A modal analysis method, device and medium for harmonic resonance of power distribution system

Abstract

The present invention discloses a modal analysis method, device and medium for harmonic resonance of a power distribution system. The method includes: establishing a node admittance matrix according to an association matrix of the power distribution system; performing modal analysis according to the node admittance matrix, and drawing a modal impedance curve diagram according to the analysis results; taking adjacent points on the modal impedance curve diagram to perform frequency point calculation to obtain a frequency point set; obtaining the modal impedance corresponding to each frequency point in the frequency point set, taking the maximum modal impedance as the maximum modal impedance of the power distribution system, and analyzing the harmonic resonance problem of the power distribution system according to the maximum modal impedance. The present invention proposes a modal analysis method, device and medium for harmonic resonance of a power distribution system. By drawing a modal impedance curve diagram and performing frequency point calculation on the diagram, the maximum modal impedance corresponding to the frequency point set can be obtained, which can solve the problem that it is difficult to calculate the maximum modal impedance of the power distribution system in a simple way in analyzing the harmonic resonance problem.

Description

Technical Field

[0001] The present invention relates to the technical field of power consumption systems, and in particular to a modal analysis method, device and medium for harmonic resonance of a power distribution system. Background Art

[0002] In order to cope with the energy crisis, power electronic devices such as renewable energy grid-connected converters have been widely used, and the power system has shown a trend of high power electronics. At present, the analysis of resonance in power systems has become one of the research hotspots. The main reasons for harmonic resonance include: the harmonic characteristics of the power electronic device itself, the weak grid characteristics of the power electronic power system, and the multi-dimensional wide-area interaction between the components of the power system. In terms of the harmonic characteristics of the power electronic device itself, the method of increasing the virtual modal impedance is usually adopted to effectively suppress the harmonic resonance problem; in terms of the weak grid characteristics of the power electronic power system, by analyzing the influence of the distribution characteristics of the submarine cable, the transmission length of the submarine cable and the control loop parameters on the high-frequency stability of the grid-connected system, the corresponding controller parameter optimization scheme is proposed.

[0003] However, when analyzing harmonic resonance problems, on the one hand, the difficulty of calculating the system modal impedance increases sharply due to the increasing complexity of system components and topological structures; on the other hand, the power electronic distribution system has many nodes, which leads to the need to repeat the process of analyzing the resonant characteristics of each node one by one, resulting in a huge amount of calculation of the system modal impedance. Summary of the invention

[0004] The present invention provides a modal analysis method, device and medium for harmonic resonance of a power distribution system, so as to solve the problem that it is difficult to calculate the maximum modal impedance of the power distribution system in a simple manner when analyzing the harmonic resonance problem.

[0005] In order to solve the above problems, the present invention provides a modal analysis method for harmonic resonance of a power distribution system, comprising:

[0006] According to the correlation matrix of the topological model in the power distribution system, a node admittance matrix is ​​established by representing the current and current in the form of complex frequency domain; wherein the topological model is established according to the output admittance and transfer function of the power distribution system;

[0007] Performing modal analysis according to the node admittance matrix, and drawing a modal impedance curve diagram according to the analysis results;

[0008] Within a preset frequency range, adjacent points on the modal impedance curve are taken to calculate the frequency points in a manner of gradually approaching the resonance peak to obtain a frequency point set;

[0009] The modal impedance corresponding to each frequency point in the frequency point set is obtained, the maximum modal impedance is used as the maximum modal impedance of the power distribution system, and the harmonic resonance problem of the power distribution system is analyzed according to the maximum modal impedance.

[0010] The present invention converts the data of the power distribution system into a complex frequency domain function, which can more easily analyze the voltage and current characteristics of the power distribution system, so that the obtained node admittance matrix can clearly analyze and reflect the relationship between the current and voltage of the power distribution system; by drawing the modal impedance curve, the modal impedance at different frequency points can be known; the method of taking adjacent points on the modal impedance curve to perform frequency point calculation can gradually adjust the calculation step size, and then gradually approach the resonant peak on the modal impedance curve, so as to obtain accurate frequency points on the modal impedance curve to form a frequency point set, so as to use the maximum modal impedance corresponding to the frequency point set as the maximum modal impedance of the power distribution system, so as to analyze the harmonic resonance problem of the power distribution system.

[0011] Compared with the prior art, the present invention can obtain the maximum modal impedance corresponding to the frequency point set as the maximum modal impedance of the power distribution system by drawing a modal impedance curve and performing frequency point calculation on the curve, and the method for obtaining the maximum modal impedance is simple and effective; in the process of impedance acquisition, since the model and the curve are constructed by a small amount of data, the problem of large amount of calculation can be avoided, and the time for obtaining the maximum modal impedance of the power distribution system can be saved while simplifying the calculation. Therefore, it can solve the problem that it is difficult to calculate the maximum modal impedance of the power distribution system in a simple way when analyzing the harmonic resonance problem.

[0012] As a preferred solution, according to the correlation matrix of the topological model in the power distribution system, the node admittance matrix is ​​established by representing the current and current in the form of complex frequency domain, specifically:

[0013] Using the correlation matrix of the topological model of the power distribution system, the KCL equation and the KVL equation in complex frequency domain are respectively expressed to obtain the current expression and the voltage expression;

[0014] Establish branch equations based on branch voltage vectors and voltage source vectors;

[0015] The current expression, the voltage expression and the branch equation are solved simultaneously to obtain the node admittance matrix.

[0016] In this preferred embodiment, since complex frequency domain analysis provides a concise way to describe the behavior of the system, by converting the data of the power distribution system into complex frequency domain functions, it is easier to analyze the voltage and current characteristics of the power distribution system, so that the obtained node admittance matrix can clearly analyze and reflect the relationship between the current and voltage of the power distribution system.

[0017] As a preferred solution, a modal analysis is performed according to the node admittance matrix, and a modal impedance curve is drawn according to the analysis results, specifically:

[0018] Establishing a node voltage-current expression of the power distribution system according to the node admittance matrix;

[0019] Performing parameter decomposition on the node admittance matrix to obtain a first expression including a diagonal eigenvalue matrix and a right eigenvector matrix;

[0020] Simultaneously solving the node voltage-current expression and the first expression to obtain a second expression representing the relationship between the modal voltage vector and the modal current vector;

[0021] The diagonal eigenvalue matrix and the right eigenvector matrix in the second expression are defined as modal voltage vectors to obtain a modal impedance matrix, and the modal impedance curve diagram is plotted according to the modal impedance matrix.

[0022] This preferred solution can know the modal impedance at different frequency points by drawing a modal impedance curve.

[0023] As a preferred solution, the modal impedance curve diagram is drawn according to the modal impedance matrix, specifically:

[0024] By eliminating the right eigenvector matrix in the second expression, a critical matrix is ​​obtained;

[0025] Constructing a participation factor set according to the diagonal elements in the critical matrix; wherein the magnitude of the participation factor in the participation factor set represents the degree of distortion caused by harmonic injection into the power distribution system;

[0026] The modal impedance graph is plotted based on the modal impedance matrix and the participation factor set.

[0027] This preferred scheme eliminates the critical matrix obtained by the right eigenvector matrix, and can be used to evaluate the influence of each component or node in the power distribution system on the overall system performance. The diagonal elements can both observe the critical mode and reflect the excitability of the critical mode. Therefore, the participation factor set established in this way can indirectly reflect the distortion caused by harmonic injection into the power distribution system and the size of the modal impedance. Therefore, the modal impedance curve diagram drawn on the basis of the modal impedance matrix and the participation factor set can intuitively and effectively reflect the size of the modal impedance at different frequency points.

[0028] As a preferred solution, within a preset frequency range, adjacent points on the modal impedance curve are taken to calculate the frequency points in a manner of gradually approaching the resonance peak to obtain a frequency point set, specifically:

[0029] Within a preset frequency range, a point-by-point modal analysis is performed with a first step length, and a first coefficient corresponding to a first frequency point on the modal impedance curve is obtained according to a preset coefficient formula; wherein the coefficient formula is established by a frequency point and an adjacent point of the frequency point;

[0030] If the first coefficient is greater than a preset value, the first frequency point is added to the initial frequency point set, and based on the second frequency point, the first step is taken to re-perform point-by-point modal analysis; wherein the second frequency point is closer to the resonant peak on the modal impedance curve than the first frequency point;

[0031] If the first coefficient is less than or equal to the preset value, a new step size is obtained by adjusting the step size to perform point-by-point modal analysis until the coefficient calculated according to the coefficient formula is greater than the preset value;

[0032] The frequency point set is formed by the initial frequency point set.

[0033] In this preferred embodiment, since the modal impedance curve diagram shows the general shape of the modal impedance curve, the modal impedance change rate is large near the resonance peak, and the modal impedance change tends to be gentle away from the resonance peak. Therefore, through the step analysis method, the resonance peak on the modal impedance curve diagram can be effectively approached step by step, so as to obtain accurate frequency points on the modal impedance curve diagram to form a frequency point set.

[0034] As a preferred solution, the topological model is established based on the output admittance and transfer function of the power distribution system, specifically:

[0035] When a preset controller is used to control the current of the power distribution system, a first transfer function is obtained, and a first harmonic model of the grid-connected converter is established according to the first transfer function;

[0036] Under a preset hth harmonic, a second harmonic model of the long transmission line is established according to the wave impedance and propagation constant of the long transmission line;

[0037] Establishing a third harmonic model of the power load according to the equivalent resistance and equivalent reactance of the load in the power distribution system;

[0038] The topology model is composed of the first harmonic model, the second harmonic model and the third harmonic model.

[0039] The power distribution system of this preferred solution is the process of distributing electric energy from the transmission system to the end users, and mainly involves grid-connected converters, long transmission lines and power loads. Therefore, by establishing harmonic models of grid-connected converters, long transmission lines and power loads respectively to form a topological model of the power distribution system, the topological model can abstractly represent the structure and operating status of the distribution network, so as to provide the connection relationship between various devices and components in the power grid and the interaction information between them, providing a solid data foundation for subsequent calculations.

[0040] As a preferred solution, when a preset controller is used to control the current of the power distribution system, a first transfer function is obtained, and a first harmonic model of the grid-connected converter is established according to the first transfer function, specifically:

[0041] The cut-off frequency of the phase-locked loop is set to be lower than the fundamental frequency of the power distribution system, and a proportional resonant controller is used to control the current of the power distribution system;

[0042] The first transfer function of the proportional resonant controller is acquired, and a first harmonic model of the grid-connected converter is established according to the transformer equivalent inductance and the first transfer function.

[0043] In this preferred solution, since the phase-locked loop can only affect the output admittance of the converter within its control bandwidth, the impact of the phase-locked loop can be ignored by setting the cutoff frequency of the phase-locked loop to be lower than the fundamental frequency of the power distribution system, thereby simplifying the model and analysis process.

