WO2022110528A1 - 一种磁路功率的计算方法 - Google Patents

一种磁路功率的计算方法 Download PDF

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WO2022110528A1
WO2022110528A1 PCT/CN2021/073268 CN2021073268W WO2022110528A1 WO 2022110528 A1 WO2022110528 A1 WO 2022110528A1 CN 2021073268 W CN2021073268 W CN 2021073268W WO 2022110528 A1 WO2022110528 A1 WO 2022110528A1
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magnetic
magnetic circuit
power
circuit
virtual
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French (fr)
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程明
王政
朱新凯
秦伟
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东南大学
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R33/00—Arrangements or instruments for measuring magnetic variables
    • G01R33/12—Measuring magnetic properties of articles or specimens of solids or fluids
    • G01R33/1253—Measuring galvano-magnetic properties
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R21/00—Arrangements for measuring electric power or power factor
    • G01R21/001—Measuring real or reactive component; Measuring apparent energy
    • G01R21/002—Measuring real component
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R21/00—Arrangements for measuring electric power or power factor
    • G01R21/001—Measuring real or reactive component; Measuring apparent energy
    • G01R21/003—Measuring reactive component
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R21/00—Arrangements for measuring electric power or power factor
    • G01R21/133—Arrangements for measuring electric power or power factor by using digital technique
    • G01R21/1331—Measuring real or reactive component, measuring apparent energy
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation

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  • the invention relates to the field of magnetic circuit theory and application, in particular to the calculation and analysis of magnetic circuit power.
  • Magnetic circuit theory is a magnetic circuit analysis method established by dual circuit theory, and it is one of the important theories in electromagnetism. In certain cases, the equivalent magnetic circuit can be described by mathematical formulas that are dual to classical principles such as Kirchhoff's law and Ohm's law in circuit theory.
  • the magnetic circuit analysis method can be used to analyze the magnetic field of electromagnetic equipment, and the complex and abstract practical analysis problems can be simplified into simple mathematical logic descriptions, which can reduce the design time and cost of electromagnetic equipment. Therefore, the magnetic circuit analysis method has gradually attracted the attention of relevant researchers.
  • the magnetic circuit analysis method compensates for the finite element method. lack of legal principles.
  • the magnetic potential and magnetic flux of the magnetic circuit are analyzed and calculated mainly according to Ohm's law of the magnetic circuit and Kirchhoff's law of the magnetic circuit, and the magnetic circuit has never been considered.
  • the power problem of the magnetic circuit, and the calculation and analysis of the power in the magnetic circuit have not been paid much attention.
  • the existing magnetic circuit analysis methods model the magnetic circuit through linear magnetic permeability, nonlinear magnetic permeability, permanent magnet magnetic potential, winding magnetic potential and other magnetic circuit components, and do not consider the magnetic potential and the magnetic circuit in the magnetic circuit. pass phase relationship.
  • the technical problem to be solved by the present invention is that, aiming at the power problem of the magnetic circuit and the phase problem of the magnetic potential and the magnetic flux in the magnetic circuit, a calculation method of the magnetic circuit power is proposed.
  • Magnetic resistance and magnetic reactance draw the magnetic circuit vector diagram and calculate the virtual power of the magnetic circuit.
  • the mathematical relationship between the virtual power of the magnetic circuit and the electric power is derived from the reduction factor of the virtual power of the magnetic circuit and the electric power, so that the electric power can be directly calculated from the magnetic quantities such as the magnetic potential and the magnetic flux in the magnetic circuit.
  • the present invention proposes a method for calculating magnetic circuit power, and the specific process is as follows:
  • R mc is the magnetic resistance value of the magnetic circuit linked by the inductance element
  • X mc is the magnetic reactance of the magnetic circuit
  • L mc is the magnetic inductance value of the magnetic induction element
  • j is the imaginary unit
  • ⁇ is the change of the magnetic flux in the magnetic circuit angular frequency
  • the method for calculating the magnetic circuit power proposed by the present invention also includes verifying whether the magnetic circuit topology including the magnetic induction element satisfies the magnetic circuit Ohm's law before calculating the virtual active power and reactive power of the magnetic circuit in S6 ,which is:
  • j is the imaginary unit
  • R mc is the magnetic resistance value of the magnetic circuit linked by the inductance element
  • ⁇ is the angular frequency of the magnetic flux change in the magnetic circuit
  • L mc is the magnetic inductance value of the magnetic induction element
  • the size of the magnetic induction value of the magnetic induction element L mc is related to the number of turns N r of the short-circuit coil and the resistance R r of the short-circuit coil, that is, The unit of magnetic induction is ⁇ -1 ; the magnetic induction element has a hindering effect on the alternating magnetic flux, but has no hindering effect on the constant magnetic flux.
  • the magnitude of the magnetic flux resistance, ⁇ is the angular frequency of the magnetic flux change in the magnetic circuit.
  • the method for calculating the magnetic circuit power proposed by the present invention includes the magnetic potential in the equivalent magnetic circuit vector model.
