Coupler and pseudo-power balance principle and reciprocity theorem adaptive judgment method

Abstract

The present invention relates to a coupler and a pseudo-power balance principle and a reciprocity theorem adaptation judgment method, in particular, a cluster coupler constructed by a single-phase coupler and a circuit network containing the coupler and a pseudo-power balance principle and a reciprocity theorem adaptation judgment method, which belongs to a circuit modeling and measurement verification method. The single-phase coupler is composed of a proportional controlled source, and there are two types of mutual transformers and mutual converters, and there are two special cases of cotransformers and inverters, and gyrators and inverters. The two-phase coupler is composed of a single-phase coupler, which is called a cluster coupler when expressed in single-phase form. There are two types of cluster mutual transformers and cluster mutual converters, and there are three special cases of complex mutual transformers and Erwin mutual transformers and N-type mutual transformers, complex mutual converters and Erwin mutual converters and N-type mutual converters, and there are four special cases of complex mutual transformers, Erwin mutual transformers, complex mutual converters and Erwin mutual converters. The coupler has very strong parameter transformation characteristics and complex signal operation functions, and has great practical value for the applicability judgment method of the pseudo-power balance principle and reciprocity theorem of the circuit network containing the coupler.

Description

Technical Field

[0001] The present invention relates to a method for determining the suitability of a coupler, a pseudo-power balance principle and a reciprocity theorem, and in particular to a method for determining the suitability of a cluster coupler constructed using a single-phase coupler and a circuit network containing the coupler, and belongs to a circuit modeling and measurement verification method. Background Art

[0002] With the development of society and technology, the application of circuits is becoming more and more common, but at the same time, circuits are becoming increasingly complex, from simple parallel circuits, series-parallel conversion circuits, three-way triangle conversion circuits to super-complex circuits, from single-port circuit networks, dual-port circuit networks to multi-port circuit networks, from single-phase circuits, two-wing circuits, two-phase circuits to three-phase circuits and even multi-phase circuits, from static circuits, steady-state circuits to dynamic circuits, from general circuits, coupling circuits or transmission circuits to control circuits, from fully symmetrical circuits, quasi-symmetrical circuits to asymmetrical circuits, from linear circuits, nonlinear circuits to switching circuits, digital circuits, circuits are developing rapidly, but at the same time they bring huge difficulties in circuit analysis, calculation and design. How to analyze circuits, improve circuit analysis principles, rules and methods, build a complete circuit analysis system, simplify circuits and reduce the difficulty of circuit design, reduce the complexity of circuits, and reduce the cost of circuits is of great significance.

[0003] The knowledge system framework of circuits consists of three levels: basic layer, method layer and application layer. Figure 1 shown.

[0004] The basic layer includes: basic physical quantities and their reference directions, node loops and Kirchhoff's laws, component branches and their volt-ampere characteristics, structural topology and matrix expressions of constraint relationships. Among them: the reference direction, Kirchhoff's laws and volt-ampere characteristics are called the three core basic knowledge points for circuit analysis and solution.

[0005] Table of variable symbols used for basic circuit physical quantities voltage and current:

[0006]

[0007] in: is an imaginary unit, that is, κ 2 =-1, κ 3 =-κ、κ 4 =1.

[0008] Commonly used two-terminal components include: ideal independent power supply, conversion element, ideal electric meter; ideal independent power supply: ideal independent voltage source, ideal independent current source, ideal independent power source; conversion element: resistance element, energy storage element, resistance element: positive resistance element, negative resistance element, energy storage element: inductance element, capacitance element; ideal electric meter: ideal voltmeter, ideal ammeter, universal power meter; universal power meter is regarded as a combination of ideal voltmeter and ideal ammeter. In addition to power, it can also measure voltage and current. The universal power meter can measure any form of voltage, current and power and their various required characteristic values.

[0009] Circuit elements are needed to build a circuit network. The graphic symbols and classification of the elements at both ends of the circuit are as follows: Figure 2 shown.

[0010] When analyzing circuits, actual independent power supply components are often used: actual independent voltage source, actual independent current source, actual independent power supply. The actual independent power supply component formation process is as follows: Figure 3 shown.

[0011] Basic modules are also needed to build complex networks: dual-port basic module, ideal controlled source module, and ideal coupling module.

[0012] Two-port basic module: two-port basic power module, two-port basic transformation module. Two-port basic power module: composed of ideal power supply. Two-port basic transformation module: two-port pure resistance or pure impedance T-type network, Π-type network.

[0013] There are three types of ideal controlled source modules: ideal proportional controlled source, ideal integral controlled source and ideal power controlled source.

[0014] Ideal proportional controlled source: voltage controlled voltage source VCVS, input-output relationship: u s =αu c ; Current controlled current source CCCS, input and output relationship: i s =βi c ; Current controlled voltage source CCVS, input-output relationship: u s =ri c ; Voltage controlled current source VCCS, input and output relationship: i s =gu c ; Graphic symbols are as follows Figure 4a , 4b , 4c, and 4d.

[0015] Ideal integral controlled source: voltage integral voltage source VIVS, input-output relationship: u s =F u ∫u i dt; current integrating current source CICS, input-output relationship: i s =Fi ∫i i dt; current integrating voltage source CIVS, input-output relationship: u s =Ξ∫i i dt; voltage integral current source VICS, input-output relationship: i s =Γ∫u i dt; the graphic symbols are as follows Figure 5a , 5b , 5c, and 5d.

[0016] Ideal power controlled source: voltage controlled power source p s =I u c , current controlled power source p s =U i c , power control voltage source u s =I -1 p c =I -1 u c i c , power control current source i s =U -1 p c =U -1 u c i c , power control power source p s =Kp c =Ku c i c , the graphic symbols are as follows Figure 6a , 6b , 6c, 6d, and 6e.

[0017] The ideal controlled power module can not only construct circuits with complex functions, but also greatly increase the flexibility of circuit construction, especially playing a key role in the construction of control circuits.

[0018] The ideal coupling module, also known as a coupler, is a dual-port bidirectional coupling element. There are two types of couplers: interconverters and inter-converters.

[0019] The relationship between the primary and secondary sides of the transformer: p2=u2i2=αu1βi1=αβp1, the graphic symbol is as follows Figure 7 As shown, when αβ=1, that is, p2=p1, it is called a cotransformer, and when αβ=-1, that is, p2=-p1, it is called an inverter or a flyback converter.

[0020] The relationship between the primary and secondary sides of the interconverter: p2=u2i2=ri1gu1=rgp1, the graphic symbol is as follows Figure 8 As shown, when rg=1, that is, p2=p1, it is called a gyrator, and when rg=-1, that is, p2=-p1, it is called an inverter or return device.

[0021] The method layer includes three basic methods for circuit analysis and solution: equivalent transformation method, correlation method, and qualitative analysis method.

[0022] Equivalent transformation method: also known as equivalent circuit method, is to use the equivalent transformation principle to convert complex circuits into simple circuits step by step, and use the solution results as known conditions to solve the circuit for one step of restoration, and use the solution results as known conditions to solve the circuit for further restoration, and so on until all the required results are obtained or the entire original circuit is solved. Equivalent transformation method is a physical method. The equivalent transformation principles used in the equivalent transformation method include: series-parallel equivalent transformation of ideal power supply, source transfer rule of ideal power supply, series-parallel equivalent transformation of resistance or impedance, three-pronged triangle equivalent transformation of resistance or impedance, mutual equivalent transformation of actual voltage source and actual current source, open circuit and short circuit extreme equivalent transformation, ideal coupling module port network equivalent migration principle, co-converter joint equivalent principle, inverter return to base equivalent principle, co-converter return to base equivalent principle, ideal controlled source equivalent principle, etc.

[0023] Association method: Given the parameters and excitation of a circuit, the method of solving the circuit response by establishing the KCL equation of an independent node, the KVL equation of a basic loop, and the VCR equation of a branch. Commonly used specific methods include: basic relationship method, branch current method, branch voltage method, node potential method, cut-set potential method, mesh circulation method, loop current method, tree branch voltage method, connected branch current method, etc. The association method solves all the responses of the entire circuit at once. The association method is a mathematical method.

[0024] Qualitative analysis method: use the determinism principle, substitution theorem, superposition principle, Thevenin-Norton theorem, flyback de-excitation principle, power externalization principle, inversion principle, power separability principle or power reuse principle, Tellegen's theorem, which is the power conservation theorem and pseudo-power conservation theorem, pseudo-power balance principle, reciprocity theorem, duality principle and other methods to analyze and solve circuits.

[0025] Circuit theorems are an important part of the circuit knowledge system and an important method for circuit analysis and research. Among them: Tellegen's first theorem is the power conservation theorem, Tellegen's second theorem is the quasi-power conservation theorem, and the reciprocity theorem is the ultimate quasi-power balance principle of two ports. The quasi-power balance principle is the bridge that connects Tellegen's second theorem with the reciprocity theorem.

[0026] Inversion principle: It includes three principles: reference direction inversion principle, isolated circuit inversion principle and port network inversion principle. It is an important principle about circuit symmetry, namely positive symmetry and antisymmetry.

[0027] Principle of reference direction inversion: when both reference directions of voltage and current of the two-terminal elements are reversed, the relationship expression between the parameter and the physical quantity remains unchanged, and the power formula remains unchanged; but when one of them is reversed, the relationship expression between the parameter and the physical quantity is reversed, and the power formula becomes negative; when both reference directions of voltage or current on both sides of the two-port network are reversed at the same time, the relationship between the parameter and the physical quantity remains unchanged, and the power formula remains unchanged; but when both reference directions of voltage and current on one side are reversed, the relationship expression is reversed, but the power formula remains unchanged.