[0044] As a preferred solution, under the preset hth harmonic, according to the wave impedance and propagation constant of the long transmission line, a second harmonic model of the long transmission line is established, specifically:

[0045] Under a preset hth harmonic, the wave impedance and the propagation constant of the long transmission line are calculated according to the total series resistance and series reactance of the line;

[0046] Through a preset formula, according to the order of the h-th harmonic, the wave impedance and the propagation constant, the line equivalent impedance under the h-th harmonic and the line equivalent admittance under the h-th harmonic are calculated, and the second harmonic model is established according to the line equivalent impedance under the h-th harmonic and the line equivalent admittance under the h-th harmonic.

[0047] The present invention also provides a modal analysis device for harmonic resonance of a power distribution system, comprising a matrix module, a curve module, a frequency module and an impedance module;

[0048] wherein the matrix module is used to establish a node admittance matrix in a manner of current and current representation in a complex frequency domain according to an association matrix of a topological model in a power distribution system; wherein the topological model is established according to the output admittance and transfer function of the power distribution system;

[0049] The curve module is used to perform modal analysis according to the node admittance matrix and draw a modal impedance curve diagram according to the analysis results;

[0050] The frequency module is used to obtain adjacent points on the modal impedance curve within a preset frequency range, calculate the frequency points in a manner of gradually approaching the resonance peak, and obtain a frequency point set;

[0051] The impedance module is used to obtain the modal impedance corresponding to each frequency point in the frequency point set, take the maximum modal impedance as the maximum modal impedance of the power distribution system, and analyze the harmonic resonance problem of the power distribution system based on the maximum modal impedance.

[0052] As a preferred solution, the matrix module includes an expression unit, a branch unit and an admittance unit;

[0053] The expression unit is used to use the correlation matrix of the topological model of the power distribution system to express the KCL equation and the KVL equation in complex frequency domain to obtain the current expression and the voltage expression;

[0054] The branch unit is used to establish a branch equation according to the branch voltage vector and the voltage source vector;

[0055] The admittance unit is used to simultaneously solve the current expression, the voltage expression and the branch equation to obtain the node admittance matrix.

[0056] As a preferred solution, the curve module includes a construction unit, a decomposition unit, a solution unit and a curve unit;

[0057] Wherein, the construction unit is used to establish a node voltage-current expression of the power distribution system according to the node admittance matrix;

[0058] The decomposition unit is used to perform parameter decomposition on the node admittance matrix to obtain a first expression including a diagonal eigenvalue matrix and a right eigenvector matrix;

[0059] The solving unit is used to simultaneously solve the node voltage-current expression and the first expression to obtain a second expression representing the relationship between the modal voltage vector and the modal current vector;

[0060] The curve unit is used to define the diagonal eigenvalue matrix and the right eigenvector matrix in the second expression as modal voltage vectors, obtain a modal impedance matrix, and draw the modal impedance curve according to the modal impedance matrix.

[0061] As a preferred solution, the curve unit includes a matrix sub-unit, an element sub-unit and a curve sub-unit;

[0062] Wherein, the matrix subunit is used to obtain a critical matrix by eliminating the right eigenvector matrix in the second expression;

[0063] The element subunit is used to construct a participation factor set according to the diagonal elements in the critical matrix; wherein the magnitude of the participation factor in the participation factor set represents the degree of distortion caused by the injection of harmonics into the power distribution system;

[0064] The curve subunit is used to draw the modal impedance curve diagram according to the modal impedance matrix and the participation factor set.

[0065] As a preferred solution, the frequency module includes a coefficient unit, a close unit, a far unit and a constituent unit;

[0066] The coefficient unit is used to perform point-by-point modal analysis with a first step length within a preset frequency range, and obtain a first coefficient corresponding to a first frequency point on the modal impedance curve according to a preset coefficient formula; wherein the coefficient formula is established by a frequency point and an adjacent point of the frequency point;

[0067] The approach unit is used to add the first frequency point to the initial frequency point set if the first coefficient is greater than a preset value, and take the first step length to re-perform point-by-point modal analysis based on the second frequency point; wherein the second frequency point is closer to the resonant peak on the modal impedance curve than the first frequency point;

[0068] The away unit is used for obtaining a new step size by adjusting the step size to perform point-by-point modal analysis if the first coefficient is less than or equal to the preset value, until the coefficient calculated according to the coefficient formula is greater than the preset value;

[0069] The forming unit is configured to form the frequency point set from the initial frequency point set.

[0070] As a preferred solution, the matrix module includes a current conversion unit, a transmission unit, a load unit and a topology unit;

[0071] The current conversion unit is used to obtain a first transfer function when a preset controller is used to control the current of the power distribution system, and to establish a first harmonic model of the grid-connected converter according to the first transfer function;

[0072] The transmission unit is used to establish a second harmonic model of the long transmission line according to the wave impedance and propagation constant of the long transmission line under a preset hth harmonic;

[0073] The load unit is used to establish a third harmonic model of the power load according to the equivalent resistance and equivalent reactance of the load in the power distribution system;

[0074] The topology unit is used to form the topology model by using the first harmonic model, the second harmonic model and the third harmonic model.

[0075] As a preferred solution, the current conversion unit includes a control subunit and a current conversion subunit;

[0076] Wherein, the control subunit is used to set the cutoff frequency of the phase-locked loop to be lower than the fundamental frequency of the power distribution system, and use a proportional resonant controller to control the current of the power distribution system;

[0077] The converter unit is used to obtain the first transfer function of the proportional resonant controller and establish a first harmonic model of the grid-connected converter according to the transformer equivalent inductance and the first transfer function.

[0078] As a preferred solution, the transmission unit includes a constant subunit and an admittance subunit;

[0079] Wherein, the constant subunit is used to calculate the wave impedance and the propagation constant of the long transmission line according to the total series resistance and series reactance of the line under the preset hth harmonic;

[0080] The admittance subunit is used to calculate the line equivalent impedance and the line equivalent admittance under the h-th harmonic according to the order of the h-th harmonic, the wave impedance and the propagation constant through a preset formula, and establish the second harmonic model according to the line equivalent impedance and the line equivalent admittance under the h-th harmonic.

[0081] The present invention also provides a storage medium having a computer program stored thereon. The computer program is called and executed by a computer to implement the modal analysis method for harmonic resonance of a power distribution system as described above. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] Figure 1 It is a flow chart of a modal analysis method for harmonic resonance of a power distribution system provided by an embodiment of the present invention;

[0083] Figure 2 is a topological structure diagram of a typical three-phase grid-connected converter provided in an embodiment of the present invention;

[0084] Figure 3 is a block diagram of a typical three-phase grid-connected converter provided by an embodiment of the present invention;

[0085] Figure 4 is an equivalent circuit diagram of a grid-connected converter provided by an embodiment of the present invention;

[0086] Figure 5 is a π-type equivalent circuit diagram of a uniform transmission line provided by an embodiment of the present invention;

[0087] Figure 6 is a load equivalent model diagram provided by an embodiment of the present invention;

[0088] Figure 7 is a modal impedance curve diagram provided by an embodiment of the present invention;

[0089] Figure 8 is a basic flow chart of variable step-size modal analysis provided by an embodiment of the present invention;

[0090] Fig. 9 is a diagram of a three-busbar test system provided by an embodiment of the present invention;

[0091] Fig.10 is a resonant modal impedance curve diagram of a test system provided by an embodiment of the present invention;

[0092] Fig.11 is a topological structure diagram of a calculation example system provided by an embodiment of the present invention;

[0093] Fig.12 is a diagram of resonant modal analysis results for different numbers of converters provided by an embodiment of the present invention;

[0094] Fig.13 1 is a diagram of the resonant modal analysis result when the unit length resistance r0 changes at the fundamental frequency provided by an embodiment of the present invention;

[0095] Fig.14 1 is a diagram of the resonant modal analysis result when the unit length reactance x0 changes at the fundamental frequency provided by an embodiment of the present invention;

[0096] Fig.15 1 is a diagram showing the resonant modal analysis result when the resistance per unit length changes at the fundamental frequency provided by an embodiment of the present invention;

[0097] Fig.16 It is a structural schematic diagram of a modal analysis device for harmonic resonance of a power distribution system provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0098] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0099] In the description of the present application, it should be understood that the terms "first", "second" and "third" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first", "second" and "third" may explicitly or implicitly include one or more of the features. In the description of the present application, unless otherwise specified, "several" means two or more.

[0100] A modal analysis method for harmonic resonance of a power distribution system provided in an embodiment of the present invention is mainly used in the case where it is difficult to calculate the maximum modal impedance of the power distribution system in a simple manner when analyzing the harmonic resonance of the power distribution system.

[0101] Embodiment 1:

[0102] See also Figure 1 The embodiment of the present invention provides a modal analysis method for harmonic resonance of a power distribution system, including S1 to S4, and the specific implementation steps are as follows:

[0103] S1. According to the correlation matrix of the topological model in the power distribution system, a node admittance matrix is ​​established by representing the current and current in the form of complex frequency domain; wherein the topological model is established according to the output admittance and transfer function of the power distribution system.

[0104] In step S1 of the embodiment of the present invention, S1 includes S1.1 to S1.9; wherein S1.1 is the process of constructing the first harmonic model, S1.2 is the process of constructing the series impedance z0 and the parallel admittance y0, and S1.3 is the process of constructing the wave impedance Z s and propagation constant γ, S1.4 is the process of constructing the second harmonic model, S1.5 is the process of constructing the third harmonic model, S1.6 is the process of constructing the topological model, S1.7 is the process of constructing the association matrix A, S1.8 is the process of constructing the branch equation, S1.9 is the process of constructing the node admittance matrix; and S1.2 to S1.4 are the complete process of constructing the second harmonic model, specifically:

[0105] S1.1. Presetting the power distribution system, including: setting the cutoff frequency of the phase-locked loop (PLL) to be lower than the fundamental frequency of the power distribution system, assuming that the DC voltage of the converter is constant;

[0106] Current control of the distribution system using a proportional resonant (PR) controller in a stationary αβ coordinate system;

[0107] Ignoring sampling and control delays, the first transfer function G of the proportional resonant controller is obtained c (s), and according to the transformer equivalent inductance and the first transfer function G c (s) Calculate the output admittance Y of the converter s (s) and the transfer function G of the filter inductor current to its reference value s (s);

[0108] According to the converter output admittance Y s (s) and the transfer function G of the filter inductor current to its reference value s (s), establish the first harmonic model of the grid-connected converter;

[0109] Among them, the first transfer function is:

[0110]

[0111] The output admittance of the converter is:

[0112]

[0113] The transfer function of the filter inductor current to its reference value is:

[0114]

[0115] Among them, K p and K r are the proportional coefficient and resonance coefficient, ω c is the gain bandwidth, ω0 is the fundamental frequency of the AC system, and s is the differential operator;

[0116] i is the filter inductor current, u t is the three-phase PCC voltage, i * is the reference value of the filter inductor current, L f and C f are the filter inductor and filter capacitor on the inverter side, K c is the capacitor current feedback constant, L t is the transformer equivalent inductance.

