An ac system wideband impedance envelope method and related apparatus

Abstract

The application discloses an alternating current system wide frequency band impedance envelope method, and belongs to the technical field of impedance envelope. The method comprises the following steps: establishing a Norton equivalent circuit of an internal power supply of an alternating current system; according to the relationship between the Norton equivalent circuit of the internal power supply of the alternating current system and the voltage and current of each node, obtaining equivalent impedance of the alternating current system based on a kron reduction theory; and finally, superimposing the equivalent impedance of the alternating current system under each operation mode and the connection node of the external equipment into the same coordinate system, so that the harmonic equivalent impedance of the alternating current system and the mutual impedance between the nodes can be calculated simultaneously, and the concept of the impedance envelope line of the alternating current system is proposed to describe the change range of the impedance when the operation mode of the system changes.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of impedance envelope, and particularly relates to an alternating current system wideband impedance envelope method and related equipment. BACKGROUND

[0002] In the future, new energy will realize a major change from an auxiliary power source to a main power source. However, with large-scale access of new energy to a power grid, when the power grid is weak, the fast control characteristics of new energy grid-connected equipment and the power grid interact with each other, which may cause a wideband oscillation problem. The wideband oscillation problem restricts the new energy sending capacity and affects the safe and stable operation of a power system. Therefore, it is necessary to analyze the stability of a new power system to ensure the safe and stable operation of the power system.

[0003] As a simple and effective method for analyzing the stability of a complex power electronic system, impedance analysis is a key link. In the past research, when the impedance analysis method is applied to system stability analysis, a grid-connected inverter, a wind turbine generator and a photovoltaic generator are modeled in detail, and a simple RLC network is used to replace an alternating current system. However, the actual alternating current system is very complex, which is composed of transformers, lines and various elements, and has various topological structures. Moreover, the impedance of the alternating current system is not fixed, but changes with the change of various factors such as the parameters of elements in the network and the operation mode of the system. Simplifying the network cannot completely reflect the frequency response of the actual alternating current system.

[0004] At present, although the mathematical model of each element is established, and the method of injecting a unit current is proposed to solve the harmonic impedance of an alternating current system, the current method cannot simultaneously solve the harmonic impedance of the alternating current system and the mutual impedance between multiple nodes, and the complexity of the alternating current system and the influence of the operating condition on the harmonic impedance are not fully considered. SUMMARY

[0005] The application provides an alternating current system wideband impedance envelope method and related equipment, which solves the problem that the harmonic impedance of the alternating current system and the mutual impedance between multiple nodes cannot be simultaneously solved.

[0006] To achieve the above object, the application provides the following technical scheme.

[0007] An alternating current system wideband impedance envelope method comprises the following steps:

[0008] The relationship between the voltages and currents of each node of the alternating current system is established, a node admittance matrix is formed, the nodes of the alternating current system are classified according to whether they are connected with external equipment, and the admittance matrix of the nodes is blocked according to the classification result;

[0009] The Norton equivalent circuit of the internal power supply at the node not connected with the external equipment is established, and the equivalent impedance of the AC system viewed from the node connected with the external equipment is obtained according to the established Norton equivalent circuit and the relationship between the voltage and current of each node of the AC system;

[0010] The operation mode of the AC system is changed, and the equivalent impedances of the AC system viewed from the node connected with the external equipment under each operation mode are superposed in the same coordinate system;

[0011] An ellipse with the minimum area is drawn on the coordinate system to enclose all the impedance scatter points, and the ellipse is the impedance envelope of the AC system.

[0012] Preferably, the Norton equivalent circuit of the internal power supply at the node not connected with the external equipment is as follows:

[0013]

[0014] The output current of the node not connected with the external equipment but connected with the internal power supply, the output current of the node not connected with the external equipment and not connected with the internal power supply, the admittance in the Norton equivalent circuit of the node connected with the external equipment but connected with the internal power supply, the admittance in the Norton equivalent circuit of the node not connected with the external equipment and not connected with the internal power supply, the current vector of the current source in the Norton equivalent circuit of the node connected with the external equipment but connected with the internal power supply, the current vector of the current source in the Norton equivalent circuit of the node not connected with the external equipment and not connected with the internal power supply, =0.