  • magnetic flux The four magnetic circuit lumped variables of magnetoresistance R mc and magnetic induction L mc , according to the equivalent magnetic circuit vector model, when the equivalent magnetic circuit model and the equivalent circuit model are linked by a vector, the electromagnetic vector diagram formed The phase relationship between the circuit vector and the magnetic circuit vector can be displayed at the same time.
  • the virtual active power of the magnetic circuit is defined as the imaginary part of the virtual complex power.
  • the expression of the virtual active power of the magnetic circuit is:
  • the virtual reactive power of the magnetic circuit is defined as the real part of the virtual complex power.
  • the expression of the magnetic circuit virtual reactive power is:
  • the reduction factor of the magnetic circuit virtual power and the electric power is:
  • the reduction factor is j ⁇ ; that is,
  • the present invention adopts the above technical scheme, and the beneficial effects compared with the prior art are as follows:
  • the magnetic circuit power calculation method proposed by the present invention can calculate and analyze the virtual power in the magnetic circuit through the magnetic circuit vector, and then calculate the electric power of the magnetic circuit.
  • the electric power cannot be calculated by the circuit vector, the electric power can be solved by the magnetic circuit vector, which provides a new path for the calculation and analysis of the power.
  • the magnetic circuit vector diagram proposed by the present invention can clearly show the amplitude and phase relationship of each vector in the magnetic circuit, realize the synthesis and decomposition of the magnetic circuit vector in any direction, and can effectively express the magnetic circuit vector
  • the virtual active component and the virtual reactive component are convenient for researchers to analyze and calculate the magnetic circuit.
  • the magnetic circuit vector diagram proposed by the present invention can be drawn, and by changing the virtual active component or virtual reactive component of the magnetic circuit vector, the size and direction, and then change the electric active power or electric reactive power of the magnetic circuit.
  • FIG. 1 is an equivalent magnetic circuit vector model of the present invention.
  • FIG. 2 is a magnetic circuit vector diagram of the present invention.
  • FIG. 3 is a flow chart of the magnetic circuit power calculation of the present invention.
  • Figure 4 shows the excitation current and magnetic flux waveforms of the magnetic circuit under test after adding the magnetic induction element.
  • FIG. 5 is a comparison diagram of the actual measured electric power and the electric power calculated by applying the present invention.
  • the invention proposes a method for calculating magnetic circuit power, the core content of which is based on the equivalent magnetic circuit vector model, through the proposed magnetic circuit vector diagram to calculate the magnetic potential, magnetic flux, magnetic resistance,
  • the magnetic reactance is analyzed, the active power, reactive power and complex power in the dual circuit are analyzed, and the calculation method of the virtual active power, virtual reactive power and virtual complex power of the magnetic circuit is proposed.
  • the electric power of the magnetic circuit is calculated from the virtual power of the magnetic circuit.
  • the magnetic potential is included magnetic flux
  • the four magnetic circuit lumped variables, the magnetoresistance R mc and the magnetic induction L mc are dual to the voltage in the equivalent circuit vector model.
  • current The four circuit lumped variables of resistance R and inductance L, namely The equivalent magnetic circuit vector model is shown in Figure 1.
  • the magnetoresistance in the magnetic circuit represents the constant resistance of the magnetic circuit to the magnetic flux, which hinders both the alternating magnetic flux and the constant magnetic flux.
  • the magnetoresistance can change the magnitude of the magnetic flux, but does not change its phase.
  • the excitation frequency of the magnetic circuit increases, the reluctance value of the magnetic circuit increases due to the skin effect of the magnetic flux.
  • the reluctance value of the magnetic circuit increases due to the saturation of the magnetic circuit.
  • the magnetic induction L mc hinders the change of the magnetic flux in the magnetic circuit, and the magnetic induction has a hindering effect on the alternating magnetic flux, but has no hindering effect on the constant magnetic flux.
  • the calculation formula of the magnetic induction element is N r is the number of turns of the magnetic induction element, and R r is the resistance value of the magnetic induction element.
  • the magnetic reactance value satisfies the formula
  • a vector diagram of the magnetic circuit can be drawn, as shown in Figure 2, Represents the back EMF on the field coil. along the magnetic flux Direction and perpendicular flux Direction vs. Magnetic Potential Orthogonal decomposition, the magnetic voltage drop on the magnetoresistance (for the virtual reactive component) can be obtained as The magnetic voltage drop on the magnetic induction (corresponding to the virtual active component) is and satisfy
  • the formed electromagnetic vector diagram when the equivalent magnetic circuit model and the equivalent circuit model are linked by a vector (such as a magnetic flux vector), the formed electromagnetic vector diagram can show the circuit vector and the magnetic circuit vector at the same time phase relationship.
  • the virtual active power of the magnetic circuit is defined as the imaginary part of the virtual complex power, and the expression of the virtual active power of the magnetic circuit is
  • the virtual reactive power of the magnetic circuit is defined as the real part of the virtual complex power, and the expression of the virtual reactive power of the magnetic circuit is
  • the virtual power of the magnetic circuit satisfies the following relationship, that is,
  • the reduction factor of the virtual power of the magnetic circuit and the electric power is In particular, when the magnetic potential and magnetic flux in the magnetic circuit are sinusoidal, the reduction factor is j ⁇ .