[0117] To apply the embodiments of the present invention, please refer to Figure 2 , Figure 2 is a typical three-phase grid-connected converter topology diagram provided in an embodiment of the present invention, which shows the structure of the grid-connected converter; wherein, U dc is the DC side voltage, L f and C fThey are the filter inductor and filter capacitor on the inverter side respectively; the converter is connected to the PCC through a transformer, and the transformer is equivalent to the inductor L tt ;u t(abc) is the three-phase PCC voltage, i (abc) and u (abc) are the filter inductor current and filter capacitor voltage respectively, K pwm is the inverter gain, K c is the capacitor current feedback constant.

[0118] To apply the embodiments of the present invention, please refer to Figure 3 and Figure 4 , Figure 3 : is a block diagram of a typical three-phase grid-connected converter provided in an embodiment of the present invention, which represents the first harmonic model of the grid-connected converter; wherein the grid-connected converter can be equivalent to a controlled current source G s i* and converter output admittance Y s Parallel form;

[0119] Figure 4 is an equivalent circuit diagram of a grid-connected converter provided by an embodiment of the present invention, which represents an equivalent form of the grid-connected converter and shows that the grid-connected converter is equivalent to a controlled current source G s i* and converter output admittance Y s The parallel form of

[0120] And, Y s and Y s (s) refers to the output admittance of the converter, G s and G s (s) both refer to the transfer function from the filter inductor current to its reference value. The difference is that they are expressed in different forms.

[0121] In this embodiment S1.1, since the phase-locked loop can only affect the output admittance of the converter within its control bandwidth, the influence of the phase-locked loop can be ignored by setting the cutoff frequency of the phase-locked loop to be lower than the fundamental frequency of the power distribution system. Since the DC side capacitance is large enough, it can be assumed that the DC voltage of the converter is constant, so as to simplify the model and analysis process.

[0122] S1.2. At the fundamental frequency, obtain the series impedance z0 per unit length and the shunt admittance y0 per unit length of the line;

[0123] Among them, the series impedance per unit length of the line is:

[0124]

[0125] The shunt admittance per unit length is:

[0126]

[0127] Where z0 is the series impedance per unit length of the line, y0 is the shunt admittance per unit length of the line, r0, x0 and b0 are the series resistance, series reactance and shunt susceptance per unit length of the line at the fundamental frequency, R, X and B are the total series resistance, series reactance and shunt susceptance of the line, respectively. tot is the line length, and j is the imaginary unit.

[0128] S1.3. Based on the series impedance z0 per unit length of the line and the shunt admittance y0 per unit length obtained at the fundamental frequency, the wave impedance Z of the long transmission line is calculated according to the total series resistance and series reactance of the line under the preset hth harmonic. s and the propagation constant γ;

[0129] Among them, the wave impedance under the hth harmonic is:

[0130]

[0131] The propagation constant for the hth harmonic is:

[0132]

[0133] The wave speed under the hth harmonic is:

[0134]

[0135] For the parameter z h and h have:

[0136]

[0137]

[0138] Among them, z h and h They are the series impedance per unit length and the shunt admittance per unit length of the line under the hth harmonic respectively.

[0139] S1.4, through the preset formula, according to the order of h harmonics, wave impedance Z s and propagation constant γ, the equivalent impedance Z of the line under the hth harmonic is calculated eq (h) and hth harmonic equivalent line admittance Y eq (h), and according to the equivalent impedance Z of the line under the hth harmonic eq (h) and hth harmonic equivalent line admittance Y eq (h) establishing a second harmonic model;

[0140] Among them, the equivalent impedance of the line under the hth harmonic is:

[0141]

[0142] The equivalent line admittance under the hth harmonic is:

[0143]

[0144] Where h is the harmonic order.

[0145] To apply the embodiments of the present invention, please refer to Figure 5 , Figure 5 is a π-type equivalent circuit diagram of a uniform transmission line provided by an embodiment of the present invention, showing a second harmonic model of a long transmission line, specifically indicating that the length is l tot The π-type equivalent circuit of the transmission line considering the distributed parameter effect under the hth harmonic; where Z eq (h) and Y eq (h) are the equivalent series impedance and equivalent parallel admittance of the line under the hth harmonic.

[0146] S1.5. Obtain the equivalent impedance Z of the load at the fundamental frequency L ;

[0147] The equivalent impedance Z of the load at the fundamental frequency L On this basis, the equivalent impedance Z of the load under the hth harmonic in the harmonic analysis is calculated. L (h);

[0148] According to the equivalent impedance Z of the load under the hth harmonic L (h) Establish the third harmonic model of power load;

[0149] Among them, the equivalent impedance of the load at the fundamental frequency is:

[0150]

[0151] For the parameter R L and X L :

[0152]

[0153]

[0154] The equivalent impedance of the load under the hth harmonic is:

[0155] Z L (h) = R L +jhX L

[0156] Among them, R L is the equivalent resistance of the load, X L is the equivalent reactance of the load; P L The three-phase active power absorbed by the load; QL is the three-phase reactive power absorbed by the load, S L is the three-phase complex power absorbed by the load, U L is the line voltage at the node at the load.

[0157] To apply the embodiments of the present invention, please refer to Figure 6 , Figure 6 is a load equivalent model diagram provided by an embodiment of the present invention, which shows the third harmonic model of the power load, specifically indicating that after the load absorbs the power, Figure 6 The third harmonic model shown is used to represent the load, and the third harmonic model is in the form of components connected in series.

[0158] S1.6. The topological model is composed of the first harmonic model, the second harmonic model and the third harmonic model.

[0159] In the present embodiment S1.1 to S1.6, the power distribution system is the process of distributing electric energy from the transmission system to the end user, which mainly involves the grid-connected converter, the long transmission line and the power load. Therefore, by respectively establishing the harmonic models of the grid-connected converter, the long transmission line and the power load to form the topological model of the power distribution system, the topological model can abstractly represent the structure and operation status of the distribution network, so as to provide the connection relationship between various devices and components in the power grid and the interaction information between them, and provide a solid data foundation for subsequent calculations;

[0160] Furthermore, this embodiment will greatly reduce the difficulty of analyzing harmonic resonance by modeling each component of the power distribution system separately and then associating the models of each component through system connection relationships.

[0161] S1.7. Obtain the association matrix A of the topological model in the power distribution system, specifically:

[0162] For any one with n t = A directed graph of a network with n+1 nodes and b branches. The association between each node and each branch can be expressed using a node-branch association matrix A a To express; A a Each row corresponds to a node, and each column corresponds to a branch, where each element a ik The definitions are as follows ①, ② and ③:

[0163] ① If node i and branch b k No correlation, then a ik =0;

[0164] ② If node i and branch b k There is a connection, and branch b k The reference direction is away from node i (i.e., positive association), then a ik=1;

[0165] ③ If node i and branch b k There is a connection, and branch b k The reference direction is towards node i (i.e., reverse association), then a ik = -1;

[0166] It can be proved that any t The matrix A of a directed graph with nodes and b branches a The rank of is always n=n t ―1, which means that the matrix A a Only n rows in the graph are linearly independent. If we randomly select a node as a reference node in the directed graph, and only for n=n t ―1 non-reference node to establish a node-branch association matrix, then this matrix is ​​obtained from matrix A a The result of deleting a row corresponding to the reference node is called the reduced node-branch association matrix, or association matrix for short, and is represented by symbol A.

[0167] Furthermore, the incidence matrix A is an n×b matrix whose rank is equal to the number of rows n, and whose rows are linearly independent.

[0168] S1.8. Use the association matrix A of the topological model of the power distribution system to express the KCL (Kirchhoff's current law) equation and the KVL (Kirchhoff's voltage law) equation in complex frequency domain to obtain the current expression and voltage expression;

[0169] Establish branch equations based on branch voltage vectors and voltage source vectors;

[0170] The current expression is:

[0171] AI b (s)=0

[0172] The voltage expression is:

[0173] U b (s) = A T U n (s)

[0174] The branch equation is:

[0175] I b (s)=Y b (s)[U b (s)―U s (s)]+I s (s)

[0176] Among them, U s (s) is a b-dimensional voltage source vector, whose elements are the voltages of the voltage sources of each branch; Is (s) is a b-dimensional current source vector, whose elements are the currents of each branch current source; Y b (s) is the branch admittance matrix of the network. For a network without coupled inductor components, the matrix Y b (s) is a diagonal square matrix, and the elements on its main diagonal are the complex frequency domain admittances of each branch of the network.

[0177] In this embodiment S1.8, since complex frequency domain analysis provides a concise way to describe the behavior of the system, by converting the data of the distribution power system into a complex frequency domain function, it is easier to analyze the voltage and current characteristics of the distribution power system, so that the subsequent node admittance matrix can clearly analyze and reflect the relationship between the current and voltage of the distribution power system.

[0178] S1.9. Solve the current expression, voltage expression and branch equations simultaneously to obtain the node admittance matrix, which is:

[0179] First, substitute the branch equation into the current expression to obtain the first equation:

[0180] AY b (s)[U b (s)―U s (s)]+AI s (s)=0

[0181] Next, substitute the voltage expression into the first equation and rearrange it to get the second equation:

[0182] AY b (s)A T U n (s)=AY b (s)U s (s)―AI s (s)

[0183] The second equation represents a set of node equations with n node voltages as unknown quantities, that is, node equations in matrix form.

[0184] Again, order:

[0185]

[0186]

[0187] Finally, the node equations in matrix form can be simplified to the node admittance matrix:

[0188] Y n (s)U n (s)=I n (s)

[0189] Among them, I n (s) is called the node current source vector, and each element of it represents the algebraic sum of the currents of each current source (including equivalent current sources) flowing into the corresponding node; Y n (s) is called the node admittance matrix; Y n (s)U n (s) is an n-dimensional vector, each element of which represents the algebraic sum of the currents flowing out of the corresponding node through the impedance branches connected to the node under the joint action of the node voltage; U n (s) is the n-dimensional voltage source vector.

[0190] It should be noted that the first embodiment uses the modal analysis method to perform parameter analysis. The modal analysis method is based on the node admittance matrix Y n An effective tool for system resonance analysis is to convert the vector in the physical coordinate system into the modal coordinate system for analysis; therefore, the core idea of ​​this embodiment is: for a multi-node network, the parallel resonance and the network node admittance matrix Y n In extreme cases, Y n The eigenvalue of tends to 0, that is, Y n The array tends to be a singular array, Y n -1 When a maximum value appears, the system generates overvoltage and parallel resonance occurs.

[0191] S2. Perform modal analysis based on the node admittance matrix and draw a modal impedance curve based on the analysis results.

