CN118841943A - Power grid harmonic distribution calculation method and device, storage medium and computer equipment - Google Patents

Abstract

The power grid harmonic distribution calculation method, device, storage medium and computer equipment provided by the present application, after constructing the measurement equation based on the key node harmonic voltage, branch harmonic current and measurement error, can use the weighted least square method to solve the measurement equation to obtain the branch harmonic current of each node in the power system at different harmonic orders, so that the demand for the installation of broadband measurement devices in the power grid can be reduced without relying on simulation software, and then the accurate calculation of the system harmonic distribution can be achieved when fewer broadband measurement devices are installed; the present application can also calculate the harmonic active power value injected by each node into the power system according to the branch harmonic current of each node, and determine the location of the harmonic source in the power system according to the numerical value of each harmonic active power value. This process takes into account the injection of multiple harmonic sources, thereby providing a new solution for the harmonic distribution calculation of large-scale AC power grids.

Description

Power grid harmonic distribution calculation method, device, storage medium and computer equipment

Technical Field

The present application relates to the technical field of power systems, and in particular to a method, device, storage medium and computer equipment for calculating harmonic distribution of a power grid.

Background Art

With the continuous development of DC transmission technology, the power grid is showing a trend of AC-DC hybrid development. At the same time, the extensive application of new energy power generation technology and power electronics technology has injected a large number of harmonics into the system while improving the controllability and flexibility of the system, which has complicated the harmonic situation in the system, led to the deterioration of power quality, and caused problems such as increased power loss and accelerated aging of equipment. Due to the nonlinear characteristics of power electronic devices, the harmonic problems of power systems containing a high proportion of power electronic equipment are broadband and multi-source. Accurate measurement and state estimation of harmonics and accurate calculation of the harmonic distribution in the power grid are the prerequisites for carrying out power quality management and ensuring safe, reliable and stable operation of the power grid.

In the prior art, when calculating the harmonic distribution in the power grid, a dynamic harmonic distribution calculation model is generally used based on the extraction of harmonic source characteristics. The model obtains the characteristic components of the harmonic source fluctuations through wavelet filtering, uses the slow fluctuation components to calculate the state transfer matrix, and uses the fast fluctuation components to calculate the system noise covariance matrix. However, the model only targets ordinary harmonic sources and does not take into account the existing new harmonic sources such as flexible direct current transmission and distributed energy. In addition, the prior art has also established a mathematical model for harmonic distribution analysis of a DG distribution network, and proposed a harmonic distribution calculation method for a DG distribution network combined with transient simulation, but this method has not been proven to be applicable to large-scale transmission networks, and the method relies on simulation software and is difficult to use independently.

Summary of the invention

The purpose of the present application is to solve at least one of the above-mentioned technical defects, especially the technical defect that the prior art cannot accurately measure and calculate the harmonic distribution in the power grid containing new harmonic sources.

The present application provides a method for calculating power grid harmonic distribution, the method comprising:

Obtaining, by means of a broadband measuring device installed in the power system, node harmonic voltages of key nodes at different harmonic orders, branch harmonic currents of branches connected to the broadband measuring device at different harmonic orders, and measurement errors of the broadband measuring device when measuring at different harmonic orders;

Based on the node harmonic voltage, branch harmonic current and measurement error at different harmonic orders, the measurement equations at different harmonic orders are constructed;

The measurement equation is solved using a weighted least square method to obtain branch harmonic currents of various nodes in the power system at different harmonic orders;

The harmonic active power value injected by each node into the power system is calculated according to the branch harmonic current of each node, and the location of the harmonic source in the power system is determined according to the numerical value of each harmonic active power value.

Optionally, before obtaining the node harmonic voltages of key nodes at different harmonic orders by a broadband measurement device installed in the power system, the method further includes:

Based on the harmonic distribution calculation requirements of the power system, a 0-1 integer programming model is constructed;

After solving the 0-1 integer programming model, the location where the broadband measurement device is installed in the power system is determined according to the solution result.

Optionally, constructing measurement equations at different harmonic orders based on node harmonic voltages, branch harmonic currents and measurement errors at different harmonic orders includes:

According to the node harmonic voltage, branch harmonic current and measurement error under different harmonic orders, the node voltage measurement equation and branch injection current measurement equation under different harmonic orders are constructed;

Determine a measurement matrix corresponding to node harmonic voltages and branch harmonic currents at different harmonic orders in the power system;

According to the node voltage measurement equations under different harmonic orders, the branch injection current measurement equations and the corresponding measurement matrices, the synchronous phasor measurement equations are constructed.