[0015] Preferably, the equivalent impedance of the AC system viewed from the node connected with the external equipment is as follows:

[0016]

[0017] wherein , , is the block matrix obtained by blocking the admittance matrix of the node of the AC system, represents the self-admittance matrix of the node not connected with the external equipment in the AC system, represents the self-admittance matrix of the node connected with the external equipment, , is the mutual admittance matrix of the two types of nodes, 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.

[0018] Preferably, a minimum-area ellipse is drawn on the coordinate system by using nonlinear programming to enclose all the wide-band harmonic impedance scatter points of the AC system in different operating modes;

[0019] The specific steps for drawing a minimum-area ellipse on the coordinate system to enclose all the impedance scatter points are as follows:

[0020] First, the outermost convex hull of all the impedance scatter points is obtained, and the convex hull is connected into a closed curve, and then the coordinates of the closed curve are substituted into the nonlinear constraint condition to obtain the elliptical envelope.

[0021] An AC system wide-band impedance envelope system comprises:

[0022] The classification module is configured 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 the nodes are connected to external equipment, and block the admittance matrix of the nodes according to the classification result;

[0023] The equivalent impedance obtaining module is configured to establish a Norton equivalent circuit of the internal power supply of the AC system, and obtain the equivalent impedance of the AC system seen from the node connected to external equipment according to the established Norton equivalent circuit and the relationship between the voltage and current of each node of the AC system;

[0024] The superposition module is configured to change the operating mode of the AC system, and superimpose the equivalent impedance of the AC system seen from the node connected to external equipment in each operating mode in the same coordinate system;

[0025] The envelope line obtaining module is configured to draw a minimum-area ellipse on the coordinate system to enclose all the impedance scatter points, and the ellipse is the impedance envelope line of the AC system.

[0026] Preferably, in the equivalent impedance obtaining module, the Norton equivalent circuit of the internal power supply of the AC system is as follows:

[0027]

[0028] the output current of the node not connected to external equipment but connected to the internal power supply, the output current of the node not connected to external equipment and not connected to the internal power supply, the admittance in the Norton equivalent circuit of the node connected to external equipment but connected to the internal power supply, the admittance in the Norton equivalent circuit of the node not connected to external equipment and not connected to the internal power supply, the current vector of the current source in the Norton equivalent circuit of the node connected to external equipment but connected to the internal power supply, the current vector of the current source in the Norton equivalent circuit of the node not connected to external equipment and not connected to the internal power supply, and =0.

[0029] Preferably, in the equivalent impedance obtaining module, the equivalent impedance of the alternating current system viewed from the external device connection node is:

[0030]

[0031] wherein , , is a block matrix obtained by blocking the admittance matrix of the alternating current system node, represents the self-admittance matrix of the node in the alternating current system not connected with the external device, represents the self-admittance matrix of the node connected with the external device, , is the mutual admittance matrix of the two types of nodes, represents the matrix composed of the admittance of each equivalent circuit after the internal power source of the alternating current system is equivalent to the Norton circuit.

[0032] Preferably, in the envelope obtaining module, a non-linear programming method is used to draw an ellipse with the minimum area on the coordinate system to enclose all the impedance scatter points.

[0033] The specific steps of drawing an ellipse with the minimum area on the coordinate system to enclose all the impedance scatter points are as follows:

[0034] First, the convex hull of all the outermost impedance scatter points is obtained, and the convex hull is connected into a closed curve, and then the coordinates of the convex hull are substituted into the non-linear constraint condition to obtain the elliptical envelope.

[0035] A computer device comprises a memory, a processor, and a computer program stored in the memory and executable on the processor, and the processor implements the steps of the alternating current system wide frequency band impedance envelope method when executing the computer program.

[0036] A computer readable storage medium stores a computer program, and the computer program implements the steps of the alternating current system wide frequency band impedance envelope method when executed by a processor.