  • a magnetic induction element L mc1 constructed of a short-circuit coil is added to the magnetic circuit. According to the formula The calculated magnetic induction value is 68.353 ⁇ -1 .
  • the excitation current and magnetic flux waveform of the transformer are shown in Figure 4.
  • the magnitude and phase of given by the formula
  • the magnitude of the magneto-impedance value is 41038.6 ⁇ -1
  • the magneto-impedance angle is 57.7°.
  • the magnetoresistance value can be obtained as 21929.07H -1 , according to the formula It can be obtained that the magnetic induction value is 110.4165 ⁇ -1 , verifying the equation established.
  • the present invention proposes a calculation method of magnetic circuit power.
  • the above descriptions are only the preferred embodiments of the present invention, and the protection scope of the present invention is not limited to the above-mentioned embodiments, but any equivalent modifications or changes made by those of ordinary skill in the art based on the contents disclosed in the present invention should be included in the The scope of protection described in the claims.

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Abstract

本发明公开一种磁路功率的计算方法，本发明针对磁路的功率问题以及磁路中磁势与磁通的相位问题，在等效磁路矢量模型的基础上，绘制了磁路矢量图，通过磁路矢量图对磁路中的磁势、磁通、磁阻、磁抗进行分析，提出了磁路的虚拟有功功率、虚拟无功功率、虚拟复功率的计算方法；由磁路虚拟功率与电功率的归算因子，推导出磁路虚拟功率与电功率的数学关系，从而可直接由磁路中磁势、磁通等磁量计算得到电功率。本发明所提出的磁路功率计算方法，能够通过磁路矢量计算并分析磁路中的虚拟功率，进而归算出磁路的电功率；当无法通过电路矢量计算电功率时，可以通过磁路矢量求解电功率。

Description

一种磁路功率的计算方法 技术领域
本发明涉及磁路理论及应用领域，尤其涉及磁路功率的计算与分析。
背景技术
近年来，随着电气化和计算机技术的发展，各种不同结构特点、不同工作原理、不同性能优势的电机、变压器、无线充电装置等新型强电磁耦合设备大量涌现。目前这些新型电磁设备的早期设计主要依靠麦克斯韦方程组进行二维或三维有限元分析，计算复杂，耗费时间，成本较高。磁路理论是通过对偶电路理论建立的一种磁路分析方法，是电磁学中的重要理论之一。在特定情况下，等效磁路可通过对偶于电路理论中基尔霍夫定律、欧姆定律等经典原理的数学公式进行描述。在实际问题中，可以应用磁路分析方法对电磁设备进行磁场分析，将复杂抽象的实际分析问题简化为简单原理性的数学逻辑描述，能够减少电磁设备设计时间，节约设计成本。因此，磁路分析方法逐渐受到相关研究者的关注。
国内的磁路分析方法研究开始于20世纪八十年代，国内高校以及研究机构的相关领域专家在这方面取得了许多研究成果。沈阳工业大学的唐任远院士在《现代永磁电机理论与设计》中提出了永磁电机磁路的基本原理，虽然磁路法的计算速度快，但是该方法计算精度不高，在实际应用中往往采用一些由工程经验得出的修正系数对计算结果进行修正。南斯拉夫学者Vlado Ostovic在总结多种经典磁路理论的基础上，提出了一种动态磁网络模型的数值计算方法，在1999年他将三维动态磁网络方法成功应用在爪极发电机中。浙江大学陈晓刚等学者提出了永磁同步电机的磁网络模型，并在所搭建的模型上验证了动态磁网络法的快速性。随着ANSOFT、JAMG等商业化有限元软件的普及，磁路分析方法越来越多地用于电磁装备的三维电磁分析以及结构分析，例如无线电能传输装置模型、磁通切换电机模型、高频变压器模型以等新型电磁设备。
东南大学程明等学者提出磁路分析法与二维有限元法相结合的混合分析法，并将之应用于研究永磁体轴向分段对涡流损耗的影响，通过磁路分析方法弥补了有限元法原理上的不足。在现有磁路分析方法或磁网络分析方法应用过程中，主要根据磁路的欧姆定律、磁路的基尔霍夫定律对磁路的磁势、磁通进行分析计算，从未考虑过磁路的功率问题，磁路中功率的计算及分析未得到重视。除此之外，现有的磁路分析方法通过线性磁导、非线性磁导以及永磁磁势、绕组磁势等磁路元件对磁路进行建模，未考虑磁路中磁势与磁通的相位关系。
发明内容
本发明所要解决的技术问题在于，针对磁路的功率问题以及磁路中磁势与磁通的相位问题，提出了一种磁路功率的计算方法，通过磁路中的磁势、磁通、磁阻、磁抗绘制了磁路矢量图，计算出磁路的虚拟功率。由磁路虚拟功率与电功率的归算因子，推导出磁路虚拟功率与电功率的数学关系，从而可直接由磁路中磁势、磁通等磁量计算得到电功率。
本发明所采用的技术方案具体如下：
本发明提出一种磁路功率的计算方法，具体过程如下：
S1、当被测磁路稳定运行时，计算磁路中的磁势
Figure PCTCN2021073268-appb-000001