Optionally, the node voltage measurement equation is:

In the above formula, the subscript M represents the quantity measurement, and the subscript S represents the state quantity. It represents the hth node harmonic voltage measurement of node i, represents the h-order node harmonic voltage state quantity of node i, I represents the unit matrix with the same dimension as the node harmonic voltage measurement quantity, η _i represents the node harmonic voltage measurement error at node i in the case of h-order harmonic;

The branch injection current measurement equation is:

In the above formula, It represents the measurement of the hth branch harmonic current injected into node i, It represents the node harmonic voltage state quantity of node j under the condition of h-order harmonic, represents the matrix element related to the hth harmonic of node i and node j in the node admittance matrix under the condition of hth harmonic, and n represents the total number of nodes in the power system; It represents the measurement of the amount of current injected between nodes i and j under the condition of harmonic h. represents the self-admittance in the admittance matrix of node i in the case of hth harmonic, represents the admittance between nodes i and j in the case of hth harmonic;

The synchronized phasor measurement equation is:

In the above formula, Indicates the node harmonic voltage measurement of key nodes where broadband measurement devices are installed. It indicates the measurement of branch harmonic current connected to the key node where the broadband measurement device is installed. represents the branch harmonic current state quantity of each node to be determined, The quantity measured is the measurement matrix of node harmonic voltage, The measured quantity is the measurement matrix of branch harmonic current.

Optionally, the method of using a weighted least square method to solve the measurement equation to obtain branch harmonic currents of various nodes in the power system at different harmonic orders includes:

Constructing a harmonic distribution calculation model according to the node voltage measurement equation and the branch injection current measurement equation under different harmonic orders, and the synchronous phasor measurement equation;

The harmonic distribution calculation model is solved using a weighted least square method to obtain branch harmonic currents of various nodes in the power system at different harmonic orders.

Optionally, the harmonic distribution calculation model is:

Z＝HX+ε

Wherein, Z is the m×1-dimensional measurement phasor, X is the n×1-dimensional state quantity phasor to be determined, Z and X are determined according to the selected measurement and state quantity and phasor measurement equations, H is the m×n-dimensional measurement matrix, which is mainly determined by the network topology and component harmonic parameters in the power system, ε represents the m×l-dimensional measurement error phasor, m represents the number of measurement, and n represents the number of state quantities to be determined;

The objective function of the weighted least squares method is:

J(x)＝(Z-HX) ^T W(Z-HX)

In the above formula, Represents the estimated value of the state quantity X;

when When , the objective function reaches its minimum value, that is:

min J(x)＝(Z-HX) ^T W(Z-HX)

Differentiate the residual sum of squares to find the maximum value, and obtain the harmonic distribution calculation equation based on the weighted least squares principle:

Wherein, W=R ^-1 , W is the m-th order measurement weight matrix, and R is the diagonal matrix of the measurement error variance of each measurement data;

Solving the above equation, we can get the weighted least squares solution of the harmonic distribution calculation model:

Optionally, determining the location of the harmonic source in the power system according to the numerical values of each harmonic active power value includes:

If the value of at least one harmonic active power value is positive and exceeds a preset value, the node of the at least one harmonic active power value injected into the power system is determined to be the location of the harmonic source.

The present application also provides a power grid harmonic distribution calculation device, comprising:

A data acquisition module, used to acquire, through a broadband measurement device installed in the power system, node harmonic voltages of key nodes at different harmonic orders, branch harmonic currents of branches connected to the broadband measurement device at different harmonic orders, and measurement errors of the broadband measurement device when measuring at different harmonic orders;

A measurement equation construction module is used to construct measurement equations under different harmonic orders based on node harmonic voltages, branch harmonic currents and measurement errors under different harmonic orders;

A harmonic current determination module, used to solve the measurement equation using a weighted least square method to obtain branch harmonic currents of various nodes in the power system at different harmonic orders;

The harmonic source positioning module is used to calculate the harmonic active power value injected by each node into the power system according to the branch harmonic current of each node, and determine the location of the harmonic source in the power system according to the numerical value of each harmonic active power value.

The present application also provides a computer-readable storage medium, in which computer-readable instructions are stored. When the computer-readable instructions are executed by one or more processors, the one or more processors execute the steps of the power grid harmonic distribution calculation method as described in any of the above embodiments.

