CN101719671A

CN101719671A - Method for analyzing structural properties of RLC electric network

Info

Publication number: CN101719671A
Application number: CN200910244973A
Authority: CN
Inventors: 王宗涛
Original assignee: Tianjin University of Technology
Current assignee: Tianjin University of Technology
Priority date: 2009-12-22
Filing date: 2009-12-22
Publication date: 2010-06-02

Abstract

The invention relates to a method for analyzing structural properties of an RLC electric network, which has the functions of drawing the graph of an electric network, analyzing a topological structure of the electric network, generating a state equation and an output equation, analyzing the structural properties of the electric network, simulating the electric network and the like. The aim of drawing the graph of the electric network is to draw the graph of the RLC electric network to be analyzed; the function of analyzing the topological structure of the electric network can realize the selection of branches and links, and number the selected branches and links; the state equation and the output equation of the electric network can be obtained after the selection of a state variable; the structural properties (controllability and observability) can be analyzed according to the state equation and the output equation; and the function of simulating the electric network can realize the simulation of a specific electric network. The method has the advantages that: by adopting the symbolic operation of the electric network, the structural performance of the electric network can be directly analyzed, which is universal; and the simulation of the electric network can be implemented when elements of the electric network are endowed with detail parameters.

Description

A Method for Analyzing the Structural Properties of RLC Electrical Networks

【技术领域】：本发明属于电网络和自动控制技术领域。本发明通过对电网络拓扑结构的分析，可以得到电网络的结构性质(如能控性和能观性等)。本方法提供了电网络拓扑结构(包括节点、树枝、连支的确定)的分析方法、状态变量的选择方法、状态方程和输出方程的生成方法、电网络结构性质的分析方法以及电网络仿真的方法。[Technical Field]: The present invention belongs to the technical field of electric network and automatic control. The present invention can obtain the structural properties (such as controllability and observability, etc.) of the electric network by analyzing the topological structure of the electric network. This method provides the analysis method of electrical network topology (including the determination of nodes, branches, and connections), the selection method of state variables, the generation method of state equation and output equation, the analysis method of electrical network structure properties, and the method of electrical network simulation. method.

【背景技术】：以前人们对电网络性质的研究主要是基于实数域研究，即电网络中的元件都是有具体的参数值。这样虽然可以分析网络的性质，但由于直接采用电网络中的参数计算，往往得到的只是特定电网络的结论，对于电网络的结构性质不具备普遍性，因而研究电网络的结构性质需要另外寻找方法。如果不赋予电网络具体的参数值，而是直接采用符号运算，这样得到的结论与具体的参数就没有关系，而仅仅与电网络的结构有关。这样就可以从结构上去研究电网络，适用于分析电网络的结构性能。基于该方法，可以进行电网络拓扑结构(包括节点、树枝、连支的确定)分析、状态变量选择、状态方程和输出方程的生成、电网络结构性质的分析以及电网络仿真。目前电路方面的设计软件主要有Protel、Orcad、Viewlogic、Mentor Graphics等，它们主要应用于电路设计，并不能分析电网络的结构性质。Pspice可以实现电网络图形绘制和数值计算，但它同样不能进行电网络的结构性质分析。[Background Technology]: Previously, people's research on the properties of electrical networks was mainly based on real number field research, that is, the components in the electrical network have specific parameter values. Although the properties of the network can be analyzed in this way, due to the direct calculation of the parameters in the electrical network, the conclusions of the specific electrical network are often obtained, which is not universal for the structural properties of the electrical network, so the study of the structural properties of the electrical network requires additional research. method. If you do not assign specific parameter values to the electrical network, but directly use symbolic operations, the conclusions obtained in this way have nothing to do with specific parameters, but only with the structure of the electrical network. In this way, the electrical network can be studied from the structure, which is suitable for analyzing the structural performance of the electrical network. Based on this method, the analysis of electrical network topology (including the determination of nodes, branches, and connections), the selection of state variables, the generation of state equations and output equations, the analysis of electrical network structure properties, and electrical network simulation can be performed. At present, the circuit design software mainly includes Protel, Orcad, Viewlogic, Mentor Graphics, etc. They are mainly used in circuit design, and cannot analyze the structural properties of electrical networks. Pspice can realize electrical network graphics drawing and numerical calculation, but it also cannot analyze the structural properties of electrical network.

