CN110045277A - Intelligent electric energy meter built-in load switch Dynamic Characteristics Analysis Method, system and medium - Google Patents

Intelligent electric energy meter built-in load switch Dynamic Characteristics Analysis Method, system and medium Download PDF

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CN110045277A
CN110045277A CN201910423279.7A CN201910423279A CN110045277A CN 110045277 A CN110045277 A CN 110045277A CN 201910423279 A CN201910423279 A CN 201910423279A CN 110045277 A CN110045277 A CN 110045277A
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reed
load switch
armature
electric energy
energy meter
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熊德智
陈向群
柳青
杨茂涛
黄瑞
吴志勇
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State Grid Corp of China SGCC
State Grid Hunan Electric Power Co Ltd
Metering Center of State Grid Hunan Electric Power Co Ltd
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State Grid Corp of China SGCC
State Grid Hunan Electric Power Co Ltd
Metering Center of State Grid Hunan Electric Power Co Ltd
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01RMEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/327Testing of circuit interrupters, switches or circuit-breakers
    • G01R31/3277Testing of circuit interrupters, switches or circuit-breakers of low voltage devices, e.g. domestic or industrial devices, such as motor protections, relays, rotation switches
    • G01R31/3278Testing of circuit interrupters, switches or circuit-breakers of low voltage devices, e.g. domestic or industrial devices, such as motor protections, relays, rotation switches of relays, solenoids or reed switches

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  • General Physics & Mathematics (AREA)
  • Tests Of Circuit Breakers, Generators, And Electric Motors (AREA)

Abstract

本发明公开了一种智能电能表内置负荷开关动态特性分析方法,包括:S01、获取智能电能表内置负荷开关的衔铁不同角位移α和不同线圈电流值i条件下的线圈磁通量φ2和电磁吸力矩Mx,得到电磁系统静态数据;S02、获取衔铁不同角位移α条件下的簧片形变位移Δx、反力Ff和反力矩Mf,得到触簧系统反力静态数据;S03、基于电磁系统静态数据和触簧系统反力静态数据,采用四阶Runge‑Kutta法进行分析,得到动态特性参数条件下的动态特性数据;S04、对步骤S03中得到的动态特性数据进行分析以评估负荷开关的可靠性。本发明还相应公开了一种与上述方法相对应的系统及介质。本发明的方法、系统及介质均具有分析精准可靠等优点。

The invention discloses a method for analyzing the dynamic characteristics of a built-in load switch of a smart electric energy meter, comprising: S01. Obtaining the coil magnetic flux φ 2 and the electromagnetic suction under the conditions of different angular displacements α of the armature of the built-in load switch of the intelligent electric energy meter and different coil current values i Moment M x , obtain the static data of the electromagnetic system; S02, obtain the reed deformation displacement Δx, reaction force F f and reaction torque M f under the condition of different angular displacement α of the armature, and obtain the static data of the reaction force of the contact spring system; S03, based on the electromagnetic The static data of the system and the static data of the reaction force of the contact spring system are analyzed by using the fourth-order Runge-Kutta method to obtain dynamic characteristic data under the condition of dynamic characteristic parameters; S04, analyze the dynamic characteristic data obtained in step S03 to evaluate the load switch reliability. The present invention also discloses a system and a medium corresponding to the above method. The method, system and medium of the present invention all have the advantages of accurate and reliable analysis.

Description

智能电能表内置负荷开关动态特性分析方法、系统及介质Dynamic characteristic analysis method, system and medium of built-in load switch of smart energy meter

技术领域technical field

本发明主要涉及电能表技术领域,特指一种智能电能表内置负荷开关动态特性分析方法、系统及介质。The invention mainly relates to the technical field of electric energy meters, in particular to a dynamic characteristic analysis method, system and medium of a built-in load switch of a smart electric energy meter.

背景技术Background technique

电能表用内置负荷开关的质量好坏直接关系到客户服务质量和电网运行安全。全国大规模开展低压集抄建设以来,国网公司话务量巨大,受理的计量故障报修业务中,电能表用内置负荷开关故障处于较高比例,占整个计量故障报修的60%,内置负荷开关的质量问题已给电网公司带来了巨大的经济损失和不良的社会影响。因此,提升内置负荷开关的可靠性,从本质上提升内置负荷开关的质量,减少因内置负荷开关失效而导致的故障,对于提升优质服务水平,确保电网稳定,节约企业人力、物力、财力,具有重大的社会意义和经济意义。The quality of the built-in load switch for electric energy meters is directly related to the quality of customer service and the safety of power grid operation. Since the large-scale construction of low-voltage centralized reading has been carried out across the country, the State Grid Corporation has had a huge amount of traffic. Among the metering fault repair services accepted, the built-in load switch for electric energy meters has a high proportion of faults, accounting for 60% of the entire metering fault repairs. The built-in load switch The quality problem has brought huge economic losses and bad social impact to power grid companies. Therefore, improving the reliability of the built-in load switch, essentially improving the quality of the built-in load switch, reducing the failure caused by the failure of the built-in load switch, for improving the quality of service level, ensuring the stability of the power grid, and saving the manpower, material and financial resources of enterprises, it has significant social and economic significance.

通过分析,电能表用内置负荷开关操作频率较低,但对可靠性要求较高,一般在用户欠费或短路等特殊情况下才会操作分闸,在用户缴费完成后或恢复正常时操作合闸。同时,在用户电费充裕及状态正常时,内置负荷开关不应动作,保证用户正常用电;当线路发生过载或短路故障时,应及时动作,断开故障电流,以保护线路及用电设备。电能表内置负荷开关在动作过程中表现出来的动态特性(比如角速度、角加速度等)是衡量其性能和可靠性的重要指标。在各种静止状态下,吸、反力特性配合的好坏直接影响动态特性的优劣,并最终影响内置负荷开关寿命的长短。而触点分断电弧侵蚀是导致触点失效,内置负荷开关寿命较短的主要原因,影响触点侵蚀及失效的另一个较为重要原因是触点闭合弹跳。对于应用场景为交流电负荷,仅靠触点分离拉灭电弧的电能表内置负荷开关,增大触点分离速度是减轻分断燃弧侵蚀、抑制或防止闭合弹跳的重要手段。目前对于负荷开关的此项特性并未有相应的关注,也没有相应的测量装置,且通过测量装置也无法精准的得到上述结果,从而无法实现对其可靠性的监测及改良。Through analysis, the built-in load switch for electric energy meters has a low operating frequency, but has high reliability requirements. Generally, the open switch will be operated under special circumstances such as user arrears or short-circuit, and the operation will be closed after the user's payment is completed or when it returns to normal. brake. At the same time, when the user's electricity bill is sufficient and the state is normal, the built-in load switch should not act to ensure the normal power consumption of the user; when the line is overloaded or short-circuited, it should act in time to disconnect the fault current to protect the line and electrical equipment. The dynamic characteristics (such as angular velocity, angular acceleration, etc.) of the built-in load switch of the electric energy meter during the action process are important indicators to measure its performance and reliability. In various static states, the coordination of suction and reaction force characteristics directly affects the quality of dynamic characteristics, and ultimately affects the life of the built-in load switch. The contact breaking arc erosion is the main reason for the contact failure and the short life of the built-in load switch. Another important reason that affects the contact erosion and failure is the contact closure bounce. For the application scenario of AC load, the built-in load switch of the electric energy meter that only relies on contact separation to pull out the arc, increasing the contact separation speed is an important means to reduce the erosion of the breaking arc and suppress or prevent the closing bounce. At present, there is no corresponding attention to this characteristic of the load switch, and there is no corresponding measurement device, and the above results cannot be accurately obtained through the measurement device, so that the monitoring and improvement of its reliability cannot be realized.

发明内容SUMMARY OF THE INVENTION

本发明要解决的技术问题就在于:针对现有技术存在的技术问题,本发明提供一种分析过程简单、分析结果精准的智能电能表内置负荷开关动态特性分析方法、系统及介质。The technical problem to be solved by the present invention is as follows: in view of the technical problems existing in the prior art, the present invention provides a method, system and medium for analyzing the dynamic characteristics of a built-in load switch of a smart electric energy meter with simple analysis process and accurate analysis results.

为解决上述技术问题,本发明提出的技术方案为:In order to solve the above-mentioned technical problems, the technical scheme proposed by the present invention is:

一种智能电能表内置负荷开关动态特性分析方法,包括以下步骤:A method for analyzing the dynamic characteristics of a built-in load switch of a smart electric energy meter, comprising the following steps:

S01、获取智能电能表内置负荷开关的衔铁不同角位移α和不同线圈电流值i条件下的线圈磁通量φ2和电磁吸力矩Mx,得到电磁系统静态数据;S01. Obtain the coil magnetic flux φ 2 and the electromagnetic suction torque M x under the conditions of different angular displacements α of the armature of the built-in load switch of the smart energy meter and different coil current values i, and obtain the static data of the electromagnetic system;

S02、获取衔铁不同角位移α条件下的簧片形变位移Δx、反力Ff和反力矩Mf,得到触簧系统反力静态数据;S02, obtain the reed deformation displacement Δx, reaction force F f and reaction moment M f under different angular displacement α conditions of the armature, and obtain the static data of the reaction force of the contact spring system;

S03、基于电磁系统静态数据和触簧系统反力静态数据,采用四阶Runge-Kutta法进行分析,得到动态特性参数条件下的动态特性数据;S03. Based on the static data of the electromagnetic system and the static data of the reaction force of the contact spring system, the fourth-order Runge-Kutta method is used for analysis to obtain the dynamic characteristic data under the condition of dynamic characteristic parameters;

S04、对步骤S03中得到的动态特性数据进行分析以评估负荷开关的可靠性。S04, analyze the dynamic characteristic data obtained in step S03 to evaluate the reliability of the load switch.

