AC system broadband impedance envelope method and related equipment

Abstract

The invention discloses a broadband impedance enveloping method for an alternating current system, which belongs to the technical field of impedance enveloping, and comprises the following steps of: establishing a Norton equivalent circuit of an internal power supply of the alternating current system, and obtaining equivalent impedance of the alternating current system based on a kron reduction theory according to the Norton equivalent circuit of the internal power supply of the alternating current system and a relationship between the Norton equivalent circuit of the internal power supply of the alternating current system and voltage and current of each node; and finally, the equivalent impedances of the alternating current system seen from the nodes connected with the external equipment in all the operation modes are superposed in the same coordinate system, the harmonic equivalent impedances of the alternating current system seen from the multiple nodes and the mutual impedance between the harmonic equivalent impedances can be calculated at the same time, and the concept of an impedance envelope of the alternating current system is provided. The method is used for describing the impedance change range when the system operation mode changes.

Description

Technical Field

[0001] The invention belongs to the technical field of impedance envelope, and in particular relates to a wide-band impedance envelope method for an AC system and related equipment. Background Art

[0002] In the future, new energy will achieve a major transformation from auxiliary power source to main power source. However, with the large-scale access of new energy to the power grid, when the power grid strength is weak, the rapid control characteristics of new energy grid-connected equipment interact with the power grid, which may cause broadband oscillation problems. Typical cases are the frequent sub / super synchronous oscillation problems in the power grids in Hami, Xinjiang, Guyuan, Hebei, etc. The broadband oscillation problem restricts the transmission capacity of new energy and affects the safe and stable operation of the power system. Therefore, it is necessary to conduct stability analysis on the new power system to ensure the safe and stable operation of the power system.

[0003] Impedance analysis is a simple and effective method for analyzing the stability of complex power electronic systems, and impedance modeling is a key link. In previous studies, when applying impedance analysis to analyze system stability, detailed impedance modeling is usually performed on grid-connected inverters, wind turbines, and photovoltaic generators, and a simple RLC network is used instead of the AC system. However, actual AC systems are very complex. They are composed of multiple components such as transformers and lines, with a variety of topological structures, and their impedance is not fixed, but will change with changes in factors such as the parameters of each component in the network and the operating mode of the system. Simplified networks cannot fully reflect the frequency response of actual AC systems.

[0004] At present, the research on broadband harmonic impedance of AC system has established mathematical models of various components and proposed methods such as unit current injection to solve the harmonic impedance seen by a certain node of AC system. However, the current method cannot simultaneously obtain the harmonic impedance of AC system seen by multiple nodes and the mutual impedance between them, and does not fully consider the complexity of AC system and the influence of operating conditions on its harmonic impedance. Summary of the invention

[0005] The present invention provides an AC system wideband impedance envelope method and related equipment, which solves the problem that the harmonic impedance of the AC system seen by multiple nodes and the mutual impedance between them cannot be obtained simultaneously.

[0006] To achieve the above object, the present invention provides the following technical solutions: A wideband impedance envelope method for an AC system, comprising: Establish the relationship between the voltage and current of each node of the AC system to form a node admittance matrix, classify the nodes of the AC system according to whether they are connected to external devices, and divide the admittance matrix of the nodes into blocks according to the classification results; Establish a Norton equivalent circuit of the internal power supply of the AC system at the node not connected to the external device, and obtain the equivalent impedance of the AC system seen by the node connected to the external device based on the relationship between the established Norton equivalent circuit and the voltage and current of each node of the AC system; Change the operation mode of the AC system, and superimpose the equivalent impedance of the AC system seen by the nodes connected to the external equipment in each operation mode in the same coordinate system; Draw an ellipse with the smallest area on the coordinate system to enclose all impedance scattered points. This ellipse is the impedance envelope of the AC system.

[0007] Preferably, the Norton equivalent circuit of the internal power supply of the AC system at the node not connected to the external device is:

[0008] The output current of a node that is not connected to an external device but is connected to an internal power supply, is the output current of a node that is not connected to an external device and is not connected to an internal power supply. is the admittance in the Norton equivalent circuit of a node connected to an external device but connected to an internal power supply, is the admittance in the Norton equivalent circuit of a node that is not connected to external devices and is not connected to an internal power supply, is the current vector of the current source in the Norton equivalent circuit of the node connected to the external device but connected to the internal power supply, is the current vector of the current source in the Norton equivalent circuit of a node that is not connected to an external device and is not connected to an internal power supply, Y2=0 and =0.