【发明内容】：本发明目的是克服现有技术存在的上述不足，提供一种RLC电网络结构性质的分析方法，该方法基于电网络元件的符号运算来进行结构性质分析。基于该方法，可以绘制电网络图形、可以进行电网络拓扑结构(包括节点、树枝、连支的确定)分析、状态方程和输出方程的生成、电网络结构性质的分析以及电网络仿真。[Summary of the invention]: The purpose of the present invention is to overcome the above-mentioned deficiencies in the prior art, and provide a method for analyzing the structural properties of an RLC electrical network. The method analyzes the structural properties based on the symbolic operation of the electrical network components. Based on this method, it is possible to draw electrical network graphs, analyze electrical network topology (including the determination of nodes, branches, and connections), generate state equations and output equations, analyze electrical network structural properties, and perform electrical network simulation.

本发明所述的“电网络”是指电器元件的相互连接，在本发明中仅仅研究集总参数网络，不涉及偏微分方程或者差分方程。得到的电网络系统方程不含积分，是一阶微分方程组。可以设定电压器电压的初值(全电容器回路除外)和电感器电流的初值(全电感器割集除外)。从拓扑结构上讲，树支电压是所有电压的基底，我们尽可能地把电容器置于树枝中。对于所有的支路电流，连支电流是基底，我们尽可能地把电感器置于连支中。所有的电压源按树支处理，所有的电流源按连支处理。当电网络中出现了全电容器回路，则将其中一个电容器设置为连支；当电网络中出现全电感器割集，则将其中一个电感器设置为树支。The "electrical network" mentioned in the present invention refers to the interconnection of electrical components. In the present invention, only lumped parameter networks are studied, and partial differential equations or differential equations are not involved. The obtained electrical network system equations do not contain integrals and are first-order differential equations. The initial value of the voltage of the voltage transformer (except the full capacitor circuit) and the initial value of the inductor current (except the full inductor cut set) can be set. Topologically speaking, the branch voltage is the base of all voltages, and we place capacitors in the branches as much as possible. For all branch currents, the tie current is the base, and we place the inductor in the tie as much as possible. All voltage sources are treated as tree branches, and all current sources are treated as connected branches. When a full capacitor loop appears in the electrical network, one of the capacitors is set as a connected branch; when a full inductor cut set appears in the electrical network, one of the inductors is set as a tree branch.

本发明提供的RLC电网络结构性质的分析方法，通过绘制电网络图形和电网络拓扑分析，生成电网络的状态方程和输出方程，从而进行电网络控制性能分析和电网络仿真；本方法通过对电网络的拓扑结构性质分析来研究电网络的结构性质，从而为研究电网络结构性质的研究提供了新的途径；该方法具体包括：The method for analyzing the structural properties of the RLC electrical network provided by the present invention generates state equations and output equations of the electrical network by drawing electrical network graphics and analyzing the topology of the electrical network, thereby performing electrical network control performance analysis and electrical network simulation; The analysis of the topological structure properties of the electrical network is used to study the structural properties of the electrical network, thus providing a new way for the study of the structural properties of the electrical network; the method specifically includes:

第一、绘制待分析的电网络图形；First, draw the electrical network graph to be analyzed;

第二、进行拓扑分析，拓扑分析的方法及内容包括：Second, perform topology analysis. The methods and contents of topology analysis include:

1)在电网络中统一规定了电压的参考方向；对于电阻、电容、电感等元件，当元器件水平放置时左为正、右为负，当元器件垂直放置时上为正、下为负；对于电压源、电流源元件，默认电压参考方向与电压源、电流源的放置位置一致；1) The reference direction of the voltage is uniformly specified in the electrical network; for components such as resistors, capacitors, and inductors, when the components are placed horizontally, the left is positive and the right is negative; when the components are placed vertically, the upper is positive and the lower is negative. ;For voltage source and current source components, the default voltage reference direction is consistent with the placement position of voltage source and current source;