[0192] In step S2 of the embodiment of the present invention, S2 includes S2.1 to S2.3; S2.1 is a process of constructing a modal impedance matrix, S2.2 is a process of constructing a critical matrix and a participation factor set, and S2.3 is a process of drawing a modal impedance curve diagram, specifically:

[0193] S2.1. Assuming that the system has parallel resonance at frequency f, the node voltage-current expression of the power distribution system is established based on the node admittance matrix;

[0194] Perform parameter decomposition on the node admittance matrix to obtain a first expression including a diagonal eigenvalue matrix Λ, a left eigenvector matrix L, and a right eigenvector matrix T;

[0195] By substituting the first expression into the node voltage-current expression, the node voltage-current expression and the first expression are solved simultaneously to obtain a second expression representing the relationship between the modal voltage vector and the modal current vector;

[0196] The second expression is simplified by defining U = TV as the modal voltage vector and J = TI as the modal current vector, yielding the modal impedance matrix U = Λ ―1J;

[0197] The node voltage-current expression is:

[0198]

[0199] The first expression is:

[0200] Y n =LΛT

[0201] The second expression is:

[0202] TV=Λ ―1 TI

[0203] The modal impedance matrix can also be expressed in matrix form:

[0204]

[0205] Among them, Y n represents the node admittance matrix at frequency f, V represents the node voltage vector, I represents the node current injection vector; Λ is the diagonal eigenvector matrix; L and T are the left eigenvector matrix and the right eigenvector matrix, respectively, L = T -1 .

[0206] It should be noted that for the matrix form of the modal impedance matrix, since the inverse of the diagonal eigenmatrix Λ has impedance properties, the inverse matrix of the diagonal eigenmatrix is ​​defined as the modal impedance matrix Z; when the mode λ k When it approaches zero, if a small modal current J k is injected, a very large modal voltage U k will be generated; since other modal voltages are not coupled to the modal current J k, other modal voltages are not affected. In addition, the smallest eigenvalue in the diagonal eigenmatrix is ​​called the critical mode, and the corresponding frequency is called the resonant frequency; the left and right eigenvectors of the smallest eigenvalue are called critical eigenvectors.

[0207] S2.2, assuming that the mode λ1 in the diagonal eigenmatrix Λ is the smallest, that is, mode 1 is the critical mode, multiply both sides by the right eigenvector matrix L to eliminate the right eigenvector matrix in the second expression, and obtain the critical matrix V1;

[0208] Construct participation factor set PF based on diagonal elements in critical matrix V1 bm ; Among them, the participation factor set PF bm The size of the participation factor indicates the degree of distortion caused by harmonic injection into the power distribution system;

[0209] Among them, the critical matrix is:

[0210]

[0211] The set of participating factors is:

[0212] PF bm =L bm T mb

[0213] Among them, L bm T mb Corresponding to the diagonal elements of the submatrix where the left eigenvector L and the right eigenvector T in the critical matrix V1 are located, b is the bus number and m is the mode number.

[0214] It should be noted that the larger the participation factor in the participation factor set, the easier it is to observe the influence of harmonics, and the greater the distortion caused by harmonic injection; the bus with the highest excitation is the most effective position to inject signals to eliminate harmonics, and the node with the largest participation factor can be considered as the center of resonance; in addition, the sum of the participation factors of all nodes is 1.

[0215] S2.3, according to the modal impedance matrix and participation factor set PF bm , the modal impedance is calculated at each frequency point, all the calculated modal impedance values ​​are combined to form a curve, and the modal impedance curve diagram is obtained.

[0216] In Example S2, the critical matrix obtained by eliminating the right eigenvector matrix can be used to evaluate the influence of each component or node in the power distribution system on the overall system performance. The diagonal elements can both observe the critical mode and reflect the excitability of the critical mode. Therefore, the participation factor set established in this way can indirectly reflect the distortion caused by harmonic injection into the power distribution system and the size of the modal impedance. Therefore, the modal impedance curve diagram drawn on the basis of the modal impedance matrix and the participation factor set can intuitively and effectively reflect the size of the modal impedance at different frequency points, and can quickly know the modal impedance at different frequency points.

[0217] S3. Within a preset frequency range, adjacent points on the modal impedance curve are taken to calculate the frequency points in a manner of gradually approaching the resonance peak to obtain a frequency point set.

[0218] In step S3 of the embodiment of the present invention, S3 includes S3.1 to S3.2; S3.1 is a presetting process, and S3.2 is a process of constructing a frequency point set, which is specifically:

[0219] To apply the embodiments of the present invention, please refer to Figure 7 , Figure 7is a modal impedance curve diagram provided by an embodiment of the present invention, which shows the general form of the modal impedance curve. It can be seen that near the resonance peak, the modal impedance change rate is large; while far away from the resonance peak, the modal impedance change tends to be gentle. Therefore, the step size can be appropriately increased far away from the resonance peak, and a small step size can be used near the resonance peak to obtain the precise resonance frequency.

[0220] S3.1, set the frequency range [f mim ,f max ] and analysis step {Δf2, Δf1}; wherein Δf1 is a larger step size (the first step size) used to retrieve frequency points far from the resonance peak; Δf2 is a smaller step size used to retrieve frequency points near the resonance peak;

[0221] S3.2, in the frequency range [f mim ,f max ], perform point-by-point modal analysis with a larger step size Δf1, and obtain the first coefficient K corresponding to the first frequency point on the modal impedance curve according to a preset coefficient formula; wherein the coefficient formula is established by the frequency point and the adjacent points of the frequency point;

[0222] The coefficient formula is:

[0223]

[0224] Where Z(·) is the modal impedance corresponding to point (·), f(·) is the frequency corresponding to point (·), and Δf is the frequency step. When points k―2, k―1, and k are on the same side (left / right) of the resonance peak, K>0; it can be proved that there are always three points k―2, k―1, and k with K≤0, so that the resonance frequency f r ∈[f(k-2),f(k)]; therefore, the parameters can be adjusted according to the sign of K.

[0225] If the first coefficient K is greater than zero (K>0), the first frequency point is added to the initial frequency point set, and based on the second frequency point, a larger step size Δf1 is taken to re-perform point-by-point modal analysis; wherein the second frequency point is closer to the resonant peak on the modal impedance curve than the first frequency point;

[0226] If the first coefficient K is less than or equal to zero (K≤0), the analysis step size is switched to a smaller step size Δf2 by step size adjustment and the search is continued until the coefficient calculated according to the coefficient formula is greater than zero (K>0), that is, until the set frequency point is far away from the resonant frequency point, and then the step size is switched back to Δf1 for search;

[0227] A frequency point set is formed by an initial frequency point set.

[0228] In this embodiment S3, since the modal impedance curve diagram shows the general form of the modal impedance curve, the modal impedance change rate is large near the resonance peak, and the modal impedance change tends to be gentle away from the resonance peak. Therefore, through the step analysis method, the resonance peak on the modal impedance curve diagram can be effectively approached step by step, so as to obtain accurate frequency points on the modal impedance curve diagram to form a frequency point set.

[0229] S4. Obtain the modal impedance corresponding to each frequency point in the frequency point set, take the maximum modal impedance as the maximum modal impedance of the power distribution system, and analyze the harmonic resonance problem of the power distribution system based on the maximum modal impedance.

[0230] In the embodiment of the present invention, step S4 includes S4.1 to S4.3; S4.1 is to obtain the maximum modal impedance Z m (k) The process of performing harmonic resonance analysis, S4.2 is the process of analyzing the influence of the number of converters on the resonance characteristics, and S4.3 is the process of analyzing the influence of line parameters on the resonance characteristics, specifically:

[0231] S4.1. Obtain the modal impedance {Z(k)} corresponding to each frequency point in the frequency point set, and take the maximum modal impedance as the maximum modal impedance Z of the power distribution system. m (k), i.e. Z m (k) = max{Z(k)};

[0232] According to the maximum modal impedance Z m (k) Analyze the harmonic resonance problem of power distribution system.

[0233] To apply the embodiments of the present invention, please refer to Figure 8 , Figure 8 : is a basic flow chart of the variable step modal analysis provided by an embodiment of the present invention, showing the general process of obtaining the maximum modal impedance based on the modal impedance curve diagram according to the modal analysis method provided by this embodiment, specifically:

[0234] 1. Start.

[0235] 2. Set the frequency range [f min ,f max ].

[0236] 3. Set the frequency step {Δf2, Δf1}, Δf1>Δf2.

[0237] 4. k=1, Δf=Δf1: Set k=1, corresponding to the first frequency point; let the initial step length Δf be Δf1.

[0238] 5. f(k) = f min :Let the first frequency point f(k) be f min .

[0239] 6. Calculate the node admittance matrix Y n (k): Calculate the node admittance matrix Y corresponding to the current frequency point f(k) n (k).

[0240] 7. Calculate the modal impedance vector Z(k): Calculate the modal impedance vector Z(k) corresponding to the current frequency point f(k).

[0241] 8. Obtain participation factor: Calculate the participation factor corresponding to the current frequency point f(k).

[0242] 9. Judgment f≤f max :Judge the current step length Δf≤f max If not, jump to step 17; if so, jump to step 10.

[0243] 10. Calculate coefficient K: According to the coefficient formula, substitute the current k value to calculate the coefficient K.

[0244] 11. Determine if K>0: Determine if K>0, if not, jump to step 12; if so, jump to step 14.

[0245] 12. A=f(k), k=k-3: Let the preset value A=f(k), let k=k-3.

[0246] 13. Δf=Δf2: let the current step length Δf be Δf2.

[0247] 14. Determine f(k)>A: Determine f(k)>A. If not, jump to step 16; if so, jump to step 15.

[0248] 15. Δf=Δf1: let the current step length Δf be Δf1.

[0249] 16. k=k+1; f(k)=f(k-1)+Af: Let k=k+1, let f(k)=f(k2-1)+Δf, that is, assign a new value to the current frequency point f(k).

[0250] 17. Output results: The node admittance matrix Y corresponding to all the frequency points that have undergone modal analysis n (k), modal impedance vector Z(k) and participation factor, calculate the modal impedance corresponding to the frequency point, and obtain several modal impedances; take the maximum value Z among several modal impedances m (k) = max{Z(k)} is taken as the maximum modal impedance of the power distribution system and output.

[0251] It should be noted that, in this flowchart, steps 6 to 8 are the process of performing modal analysis, and steps 10 to 16 are the process of performing step size adjustment.

[0252] To apply the embodiments of the present invention, please refer to Fig. 9 and Fig.10 , Fig. 9 is a diagram of a three-busbar test system provided by an embodiment of the present invention, showing a Fig. 9 The test system analyzes the effectiveness of the modal analysis method provided in this embodiment. There are three buses in the system, which can be excited to produce or observe harmonic resonance; and Fig. 9 Each complex number in is the impedance or admittance of the corresponding element at the fundamental wave;

[0253] Fig.10 is a resonant modal impedance curve diagram of the test system provided by an embodiment of the present invention, Fig.10 The modal impedance curve shows that the system resonant frequencies are 51.6pu and 9.6pu. Fig.10 It shows that near the resonant frequency, the method proposed in this embodiment is almost completely consistent with the traditional method; only far away from the resonant frequency, there are certain differences between the method proposed in this embodiment and the traditional method, but this does not affect the accuracy of resonant frequency identification. When analyzing 1 to 60 harmonics with a step size of 0.1Hz, the traditional method requires 29502 iterations, while the method proposed in this embodiment only requires 4030 iterations. It can be seen that the modal analysis method provided in this embodiment can save a lot of computing power.