[0037] Compared with the prior art, the present application has the following beneficial effects: the present application provides an AC system wideband impedance envelope method, an AC system impedance equivalent method based on kron reduction, classification of nodes, obtaining of the AC system equivalent impedance viewed from the nodes connected with external equipment, simultaneous calculation of the AC system harmonic impedance viewed from multiple nodes and the mutual impedance therebetween. The present application proposes the concept of AC system impedance envelope to describe the change range of the impedance when the system operation mode changes. The present application proposes a calculation method of the mathematical expression of the impedance envelope based on the method of nonlinear programming, superimposes the AC system harmonic impedance viewed from the nodes connected with external equipment under various operation modes in the same coordinate system, and above the impedance scatter points are contained in the elliptical envelope as constraint conditions, converts the impedance envelope calculation into a nonlinear programming problem, and thus obtains the specific expression of the impedance envelope. BRIEF DESCRIPTION OF DRAWINGS

[0038] Figure 1 Flow chart of the AC system wideband impedance envelope method of the present application;

[0039] Figure 2 Schematic diagram of a simple power system in the embodiment of the present application;

[0040] Figure 3 Schematic diagram of the Norton equivalent circuit form of the nodes not connected with external equipment in the embodiment of the present application;

[0041] Figure 4 IEEE39 node system topological graph in the embodiment of the present application;

[0042] Figure 5 IEEE14 node system topological graph in the embodiment of the present application;

[0043] Figure 6 Equivalent impedance amplitude graph of the AC system viewed from the 16 nodes of the IEEE39 node system in the embodiment of the present application;

[0044] Figure 7 Equivalent impedance phase graph of the AC system viewed from the 16 nodes of the IEEE39 node system in the embodiment of the present application;

[0045] Figure 8 Equivalent impedance real part and imaginary part graph of the AC system viewed from the 16 nodes of the IEEE39 node system in the embodiment of the present application;

[0046] Figure 9 Equivalent impedance amplitude graph of the AC system viewed from the 2 nodes of the IEEE14 node system in the embodiment of the present application;

[0047] Figure 10For the embodiment of the present application, the phase diagram of the equivalent impedance of the AC system viewed from the 2nd node of the IEEE14 node system is shown in the figure;

[0048] Figure 11 For the embodiment of the present application, the real and imaginary part diagram of the equivalent impedance of the AC system viewed from the 2nd node of the IEEE14 node system is shown in the figure;

[0049] Figure 12 For the embodiment of the present application, the elliptical diagram is shown in the figure;

[0050] Figure 13 For the embodiment of the present application, the impedance envelope viewed from the 16th node of the IEEE39 node system is shown in the figure;

[0051] Figure 14 For the embodiment of the present application, the improved impedance envelope viewed from the 2nd node of the IEEE14 node system is shown in the figure

[0052] Figure 15 For the embodiment of the present application, the system block diagram of the AC system wideband impedance envelope is shown in the figure. DETAILED DESCRIPTION

[0053] In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described below in connection with the accompanying drawings of the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, but not all the embodiments. The components of the embodiments of the present application described and shown in the accompanying drawings can be arranged and designed in various different configurations.

[0054] Therefore, the detailed description of the embodiments of the present application provided below in the accompanying drawings is not intended to limit the scope of the claimed present application, but only represents selected embodiments of the present application. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present application without creative labor are within the scope of protection of the present application.

[0055] It should be noted that: similar reference numbers and letters represent similar items in the following drawings, therefore, once an item is defined in one drawing, it does not need to be further defined and explained in the subsequent drawings.

[0056] In order for those skilled in the art to better understand the technical solutions of the present application, the present application will be further described in detail below in connection with the accompanying drawings.

[0057] As shown in the figure, Figure 1 The present application provides an AC system wideband impedance envelope method, comprising:

[0058] S101, a relationship between voltage and current of each node of the AC system is established, a node admittance matrix is formed, nodes of the AC system are classified according to whether or not connected with external equipment, and the node admittance matrix is blocked according to the classification result;

[0059] S102, a Norton equivalent circuit of internal power supply of the AC system is established, and equivalent impedance of the AC system viewed from the node connected with external equipment is obtained according to the established Norton equivalent circuit and the relationship between voltage and current of each node of the AC system;

[0060] S103, the equivalent impedance of the AC system viewed from the node connected with external equipment under each operation mode is superimposed in the same coordinate system by changing the operation mode of the AC system;

[0061] S104, an ellipse with the minimum area is drawn on the coordinate system to enclose all impedance scatter points, and the ellipse is the impedance envelope of the AC system.

[0062] The Norton equivalent circuit of internal power supply of the AC system is as follows:

[0063]

[0064] The output current of the node not connected with external equipment but connected with internal power supply, is the output current of the node not connected with external equipment and not connected with internal power supply, is the admittance in the Norton equivalent circuit of the node connected with external equipment but connected with internal power supply, is the admittance in the Norton equivalent circuit of the node not connected with external equipment and not connected with internal power supply, is the current vector of the current source in the Norton equivalent circuit of the node connected with external equipment but connected with internal power supply, is the current vector of the current source in the Norton equivalent circuit of the node not connected with external equipment and not connected with internal power supply, Y2=0 and =0.