优选地,所述步骤S01的具体过程为:Preferably, the specific process of the step S01 is:

S11、由负荷开关磁系统结构,依据等效磁路法,建立计及铁芯与衔铁之间漏磁阻的负荷开关等效磁路模型;S11. According to the magnetic system structure of the load switch, according to the equivalent magnetic circuit method, establish an equivalent magnetic circuit model of the load switch that takes into account the leakage magnetic resistance between the iron core and the armature;

S12、依据计及铁芯与衔铁之间漏磁阻的负荷开关等效磁路模型,计算负荷开关等效磁路模型中各工作气隙的磁通值φpiS12. Calculate the magnetic flux value φ pi of each working air gap in the equivalent magnetic circuit model of the load switch according to the equivalent magnetic circuit model of the load switch that takes into account the leakage magnetic resistance between the iron core and the armature;

S13、通过工作气隙对应的截面积Spi,计算各工作气隙对应的电磁吸力Fi,从而得到电磁吸力矩MxS13 , calculating the electromagnetic suction force F i corresponding to each working air gap through the cross-sectional area S pi corresponding to the working air gap, thereby obtaining the electromagnetic suction torque M x .

优选地,在步骤S13中,电磁吸力Fi通过麦克斯韦电磁力计算公式进行计算:Preferably, in step S13, the electromagnetic attraction force F i is calculated by Maxwell's electromagnetic force calculation formula:

式中φpi表示通过工作气隙的磁通,Spi表示工作气隙对应的截面积,μ0表示真空磁导率,μ0=4π×10-7Wb/(A·m);where φ pi represents the magnetic flux passing through the working air gap, S pi represents the cross-sectional area corresponding to the working air gap, μ 0 represents the vacuum permeability, μ0=4π×10-7Wb/(A m);

电磁吸力矩Mx为:The electromagnetic attraction torque Mx is:

Mx=F2r12+F3r21-F1r11-F4r22M x =F 2 r 12 +F 3 r 21 -F 1 r 11 -F 4 r 22 ;

其中长左衔铁长r11;长右衔铁长r21;短左衔铁长r12;短右衔铁长r22The length of the long left armature is r 11 ; the length of the long right armature is r 21 ; the length of the short left armature is r 12 ; the length of the short right armature is r 22 .

优选地,所述步骤S02中得到反力矩的具体过程为:Preferably, the concrete process that obtains reaction torque in described step S02 is:

S21、将智能电能表内置负荷开关中各层簧片分成n段,建立各层各段对应的数学函数模型;S21. Divide each layer of reeds in the built-in load switch of the smart energy meter into n segments, and establish a mathematical function model corresponding to each layer and each segment;

S22、获取各层各段簧片中的截面弯矩,并结合对应数学模型,得到各层各段簧片的子柔度;S22. Obtain the bending moments of the sections in the reeds of each layer and section, and combine the corresponding mathematical models to obtain the sub-compliance of the reeds of each layer and section;

S23、通过各层各段簧片的子柔度,得到各层簧片在受点力处的柔度;S23. Obtain the flexibility of each layer of reeds at the point of force through the sub-compliance of each layer and each section of the reed;

S24、通过各层簧片在受点力处的柔度和刚度,再结合衔铁不同角位移α,得到整体簧片作用于衔铁上的反力矩。S24, through the flexibility and stiffness of each layer of reeds at the point where the force is applied, combined with the different angular displacements α of the armature, the reaction moment of the whole reed acting on the armature is obtained.

优选地,所述步骤S21中,将智能电能表内置负荷开关中各层簧片分成三段,分别为依次连接的直线段S1、曲线段S2和直线段S3。Preferably, in the step S21, each layer of reeds in the built-in load switch of the smart energy meter is divided into three sections, which are respectively a straight section S1, a curved section S2 and a straight section S3 connected in sequence.

优选地,所述步骤S22中,各层各段簧片的子柔度为:Preferably, in the step S22, the sub-compliance of each layer and each segment of the reed is:

其中Mwf表示簧片弯矩、E表示簧片的材料弹性模量、I表示簧片截面惯性矩、s表示簧片弧长、Pf为受力点的作用力。Where M wf represents the bending moment of the reed, E represents the elastic modulus of the reed material, I represents the moment of inertia of the reed section, s represents the arc length of the reed, and P f is the force at the point of force.

优选地,所述步骤S24中,通过各层簧片在受点力处的柔度,得到各层簧片在受点力处的反力,从而得到整体簧片作用于智能电能表内置负荷开关的衔铁上的反力矩。Preferably, in the step S24, the reaction force of each layer of reeds at the point of force is obtained through the flexibility of each layer of reeds at the point of force, so as to obtain that the whole reed acts on the load switch inside the smart energy meter reaction torque on the armature.

优选地,三层簧片在受力点的反力:Preferably, the reaction force of the three-layer reed at the force point:

其中,Δx为簧片在f处的形变位移,其中三层簧片的柔度分别为Cff1、Cff2、Cff3,刚度分别为G1、G2、G3Among them, Δx is the deformation displacement of the reed at f, wherein the flexibility of the three-layer reed is C ff1 , C ff2 , and C ff3 , and the stiffnesses are G 1 , G 2 , and G 3 ;

Δx=α·r11-xc0 Δx=α·r 11 -x c0

式中xc0为簧片形变位移初始值,α为衔铁角位移,αr11为衔铁线位移;where x c0 is the initial value of the deformation and displacement of the reed, α is the angular displacement of the armature, and αr 11 is the displacement of the armature wire;

三层簧片的反力作用在衔铁上的反力矩:The reaction torque of the reaction force of the three-layer reed acting on the armature:

第一模块,用于获取智能电能表内置负荷开关的衔铁不同角位移α和不同线圈电流值i条件下的线圈磁通量φ2和电磁吸力矩Mx,形成电磁系统静态数据;The first module is used to obtain the coil magnetic flux φ 2 and the electromagnetic suction torque M x under the conditions of different angular displacements α of the armature of the built-in load switch of the smart energy meter and different coil current values i, and form the static data of the electromagnetic system;

第二模块,用于获取衔铁不同角位移α条件下的簧片形变位移Δx、反力Ff和反力矩Mf,得到触簧系统反力静态数据;The second module is used to obtain the reed deformation displacement Δx, the reaction force F f and the reaction moment M f under the condition of different angular displacement α of the armature, and obtain the static data of the reaction force of the contact spring system;

第三模块,用于基于电磁系统静态数据和触簧系统反力静态数据,采用四阶Runge-Kutta进行分析,得到动态特性参数条件下的动态特性数据;The third module is used to analyze the fourth-order Runge-Kutta based on the static data of the electromagnetic system and the static data of the reaction force of the contact spring system to obtain the dynamic characteristic data under the condition of the dynamic characteristic parameters;

第四模块,用于对步骤S03中得到的动态特性数据进行分析以评估负荷开关的可靠性。The fourth module is used to analyze the dynamic characteristic data obtained in step S03 to evaluate the reliability of the load switch.

本发明进一步公开了一种计算机可读存储介质,所述计算机可读存储介质上存储有计算机程序,所述计算机程序被处理器执行时实现如上所述的智能电能表内置负荷开关动态特性分析方法的步骤。The present invention further discloses a computer-readable storage medium, where a computer program is stored on the computer-readable storage medium, and when the computer program is executed by a processor, the above-mentioned method for analyzing the dynamic characteristics of a built-in load switch of a smart electric energy meter is realized. A step of.

与现有技术相比,本发明的优点在于:Compared with the prior art, the advantages of the present invention are:

本发明的智能电能表内置负荷开关动态特性分析方法、系统及介质,通过电磁系统静态数据和触簧系统反力静态数据,采用四阶Runge-Kutta法进行分析,得到动态特性参数条件下的动态特性数据,再与设定的标准值进行对比,从而判断负荷开关工作的可靠性,也便于后续对负荷开关各参数进行优化以形成闭环;另外,上述得到动态特性数据的过程简单且结果精准。The intelligent electric energy meter of the present invention has a built-in load switch dynamic characteristic analysis method, system and medium. The fourth-order Runge-Kutta method is used to analyze the static data of the electromagnetic system and the static data of the reaction force of the contact spring system to obtain the dynamic characteristic parameters under the condition of dynamic characteristic parameters. The characteristic data is then compared with the set standard value to judge the reliability of the load switch operation, and it is also convenient for the subsequent optimization of the parameters of the load switch to form a closed loop; in addition, the above process of obtaining dynamic characteristic data is simple and the result is accurate.

附图说明Description of drawings

图1为本发明的方法流程图。FIG. 1 is a flow chart of the method of the present invention.

图2为本发明的质量特性分析流程图。FIG. 2 is a flow chart of the quality characteristic analysis of the present invention.

图3为本发明的负荷开关磁系统结构示意图。FIG. 3 is a schematic structural diagram of the load switch magnetic system of the present invention.

图4为本发明的计及漏磁的等效磁路图。FIG. 4 is an equivalent magnetic circuit diagram of the present invention considering magnetic flux leakage.

图5为本发明的工作气隙示意图。FIG. 5 is a schematic diagram of the working air gap of the present invention.