[0254] To apply the embodiments of the present invention, please refer to Fig.11 , Fig.11 is a topological structure diagram of a calculation example system provided by an embodiment of the present invention, showing a simplified topological structure of a power distribution system;

[0255] Table 1 Transmission line parameters

[0256]

[0257]

[0258] Table 2 Converter parameters

[0259]

[0260] To apply the embodiment of the present invention, please refer to Table 1 and Table 2. Table 1 is a transmission line parameter table provided in this embodiment, which shows the details of the parameters of the transmission line when it is assumed that the parameters of each section of the transmission line are consistent in order to simplify the analysis;

[0261] Table 2 is a parameter table of the converter provided in this embodiment, indicating the details of the parameters of the converter when the converters in the system use the same parameters;

[0262] And, the system node admittance matrix Y under the hth harmonic n (h) is:

[0263]

[0264] S4.2. Analyze the influence of the number of converters on the resonance characteristics, specifically:

[0265] Table 3 Resonance modal analysis results of different numbers of converters

[0266]

[0267] To apply the embodiments of the present invention, please refer to Fig.12 and Table 3, Fig.12 is a diagram of the resonant modal analysis results of different numbers of converters provided by an embodiment of the present invention, and Table 3 is the resonant modal analysis results of different numbers of converters, Fig.12 and Table 3 show the resonant modal analysis results when power electronic converters such as charging piles and distributed photovoltaics are connected to the grid in cluster form, assuming that there are n converters connected in parallel at the node;

[0268] From the results of modal analysis, it can be seen that there are obviously two types of resonant mode risks in the power distribution system: one is low-frequency resonance and the other is high-frequency resonance. As n increases, the center frequency of the low-frequency resonance decreases slightly, while the center frequency of the high-frequency resonance remains unchanged.

[0269] S4.3. Analyze the influence of line parameters on resonance characteristics, specifically:

[0270] To apply the embodiments of the present invention, please refer to Fig.13 , Fig.14 and Fig.15 , Fig.13 is a diagram of the resonant modal analysis result when the unit length resistance r0 changes at the fundamental frequency provided by an embodiment of the present invention, Fig.14 is a diagram of the resonant mode analysis result when the unit length reactance x0 changes at the fundamental frequency provided by an embodiment of the present invention, Fig.15 1 is a diagram showing the resonant modal analysis result when the resistance per unit length changes at the fundamental frequency provided by an embodiment of the present invention;

[0271] The distribution network is at the end of the power system, and the line distribution parameters have an impact on the system resonance characteristics. Fig.13 , Fig.14 and Fig.15 The results of resonant modal analysis when the line distributed parameters change are shown. As can be seen from the figure:

[0272] (1) The line distribution parameters such as unit length resistance r0, unit length reactance x0 and unit length resistance nb0 at the fundamental frequency have an impact on both high and low frequency resonant frequencies;

[0273] (2) As the unit length resistance r0 increases at the fundamental frequency, the center frequency of the resonance remains basically unchanged, and the modal impedance peak decreases, indicating that the resonance is suppressed to a certain extent;

[0274] (3) As the reactance per unit length x0 increases, the center frequency of the high-frequency resonance increases and the modal impedance peak increases, while the center frequency of the low-frequency resonance decreases and the modal impedance peak decreases, indicating that the resonance is further deteriorated;

[0275] (4) As the resistance per unit length increases, the center frequencies of high and low frequency resonances decrease and the modal impedance peaks decrease.

[0276] In general, the embodiments of the present invention have the following beneficial effects:

[0277] This embodiment converts the data of the power distribution system into a complex frequency domain function, which can more easily analyze the voltage and current characteristics of the power distribution system, so that the obtained node admittance matrix can clearly analyze and reflect the relationship between the current and voltage of the power distribution system; by drawing the modal impedance curve, the modal impedance at different frequency points can be known; by taking adjacent points on the modal impedance curve to perform frequency point calculations, the calculation step size can be gradually adjusted, and then gradually approaching the resonant peak on the modal impedance curve, so as to obtain accurate frequency points on the modal impedance curve to form a frequency point set, so that the maximum modal impedance corresponding to the frequency point set is used as the maximum modal impedance of the power distribution system, so as to analyze the harmonic resonance problem of the power distribution system.

[0278] Furthermore, this embodiment reduces the number of repeated analyses by changing the analysis step in real time, thereby greatly accelerating the analysis speed while ensuring the analysis accuracy, and can effectively save harmonic resonance analysis time.

[0279] Embodiment 2:

[0280] See also Fig.16 , an embodiment of the present invention provides a modal analysis device for harmonic resonance of a power distribution system, comprising a matrix module 10, a curve module 20, a frequency module 30 and an impedance module 40;

[0281] The matrix module 10 is used to establish a node admittance matrix in a manner of representing current and current in a complex frequency domain according to the correlation matrix of the topological model in the power distribution system; wherein the topological model is established according to the output admittance and transfer function of the power distribution system;

[0282] The curve module 20 is used to perform modal analysis according to the node admittance matrix and draw a modal impedance curve according to the analysis results;

[0283] The frequency module 30 is used to obtain adjacent points on the modal impedance curve within a preset frequency range, calculate the frequency points in a manner of gradually approaching the resonance peak, and obtain a frequency point set;

[0284] The impedance module 40 is used to obtain the modal impedance corresponding to each frequency point in the frequency point set, take the maximum modal impedance as the maximum modal impedance of the power distribution system, and analyze the harmonic resonance problem of the power distribution system according to the maximum modal impedance.

[0285] In one embodiment, the matrix module 10 includes a control subunit, a current conversion subunit, a parameter unit, a constant subunit, an admittance subunit, a load unit, a topology unit, an association unit, an expression unit, a branch unit, an admittance unit, a parameter unit, a constant subunit, and an admittance subunit;

[0286] Among them, the control subunit and the conversion subunit are the process of constructing the first harmonic model, the parameter unit is the process of constructing the series impedance z0 and the parallel admittance y0, and the constant subunit is the process of constructing the wave impedance Z s and propagation constant γ, the admittance subunit is the process of constructing the second harmonic model, the load unit is the process of constructing the third harmonic model, the topology unit is the process of constructing the topology model, the association unit is the process of constructing the association matrix A, the expression unit and the branch unit are the processes of constructing the branch equation, and the admittance unit is the process of constructing the node admittance matrix; and the parameter unit, the constant subunit and the admittance subunit are the complete process of constructing the second harmonic model, specifically:

[0287] The control subunit is used to pre-set the power distribution system, including: setting the cut-off frequency of the phase-locked loop (PLL) to be lower than the fundamental frequency of the power distribution system, assuming that the DC voltage of the converter is constant;

[0288] The control subunit is further used to perform current control on the power distribution system using an acquisition proportional resonance (PR) controller in a stationary αβ coordinate system;

[0289] The converter unit is used to obtain the first transfer function G of the proportional resonant controller while ignoring the sampling and control delays. c (s), and according to the transformer equivalent inductance and the first transfer function G c (s) Calculate the output admittance Y of the converter s (s) and the transfer function G of the filter inductor current to its reference value s (s);

[0290] The converter unit is also used to output the admittance Y of the converter. s (s) and the transfer function G of the filter inductor current to its reference value s (s), establish the first harmonic model of the grid-connected converter;

[0291] Among them, the first transfer function is:

[0292]

[0293] The output admittance of the converter is:

[0294]

[0295] The transfer function of the filter inductor current to its reference value is:

[0296]

[0297] Among them, K p and K r are the proportional coefficient and resonance coefficient, ω c is the gain bandwidth, ω0 is the fundamental frequency of the AC system, and s is the differential operator;

[0298] i is the filter inductor current, u t is the three-phase PCC voltage, i * is the reference value of the filter inductor current, L f and C f are the filter inductor and filter capacitor on the inverter side, K c is the capacitor current feedback constant, L t is the transformer equivalent inductance.

[0299] To apply the embodiments of the present invention, please refer to Figure 2 , Figure 2 is a typical three-phase grid-connected converter topology diagram provided in an embodiment of the present invention, which shows the structure of the grid-connected converter; wherein, U dc is the DC side voltage, L f and C f They are the filter inductor and filter capacitor on the inverter side respectively; the converter is connected to the PCC through a transformer, and the transformer is equivalent to the inductor L tt ;u t(abc) is the three-phase PCC voltage, i (abc) and u (abc) are the filter inductor current and filter capacitor voltage respectively, K pwm is the inverter gain, K c is the capacitor current feedback constant.

[0300] To apply the embodiments of the present invention, please refer to Figure 3 and Figure 4 , Figure 3 : is a block diagram of a typical three-phase grid-connected converter provided in an embodiment of the present invention, which represents the first harmonic model of the grid-connected converter; wherein the grid-connected converter can be equivalent to a controlled current source G s i* and converter output admittance Y sParallel form;

[0301] Figure 4 is an equivalent circuit diagram of a grid-connected converter provided by an embodiment of the present invention, which represents an equivalent form of the grid-connected converter and shows that the grid-connected converter is equivalent to a controlled current source G s i* and converter output admittance Y s The parallel form of

[0302] And, Y s and Y s (s) refers to the output admittance of the converter, G s and G s (s) both refer to the transfer function from the filter inductor current to its reference value. The difference is that they are expressed in different forms.

[0303] In the control subunit and the converter subunit of the present embodiment, since the phase-locked loop can affect the output admittance of the converter only within its control bandwidth, the influence of the phase-locked loop can be ignored by setting the cut-off frequency of the phase-locked loop to be lower than the fundamental frequency of the power distribution system. Since the DC side capacitance is large enough, it can be assumed that the DC voltage of the converter is constant, so as to simplify the model and the analysis process.

[0304] The parameter unit is used to obtain the series impedance z0 per unit length and the shunt admittance y0 per unit length of the line at the fundamental frequency;

[0305] Among them, the series impedance per unit length of the line is:

[0306]

[0307] The shunt admittance per unit length is:

[0308]

[0309] Where z0 is the series impedance per unit length of the line, y0 is the shunt admittance per unit length of the line, r0, x0 and b0 are the series resistance, series reactance and shunt susceptance per unit length of the line at the fundamental frequency, R, X and B are the total series resistance, series reactance and shunt susceptance of the line, respectively. tot is the line length, and j is the imaginary unit.

[0310] The constant subunit is used to calculate the wave impedance Z of the long transmission line according to the total series resistance and series reactance of the line under the preset hth harmonic based on the series impedance z0 per unit length of the line and the shunt admittance y0 per unit length obtained at the fundamental frequency. s and the propagation constant γ;

[0311] Among them, the wave impedance under the hth harmonic is:

[0312]

[0313] The propagation constant for the hth harmonic is:

[0314]

[0315] The wave speed under the hth harmonic is:

[0316]

[0317] For the parameter z h and h have:

[0318]

[0319]

[0320] Among them, z h and h They are the series impedance per unit length and the shunt admittance per unit length of the line under the hth harmonic respectively.