[0065] The equivalent impedance of the AC system viewed from the node connected with external equipment is as follows:

[0066]

[0067] wherein , , is the blocked matrix obtained by blocking the node admittance matrix of the AC system, represents the self-admittance matrix of the node not connected with external equipment in the AC system, represents the self-admittance matrix of the node connected with external equipment, , is the mutual admittance matrix of the two types of nodes, Y represents the matrix composed of admittance in each equivalent circuit after the internal power supply of the alternating current system is equivalent to the Norton circuit.

[0068] An ellipse with the minimum area is drawn on the coordinate system in a non-linear programming manner to surround all impedance scatter points;

[0069] The specific steps of drawing an ellipse with the minimum area on the coordinate system to surround all impedance scatter points are as follows:

[0070] First, the convex hull of all impedance scatter points is obtained, and the convex hull is connected into a closed curve, and then the coordinates are substituted into the non-linear constraint condition to obtain the elliptical envelope.

[0071] Another embodiment of the application provides an alternating current system wideband impedance envelope method, comprising,

[0072] As shown in Figure 2 , a schematic diagram of a simple power system is shown, nodes a and b have source loads or power supplies, nodes c and d are not connected to the outside world and do not have source loads or power supplies, nodes e and f are connected to external devices, and the external devices here can be converters and the like. This embodiment calculates the equivalent impedance from nodes e and f.

[0073] The nodes are divided into three categories, the first category is connected to the internal power supply but not connected to the external device (a, b), the second category is not connected to the external device and not connected to the internal power supply (c, d), and the third category is connected to the external device (e, f), which are represented by subscripts 1, 2 and 3 respectively. Then

[0074] (1)

[0075] wherein, , is a column vector containing two elements, and is a 2*2 matrix.

[0076] The alternating current power supply at the first and second category nodes is modeled as a Figure 3 Norton equivalent circuit as shown in the figure, so that

[0077] (2)

[0078] , represents the output current of the alternating current system internal power supply, and it should be noted that although the second category 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 category node, and the Norton equivalent circuit of the virtual power supply has Y 2=0 and =0.

[0079] From the first two rows of formula (1)

[0080] (3)

[0081] Combining equations (2) and (3), we get

[0082] (4)

[0083] From the third row of equation (1), we get

[0084] (5)

[0085] Substituting equation (4) into equation (5) yields

[0086] (6)

[0087] in , , , .

[0088] If written in the form of equation (6), there is no need to distinguish between type 1 and type 2 nodes, the physical meaning is clearer, and it is easier to modify when removing the power supply at type 1 node or adding the power supply at type 2 node.

[0089] Since the admittance matrix and voltage-current vector are identical in both the first and second types of nodes when the expression is written in the form of equation (6), there is no need to distinguish between the first and second types of nodes during subsequent calculations. That is, there is no need to consider whether nodes not connected to the outside are connected to the internal power supply of the AC system. Furthermore, if it is necessary to remove the power supply of a node in the first type of node after the expression is written in the form of equation (6), only the corresponding node needs to be removed. Y gi and I s1i Set to 0; similarly, if it is necessary to add power to a certain node in the second type of node, simply set the corresponding node's power level to 0. Y gj and I s2j Simply change it to the admittance and current in the Norton equivalent circuit of the added power supply.

[0090] If we classify all first and second-class nodes as first-class nodes, and classify third-class nodes as second-class nodes, then equation (6) can be rewritten as follows:

[0091] (7)

[0092] in

[0093]

[0094] (8)

[0095]

[0096] (9)

[0097] Since the difference between the terminal voltage waveform and the fundamental waveform at any instant in the actual operation of the generator is limited 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 grounded admittance, i.e.

[0098] (10)

[0099] Formula (10) is the equivalent impedance of the AC system from the perspective of nodes e and f.

[0100] Overall, the AC system impedance equivalent method based on kron reduction classifies nodes, obtains the equivalent impedance of the AC system from the perspective of the nodes connected to external equipment, and can calculate the harmonic impedance of the AC system from the perspective of multiple nodes and the mutual impedance between them.