[0009] Preferably, the equivalent impedance of the AC system seen by the node connected to the external device is:

[0010] in , , To divide the AC system node admittance matrix into blocks, the obtained block matrix is Represents the self-admittance matrix of nodes in the AC system that are not connected to external devices, represents the self-admittance matrix of the nodes connected to the external device, , is the mutual admittance matrix of two types of nodes, It represents the matrix composed of the admittances in each equivalent circuit after the internal power supply of the AC system is equivalent to the Norton circuit.

[0011] Preferably, a nonlinear programming method is used to draw an ellipse with the smallest area on the coordinate system to surround all the broadband harmonic impedance scatter points under different operating modes of the AC system; The specific steps to draw an ellipse with the smallest area on the coordinate system to surround all impedance scattered points are: First, the outermost convex hull of all impedance scatter points is obtained and connected into a closed curve. Then, the coordinates of the closed curve are substituted into the nonlinear constraint conditions to obtain the elliptical envelope.

[0012] An AC system wide-band impedance envelope system, comprising: Classification module: used to establish the relationship between the voltage and current of each node of the AC system, form a node admittance matrix, classify the nodes of the AC system according to whether they are connected to external devices, and divide the admittance matrix of the node into blocks according to the classification results; Equivalent impedance acquisition module: used to establish the Norton equivalent circuit of the internal power supply of the AC system, and obtain the equivalent impedance of the AC system seen by the node connected to the external device based on the relationship between the established Norton equivalent circuit and the voltage and current of each node of the AC system; Superposition module: used to change the operation mode of the AC system and superimpose the equivalent impedance of the AC system seen by the nodes connected to the external equipment in each operation mode in the same coordinate system; Envelope acquisition module: used to draw an ellipse with the smallest area on the coordinate system to enclose all impedance scattered points. The ellipse is the impedance envelope of the AC system.

[0013] Preferably, in the equivalent impedance acquisition module, the Norton equivalent circuit of the internal power supply of the AC system is established as:

[0014] The output current of a node that is not connected to an external device but is connected to an internal power supply, is the output current of a node that is not connected to an external device and is not connected to an internal power supply. is the admittance in the Norton equivalent circuit of a node connected to an external device but connected to an internal power supply, is the admittance in the Norton equivalent circuit of a node that is not connected to external devices and is not connected to an internal power supply, is the current vector of the current source in the Norton equivalent circuit of the node connected to the external device but connected to the internal power supply, is the current vector of the current source in the Norton equivalent circuit of a node that is not connected to an external device and is not connected to an internal power supply, Y2=0 and =0.

[0015] Preferably, in the equivalent impedance acquisition module, the equivalent impedance of the AC system seen by the node connected to the external device is:

[0016] in , , To divide the AC system node admittance matrix into blocks, the obtained block matrix is Represents the self-admittance matrix of nodes in the AC system that are not connected to external devices, represents the self-admittance matrix of the nodes connected to the external device, , is the mutual admittance matrix of two types of nodes, It represents the matrix composed of the admittances in each equivalent circuit after the internal power supply of the AC system is equivalent to the Norton circuit.

[0017] Preferably, in the envelope acquisition module, a nonlinear programming method is used to draw an ellipse with the smallest area on the coordinate system to surround all impedance scattered points; The specific steps to draw an ellipse with the smallest area on the coordinate system to surround all impedance scattered points are: First, the outermost convex hull of all impedance scatter points is obtained and connected into a closed curve. Then, the coordinates of are substituted into the nonlinear constraints to obtain the elliptical envelope.

[0018] A computer device comprises a memory, a processor and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the steps of a wide-band impedance envelope method for an AC system are implemented.

[0019] A computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the computer program implements the steps of a wide-band impedance envelope method for an AC system.