图6为本发明的簧片自柔度与互柔度的分段计算模型图。FIG. 6 is a diagram of a segmented calculation model of the self-compliance and mutual compliance of the reed according to the present invention.

图7为本发明中单层簧片子柔度段示意图。FIG. 7 is a schematic diagram of the sub-compliance section of the single-layer reed in the present invention.

图8为本发明中基于静态数据的动态特性分析流程图。FIG. 8 is a flow chart of dynamic characteristic analysis based on static data in the present invention.

图9为本发明中内置负荷开关线圈等效电路图。FIG. 9 is an equivalent circuit diagram of the built-in load switch coil in the present invention.

图10为本发明中动态特性计算流程图。FIG. 10 is a flow chart of dynamic characteristic calculation in the present invention.

图11为本发明中衔铁角速度示意图。FIG. 11 is a schematic diagram of the angular velocity of the armature in the present invention.

图12为本发明中衔铁角加速度示意图。FIG. 12 is a schematic diagram of the angular acceleration of the armature in the present invention.

具体实施方式Detailed ways

以下结合说明书附图和具体实施例对本发明作进一步描述。The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

如图1所示,本实施例的智能电能表内置负荷开关动态特性分析方法,包括以下步骤:As shown in FIG. 1 , the method for analyzing the dynamic characteristics of a built-in load switch of a smart electric energy meter in this embodiment includes the following steps:

S01、获取智能电能表内置负荷开关的衔铁不同角位移α和不同线圈电流值i条件下的线圈磁通量φ2和电磁吸力矩Mx,得到电磁系统静态数据;S01. Obtain the coil magnetic flux φ 2 and the electromagnetic suction torque M x under the conditions of different angular displacements α of the armature of the built-in load switch of the smart energy meter and different coil current values i, and obtain the static data of the electromagnetic system;

S02、获取衔铁不同角位移α条件下的簧片形变位移Δx、反力Ff和反力矩Mf,得到触簧系统反力静态数据;S02, obtain the reed deformation displacement Δx, reaction force F f and reaction moment M f under different angular displacement α conditions of the armature, and obtain the static data of the reaction force of the contact spring system;

S03、基于电磁系统静态数据和触簧系统反力静态数据,采用四阶Runge-Kutta法进行分析,得到动态特性参数条件下的动态特性数据(如衔铁角速度、衔铁角加速度等);S03. Based on the static data of the electromagnetic system and the static data of the reaction force of the contact spring system, the fourth-order Runge-Kutta method is used for analysis, and the dynamic characteristic data (such as armature angular velocity, armature angular acceleration, etc.) under the condition of dynamic characteristic parameters are obtained;

S04、对步骤S03中得到的动态特性数据进行分析以评估负荷开关的可靠性。S04, analyze the dynamic characteristic data obtained in step S03 to evaluate the reliability of the load switch.

本发明的智能电能表内置负荷开关动态特性分析方法,通过电磁系统静态数据和触簧系统反力静态数据,采用四阶Runge-Kutta法进行分析,得到动态特性参数条件下的动态特性数据,再与设定的标准值进行对比,从而判断负荷开关工作的可靠性,也便于后续对负荷开关各参数进行优化以形成闭环;另外,上述得到动态特性数据的过程简单且结果精准。The intelligent electric energy meter built-in dynamic characteristic analysis method of the load switch of the present invention adopts the fourth-order Runge-Kutta method to analyze the static data of the electromagnetic system and the static data of the reaction force of the contact spring system, and obtains the dynamic characteristic data under the condition of the dynamic characteristic parameters, and then It is compared with the set standard value to judge the reliability of the load switch operation, and it is also convenient for subsequent optimization of the parameters of the load switch to form a closed loop; in addition, the above process of obtaining dynamic characteristic data is simple and the result is accurate.

电能表内置负荷开关的设计参数包括电磁系统参数和触簧系统参数,这些参数的取值对吸力特性、反力特性及吸、反力的配合特性有着重要影响,而这些影响又最终通过动态特性体现出来,继而影响负荷开关的性能指标。因此,设计参数的最终取值需要以性能指标最佳为目标进行参数优化工作。要完成参数优化任务,首先需要研究单因素变化时,各设计参数与静态特性、动态特性之间的关系,从而由众多设计参数中筛选出对静、动态特性影响比较显著的关键参数,为下一步的参数设计与参数优化工作奠定基础。质量特性分析流程如图2所示。The design parameters of the built-in load switch of the electric energy meter include electromagnetic system parameters and contact spring system parameters. The values of these parameters have an important impact on the suction characteristics, reaction force characteristics and the matching characteristics of suction and reaction forces. It is reflected, which in turn affects the performance indicators of the load switch. Therefore, the final value of the design parameters needs to be optimized with the goal of the best performance index. To complete the parameter optimization task, it is first necessary to study the relationship between each design parameter and the static and dynamic characteristics when a single factor changes, so as to screen out the key parameters that have a significant impact on the static and dynamic characteristics from many design parameters. One-step parameter design and parameter optimization work to lay the foundation. The quality characteristic analysis process is shown in Figure 2.

下面结合一具体实施例对上述方法做详细说明:Below in conjunction with a specific embodiment, above-mentioned method is described in detail:

1、静态吸力模型建立:1. Establishment of static suction model:

磁路法和磁场法是求解电磁系统常用分析方法。磁路法操作方法简单,计算数据量小,但精度不够高,只能较为粗浅反映电磁铁的力学性能。磁场法精度比较高,但计算量大,磁场法的较常用的代表性方法是有限元法。The magnetic circuit method and the magnetic field method are commonly used analytical methods for solving electromagnetic systems. The magnetic circuit method has a simple operation method and a small amount of calculation data, but the accuracy is not high enough, and it can only reflect the mechanical properties of the electromagnet relatively shallowly. The magnetic field method has high precision, but a large amount of calculation. The most commonly used representative method of the magnetic field method is the finite element method.

针对电能表内置负荷开关质量特性分析问题,如果使用磁场法进行仿真计算则计算数量巨大,这在普通实验室是无法完成的。因此必须基于等效磁路法,建立计及漏磁的内置负荷开关等效磁路,兼顾计算速度与计算精度,从而实现电能表内置负荷开关静态特性的快速计算。For the analysis of the quality characteristics of the built-in load switch of the electric energy meter, if the magnetic field method is used for simulation calculation, the number of calculations is huge, which cannot be completed in ordinary laboratories. Therefore, an equivalent magnetic circuit of the built-in load switch must be established based on the equivalent magnetic circuit method, taking into account the magnetic flux leakage, taking into account the calculation speed and calculation accuracy, so as to realize the rapid calculation of the static characteristics of the built-in load switch of the electric energy meter.

由负荷开关磁系统结构(如图3所示),依据等效磁路法,建立计及铁芯与衔铁之间漏磁阻的负荷开关等效磁路模型(如图4所示)。Based on the structure of the load switch magnetic system (as shown in Figure 3) and based on the equivalent magnetic circuit method, an equivalent magnetic circuit model of the load switch (as shown in Figure 4) is established that takes into account the leakage magnetic resistance between the iron core and the armature.

图4中,Fm为永磁铁等效磁势、Rm为永磁铁等效磁阻;IW为线圈绕组磁势;R1,R2,R3,R4分别为衔铁与轭铁之间所构成的工作气隙磁阻;Ra1,Ra2,Rb1,Rb2,Rc1,Rc2,Rd分别为等效纯铁材料磁阻;Rs为铁芯与衔铁之间的漏磁阻,漏磁系数k1=k2=0.5(系统结构对称);φ12345为各回路磁通,各参数的计算方式如下:In Figure 4, F m is the equivalent magnetic potential of the permanent magnet, R m is the equivalent magnetic resistance of the permanent magnet; IW is the magnetic potential of the coil winding; R 1 , R 2 , R 3 , and R 4 are the gap between the armature and the yoke, respectively The formed working air gap magnetoresistance; R a1 , R a2 , R b1 , R b2 , R c1 , R c2 , R d are the equivalent pure iron material magnetoresistance respectively; R s is the leakage between the iron core and the armature Magnetic resistance, leakage coefficient k 1 =k 2 =0.5 (system structure is symmetrical); φ 1 , φ 2 , φ 3 , φ 4 , φ 5 are the magnetic fluxes of each circuit, and the calculation methods of each parameter are as follows:

(1)永磁铁等效磁势与等效磁阻(1) Equivalent magnetic potential and equivalent reluctance of permanent magnets

将磁路模型中的永磁铁等效为磁势Fm与磁阻Rm的组合(见图4)。该永磁铁的永磁材料为钕铁硼,钕铁硼的回复线与去磁曲线重合且基本为一条直线,故内置负荷开关永磁铁在等效磁路中其等效磁势与等效磁阻为:The permanent magnet in the magnetic circuit model is equivalent to the combination of the magnetic potential F m and the reluctance R m (see Figure 4). The permanent magnet material of the permanent magnet is NdFeB, the return line of NdFeB coincides with the demagnetization curve and is basically a straight line, so the equivalent magnetic potential of the built-in load switch permanent magnet in the equivalent magnetic circuit is the same as the equivalent magnetic field. resistance is:

式中Hc、μm分别表示永磁铁的矫顽力和磁导率,lm、Sm分别表示永磁铁的长度和截面积。where H c and μ m represent the coercivity and permeability of the permanent magnet, respectively, and lm and S m represent the length and cross-sectional area of the permanent magnet, respectively.