[0101] Kron Reduction (Kron Reduction) is a graph simplification method widely used in the fields of power system analysis, circuit theory, network theory, etc. This method is mainly used to eliminate or simplify internal nodes in physical network systems, while preserving the main electrical characteristics or network structure of the system.

[0102] Calculation results

[0103] In this embodiment, node 16 of the IEEE39 node system and node 2 of the improved IEEE14 node radial network system are selected as the viewing nodes, and the equivalent impedance of the AC system from the selected nodes is calculated. It should be noted here that the improved IEEE14 node system has loads connected to nodes 1, 2, 4, 6, 7, 8, 22, and 23 based on the original IEEE14 node radial network system. This is because the radial network is mainly used in distribution network systems, which are networks connecting the transmission network and end users, so there should be more loads in the distribution network. Therefore, the above improvement is made. The topological structures of the IEEE39 node system and the improved IEEE14 node system are shown in Figure 4 and Figure 5 .

[0104] 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 perspective of node 16 of the IEEE39 node system are shown in Figure 6 ,​7 and 8 are shown.

[0105] The results of looking into the AC system from the IEEE 14-bus system 2 nodes are shown in Figure 9 , 10 and 11.

[0106] From Figure 6 , 7 , 8, 9, 10 and 11, the model established and the method proposed in this embodiment are applied, the error of the equivalent impedance of the AC system calculated is very small compared with the equivalent impedance of the AC system measured by applying the impedance measurement module of the PSCAD platform, which can verify the correctness of the calculation results of this embodiment.

[0107] Wideband harmonic impedance envelope method of AC system

[0108] The equivalent impedance of the AC system is not fixed and unchangeable, and it will change with the change of the parameters of each element in the network, the operation mode of the system and other factors. Therefore, in the actual application of filter design and AC-DC interconnection system stability judgment, a range of system impedance is needed, and the boundary of the range is defined as the impedance envelope. On the basis of correctly calculating the harmonic impedance of the AC system looking into a node, the equivalent impedance under each operation mode is superimposed in 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. Then draw an ellipse with the smallest area to enclose all the impedance scatter points, and the ellipse is the impedance envelope of the typical AC system, and the schematic diagram of the ellipse is shown in Figure 12 .

[0109] After obtaining the impedance scatter points under different operation modes, the drawing of the elliptical impedance envelope can be regarded as a nonlinear programming problem. The schematic diagram of the ellipse is shown in the above figure, and the expression is

[0110] (11)

[0111] wherein (x0, y0) is the center of the ellipse, a and b are respectively half of the length of the major axis and the minor axis of the ellipse, and θ is the included angle between the major axis of the ellipse and the x-axis. , a, b x

[0112] The area formula of the ellipse is

[0113] (12)

[0114] The objective of the linear programming problem is to minimize the area of the ellipse. The objective function is the area of the ellipse shown in formula (12), and the decision variables are x0, y0, a, b, and θ. , , a, b, ​​​​The constraint condition is that any scattered point of impedance is within the ellipse, which can be expressed as: for any impedance scattered point coordinate (x, y), x2+ y2< 1. , ) all have

[0115] (13)

[0116] The planning of the objective function or the constraint function which is a nonlinear function of the optimization variable is a nonlinear planning. Four different algorithms are applied in the system function of nonlinear planning in MATLAB: the interior point method, the sequential quadratic programming algorithm, the effective set method and the trust region effective algorithm. The interior point method is adopted in this embodiment.

[0117] The interior point method generally has the barrier function interior point method and the primal-dual interior point method. The barrier function interior point method is adopted in this embodiment. The barrier function interior point method is a method of maintaining strict feasibility. It always starts from a feasible point and searches within the feasible region. Thus, this method is only applicable to the nonlinear optimization problem with only inequality constraints. The basic idea of the barrier function interior point method is to introduce a barrier term about the constraint on the objective function. When the iteration point approaches the boundary of the feasible region from the inside of the feasible region, the barrier term will tend to infinity to force the iteration point to return to the inside of the feasible region, so as to maintain the strict feasibility of the iteration point. Further, the solution of the constraint problem is converted into the solution of a series of easy sub-problems, so as to obtain the optimal approximation solution of the original problem.