[0028] Isolated circuit inversion principle: if all excitations are reversed, all responses will be reversed. Corollary: if all excitations are enlarged N times, all responses will also be enlarged N times; if all excitation modes are enlarged N times, all response modes will also be enlarged N times; all excitation angles will increase Then all response angles increase in the same way When all parameters are real numbers, all excitations are conjugated or anti-conjugated, and all responses are conjugated or anti-conjugated. When all parameters are imaginary numbers, all excitations are conjugated or anti-conjugated, and all responses are anti-conjugated or conjugated. Excitation: voltage of an ideal voltage source, current of an ideal current source. When all dimensioned parameters are negated, the dimensioned primitive parameters are negated, and the dimensionless primitive parameters remain unchanged. When all parameters are conjugated or anti-conjugated, the primitive parameters are conjugated or anti-conjugated. Primitive parameters: parameters or coefficients of each single term of the superposition principle polynomial.

[0029] Port network inversion principle: when all parameters are negated, the equivalent parameters are negated; when all parameters are real numbers, all parameters are conjugated or anti-conjugated, the equivalent parameters are conjugated or anti-conjugated; when all parameters are imaginary numbers, all parameters are conjugated or anti-conjugated, the equivalent parameters are anti-conjugated or conjugated; when all dimensioned parameters are negated, all dimensioned equivalent parameters are negated, dimensionless equivalent parameters remain unchanged, and all parameters are conjugated or anti-conjugated, all equivalent parameters are conjugated or anti-conjugated. Parameters: electromotive force of voltage source, electromotive force vector of current source. Dimensioned parameters: resistance, inductance, reactance, impedance or conductance, capacitance, susceptance, admittance with dimensions; dimensionless parameters: proportionality factor without dimensions, voltage magnification, current magnification, power magnification, etc.

[0030] The application layer includes: DC static circuit, AC steady-state circuit, and dynamic circuit. DC static circuit: composed of power supply and resistor. AC steady-state circuit: composed of simple harmonic or multi-harmonic AC power supply and resistor, inductor, capacitor. Dynamic circuit: composed of step DC power supply, step AC power supply, function power supply or impulse power supply and resistor, inductor, capacitor and switch elements.

[0031] When analyzing the circuit structure, the whole circuit is composed of branches. The branches are divided into three types: single-element branches, series branches and parallel branches. The series branches are composed of two-end components in series, and the parallel branches are composed of two-end components in parallel. The branch has two external terminals. The branch terminal and its connecting wire are regarded as a point called a node, and the closed path formed by the branch is called a loop.

[0032] The port network is composed of branches. When the circuit is running, there is power exchange between the port network and the port network or the external circuit; the independent circuit is composed of port networks. There is no power exchange between the independent circuit and other circuits, but there is information exchange; the isolated circuit is composed of independent circuits. There is neither power exchange nor information exchange between the isolated circuit and other circuits. The circuit structure hierarchy diagram is as follows Fig. 9 As shown, the circuit structure hierarchy diagram is as follows Fig.10 shown.

[0033] According to the different composition properties, circuit networks can be divided into two types: unexcited networks and excited networks. Unexcited network: a network without an ideal independent power supply and an externally excited controlled power supply; excited network: a network with an ideal independent power supply or an externally excited controlled power supply. Then a passive network must be an unexcited network, and an excited network must be an active network, but not necessarily vice versa.

[0034] According to the degree of similarity, the two circuits can be similar, equivalent and identical. Similar circuits can be classified into three categories: isotopic circuits, homeomorphic circuits and isomorphic circuits. Isotopic circuits: two circuits with the same topology; homeomorphic circuits: two circuits that are equivalent after de-excitation; isomorphic circuits: two circuits that are identical after de-excitation; equivalent circuits: two circuits with the same external characteristics.

[0035] According to the different forms of symmetry, circuits can be divided into two types: symmetrical circuits and asymmetrical circuits. Symmetrical circuits refer to circuits with symmetrical structures, i.e., circuits with the same topology and equal parameters, while asymmetrical circuits refer to circuits with asymmetrical structures, i.e., circuits with different topologies or unequal parameters. According to the different harmonic components, symmetrical circuits can also be divided into simple harmonic symmetrical circuits and multi-harmonic symmetrical circuits. Simple harmonic symmetrical circuits refer to symmetrical circuits with excitation of simple harmonic single sequence, i.e., single frequency and one phase sequence, while multi-harmonic symmetrical circuits refer to symmetrical circuits with excitation of multi-harmonic multi-sequence, i.e., multiple frequencies or multiple phase sequences.

[0036] The two-phase circuit is the most basic form of circuit. It is two groups of circuits that are vertically orthogonal in space and have the same form and topology. When the structure is expressed in single-phase form, the two-phase circuit is called a cluster circuit. The parameter is the cluster number and the physical quantity is a complex number. The formation of the cluster circuit is as follows: Fig.11 When the structure is expressed in single-phase form, the symmetrical two-phase circuit is called a complex circuit, and both the parameters and physical quantities are complex numbers.

[0037] The two-phase resistance, conductance, reactance, susceptance, impedance and admittance are called cluster resistance, cluster conductance, cluster reactance, cluster susceptance and cluster impedance and cluster admittance in single-phase form, which can be decomposed into two parts with positive sequence symmetry and reverse sequence symmetry, which are called complex resistance, complex conductance, complex reactance, complex susceptance and complex impedance, complex admittance and Erratic resistance, Erratic conductance, Erratic reactance, Erratic susceptance and Erratic impedance and admittance respectively. The relationship between cluster parameters, complex parameters and Erratic parameters is as follows: Fig.12a , 12b , Fig.13a , 13b , Fig.14a , 14b shown.

[0038] Common two-phase physical quantities and their effective values:

[0039] ü(t)=u x (t)+κu y (t)=U(t)∠α(t),

[0040]

[0041] Definition of common two-phase physical quantities instantaneous complex power and average complex power:

[0042] ü(t)=U(t)∠α(t),

[0043]

[0044] S(t)=U(t)I(t), ψ(t)=α(t)-β(t), p(t)=S(t)cos[ψ(t)], Q(t)=S(t)sin[ψ(t)]

[0045]

[0046] A symmetrical two-phase circuit is a two-phase circuit with symmetrical structure. It is called a complex circuit when it is expressed in single-phase form. According to the different harmonic components, there are two types of complex circuits: simple harmonic complex circuits and multi-harmonic complex circuits. The excitation of an AC simple harmonic complex circuit is a cyclotron, and all responses are also cyclotrons of the same frequency. The excitation or response of a multi-harmonic complex circuit is the superposition of multiple cyclotrons of different frequencies or different phase sequences.

[0047] Complex circuit operations:

[0048] 1. Simple harmonic alternating current and its effective value:

[0049]

[0050]

[0051] Multiharmonic AC quantities and their effective values:

[0052]

[0053]

[0054] 2. Average complex power of simple harmonic alternating current:

[0055]

[0056]

[0057] S=UI, ψ=α-β, P=S cos(ψ), Q=S sin(ψ)

[0058] The average complex power of a multiharmonic AC quantity:

[0059]

[0060] 3. Addition and subtraction of simple harmonic alternating current quantities:

[0061]

[0062]

[0063] Addition and subtraction of multi-harmonic AC quantities:

[0064]

[0065]

[0066] 4. Definition of simple harmonic alternating current impedance and admittance:

[0067]

[0068]

[0069] The impedance and admittance of multiharmonic AC quantities are:

[0070]

[0071]

[0072] Generally, impedance or admittance is nonlinear with respect to angular frequency, that is, impedance or admittance is a nonlinear function of angular frequency.

[0073] The voltage and current of multi-harmonic periodic functions, that is, the voltage and current with multiple frequency points, each frequency point corresponds to an impedance or admittance. The angular frequency function of the impedance or admittance can be obtained by connecting the frequency points into a broken line or by curve fitting.

[0074] 5. The relationship between the voltage and current of simple harmonic alternating current is:

[0075]

[0076]

[0077] The relationship between the voltage and current of multi-harmonic AC quantities is:

[0078]

[0079]

[0080] Using a broken line or curve fitting method to obtain the angular frequency function of impedance or admittance is an engineering method. Although the expression of impedance or admittance obtained by the mechanism modeling method is not as complete, this engineering method is particularly suitable for modeling actual objects, especially complex objects that cannot be modeled by mechanism.

[0081] The sinusoidal alternating current quantity of a single-phase sinusoidal alternating current circuit can be regarded as the superposition of two rotating quantities with opposite rotation directions. The single-phase sinusoidal alternating current circuit is often calculated using the mapping method, that is, mapping the single-phase sinusoidal alternating current circuit to a fully symmetrical complex circuit for calculation.

[0082] The mapping method of single-phase sinusoidal AC circuit is more intuitive than the phasor method, and can be directly used for the calculation of multi-harmonic or periodic voltage and current circuits, especially after the impedance or admittance of the branch or network is obtained by the mechanism modeling method.

[0083] There are three ways to connect components or branches in a three-phase circuit: triangle, three-pronged and three-pronged. The three-pronged and three-pronged circuits are collectively called star. The three-pronged circuit has the strongest ability to express zero-line signals. The sum of the three-phase voltages in a triangle is always zero, and the sum of the three-phase currents in a three-pronged circuit is always zero. Components in a triangle connection and components in a three-pronged circuit can be interchanged.