(2)线圈磁势(2) Coil magnetic potential

线圈磁势IW是线圈自身所产生的磁压,线圈磁势的计算公式为:The coil magnetic potential IW is the magnetic pressure generated by the coil itself. The calculation formula of the coil magnetic potential is:

IW=U0·W/R(2)IW=U 0 ·W/R(2)

式中U0表示线圈的操作电压,W表示线圈的固有匝数,R表示线圈的固有电阻。In the formula, U 0 represents the operating voltage of the coil, W represents the inherent number of turns of the coil, and R represents the inherent resistance of the coil.

(3)气隙磁阻(3) Air gap magnetoresistance

内置负荷开关衔铁左右端与轭铁之间形成了四个对称的工作气隙,该气隙结构为桥式对称分布的梯台型结构。工作气隙示意图如图5所示,梯台型气隙磁阻的计算公式为:Four symmetrical working air gaps are formed between the left and right ends of the built-in load switch armature and the yoke, and the air gap structure is a bridge-type symmetrically distributed ladder-type structure. The schematic diagram of the working air gap is shown in Figure 5. The calculation formula of the ladder-type air gap reluctance is:

式中R表示磁阻,G表示磁导,μ0表示真空磁导率,r表示气隙长度。在工作气隙1磁阻R1的计算中,r取值为r11-r13;在工作气隙2磁阻R2的计算中,r取值为r12-r13;在工作气隙3磁阻R3的计算中,r取值为r21-r23;在工作气隙4磁阻R4的计算中,r取值为r22-r23。r1为衔铁宽,r2为轭铁宽ke,R1、R3计算中r1指的是长衔铁宽kl;R2、R4计算中r1指的是短衔铁宽ks(轭铁宽ke、短衔铁宽ks)。θ为衔铁与轭铁极面之间的夹角,在内置负荷开关断开状况下,θ=0.09;在内置负荷开关闭合状况下,θ=0.11;当角位移α≤0.09时,θ=0.09-α;当0.09<α≤0.11时,θ=α-0.09(角度单位:rad)。In the formula, R is the magnetoresistance, G is the permeability, μ 0 is the vacuum permeability, and r is the air gap length. In the calculation of the magnetic resistance R 1 of the working air gap 1, the value of r is r11-r13; in the calculation of the magnetic resistance R 2 of the working air gap 2, the value of r is r12-r13; in the magnetic resistance R of the working air gap 3 In the calculation of 3 , the value of r is r21-r23; in the calculation of the magnetic resistance R4 of the working air gap 4 , the value of r is r22-r23. r1 is the armature width, r2 is the yoke width ke, in the calculation of R 1 and R 3 , r1 refers to the long armature width kl; in the calculation of R 2 and R 4 , r1 refers to the short armature width ks (yoke width ke, short armature width ks) armature width ks). θ is the angle between the armature and the pole face of the yoke. When the built-in load switch is disconnected, θ=0.09; when the built-in load switch is closed, θ=0.11; when the angular displacement α≤0.09, θ=0.09 -α; when 0.09<α≤0.11, θ=α-0.09 (angle unit: rad).

依照式(3),在测量关键参数后即可计算各气隙磁阻。According to formula (3), the reluctance of each air gap can be calculated after measuring the key parameters.

(4)漏磁阻(4) leakage magnetic resistance

衔铁与铁芯间漏磁阻的计算公式如下:The formula for calculating the leakage magnetic resistance between the armature and the iron core is as follows:

Rs=Lpa/(μ0Spa)(4)R s =L pa /(μ 0 Spa )(4)

式中Lpa表示铁芯外径到衔铁距离,Spa表示短衔铁的底面积。In the formula, L pa represents the distance from the outer diameter of the iron core to the armature, and S pa represents the bottom area of the short armature.

(5)导磁体磁阻(5) magnetoresistance

Ra1,Ra2,Rb1,Rb2,Rc1,Rc2,Rd分别为电磁系统各部件等效磁阻,其中Ra1与Ra2分别表示上左和上右衔铁磁阻,Rb1与Rb2分别表示下左和下右衔铁磁阻,Rc1与Rc2分别表示左右轭铁的磁阻,Rd表示铁芯磁阻。可采用以下公式来计算电磁系统各部件导磁体的磁阻。R a1 , R a2 , R b1 , R b2 , R c1 , R c2 , R d are the equivalent reluctance of each component of the electromagnetic system, respectively, where R a1 and R a2 represent the upper left and upper right armature reluctance, respectively, R b1 and R b2 represent the lower left and lower right armature magnetoresistance respectively, R c1 and R c2 respectively represent the magnetoresistance of the left and right yokes, and R d represent the iron core magnetoresistance. The following formula can be used to calculate the reluctance of the magnetic conductor of each component of the electromagnetic system.

R=L/(μS)(5)R=L/(μS)(5)

式中,S、L分别表示导磁体的横截面积与长度,μ表示导磁体的磁导率。In the formula, S and L represent the cross-sectional area and length of the magnetizer, respectively, and μ represents the magnetic permeability of the magnetizer.

因为内置负荷开关导磁体均为软磁材料,由于其磁导率与磁通密切相关且呈非线性变化,因此采用基于电工纯铁的磁化曲线来计算各导磁体的磁导率。首先在表中标出密度足够大的电工纯铁的磁化曲线(H,B),然后利用拉格朗日插值法可求得曲线上任意一点的B值所对应的磁导率μ值。比如,求解落在(Hi-1,Bi-1)和(Hi,Bi)之间B所对应的μ值的具体方法为:Because the built-in load switch magnetizers are all soft magnetic materials, and their permeability is closely related to the magnetic flux and changes non-linearly, the magnetization curve based on electrical pure iron is used to calculate the permeability of each magnetizer. First, mark the magnetization curve (H, B) of electrical pure iron with sufficient density in the table, and then use the Lagrangian interpolation method to obtain the permeability μ value corresponding to the B value at any point on the curve. For example, the specific method for solving the μ value corresponding to B falling between (H i-1 ,B i-1 ) and (H i ,B i ) is:

(6)工作气隙磁通(6) Working air gap magnetic flux

依据图3的计及漏磁的等效磁路模型和回路电流法,可得以下方程组:According to the equivalent magnetic circuit model and the loop current method considering the leakage flux in Fig. 3, the following equations can be obtained:

其矩阵形式表示为:Its matrix form is expressed as:

n=Fb n =F b

式中R表示回路磁阻矩阵;Фn表示回路磁通矩阵;Fb表示回路磁势向量矩阵。In the formula, R represents the loop magnetoresistance matrix; Ф n represents the loop magnetic flux matrix; F b represents the loop magnetic potential vector matrix.

由于方程组(7)为多元一次方程组,在已知回路磁阻矩阵R和回路磁势向量矩阵Fb的情况下,采用高斯列主元消去法则可以求解得到Фn。R中永磁等效磁阻、漏磁阻、工作气隙磁阻可利用已知参数求得,与待求量磁通相关的各导磁体磁阻需采用迭代求解。首先将所有的导磁体的磁阻设为零,代入方程组(7)从而求得各支路磁通φ(i),将φ(i)除以对应导磁体的截面积,求得对应的磁感应强度Bi,通过Bi查询磁化曲线可得Hi。然后再由Hili=φ(i)Ri求出导磁体磁阻Ri,将它再次代入回路方程组,进行高斯迭代,求出新的φ(i+1),直到为止(ε表示计算精度,通常取值0.001)。Since the equation system (7) is a multivariate first-order equation system, when the loop magnetoresistance matrix R and the loop magnetic potential vector matrix F b are known, the Gaussian column pivoting rule can be used to solve Ф n . The permanent magnet equivalent reluctance, leakage reluctance, and working air-gap reluctance in R can be obtained by using known parameters, and the reluctance of each magnet conductor related to the magnetic flux to be determined needs to be solved iteratively. First, set the reluctance of all magnetizers to zero, and substitute them into equation (7) to obtain the magnetic flux φ(i) of each branch. Divide φ(i) by the cross-sectional area of the corresponding magnetizer to obtain the corresponding Magnetic induction B i , H i can be obtained by querying the magnetization curve of B i . Then find the magnetoresistance R i from H i l i =φ(i)R i , substitute it into the loop equation system again, and perform Gaussian iteration to find a new φ(i+1) until up to (ε represents the calculation accuracy, usually 0.001).

依据求得的各回路磁通值,计算得到各工作气隙的磁通值。According to the obtained magnetic flux value of each circuit, the magnetic flux value of each working air gap is calculated.

(7)电磁吸力(7) Electromagnetic suction

电磁吸力Fi(i=1,2,3,4)通过麦克斯韦电磁力计算公式进行计算。The electromagnetic attraction force F i (i=1, 2, 3, 4) is calculated by Maxwell's electromagnetic force calculation formula.

式中φpi表示通过工作气隙的磁通,Spi表示工作气隙对应的截面积,μ0表示真空磁导率,μ0=4π×10-7Wb/(A·m)。In the formula, φ pi represents the magnetic flux passing through the working air gap, S pi represents the cross-sectional area corresponding to the working air gap, μ 0 represents the vacuum permeability, and μ0=4π×10-7Wb/(A·m).

合成吸力矩Mx为:The synthetic suction moment Mx is:

Mx=F2r12+F3r21-F1r11-F4r22 (10)M x =F 2 r 12 +F 3 r 21 -F 1 r 11 -F 4 r 22 (10)

工作气隙1处的合力F可通过M=Fr11进行规算得到:The resultant force F at the working air gap 1 can be calculated by M=Fr 11 :

依据上述公式,可求得不同工作气隙的归算合力。According to the above formula, the reduced resultant force of different working air gaps can be obtained.