[0118] Suppose that the objective function of the nonlinear planning is min f ( x ), and the constraint condition set is g i ( x ) ≥ 0 Then, the auxiliary function is constructed, and the minimum value of the auxiliary function is solved, that is, min F ( x, μ ) = f ( x ) + μB ( x ), wherein μ is a very small positive number, B ( x ) is the barrier function. The objective function and the constraint condition have been described in the foregoing.

[0119] The barrier function B ( x ) generally needs to meet the conditions of continuity within the feasible region and tending to infinity when x approaches the boundary of g i ( x ) = 0 . B ( x) tends to infinity, two commonly used barrier functions are inverse barrier function ( B ( x ) = ∑ li=11 / g i ( x )) and logarithmic barrier function ( B ( x ) =－ ∑ li=1 ln g i ( x )。

[0120] The general solution process is to first let F ( x, μ ) for each value in the vector x , that is, the decision variable, respectively, make these derivatives 0, that is ∂F ( x, μ )⁄( ∂x_i ) =0 , find the expression of each decision variable about the penalty factor μ x i = h ( μ ) at this time. Let μ approach zero, calculate the decision variable value, at this time F ( x, μ ) = f ( x ). Find the Hessian matrix F ( x, μ ) of Hesse = ▽2F ( x, μ ), if it is a positive definite matrix, then F ( x, μ ) has a local minimum at this time, if it is a negative definite matrix, then F ( x, μ ) has a local maximum at this time, if it is an indefinite matrix, then F ( x, μ ) is not an extreme value at this point.

[0121] After solving the nonlinear programming problem, an elliptical envelope with the smallest area that can enclose all impedance scatter points l 0.

[0122] However, this method has a defect, 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 to calculate the convex hull of the matrix to first get the outermost convex hull of all impedance scatter points, and connect it into a closed curve l 1, at this time, as long as the ellipse encloses l 1, it will certainly enclose all impedance scatter points. Then lThe coordinates of 1 ( x i , y i Substituting the nonlinear constraints, we obtain the corresponding elliptical envelope. (Due to the composition...) l The number of scatter points for 1 is much smaller than the number of scatter points for impedance. Using this method can greatly reduce the number of nonlinear constraint inequalities, thereby improving the calculation speed.

[0123] As can be seen from the calculation process of this method, theoretically... l 1 can also be used as the impedance envelope, and its area is smaller than that of an ellipse. However, l 1 is an irregularly shaped closed curve; only the coordinates of its constituent points can be obtained, making it difficult to derive an analytical expression. In contrast, an ellipse... l Using 0 as the expression for the impedance envelope is clearer. Furthermore, the calculation of the impedance envelope is intended to define the range of impedance transformation under different operating modes; therefore, allowing a certain margin in the definition of this range is more reasonable. Thus, this embodiment uses an ellipse. l 0 is used as the impedance envelope.

[0124] This section uses node 16 of the IEEE 39-node system and node 2 of the improved IEEE 14-node system as input nodes to obtain the equivalent impedance and envelope of the AC system under different operating modes.

[0125] Table 1. Values ​​of decision variables for the IEEE 39-node system

[0126]

[0127] Figure 13 The impedance envelope is viewed from node 16 of the IEEE 39-node system. Operating mode 1 involves lines 16-17 being out of service; operating mode 2 involves lines 17-27 being out of service; and operating mode 3 involves transformers 22-35 being out of service. In this example, the decision variables are... , a, b The values ​​of are shown in Table 1, where The unit is radians. Substituting the values ​​of the decision variables into equation (11) yields the expression for the impedance envelope.

[0128] Table 2. Values ​​of decision variables for the improved IEEE 14-node system

[0129]

[0130] Figure 14In order to improve the impedance envelope of the IEEE14 node system from node 2, wherein the operation mode 1 is that the load at node 6 is out of operation, the operation mode 2 is that the load at node 11 is out of operation, and the operation mode 3 is that the load of the same size as node 4 is put into operation at node 5, in the calculation example, the values of the decision variables are shown in Table 2, wherein In radian.

[0131] The embodiment introduces the calculation method of the impedance envelope when the system operation mode changes by taking the improved IEEE14 node system and the IEEE39 node system as examples. In actual application, according to different scenes, a plurality of operation modes with high possibility of system occurrence are selected, the impedances in different operation modes are superposed on the same coordinate system, and then the method proposed in the embodiment is applied to calculate the impedance envelope.