[0084] Three-phase circuits are divided into three-phase symmetrical circuits and three-phase asymmetrical circuits. Three-phase symmetrical circuits refer to circuits with symmetrical three-phase structural parameters. Three-phase symmetrical circuits are further divided into three-phase fully symmetrical circuits and three-phase quasi-symmetrical circuits. Three-phase fully symmetrical circuits are also called three-phase true symmetrical circuits, which refer to three-phase symmetrical circuits with symmetrical excitation, i.e., the sum of the three-phase excitation is zero. Three-phase quasi-symmetrical circuits refer to three-phase symmetrical circuits with asymmetrical excitation, i.e., the sum of the three-phase excitation is not zero. Three-phase fully symmetrical circuits are also divided into three-phase simple harmonic fully symmetrical circuits and three-phase multi-harmonic fully symmetrical circuits. Three-phase simple harmonic fully symmetrical circuits refer to three-phase fully symmetrical circuits with simple harmonic excitation and single sequence, i.e., single frequency and one phase sequence. The voltage and current of a three-phase fully symmetrical circuit only contain sequence components, so a three-phase fully symmetrical circuit is also called an ordered circuit or a differential mode circuit; the voltage and current of a three-phase quasi-symmetrical circuit also contain disordered components, and a three-phase symmetrical circuit composed of disordered components is called a disordered circuit or a common mode circuit.

[0085] According to the superposition principle, a three-phase symmetrical circuit can be decomposed into the superposition of a three-phase ordered circuit and a three-phase disordered circuit. The three-phase ordered circuit is solved by the conversion method into a complex circuit or the mapping method to a complex circuit; the three-phase disordered circuit is three identical single-phase circuits, which can be combined into a single-phase circuit and then solved by the method of mapping to a complex circuit.

[0086] Conversion method: convert the three-phase fully symmetrical AC circuit into a two-phase circuit for solution, which is often used for relatively simple three-phase symmetrical AC circuits. Mapping method: each phase of the three-phase fully symmetrical AC circuit is mapped as a single phase into a two-phase circuit for solution, which is often used for complex three-phase symmetrical AC circuits. The mapping method does not change the circuit pattern and is more flexible to use, so it has a wide range of applications, especially when three-phase components are connected by voltage division, rotation and phase shifting.

[0087] The addition and subtraction operations of three-phase sinusoidal alternating quantities and three-phase multi-harmonic alternating quantities, the impedance and admittance calculations of simple harmonic sinusoidal alternating quantities and multi-harmonic alternating quantities, and the calculations of the relationship between voltage and current of simple harmonic sinusoidal alternating quantities and multi-harmonic alternating quantities are all consistent with the calculations of single-phase AC circuits.

[0088] The calculation formula of Tellegen's first theorem in two basic circuits is:

[0089] Power conservation theorem for a single-phase circuit with N branches:

[0090]

[0091] The complex power conservation theorem of a cluster circuit or complex circuit with N branches:

[0092]

[0093] Among them: the sign of the algebraic sum is determined by the self-correlation relationship between the voltage reference direction and the current reference direction.

[0094] The reference directions of the branches with the same number in the two circuits with the same extension are the same. The first type of total pseudo-power is: the algebraic sum of the product of the branch voltage of circuit one with the same extension and the current of the corresponding branch of circuit two with the same extension. The second type of total pseudo-power is: the algebraic sum of the product of the branch voltage of circuit two with the same extension and the current of the corresponding branch of circuit one with the same extension. The total pseudo-complex power is: the algebraic sum of the pseudo-complex powers formed by the cluster circuits or complex circuits with the same extension. Among them: the same number means the same number, that is, they are in the same position in the topology diagram.

[0095] The calculation formula of Tellegen's second theorem in two basic circuits is:

[0096] The quasi-power conservation theorem of the N-branch isotope circuit a single-phase circuit and b single-phase circuit:

[0097]

[0098]

[0099] The quasi-complex power conservation theorem of the a-cluster circuit or complex circuit and b-cluster circuit or complex circuit with N branches:

[0100]

[0101]

[0102] Among them: the sign of the algebraic sum is determined by the correlation between the voltage reference direction and the current reference direction.

[0103] Dynamic circuit analysis: time domain analysis method, differential operator method, convolution analysis method, frequency domain analysis method, and complex frequency domain analysis method.

[0104] Time domain transient analysis methods for first-order dynamic circuits: typical circuit method, three-element method, three-component method, and five-component method.

[0105] The typical circuit method, three-component method and five-component method are also applicable to transient analysis of second-order dynamic circuits and high-order dynamic circuits.

[0106] The quasi-power balance principle and the reciprocity theorem can be applied not only to single-phase circuits but also to two-phase circuits. It is very important that they are widely used, but the applicable conditions and scope of the two have always been unclear. Since there is no definition and specification of two-phase couplers, the applicability of the quasi-power balance principle and the reciprocity theorem for single-phase circuits and two-phase circuits containing couplers is a blank. Therefore, it is very meaningful to clarify the applicable conditions of the quasi-power balance principle and the reciprocity theorem for circuit networks containing couplers. Summary of the invention

[0107] The technical problems to be solved by the present invention are:

[0108] 1. Use controlled source to build a single-phase coupler;

[0109] 2. Use single-phase couplers to build cluster couplers;

[0110] 3. The single-phase circuit pseudo-power balance principle and the reciprocity theorem applicability judgment method;

[0111] 4. Method for judging the applicability of the quasi-complex power balance principle and complex reciprocity theorem of cluster circuits.

[0112] The invention provides a coupler and a pseudo-power balance principle and a reciprocity theorem adaptation method.

[0113] The technical problem to be solved by the present invention is achieved through the following technical solutions.

[0114] A single-phase coupler having a primary port and a secondary port;

[0115] The single-phase coupler consists of a proportional controlled source and is of two types: single-phase and single-phase converters;

[0116] The single-phase inverter consists of a voltage-controlled voltage source u2 = αu1 and a current-controlled current source i1 = β -1i2, the control input port of the voltage-controlled voltage source, i.e., the voltage sensor u1, and the power output port of the current-controlled current source, i.e., the controlled current source i1, are connected in parallel as the primary port of the single-phase inverter, and the control input port of the current-controlled current source, i.e., the current sensor i2, and the power output port of the voltage-controlled voltage source, i.e., the controlled voltage source u2, are connected in series as the secondary port of the single-phase inverter; or the single-phase inverter is composed of a voltage-controlled voltage source u1=α -1 u2 and a current-controlled current source i2 = βi1, the control input port of the current-controlled current source, i.e., the current sensor i1, and the power output port of the voltage-controlled voltage source, i.e., the controlled voltage source u1, are connected in series as the primary port of the single-phase inverter, and the control input port of the voltage-controlled voltage source, i.e., the voltage sensor u2, and the power output port of the current-controlled current source, i.e., the controlled current source i2, are connected in parallel as the secondary port of the single-phase inverter;

[0117] The parameters of the single-phase transformer are: The control relationship is

[0118] The single-phase converter consists of two current-controlled voltage sources u2 = ri1 and u1 = g -1 i2, the control input port of the first current-controlled voltage source, i.e., the current sensor i1, and the power output port of the second current-controlled voltage source, i.e., the controlled voltage source u1, are connected in series as the primary port of the single-phase converter, and the control input port of the second current-controlled voltage source, i.e., the current sensor i2, and the power output port of the first current-controlled voltage source, i.e., the controlled voltage source u2, are connected in series as the secondary port of the single-phase converter; or the single-phase converter is composed of two voltage-controlled current sources i1=r -1 u2 and i2 = gu1, the control input port of the second voltage-controlled current source, i.e., the voltage sensor u1, and the power output port of the first voltage-controlled current source, i.e., the controlled current source i1, are connected in parallel as the primary port of the single-phase converter, and the control input port of the first voltage-controlled current source, i.e., the voltage sensor u2, and the power output port of the second voltage-controlled current source, i.e., the controlled current source i2, are connected in parallel as the secondary port of the single-phase converter;

[0119] The parameters of the constructed single-phase converter are The control relationship is

[0120] Single-phase inverter, αβ=1 is a single-phase co-inverter, αβ=-1 is a single-phase inverter or a single-phase flyback inverter;

[0121] Single-phase rotator, rg=1 is a single-phase rotator, rg=-1 is a single-phase rotator or single-phase return rotator.

[0122] A cluster coupler including a single-phase coupler having a primary side complex port and a secondary side complex port;

[0123] The cluster coupler is composed of single-phase couplers and there are two types: cluster interconverter and cluster interconverter;

[0124] The transformer consists of four parameters: α 11 / β 11 , α 12 / β 12 , α 21 / β 21 , α 22 / β 22 The single phase transformer is composed of 11 / β 11 The primary port of the single-phase inverter α 12 / β 12 The primary side ports of the transformer are connected in parallel to form the first primary side port of the transformer. 21 / β 21 The primary port of the single-phase inverter α 22 / β 22 The primary side ports of the transformer are connected in parallel to form the second primary side port of the transformer, and the two primary side ports of the transformer are combined into a primary side complex port; the single-phase transformer α 11 / β 11 The secondary port of the single-phase inverter α 21 / β 21 The secondary ports of the transformer are connected in series to form the first secondary port of the transformer. 12 / β 12 The secondary port of the single-phase inverter α 22 / β 22 The secondary side ports of the transformer are connected in series to form the second secondary side port of the transformer, and the two secondary side ports of the transformer are combined into a secondary side complex port;

[0125] The control relationship of the cluster transformer thus formed is: The parameters are: in:

[0126] Or the primary ports of the single-phase transformers constituting the cluster transformer are connected in series and the secondary ports are connected in parallel;

[0127] The control relationship of the cluster transformer thus formed is: The parameters are: in:

[0128] The bundle interconverter consists of four parameters: r 11 / g 11 、r 12 / g12 、r 21 / g 21 、r 22 / g 22 The single-phase converter is composed of 11 / g 11 The primary port of the single-phase converter 12 / g 12 The primary side ports of the cascaded converter form the first primary side port of the cluster converter. 21 / g 21 The primary port of the single-phase converter 22 / g 22 The primary ports of the single-phase converter are connected in series to form the second primary port of the cluster converter, and the two primary ports of the cluster converter are combined into a primary complex port; 11 / g 11 The secondary port of the single-phase converter 21 / g 21 The secondary ports of the 1st secondary port of the cluster converter are connected in series to form the first secondary port of the single-phase converter. 12 / g 12 The secondary port of the single-phase converter 22 / g 22 The secondary side ports of the cluster interconverter are connected in series to form the second secondary side port of the cluster interconverter, and the two secondary side ports of the cluster interconverter are combined into a secondary side complex port;

[0129] The control relationship of the cluster converter thus formed is: The parameters are: in:

[0130] Or the primary side ports and the secondary side ports of the single-phase converters constituting the cluster converter are connected in parallel;

[0131] The control relationship of the cluster converter thus formed is: The parameters are: in:

[0132] Plexus transformer, Right now For complex interconverter, Right now For the interconverter, Right now or Right now It is a transformer;

[0133] Plexus interconverter, Right now is a complex interconverter, Right now For the interconverter, Right now or Right now It is a mutual converter.