参照上述建立的电能表内置负荷开关静态吸力快速计算模型,采用如下方法:Referring to the fast calculation model of static suction of built-in load switch of electric energy meter established above, the following methods are adopted:

1).永磁体等效磁势与等效磁阻计算:计算永磁体截面积sc=hc×kc;根据式(1)计算永磁体等效磁势Fm和等效磁阻Rm;1). Calculation of the equivalent magnetic potential and equivalent magnetic resistance of the permanent magnet: Calculate the cross-sectional area of the permanent magnet sc=hc×kc; calculate the equivalent magnetic potential Fm and equivalent magnetic resistance Rm of the permanent magnet according to formula (1);

2).利用式(2)计算线圈磁势IW;2). Use formula (2) to calculate the coil magnetic potential IW;

3).利用梯台型气隙计算公式(3),分别计算静态条件下4个气隙磁阻R1、R2、R3、R4;3). Using the ladder-type air gap calculation formula (3), calculate the 4 air gap magnetic resistances R1, R2, R3, R4 under static conditions respectively;

4).基于计及漏磁的磁路模型,利用公式(4),计算得到电磁线圈与下衔铁之间的漏磁阻Rs;4). Based on the magnetic circuit model considering the magnetic flux leakage, the leakage magnetic resistance Rs between the electromagnetic coil and the lower armature is calculated by using the formula (4);

5).考虑到衔铁、轭铁、铁芯在计算磁阻时均可等同于纯铁材料,利用电工纯铁的磁化曲线和拉格朗日插值法,依据公式(6),分别求出对应磁场强度B值下的磁导率μ,依据公式(5),分别求得长衔铁左、右磁阻Ra1、Ra2,短衔铁左、右磁阻Rb1、Rb2,左、右轭铁磁阻Rc1、Rc2,铁芯磁阻Rd。5). Considering that the armature, yoke and iron core can be equivalent to pure iron materials when calculating the magnetic resistance, using the magnetization curve of electric pure iron and the Lagrangian interpolation method, according to formula (6), the corresponding According to formula (5), the magnetic permeability μ under the value of magnetic field strength can be obtained respectively by obtaining the left and right magnetoresistances Ra1 and Ra2 of the long armature, the left and right magnetoresistances Rb1 and Rb2 of the short armature, and the magnetoresistance Rc1 of the left and right yokes. , Rc2, iron core magnetoresistance Rd.

6).依据等效磁路模型,建立磁路回路方程组,得到回路磁阻矩阵R、回路磁通矩阵Φn、回路磁势向量矩阵Fb之间的关系矩阵RmnΦn=Fb,在已知R、Fb的条件下,可利用高斯列主元消去法求解Φn。6). According to the equivalent magnetic circuit model, establish a magnetic circuit circuit equation system, and obtain the relationship matrix RmnΦn=Fb between the circuit magnetoresistance matrix R, the circuit magnetic flux matrix Φn, and the circuit magnetic potential vector matrix Fb. Under the condition of Fb, the Gaussian column pivoting method can be used to solve Φn.

7).求解回路磁阻矩阵R。由于R中的元素Rm、R1、R2、R3、R4、Rs已知,只需求解各导磁体磁阻,各导磁体磁阻与待求回路磁通Φn(n=1,2,3,4,5)有关,需采用迭代的方式进行计算求解。7). Solve the loop magnetoresistance matrix R. Since the elements Rm, R1, R2, R3, R4, and Rs in R are known, it is only necessary to solve the magnetoresistance of each magnetizer. ,5), it needs to be calculated and solved in an iterative way.

①首先令各导磁体磁阻为零,代入到方程组(7)中,求出各回路对应磁通Φn(0)(n=1,2,3,4 5);① First, set the magnetic resistance of each magnet conductor to zero, and substitute it into the equation system (7) to obtain the corresponding magnetic flux Φn(0) of each loop (n=1, 2, 3, 4 5);

②计算各导磁体的截面积。利用sc=hl×kl计算长衔铁截面积;利用ss=hs×ks计算短衔铁截面积;利用se=heh×ke计算轭铁截面积;②Calculate the cross-sectional area of each magnet conducting body. Use sc=hl×kl to calculate the cross-sectional area of the long armature; use ss=hs×ks to calculate the cross-sectional area of the short armature; use se=heh×ke to calculate the cross-sectional area of the yoke;

③利用B(i)=φ(i)/S(S分别为sc、ss、se;φ(i)为对应导磁体磁通;i=0,1,2...)分别求解对应磁导体的磁感应强度,通过查询纯铁磁化曲线得到对应磁场强度Hi。③Using B(i)=φ(i)/S (S are sc, ss, se respectively; φ(i) is the magnetic flux of the corresponding magnetic conductor; i=0, 1, 2...) to solve the corresponding magnetic conductor respectively The magnetic induction intensity of , and the corresponding magnetic field intensity Hi is obtained by querying the magnetization curve of pure iron.

④利用H(i)L=φ(i)R(i)分别求取对应条件下导磁体的磁阻(求取Ra1、Ra2时,L=cl/2;求取Rb1、Rb2时,L=cs/2;求取Rc1、Rc2时,L=ce+heg;求取Rd时,L=ct);④Using H(i)L=φ(i)R(i) to obtain the magnetoresistance of the magnetizer under the corresponding conditions respectively (when obtaining Ra1 and Ra2, L = cl/2; when obtaining Rb1 and Rb2, L = cs/2; when finding Rc1 and Rc2, L=ce+heg; when finding Rd, L=ct);

⑤将求取的磁阻矩阵Rmn(i)(i为迭代次数)回代方程组,利用高斯迭代法求出新的磁通矩阵Φn(i+1);⑤ Substitute the obtained magnetoresistance matrix Rmn(i) (i is the number of iterations) back into the equation system, and use the Gauss iteration method to obtain a new magnetic flux matrix Φn(i+1);

⑥判断:若(ε为计算精度,一般取0.001),则计算终止;若则重复步骤③、④、⑤,直至 ⑥ Judgment: If (ε is the calculation accuracy, generally 0.001), the calculation is terminated; if Then repeat steps ③, ④, ⑤ until

8)电磁吸力合力矩计算:8) Calculation of the resultant moment of electromagnetic attraction:

①计算工作气隙磁通值。依据计及漏磁的磁路模型,工作气隙1的磁通值Φp1=Φ4;工作气隙2的磁通值Φp2=Φ1-Φ4;工作气隙3的磁通值Φp3=Φ5;工作气隙4的磁通值Φp4=ΦΦ5;①Calculate the magnetic flux value of the working air gap. According to the magnetic circuit model considering magnetic flux leakage, the magnetic flux value of working air gap 1 is Φp1=Φ4; the magnetic flux value of working air gap 2 is Φp2=Φ1-Φ4; the magnetic flux value of working air gap 3 is Φp3=Φ5; The magnetic flux value of gap 4 is Φp4=ΦΦ5;

②计算工作气隙对应的截面积;② Calculate the cross-sectional area corresponding to the working air gap;

③利用公式(9)计算4个工作气隙分别对应的吸力 ③Using formula (9) to calculate the suction corresponding to the four working air gaps

④利用公式(10)计算吸力的合力矩Mx。④ Use formula (10) to calculate the resultant moment Mx of the suction.

相应的模型输入:内置负荷开关电磁系统物理参数向量D{永磁体宽kc;永磁体长cc;永磁体厚度hc;永磁矫顽力(修正后数值)Hc;永磁磁导率um;长衔铁长cl;长衔铁宽kl;长衔铁厚度hl;长左衔铁长r11;长右衔铁长r21;短衔铁长cs;短衔铁宽ks;短衔铁厚度hs;短左衔铁长r12;短右衔铁长r22;轭铁长ce;轭铁宽ke;轭铁厚度heh;轭铁高heg;左轭铁至中心距离r13;右轭铁至中心距离r23;铁芯长ct;铁芯外径到短衔铁底部距离Lpa};Corresponding model input: built-in load switch electromagnetic system physical parameter vector D {permanent magnet width kc; permanent magnet length cc; permanent magnet thickness hc; permanent magnet coercive force (corrected value) Hc; permanent magnet permeability um; length armature length cl; long armature width kl; long armature thickness hl; long left armature length r11; long right armature length r21; short armature length cs; short armature width ks; short armature thickness hs; short left armature length r12; short right armature Length r22; yoke length ce; yoke width ke; yoke thickness heh; yoke height heg; left yoke to center distance r13; right yoke to center distance r23; core length ct; core outer diameter to short The distance from the bottom of the armature Lpa};

输出:电磁吸力合力矩Mx。Output: Electromagnetic attraction force torque Mx.

2、静态反力模型建立:2. Establishment of static reaction force model:

基于可用于计算任何复杂形体簧片的离散型统一数值计算模型和变形能法,在保证较高计算精度的条件下对建立的计算模型进行少量的分段。Based on the discrete unified numerical calculation model and deformation energy method, which can be used to calculate any complex reeds, the established calculation model is segmented a little under the condition of ensuring high calculation accuracy.