[0132] As shown in Figure 15 The application further provides an alternating current system wideband impedance envelope system, which comprises:

[0133] The classification module is used for establishing the relationship between the voltages and currents of each node of the alternating current system, forming a node admittance matrix, classifying the nodes of the alternating current system according to whether the nodes are connected with external equipment, and blocking the admittance matrix of the nodes according to the classification results;

[0134] The equivalent impedance acquisition module is used for establishing a Norton equivalent circuit of the internal power supply at the node not connected with external equipment, and acquiring the equivalent impedance of the alternating current system from the node connected with external equipment according to the established Norton equivalent circuit and the relationship between the voltages and currents of each node of the alternating current system;

[0135] The superposition module is used for changing the operation mode of the alternating current system, and superposing the equivalent impedances of the alternating current system from the node connected with external equipment under each operation mode in the same coordinate system;

[0136] The envelope line acquisition module is used for drawing an ellipse with the minimum area on the coordinate system to enclose all impedance scatter points, and the ellipse is the impedance envelope line of the alternating current system.

[0137] In the equivalent impedance acquisition module, the Norton equivalent circuit of the internal power supply at the node not connected with external equipment is:

[0138]

[0139] The output current of the node not connected with external equipment but connected with the internal power supply, is the output current of the node not connected with external equipment and not connected with the internal power supply, is the admittance in the Norton equivalent circuit of the node connected with external equipment but connected with the internal power supply, The admittance of the Norton equivalent circuit of the node not connected with the external device and not connected with the internal power supply, The current vector of the current source in the Norton equivalent circuit of the node connected with the external device and connected with the internal power supply, The current vector of the current source in the Norton equivalent circuit of the node not connected with the external device and not connected with the internal power supply, Y2=0 and =0.

[0140] In the equivalent impedance obtaining module, the equivalent impedance of the node looking into the alternating current system connected with the external device is:

[0141]

[0142] Wherein , , The block matrix obtained by blocking the node admittance matrix of the alternating current system, Indicates the self-admittance matrix of the node not connected with the external device in the alternating current system, Indicates the self-admittance matrix of the node connected with the external device, , The mutual admittance matrix of the two types of nodes, Indicates the matrix composed of the admittance in each equivalent circuit after the node not connected with the external device is equivalent to the Norton circuit.

[0143] In the envelope line obtaining module, a non-linear programming method is used to draw an ellipse with the minimum area in the coordinate system to surround all impedance scatter points;

[0144] The specific steps of drawing an ellipse with the minimum area in the coordinate system to surround all impedance scatter points are as follows:

[0145] First, the convex hull of all impedance scatter points is obtained, and the convex hull is connected into a closed curve, and then the coordinates of the convex hull are substituted into the non-linear constraint condition to obtain the elliptical envelope line.

[0146] An embodiment of the present application provides a terminal device. The terminal device of the embodiment comprises 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 each of the method embodiments described above are implemented. Alternatively, when the processor executes the computer program, the functions of each module / unit in each of the device embodiments described above are implemented.

[0147] The computer program can be divided into one or more modules / units, which are stored in the memory and executed by the processor to complete the present application.

[0148] The terminal device can be a desktop computer, a notebook computer, a palm computer, a cloud server, and the like. The terminal device can include, but is not limited to, a processor and a memory.

[0149] The processor can be a central processing unit (CPU), and can also be other general-purpose processors, a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field-programmable gate array (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, and the like.

[0150] The memory can be used to store the computer program and / or modules, and the processor can realize various functions of the terminal device by running or executing the computer program and / or modules stored in the memory, and calling data stored in the memory.

[0151] The modules / units integrated in the terminal device, if realized in the form of software function units and sold or used as independent products, can be stored in a computer readable storage medium. Based on this understanding, all or part of the processes in the above-mentioned embodiment methods can also be completed by a computer program instructing related hardware, and the computer program can be stored in a computer readable storage medium. When the processor executes the computer program, the steps of the above-mentioned various method embodiments can be realized. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or some intermediate forms, etc. The computer readable medium can include any entity or device capable of carrying the computer program code, recording medium, U disk, mobile hard disk, magnetic disk, optical disk, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signal, telecommunication signal, and software distribution medium, etc. It should be noted that the contents included 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, the computer readable medium does not include electrical carrier signals and telecommunication signals.