和磁通
Figure PCTCN2021073268-appb-000002
S2、根据公式
Figure PCTCN2021073268-appb-000003
求解磁路的磁阻抗值Z mc和磁阻抗角
Figure PCTCN2021073268-appb-000004
S3、求解磁路磁阻值、磁抗值、磁感值，计算公式分别为：
Figure PCTCN2021073268-appb-000005
X mc＝jωL mc；
其中，R mc为电感元件所匝链磁路的磁阻值，X mc表示磁路的磁抗，L mc表示磁感元件的磁感值，j表示虚数单位，ω为磁路中磁通变化的角频率；
S4、选择参考坐标系，绘制磁路矢量图；
S5、根据磁路矢量图，将磁路中的磁势
Figure PCTCN2021073268-appb-000006
对磁通
Figure PCTCN2021073268-appb-000007
进行正交分解，得到沿磁通方向的磁压降
Figure PCTCN2021073268-appb-000008
以及垂直磁通方向的磁压降
Figure PCTCN2021073268-appb-000009
S6、由公式
Figure PCTCN2021073268-appb-000010
计算磁路的虚拟有功功率，由公式
Figure PCTCN2021073268-appb-000011
求计算磁路的虚拟无功功率；
S7、求解磁路的虚拟复功率
Figure PCTCN2021073268-appb-000012
具体公式为：
Figure PCTCN2021073268-appb-000013
S8、根据磁路虚拟功率与电功率归算因子jω求解相应的电功率；即：
电有功功率P e＝ωP mc，电无功功率Q e＝ωQ mc，电复功率
Figure PCTCN2021073268-appb-000014
进一步，本发明所提出的一种磁路功率的计算方法，还包括在S6计算磁路的虚拟有功功率、无功功率之前，对包含磁感元件的磁路拓扑是否满足磁路欧姆定律进行验证，即：
Figure PCTCN2021073268-appb-000015
其中，j表示虚数单位，R mc为电感元件所匝链磁路的磁阻值，ω为磁路中磁通变化的角频率，L mc表示磁感元件的磁感值，
Figure PCTCN2021073268-appb-000016
表示磁路中的磁通矢量，
Figure PCTCN2021073268-appb-000017
表示磁路中的磁势矢量。
进一步，本发明所提出的一种磁路功率的计算方法，磁感元件磁感值的大小L mc与短路线圈的匝数N r和短路线圈的电阻R r有关，即
Figure PCTCN2021073268-appb-000018
磁感的单位为Ω -1；磁感元件对交变磁通有阻碍作用，对于恒定磁通无阻碍作用，定义磁抗的表达式为X mc＝ωL mc，来描述磁感元件对于交变磁通阻碍作用的大小，ω为磁路中磁通变化的角频率。
进一步，本发明所提出的一种磁路功率的计算方法，在等效磁路矢量模型中，包括磁势
Figure PCTCN2021073268-appb-000019
磁通
Figure PCTCN2021073268-appb-000020
磁阻R mc和磁感L mc四个磁路集总变量，根据所述等效磁路矢量模型，当等效磁路模型与等效电路模型通过矢量进行链接时，所构成的电磁矢量图能够同时展示出电路矢量与磁路矢量相位关系。
进一步，本发明所提出的一种磁路功率的计算方法，结合磁路矢量图，磁路的虚拟复功率的表达式为
Figure PCTCN2021073268-appb-000021
进一步，本发明所提出的一种磁路功率的计算方法，磁路的虚拟有功功率定义为虚拟复功率的虚部，结合磁路矢量图，磁路的虚拟有功功率的表达式为
Figure PCTCN2021073268-appb-000022
进一步，本发明所提出的一种磁路功率的计算方法，磁路的虚拟无功功率定义为虚拟复功率的实部，结合磁路矢量图，磁路虚拟无功功率的表达式为
Figure PCTCN2021073268-appb-000023
进一步，本发明所提出的一种磁路功率的计算方法，磁路虚拟功率与电功率的归算因子为
Figure PCTCN2021073268-appb-000024
当磁路中的磁势、磁通为正弦量时，归算因子为jω；即,
电有功功率的表达式为:
Figure PCTCN2021073268-appb-000025
电无功功率的表达式为
Figure PCTCN2021073268-appb-000026
电复功率的表达式为
Figure PCTCN2021073268-appb-000027
本发明采用以上技术方案，与现有技术相比的有益效果如下：
1.本发明所提出的磁路功率计算方法，能够通过磁路矢量计算并分析磁路中的虚拟功率，进而归算出磁路的电功率。当无法通过电路矢量计算电功率时，可以通过磁路矢量求解电功率，为功率的计算、分析提供了一条新路径。
2.本发明所提出的磁路矢量图，能够清晰地展示磁路中各个矢量的幅值与相位关系，在任意方向上实现对磁路矢量的合成、分解，可以有效地表示出磁路矢量的虚拟有功分量以及虚拟无功分量，方便科研人员对磁路进行分析计算。
3.根据磁路的实际功率的设计需求，可以绘制出本发明所提出的磁路矢量图，通过改变磁路矢量的虚拟有功分量或虚拟无功分量，有目的地改变磁路矢量的大小和方向，进而改变磁路的电有功功率或电无功功率。
附图说明
图1为本发明的等效磁路矢量模型。
图2为本发明的磁路矢量图。
图3为本发明的磁路功率计算流程图。
图4为加入磁感元件后被测磁路的励磁电流与磁通波形。
图5为实际测量电功率和应用本发明所归算出电功率的对比图。
具体实施方式
以下结合附图对本发明的技术方案做进一步详细说明。
本发明提出了一种磁路功率的计算方法，其核心内容是在等效磁路矢量模型的基础上，通过所提出的磁路矢量图对磁路中的磁势、磁通、磁阻、磁抗进行分析，对偶电路中的有功功率、无功功率、复功率，提出了磁路的虚拟有功功率、虚拟无功功率、虚拟复功率的计算方法。结合所提出的归算因子，由磁路的虚拟功率归算出磁路的电功率。
在等效磁路矢量模型中，包括磁势
Figure PCTCN2021073268-appb-000028
磁通
Figure PCTCN2021073268-appb-000029