[0020] Compared with the prior art, the present invention has the following beneficial effects: The present invention provides a wide-band impedance envelope method for an AC system. Based on the AC system impedance equivalent method of Kron reduction, the nodes are classified to obtain the equivalent impedance of the AC system seen by the node connected to the external device, and the harmonic impedance of the AC system seen by multiple nodes and the mutual impedance between them can be calculated simultaneously. The present invention proposes the concept of the impedance envelope of the AC system to describe the range of change of its impedance when the system operation mode changes. Based on the nonlinear programming method, the present invention proposes a method for calculating the mathematical expression of the impedance envelope, superimposing the harmonic impedance of the AC system seen by the node connected to the external device under various operation modes in the same coordinate system, and taking the above impedance scatter points as being contained in the elliptical envelope as a constraint condition, the impedance envelope calculation is transformed into a nonlinear programming problem, thereby obtaining a specific expression of the impedance envelope. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1A flow chart of a wide-band impedance envelope method for an AC system according to the present invention; Figure 2 A schematic diagram of a simple power system according to an embodiment of the present invention; Figure 3 A schematic diagram of a Norton equivalent circuit of a node not connected to an external device according to an embodiment of the present invention; Figure 4 This is a topology diagram of the IEEE39 node system according to an embodiment of the present invention; Figure 5 This is a topology diagram of the IEEE 14-node system according to an embodiment of the present invention; Figure 6 This is a graph of equivalent impedance amplitude of an AC system viewed from 16 nodes of an IEEE39 node system according to an embodiment of the present invention; Figure 7 This is an equivalent impedance phase diagram of an AC system viewed from 16 nodes of an IEEE 39 node system according to an embodiment of the present invention; Figure 8 This is a diagram of the real and imaginary parts of the equivalent impedance of the AC system from the perspective of 16 nodes in the IEEE 39 node system according to an embodiment of the present invention; Fig. 9 This is a graph of equivalent impedance amplitude of an AC system viewed from node 2 of an IEEE 14-node system according to an embodiment of the present invention; Fig.10 This is an equivalent impedance phase diagram of an AC system viewed from 2 nodes of an IEEE 14-node system according to an embodiment of the present invention; Fig.11 This is a diagram of the real and imaginary parts of the equivalent impedance of the AC system as viewed from 2 nodes of the IEEE 14-node system according to an embodiment of the present invention; Fig.12 This is a schematic diagram of an ellipse according to an embodiment of the present invention; Fig.13 The impedance envelope of the embodiment of the present invention viewed from the 16th node of the IEEE 39 node system; Fig.14 Improvement of the impedance envelope of node 2 in the IEEE 14-node system according to the embodiment of the present invention Fig.15 The present invention is a block diagram of a wide-band impedance envelope system of an AC system. DETAILED DESCRIPTION

[0022] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings here can be arranged and designed in various different configurations.

[0023] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0024] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, further definition and explanation thereof is not required in subsequent drawings.

[0025] In order to enable those skilled in the art to better understand the technical solution of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings.

[0026] like Figure 1 As shown, the present invention provides a wide-band impedance envelope method for an AC system, comprising: S101 establishes the relationship between the voltage and current of each node of the AC system to form a node admittance matrix, classifies the nodes of the AC system according to whether they are connected to external devices, and divides the admittance matrix of the nodes into blocks according to the classification results; S102 establishes a Norton equivalent circuit of the internal power supply of the AC system, and obtains the equivalent impedance of the AC system seen by the node connected to the external device according to the relationship between the established Norton equivalent circuit and the voltage and current of each node of the AC system; S103 changes the operation mode of the AC system, and superimposes the equivalent impedance of the AC system seen by the node connected to the external device in each operation mode in the same coordinate system; S104 draws an ellipse with the smallest area on the coordinate system to surround all impedance scattered points. The ellipse is the impedance envelope of the AC system.

[0027] The Norton equivalent circuit for the internal power supply of the AC system is:

[0028] The output current of a node that is not connected to an external device but is connected to an internal power supply, is the output current of a node that is not connected to an external device and is not connected to an internal power supply. is the admittance in the Norton equivalent circuit of a node connected to an external device but connected to an internal power supply, is the admittance in the Norton equivalent circuit of a node that is not connected to external devices and is not connected to an internal power supply, is the current vector of the current source in the Norton equivalent circuit of the node connected to the external device but connected to the internal power supply, is the current vector of the current source in the Norton equivalent circuit of a node that is not connected to an external device and is not connected to an internal power supply, Y2=0 and =0.

[0029] The equivalent impedance of the AC system seen by the node connected to the external device is:

[0030] in , , To divide the AC system node admittance matrix into blocks, the obtained block matrix is Represents the self-admittance matrix of nodes in the AC system that are not connected to external devices, represents the self-admittance matrix of the nodes connected to the external device, , is the mutual admittance matrix of two types of nodes, It represents the matrix composed of the admittances in each equivalent circuit after the internal power supply of the AC system is equivalent to the Norton circuit.