[0134] Complex Interconverter is a complex covariant, For complex inverter, It is a complex left inverter, It is a complex right inverter;

[0135] Einstein Interconverter is an Eichhorn covariant, For the inverter, It is an Erzograndiator. It is the right transformer;

[0136] Complex interconverter For the revolver, For the complex inverter, It is a left turner. It is a right turner;

[0137] Erraconverter For the gyrator, For the reverse device, It is a left turner. It is a right turner.

[0138] A single-phase circuit quasi-power balance principle using a single-phase coupler and a two-port network reciprocity theorem adaptive judgment method, which is applicable not only to DC circuits but also to general static circuits;

[0139] Step 1: Pseudo power balance of single-phase circuit: ∑u bk i ak =p TG =δp TR =δ∑u ak i bk , the classification feature δ is any real number, that is, any balance; when δ = 1, p TG =p TR The two pseudo powers of the same extension circuit are equal, and the pseudo power balance is equal value balance; when δ = -1, p TG =-p TR The two pseudo powers of the same extension circuit are opposite, and the pseudo power balance is the opposite value balance; the two total pseudo powers of the same extension single-phase circuit are both equal and opposite, and the total pseudo power is both equal value balance and opposite value balance, that is, arbitrary balance;

[0140] Step 2: The residual pseudo-power or the pseudo-power at the port of the cotransformer is both equally balanced and inversely balanced, i.e., arbitrarily balanced; the residual pseudo-power or the pseudo-power at the port of the gyrator is inversely balanced; the residual pseudo-power or the pseudo-power at the port of the inverter is equally balanced; and the residual pseudo-power or the pseudo-power at the port of the pure resistance network is equally balanced;

[0141] Step 3: Reciprocity forms of two-port networks: arbitrary reciprocity, equal reciprocity and inverse reciprocity; arbitrary reciprocity: u b1 i a1 +u b2 i a2 =p G =δp R =δ(u a1 i b1 +u a2 i b2 ), δ is any real number, that is, the two-port pseudo-power of the two ports of the two-port network is arbitrarily balanced; equivalent reciprocity: δ = 1, that is, u b1 i a1 +u b2 i a2 =p G =p R =u a1 i b1 +u a2 i b2 The two ports of a two-port network have equal quasi-power; the inverse value is reciprocal: δ = -1, i.e. u b1 i a1 +u b2 i a2 =p G =-p R =-u a1 i b1 -u a2 i b2 The two ports of the two-port network have opposite quasi-power; the cotransformer is both equivalent and inversely reciprocal, that is, arbitrary reciprocity; the gyrator is inversely reciprocal; the inverter is equivalent and reciprocal; and the pure resistance two-port network is equivalent and reciprocal.

[0142] A quasi-complex power balance principle of cluster circuits using cluster couplers and an adaptive judgment method for the complex reciprocity theorem of cluster two-port networks, which is applicable not only to DC circuits but also to general steady-state circuits;

[0143] Step 1: Simulate power balance of the same extension circuit: Classification feature is any cluster number, that is, any balance; it includes two special cases of quasi-complex power balance: Proportional balance and Conjugate balance; proportional balance: when When When It is left-bend equilibrium when When , it is right-hand equilibrium; conjugate equilibrium: when When When The left yoke is balanced when When , it is right yoke balanced; the total quasi-complex power of the same topology cluster circuit is both proportionally balanced and conjugate balanced, that is, arbitrary balanced;

[0144] The second step: the quasi-complex power of the remainder of the complex cotransformer or the quasi-complex power of the port is both proportionally balanced and conjugate balanced, that is, arbitrarily balanced, the quasi-complex power of the remainder of the complex gyrator or the quasi-complex power of the port is negatively yoke balanced, the quasi-complex power of the remainder of the complex inverter or the quasi-complex power of the port is positively yoke balanced, the quasi-complex power of the remainder of the complex left rotator or the quasi-complex power of the port is right-yoke balanced, the quasi-complex power of the remainder of the complex right rotator or the quasi-complex power of the port is left-yoke balanced, the quasi-complex power of the remainder of the complex pure resistance network or the quasi-complex power of the port is positively yoke balanced, and the quasi-complex power of the remainder of the complex pure reactance network or the quasi-complex power of the port is negatively yoke balanced;

[0145] The quasi-complex power of the remaining part of the Errachidia gyrator or the quasi-complex power of the port is balanced, the quasi-complex power of the remaining part of the Errachidia inverter or the quasi-complex power of the port is balanced, and the quasi-complex power of the remaining part of the Errachidia impedance network or the quasi-complex power of the port is balanced;

[0146] Step 3: Reciprocity forms of two-port networks: arbitrary reciprocity, proportional reciprocity and conjugate reciprocity, arbitrary reciprocity: For any number of clusters, the quasi-complex power of the two ports of the two-port network can be balanced arbitrarily; the ratio is reciprocal There are four types: equal value reciprocity and inverse value reciprocity, left fold reciprocity and right fold reciprocity, conjugate reciprocity There are four types: positive yoke reciprocity and negative yoke reciprocity, left yoke reciprocity and right yoke reciprocity; equivalent reciprocity: Right now Reciprocity of inverse value: Right now Left-fold reciprocity: Right now Right fold reciprocity: Right now Conjugate reciprocity: Right now Yoked reciprocity: Right now Left yoke reciprocity: Right now Right yoke reciprocity: Right now The complex cotransformer is both proportionally reciprocal and conjugately reciprocal, that is, arbitrary reciprocity. The negative yoke of the complex gyrator is reciprocal, the positive yoke of the complex inverter is reciprocal, the right yoke of the complex left gyrator is reciprocal, the left yoke of the complex right gyrator is reciprocal, the positive yoke of the complex pure resistance two-port network is reciprocal, and the negative yoke of the complex pure reactance two-port network is reciprocal; the Erratic gyrator is anti-value reciprocal, the Erratic inverter is equivalent reciprocal, and the Erratic impedance two-port network is equivalent reciprocal.

[0147] Ideal coupling module is also called ideal coupler, or coupler for short. It can be composed of controlled sources and is a two-port bidirectional coupling element. Single-phase couplers are available in two forms: single-phase transformer and single-phase converter. Single-phase transformer is called transformer for short. It consists of a voltage-controlled voltage source and a current-controlled current source. Fig.15 As shown; the single-phase converter is referred to as the interconverter, which is composed of two current-controlled voltage sources or two voltage-controlled current sources, such as Fig.16 shown.

[0148] The coupler is composed of a controlled source, which can be regarded as a coupler with two parameters, one of which is infinite. A single-phase transformer with two parameters, one of which is infinite, is transformed into a voltage-controlled voltage source or a current-controlled current source, such as Fig.17a , 17b As shown. If one of the two parameters of a single-phase converter is infinite, it can be transformed into a current-controlled voltage source or a voltage-controlled current source. Fig.18a , 18b shown.

[0149] The two-phase coupling module, also known as the two-phase coupler, is composed of a single-phase coupler and has a very strong conversion function. It has two forms: a two-phase transformer and a two-phase converter. Each form has several special cases such as a positive-sequence symmetrical two-phase coupler, a reverse-sequence symmetrical two-phase coupler, and a right-sequence symmetrical two-phase coupler.

[0150] When a two-phase coupler is expressed in single-phase form, it is called a cluster coupler. A cluster coupler is also a two-port bidirectional coupling element, and it also has two forms: cluster interconverter and cluster inter-converter.

[0151] The single-phase form of a two-phase transformer is a cluster transformer, and its graphic symbol is as follows: Fig.19 As shown, the single-phase form of the positive-sequence symmetrical two-phase transformer is a complex transformer, the single-phase form of the reverse-sequence symmetrical two-phase transformer is an Erroneous transformer, and the single-phase form of the n-sequence symmetrical two-phase transformer is a n-transformer.

[0152] The single-phase form of a two-phase converter is a cluster converter, and its graphic symbol is as follows: Fig. 20 As shown, the single-phase form of the positive-sequence symmetrical two-phase converter is the complex converter, the single-phase form of the reverse-sequence symmetrical two-phase converter is the Er converter, and the single-phase form of the n-sequence symmetrical two-phase converter is the n-converter.

[0153] The cluster transformer is composed of four single-phase transformers connected in series or in series-parallel. Fig.21a, 21b As shown, the cluster converter is composed of four single-phase converters connected in series or in parallel, as shown in FIG. Fig.22a , 22b shown.

[0154] There are four special cases of complex interconverters: complex coconverter, complex inverter, complex left transformer, and complex right transformer;

[0155] There are four special cases of Errachid transformers: Errachid co-transformer, Errachid anti-transformer, Errachid left-transformer and Errachid right-transformer.

[0156] There are four special cases of complex interconverters: complex gyrators, complex reverse gyrators, complex left gyrators, and complex right gyrators;

[0157] There are four special cases of Errachid interconverters: Errachid rotator, Errachid reverser, Errachid left rotator and Errachid right rotator.