2)在绘制电网络完成以后，接下来进行拓扑结构分析，首先得到一个树，确定树支和连支。默认电压源、电容器为树支，电流源、电感器为连支；当存在全电容器回路，则将其中一个电容器设置为连支；当存在全电感器割集，则将其中一个电感器设置为树支；电阻器默认为连支，然后查询电阻两端是否存在树支通路，如果不存在树支通路则将电阻设置为树支；2) After the drawing of the electrical network is completed, the topological structure analysis is carried out next. First, a tree is obtained, and the branches and connected branches of the tree are determined. By default, the voltage source and capacitor are tree branches, and the current source and inductor are connected branches; when there is a full capacitor circuit, one of the capacitors is set as a connected branch; when there is a full inductor cut set, one of the inductors is set as Tree branch; the resistor is connected by default, then check whether there is a tree branch path at both ends of the resistor, if there is no tree branch path, set the resistor as a tree branch;

3)编写一个回路矩阵或割集矩阵时，先进行树支和连支编号；在拓扑结构关系中，设置了电压和电流向量的分块，并编写了基本回路矩阵的基尔霍夫电压方程和基本割集的基尔霍夫电流方程。3) When writing a loop matrix or a cut-set matrix, number the tree branches and connected branches first; in the topology relationship, set the division of voltage and current vectors, and write the Kirchhoff voltage equation of the basic loop matrix and Kirchhoff's current equations for elementary cut sets.

第三、生成状态方程和输出方程，具体方法是：选择树枝电容和连支电感作为状态变量，输出变量根据需要进行选择。Third, generate the state equation and the output equation, the specific method is: select the branch capacitance and the connection inductance as the state variables, and select the output variables according to the needs.

第四、进行结构性质分析，具体方法是：本方法中的结构性质主要是指结构能控性和结构能观性。通过能控性矩阵T_c＝[B A*B]，进行计算电网络的结构是否可控，这里A、B指的是电网络方程的系数矩阵；通过能观性矩阵T_o＝[C；C*A]，进行计算电网络的输出是否可观，这里C指的是电网络输出方程的系数矩阵。Fourth, analyze the structural properties. The specific method is: the structural properties in this method mainly refer to the controllability and observability of the structure. Through the controllability matrix T _c =[B A*B], calculate whether the structure of the electrical network is controllable, where A and B refer to the coefficient matrix of the electrical network equation; through the observability matrix T _o =[C;C *A] to calculate whether the output of the electrical network is considerable, where C refers to the coefficient matrix of the output equation of the electrical network.

第五、进行电网络仿真；Fifth, conduct electrical network simulation;

在本方法中，电网络分析采用了符号，避免了具体参数值的参与，因而分析的结果具有一般性，代表了电网络的结构性质；同时本方法可以实现电网络仿真，把具体的参数值代进去第四步中的状态方程和输出方程，就可以得到特定参数电网络的结构性质。In this method, symbols are used in the electrical network analysis, which avoids the participation of specific parameter values, so the analysis results are general and represent the structural properties of the electrical network; at the same time, this method can realize electrical network simulation, and the specific parameter values By substituting the state equation and output equation in the fourth step, the structural properties of the electrical network with specific parameters can be obtained.

在上述第四步和第五步中，在电网络进行符号运算后，得到的结构性质不会因为参数的改变而发生改变，而在电网络仿真中，结构性质同时取决于电网络结构和电网络元件参数。In the fourth and fifth steps above, after the symbolic operation of the electrical network, the obtained structural properties will not change due to the change of parameters, while in the electrical network simulation, the structural properties depend on both the electrical network structure and the electrical network structure. Network element parameters.

第六、给出分析结果。Sixth, give the analysis results.

上述几个步骤是一个整体，绘制待分析的电网络图形的目的在于分析电网络的结构性质，并规定了电压的参考方向。拓扑分析的关键在于选择一个树，拓扑分析为状态方程的生成提供基础。在生成状态方程时，需要设定状态变量和输出变量，本方法对状态变量进行了约定，而输出变量则根据需要进行选择。通过能控性矩阵T_c＝[B A*B]，可以计算出电网络的结构是否可控；通过能观性矩阵T_o＝[C；C*A]，可以计算出电网络的输出是否可观。电网络仿真的目的在于验证具体的电网络，把电网络元件的参数值输入进去可以得到特定参数电网络的结构性质。The above steps are a whole. The purpose of drawing the graph of the electrical network to be analyzed is to analyze the structural properties of the electrical network and specify the reference direction of the voltage. The key of topology analysis is to choose a tree, and topology analysis provides the basis for the generation of state equations. When generating the state equation, the state variables and output variables need to be set. This method stipulates the state variables, and the output variables are selected according to the needs. Through the controllability matrix T _c =[B A*B], it can be calculated whether the structure of the electrical network is controllable; through the observability matrix T _o =[C; C*A], it can be calculated whether the output of the electrical network is observable . The purpose of the electrical network simulation is to verify the specific electrical network, and the structural properties of the electrical network with specific parameters can be obtained by inputting the parameter values of the electrical network components.