磁阻R mc和磁感L mc四个磁路集总变量，四者关系对偶于等效电路矢量模型中的电压
Figure PCTCN2021073268-appb-000030
电流
Figure PCTCN2021073268-appb-000031
电阻R和电感L四个电路集总变量，即
Figure PCTCN2021073268-appb-000032
等效磁路矢量模型如图1所示。
在等效磁路矢量模型中，磁势
Figure PCTCN2021073268-appb-000033
的计算公式为
Figure PCTCN2021073268-appb-000034
其单位为安匝，N m为励 磁线圈匝数，
Figure PCTCN2021073268-appb-000035
为励磁线圈中的电流。磁路中的磁通满足
Figure PCTCN2021073268-appb-000036
磁路中的磁阻表示磁路对磁通的恒定阻碍作用，它既阻碍交变磁通，也阻碍恒定磁通。在无磁感元件的磁路中，当磁势恒定时，磁阻可以改变磁通的大小，但不改变其相位。当磁路的励磁频率增加时，磁路的磁阻值由于磁通的集肤效应随之增加，当磁路的磁通增加时，磁路的磁阻值由于磁路饱和也会增加。
进一步，磁感L mc阻碍着磁路中磁通的变化，磁感对交变的磁通有阻碍作用，对于恒定的磁通无阻碍作用。磁感元件的计算式为
Figure PCTCN2021073268-appb-000037
N r为磁感元件的匝数，R r为磁感元件的电阻值。为了描述磁感大小对于交变磁通的阻碍作用，定义磁抗的表达式为X mc＝ωL mc，ω为磁路中磁通变化的角频率。
磁路中的磁阻抗值可由
Figure PCTCN2021073268-appb-000038
计算，磁路中的磁阻抗角可由φ mc＝arctan(ωL mc/R mc)计算，磁阻值满足公式
Figure PCTCN2021073268-appb-000039
磁抗值满足公式
Figure PCTCN2021073268-appb-000040
进一步，根据磁路等效矢量模型，可绘制磁路的矢量图，如图2所示，
Figure PCTCN2021073268-appb-000041
表示励磁线圈上的反电动势。以沿磁通
Figure PCTCN2021073268-appb-000042
方向和垂直磁通
Figure PCTCN2021073268-appb-000043
方向对磁势
Figure PCTCN2021073268-appb-000044
进行正交分解，可以得到磁阻上的磁压降(对于虚拟无功分量)为
Figure PCTCN2021073268-appb-000045
磁感上的磁压降(对应虚拟有功分量)为
Figure PCTCN2021073268-appb-000046
并且满足
Figure PCTCN2021073268-appb-000047
根据所提出的等效磁路矢量模型，当等效磁路模型与等效电路模型通过矢量进行链接时(如磁通矢量)，所构成的电磁矢量图能够同时展示出电路矢量与磁路矢量相位关系。
结合磁路矢量图，磁路虚拟复功率的表达式为：
Figure PCTCN2021073268-appb-000048
磁路的虚拟有功功率定义为虚拟复功率的虚部，磁路的虚拟有功功率的表达式为
Figure PCTCN2021073268-appb-000049
磁路的虚拟无功功率定义为虚拟复功率的实部，磁路虚拟无功功率的表达式为
Figure PCTCN2021073268-appb-000050
磁路的虚拟功率之间满足如下关系，即，
Figure PCTCN2021073268-appb-000051
磁路虚拟功率与电功率的归算因子为
Figure PCTCN2021073268-appb-000052
特别地，当磁路中的磁势、磁通为正弦量时，归算因子为jω。
即电有功功率的表达式为：
Figure PCTCN2021073268-appb-000053
电无功功率的表达式为：
Figure PCTCN2021073268-appb-000054
电复功率的表达式为：
Figure PCTCN2021073268-appb-000055
基于以上所述的等效磁路矢量模型，本发明所提出的一种计算磁路功率的方法具体过程如下：
S1、当被测磁路稳定运行时，计算磁路中的磁势
Figure PCTCN2021073268-appb-000056
和磁通
Figure PCTCN2021073268-appb-000057
S2、根据公式
Figure PCTCN2021073268-appb-000058
求解磁路的磁阻抗值Z mc和磁阻抗角
Figure PCTCN2021073268-appb-000059
S3、由公式
Figure PCTCN2021073268-appb-000060
求解磁路磁阻值，由公式
Figure PCTCN2021073268-appb-000061
求解磁抗值，由公式X mc＝jωL mc进一步求解磁路磁感值。
S4、选择参考坐标系，绘制磁路矢量图。
S5、根据磁路矢量图，将磁路中的磁势
Figure PCTCN2021073268-appb-000062
对磁通
Figure PCTCN2021073268-appb-000063
进行正交分解，得到沿磁通方向的对应虚拟无功分量的磁压降
Figure PCTCN2021073268-appb-000064
和垂直磁通方向的对应虚拟有功分量的磁压降
Figure PCTCN2021073268-appb-000065
S6、由公式
Figure PCTCN2021073268-appb-000066
计算磁路的虚拟有功功率，由公式
Figure PCTCN2021073268-appb-000067
求计算磁路的虚拟无功功率。
S7、根据公式
Figure PCTCN2021073268-appb-000068
求解磁路的虚拟复功率。
S8、根据磁路虚拟功率与电功率归算因子为jω求解相应的电功率。即P e＝ωP mc， Q e＝ωQ mc，
Figure PCTCN2021073268-appb-000069
为了计算出变压器的有功功率和无功功率，绘制出了磁路功率计算方法的流程图，如图3所示。首先，当变压器空载运行时，通过公式
Figure PCTCN2021073268-appb-000070