The present application also provides a computer device, comprising: one or more processors, and a memory;

The memory stores computer-readable instructions, and when the computer-readable instructions are executed by the one or more processors, the steps of the method for calculating power grid harmonic distribution as described in any one of the above embodiments are performed.

It can be seen from the above technical solutions that the embodiments of the present application have the following advantages:

The present application provides a method, device, storage medium and computer equipment for calculating the harmonic distribution of a power grid. When calculating the harmonic distribution of a power grid, a broadband measurement device installed in the power system can be used to obtain the node harmonic voltages of key nodes at different harmonic orders, the branch harmonic currents of each branch connected to the broadband measurement device at different harmonic orders, and the measurement errors of the broadband measurement device when measuring at different harmonic orders; then, the present application can construct measurement equations at different harmonic orders based on the node harmonic voltages, branch harmonic currents and measurement errors at different harmonic orders; and then use the weighted least squares method to calculate the harmonic distribution of a power grid. The measurement equation is solved by multiplication, and then the branch harmonic current of each node in the power system at different harmonic orders is obtained; and the method for solving the harmonic distribution equation based on the weighted least squares method can reduce the demand for the number of broadband measurement devices installed in the power grid, and then the accurate calculation of the system harmonic distribution can be achieved when fewer broadband measurement devices are installed; finally, the present application can calculate the harmonic active power value injected by each node into the power system according to the branch harmonic current of each node, and determine the location of the harmonic source in the power system according to the numerical value of each harmonic active power value. This process not only takes into account the injection of multiple harmonic sources, thereby providing a new solution for the harmonic distribution calculation of large-scale AC power grids, but also can achieve accurate calculation of harmonic distribution by obtaining measurement data of a small number of broadband measurement devices without relying on simulation software. In addition, the present application can also be used in the calculation of uncertain harmonic currents, as an intermediate step in the calculation of uncertain harmonic currents, to participate in iteration and realize real-time display of harmonic currents.

BRIEF DESCRIPTION OF THE DRAWINGS

In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

FIG1 is a schematic diagram of a flow chart of a method for calculating harmonic distribution of a power grid provided in an embodiment of the present application;

FIG2 is a schematic diagram of a basic framework for harmonic distribution calculation provided in an embodiment of the present application;

FIG3 is a schematic structural diagram of a π-type equivalent harmonic model of a transmission line or transformer branch provided in an embodiment of the present application;

FIG4 is a topological diagram of an IEEE 14-node AC/DC system provided in an embodiment of the present application;

FIG5 is a schematic diagram of the structure of a power grid harmonic distribution calculation device provided in an embodiment of the present application;

FIG6 is a schematic diagram of the internal structure of a computer device provided in an embodiment of the present application.

DETAILED DESCRIPTION

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.

In one embodiment, as shown in FIG1 , FIG1 is a flow chart of a method for calculating harmonic distribution of a power grid provided by an embodiment of the present application; the present application provides a method for calculating harmonic distribution of a power grid, and the method may include:

S110: Obtain node harmonic voltages of key nodes at different harmonic orders, branch harmonic currents of branches connected to the broadband measuring device at different harmonic orders, and measurement errors of the broadband measuring device when measuring at different harmonic orders through a broadband measuring device installed in the power system.

In this embodiment, in order to deal with the harmonic problem of the power grid, the existing high-performance broadband measurement device can be put into use to achieve accurate synchronous measurement of 1st to 50th harmonics and interharmonics, providing a good hardware foundation and data support for further harmonic distribution calculation.

Furthermore, after the present application puts the broadband measuring device into the power system, the node harmonic voltage of the key nodes at different harmonic orders, the branch harmonic current of each branch connected to the broadband measuring device at different harmonic orders, and the measurement error of the broadband measuring device when measuring at different harmonic orders can be obtained through the installed broadband measuring device. In this way, the node harmonic voltage and branch harmonic current can be used as measurement quantities, and the branch harmonic current can be used as a state quantity to calculate the harmonic distribution, and the measurement error of the broadband measuring device when measuring at different harmonic orders can be taken into account, thereby effectively improving the accuracy of the harmonic distribution calculation results.

It can be understood that the key nodes in the present application refer to the nodes in the power system where the broadband measurement device is installed. The present application constructs a measurement equation by obtaining the node harmonic voltage of the key nodes where the broadband measurement device is installed, as well as the branch harmonic current and measurement error of each branch connected to the broadband measurement device, so as to obtain the branch harmonic current of all nodes in the power system by solving the measurement equation. This can effectively save the harmonic distribution calculation time and improve the calculation efficiency.