本发明的优点和积极效果：Advantage and positive effect of the present invention:

本发明的优越性在于：采用电网络符号运算，可以直接分析电网络的结构性能，具有普遍性；在赋予电网络元件具体参数时可以实现电网络的模拟。The advantage of the present invention is that: the structural performance of the electrical network can be directly analyzed by adopting the electrical network symbol operation, which has universality; the simulation of the electrical network can be realized when specific parameters are assigned to the electrical network components.

【附图说明】：[Description of drawings]:

图1是电网络结构性质的分析方法的流程图。Figure 1 is a flowchart of a method for analyzing structural properties of electrical networks.

图2是电网络示意图。Figure 2 is a schematic diagram of the electrical network.

图3是电网络拓扑分析。Figure 3 is an electrical network topology analysis.

图4是状态方程显示及能控性分析。Figure 4 shows the state equation display and controllability analysis.

【具体实施方式】：【Detailed ways】:

实施例1：Example 1:

(1)绘制待分析的电网络(如图2所示)，其结构具有一定的对称性，右边的两个支路分别具有一个电阻元件和一个电容元件。通过本案例的分析将说明本方法在电网络结构性质分析中的优越性。(1) Draw the electrical network to be analyzed (as shown in Figure 2), its structure has a certain symmetry, and the two branches on the right have a resistive element and a capacitive element respectively. The analysis of this case will illustrate the superiority of this method in the analysis of electrical network structure properties.

(2)进行拓扑分析(图3)(2) Perform topology analysis (Figure 3)

1)在电网络中统一规定了电压的参考方向。对于电阻、电容、电感等元件，当元器件水平放置时左为正、右为负，当元器件垂直放置时上为正、下为负。对于电压源、电流源元件，默认电压参考方向与电压源、电流源的放置位置一致。1) The reference direction of the voltage is uniformly specified in the electrical network. For components such as resistors, capacitors, and inductors, when the components are placed horizontally, the left is positive and the right is negative. When the components are placed vertically, the top is positive and the bottom is negative. For voltage source and current source components, the default voltage reference direction is consistent with the placement of the voltage source and current source.

2)默认电压源、电容器为树支，电流源、电感器为连支；当存在全电容器回路，则将其中一个电容器设置为连支；当存在全电感器割集，则将其中一个电感器设置为树支；电阻器默认为连支，然后查询电阻两端是否存在树支通路，如果不存在树支通路则将电阻设置为树支。2) By default, the voltage source and capacitor are tree branches, and the current source and inductor are connected branches; when there is a full capacitor loop, set one of the capacitors as a connected branch; when there is a full inductor cut set, set one of the inductors Set it as a tree branch; the resistor is connected by default, and then check whether there is a tree branch path at both ends of the resistor. If there is no tree branch path, set the resistor as a tree branch.

3)编写一个回路矩阵或割集矩阵时，先对树支和连支编号。在拓扑结构关系中，设置了电压和电流向量的分块，并编写了基本回路矩阵的基尔霍夫电压方程和基本割集的基尔霍夫电流方程。3) When writing a circuit matrix or a cut set matrix, number the tree branches and connected branches first. In the topological structure relation, the division of voltage and current vectors is set, and the Kirchhoff voltage equation of the basic circuit matrix and the Kirchhoff current equation of the basic cut set are written.

根据上述说明，将电压源V1设置为树支、电容C1和C2设置为树支、所有电阻都默认为连支。由于电阻R1两端没有树支通路，因而设置R1为树支，而电阻R2和R3两端均形成了树支通路，因而仍然为连支。According to the above description, the voltage source V1 is set as a tree branch, the capacitors C1 and C2 are set as tree branches, and all resistors are defaulted as connected branches. Since there is no tree branch path at both ends of the resistor R1, R1 is set as a tree branch, and the tree branch paths are formed at both ends of the resistors R2 and R3, so they are still connected branches.