[0158] The parameters and physical variables of a single-phase circuit are all real numbers, so a single-phase circuit is also called a real circuit. In the analysis of multi-phase circuits, two-phase circuits are an important foundation. The relationship between two-phase variables is often expressed in matrix form, which is a unified and standardized form. However, the two-phase circuit and its matrix representation are relatively complex, and the symmetry characteristics are not very intuitive. Two-phase circuits have two forms: symmetrical and asymmetrical. A symmetrical two-phase circuit in single-phase form is called a complex circuit, and both parameters and physical variables are complex numbers; while an asymmetrical two-phase circuit in single-phase form is called a cluster circuit, and parameters are expressed in cluster numbers, and physical variables are expressed in complex numbers. The two-phase circuit in the form of a cluster circuit is simple, intuitive, and convenient to calculate.

[0159] Complex number: A combination of two real numbers, the real part and the imaginary part. The imaginary part with the imaginary unit κ is called an imaginary number. The imaginary unit is regarded as a constant during calculation, and κ 2 =-1, the complex number corresponds to a plane vector and therefore has the same properties as the plane vector.

[0160] Properties of complex numbers:

[0161] 1. Expression of plural numbers:

[0162] 2. Conjugation of complex numbers:

[0163] 3. Addition and subtraction of complex numbers:

[0164] 4. Multiplication and division of complex numbers:

[0165] 5. Conjugate operation:

[0166] Bunch number: The combination of two complex numbers in the complex part and the yoke part. The yoke part with the conjugate operator @ is called the yoke number, such as It is called the complex part or the original part. It is called the yoke or the yoke. That is, the conjugate number or the errone. The bundle number is a generic number containing the conjugate operator @, which is also called the conjugate factor @@ = 1, The conjugate operator @ is a right-hand operator that only transforms the bundle or complex numbers and variables on its right, but has no effect on the numbers or variables on its left. Bunch numbers can be regarded as a generalized complex number operator.

[0167] Generic number: It is composed of a common number and an operator identifier. During the calculation process, the operator identifier is regarded as an operator and does not have the commutative law of multiplication.

[0168] All numbers: are composed of constants and characteristic identifiers. During the calculation process, the characteristic identifiers are regarded as constants and have the commutative law of multiplication.

[0169] Properties of bundle numbers:

[0170] 1. Conjugate of bundle number: Complex conjugation, yoke conjugation;

[0171] 2. Return of cluster number: Complex conjugation, yoke negation;

[0172] 3. Addition and subtraction of cluster numbers: Addition and subtraction of the complex part, addition and subtraction of the yoke part; and:

[0173] 4. Multiplication of cluster numbers: The product is a bundle number; it does not have the commutative law But the associative law and: but:

[0174] 5. Modular mark of cluster number: The difference between the squares of the moduli of the complex part and the yoke part;

[0175] 6. The reciprocal of the cluster number: The return of the bundle number divided by the modulus, where:

[0176] 7. Multiplying a complex number by a cluster number: The product is complex, and No commutative law But the associative law

[0177] 8. Analysis of cluster numbers: special case:

[0178] The principle of pseudo-power balance in single-phase circuit: arbitrary pseudo-power balance of Tongtuo circuit ∑u bk i ak =pTG =δp TR =δ∑u ak i bk , where δ is an arbitrary real number; when δ=+1, the two pseudo powers of the same extension circuit are equal p TR =+p TG , at this time, the quasi-power balance is called equivalent balance; when δ = -1, the two quasi-powers of the same extension circuit are opposite TR =-p TG , at this time, the pseudo-power balance is called the opposite balance. The two total pseudo-powers of the same extension single-phase circuit are both equal and opposite, and the total pseudo-power is both equal and opposite, that is, arbitrary balance or absolute balance.

[0179] Reciprocity theorem of single-phase circuit: If the ports of a two-port network are quasi-power equal-value balanced, it is called equal-value reciprocity; if the ports are quasi-power opposite-value balanced, it is called opposite-value reciprocity; if both equal-value reciprocity and opposite-value reciprocity are satisfied at the same time, it is called arbitrary reciprocity.

[0180] Pseudo power of single-phase inverter: Single-phase co-converter αβ=1 then p G =p R =0→p G =δp R →p G +p′ G =p TG =δp TR =δ(p R +p′ R )→p′ G =δp′ R The residual pseudo-power or port pseudo-power of the homotopic single-phase circuit containing the cotransformer can be arbitrarily balanced, and the cotransformer has arbitrary reciprocity.

[0181] Pseudo power of single-phase converter: Single-phase gyrator rg=1 then p G =-p R →p G +p′ G =p TG =-p TR =-(p R +p′ R )→p′ G =-p′ R , the residual pseudo-power or port pseudo-power of the same extension single-phase circuit containing the gyrator is reverse balanced, and the gyrator has reverse reciprocity; if the inverter rg=-1, then p G =+p R →p G +p′ G =p TG =+p TR =+(p R+p′ R )→p′ G =+p′ R The residual pseudo-power or port pseudo-power of the homotopic single-phase circuit containing the inverter is equally balanced, and the inverter has equal reciprocity.

[0182] Two types of pseudo-power of pure resistance network: The remainder of the pure resistance network is quasi-power equal balance, the port is quasi-power equal balance, and the pure resistance two-port network has equal reciprocity.

[0183] The principle of quasi-complex power balance of cluster circuits: Arbitrary quasi-complex power balance of cluster circuits with the same extension in is any cluster number; it includes two special cases of quasi-complex power balance: Proportional balance and Conjugate balance; quasi-complex power ratio balance: in For any complex number, it also contains four special columns: Right now Equivalence balance, Right now Counter-balance, Right now Fold left to balance, Right now Right-fold balance; quasi-complex power conjugate balance: in Any plural number, including four special columns: Right now Yoke balance, Right now Yoke balance, Right now Left yoke balance, Right now Right yoke balance. The total quasi-complex power of the same topology circuit is both proportionally balanced and conjugate balanced, that is, arbitrary balanced or absolutely balanced;

[0184] Complex reciprocity theorem of complex circuits: If the quasi-complex powers of the ports of a two-port network are arbitrarily balanced, they are arbitrarily reciprocal or absolutely reciprocal. If the quasi-complex powers of the ports are proportionally balanced, they are proportionally reciprocal. If the quasi-complex powers of the ports are conjugately balanced, they are conjugate reciprocal. Proportional reciprocity: If the quasi-complex powers of the complex ports are equally balanced, it is called equivalent reciprocity. If the quasi-complex powers of the complex ports are oppositely balanced, it is called oppositely balanced. If the quasi-complex powers of the complex ports are left-folded balanced, it is called left-folding reciprocity. If the quasi-complex powers of the complex ports are right-folded balanced, it is called right-folding reciprocity. Conjugate reciprocity: If the quasi-complex powers of the complex ports are positive conjugate balanced, it is called positive conjugate reciprocity. If the quasi-complex powers of the complex ports are negatively conjugated balanced, it is called negative conjugate reciprocity. If the quasi-complex powers of the complex ports are left-folded balanced, it is called left-folding reciprocity. If the quasi-complex powers of the complex ports are right-folded balanced, it is called right-folding reciprocity.

[0185] The quasi-complex power of the complex transformer: Complex Covariant but The remainder quasi-complex power or the port quasi-complex power of the isotopic cluster circuit containing the complex cotransformer is arbitrarily balanced, and the complex cotransformer has arbitrary reciprocity.

[0186] The quasi-complex power of the complex interconverter: Revolver but The residual pseudo-power or port pseudo-power negative yoke balance of the isotopic cluster circuit containing the complex gyrator, the complex gyrator has negative yoke reciprocity; the complex gyrator but The residual pseudo-power or port pseudo-power positive conjugate balance of the isotopic cluster circuit containing the complex invertor, the complex invertor has positive conjugate reciprocity; the complex left rotator but The residual pseudo-power or port pseudo-power of the isotopic cluster circuit containing a complex left rotator is right-yoke balanced, and the complex left rotator has right-yoke reciprocity; the complex right rotator but The remainder pseudo-power or port pseudo-power of the isotopic cluster circuit containing the complex right rotator is left-yoke balanced, and the complex right rotator has left-yoke reciprocity.

[0187] Two types of quasi-complex powers of complex pure resistance networks: The remainder of the complex pure resistor network is quasi-power sine-conjugate balanced, the port is quasi-power sine-conjugate balanced, and the complex pure resistor two-port network has sine-conjugate reciprocity.

[0188] Two quasi-complex powers of complex pure reactance networks: The remainder of the complex pure reactance network is quasi-power negative yoke balanced, the port is quasi-power negative yoke balanced, and the complex pure reactance two-port network has negative yoke reciprocity.

[0189] The quasi-complex power of the interconverter: Rotator but The residual pseudo-power or port pseudo-power of the same extension single-phase circuit containing the gyrator is reversed and balanced. The gyrator has reverse reciprocity; but The residual pseudo-power or port pseudo-power of the homotopic single-phase circuit containing the Errachidia inverter is equally balanced, and the Errachidia inverter has equal reciprocity.

[0190] Two quasi-complex powers of the EI impedance network: The remainder of the Erratic impedance network is quasi-power equal-balanced, and the port is quasi-power equal-balanced. The Erratic impedance two-port network has equal-value reciprocity.

[0191] The quasi-power balance principle and reciprocity theorem are applicable to single-phase circuits, two-phase circuits, cluster circuits, complex circuits, as well as static circuits, steady-state circuits, and transient circuits.

[0192] The coupler also has an important port external network migration principle: the port external network can be equivalently migrated between the primary side and the secondary side. This principle can greatly simplify the analysis and calculation of the circuit. The equivalent migration of the coupler is as follows: Fig.23 shown.