S120: Constructing measurement equations at different harmonic orders based on node harmonic voltages, branch harmonic currents, and measurement errors at different harmonic orders.

In this step, after obtaining the node harmonic voltage and branch harmonic current at different harmonic orders and the measurement error of the wideband measurement device at different harmonic orders through S110, the measurement equations at different harmonic orders can be constructed based on the node harmonic voltage, branch harmonic current and measurement error at different harmonic orders, so that the corresponding state quantity can be obtained by solving the measurement equation.

It can be understood that the calculation of harmonic distribution requires the establishment of a basic mathematical model that can link quantity measurement with state quantity. This model is usually composed of current measurement, voltage measurement or their variations. Combined with basic circuit principles, it is possible to establish a basic mathematical model for the harmonic distribution calculation problem, that is, the measurement equation of the present application. By solving the measurement equation, the value of the state quantity can be obtained, and then the location of the harmonic source in the power system can be determined.

S130: Solve the measurement equation using the weighted least square method to obtain branch harmonic currents of various nodes in the power system at different harmonic orders.

In this step, after establishing the measurement equations under different harmonic orders according to the measurement matrix and measurement error under different harmonic orders through S120, the present application can use the weighted least squares method to solve the measurement equations, so that the branch harmonic currents of each node in the power system under different harmonic orders can be obtained.

It should be noted that solving the harmonic distribution calculation model is essentially solving the objective function, that is, calculating according to the selected criteria to obtain the optimal estimate of the objective function. Therefore, the present application can select the corresponding solution method based on the characteristics of the basic mathematical model constructed. For example, based on the measurement characteristics of the synchronous phasor measurement device and the linear characteristics of the basic mathematical model constructed, the present application can use the weighted least squares method to improve the error distribution between different measurement data to solve the harmonic distribution calculation model, so that the branch harmonic currents of each node in the power system at different harmonic orders can be quickly obtained.

S140: Calculate the harmonic active power value injected by each node into the power system according to the branch harmonic current of each node, and determine the location of the harmonic source in the power system according to the numerical value of each harmonic active power value.

In this step, after obtaining the branch harmonic currents of each node in the power system at different harmonic orders through S130, the harmonic source location can be further analyzed. For example, the present application can calculate the harmonic active power value injected by each node into the power system according to the branch harmonic current of each node, and determine the location of the harmonic source in the power system according to the numerical value of each harmonic active power value.

For example, after obtaining the branch harmonic currents of each node at different harmonic orders, the present application can use the node injection current equation to further obtain the harmonic voltage value of each node, and calculate the harmonic active power value injected into each node according to the node injection active power formula, and then determine the location of the harmonic source in the power system according to the numerical value of each harmonic active power value.

The above node injected active power formula can be obtained through the prior art, and the above node injected current equation is expressed as follows:

In the above formula, It represents the measurement of the hth branch harmonic current injected into node i, It represents the node harmonic voltage state quantity of node j under the condition of h-order harmonic, It represents the matrix element related to the hth harmonic of node i and node j in the node admittance matrix under the condition of hth harmonic, and n represents the total number of nodes in the power system.

In the above embodiment, when calculating the harmonic distribution of the power grid, the node harmonic voltage of the key node at different harmonic orders, the branch harmonic current of each branch connected to the broadband measurement device at different harmonic orders, and the measurement error of the broadband measurement device when measuring at different harmonic orders can be obtained through the broadband measurement device installed in the power system; then, the present application can construct measurement equations at different harmonic orders based on the node harmonic voltage, branch harmonic current and measurement error at different harmonic orders; then the weighted least squares method is used to solve the measurement equation, and then the branch harmonic current of each node in the power system at different harmonic orders is obtained; and the harmonic distribution equation solving method based on the weighted least squares method can reduce the demand for the number of broadband measurement devices installed in the power grid, and then realize the accurate calculation of the system harmonic distribution when fewer broadband measurement devices are installed; finally, the present application can calculate the harmonic active power value injected by each node into the power system according to the branch harmonic current of each node, and determine the location of the harmonic source in the power system according to the numerical value of each harmonic active power value. This process not only takes into account the injection of multiple harmonic sources, thus providing a new solution for the harmonic distribution calculation of large-scale AC power grids, but also can achieve accurate calculation of harmonic distribution by acquiring measurement data from a small number of broadband measurement devices without relying on simulation software. In addition, the present application can also be used in uncertain harmonic power flow calculations, as an intermediate step in uncertain harmonic power flow calculations, to participate in iterations and achieve real-time display of harmonic power flows.