[0031] Use nonlinear programming to draw an ellipse with the smallest area on the coordinate system to surround all impedance scattered points; The specific steps to draw an ellipse with the smallest area on the coordinate system to surround all impedance scattered points are: First, the outermost convex hull of all impedance scatter points is obtained and connected into a closed curve. Then, the coordinates of are substituted into the nonlinear constraints to obtain the elliptical envelope.

[0032] Another embodiment of the present invention provides a wideband impedance envelope method for an AC system, comprising: like Figure 2 As shown, a schematic diagram of a simple power system is shown, where nodes a and b have active loads or power supplies, nodes c and d are not connected to the outside and have no active loads or power supplies, and nodes e and f are connected to external devices, where the external devices may be converters, etc. This embodiment calculates the equivalent impedance seen from nodes e and f.

[0033] The nodes are divided into three categories: the first category is connected to the internal power supply but not to external devices (a, b), the second category is not connected to external devices and not to the internal power supply (c, d), and the third category is connected to external devices (e, f), represented by subscripts 1, 2, and 3 respectively. Then there is (1) in, , It is a column vector containing two elements, which is a 2*2 matrix.

[0034] The AC system power supply at the first and second type nodes is modeled as Figure 3 The Norton equivalent circuit form shown is (2) , Represents the output current of the power supply inside the AC system. It should be noted that although the second type of node is not connected to the power supply at this time, in order to facilitate subsequent derivation and expression, it is assumed that a virtual power supply is connected to the second type of node. The Norton equivalent circuit of the virtual power supply is Y 2=0 and =0.

[0035] From the first two lines of formula (1), we can get (3) Combining equations (2) and (3), we get (4) From the third line of formula (1), we get (5) Substituting equation (4) into equation (5), we get (6) in , , , .

[0036] Written in the form of formula (6), it is no longer necessary to distinguish between type 1 and type 2 nodes, the physical meaning is clearer, and it is also easier to modify when removing power from a type 1 node or adding power to a type 2 node.

[0037] Since the form of the admittance matrix and the voltage and current vector in the first and second types of nodes are exactly the same after the expression is written in the form of formula (6), there is no need to distinguish between the first and second types of nodes in the subsequent calculation, that is, there is no need to pay attention to whether the nodes that are not connected to the outside are connected to the internal power supply of the AC system. In addition, after the expression is written in the form of formula (6), if it is necessary to remove the power supply of a node in the first type of node, it is only necessary to replace the corresponding node with the power supply of the node. Y gi and I s1i Similarly, if you need to increase power at a node in the second type of node, just set the corresponding node Y gj and I s2j Just change it to the admittance and current in the Norton equivalent circuit of the added power supply.

[0038] If we classify the first and second class nodes as first class nodes, and classify the third class nodes as second class nodes, then equation (6) can be rewritten as (7) in

[0039] (8)

[0040] (9) Since the difference between the terminal voltage waveform and the fundamental waveform at any moment in actual operation of the generator is limited to within 5% of the fundamental amplitude, it can be considered that the potential of the generator mainly exists in the fundamental network. Therefore, when performing harmonic analysis, it is reasonable to treat the generator as a grounding admittance, that is, .but (10) Formula (10) is the equivalent impedance of the AC system seen from nodes e and f.

[0041] In general, the AC system impedance equivalent method based on Kron reduction is used to classify nodes and obtain the AC system equivalent impedance seen by the nodes connected to external devices. The AC system harmonic impedance seen by multiple nodes and the mutual impedance between them can be calculated simultaneously.

[0042] Among them, Kron Reduction is a graph simplification method widely used in power system analysis, circuit theory, network theory, etc. This method is mainly used to eliminate or simplify internal nodes in physical network systems while retaining the main electrical characteristics or network structure of the system.

[0043] Calculation results This embodiment selects node 16 of the IEEE39 node system and node 2 of the improved IEEE14 node radial network system as the input nodes, and calculates the equivalent impedance of the AC system observed from the selected nodes. It should be noted here that the improved IEEE14 node system, based on the original IEEE14 node radial network system, has loads connected at nodes 1, 2, 4, 6, 7, 8, 22, and 23. This is because radial networks are mostly used in distribution network systems. The distribution network is a network that connects the transmission network and the end users. Therefore, there should be more loads in the distribution network, so the above improvements are made to it. The topological structures of the IEEE39 node system and the improved IEEE14 node system are as follows Figure 4 and Figure 5 shown.