[0193] The two-phase coupler or cluster coupler constructed with a single-phase coupler has very strong parameter transformation characteristics and complex signal operation functions, which greatly enhances the circuit's signal processing capabilities. For circuit networks containing couplers, the improvement of the applicability judgment method of the pseudo-power balance principle and the reciprocity theorem has greatly expanded the scope of application of the pseudo-power balance principle and the reciprocity theorem, which has great practical value. BRIEF DESCRIPTION OF THE DRAWINGS

[0194] Figure 1 Knowledge framework of circuits;

[0195] Figure 2 Classification of commonly used two-terminal components;

[0196] Figure 3 Relationship diagram of actual voltage source, actual current source and actual power supply;

[0197] Figure 4a , 4b , 4c, 4d Ideal proportional controlled sources: Graphic symbols for voltage-controlled voltage source, current-controlled current source, current-controlled voltage source, and voltage-controlled current source;

[0198] Figure 5a , 5b , 5c, 5d Graphic symbols of ideal integral controlled sources: voltage-integrating voltage source, current-integrating current source, current-integrating voltage source, voltage-integrating current source;

[0199] Figure 6a , 6b , 6c, 6d, 6e Ideal power controlled sources: voltage controlled power source, current controlled power source, power controlled voltage source, power controlled current source, graphic symbols of power controlled power source;

[0200] Figure 7 Graphical symbol for single-phase transformer;

[0201] Figure 8 Graphic symbol for single-phase converter;

[0202] Fig. 9 The structural level of the circuit;

[0203] Fig.10 Structural levels of circuits;

[0204] Fig.11The two-phase circuit forms a schematic diagram of a cluster circuit;

[0205] Fig.12a , 12b The cluster resistance formed by two single-phase resistors, the cluster conductance formed by two single-phase conductances;

[0206] Fig.13a , 13b Cluster reactance formed by two single-phase reactances, cluster susceptance formed by two single-phase susceptances;

[0207] Fig.14a , 14b The bundle impedance formed by two single-phase impedances, the bundle admittance formed by two single-phase admittances;

[0208] Fig.15 A single-phase inverter model constructed using a proportional controlled source;

[0209] Fig.16 A single-phase converter model constructed using a proportional controlled source;

[0210] Fig.17a , 17b The single-phase transformer is transformed into a single-phase controlled source;

[0211] Fig.18a , 18b The single-phase converter is transformed into a single-phase controlled source;

[0212] Fig.19 Graphical symbol for a two-phase transformer;

[0213] Fig. 20 Graphic symbol for a two-phase converter;

[0214] Fig.21a , 21b A two-phase transformer model constructed using a single-phase transformer;

[0215] Fig.22a , 22b A two-phase converter model constructed using a single-phase converter;

[0216] Fig.23 Schematic diagram of equivalent migration of port network of two-phase coupler;

[0217] Fig.24 A single-phase coconverter model constructed using a controlled source;

[0218] Fig.25 A single-phase inverter model constructed using a controlled source;

[0219] Fig.26 A single-phase gyrator model constructed using a controlled source;

[0220] Fig. 27A single-phase inverter model constructed using a controlled source;

[0221] Fig.28 A complex interconverter constructed using a single-phase interconverter;

[0222] Fig.29 Schematic diagram of equivalent migration of complex interconverter;

[0223] Fig.30 Complex interconverter equivalent migration example;

[0224] Fig.31 A complex interconverter constructed using a single-phase interconverter;

[0225] Fig.32 Schematic diagram of equivalent migration of complex interconverter;

[0226] Fig.33 Complex interconverter equivalent migration example;

[0227] Fig.34 An Ehrlich interconverter constructed using a single-phase interconverter;

[0228] Fig.35 An Ehrlich interconverter constructed using a single-phase interconverter. DETAILED DESCRIPTION

[0229] The present invention is described in detail below with reference to the accompanying drawings.

[0230] Example 1

[0231] Single-phase co-converter and single-phase inverter

[0232] The single-phase co-converter consists of a single-phase voltage-controlled voltage source with parameter α = ρ and a single-phase voltage-controlled voltage source with parameter β -1 =ρ single-phase current control current source cross-connected, the coupling relationship of the single-phase co-converter is Structure Fig.24 shown.

[0233] The single-phase inverter consists of a single-phase voltage-controlled voltage source with parameter α = ρ and a single-phase voltage-controlled voltage source with parameter β. -1 =-ρ single-phase current control current source cross-connection, the coupling relationship of the single-phase inverter is Structure Fig.25 shown.

[0234] Principle of equivalent migration of single-phase mutual transformer: the network connected to the port can be equivalently migrated between the two ports of the mutual transformer, and the structural topology does not change during the equivalent migration, that is, only the size of the parameter is changed during the equivalent migration, and the nature of the parameter, the network structure form and the connection direction are not changed.

[0235] Example 2

[0236] Single-phase gyrator and single-phase inverter

[0237] The single-phase gyrator consists of a single-phase current-controlled voltage source with parameter r = ρ and a single-phase current-controlled voltage source with parameter g. -1 =ρ single-phase current control voltage source cross-connected, the coupling relationship of the single-phase gyrator is Structure Fig.26 shown.

[0238] The single-phase inverter consists of a single-phase current-controlled voltage source with parameter r = ρ and a single-phase current-controlled voltage source with parameter g. -1 =-ρ single-phase current control voltage source cross-connected, the coupling relationship of the single-phase inverter is Structure Fig. 27 shown.

[0239] The equivalent migration principle of a single-phase converter: The network connected to the port can be equivalently migrated between the two ports of the converter. The structural topology changes during the equivalent migration. The structure of the network before and after the equivalent migration is in a dual relationship, that is, the equivalent migration will change the properties of the parameters and the structural form of the network, but will not change the connection direction. The equivalent migration principle of the converter is only applicable to planar circuits or spherical circuits.

[0240] Example 3

[0241] Complex interconverters and complex interconverters

[0242] The complex transformer consists of two parameters: The single-phase transformer and the two parameters are and The single-phase transformers are connected in series and cross-connected, and the coupling relationship of the complex transformer is Structure Fig.28 shown.

[0243] The equivalent migration principle of the complex transformer: the network connected to the port can be equivalently migrated between the two ports of the transformer. The structural topology does not change during the equivalent migration, that is, only the size of the parameter is changed during the equivalent migration, and the nature of the parameter, the network structure form and the connection direction are not changed. The equivalent migration diagram of the complex transformer port network is as follows: Fig.29 shown.

[0244] Equivalent migration relation table of complex transformer:

[0245]

[0246] The equivalent migration example of the complex transformer port network is as follows: Fig.30 shown.

[0247] The equivalent migration principle of the cotransformer: the ideal power supply and ideal meter, conversion element or component, two-terminal network and two-port network adjacent to the cotransformer can be equivalently migrated between the primary loop and the secondary loop of the cotransformer. During the migration, only the size of the parameter is changed, and the nature of the parameter, the network structure and the connection direction are not changed. When the ideal voltage source and ideal voltmeter migrate from the primary side to the secondary side When the ideal current source and ideal ammeter migrate from the primary side to the secondary side When the ideal voltage source and ideal voltmeter migrate from the secondary side to the primary side When the ideal current source and ideal current meter migrate from the secondary side to the primary side The resistance parameter of the conversion element or component when it migrates from the primary side to the secondary side or and Conductivity parameters or and Resistive parameters when the secondary side migrates to the primary side or and Conductivity parameters or and The open circuit and short circuit properties remain unchanged when the primary side migrates to the secondary side or the secondary side migrates to the primary side.

[0248] Equivalent migration principle of inverter: Similar to the equivalent migration principle of cotransformer, the voltage change and current change are one the same and the other opposite, and the resistance and conductance, inductance and capacitance, impedance and admittance change their positive and negative polarities during migration.

[0249] The complex interconverter consists of two parameters: The single-phase converter and the two parameters are and The single-phase converters are connected in series in a cross-connection manner, and the coupling relationship of the complex converter is Structure Fig.31 shown.

[0250] The equivalent migration principle of complex interconverters: The network connected to the port can be equivalently migrated between the two ports of the interconverter. During the equivalent migration, the structural topology changes. The structure of the network before and after the equivalent migration is in a dual relationship, that is, the equivalent migration will change the nature of the parameters and the structural form of the network, but will not change the connection direction. The equivalent migration principle of the interconverter is only applicable to planar circuits or spherical circuits. The equivalent migration diagram of the port network of the complex interconverter is shown in the figure below. Fig.32 shown.

[0251] Equivalent migration relation table of complex interconverter:

[0252]

[0253] The equivalent migration example of the multiplexer port network is as follows: Fig.33 shown.

[0254] The equivalent migration principle of the gyrator: the ideal power supply and ideal meter, conversion element or component, two-terminal network and two-port network adjacent to the gyrator can be equivalently migrated between the primary loop and the secondary loop of the gyrator. The migration not only changes the size of the parameter, but also changes the nature of the parameter and the topological structure of the network. The ideal current source and ideal ammeter become ideal voltage source and ideal voltmeter when they migrate from the primary side to the secondary side. The ideal voltage source and ideal voltmeter become ideal current source and ideal ammeter when they migrate from the primary side to the secondary side. The ideal current source and ideal ammeter become ideal voltage source and ideal voltmeter when they migrate from the secondary side to the primary side. The ideal voltage source and ideal voltmeter become ideal current source and ideal ammeter when they migrate from the secondary side to the primary side. When the conductance migrates from the primary side to the secondary side, it becomes resistance. When resistance migrates from the primary side to the secondary side, it becomes conductance. When the capacitor migrates from the primary side to the secondary side, it becomes an inductor. When the inductor migrates from the primary side to the secondary side, it becomes a capacitor. When the admittance migrates from the primary side to the secondary side, it becomes impedance When the impedance moves from the primary side to the secondary side, it becomes admittance. During migration, the open circuit becomes a short circuit, and the short circuit becomes an open circuit. When the circuit network migrates from the primary side to the secondary side, its topological structure changes in a dual way: series and parallel are interchanged, triangular and triangle are interchanged, and nodes and meshes are interchanged. However, the energy input and output direction of each element remains unchanged when migrating between the secondary side and the primary side, or the reference direction relative to the rotator remains unchanged.