[0152] Although the embodiments of the present application have been described above with reference to the accompanying drawings, the present application is not limited to the above-described specific embodiments and areas of application, and the above-described specific embodiments are merely illustrative and instructive, but are not restrictive. Those skilled in the art can make various modifications under the teachings of the specification, and such modifications are also within the scope of the present application protected by the claims.

Claims

1. A broadband impedance envelope method for an AC system, characterized in that, include: Establish the relationship between voltage and current at 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 equipment, and divide the node admittance matrix into blocks according to the classification results. Establish the Norton equivalent circuit of the internal power supply of the AC system at the node not connected to external equipment, and obtain the equivalent impedance of the AC system at the node connected to external equipment based on the relationship between the established Norton equivalent circuit and the voltage and current of each node of the AC system. By changing the operating mode of the AC system, the equivalent impedance of the AC system viewed from the connection nodes of external devices under each operating mode is superimposed in the same coordinate system. Draw an ellipse with the smallest area on the coordinate system that encloses all the impedance points. This ellipse is the impedance envelope of the AC system. Using nonlinear programming, draw an ellipse with the smallest area on the coordinate system to enclose all 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 that encloses all impedance scatter points are as follows: First, obtain the outermost convex hull of all impedance points and connect them into a closed curve. Then, substitute the coordinates of the closed curve into the nonlinear constraint conditions to obtain an elliptical envelope.

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

3. The broadband impedance envelope method for an AC system according to claim 1, characterized in that, The equivalent impedance of the AC system seen from the connection node to the external device is: in , , To divide the nodal admittance matrix of the AC system into blocks, the resulting block matrix is... This represents the self-admittance matrix of a node in an AC system that is not connected to external devices. This represents the self-admittance matrix of a node connected to an external device. , Let the mutual admittance matrix be the matrix between the two types of nodes. This represents the matrix of admittances in each equivalent circuit after the internal power supply of an AC system is equivalent to a Norton circuit.

4. A broadband impedance envelope system for an AC system, characterized in that, include: Classification module: Used to establish the relationship between voltage and current of each node in the AC system, form the node admittance matrix, classify the nodes of the AC system according to whether they are connected to external equipment, and divide the node admittance matrix 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 from the connection node with external equipment 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 operating mode of the AC system and superimpose the equivalent impedance of the AC system viewed from the connection nodes of external devices under various operating modes in the same coordinate system; Envelope acquisition module: used to draw an ellipse with the smallest area on the coordinate system that encloses all impedance points. This ellipse is the impedance envelope of the AC system. In the envelope acquisition module, a nonlinear programming approach is used to draw an ellipse with the smallest area on the coordinate system to enclose all impedance scatter points. The specific steps to draw an ellipse with the smallest area on the coordinate system that encloses all impedance scatter points are as follows: First, obtain the outermost convex hull of all impedance points and connect them into a closed curve. Then, substitute the coordinates of the points into the nonlinear constraint conditions to obtain the elliptical envelope.

5. A broadband impedance envelope system for an AC system according to claim 4, characterized in that, In the equivalent impedance acquisition module, the Norton equivalent circuit for the internal power supply of the AC system is established as follows: The output current of a node that is not connected to an external device but is connected to an internal power supply. The output current of a node that is not connected to external devices or an internal power supply. The admittance in the Norton equivalent circuit for a node connected to an external device but connected to an internal power supply. The admittance in the Norton equivalent circuit for nodes that are not connected to external devices or internal power supplies. This represents the current vector of the current source in the Norton equivalent circuit of a node connected to an external device but connected to an internal power supply. For the current vector of the current source in the Norton equivalent circuit of a node that is not connected to external devices or internal power sources, Y2=0. =0.

6. The wideband impedance envelope system for an AC system according to claim 4, characterized in that, In the equivalent impedance acquisition module, the AC system equivalent impedance viewed from the connection node with the external device is: in , , To divide the nodal admittance matrix of the AC system into blocks, the resulting block matrix is... This represents the self-admittance matrix of a node in an AC system that is not connected to external devices. This represents the self-admittance matrix of a node connected to an external device. , Let the mutual admittance matrix be the matrix between the two types of nodes. This represents the matrix of admittances in each equivalent circuit after the internal power supply of an AC system is equivalent to a Norton circuit.

7. 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, it implements the steps of the wideband impedance envelope method for an AC system as described in any one of claims 1 to 3.

8. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the wideband impedance envelope method for an AC system as described in any one of claims 1 to 3.

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