[0044] The calculation results of the method proposed in this embodiment are compared with the calculation results of the impedance measurement module of the PSCAD simulation platform. The results of the AC system from the IEEE 39-node system 16 nodes are as follows: Figure 6 , 7 and 8; The result of looking at the 2-node AC system from the IEEE 14-node system is as follows Fig. 9 , 10 and 11.

[0045] Depend on Figure 6 , 7 , 8, 9, 10 and 11, the equivalent impedance of the AC system calculated by using the model established in this embodiment and the method proposed has a small error with the equivalent impedance of the AC system measured by the impedance measurement module of the PSCAD platform, which can verify the correctness of the calculation results of this embodiment.

[0046] Wideband Harmonic Impedance Envelope Method for AC System The equivalent impedance of the AC system is not fixed. It will change with the changes in the parameters of each component in the network, the operating mode of the system and other factors. Therefore, in practical applications such as filter design and stability judgment of AC / DC interconnected systems, a range of system impedance variation is required, and the boundary of this range is defined as the impedance envelope. On the basis of correctly calculating the harmonic impedance of the AC system seen at a certain node, change the operating mode of the system, and superimpose the equivalent impedances under various operating modes on the same coordinate system. The horizontal axis of the coordinate system is the real part of the impedance, and the vertical axis is the imaginary part of the impedance. Draw an ellipse with the smallest area to enclose all the impedance scatter points. This ellipse is the impedance envelope of a typical AC system. The schematic diagram of the ellipse is shown as follows. Fig.12 shown.

[0047] After obtaining the impedance scatter points under different operating modes, drawing the elliptical impedance envelope can be regarded as a nonlinear programming problem. The ellipse diagram is shown in the figure above, and its expression is (11) in( , ) is the center of the ellipse, a, b are half the length of the major and minor axes of the ellipse, respectively. is the major axis of the ellipse and x The angle of the axis.

[0048] The formula for the area of ​​an ellipse is (12) The goal of this linear programming problem is to minimize the area of ​​the ellipse. The objective function is the area of ​​the ellipse shown in equation (12), and the decision variable is , , a, b, The constraint condition is that any scattered point of impedance is within the ellipse, which can be expressed as: , ) (13) The programming of nonlinear functions whose objective function or constraint function is the optimization variable is nonlinear programming. The system function of nonlinear programming in MATLAB applies four different algorithms: interior point method, sequential quadratic programming algorithm, effective set method, and trust region effective algorithm. This embodiment adopts the interior point method.

[0049] There are generally two types of interior point methods: barrier function interior point method and primal-dual interior point method. This embodiment uses the barrier function interior point method. The barrier function interior point method is a type of method that maintains strict feasibility. It always starts from a feasible point and searches within the feasible domain. Therefore, this type of method is only applicable to nonlinear optimization problems with only inequality constraints. The basic idea of ​​the barrier function interior point method is to introduce an obstacle term about the constraint on the objective function. When the iteration point approaches the boundary of the feasible domain from the inside of the feasible domain, the obstacle term will tend to infinity to force the iteration point to return to the inside of the feasible domain, thereby maintaining the strict feasibility of the iteration point. Then, the solution of the constraint problem is transformed into the solution of a series of easy sub-problems, thereby obtaining the optimal approximate solution to the original problem.

[0050] Assume that the objective function of nonlinear programming is min f ( x ), the set of constraints is g i ( x ) ≥ 0 , then construct an auxiliary function and find the minimum value of the auxiliary function, that is, f ( x,μ ) = f ( x ) +μB ( x ),in μ Take a small positive number, B ( x ) is the barrier function, and the objective function and constraints here have been explained in the previous article.

[0051] Barrier function B ( x ) generally needs to satisfy the continuity and x tend to g i ( x ) = 0 The borders of B ( x) tends to infinity. Two commonly used barrier functions are the inverse barrier function ( B ( x ) = ∑ li=11 / g i ( x )) and the logarithmic barrier function ( B ( x ) =－ ∑ li=1ln g i ( x )).

[0052] The general solution process is shilling F ( x,μ ) for vector x For each value (i.e., decision variable) in , we take partial derivatives to make these derivatives equal to 0, i.e. ∂F ( x,μ )⁄( ∂x_i ) =0 , find the expression of each decision variable with respect to the penalty factor μ at this time x i = h ( μ ). Let μ approach zero and calculate the decision variable value. F ( x,μ ) = f ( x ). Find F ( x,μ ) Hesse = ▽2F ( x,μ ), if it is a positive definite matrix, then F ( x,μ ) has a local minimum, if it is a negative definite matrix then F ( x,μ ) has a local maximum value. If it is an indefinite matrix, then F ( x,μ ) is not an extreme value here.