[0255] The equivalent migration principle of the inverter is similar to the equivalent migration principle of the gyrator. The voltage-to-current and current-to-voltage are the same and the other is opposite. The positive and negative polarities of resistance and conductance, inductance and capacitance, impedance and admittance change during the migration transformation.

[0256] Example 4

[0257] Erwin Transformer and Erwin Transformer

[0258] The interconverter consists of two parameters: and The single-phase transformer and the two parameters are The single-phase transformers are connected in series and cross-connected. The coupling relationship of the transformer is: Structure Fig.34 shown.

[0259] The principle of equivalent migration of the interconverter: the network connected to the port can be equivalently migrated between the two ports of the interconverter, and the structural topology does not change during the equivalent migration, that is, only the size of the parameter is changed during the equivalent migration, and the nature of the parameter, the network structure form and the connection direction are not changed.

[0260] Equivalent migration relationship table of Einstein interconverter:

[0261]

[0262] The interconverter consists of two parameters: and The single-phase converter and the two parameters are The single-phase converters are connected in series in a cross-series manner. The coupling relationship of the Ehrlich-Holstein converter is: Structure Fig.35 shown.

[0263] The equivalent migration principle of the interconverter: the network connected to the port can be equivalently migrated between the two ports of the interconverter. The structural topology changes during the equivalent migration. The structure of the network before and after the equivalent migration is in a dual relationship, that is, the equivalent migration will change the properties of the parameters and the structural form of the network, but will not change the connection direction. The equivalent migration principle of the interconverter is only applicable to planar circuits or spherical circuits.

[0264] Equivalent migration relation table of Erwin converter:

[0265]

[0266] Example 5

[0267] Applicability judgment of quasi-power balance principle and reciprocity theorem

[0268] Tongtuo circuit has two types of pseudo power: red pseudo power and green pseudo power.

[0269] Red pseudo power: the branch voltage of the first circuit multiplied by the corresponding branch current of the second circuit;

[0270] Green pseudo power: the branch voltage of the second circuit multiplied by the corresponding branch current of the first circuit;

[0271] Total pseudo-power: the algebraic sum of the red pseudo-power or green pseudo-power of all branches;

[0272] Residual pseudo-power: the algebraic sum of the red pseudo-power or green pseudo-power of all branches of the remaining same circuit after removing the same port network;

[0273] Port pseudo power: the algebraic sum of the port red pseudo power or port green pseudo power of the same port network.

[0274] The forms of pseudo-power balance: arbitrary balance, that is, the green pseudo-power and the red pseudo-power are both zero or equal and opposite, two special cases: equal balance, that is, the green pseudo-power and the red pseudo-power are equal, and opposite balance, that is, the green pseudo-power and the red pseudo-power are opposite.

[0275] The forms of reciprocity in a two-port network: arbitrary reciprocity means that the port quasi-power of the two-port network is arbitrarily balanced, and there are two special cases: equal reciprocity means that the port quasi-power of the two-port network is equal-balanced, and inverse reciprocity means that the port quasi-power of the two-port network is inversely balanced.

[0276] The reciprocity of a two-port network, i.e., the quasi-power balance of two-port network ports, is a special case of quasi-power balance.

[0277] The total pseudo power of the Tongtuo circuit can be balanced arbitrarily;

[0278] The remaining pseudo-power of the cotransformer or the pseudo-power of the port can be arbitrarily balanced or reciprocal;

[0279] The gyrator residual pseudo-power or port pseudo-power is inversely balanced or reciprocally reversed;

[0280] The residual pseudo-power of the inverter or the pseudo-power of the port is balanced or reciprocal;

[0281] The remainder pseudo-power or port pseudo-power of a pure resistance network is equally balanced or reciprocally equivalent.

[0282] Example 6

[0283] Applicability judgment of quasi-complex power balance principle and complex reciprocity theorem

[0284] There are two types of quasi-complex power in the same extension circuit: red quasi-complex power and green quasi-complex power.

[0285] Red quasi-complex power: the branch voltage of the first circuit multiplied by the conjugate of the corresponding branch current of the second circuit;

[0286] Green quasi-complex power: the branch voltage of the second circuit multiplied by the conjugate of the corresponding branch current of the first circuit;

[0287] Total quasi-complex power: the algebraic sum of the red quasi-complex power or green quasi-complex power of all branches;

[0288] Remaining quasi-complex power: the algebraic sum of the red quasi-complex power or green quasi-complex power of all branches of the remaining same topology circuit after removing the same port network;

[0289] Port quasi-complex power: the algebraic sum of the red quasi-complex power or the green quasi-complex power of the same port network.

[0290] The forms of quasi-complex power balance in cluster circuits: arbitrary balance, that is, the green quasi-complex power and the red quasi-complex power are both zero or equal and opposite or positive conjugate and negative conjugate, two special cases: proportional balance, that is, the green quasi-complex power and the red quasi-complex power are in any proportion, conjugate balance, that is, the green quasi-complex power and the conjugate of the red quasi-complex power are in any proportion, four special cases of proportional balance: equal balance, that is, the green quasi-complex power and the red quasi-complex power are equal, inverse balance, that is, the green quasi-complex power and the red quasi-complex power are opposite, left-fold balance, that is, the green quasi-complex power and the red quasi-complex power multiplied by κ are equal, right-fold balance, that is, the green quasi-complex power and the red quasi-complex power multiplied by κ are opposite, four special cases of conjugate balance: positive conjugate balance, that is, the conjugate of the green quasi-complex power and the red quasi-complex power are equal, negative conjugate balance, that is, the green quasi-complex power and the red quasi-complex power are opposite, left-conjugate balance, that is, the green quasi-complex power and the red quasi-complex power conjugate multiplied by κ are equal, right-conjugate balance, that is, the green quasi-complex power and the red quasi-complex power conjugate multiplied by κ are opposite.

[0291] The forms of reciprocity in a two-port network: arbitrary reciprocity, two special cases: proportional reciprocity and conjugate reciprocity, four special cases of proportional reciprocity: equal value reciprocity, inverse value reciprocity, left-folding reciprocity and right-folding reciprocity, four special cases of conjugate reciprocity: positive conjugate reciprocity, negative conjugate reciprocity, left-folding reciprocity and right-folding reciprocity.

[0292] Reciprocity of two-port networks, i.e., quasi-complex power balance of two-port network ports, is a special case of quasi-complex power balance.

[0293] The total quasi-complex power of the same extension circuit can be balanced arbitrarily;

[0294] The remaining quasi-complex power of the complex cotransformer or the quasi-complex power of the port is arbitrarily balanced or arbitrarily reciprocal;

[0295] The quasi-complex power of the rest of the gyrator or the quasi-complex power of the port negative yoke balance or negative yoke reciprocity;

[0296] The quasi-complex power of the remainder of the complex inverter or the quasi-complex power of the port is yoke balanced or yoke reciprocal;

[0297] The remaining quasi-complex power of the left-hand rotator or the quasi-complex power of the port is right yoke balanced or right yoke reciprocal;

[0298] The remaining quasi-complex power of the right-hand converter or the quasi-complex power of the port is balanced on the left yoke or reciprocal on the left yoke;

[0299] The remainder of the complex pure resistance network is quasi-complex power or the port is quasi-complex power yoke balance or yoke reciprocity;

[0300] The remainder of the complex pure reactance network is quasi-complex power or the port is quasi-complex power, negative yoke balance or negative yoke reciprocity;

[0301] The quasi-complex power of the remaining part of the gyrator or the quasi-complex power of the port is balanced or reciprocated;

[0302] The quasi-complex power of the remaining part of the inverter or the quasi-complex power of the port is balanced or reciprocal;

[0303] The remainder quasi-complex power of the bad impedance network or the quasi-complex power of the port is equally balanced or equally reciprocal.

Claims

1. A single-phase coupler having a primary port and a secondary port; characterized in that: The single-phase coupler consists of a proportional controlled source and is of two types: single-phase and single-phase converters; The single-phase inverter consists of a voltage-controlled voltage source u2 = αu1 and a current-controlled current source i1 = β -1 i2, the control input port of the voltage-controlled voltage source, i.e., the voltage inductor u1, and the power output port of the current-controlled current source, i.e., the controlled current source i1, are connected in parallel as the primary port of the single-phase inverter, and the control input port of the current-controlled current source, i.e., the current inductor i2, and the power output port of the voltage-controlled voltage source, i.e., the controlled voltage source u2, are connected in series as the secondary port of the single-phase inverter; Or a single-phase inverter is controlled by a voltage source u1 = α -1 u2 and a current-controlled current source i2 = βi1, the control input port of the current-controlled current source, i.e., the current sensor i1, and the power output port of the voltage-controlled voltage source, i.e., the controlled voltage source u1, are connected in series as the primary port of the single-phase inverter, and the control input port of the voltage-controlled voltage source, i.e., the voltage sensor u2, and the power output port of the current-controlled current source, i.e., the controlled current source i2, are connected in parallel as the secondary port of the single-phase inverter; the parameters of the single-phase inverter are: The control relationship is The single-phase converter consists of two current-controlled voltage sources u2 = ri1 and u1 = g -1 i2, the control input port of the first current-controlled voltage source, i.e., the current sensor i1, and the power output port of the second current-controlled voltage source, i.e., the controlled voltage source u1, are connected in series as the primary port of the single-phase converter, and the control input port of the second current-controlled voltage source, i.e., the current sensor i2, and the power output port of the first current-controlled voltage source, i.e., the controlled voltage source u2, are connected in series as the secondary port of the single-phase converter; or the single-phase converter is composed of two voltage-controlled current sources i1=r -1 u2 and i2 = gu1, the control input port of the second voltage-controlled current source, i.e., the voltage sensor u1, and the power output port of the first voltage-controlled current source, i.e., the controlled current source i1, are connected in parallel as the primary port of the single-phase converter, and the control input port of the first voltage-controlled current source, i.e., the voltage sensor u2, and the power output port of the second voltage-controlled current source, i.e., the controlled current source i2, are connected in parallel as the secondary port of the single-phase converter; the parameters of the single-phase converter are: The control relationship is 2. The single-phase coupler according to claim 1, characterized in that: The single-phase inverter, αβ=1 is a single-phase co-inverter, and αβ=-1 is a single-phase inverter or a single-phase flyback inverter; The single-phase converter described above, rg=1 is a single-phase rotator, and rg=-1 is a single-phase converter or a single-phase return rotator.