(3)生成状态方程和输出方程(图4)(3) Generate state equation and output equation (Figure 4)

由于电容C1和C2都位于树支上，因而程序将它们的电压都是状态变量并构成了状态向量。本例选择C1电流和C2电压作为输出变量。根据(2)的拓扑分析，程序给出了状态方程和输出方程：Since capacitors C1 and C2 are located on the branches, the program regards their voltages as state variables and constitutes a state vector. This example selects C1 current and C2 voltage as output variables. According to the topological analysis of (2), the program gives the state equation and output equation:

$[\begin{matrix} {\overset{\cdot &Center Dot;}{v v}}_{{C C}_{11}} \\ {\overset{\cdot &Center Dot;}{v v}}_{{C C}_{22}} \end{matrix}] = = [\begin{matrix} - - \frac{{R R}_{22} + + {R R}_{33}}{{C C}_{11} (({R R}_{11} {R R}_{22} + + {R R}_{22} {R R}_{33} + + {R R}_{11} {R R}_{33}))} & \frac{{R R}_{33}}{{C C}_{11} (({R R}_{11} {R R}_{22} + + {R R}_{22} {R R}_{33} + + {R R}_{11} {R R}_{33}))} \\ \frac{{R R}_{33}}{{C C}_{22} (({R R}_{11} {R R}_{22} + + {R R}_{22} {R R}_{33} + + {R R}_{11} {R R}_{33}))} & - - \frac{{R R}_{11} + + {R R}_{33}}{{C C}_{22} (({R R}_{11} {R R}_{22} + + {R R}_{22} {R R}_{33} + + {R R}_{11} {R R}_{33}))} \end{matrix}] [\begin{matrix} {v v}_{{C C}_{11}} \\ {v v}_{{C C}_{22}} \end{matrix}]$

$+ + [\begin{matrix} \frac{{R R}_{22}}{{C C}_{11} (({R R}_{11} {R R}_{22} + + {R R}_{22} {R R}_{33} + + {R R}_{11} {R R}_{33}))} \\ \frac{{R R}_{11}}{{C C}_{22} (({R R}_{11} {R R}_{22} + + {R R}_{22} {R R}_{33} + + {R R}_{11} {R R}_{33}))} \end{matrix}] {V V}_{11}$

$[\begin{matrix} {i i}_{{C C}_{11}} \\ {v v}_{{C C}_{22}} \end{matrix}] [\begin{matrix} - - \frac{{R R}_{22} + + {R R}_{33}}{{R R}_{11} {R R}_{22} + + {R R}_{22} {R R}_{33} + + {R R}_{33} {R R}_{11}} & \frac{{R R}_{33}}{{R R}_{11} {R R}_{22} + + {R R}_{22} {R R}_{33} + + {R R}_{33} {R R}_{11}} \\ 00 & 11 \end{matrix}] [\begin{matrix} {v v}_{{C C}_{11}} \\ {v v}_{{C C}_{22}} \end{matrix}]$

$+ + [\begin{matrix} \frac{{R R}_{22}}{(({R R}_{22} + + {R R}_{33})) {R R}_{11} + + {R R}_{22} {R R}_{33}} \\ 00 \end{matrix}] {V V}_{11}$

(4)结构性质分析(能控性和能观性分析)(4) Structural property analysis (controllability and observability analysis)

然后我们通过能控性矩阵T_c＝[B A*B]，这里A、B指的是电网络方程的系数矩阵。根据(3)的状态方程和输出，可以得到T_c＝2，而A的阶数也为2，两者是相等的，这说明电网络的结构性质是可控的。也可得到能观性矩阵T_o＝[C；C*A]，这里C指的是电网络输出方程的系数矩阵。经过运算T_o＝2，而A的阶数也为2，两者是相等的，这说明电网络的结构性质是可观的。Then we pass the controllability matrix T _c =[B A*B], where A and B refer to the coefficient matrix of the electrical network equation. According to the state equation and output of (3), it can be obtained that T _c = 2, and the order of A is 2, both of which are equal, which shows that the structural properties of the electrical network are controllable. The observability matrix T _o =[C; C*A] can also be obtained, where C refers to the coefficient matrix of the output equation of the electrical network. After calculation T _o = 2, and the order of A is 2, both are equal, which shows that the structural properties of the electrical network are considerable.