图6中,簧片上指定点e、f处的自柔度Cee、Cff及互柔度Cef可采用变形能法计算得出:In Figure 6, the self-compliance C ee , C ff and mutual compliance C ef at the specified points e and f on the reed can be calculated by the deformation energy method:

式中Pe表示e点作用力、Mwe表示由该力产生的簧片弯矩;Pf表示f点作用力、Mwf表示由该力产生的簧片弯矩;E表示簧片的材料弹性模量、I表示簧片截面惯性矩、s表示簧片弧长,这三个量在计算时均为定值。where P e represents the force at point e, M we represents the bending moment of the reed produced by the force; P f represents the force at point f, M wf represents the bending moment of the reed produced by the force; E represents the material of the reed The elastic modulus, I represents the moment of inertia of the reed section, and s represents the reed arc length. These three quantities are all fixed values in the calculation.

如果将簧片分成n段:S1,S2,...,Sn,则可得到自柔度与互柔度计算公式:If the reed is divided into n segments: S 1 , S 2 , ..., Sn , the calculation formulas of self-compliance and mutual compliance can be obtained:

式中,分别表示为自柔度Cee、Cff及互柔度Cef的i段子柔度(i=1,2,...,n),簧片的柔度等于各分段子柔度之和。In the formula, Respectively expressed as the i-section sub- compliances (i=1, 2, .

电能表内置负荷开关的簧片子柔度段可归结为直线型和曲线型两类,这样可简化其用于柔度计算的数学模型。电能表内置负荷开关簧片由两段直线型和一段曲线形组成,可以利用3段进行等效,即将其等效为两段直线型和一段曲线型簧片进行计算。由于只存在一个力作用点,因此建模计算过程中,只存在自柔度,不存在互柔度。单层簧片子柔度段Si(i=1,2,3)如图7所示,其数学模型如下。The reed sub-compliance segment of the built-in load switch of the electric energy meter can be classified into two types: linear and curved, which can simplify its mathematical model for compliance calculation. The built-in load switch reed of the electric energy meter is composed of two straight sections and one curved section. It can be equivalent to three sections, that is, it is equivalent to two straight sections and one curved section for calculation. Since there is only one force action point, there is only self-compliance and no mutual compliance in the modeling and calculation process. The single-layer reed sub-compliance segment S i (i=1, 2, 3) is shown in Figure 7, and its mathematical model is as follows.

子柔度段S1的数学函数模型为:The mathematical function model of the sub-flexibility segment S1 is:

y=-y0(xf≤x≤xa) (14)y=-y 0 (x f ≤x≤x a ) (14)

子柔度段S2的数学函数模型为:The mathematical function model of the sub-flexibility segment S2 is:

子柔度段S3的数学函数模型为:The mathematical function model of the sub-flexibility segment S3 is:

y=-y0(xb≤x≤xb+x1) (16)y=-y 0 (x b ≤x≤x b +x 1 ) (16)

式中xa=-xb,xf=xa-x0where x a =-x b , x f =x a -x 0 .

由于力Pf的作用点为触点,即S1的端点,所以三段簧片Si(i=1,2,3)子柔度段x处簧片截面弯矩为:Since the action point of the force P f is the contact point, that is, the end point of S1, the bending moment of the reed section at the sub-flexibility section x of the three-section reed Si (i=1, 2, 3) is:

Mwf=Pf|x-xf| (17)M wf =P f |xx f | (17)

从而自柔度Cff的i段子柔度分别为:Therefore, the flexibility of the i segment of the self-compliance Cff is:

由于3段簧片的截面均为矩形,因此其截面矩计算公式为:Since the cross-sections of the three-section reeds are all rectangular, the formula for calculating the cross-section moment is:

式中chp为簧片截面的长,hhp为簧片截面的厚度。where c hp is the length of the reed section, and h hp is the thickness of the reed section.

对于S1段:For S1 segment:

对于S2段:For S2 segment:

其中,依据式(14)可计算得到:Among them, it can be calculated according to formula (14):

将式(20)代入式(19)计算可得:Substitute equation (20) into equation (19) to calculate:

对于S3段:For S3 segment:

簧片整体在动触头f处的柔度:The overall flexibility of the reed at the moving contact f:

簧片的刚度:Stiffness of the reed:

依据以上公式,分别代入三层簧片的设计参数,计算得到三层簧片的柔度Cff1、Cff2、Cff3,刚度G1、G2、G3According to the above formula, the design parameters of the three-layer reed are respectively substituted, and the flexibility C ff1 , C ff2 , C ff3 , and the stiffness G 1 , G 2 , and G 3 of the three-layer reed are calculated.

三层簧片在f处的反力:The reaction force of the three-layer reed at f:

其中,Δx为簧片在f处的形变位移:Among them, Δx is the deformation displacement of the reed at f:

Δx=α·r11-xc0 (28)Δx=α·r 11 -x c0 (28)

式中xc0为簧片形变位移初始值,α为衔铁角位移,αr11为衔铁线位移(即衔铁行程)。In the formula, x c0 is the initial value of the deformation and displacement of the reed, α is the angular displacement of the armature, and αr 11 is the displacement of the armature wire (ie the armature stroke).

三层簧片的反力作用在衔铁上的反力矩:The reaction torque of the reaction force of the three-layer reed acting on the armature:

参照上述建立的电能表内置负荷开关静态反力快速计算模型,执行如下步骤:Referring to the fast calculation model of the static reaction force of the built-in load switch of the electric energy meter established above, perform the following steps:

1.将3层簧片分别按图7分为两个直线段S1、S3和一个曲线段S2,分别对各层各段簧片建立数学模型(3)、(4)、(5);1. Divide the three-layer reeds into two straight line segments S1, S3 and one curved segment S2 according to Figure 7, respectively, and establish mathematical models (3), (4), (5) for each layer and each segment of the reeds;

2.自柔度Cff的计算:2. Calculation of self-compliance Cff :

①利用式(6)计算Si子柔度段x处簧片截面弯矩Mwf①Using formula (6) to calculate the bending moment M wf of the reed section at the sub-compliance section x;

②将(6)代入到(2)得到i段簧片自柔度的通用计算公式(7);②Substitute (6) into (2) to get the self-compliance of the i-section reed The general calculation formula (7) of ;

③利用式(6),结合三段簧片的数学模型,分别求得三段簧片子柔度 ③Using Equation (6), combined with the mathematical model of the three-section reed, obtain the sub-compliance of the three-section reed respectively

④将三段簧片子柔度代入到式(14)求得簧片整体在受力点f处的自柔度Cff④ Flexibility of the three-section reed Substitute into formula (14) to obtain the self-compliance Cff of the whole reed at the force point f;

3.采用式(15)得到簧片的刚度G;3. Use formula (15) to obtain the stiffness G of the reed;

4.采用步骤2、3,分别代入三层簧片的设计参数,计算得到三层簧片的柔度Cff1、Cff2、Cff3,刚度G1、G2、G34. Using steps 2 and 3, respectively substitute the design parameters of the three-layer reed, and calculate the flexibility C ff1 , C ff2 , C ff3 , and the stiffness G 1 , G 2 , and G 3 of the three-layer reed;

5.采用式(16)得到三层簧片在f处的反力Ff5. Use formula (16) to obtain the reaction force F f of the three-layer reed at f ;

6.采用式(18)得到三层簧片反力作用在衔铁上的反力矩Mf6. Use formula (18) to obtain the reaction moment M f of the three-layer reed reaction force acting on the armature.

其中数学模型的输入:触簧系统物理参数向量C{簧片材料弹性模量E;上层簧片截面长chp1;上层簧片截面厚hhp1;中层簧片截面长chp2;中层簧片截面厚hhp2;下层簧片截面长chp3;下层簧片截面厚hhp3;上层第一段直线型簧片长x01;上层第二段直线型簧片长x11;上层Ω弯形簧片高y01+R1;中层第一段直线型簧片长x02;中层第二段直线型簧片长x12;中层Ω弯形簧片高y02+R2;下层第一段直线型簧片长x03;下层第二段直线型簧片长x13;下层Ω弯形簧片高y03+R3}The input of the mathematical model: physical parameter vector C{reed material elastic modulus E; upper reed section length c hp1 ; upper reed section thickness h hp1 ; middle layer reed section length c hp2 ; middle layer reed section Thickness h hp2 ; section length of lower reed c hp3 ; section thickness of lower reed h hp3 ; the length of the first straight reed of the upper layer x 01 ; the length of the second straight reed of the upper layer x 11 ; the upper Ω curved reed Height y 01 +R 1 ; the length of the first straight reed in the middle layer x 02 ; the length of the second straight reed in the middle layer x 12 ; the height of the Ω curved reed in the middle layer y 02 +R 2 ; the first straight reed in the lower layer Length of reed x 03 ; length of the second straight reed of the lower layer x 13 ; height of the Ω curved reed of the lower layer y 03 +R 3 }

数学模型的输出:反力矩Mf The output of the mathematical model: the reaction torque M f

最后,利用电能表内置负荷开关的静态吸力和反力特性的快速计算方法,计算出相应的静态数据表,然后将其输入到动态特性分析模型进行计算,即可得到电能表内置负荷开关衔铁加速度、角加速度等动态特性计算结果。如图8所示。Finally, use the fast calculation method of the static suction and reaction force characteristics of the built-in load switch of the electric energy meter to calculate the corresponding static data table, and then input it into the dynamic characteristic analysis model for calculation, the armature acceleration of the built-in load switch of the electric energy meter can be obtained. , angular acceleration and other dynamic characteristics calculation results. As shown in Figure 8.