[0321] The admittance subunit is used to adjust the harmonic according to the order of the hth harmonic and the wave impedance Z by a preset formula. s and propagation constant γ, the equivalent impedance Z of the line under the hth harmonic is calculated eq (h) and hth harmonic equivalent line admittance Y eq (h), and according to the equivalent impedance Z of the line under the hth harmonic eq (h) and hth harmonic equivalent line admittance Y eq (h) establishing a second harmonic model;

[0322] Among them, the equivalent impedance of the line under the hth harmonic is:

[0323]

[0324] The equivalent line admittance under the hth harmonic is:

[0325]

[0326] Where h is the harmonic order.

[0327] To apply the embodiments of the present invention, please refer to Figure 5 , Figure 5 is a π-type equivalent circuit diagram of a uniform transmission line provided by an embodiment of the present invention, showing a second harmonic model of a long transmission line, specifically indicating that the length is l tot The π-type equivalent circuit of the transmission line considering the distributed parameter effect under the hth harmonic; where Z eq (h) and Y eq(h) are the equivalent series impedance and equivalent parallel admittance of the line under the hth harmonic.

[0328] Load unit, used to obtain the equivalent impedance Z of the load at the fundamental frequency L ;

[0329] Load unit, also used for the equivalent impedance Z of the load at the fundamental frequency L On this basis, the equivalent impedance Z of the load under the hth harmonic in the harmonic analysis is calculated. L (h);

[0330] Load unit, also used to calculate the equivalent impedance Z of the load under the hth harmonic L (h) Establish the third harmonic model of power load;

[0331] Among them, the equivalent impedance of the load at the fundamental frequency is:

[0332]

[0333] For the parameter R L and X L :

[0334]

[0335]

[0336] The equivalent impedance of the load under the hth harmonic is:

[0337] Z L (h) = R L +jhX L

[0338] Among them, R L is the equivalent resistance of the load, X L is the equivalent reactance of the load; P L The three-phase active power absorbed by the load; Q L is the three-phase reactive power absorbed by the load, S L is the three-phase complex power absorbed by the load, U L is the line voltage at the node at the load.

[0339] To apply the embodiments of the present invention, please refer to Figure 6 , Figure 6 is a load equivalent model diagram provided by an embodiment of the present invention, which shows the third harmonic model of the power load, specifically indicating that after the load absorbs the power, Figure 6 The third harmonic model shown is used to represent the load, and the third harmonic model is in the form of components connected in series.

[0340] The topology unit is used to form a topology model by using the first harmonic model, the second harmonic model and the third harmonic model.

[0341] In the control subunit-topology unit of this embodiment, the power distribution system is the process of distributing electric energy from the transmission system to the end user, which mainly involves the grid-connected converter, the long transmission line and the power load. Therefore, by respectively establishing the harmonic models of the grid-connected converter, the long transmission line and the power load to form the topological model of the power distribution system, the topological model can abstractly represent the structure and operation status of the distribution network, so as to provide the connection relationship between various devices and components in the power grid and the interaction information between them, and provide a solid data foundation for subsequent calculations;

[0342] Furthermore, this embodiment will greatly reduce the difficulty of analyzing harmonic resonance by modeling each component of the power distribution system separately and then associating the models of each component through system connection relationships.

[0343] The association unit is used to obtain the association matrix A of the topological model in the power distribution system, specifically:

[0344] For any one with n t = A directed graph of a network with n+1 nodes and b branches. The association between each node and each branch can be expressed using a node-branch association matrix A a To express; A a Each row corresponds to a node, and each column corresponds to a branch, where each element a ik The definitions are as follows ①, ② and ③:

[0345] ① If node i and branch b k No correlation, then a ik =0;

[0346] ② If node i and branch b k There is a connection, and branch b k The reference direction is away from node i (i.e., positive association), then a ik =1;

[0347] ③ If node i and branch b k There is a connection, and branch b k The reference direction is towards node i (i.e., reverse association), then a ik = -1;

[0348] It can be proved that any t The matrix A of a directed graph with nodes and b branches a The rank of is always n=n t ―1, which means that the matrix A aOnly n rows in the graph are linearly independent. If we randomly select a node as a reference node in the directed graph, and only for n=n t ―1 non-reference node to establish a node-branch association matrix, then this matrix is ​​obtained from matrix A a The result of deleting a row corresponding to the reference node is called the reduced node-branch association matrix, or association matrix for short, and is represented by symbol A.

[0349] Furthermore, the incidence matrix A is an n×b matrix whose rank is equal to the number of rows n, and whose rows are linearly independent.

[0350] An expression unit, for using an association matrix A of a topological model in a power distribution system to express a KCL (Kirchhoff's current law) equation and a KVL (Kirchhoff's voltage law) equation in complex frequency domain to obtain a current expression and a voltage expression;

[0351] A branch unit, used for establishing a branch equation according to a branch voltage vector and a voltage source vector;

[0352] The current expression is:

[0353] AI b (s)=0

[0354] The voltage expression is:

[0355] U b (s) = A T U n (s)

[0356] The branch equation is:

[0357] I b (s)=Y b (s)[U b (s)―U s (s)]+I s (s)

[0358] Among them, U s (s) is a b-dimensional voltage source vector, whose elements are the voltages of the voltage sources of each branch; I s (s) is a b-dimensional current source vector, whose elements are the currents of each branch current source; Y b (s) is the branch admittance matrix of the network. For a network without coupled inductor components, the matrix Y b (s) is a diagonal square matrix, and the elements on its main diagonal are the complex frequency domain admittances of each branch of the network.

[0359] In the expression unit and branch unit of this embodiment, since complex frequency domain analysis provides a concise way to describe the behavior of the system, by converting the data of the distribution power system into a complex frequency domain function, it is easier to analyze the voltage and current characteristics of the distribution power system, so that the subsequently obtained node admittance matrix can clearly analyze and reflect the relationship between the current and voltage of the distribution power system.

[0360] The admittance unit is used to solve the current expression, voltage expression and branch equations simultaneously to obtain the node admittance matrix, which is:

[0361] First, substitute the branch equation into the current expression to obtain the first equation:

[0362] AY b (s)[U b (s)―U s (s)]+AI s (s)=0

[0363] Next, substitute the voltage expression into the first equation and rearrange it to get the second equation:

[0364] AY b (s)A T U n (s)=AY b (s)U s (s)―AI s (s)

[0365] The second equation represents a set of node equations with n node voltages as unknown quantities, that is, node equations in matrix form.

[0366] Again, order:

[0367]

[0368]

[0369] Finally, the node equations in matrix form can be simplified to the node admittance matrix:

[0370] Y n (s)U n (s)=I n (s)

[0371] Among them, I n (s) is called the node current source vector, and each element of it represents the algebraic sum of the currents of each current source (including equivalent current sources) flowing into the corresponding node; Y n (s) is called the node admittance matrix; Y n (s)U n(s) is an n-dimensional vector, each element of which represents the algebraic sum of the currents flowing out of the corresponding node through the impedance branches connected to the node under the joint action of the node voltage; U n (s) is the n-dimensional voltage source vector.

[0372] It should be noted that the second embodiment uses the modal analysis method to perform parameter analysis. The modal analysis method is based on the node admittance matrix Y n An effective tool for system resonance analysis is to convert the vector in the physical coordinate system into the modal coordinate system for analysis; therefore, the core idea of ​​this embodiment is: for a multi-node network, the parallel resonance and the network node admittance matrix Y n In extreme cases, Y n The eigenvalue of tends to 0, that is, Y n The array tends to be a singular array, Y n -1 When a maximum value appears, the system generates overvoltage and parallel resonance occurs.

[0373] In one embodiment, the curve module 20 includes a construction unit, a decomposition unit, a solution unit, a matrix subunit, an element subunit and a curve subunit; the construction unit, the decomposition unit and the solution unit are processes for constructing a modal impedance matrix, the matrix subunit and the element subunit are processes for constructing a critical matrix and a participation factor set, and the curve subunit is a process for drawing a modal impedance curve graph, specifically:

[0374] A construction unit is used to establish a node voltage-current expression of the power distribution system according to the node admittance matrix, assuming that the system has parallel resonance at a frequency f;

[0375] A decomposition unit, used for performing parameter decomposition on the node admittance matrix to obtain a first expression including a diagonal eigenvalue matrix Λ, a left eigenvector matrix L and a right eigenvector matrix T;

[0376] A solving unit, configured to simultaneously solve the node voltage-current expression and the first expression by substituting the first expression into the node voltage-current expression, so as to obtain a second expression representing the relationship between the modal voltage vector and the modal current vector;

[0377] The solving unit is also used to define U=TV as the modal voltage vector and J=TI as the modal current vector, thereby simplifying the second expression to obtain the modal impedance matrix U=Λ ―1 J;

[0378] The node voltage-current expression is:

[0379]

[0380] The first expression is:

[0381] Y n =LΛT

[0382] The second expression is:

[0383] TV=Λ ―1 TI

[0384] The modal impedance matrix can also be expressed in matrix form:

[0385]

[0386] Among them, Y n represents the node admittance matrix at frequency f, V represents the node voltage vector, I represents the node current injection vector; Λ is the diagonal eigenvector matrix; L and T are the left eigenvector matrix and the right eigenvector matrix, respectively, L = T -1 .

[0387] It should be noted that for the matrix form of the modal impedance matrix, since the inverse of the diagonal eigenmatrix Λ has impedance properties, the inverse matrix of the diagonal eigenmatrix is ​​defined as the modal impedance matrix Z; when the mode λ k When it approaches zero, if a small modal current J k is injected, a very large modal voltage U k will be generated; since other modal voltages are not coupled to the modal current J k, other modal voltages are not affected. In addition, the smallest eigenvalue in the diagonal eigenmatrix is ​​called the critical mode, and the corresponding frequency is called the resonant frequency; the left and right eigenvectors of the smallest eigenvalue are called critical eigenvectors.

[0388] The matrix subunit is used to assume that the mode λ1 in the diagonal eigenmatrix Λ is the smallest, that is, mode 1 is the critical mode, and the right eigenvector matrix L is multiplied on both sides to eliminate the right eigenvector matrix in the second expression to obtain the critical matrix V1;

[0389] The element subunit is used to construct the participation factor set PF based on the diagonal elements in the critical matrix V1 bm ; Among them, the participation factor set PF bm The size of the participation factor indicates the degree of distortion caused by harmonic injection into the power distribution system;

[0390] Among them, the critical matrix is:

[0391]

[0392] The set of participating factors is:

[0393] PF bm =L bm T mb

[0394] Among them, Lbm T mb Corresponding to the diagonal elements of the submatrix where the left eigenvector L and the right eigenvector T in the critical matrix V1 are located, b is the bus number and m is the mode number.

[0395] It should be noted that the larger the participation factor in the participation factor set, the easier it is to observe the influence of harmonics, and the greater the distortion caused by harmonic injection; the bus with the highest excitation is the most effective position to inject signals to eliminate harmonics, and the node with the largest participation factor can be considered as the center of resonance; in addition, the sum of the participation factors of all nodes is 1.

[0396] The curve subunit is used to calculate the modal impedance matrix and the participation factor set PF bm , the modal impedance is calculated at each frequency point, all the calculated modal impedance values ​​are combined to form a curve, and the modal impedance curve diagram is obtained.