3. A cluster coupler comprising the single-phase coupler of claim 1, having a primary side complex port and a secondary side complex port; characterized in that: The cluster coupler is composed of the single-phase coupler and has two types: cluster interconverter and cluster interconverter; The transformer consists of four parameters: α 11 / β 11 , α 12 / β 12 , α 21 / β 21 , α 22 / β 22 The single phase transformer is composed of 11 / β 11 The primary port of the single-phase inverter α 12 / β 12 The primary side ports of the transformer are connected in parallel to form the first primary side port of the transformer. 21 / β 21 The primary port of the single-phase inverter α 22 / β 22 The primary side ports of the transformer are connected in parallel to form the second primary side port of the transformer, and the two primary side ports of the transformer are combined into a primary side complex port; the single-phase transformer α 11 / β 11 The secondary port of the single-phase inverter α 21 / β 21 The secondary ports of the transformer are connected in series to form the first secondary port of the transformer. 12 / β 12 The secondary port of the single-phase inverter α 22 / β 22 The secondary side ports of the transformer are connected in series to form the second secondary side port of the transformer, and the two secondary side ports of the transformer are combined into a secondary side complex port; The control relationship of the cluster transformer thus formed is: The parameters are: in: Or the primary ports of the single-phase transformers constituting the cluster transformer are connected in series and the secondary ports are connected in parallel; The control relationship of the cluster transformer thus formed is: The parameters are: in: The bundle interconverter consists of four parameters: 11 / g 11 、r 12 / g 12 、r 21 / g 21 、r 22 / g 22 The single-phase converter is composed of 11 / g 11 The primary port of the single-phase converter 12 / g 12 The primary side ports of the cascaded converter form the first primary side port of the cluster converter. 21 / g 21 The primary port of the single-phase converter 22 / g 22 The primary ports of the single-phase converter are connected in series to form the second primary port of the cluster converter, and the two primary ports of the cluster converter are combined into a primary complex port; 11 / g 11 The secondary port of the single-phase converter 21 / g 21 The secondary ports of the 1st secondary port of the cluster converter are connected in series to form the first secondary port of the single-phase converter. 12 / g 12 The secondary port of the single-phase converter 22 / g 22 The secondary side ports of the cluster interconverter are connected in series to form the second secondary side port of the cluster interconverter, and the two secondary side ports of the cluster interconverter are combined into a secondary side complex port; The control relationship of the cluster converter thus formed is: The parameters are: in: Or the primary side ports and secondary side ports of the single-phase converters constituting the cluster converter are connected in parallel; The control relationship of the cluster converter thus formed is: The parameters are: in:

4. The cluster coupler according to claim 3, characterized in that: The plexi transformer, Right now For complex interconverter, Right now For the interconverter, Right now or Right now It is a transformer; The cluster interconverter, Right now is a complex interconverter, Right now For the interconverter, Right now or Right now It is a mutual converter.

5. The cluster coupler according to claim 4, characterized in that: The complex interconverter is a complex covariant, For complex inverter, It is a complex left inverter, It is a complex right inverter; The Ehrlich interconverter is an Eichhorn covariant, For the inverter, It is an Erzograndiator. It is the right converter; The complex interconverter For the revolver, For the complex inverter, It is a left turner. It is a right turner; The Ehrlich interconverter For the rotator, For the reverse device, It is a left turner. It is a right turner.

6. A single-phase circuit pseudo-power balance principle and a two-port network reciprocity theorem adaptation method using the single-phase coupler of claim 1 or 2, which is applicable not only to DC circuits but also to general static circuits; characterized in that: Step 1: Pseudo power balance of single-phase circuit: ∑u bk i ak =p TG =δp TR =δ∑u ak i bk , the classification feature δ is any real number, that is, any balance; when δ = 1, p TG =p TR The two pseudo powers of the same extension circuit are equal, and the pseudo power balance is equal value balance; when δ = -1, p TG =-p TR The two pseudo powers of the same extension circuit are opposite, and the pseudo power balance is the opposite value balance; the two total pseudo powers of the same extension single-phase circuit are both equal and opposite, and the total pseudo power is both equal value balance and opposite value balance, that is, arbitrary balance; Step 2: the residual pseudo power of the cotransformer or the pseudo power of the port is both equally balanced and inversely balanced, i.e., arbitrarily balanced; the residual pseudo power of the gyrator or the pseudo power of the port is inversely balanced; the residual pseudo power of the inverter or the pseudo power of the port is equally balanced; and the residual pseudo power of the pure resistance network or the pseudo power of the port is equally balanced; Step 3: Reciprocity forms of two-port networks: arbitrary reciprocity, equal reciprocity and inverse reciprocity; Arbitrary reciprocity: u b1 i a1 +u b2 i a2 =p G =δ pR =δ(u a1 i b1 +u a2 i b2 ), δ is any real number, that is, the two-port pseudo-power of the two ports of the two-port network is arbitrarily balanced; equivalent reciprocity: δ = 1, that is, u b1 i a1 +u b2 i a2 =p G =p R =u a1 i b1 +u a2 i b2 The two ports of a two-port network have equal quasi-power; Inverse reciprocity: δ = -1, i.e. u b1 i a1 +u b2 i a2 =p G =-p R =-u a1 i b1 -u a2 i b2 The two ports of the two-port network have opposite quasi-powers; the covariant is both equivalent and inversely reciprocal, i.e., arbitrarily reciprocal; the gyrator is inversely reciprocal; the inverter is equivalent and reciprocal; and the pure resistance two-port network is equivalent and reciprocal.

7. A method for applying the quasi-complex power balance principle of a cluster circuit and the complex reciprocity theorem of a cluster two-port network using the cluster coupler of claim 3, 4 or 5, which is applicable not only to DC circuits but also to general steady-state circuits; characterized in that: Step 1: Simulate power balance of the same extension circuit: Classification feature is any cluster number, that is, any balance; it includes two special cases of quasi-complex power balance: Proportional balance and Conjugate balance; proportional balance: when When When It is left-bend equilibrium when When , it is right-hand equilibrium; conjugate equilibrium: when When When The left yoke is balanced when When , it is right yoke balanced; the total quasi-complex power of the same topology circuit is both proportionally balanced and conjugate balanced, that is, arbitrary balanced; The second step: the residual quasi-complex power of the complex cotransformer or the quasi-complex power of the port is both proportionally balanced and conjugate balanced, that is, arbitrarily balanced, the residual quasi-complex power of the complex gyrator or the quasi-complex power of the port is negatively yoke balanced, the residual quasi-complex power of the complex invertor or the quasi-complex power of the port is positively yoke balanced, the residual quasi-complex power of the complex left rotator or the quasi-complex power of the port is right yoke balanced, the residual quasi-complex power of the complex right rotator or the quasi-complex power of the port is left yoke balanced, the residual quasi-complex power of the complex pure resistance network or the quasi-complex power of the port is positively yoke balanced, and the residual quasi-complex power of the complex pure reactance network or the quasi-complex power of the port is negatively yoke balanced; The residual quasi-complex power of the Errachidia gyrator or the quasi-complex power of the port is inversely balanced, the residual quasi-complex power of the Errachidia inverter or the quasi-complex power of the port is equally balanced, and the residual quasi-complex power of the Errachidia impedance network or the quasi-complex power of the port is equally balanced; Step 3: Reciprocity forms of the two-port network: arbitrary reciprocity, proportional reciprocity and conjugate reciprocity, arbitrary reciprocity: For any number of clusters, the quasi-complex power of the two ports of the two-port network can be balanced arbitrarily; the ratio is reciprocal There are four types: equal value reciprocity and inverse value reciprocity, left fold reciprocity and right fold reciprocity, conjugate reciprocity There are four types: positive yoke reciprocity and negative yoke reciprocity, left yoke reciprocity and right yoke reciprocity; equivalent reciprocity: Right now Reciprocity of inverse value: Right now Left-fold reciprocity: Right now Right fold reciprocity: Right now Yoke reciprocity: Right now Yoked reciprocity: Right now Left yoke reciprocity: Right now Right yoke reciprocity: Right now The complex covariant is both proportionally reciprocal and conjugately reciprocal, i.e., arbitrarily reciprocal; the complex gyrator has negative yoke reciprocity, the complex inverter has positive yoke reciprocity, the complex left gyrator has right yoke reciprocity, the complex right gyrator has left yoke reciprocity, the positive yoke of the complex pure resistance two-port network is reciprocal, and the negative yoke of the complex pure reactance two-port network is reciprocal; the Erratic gyrator has anti-value reciprocity, the Erratic inverter has equivalent reciprocity, and the Erratic impedance two-port network has equivalent reciprocity.

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