求解出磁路的磁阻值R mc＝22343.6H -1和初始磁感值L mc0＝43.34Ω -1。当磁路的励磁频率和磁路中磁通大小维持不变时，磁阻R mc基本不变。
维持磁路励磁频率为50Hz、磁通幅值恒定的条件下，在磁路中加入短路线圈构造的磁感元件L mc1，根据公式
Figure PCTCN2021073268-appb-000071
计算出磁感值为68.353Ω -1。此时，变压器等效磁路矢量模型的磁阻为R mc＝22343.6H -1，磁感为L mc2＝L mc0+L mc1＝111.6Ω -1。
加入磁感元件后变压器的励磁电流和磁通波形如图4所示。根据图4计算出变压器的磁势矢量
Figure PCTCN2021073268-appb-000072
和磁通矢量
Figure PCTCN2021073268-appb-000073
的幅值和相位，由公式
Figure PCTCN2021073268-appb-000074
计算磁路的磁阻抗值Z mc和磁阻抗角
Figure PCTCN2021073268-appb-000075
经计算，磁阻抗值的大小为41038.6Ω -1，磁阻抗角为57.7°。根据公式
Figure PCTCN2021073268-appb-000076
可以得到磁阻值为21929.07H -1，根据公式
Figure PCTCN2021073268-appb-000077
可以得到磁感值为110.4165Ω -1，验证方程
Figure PCTCN2021073268-appb-000078
成立。
根据所变压器磁路的磁势
Figure PCTCN2021073268-appb-000079
磁通
Figure PCTCN2021073268-appb-000080
磁阻R mc、磁抗X mc可绘制出变压器等效磁路模型的矢量图，如图2所示，
Figure PCTCN2021073268-appb-000081
表示励磁线圈上的反电动势。以沿磁通
Figure PCTCN2021073268-appb-000082
方向和垂直磁通
Figure PCTCN2021073268-appb-000083
方向对磁势
Figure PCTCN2021073268-appb-000084
进行正交分解，可以得到磁阻上的磁压降为
Figure PCTCN2021073268-appb-000085
磁感上的磁压降为
Figure PCTCN2021073268-appb-000086
根据公式
Figure PCTCN2021073268-appb-000087
求解磁路的虚拟有功功率，公式
Figure PCTCN2021073268-appb-000088
求解磁路的虚拟无功功率。进而由归算因子jω计算出变压器的有功功率P e＝ωP mc，变压器的无功功率Q e＝ωQ mc。对比磁路计算的有功功率P e和通过功率分析仪所测量的有功功率，对比磁路计算的无功功率Q e和测量的无功功率，结果如图5所示。通过磁路理论计算的有功功率的计算误差为2.86％，通过磁路理论计算的无功功率的计算误差为4％，该结果较好地说明了本发明所提出的磁路计算方法的正确性与有效性。
总之，本发明提出了一种磁路功率的计算方法。以上所述仅为本发明的较佳实施方式，本发 明的保护范围并不以上述实施方式为限，但凡本领域普通技术人员根据本发明所揭示内容所作的等效修饰或变化，皆应纳入权利要求书中记载的保护范围。

Claims (8)

  1. 一种磁路功率的计算方法，其特征在于，具体过程如下：
    S1、当被测磁路稳定运行时，计算磁路中的磁势
    Figure PCTCN2021073268-appb-100001
    和磁通
    Figure PCTCN2021073268-appb-100002
    S2、根据公式
    Figure PCTCN2021073268-appb-100003
    求解磁路的磁阻抗值Z mc和磁阻抗角
    Figure PCTCN2021073268-appb-100004
    S3、求解磁路磁阻值、磁抗值、磁感值，计算公式分别为：
    Figure PCTCN2021073268-appb-100005
    其中，R mc为电感元件所匝链磁路的磁阻值，X mc表示磁路的磁抗，L mc表示磁感元件的磁感值，j表示虚数单位，ω为磁路中磁通变化的角频率；
    S4、选择参考坐标系，绘制磁路矢量图；
    S5、根据磁路矢量图，将磁路中的磁势
    Figure PCTCN2021073268-appb-100006
    对磁通
    Figure PCTCN2021073268-appb-100007
    进行正交分解，得到沿磁通方向的磁压降
    Figure PCTCN2021073268-appb-100008
    以及垂直磁通方向的磁压降
    Figure PCTCN2021073268-appb-100009
    S6、由公式
    Figure PCTCN2021073268-appb-100010
    计算磁路的虚拟有功功率，由公式
    Figure PCTCN2021073268-appb-100011
    求计算磁路的虚拟无功功率；
    S7、求解磁路的虚拟复功率
    Figure PCTCN2021073268-appb-100012
    具体公式为：
    Figure PCTCN2021073268-appb-100013
    S8、根据磁路虚拟功率与电功率归算因子jω求解相应的电功率；即：
    电有功功率P e＝ωP mc，电无功功率Q e＝ωQ mc，电复功率
    Figure PCTCN2021073268-appb-100014
  2. 根据权利要求1所述的一种磁路功率的计算方法，其特征在于，还包括在S6计算磁路的虚拟有功功率、无功功率之前，对包含磁感元件的磁路拓扑是否满足磁路欧姆定律进行验证，即：
    Figure PCTCN2021073268-appb-100015
    其中，j表示虚数单位，R mc为电感元件所匝链磁路的磁阻值，ω为磁路中磁通变化的角频率，L mc表示磁感元件的磁感值，
    Figure PCTCN2021073268-appb-100016