[0397] The curve module 20 of the embodiment eliminates the critical matrix obtained by the right eigenvector matrix, and can be used to evaluate the influence of each component or node in the power distribution system on the overall system performance. The diagonal elements can both observe the critical mode and reflect the excitability of the critical mode. Therefore, the participation factor set established in this way can indirectly reflect the distortion caused by harmonic injection into the power distribution system and the size of the modal impedance. Therefore, the modal impedance curve diagram drawn on the basis of the modal impedance matrix and the participation factor set can intuitively and effectively reflect the size of the modal impedance at different frequency points, and can quickly know the modal impedance at different frequency points.

[0398] In one embodiment, the frequency module 30 includes a setting unit, a coefficient unit, a close unit, a far unit and a constituent unit; the setting unit is a pre-set process, and the coefficient unit, the close unit, the far unit and the constituent unit are processes for constructing a frequency point set, specifically:

[0399] To apply the embodiments of the present invention, please refer to Figure 7 , Figure 7 is a modal impedance curve diagram provided by an embodiment of the present invention, which shows the general form of the modal impedance curve. It can be seen that near the resonance peak, the modal impedance change rate is large; while far away from the resonance peak, the modal impedance change tends to be gentle. Therefore, the step size can be appropriately increased far away from the resonance peak, and a small step size can be used near the resonance peak to obtain the precise resonance frequency.

[0400] Setting unit, used to set the frequency range [f mim ,f max ] and analysis step {Δf2, Δf1}; wherein Δf1 is a larger step size (the first step size) used to retrieve frequency points far from the resonance peak; Δf2 is a smaller step size used to retrieve frequency points near the resonance peak;

[0401] Coefficient unit, used in the frequency range [f mim ,f max ], perform point-by-point modal analysis with a larger step size Δf1, and obtain the first coefficient K corresponding to the first frequency point on the modal impedance curve according to a preset coefficient formula; wherein the coefficient formula is established by the frequency point and the adjacent points of the frequency point;

[0402] The coefficient formula is:

[0403]

[0404] Where Z(·) is the modal impedance corresponding to point (·), f(·) is the frequency corresponding to point (·), and Δf is the frequency step. When points k―2, k―1, and k are on the same side (left / right) of the resonance peak, K>0; it can be proved that there are always three points k―2, k―1, and k with K≤0, so that the resonance frequency f r ∈[f(k-2),f(k)]; therefore, the parameters can be adjusted according to the sign of K.

[0405] The approach unit is used to add the first frequency point to the initial frequency point set if the first coefficient K is greater than zero (K>0), and take a larger step size Δf1 on the basis of the second frequency point to re-perform point-by-point modal analysis; wherein the second frequency point is closer to the resonant peak on the modal impedance curve than the first frequency point;

[0406] A distance unit is used for switching the analysis step to a smaller step Δf2 by adjusting the step size if the first coefficient K is less than or equal to zero (K≤0) and continuing to search until the coefficient calculated according to the coefficient formula is greater than zero (K>0), that is, until the set frequency point is far away from the resonant frequency point, and then switching the step size back to Δf1 for searching;

[0407] The constituting unit is used to construct a frequency point set from an initial frequency point set.

[0408] In the frequency module 30 of the present embodiment, since the modal impedance curve diagram shows the general form of the modal impedance curve, the modal impedance change rate is large near the resonance peak, and the modal impedance change tends to be gentle away from the resonance peak. Therefore, through the step analysis method, the resonance peak on the modal impedance curve diagram can be effectively approached step by step, so as to obtain accurate frequency points on the modal impedance curve diagram to form a frequency point set.

[0409] In one embodiment, the impedance module 40 includes an analysis unit, a converter unit and a line unit; the analysis unit is used to obtain the maximum modal impedance Z m(k) The process of performing harmonic resonance analysis, the converter unit is the process of analyzing the influence of the converter quantity on the resonance characteristics, and the line unit is the process of analyzing the influence of the line parameters on the resonance characteristics, specifically:

[0410] The analysis unit is used to obtain the modal impedance {Z(k)} corresponding to each frequency point in the frequency point set, and take the maximum modal impedance as the maximum modal impedance Z of the power distribution system. m (k), i.e. Z m (k) = max{Z(k)};

[0411] The analysis unit is also used to determine the maximum modal impedance Z m (k) Analyze the harmonic resonance problem of power distribution system.

[0412] To apply the embodiments of the present invention, please refer to Figure 8 , Figure 8 : is a basic flow chart of the variable step modal analysis provided by an embodiment of the present invention, showing the general process of obtaining the maximum modal impedance based on the modal impedance curve diagram according to the modal analysis device provided by this embodiment, specifically:

[0413] 1. Start.

[0414] 2. Set the frequency range [f min ,f max ].

[0415] 3. Set the frequency step {Δf2, Δf1}, Δf1>Δf2.

[0416] 4. k=1, Δf=Δf1: Set k=1, corresponding to the first frequency point; let the initial step length Δf be Δf1.

[0417] 5. f(k) = f min :Let the first frequency point f(k) be f min .

[0418] 6. Calculate the node admittance matrix Y n (k): Calculate the node admittance matrix Y corresponding to the current frequency point f(k) n (k).

[0419] 7. Calculate the modal impedance vector Z(k): Calculate the modal impedance vector Z(k) corresponding to the current frequency point f(k).

[0420] 8. Obtain participation factor: Calculate the participation factor corresponding to the current frequency point f(k).

[0421] 9. Judgment f≤f max :Judge the current step length Δf≤f maxIf not, jump to step 17; if so, jump to step 10.

[0422] 10. Calculate coefficient K: According to the coefficient formula, substitute the current k value to calculate the coefficient K.

[0423] 11. Determine if K>0: Determine if K>0, if not, jump to step 12; if so, jump to step 14.

[0424] 12. A=f(k), k=k-3: Let the preset value A=f(k), let k=k-3.

[0425] 13. Δf=Δf2: let the current step length Δf be Δf2.

[0426] 14. Determine f(k)>A: Determine f(k)>A. If not, jump to step 16; if so, jump to step 15.

[0427] 15. Δf=Δf1: let the current step length Δf be Δf1.

[0428] 16. k=k+1; f(k)=f(k-1)+Af: Let k=k+1, let f(k)=f(k2-1)+Δf, that is, assign a new value to the current frequency point f(k).

[0429] 17. Output results: The node admittance matrix Y corresponding to all the frequency points that have undergone modal analysis n (k), modal impedance vector Z(k) and participation factor, calculate the modal impedance corresponding to the frequency point, and obtain several modal impedances; take the maximum value Z among several modal impedances m (k) = max{Z(k)} is taken as the maximum modal impedance of the power distribution system and output.

[0430] It should be noted that, in this flowchart, steps 6 to 8 are the process of performing modal analysis, and steps 10 to 16 are the process of performing step size adjustment.

[0431] To apply the embodiments of the present invention, please refer to Fig. 9 and Fig.10 , Fig. 9 is a diagram of a three-busbar test system provided by an embodiment of the present invention, showing a Fig. 9 The test system analyzes the effectiveness of the modal analysis device provided in this embodiment. There are three buses in the system, which can be excited to produce or observe harmonic resonance; and Fig. 9 Each complex number in is the impedance or admittance of the corresponding element at the fundamental wave;

[0432] Fig.10 is a resonant modal impedance curve diagram of the test system provided by an embodiment of the present invention, Fig.10The modal impedance curve shows that the system resonant frequencies are 51.6pu and 9.6pu. Fig.10 It shows that near the resonant frequency, the method proposed in this embodiment is almost completely consistent with the traditional method; only at a distance from the resonant frequency, there are certain differences between the method proposed in this embodiment and the traditional method, but this does not affect the accuracy of resonant frequency identification. When analyzing 1 to 60 harmonics with a step size of 0.1Hz, the traditional method requires 29502 iterations, while the method proposed in this embodiment only requires 4030 iterations. It can be seen that the modal analysis device provided in this embodiment can save a lot of computing power.

[0433] To apply the embodiments of the present invention, please refer to Fig.11 , Fig.11 is a topological structure diagram of a calculation example system provided by an embodiment of the present invention, showing a simplified topological structure of a power distribution system;

[0434] Table 1 Transmission line parameters

[0435]

[0436]

[0437] Table 2 Converter parameters

[0438]

[0439] To apply the embodiment of the present invention, please refer to Table 1 and Table 2. Table 1 is a transmission line parameter table provided in this embodiment, which shows the details of the parameters of the transmission line when it is assumed that the parameters of each section of the transmission line are consistent in order to simplify the analysis;

[0440] Table 2 is a parameter table of the converter provided in this embodiment, indicating the details of the parameters of the converter when the converters in the system use the same parameters;

[0441] And, the system node admittance matrix Y under the hth harmonic n (h) is:

[0442]

[0443] The converter unit is used to analyze the effect of the number of converters on the resonance characteristics, specifically:

[0444] Table 3 Resonance modal analysis results of different numbers of converters

[0445]

[0446] To apply the embodiments of the present invention, please refer to Fig.12 and Table 3, Fig.12is a diagram of the resonant modal analysis results of different numbers of converters provided by an embodiment of the present invention, and Table 3 is the resonant modal analysis results of different numbers of converters, Fig.12 and Table 3 show the resonant modal analysis results when power electronic converters such as charging piles and distributed photovoltaics are connected to the grid in cluster form, assuming that there are n converters connected in parallel at the node;

[0447] From the results of modal analysis, it can be seen that there are obviously two types of resonant mode risks in the power distribution system: one is low-frequency resonance and the other is high-frequency resonance. As n increases, the center frequency of the low-frequency resonance decreases slightly, while the center frequency of the high-frequency resonance remains unchanged.

[0448] The line unit is used to analyze the influence of line parameters on the resonance characteristics, specifically:

[0449] To apply the embodiments of the present invention, please refer to Fig.13 , Fig.14 and Fig.15 , Fig.13 is a diagram of the resonant modal analysis result when the unit length resistance r0 changes at the fundamental frequency provided by an embodiment of the present invention, Fig.14 is a diagram of the resonant mode analysis result when the unit length reactance x0 changes at the fundamental frequency provided by an embodiment of the present invention, Fig.15 1 is a diagram showing the resonant modal analysis result when the resistance per unit length changes at the fundamental frequency provided by an embodiment of the present invention;

[0450] The distribution network is at the end of the power system, and the line distribution parameters have an impact on the system resonance characteristics. Fig.13 , Fig.14 and Fig.15 The results of resonant modal analysis when the line distributed parameters change are shown. As can be seen from the figure:

[0451] (1) The line distribution parameters such as unit length resistance r0, unit length reactance x0 and unit length resistance nb0 at the fundamental frequency have an impact on both high and low frequency resonant frequencies;

[0452] (2) As the unit length resistance r0 increases at the fundamental frequency, the center frequency of the resonance remains basically unchanged, and the modal impedance peak decreases, indicating that the resonance is suppressed to a certain extent;

[0453] (3) As the reactance per unit length x0 increases, the center frequency of the high-frequency resonance increases and the modal impedance peak increases, while the center frequency of the low-frequency resonance decreases and the modal impedance peak decreases, indicating that the resonance is further deteriorated;

[0454] (4) As the resistance per unit length increases, the center frequencies of high and low frequency resonances decrease and the modal impedance peaks decrease.

