to claim 1, characterized in that, In step S2, the initial conditions for the PIC-MCC simulation include plasma density, electron temperature, ion temperature, and the initial drift velocity of the residual plasma.

6. The method for equivalent circuit modeling and parameter calculation of the post-arc sheath stage of a vacuum circuit breaker according to claim 4, characterized in that, It also includes step S6: Based on the verification results obtained in step S5, the influence of different initial conditions on the equivalent circuit parameters and post-arc current is analyzed, and the obtained rules are used to optimize the parameter settings of the simulation model, and to provide a theoretical basis for the performance design and evaluation of circuit breakers.

7. A non-transitory computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the equivalent circuit modeling and parameter calculation method for the post-arc sheath stage of the vacuum circuit breaker as described in any one of claims 1 to 6.

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