In one embodiment, before obtaining the node harmonic voltages of key nodes at different harmonic orders by a broadband measurement device installed in the power system in S110, the following steps may also be included:

S101: Construct a 0-1 integer programming model based on the harmonic distribution calculation requirements of the power system.

S102: After solving the 0-1 integer programming model, determine the location where the broadband measurement device is installed in the power system according to the solution result.

In this embodiment, before obtaining the node harmonic voltages and branch harmonic currents of key nodes at different harmonic orders through the broadband measurement device installed in the power system, the present application can also construct a 0-1 integer programming model based on the harmonic distribution calculation requirements of the power system, and after solving the 0-1 integer programming model, determine the location of the broadband measurement device installed in the power system according to the solution result, and then obtain the node harmonic voltages and branch harmonic currents at different harmonic orders through the broadband measurement device at the corresponding position.

Among them, the harmonic distribution calculation requirements of this application include but are not limited to considering new harmonic sources such as flexible direct current transmission and distributed energy, as well as realizing accurate calculation of the system harmonic distribution when fewer broadband measurement devices are installed. The specific calculation requirements can be set according to the actual situation and are not limited here. After the harmonic distribution calculation requirements are determined, a 0-1 integer programming model can be established according to the requirements. Then, this application can solve the 0-1 integer programming model by exhaustive enumeration or implicit enumeration methods, and then obtain the solution result, which is the location of the broadband measurement device installed in the power system of this application.

In one embodiment, in S120, measurement equations at different harmonic orders are constructed based on node harmonic voltages, branch harmonic currents, and measurement errors at different harmonic orders, which may include:

S121: Construct node voltage measurement equations and branch injection current measurement equations at different harmonic orders according to node harmonic voltages, branch harmonic currents, and measurement errors at different harmonic orders.

S122: Determine a measurement matrix corresponding to node harmonic voltages and branch harmonic currents at different harmonic orders in the power system.

S123: Constructing a synchronous phasor measurement equation according to the node voltage measurement equation under different harmonic orders, the branch injection current measurement equation and the corresponding measurement matrix.

In this embodiment, after obtaining the node harmonic voltages and branch harmonic currents at different harmonic orders, as well as the measurement errors of the wideband measurement device when measuring at different harmonic orders, the present application can construct measurement equations at different harmonic orders based on the node harmonic voltages, branch harmonic currents and measurement errors at different harmonic orders, so that the corresponding state quantities can be obtained by solving the measurement equations.

Specifically, after obtaining the node harmonic voltage, branch harmonic current and measurement error at different harmonic orders, the present application can respectively construct the node voltage measurement equation and branch injection current measurement equation at different harmonic orders based on the node harmonic voltage, branch harmonic current and measurement error at different harmonic orders. Among them, the node voltage measurement equation uses the node harmonic voltage phasor as the quantity measurement to calculate the node harmonic voltage under harmonic conditions; and according to Kirchhoff's current law, the sum of the current flowing out of any node in the circuit at any time is always equal to the sum of the current flowing into it, so the harmonic injection current of the node where the broadband measurement device is installed can be selected as the quantity measurement, and the harmonic voltage of other nodes can be obtained by combining the network topology and component harmonic parameters, etc., and the current of the branch connected to the node can also be measured as the quantity, that is, the branch injection current measurement.

Next, the present application can determine the measurement matrix corresponding to the node harmonic voltage and branch harmonic current under different harmonic orders according to the network topology and component harmonic parameters in the power system, so that the synchronous phasor measurement equation can be constructed according to the node voltage measurement equation, branch injection current measurement equation and corresponding measurement matrix under different harmonic orders. Schematically, as shown in Figure 2, Figure 2 is a basic framework diagram of the harmonic distribution calculation provided by the embodiment of the present application; as can be seen from Figure 2, after obtaining the measurement matrix and determining the measurement and state quantities, the present application can establish a harmonic state estimation mathematical model, that is, the synchronous phasor measurement equation of the present application, and then the present application can solve the synchronous phasor measurement equation, and then determine the state quantity according to the solution result.