(5)电网络仿真(5) Electrical network simulation

在本方法中，电网络分析采用了符号，避免了具体参数值的参与，因而分析的结果具有一般性，代表了电网络的结构性质。同时本方法可以实现电网络仿真，如果把具体的参数值代进去，可以得到特定参数电网络的结构性质。现在我们对这些元件的参数进行赋值，设R₁＝R₂＝R₃＝10kΩ，C₁＝C₂＝33μF，输入电压1V那么上述的系数矩阵就变为：In this method, symbols are used in the electrical network analysis, which avoids the participation of specific parameter values, so the analysis results are general and represent the structural properties of the electrical network. At the same time, the method can realize electrical network simulation. If specific parameter values are substituted, the structural properties of the electrical network with specific parameters can be obtained. Now we assign the parameters of these components, set R ₁ =R ₂ =R ₃ =10kΩ, C ₁ =C ₂ =33μF, input voltage 1V, then the above coefficient matrix becomes:

$A A = = [\begin{matrix} - - 2.02 2.02 & 1.01 1.01 \\ 1.01 1.01 & - - 2.02 2.02 \end{matrix}] B B = = [\begin{matrix} 1.01 1.01 \\ 1.01 1.01 \end{matrix}]$

$C C = = [\begin{matrix} - - 6.667 6.667 & 3.333 3.333 \\ 00 & 11 \end{matrix}] \times \times 1010^{- - 55} D D. = = [\begin{matrix} 3.333 3.333 \\ 00 \end{matrix}] \times \times 1010^{- - 55}$

(6)分析结果(6) Analysis results

对该系数矩阵进行运算，得到能控性矩阵T_c和能观性矩阵T_o的秩分别为1和2，而其状态变量数目为2。因为能控性矩阵T_c的秩与状态变量数目不相等，因此该电网络是不可控的。而能控性矩阵T_o的秩与状态变量数目相等，因此该电网络是可观的。尽管在当前参数下是不可控的，但对于模拟元件来说，这种可能性是零，因为不可能保证R₁＝R₂＝R₃、C₁＝C₂，而且在计算时也会因为计算精度的原因，从而得到不可控但可观的结论。如果采用符号运算，就可以避开电路参数的干扰，直接分析其结构性质。电网络进行符号运算后，得到的结构性质不会因为参数的改变而发生改变，而在电网络仿真中，结构性质同时取决于电网络结构和参数。因此，本方法提供了一种电网络结构性质的分析手段，这对于研究结构是非常方便的，而且通过本方法还可以进行电网络仿真。By operating the coefficient matrix, the ranks of controllability matrix T _c and observability matrix T _o are 1 and 2 respectively, and the number of state variables is 2. Because the rank of the controllability matrix T _c is not equal to the number of state variables, the electrical network is uncontrollable. The rank of the controllability matrix T _o is equal to the number of state variables, so the electrical network is considerable. Although uncontrollable under the current parameters, for analog components, this possibility is zero, because it is impossible to guarantee that R ₁ =R ₂ =R ₃ , C ₁ =C ₂ , and the calculation will also be due to Reasons for calculation accuracy, resulting in uncontrollable but appreciable conclusions. If symbolic operation is used, the interference of circuit parameters can be avoided, and its structural properties can be directly analyzed. After symbolic operation of the electrical network, the obtained structural properties will not change due to the change of parameters, but in the electrical network simulation, the structural properties depend on both the electrical network structure and parameters. Therefore, this method provides an analysis method for the structural properties of the electrical network, which is very convenient for studying the structure, and the electrical network simulation can also be carried out by this method.