[0053] After solving the nonlinear programming problem, we can obtain an elliptical envelope with the smallest area and enclosing all impedance scatter points. l 0.

[0054] However, this method has a drawback, that is, when there are many impedance scatter points, the nonlinear programming operation speed will become very slow. Therefore, the function convhull in MATLAB is used here to calculate the convex hull of the matrix. First, the convex hull of the outermost of all impedance scatter points is obtained, and then it is connected into a closed curve. l 1. At this time, as long as the ellipse surrounds l 1, then all impedance scattered points must be enclosed. Then lThe coordinates of 1 ( x i , y i ) into the nonlinear constraints, the corresponding elliptical envelope is obtained. l The number of scattered points of 1 is much smaller than that of impedance scattered points. Using this method can greatly reduce the number of inequalities of nonlinear constraint conditions, thereby improving the calculation speed.

[0055] It can be seen from the calculation process of this method that theoretically l 1 can also be used as an impedance envelope, and its area is smaller than that of an ellipse. l 1 is an irregular closed curve. Only the coordinates of its constituent scattered points can be obtained, and it is difficult to obtain an analytical expression. l 0 is clearer as the impedance envelope expression. The calculation of the impedance envelope itself is to delineate the range of impedance transformation of the system under different operating modes, so it is more reasonable to leave a certain margin when dividing the range. Therefore, this embodiment adopts an ellipse l 0 as the impedance envelope.

[0056] This section takes node 16 of the IEEE39-node system and node 2 of the improved IEEE14-node system as input nodes to obtain the equivalent impedance and envelope of the AC system under different operating modes.

[0057] Table 1 Decision variable values ​​of IEEE39 node system

[0058] Fig.13 is the impedance envelope observed by node 16 of the IEEE39 node system, where operation mode 1 is the shutdown of line 16-17, operation mode 2 is the shutdown of line 17-27, and operation mode 3 is the shutdown of transformer 22-35. , , a, b, The values ​​of are shown in Table 1, where The system is radians. Substituting the values ​​of the decision variables into equation (11), we can get the expression of the impedance envelope.

[0059] Table 2 Decision variable values ​​of improved IEEE14-node system

[0060] Fig.14In order to improve the impedance envelope of the IEEE 14-node system from node 2, operation mode 1 is to shut down the load at node 6, operation mode 2 is to shut down the load at node 11, and operation mode 3 is to put the same load as node 4 at node 5. In this example, the values ​​of the decision variables are shown in Table 2. Measured in radians.

[0061] This embodiment takes the IEEE39 node system and the improved IEEE14 node system as examples to introduce the calculation method of the impedance envelope when considering the change of the system operation mode. In practical applications, according to different scenarios, multiple operation modes with a greater possibility of the system can be selected, and the impedances under different operation modes can be superimposed on the same coordinate system, and then the impedance envelope can be calculated by the method proposed in this embodiment.

[0062] like Fig.15 As shown, the present invention also provides an AC system wide-band impedance envelope system, comprising: Classification module: used to establish the relationship between the voltage and current of each node of the AC system, form a node admittance matrix, classify the nodes of the AC system according to whether they are connected to external devices, and divide the admittance matrix of the node into blocks according to the classification results; Equivalent impedance acquisition module: used to establish the Norton equivalent circuit of the internal power supply of the AC system at the node not connected to the external device, and obtain the equivalent impedance of the AC system seen by the node connected to the external device according to the relationship between the established Norton equivalent circuit and the voltage and current of each node of the AC system; Superposition module: used to change the operation mode of the AC system and superimpose the equivalent impedance of the AC system seen by the nodes connected to the external equipment in each operation mode in the same coordinate system; Envelope acquisition module: used to draw an ellipse with the smallest area on the coordinate system to enclose all impedance scattered points. The ellipse is the impedance envelope of the AC system.

[0063] In the equivalent impedance acquisition module, the Norton equivalent circuit of the internal power supply of the AC system at the node not connected to the external device is established as follows:

[0064] The output current of a node that is not connected to an external device but is connected to an internal power supply, is the output current of a node that is not connected to an external device and is not connected to an internal power supply. is the admittance in the Norton equivalent circuit of a node connected to an external device but connected to an internal power supply, is the admittance in the Norton equivalent circuit of a node that is not connected to external devices and is not connected to an internal power supply, is the current vector of the current source in the Norton equivalent circuit of the node connected to the external device but connected to the internal power supply, is the current vector of the current source in the Norton equivalent circuit of a node that is not connected to an external device and is not connected to an internal power supply, Y2=0 and =0.