In one embodiment, the node voltage measurement equation is:

In the above formula, the subscript M represents the quantity measurement, and the subscript S represents the state quantity. It represents the hth node harmonic voltage measurement of node i, represents the h-order node harmonic voltage state quantity of node i, I represents the unit matrix with the same dimension as the node harmonic voltage measurement quantity, η _i represents the node harmonic voltage measurement error at node i in the case of h-order harmonic;

The branch injection current measurement equation is:

In the above formula, It represents the measurement of the hth branch harmonic current injected into node i, It represents the node harmonic voltage state quantity of node j under the condition of h-order harmonic, represents the matrix element related to the hth harmonic of node i and node j in the node admittance matrix under the condition of hth harmonic, and n represents the total number of nodes in the power system; It represents the measurement of the amount of current injected between nodes i and j under the condition of harmonic h. represents the self-admittance in the admittance matrix of node i in the case of hth harmonic, It represents the admittance between nodes i and j in the case of hth harmonic.

It can be understood that if a broadband measurement device is installed at node i, the current of the branch connected to node i can be measured as a quantity, that is, the branch injection current measurement. When measuring the branch injection current, the above branch injection current measurement equation can be established through the π-type equivalent harmonic model. Schematically, as shown in Figure 3, Figure 3 is a structural schematic diagram of the π-type equivalent harmonic model of the transmission line or transformer branch provided in an embodiment of the present application; Figure 3 can clearly understand the relationship between the various parameters, and then establish the branch injection current measurement equation.

Furthermore, the present application can also transform the above branch injection current measurement equation, and the variation is as follows:

Through this variation, the synchronous phasor measurement equation can be constructed. The formula of the synchronous phasor measurement equation is as follows:

In the above formula, Indicates the node harmonic voltage measurement of key nodes where broadband measurement devices are installed. It indicates the measurement of branch harmonic current connected to the key node where the broadband measurement device is installed. represents the branch harmonic current state quantity of each node to be determined, The quantity measured is the measurement matrix of node harmonic voltage, The measured quantity is the measurement matrix of branch harmonic current.

In one embodiment, in S130, the measurement equation is solved using the weighted least square method to obtain branch harmonic currents of each node in the power system at different harmonic orders, which may include:

S131: Construct a harmonic distribution calculation model according to the node voltage measurement equation and the branch injection current measurement equation at different harmonic orders, as well as the synchronous phasor measurement equation.

S132: Use the weighted least square method to solve the harmonic distribution calculation model to obtain branch harmonic currents of various nodes in the power system at different harmonic orders.

In this embodiment, after obtaining the measurement equation, that is, the synchronous phasor measurement equation, the present application can construct a harmonic distribution calculation model based on the node voltage measurement equation and the branch injection current measurement equation under different harmonic orders, as well as the synchronous phasor measurement equation. In this way, the weighted least squares method can be used to solve the harmonic distribution calculation model, and then the branch harmonic currents of each node in the power system under different harmonic orders can be obtained.

It can be understood that, since the synchronous phasor measurement equation, the node voltage measurement equation under different harmonic orders and the branch injection current measurement equation of the present application can all be expressed by the same type of formula, therefore, the present application can establish a general mathematical model for harmonic distribution calculation through the commonality of the three, that is, the harmonic distribution calculation model. In addition, since the solution to the harmonic distribution calculation model is essentially the solution to the objective function, that is, the calculation is performed according to the selected criteria to obtain the optimal estimate of the objective function. Therefore, based on the measurement characteristics of the synchronous phasor measurement device and the linear characteristics of the basic mathematical model constructed, the present application can solve the harmonic distribution calculation model by using the weighted least squares method that improves the error distribution between different measurement data, so that the branch harmonic currents of each node in the power system at different harmonic orders can be quickly obtained.

In one embodiment, the harmonic distribution calculation model is:

Z＝HX+ε

Wherein, z is the m×1-dimensional measurement phasor, X is the n×1-dimensional state quantity phasor to be determined, Z and X are determined according to the selected measurement and state quantity and phasor measurement equations, H is the m×n-dimensional measurement matrix, which is mainly determined by the network topology and component harmonic parameters in the power system, ε represents the m×1-dimensional measurement error phasor, m represents the number of measurement, and n represents the number of state quantities to be determined.

Since the weighted least squares method is to weight the original model to make it a model without heteroscedasticity, and then use the least squares method to estimate its parameters, so as to obtain the optimal solution of the objective function. Therefore, the objective function of the weighted least squares method can be constructed in this application, and its expression is as follows:

J(x)＝(Z-HX) ^T W(Z-HX)

In the above formula, Represents the estimated value of the state quantity X.

when When , the objective function reaches the minimum value, that is:

min J(x)＝(Z-HX) ^T W(Z-HX)

Differentiate the residual sum of squares to find the maximum value, and obtain the harmonic distribution calculation equation based on the weighted least squares principle:

Wherein, W=R ⁻¹ , W is an m-order measurement weight matrix, and R is a diagonal matrix of measurement error variances of each measurement data.