本方法基于电网络理论来分析设计其状态方程和输出方程，通过研究状态方程和输出方程来分析电网络的结构性质。为了研究一般电网络的结构性质，我们采用了符号运算的方法，也就是直接采用电网络元件名称符号进行运算。这样一来状态方程和输出方程的系数矩阵也是用符号表示的，后面的运算也都是用符号表示的，所以说电网络分析的结果就避免了具体参数值的参与，因而分析的结果具有一般性，代表了电网络的结构性质。另一方面，如果把具体的参数值代进去，我们就可以得到特定电网络结构性质的一般结论，也即本方法可以进行电网络仿真。通过本方法，我们将电网络分析的拓扑结构与电网络的结构性质结合起来，可以分析电网络结构性质的一般特点，是一种研究电网络结构的方法，具有普遍性和一般性。This method analyzes and designs its state equation and output equation based on the electrical network theory, and analyzes the structural properties of the electrical network by studying the state equation and output equation. In order to study the structural properties of the general electrical network, we use the method of symbolic operation, that is, directly use the names and symbols of the electrical network components to perform calculations. In this way, the coefficient matrices of the state equation and the output equation are also represented by symbols, and the subsequent operations are also represented by symbols, so the results of the electrical network analysis avoid the participation of specific parameter values, so the analysis results have a general , representing the structural properties of the electrical network. On the other hand, if specific parameter values are substituted in, we can get general conclusions about the structural properties of a specific electric network, that is, this method can carry out electric network simulation. Through this method, we combine the topology structure of the electrical network analysis with the structural properties of the electrical network, and can analyze the general characteristics of the structural properties of the electrical network. It is a method for studying the structure of the electrical network, which is universal and general.

Claims

1. an analytical method of RLC electric network structure property, it is characterized in that it generates state equation and output equation of electric network by drawing electric network graph and electric network topology analysis, thereby carries out electric network control performance analysis and electric network emulation; This method studies the structural properties of the electrical network by analyzing the topological properties of the electrical network, thus providing a new way for the study of the structural properties of the electrical network; the method includes:

First, draw the electrical network graph to be analyzed;

Second, perform topology analysis;

Third, generate state equations and output equations;

Fourth, conduct structural property analysis;

Fifth, conduct electrical network simulation;

Sixth, give the analysis results.

2. method according to claim 1, it is characterized in that the method and the content of the topological analysis described in the second step comprise:

1) The reference direction of the voltage is uniformly specified in the electrical network; for components such as resistors, capacitors, and inductors, when the components are placed horizontally, the left is positive and the right is negative; when the components are placed vertically, the upper is positive and the lower is negative. ;For voltage source and current source components, the default voltage reference direction is consistent with the placement position of voltage source and current source;

2) By default, the voltage source and capacitor are tree branches, and the current source and inductor are connected branches; when there is a full capacitor loop, set one of the capacitors as a connected branch; when there is a full inductor cut set, set one of the inductors Set it as a tree branch; the resistor is connected by default, and then check whether there is a tree branch path at both ends of the resistor, if there is no tree branch path, set the resistor as a tree branch;

3) When writing a loop matrix or a cut-set matrix, number the tree branches and connected branches first; in the topology relationship, set the division of voltage and current vectors, and write the Kirchhoff voltage equation of the basic loop matrix and Kirchhoff's current equations for elementary cut sets.

3. The method according to claim 1, wherein the method for generating the state equation and the output equation described in the third step is: select the branch capacitance and the connection inductance as the state variable, and the output variable is selected as required.

4. The method according to claim 1, characterized in that the method for analyzing the structural properties described in the fourth step is: through the controllability matrix _Tc =[BA*B], whether the structure of the electric network can be calculated control, where A and B refer to the coefficient matrix of the electrical network equation; through the observability matrix T _o = [C; C*A], it is calculated whether the output of the electrical network is observable, where C refers to the output equation of the electrical network coefficient matrix.

5. method according to claim 1, it is characterized in that the described in the 5th step carries out electrical network emulation, in this method, electrical network analysis has adopted symbol, has avoided the participation of specific parameter value, thereby the result of analysis has Generally speaking, it represents the structural properties of the electrical network; at the same time, this method can realize the simulation of the electrical network, and the structural properties of the electrical network with specific parameters can be obtained by substituting specific parameter values.

6. The method according to claim 1, characterized in that in the fourth step and the fifth step, after the electrical network is subjected to symbolic operations, the structural properties obtained will not change due to changes in parameters, while the electrical network simulation In , the structural properties depend on both the electrical network structure and the parameters of the electrical network components.