3、建立动态特性数学模型:3. Establish a mathematical model of dynamic characteristics:

电能表内置负荷开关动作过程中,负荷开关线圈回路可以等效为图9所示的等效电路。During the action of the built-in load switch of the electric energy meter, the coil loop of the load switch can be equivalent to the equivalent circuit shown in Figure 9.

其电压平衡方程式为:Its voltage balance equation is:

由于L为定值,则有:Since L is a fixed value, Then there are:

上式中U、i、R分别为线圈电压、电流和电阻;Is为线圈的稳态电流;L为电感;T为电磁时间常数, In the above formula, U, i and R are the coil voltage, current and resistance, respectively; I s is the steady-state current of the coil; L is the inductance; T is the electromagnetic time constant,

可见,线圈通电瞬间到衔铁动作结束,线圈电流按指数规律增长,最后达到稳定状态。电能表内置负荷开关动态特性方程组是典型的一阶微分方程组,分为线圈回路微分方程、衔铁机械运动微分方程、衔铁角位移与角速度的微分关系方程以及初始值:It can be seen that from the moment the coil is energized to the end of the armature action, the coil current increases exponentially, and finally reaches a stable state. The dynamic characteristic equation system of the built-in load switch of the electric energy meter is a typical first-order differential equation system, which is divided into the coil loop differential equation, the armature mechanical motion differential equation, the differential relationship equation between the armature angular displacement and the angular velocity, and the initial value:

式中φ2为线圈磁通;U、i、R分别为线圈电压、电流和电阻;α、ω分别为衔铁角位移和角速度;J为衔铁转动惯量;Mx、Mf分别为电磁系统吸力力矩和触簧系统反力力矩;φ0、α0分别为t=0时刻的线圈磁通和衔铁角位移。where φ 2 is the magnetic flux of the coil; U, i, R are the coil voltage, current and resistance, respectively; α, ω are the angular displacement and angular velocity of the armature, respectively; J is the moment of inertia of the armature; M x , M f are the suction force of the electromagnetic system, respectively The torque and the reaction force torque of the contact spring system; φ 0 and α 0 are the coil magnetic flux and the angular displacement of the armature at the moment of t=0, respectively.

上述方程组(33)由四阶Runge-Kutta方法求解,具体如下:The above equation system (33) is solved by the fourth-order Runge-Kutta method, as follows:

目前动态特性主要通过基于静态数据的数值方法、多软件协同仿真方法和有限元瞬态求解方法来解决。基于静态数据的数值用于动态计算,而四阶Runge-Kutta法主要用于动态方程求解。四阶Runge-Kutta法求解过程如下:At present, the dynamic characteristics are mainly solved by numerical methods based on static data, multi-software co-simulation methods and finite element transient solution methods. Numerical values based on static data are used for dynamic calculations, while the fourth-order Runge-Kutta method is mainly used for dynamic equation solving. The solution process of the fourth-order Runge-Kutta method is as follows:

一阶常微分方程初值:The initial value of the first-order ordinary differential equation:

四阶Runge-Kutta法的表示形式:The representation of the fourth-order Runge-Kutta method:

式中,bi,ci,aij都是常数,c1=0,a1j=0,j=1,2,...,s-1。在四阶Runge-Kutta法中,s=4,其经典公式为:In the formula, b i , c i , a ij are all constants, c 1 =0, a 1j =0, j=1, 2,...,s-1. In the fourth-order Runge-Kutta method, s=4, and its classical formula is:

在求解电能表内置负荷开关的动态特性微分方程组时,首先将时间变量t离散化,对每一段时间步长Δt进行迭代:When solving the differential equation system of dynamic characteristics of the built-in load switch of the electric energy meter, the time variable t is first discretized, and the step size Δt is iterated for each period of time:

式中,Δt=ti+1-ti,Kφj、Lωj和Mαj(j=1,2,3,4)是Δt内四个时间点上的变化率 其具体计算公式如下:where Δt=t i+1 -t i , K φj , L ωj and M αj (j=1, 2, 3, 4) are the rate of change at four time points within Δt Its specific calculation formula is as follows:

式中,hj表示迭代时间步长,h1=0,h4=Δt。In the formula, h j represents the iteration time step, h1=0, h4=Δt.

考虑到内置负荷开关在吸合过程中,触动阶段和闭合阶段的速度、加速度、吸力矩等动态特性变化相对比较缓慢,而在运动过程中变化比较迅速,因此通过采取在不同阶段设置不同迭代时间方法,来提高计算精度和计算效率。动态特性计算流程如图10所示。首先确定需要计算的参数及迭代计算的次数,计算出衔铁的转动惯量,接着就利用Runge-Kutta法迭代求解微分方程。其中,将触动阶段时间步长和闭合阶段的时间步长设置为0.02ms,运动阶段的时间步长设置为0.01ms。当吸力矩大于反力矩时,衔铁开始运动,系统由触动阶段进入运动阶段;当衔铁的角度变化为零时,衔铁运动结束,系统由运动阶段进入闭合阶段;当电磁线圈中的电流变化量小于万分之一时,表示内置负荷开关完全闭合,该次迭代计算过程结束。Considering that the dynamic characteristics of the built-in load switch such as speed, acceleration, and suction torque change relatively slowly in the triggering and closing stages during the pull-in process, but change rapidly during the movement process, so by setting different iteration times at different stages. method to improve computational accuracy and computational efficiency. The dynamic characteristic calculation process is shown in Figure 10. First determine the parameters to be calculated and the number of iterative calculations, calculate the moment of inertia of the armature, and then use the Runge-Kutta method to iteratively solve the differential equation. Among them, the time step of the trigger stage and the time step of the closing stage are set to 0.02ms, and the time step of the movement stage is set to 0.01ms. When the suction torque is greater than the reaction torque, the armature starts to move, and the system enters the movement stage from the trigger stage; when the angle of the armature changes to zero, the armature movement ends, and the system enters the closed stage from the movement stage; when the current change in the solenoid coil is less than When it is 1/10,000, it means that the built-in load switch is completely closed, and the iterative calculation process ends.

4阶Runge-Kutta法迭代求解动态特性是基于电磁系统与触簧系统的静态数据表。为此,先在线圈电流和衔铁角位移范围内分别将电流i和角位移α均分为n和m等份,i∈[0,Is],α∈[0,0.2](单位:rad),然后用考虑漏磁的电能表内置负荷开关静态吸力快速算法求得不同i和α下的Mx和回路磁通矩阵Фn,见表1所示,根据此表,对于已知的iz和αz可以通过查表及线性插值法求得对应的电磁吸力矩Mxz。The 4th-order Runge-Kutta method iteratively solves the dynamic characteristics based on the static data table of the electromagnetic system and the contact spring system. For this purpose, firstly divide the current i and angular displacement α into equal parts of n and m respectively within the range of coil current and armature angular displacement, i∈[0,Is], α∈[ 0,0.2 ] (unit: rad ), and then use the fast algorithm of the static suction of the built-in load switch of the electric energy meter considering the magnetic flux leakage to obtain M x and the loop magnetic flux matrix Ф n under different i and α, as shown in Table 1. According to this table, for the known i z and α z can be obtained through table look-up and linear interpolation to obtain the corresponding electromagnetic attraction moment Mxz.

表1线圈磁通量和电磁吸力矩数据表Table 1 Coil magnetic flux and electromagnetic attraction torque data table

基于表1衔铁角位移数据,依据公式(25)、(26)、(27)分别计算对应点的簧片形变位移、反力和反力矩得到触簧系统反力静态数据表2。根据此表,对于已知的αz可以通过查表及线性插值法求得对应的触簧反力矩MfzBased on the angular displacement data of the armature in Table 1, according to formulas (25), (26) and (27), respectively calculate the reed deformation displacement, reaction force and reaction torque of the corresponding point to obtain the static data table 2 of the reaction force of the contact spring system. According to this table, for the known α z , the corresponding contact spring reaction torque M fz can be obtained through table look-up and linear interpolation.

表2角位移对应触簧反力矩数据表Table 2 Angular displacement corresponding to the contact spring reaction torque data table

图8所示的基于静态数据的动态特性分析流程具体步骤如下所示:The specific steps of the dynamic characteristic analysis process based on static data shown in Figure 8 are as follows:

输入:动态特性参数向量T{衔铁转动惯量J;线圈电压U;线圈磁通初始值φ0;衔铁角速度初始值ω0;衔铁角位移初始值α0};Input: dynamic characteristic parameter vector T{armature moment of inertia J; coil voltage U; coil magnetic flux initial value φ 0 ; armature angular velocity initial value ω 0 ; armature angular displacement initial value α 0 };

输出:动态特性数据(α,ω,t)Output: Dynamic characteristic data (α,ω,t)

1.获取不同角位移α和电流值i条件下的线圈磁通量φ2和电磁吸力矩Mx,形成电磁系统静态数据,如表1所示;1. Obtain the coil magnetic flux φ 2 and the electromagnetic attraction moment M x under the conditions of different angular displacement α and current value i to form the static data of the electromagnetic system, as shown in Table 1;

2.获取不同角位移α条件下的簧片形变位移Δx、反力Ff和反力矩Mf,得到触簧系统反力静态数据,如表2所示;2. Obtain the reed deformation displacement Δx, reaction force F f and reaction moment M f under different angular displacement α conditions, and obtain the static data of the reaction force of the contact spring system, as shown in Table 2;

3.基于电磁系统静态数据和触簧系统反力静态数据,采用四阶Runge-Kutta法对式(33)进行求解,得到动态特性参数条件下的动态特性数据(α,ω,t)。3. Based on the static data of the electromagnetic system and the static data of the reaction force of the contact spring system, the fourth-order Runge-Kutta method is used to solve the equation (33), and the dynamic characteristic data (α, ω, t) under the condition of the dynamic characteristic parameters are obtained.