Solving the above equation, we can get the weighted least squares solution of the harmonic distribution calculation model:

In a specific implementation, the present application can verify the technical solutions recorded in the above embodiments through the following examples. Schematically, as shown in FIG4, FIG4 is a topological relationship diagram of the IEEE 14-node AC/DC system provided in the embodiment of the present application; the present application can verify the above harmonic distribution calculation method based on the IEEE 14-node system construction example shown in FIG4, in which G represents a traditional generator, and four harmonic sources are set in the system, namely an AC load (including a distributed power supply) and two three-phase six-pulse commutation converter terminals (LCC), and a modular multilevel converter terminal (MMC), wherein the AC load is connected to node 11, the LCC is connected to nodes 5 and 14, and the MMC is connected to node 4, and the harmonic source injects harmonic current into the system. The present application can use MATPOWER in MATLAB to perform power flow calculation on the IEEE 14-node system to obtain the power flow of the system under the fundamental state. Then, the amplitude and phase angle of each harmonic current are determined by the typical spectrum of the harmonic current and the current under the fundamental state, and a measurement database and a verification database for harmonic distribution calculation are established.

It is understandable that when the AC and DC power grids are in stable operating conditions, the AC power grid mainly contains 12k±1 (k=1, 2, 3, ...) harmonics, and the DC part mainly contains 12k (k=1, 2, 3, ...) harmonics. Since the resonant frequency induced by MMC depends on a series of factors such as the equivalent impedance parameters of the port power grid, its own control and topological parameters, there is no numerical law, without loss of generality, this application can be equivalent to the harmonic current injected by MMC as a high-frequency harmonic current source of 515Hz, and its harmonic current amplitude is set to 5% of the fundamental current. The higher the harmonic amplitude, the smaller the importance, so in the following examples, the focus is on the 11th and 13th harmonics with the greatest impact and the non-integer interharmonics brought by MMC.

For example, the present application can input the harmonic order h, construct a measurement database for harmonic distribution calculation corresponding to the harmonic order for extracting broadband measurement device measurement data and verification, as shown in Table 1:

Harmonic order h Amplitude/% Phase angle/° 1 100 0.00 5 18.24 -55.68 7 11.90 -84.11 11 5.73 -143.56 13 4.01 -175.56

Table 1 Harmonic load spectrum

Next, the present application can establish a corresponding 0-1 integer programming model based on the constructed example, solve the model to obtain the location where the broadband measurement device is installed, and then extract the corresponding data from the measurement library, and combine the example to establish the h-th harmonic node admittance matrix to form the measurement matrix H for harmonic distribution calculation. The harmonic distribution calculation equation is solved using the weighted least squares method to obtain the harmonic distribution value and compare it with the actual value to verify the accuracy of the harmonic distribution calculation.

For example, the present application obtains the locations where the broadband measurement device is configured as nodes 2, 8, 10 and 13 according to the 0-1 integer programming model, selects the node harmonic voltage as the quantity measurement, and the branch harmonic current as the state quantity, and obtains the node harmonic voltage value at the broadband measurement device installed by the broadband measurement device and the branch harmonic current value of each branch connected to the broadband measurement device installed, thereby respectively constructing the quantity measurement matrix H of the 11th and 13th harmonics and the non-integer interharmonics brought by MMC. Then, the present application can add a random measurement error with a mean of 0 and a standard deviation of 0.2% to the measurement data of the broadband measurement device, respectively establish the measurement equations of the IEEE14-node system under the condition of multiple harmonic sources at 515Hz, 11th harmonic and 13th harmonic, and use the weighted least squares method to solve the harmonic distribution calculation equation based on synchronous phasor measurement to obtain the state quantity-the branch harmonic current of each node. In the case of 515Hz harmonic, focus on the injected harmonic current of MMC. In the case of 11th and 13th harmonic, focus on AC load and LCC. The calculated deviation of harmonic source node is shown in Table 2-4.

Table 2 Comparison of 515Hz harmonic current results at MMC of IEEE14 simulation system

Table 3 Comparison of 11th harmonic current results of harmonic source nodes in IEEE14 simulation system

Table 4 Comparison of 13th harmonic current results of harmonic source nodes in IEEE14 simulation system

It can be seen from Table 2-4 that the average relative error of the amplitude of the harmonic distribution calculation in the cases of 515Hz, 11th harmonic and 13th harmonic is less than 3%, that is, the average calculation accuracy is more than 97%, and the average relative error of the phase angle of the harmonic distribution calculation is less than 3.5%, that is, the average calculation accuracy is more than 96.5%. This shows that the designed harmonic distribution calculation and solution method based on wide-band synchronous phasor measurement can realize the effective calculation of the harmonic distribution of the IEEE14-node system under multiple harmonic sources.