    表示磁路中的磁通矢量，
    Figure PCTCN2021073268-appb-100017
    表示磁路中的磁势矢量。
  3. 如权利要求1所述的一种磁路功率的计算方法，其特征在于，磁感元件磁感值的大 小L mc与短路线圈的匝数N r和短路线圈的电阻R r有关，即
    Figure PCTCN2021073268-appb-100018
    磁感的单位为Ω -1；磁感元件对交变磁通有阻碍作用，对于恒定磁通无阻碍作用，定义磁抗的表达式为X mc＝ωL mc，来描述磁感元件对于交变磁通阻碍作用的大小，ω为磁路中磁通变化的角频率。
  4. 如权利要求1所述的一种磁路功率的计算方法，其特征在于，在等效磁路矢量模型中，包括磁势
    Figure PCTCN2021073268-appb-100019
    磁通
    Figure PCTCN2021073268-appb-100020
    磁阻R mc和磁感L mc四个磁路集总变量，根据所述等效磁路矢量模型，当等效磁路模型与等效电路模型通过矢量进行链接时，所构成的电磁矢量图能够同时展示出电路矢量与磁路矢量相位关系。
  5. 如权利要求1所述的一种磁路功率的计算方法，其特征在于，结合磁路矢量图，磁路的虚拟复功率的表达式为
    Figure PCTCN2021073268-appb-100021
  6. 如权利要求1所述的一种磁路功率的计算方法，其特征在于，磁路的虚拟有功功率定义为虚拟复功率的虚部，结合磁路矢量图，磁路的虚拟有功功率的表达式为
    Figure PCTCN2021073268-appb-100022
  7. 如权利要求1所述的一种磁路功率的计算方法，其特征在于，磁路的虚拟无功功率定义为虚拟复功率的实部，结合磁路矢量图，磁路虚拟无功功率的表达式为
    Figure PCTCN2021073268-appb-100023
  8. 如权利要求1所述的一种磁路功率的计算方法，其特征在于，磁路虚拟功率与电功率的归算因子为
    Figure PCTCN2021073268-appb-100024
    当磁路中的磁势、磁通为正弦量时，归算因子为jω；即：
    电有功功率的表达式为:
    Figure PCTCN2021073268-appb-100025
    电无功功率的表达式为
    Figure PCTCN2021073268-appb-100026
    电复功率的表达式为
    Figure PCTCN2021073268-appb-100027
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Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20090064060A1 (en) * 2007-08-31 2009-03-05 Kabushiki Kaisha Toshiba Apparatus and method of extracting equivalent circuit of t-type transmission circuit
CN104701845A (zh) * 2015-03-20 2015-06-10 朱鹏程 基于虚拟磁链的不平衡电网下pwm整流器直接功率控制方法
CN105826950A (zh) * 2016-05-18 2016-08-03 江苏大学 一种逆变器虚拟阻抗的矢量图分析方法
CN108494186A (zh) * 2018-04-20 2018-09-04 河北工业大学 一种提高铁氧体辅助式同步磁阻电机功率因数的优化方法
CN110174544A (zh) * 2019-04-19 2019-08-27 华北电力大学（保定） 一种变压器非对称偏磁问题的定点频域分析系统及方法
CN110188418A (zh) * 2019-05-14 2019-08-30 大连理工大学 一种永磁磁力耦合器传递转矩计算方法

Family Cites Families (16)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
DE2449697C3 (de) * 1973-10-19 1980-08-14 Hitachi, Ltd., Tokio Mechanisch-elektrischer Meßumformer
CA1118509A (fr) * 1978-10-20 1982-02-16 Gerald Roberge Variable inductance
SE511217C2 (sv) * 1997-08-18 1999-08-23 Emotron Ab Förfarande och drivsystem för reglering av en reluktansmaskin
NO319424B1 (no) * 2001-11-21 2005-08-08 Magtech As Fremgangsmate for styrbar omforming av en primaer vekselstrom/-spenning til en sekundaer vekselstrom/-spenning
WO2005076293A1 (en) * 2004-02-03 2005-08-18 Magtech As Power supply control methods and devices
JP2006337040A (ja) * 2005-05-31 2006-12-14 Uchihashi Estec Co Ltd 金属体の欠陥検出方法及びスキャニング式磁気検出器
US20070285195A1 (en) * 2006-06-13 2007-12-13 Nehl Thomas W Direct flux control system for magnetic structures
US8482181B2 (en) * 2008-06-04 2013-07-09 Convergent Power, Inc. Three phase synchronous reluctance motor with constant air gap and recovery of inductive field energy