[0455] In general, the embodiments of the present invention have the following beneficial effects:

[0456] This embodiment converts the data of the power distribution system into a complex frequency domain function, which can more easily analyze the voltage and current characteristics of the power distribution system, so that the obtained node admittance matrix can clearly analyze and reflect the relationship between the current and voltage of the power distribution system; by drawing the modal impedance curve, the modal impedance at different frequency points can be known; by taking adjacent points on the modal impedance curve to perform frequency point calculations, the calculation step size can be gradually adjusted, and then gradually approaching the resonant peak on the modal impedance curve, so as to obtain accurate frequency points on the modal impedance curve to form a frequency point set, so that the maximum modal impedance corresponding to the frequency point set is used as the maximum modal impedance of the power distribution system, so as to analyze the harmonic resonance problem of the power distribution system.

[0457] Furthermore, this embodiment reduces the number of repeated analyses by changing the analysis step in real time, thereby greatly accelerating the analysis speed while ensuring the analysis accuracy, and can effectively save harmonic resonance analysis time.

[0458] Embodiment three:

[0459] An embodiment of the present invention provides a computer-readable storage medium, wherein the computer-readable storage medium includes a stored computer program, wherein when the computer program is running, the device where the computer-readable storage medium is located is controlled to execute the modal analysis method of harmonic resonance of a power distribution system;

[0460] Wherein, the modal analysis method of harmonic resonance of the power distribution system, if implemented in the form of a software functional unit and used as an independent product, can be stored in a computer-readable storage medium. Based on such an 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, and the computer program can implement the steps of the above-mentioned various method embodiments when executed by the processor. Wherein, 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, 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, Read-Only Memory), random access memory (RAM, Random Access Memory), electrical carrier signal, telecommunication signal and software distribution medium, etc.

[0461] The above are preferred embodiments of the present invention. It should be noted that, for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications are also considered to be within the scope of protection of the present invention.

Claims

1. A modal analysis method for harmonic resonance of a power distribution system, characterized in that: include: According to the correlation matrix of the topological model of the power distribution system, the node admittance matrix is ​​established by representing the current in the form of complex frequency domain; Performing modal analysis according to the node admittance matrix, and drawing a modal impedance curve diagram according to the analysis results; Within a preset frequency range, adjacent points on the modal impedance curve are taken, and frequency point calculation is performed in a manner of gradually approaching the resonant peak to obtain a frequency point set; specifically: within the preset frequency range, point-by-point modal analysis is performed with a first step length, and a first coefficient corresponding to a first frequency point on the modal impedance curve is obtained according to a preset coefficient formula; wherein the coefficient formula is established by a frequency point and an adjacent point of the frequency point; if the first coefficient is greater than a preset value, the first frequency point is added to the initial frequency point set, and based on the second frequency point, the first step length is taken to re-perform point-by-point modal analysis; wherein the second frequency point is closer to the resonant peak on the modal impedance curve than the first frequency point; if the first coefficient is less than or equal to the preset value, a new step length is obtained by step length adjustment to perform point-by-point modal analysis until the coefficient calculated according to the coefficient formula is greater than the preset value; the frequency point set is formed by the initial frequency point set; Obtaining the modal impedance corresponding to each frequency point in the frequency point set, taking the maximum modal impedance as the maximum modal impedance of the power distribution system, and analyzing the harmonic resonance problem of the power distribution system according to the maximum modal impedance; The topological model is established based on the output admittance and transfer function of the power distribution system, specifically: The cutoff frequency of the phase-locked loop is set to be lower than the fundamental frequency of the power distribution system, and a proportional resonant controller is used to control the current of the power distribution system; the first transfer function of the proportional resonant controller is obtained, and a first harmonic model of the grid-connected converter is established according to the transformer equivalent inductance and the first transfer function; Under a preset h-th harmonic, the wave impedance and the propagation constant of the long transmission line are calculated according to the total series resistance and the series reactance of the line; through a preset formula, according to the order of the h-th harmonic, the wave impedance and the propagation constant, the line equivalent impedance under the h-th harmonic and the line equivalent admittance under the h-th harmonic are calculated, and the second harmonic model is established according to the line equivalent impedance under the h-th harmonic and the line equivalent admittance under the h-th harmonic; Establishing a third harmonic model of the power load according to the equivalent resistance and equivalent reactance of the load in the power distribution system; The topology model is composed of the first harmonic model, the second harmonic model and the third harmonic model.

2. A modal analysis method for harmonic resonance of a power distribution system as claimed in claim 1, characterized in that: According to the correlation matrix of the topological model in the power distribution system, the node admittance matrix is ​​established by representing the current in the form of complex frequency domain, which is: Using the correlation matrix of the topological model of the power distribution system, the KCL equation and the KVL equation in complex frequency domain are respectively expressed to obtain the current expression and the voltage expression; Establish branch equations based on branch voltage vectors and voltage source vectors; The current expression, the voltage expression and the branch equation are solved simultaneously to obtain the node admittance matrix.

3. A modal analysis method for harmonic resonance of a power distribution system as claimed in claim 1, characterized in that: A modal analysis is performed according to the node admittance matrix, and a modal impedance curve is drawn according to the analysis results, specifically: Establishing a node voltage-current expression of the power distribution system according to the node admittance matrix; Performing parameter decomposition on the node admittance matrix to obtain a first expression including a diagonal eigenvalue matrix and a right eigenvector matrix; Simultaneously solving the node voltage-current expression and the first expression to obtain a second expression representing the relationship between the modal voltage vector and the modal current vector; The diagonal eigenvalue matrix and the right eigenvector matrix in the second expression are defined as modal voltage vectors to obtain a modal impedance matrix, and the modal impedance curve diagram is plotted according to the modal impedance matrix.

4. A modal analysis method for harmonic resonance of a power distribution system as claimed in claim 3, characterized in that: The modal impedance curve diagram is drawn according to the modal impedance matrix, specifically: By eliminating the right eigenvector matrix in the second expression, a critical matrix is ​​obtained; Constructing a participation factor set according to the diagonal elements in the critical matrix; wherein the magnitude of the participation factor in the participation factor set represents the degree of distortion caused by harmonic injection into the power distribution system; The modal impedance graph is plotted based on the modal impedance matrix and the participation factor set.

5. A modal analysis device for harmonic resonance of a power distribution system, characterized in that: Includes matrix module, curve module, frequency module and impedance module; The matrix module is used to establish a node admittance matrix by representing the current in the form of complex frequency domain according to the correlation matrix of the topological model of the power distribution system; The curve module is used to perform modal analysis according to the node admittance matrix and draw a modal impedance curve diagram according to the analysis results; The frequency module is used to take adjacent points on the modal impedance curve diagram within a preset frequency range, calculate the frequency points in a manner of gradually approaching the resonance peak, and obtain a frequency point set; specifically: within the preset frequency range, perform point-by-point modal analysis with a first step length, and obtain a first coefficient corresponding to a first frequency point on the modal impedance curve diagram according to a preset coefficient formula; wherein the coefficient formula is established by a frequency point and an adjacent point of the frequency point; if the first coefficient is greater than a preset value, the first frequency point is added to the initial frequency point set, and based on the second frequency point, the first step length is taken to re-perform point-by-point modal analysis; wherein the second frequency point is closer to the resonance peak on the modal impedance curve diagram than the first frequency point; if the first coefficient is less than or equal to the preset value, a new step length is obtained by step length adjustment to perform point-by-point modal analysis until the coefficient calculated according to the coefficient formula is greater than the preset value; the frequency point set is composed of the initial frequency point set; The impedance module is used to obtain the modal impedance corresponding to each frequency point in the frequency point set, take the maximum modal impedance as the maximum modal impedance of the power distribution system, and analyze the harmonic resonance problem of the power distribution system according to the maximum modal impedance; The topological model is established based on the output admittance and transfer function of the power distribution system, specifically: The cutoff frequency of the phase-locked loop is set to be lower than the fundamental frequency of the power distribution system, and a proportional resonant controller is used to control the current of the power distribution system; the first transfer function of the proportional resonant controller is obtained, and a first harmonic model of the grid-connected converter is established according to the transformer equivalent inductance and the first transfer function; Under a preset h-th harmonic, the wave impedance and the propagation constant of the long transmission line are calculated according to the total series resistance and the series reactance of the line; through a preset formula, according to the order of the h-th harmonic, the wave impedance and the propagation constant, the line equivalent impedance under the h-th harmonic and the line equivalent admittance under the h-th harmonic are calculated, and the second harmonic model is established according to the line equivalent impedance under the h-th harmonic and the line equivalent admittance under the h-th harmonic; Establishing a third harmonic model of the power load according to the equivalent resistance and equivalent reactance of the load in the power distribution system; The topology model is composed of the first harmonic model, the second harmonic model and the third harmonic model.

6. A modal analysis device for harmonic resonance of a power distribution system as claimed in claim 5, characterized in that: The matrix module includes an expression unit, a branch unit and an admittance unit; The expression unit is used to use the correlation matrix of the topological model of the power distribution system to express the KCL equation and the KVL equation in complex frequency domain to obtain the current expression and the voltage expression; The branch unit is used to establish a branch equation according to the branch voltage vector and the voltage source vector; The admittance unit is used to simultaneously solve the current expression, the voltage expression and the branch equation to obtain the node admittance matrix.

7. A modal analysis device for harmonic resonance of a power distribution system as claimed in claim 5, characterized in that: The curve module includes a construction unit, a decomposition unit, a solution unit and a curve unit; Wherein, the construction unit is used to establish a node voltage-current expression of the power distribution system according to the node admittance matrix; The decomposition unit is used to perform parameter decomposition on the node admittance matrix to obtain a first expression including a diagonal eigenvalue matrix and a right eigenvector matrix; The solving unit is used to simultaneously solve the node voltage-current expression and the first expression to obtain a second expression representing the relationship between the modal voltage vector and the modal current vector; The curve unit is used to define the diagonal eigenvalue matrix and the right eigenvector matrix in the second expression as modal voltage vectors, obtain a modal impedance matrix, and draw the modal impedance curve according to the modal impedance matrix.

8. A modal analysis device for harmonic resonance of a power distribution system as claimed in claim 7, characterized in that: The curve unit includes a matrix sub-unit, an element sub-unit and a curve sub-unit; Wherein, the matrix subunit is used to obtain a critical matrix by eliminating the right eigenvector matrix in the second expression; The element subunit is used to construct a participation factor set according to the diagonal elements in the critical matrix; wherein the magnitude of the participation factor in the participation factor set represents the degree of distortion caused by the injection of harmonics into the power distribution system; The curve subunit is used to draw the modal impedance curve diagram according to the modal impedance matrix and the participation factor set.

9. A storage medium, characterized in that: The storage medium stores a computer program, which is called and executed by a computer to implement a modal analysis method for harmonic resonance of a power distribution system as described in any one of claims 1 to 4 above.

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