[0065] In the equivalent impedance acquisition module, the equivalent impedance of the AC system seen by the node connected to the external device is:

[0066] in , , To divide the AC system node admittance matrix into blocks, the obtained block matrix is Represents the self-admittance matrix of nodes in the AC system that are not connected to external devices, represents the self-admittance matrix of the nodes connected to the external device, , is the mutual admittance matrix of two types of nodes, It represents the matrix composed of admittances in each equivalent circuit after the nodes not connected to external devices are equivalent to Norton circuits.

[0067] In the envelope acquisition module, a nonlinear programming method is used to draw an ellipse with the smallest area on the coordinate system to surround all impedance scattered points; The specific steps to draw an ellipse with the smallest area on the coordinate system to enclose all impedance scattered points are: First, the outermost convex hull of all impedance scatter points is obtained and connected into a closed curve. Then, the coordinates of are substituted into the nonlinear constraints to obtain the elliptical envelope.

[0068] A terminal device is provided in one embodiment of the present invention. The terminal device of this embodiment includes: a processor, a memory, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the steps in the above-mentioned method embodiments are implemented. Alternatively, when the processor executes the computer program, the functions of the modules / units in the above-mentioned device embodiments are implemented.

[0069] The computer program may be divided into one or more modules / units, and the one or more modules / units are stored in the memory and executed by the processor to accomplish the present invention.

[0070] The terminal device may be a computing device such as a desktop computer, a notebook, a PDA, a cloud server, etc. The terminal device may include, but is not limited to, a processor and a memory.

[0071] The processor may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc.

[0072] The memory may be used to store the computer programs and / or modules, and the processor implements various functions of the terminal device by running or executing the computer programs and / or modules stored in the memory and calling the data stored in the memory.

[0073] If the module / unit integrated in the terminal device is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the present invention implements all or part of the processes in the above-mentioned embodiment method, and can also be completed by instructing the relevant hardware through a computer program. The computer program can be stored in a computer-readable storage medium. When the computer program is executed by the processor, the steps of the above-mentioned various method embodiments can be implemented. Among them, the computer program includes computer program code, and the computer program code can be in source code form, object code form, executable file or some intermediate form. The computer-readable medium may include: any entity or device capable of carrying the computer program code, recording medium, U disk, mobile hard disk, disk, optical disk, computer memory, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), electric carrier signal, telecommunication signal and software distribution medium. It should be noted that the content contained in the computer-readable medium can be appropriately increased or decreased according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable media do not include electric carrier signals and telecommunication signals.

[0074] Although the embodiments of the present invention are described above in conjunction with the accompanying drawings, the present invention is not limited to the above-mentioned specific embodiments and application fields, and the above-mentioned specific embodiments are only illustrative and instructive, rather than restrictive. Under the guidance of the specification, a person skilled in the art can also make many forms without departing from the scope of protection of the claims of the present invention, all of which belong to the scope of protection of the present invention.

Claims

1. A wideband impedance envelope method for an AC system, characterized in that: include: Establish the relationship between the voltage and current of each node of the AC system to form a node admittance matrix, classify the nodes of the AC system according to whether they are connected to external devices, and divide the admittance matrix of the nodes into blocks according to the classification results; Establish a Norton equivalent circuit of the internal power supply of the AC system at the node not connected to the external device, and obtain the equivalent impedance of the AC system seen by the node connected to the external device based on the relationship between the established Norton equivalent circuit and the voltage and current of each node of the AC system; Change the operation mode of the AC system, and superimpose the equivalent impedance of the AC system seen by the nodes connected to the external equipment in each operation mode in the same coordinate system; Draw an ellipse with the smallest area on the coordinate system to enclose all impedance scattered points. This ellipse is the impedance envelope of the AC system.