动态特性仿真与分析如下:The dynamic characteristics simulation and analysis are as follows:

采用上述方法,计算标准设计的智能电能表内置负荷开关基于静态数据的动态特性(标准设计参数见表3、4)。通过在Matlab软件中编程实现本流程方法,将通过静态吸、反力特性快速计算获得的静态吸、反力数据导入到动态特性计算程序,即可得到基于静态吸力、反力数据的电能表内置负荷开关动态特性,主要包括角速度、角加速度随时间变化的曲线等,如图11~12所示。Using the above method, calculate the dynamic characteristics of the built-in load switch of the standard designed smart energy meter based on static data (see Tables 3 and 4 for standard design parameters). This process method is implemented by programming in Matlab software, and the static suction and reaction force data obtained through the rapid calculation of the static suction and reaction force characteristics are imported into the dynamic characteristic calculation program, and the built-in electric energy meter based on the static suction and reaction force data can be obtained. The dynamic characteristics of the load switch mainly include the curves of angular velocity and angular acceleration changing with time, as shown in Figures 11-12.

由图11可以看出,衔铁转动的角速度上升趋势平滑,其最大值可达到1.45×102rad/s;同时下降速度极快,说明衔铁吸合后的稳定度较好。衔铁转动角加速度的特性曲线计算结果如图12所示。由以上计算结果分析可知,衔铁的角速度与角加速度从线圈通电开始随时间上升,在吸合点归零,表明其吸合过程已经完毕,动作时间在10ms-12ms之间,波形与实际预期相符。由仿真曲线可知,该动态特性仿真模型可正确反映在动态情况下衔铁行程、衔铁角速度和衔铁加速度的变换情况。It can be seen from Figure 11 that the upward trend of the angular velocity of the armature rotation is smooth, and its maximum value can reach 1.45×102rad/s; at the same time, the descending speed is extremely fast, indicating that the stability of the armature after the pull-in is good. The calculation result of the characteristic curve of the angular acceleration of the armature rotation is shown in Figure 12. From the analysis of the above calculation results, it can be seen that the angular velocity and angular acceleration of the armature rise with time from the time the coil is energized, and return to zero at the pull-in point, indicating that the pull-in process has been completed, the action time is between 10ms-12ms, and the waveform is consistent with the actual expectation. It can be seen from the simulation curve that the dynamic characteristic simulation model can correctly reflect the transformation of armature stroke, armature angular velocity and armature acceleration under dynamic conditions.

虽然本发明已以较佳实施例揭露如上,然而并非用以限定本发明。任何熟悉本领域的技术人员,在不脱离本发明技术方案范围的情况下,都可利用上述揭示的技术内容对本发明技术方案做出许多可能的变动和修饰,或修改为等同变化的等效实施例。因此,凡是未脱离本发明技术方案的内容,依据本发明技术实质对以上实施例所做的任何简单修改、等同变化及修饰,均应落在本发明技术方案保护的范围内。Although the present invention has been disclosed above with preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art, without departing from the scope of the technical solution of the present invention, can make many possible changes and modifications to the technical solution of the present invention by using the technical content disclosed above, or modify it into an equivalent implementation of equivalent changes. example. Therefore, any simple modifications, equivalent changes and modifications made to the above embodiments according to the technical essence of the present invention without departing from the content of the technical solutions of the present invention should fall within the protection scope of the technical solutions of the present invention.

Claims (10)

1. a kind of Intelligent electric energy meter built-in load switch Dynamic Characteristics Analysis Method, which comprises the following steps:
Under the conditions of S01, the armature difference angular displacement alpha for obtaining Intelligent electric energy meter built-in load switch and different coil current value i Coil flux amount φ2With electromagnetic attraction square Mx, obtain electromagnetic system static data;
Reed deformational displacement Δ x, counter-force F under the conditions of S02, acquisition armature difference angular displacement alphafWith countertorque Mf, obtain touching spring system System counter-force static data;
S03, it is based on electromagnetic system static data and contact spring system counter-force static data, is carried out using four step Runge-Kutta Analysis, obtains the dynamic Characteristic Data under the conditions of dynamic characteristic parameter;
S04, dynamic Characteristic Data obtained in step S03 is analyzed to assess the reliability of on-load switch.
2. Intelligent electric energy meter built-in load switch Dynamic Characteristics Analysis Method according to claim 1, which is characterized in that institute State the detailed process of step S01 are as follows:
S11, by on-load switch magnetic system structure, according to magnetic equivalent circuit method, establish the negative of leakage field resistance between meter and iron core and armature Lotus switchs equivalent magnetic circuit modeling;
The on-load switch equivalent magnetic circuit modeling of leakage field resistance, calculated load switch equivalent magnetic between S12, foundation meter and iron core and armature The flux value φ of each working gas gap in the model of roadpi
S13, pass through the corresponding sectional area S of working gas gappi, calculate the corresponding electromagnetic attraction F of each working gas gapi, to obtain electricity Magnetic torque Mx
3. Intelligent electric energy meter built-in load switch Dynamic Characteristics Analysis Method according to claim 2, which is characterized in that In step S13, electromagnetic attraction FiIt is calculated by Maxwell's electromagnetic force calculation formula:
φ in formulapiIndicate the magnetic flux by working gas gap, SpiIndicate the corresponding sectional area of working gas gap, μ0Indicate vacuum magnetic conductance Rate, μ 0=4 π × 10-7Wb/ (Am);
Electromagnetic attraction square Mx are as follows:
Mx=F2r12+F3r21-F1r11-F4r22
Wherein grow the long r of left armature11;The long right long r of armature21;The short long r of left armature12;The short long r of right armature22
4. Intelligent electric energy meter built-in load switch Dynamic Characteristics Analysis Method according to claim 1 or 2 or 3, feature It is, obtains the detailed process of countertorque in the step S02 are as follows:
S21, layer reed each in Intelligent electric energy meter built-in load switch is divided into n sections, establishes each section of corresponding mathematical function of each layer Model;
Section turn moment in S22, each each section of reed of layer of acquisition, and corresponding mathematical model is combined, obtain the son of each section of reed of each layer Flexibility;
S23, by the sub- flexibility of each section of reed of each layer, obtain flexibility of each layer reed at receptor site power;
S24, flexibility and rigidity by each layer reed at receptor site power obtain whole reed in conjunction with armature difference angular displacement alpha Act on the countertorque on armature.
5. Intelligent electric energy meter built-in load switch Dynamic Characteristics Analysis Method according to claim 4, which is characterized in that institute It states in step S21, layer reed each in Intelligent electric energy meter built-in load switch is divided into three sections, respectively sequentially connected straightway S1, curved section S2 and straightway S3.
6. Intelligent electric energy meter built-in load switch Dynamic Characteristics Analysis Method according to claim 5, which is characterized in that institute It states in step S22, the sub- flexibility of each section of reed of each layer are as follows:
Wherein MwfIndicate that reed moment of flexure, E indicate that the elasticity modulus of materials of reed, I indicate that reed cross sectional moment of inertia, s indicate reed Arc length, PfFor the active force of stress point.
7. Intelligent electric energy meter built-in load switch Dynamic Characteristics Analysis Method according to claim 6, which is characterized in that institute It states in step S24, by flexibility of each layer reed at receptor site power, obtains counter-force of each layer reed at receptor site power, thus The countertorque on armature for acting on Intelligent electric energy meter built-in load switch to whole reed.
8. Intelligent electric energy meter built-in load switch Dynamic Characteristics Analysis Method according to claim 7, which is characterized in that three Counter-force of the layer reed in stress point:
Wherein, Δ x is deformational displacement of the reed at f, wherein the flexibility of three layers of reed is respectively Cff1、Cff2、Cff3, rigidity point It Wei not G1、G2、G3
Δ x=α r11-xc0
X in formulac0For reed deformational displacement initial value, α is armature angular displacement, α r11For armature displacement of the lines;
The counter-force of three layers of reed acts on the countertorque on armature:
9. a kind of Intelligent electric energy meter built-in load switch dynamic characteristic analysis system, which is characterized in that including
First module, for obtain Intelligent electric energy meter built-in load switch armature difference angular displacement alpha and different coil current value i Under the conditions of coil flux amount φ2With electromagnetic attraction square Mx, form electromagnetic system static data;
Second module, for obtaining reed deformational displacement Δ x, counter-force F under the conditions of armature difference angular displacement alphafWith countertorque Mf, Obtain contact spring system counter-force static data;
Third module, for being based on electromagnetic system static data and contact spring system counter-force static data, using quadravalence Runge- Kutta is analyzed, and the dynamic Characteristic Data under the conditions of dynamic characteristic parameter is obtained;
4th module, for being analyzed dynamic Characteristic Data obtained in step S03 to assess the reliability of on-load switch.
10. a kind of computer readable storage medium, which is characterized in that be stored with computer on the computer readable storage medium Program is realized when the computer program is executed by processor in intelligent electric energy meter described in any one of claim 1 to 8 The step of setting on-load switch Dynamic Characteristics Analysis Method.
CN201910423279.7A 2019-05-21 2019-05-21 Intelligent electric energy meter built-in load switch Dynamic Characteristics Analysis Method, system and medium Pending CN110045277A (en)

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Application publication date: 20190723