BRMU8900816U2 (pt) * 2009-05-20 2011-01-11 Diogo Kataoka dispositivo limitador de corrente de curto-circuito com núcleo magnético de variação de relutáncia magnética sem partes móveis
US8564281B2 (en) * 2009-05-29 2013-10-22 Calnetix Technologies, L.L.C. Noncontact measuring of the position of an object with magnetic flux
SI23888A (sl) * 2011-09-28 2013-03-29 Univerza v Mariboru Fakulteta za elektrotehniko, računalništvo in informatiko Naprava in postopek testiranja za vrednotenje kvalitete magnetnih krogov
WO2014021912A1 (en) * 2012-07-30 2014-02-06 Convergent Power, Inc. Three phase synchronous reluctance motor with constant air gap and recovery of inductive field energy
CN104239652B (zh) * 2014-10-13 2017-09-15 国家电网公司 一种基于eic原理的三相五柱芯式变压器建模分析方法
CN106908745B (zh) * 2017-01-10 2019-05-28 云南电力试验研究院(集团)有限公司 一种基于低频方波的铁磁元件励磁特性和空载损耗的试验和计算方法
CN107153746B (zh) * 2017-06-02 2019-12-06 山东大学 一种内置式永磁同步电机漏磁系数解析计算方法
US10978979B2 (en) * 2017-12-12 2021-04-13 Phasetown, Llc Power factor adjustment method and apparatus through the phase control in a transformer circuit

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20090064060A1 (en) * 2007-08-31 2009-03-05 Kabushiki Kaisha Toshiba Apparatus and method of extracting equivalent circuit of t-type transmission circuit
CN104701845A (zh) * 2015-03-20 2015-06-10 朱鹏程 基于虚拟磁链的不平衡电网下pwm整流器直接功率控制方法
CN105826950A (zh) * 2016-05-18 2016-08-03 江苏大学 一种逆变器虚拟阻抗的矢量图分析方法
CN108494186A (zh) * 2018-04-20 2018-09-04 河北工业大学 一种提高铁氧体辅助式同步磁阻电机功率因数的优化方法
CN110174544A (zh) * 2019-04-19 2019-08-27 华北电力大学（保定） 一种变压器非对称偏磁问题的定点频域分析系统及方法
CN110188418A (zh) * 2019-05-14 2019-08-30 大连理工大学 一种永磁磁力耦合器传递转矩计算方法

Non-Patent Citations (4)

* Cited by examiner, † Cited by third party
Title
CHAI, FENG: "Theoretical Analysis and Calculation of Eddy Losses in Stator Windings of Large Synchronous Generator", CHINESE MASTER'S THESES FULL-TEXT DATABASE, 1 March 2010 (2010-03-01), pages 1 - 75, XP055933851 *
XU YAN ; WANG ZENGPING ; LIU QING: "A Novel Inductance Calculation Method in Power Transformer Model Based on Magnetic Circuit", TENCON 2005 : 2005 IEEE REGION 10 CONFERENCE, 1 November 2005 (2005-11-01), Piscataway, NJ , pages 1 - 4, XP031015518, ISBN: 978-0-7803-9311-0 *
ZHANG WENJUAN: "The Design of Tubular Linear Induction Motor for Lifting and Analysis of Its Starting Characteristics", CHINESE MASTER'S THESES FULL-TEXT DATABASE, 1 March 2010 (2010-03-01), pages 1 - 69, XP055933865 *
ZHOU E , GU ZHONGQI: "Magnetic Circuit Analysis and Parameter Calculation of New Reluctance Motor", SCIENCE IN CHINA,SER.A, no. 6, 30 June 1983 (1983-06-30), pages 571 - 580, XP055933860, ISSN: 1674-7216 *

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