2. The method for broadband impedance envelope of an AC system according to claim 1, characterized in that: The Norton equivalent circuit of the internal power supply of the AC system at the node not connected to the external device is: The output current of a node that is not connected to an external device but is connected to an internal power supply, is the output current of a node that is not connected to an external device and is not connected to an internal power supply. is the admittance in the Norton equivalent circuit of a node connected to an external device but connected to an internal power supply, is the admittance in the Norton equivalent circuit of a node that is not connected to external devices and is not connected to an internal power supply, is the current vector of the current source in the Norton equivalent circuit of the node connected to the external device but connected to the internal power supply, is the current vector of the current source in the Norton equivalent circuit of a node that is not connected to an external device and is not connected to an internal power supply, Y2=0 and =0.

3. The method for broadband impedance envelope of an AC system according to claim 1, characterized in that: The equivalent impedance of the AC system seen by the node connected to the external device is: in , , To divide the AC system node admittance matrix into blocks, the obtained block matrix is Represents the self-admittance matrix of nodes in the AC system that are not connected to external devices, represents the self-admittance matrix of the nodes connected to the external device, , is the mutual admittance matrix of two types of nodes, It represents the matrix composed of the admittances in each equivalent circuit after the internal power supply of the AC system is equivalent to the Norton circuit.

4. The method for broadband impedance envelope of an AC system according to claim 1, characterized in that: A nonlinear programming method is used to draw an ellipse with the smallest area on the coordinate system to surround all the broadband harmonic impedance scatter points under different operating modes of the AC system; The specific steps to draw an ellipse with the smallest area on the coordinate system to enclose all impedance scattered points are: First, the outermost convex hull of all impedance scatter points is obtained and connected into a closed curve. Then, the coordinates of the closed curve are substituted into the nonlinear constraint conditions to obtain the elliptical envelope.

5. An AC system wideband impedance envelope system, characterized in that: include: Classification module: used to establish the relationship between the voltage and current of each node of the AC system, form a node admittance matrix, classify the nodes of the AC system according to whether they are connected to external devices, and divide the admittance matrix of the node into blocks according to the classification results; Equivalent impedance acquisition module: used to establish the Norton equivalent circuit of the internal power supply of the AC system, and obtain the equivalent impedance of the AC system seen by the node connected to the external device based on the relationship between the established Norton equivalent circuit and the voltage and current of each node of the AC system; Superposition module: used to change the operation mode of the AC system and superimpose the equivalent impedance of the AC system seen by the nodes connected to the external equipment in each operation mode in the same coordinate system; Envelope acquisition module: It is used to draw an ellipse with the smallest area on the coordinate system to enclose all impedance scattered points. The ellipse is the impedance envelope of the AC system.

6. The AC system wideband impedance envelope system according to claim 5, characterized in that: In the equivalent impedance acquisition module, the Norton equivalent circuit of the internal power supply of the AC system is established as: The output current of a node that is not connected to an external device but is connected to an internal power supply, is the output current of a node that is not connected to an external device and is not connected to an internal power supply. is the admittance in the Norton equivalent circuit of a node connected to an external device but connected to an internal power supply, is the admittance in the Norton equivalent circuit of a node that is not connected to external devices and is not connected to an internal power supply, is the current vector of the current source in the Norton equivalent circuit of the node connected to the external device but connected to the internal power supply, is the current vector of the current source in the Norton equivalent circuit of a node that is not connected to an external device and is not connected to an internal power supply, Y2=0 and =0.

7. The AC system wideband impedance envelope system according to claim 5, characterized in that: In the equivalent impedance acquisition module, the equivalent impedance of the AC system seen by the node connected to the external device is: in , , To divide the AC system node admittance matrix into blocks, the obtained block matrix is Represents the self-admittance matrix of nodes in the AC system that are not connected to external devices, represents the self-admittance matrix of the nodes connected to the external device, , is the mutual admittance matrix of two types of nodes, It represents the matrix composed of the admittances in each equivalent circuit after the internal power supply of the AC system is equivalent to the Norton circuit.

8. The AC system wideband impedance envelope system according to claim 5, characterized in that: In the envelope acquisition module, a nonlinear programming method is used to draw an ellipse with the smallest area on the coordinate system to surround all impedance scattered points; The specific steps to draw an ellipse with the smallest area on the coordinate system to enclose all impedance scattered points are: First, the outermost convex hull of all impedance scatter points is obtained and connected into a closed curve. Then, the coordinates of are substituted into the nonlinear constraints to obtain the elliptical envelope.

9. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the steps of the wide-band impedance envelope method for an AC system as claimed in any one of claims 1 to 4 are implemented.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the steps of the wide-band impedance envelope method for an AC system as claimed in any one of claims 1 to 4 are implemented.

Images