In one embodiment, determining the location of the harmonic source in the power system according to the numerical values of each harmonic active power value in S140 may include:

S141: If the value of at least one harmonic active power value is positive and exceeds a preset value, determine that the node of the at least one harmonic active power value injected into the power system is the location of the harmonic source.

In this embodiment, after obtaining the harmonic active power value injected by each node, the present application can determine the location of the harmonic source in the power system according to the numerical value of each harmonic active power value. For example, the present application can determine whether a node is a harmonic source based on the positive and negative harmonic active power injected by the node into the system based on the harmonic source positioning calculated by the harmonic distribution. If the harmonic active power injected into the system is positive, the node is a harmonic injection source, and vice versa, if it is negative, the node is a harmonic absorption source. In addition, in order to obtain a more accurate positioning result, the present application can also compare the harmonic active power value with a positive value with a preset numerical value. If it exceeds the preset numerical value, it is finally determined to be the location of the harmonic source.

Indicatively, the present application obtains the harmonic active power value of each node from the node injection active power formula as shown in Table 5:

Table 5 Harmonic active power values injected into each node

According to the above table, it is easy to know that there are four harmonic sources in the system, located at nodes 4, 5, 11 and 14, respectively. The harmonic source type of node 4 is a non-integer interharmonic of 515Hz, and the harmonic source types of nodes 5, 11 and 14 are 11th and 13th, which is consistent with the set harmonic source situation. In addition to these four harmonic sources, there are also other individual nodes whose harmonic active power is positive, but because its value is extremely small, it can be judged that it is an error within the allowable range in the measurement and distribution calculation process. Therefore, the harmonic source positioning method based on harmonic distribution calculation adopted in this application can basically and correctly realize the positioning of the harmonic sources in the system.

The power grid harmonic distribution calculation device provided in an embodiment of the present application is described below. The power grid harmonic distribution calculation device described below and the power grid harmonic distribution calculation method described above can be referenced to each other.

In one embodiment, as shown in FIG5 , FIG5 is a schematic diagram of the structure of a power grid harmonic distribution calculation device provided by an embodiment of the present application; the present application also provides a power grid harmonic distribution calculation device, which may include a data acquisition module 210, a measurement equation construction module 220, a harmonic current determination module 230, and a harmonic source positioning module 240, specifically including the following:

The data acquisition module 210 is used to obtain the node harmonic voltage of the key node at different harmonic orders, the branch harmonic current of each branch connected to the broadband measurement device at different harmonic orders, and the measurement error of the broadband measurement device when measuring at different harmonic orders through a broadband measurement device installed in the power system.

The measurement equation construction module 220 is used to construct measurement equations at different harmonic orders based on node harmonic voltages, branch harmonic currents and measurement errors at different harmonic orders.

The harmonic current determination module 230 is used to solve the measurement equation using a weighted least square method to obtain branch harmonic currents of various nodes in the power system at different harmonic orders.

The harmonic source positioning module 240 is used to calculate the harmonic active power value injected by each node into the power system according to the branch harmonic current of each node, and determine the location of the harmonic source in the power system according to the numerical value of each harmonic active power value.

In the above embodiment, when calculating the harmonic distribution of the power grid, the node harmonic voltage of the key node at different harmonic orders, the branch harmonic current of each branch connected to the broadband measurement device at different harmonic orders, and the measurement error of the broadband measurement device when measuring at different harmonic orders can be obtained through the broadband measurement device installed in the power system; then, the present application can construct measurement equations at different harmonic orders based on the node harmonic voltage, branch harmonic current and measurement error at different harmonic orders; then the weighted least squares method is used to solve the measurement equation, and then the branch harmonic current of each node in the power system at different harmonic orders is obtained; and the harmonic distribution equation solving method based on the weighted least squares method can reduce the demand for the number of broadband measurement devices installed in the power grid, and then realize the accurate calculation of the system harmonic distribution when fewer broadband measurement devices are installed; finally, the present application can calculate the harmonic active power value injected by each node into the power system according to the branch harmonic current of each node, and determine the location of the harmonic source in the power system according to the numerical value of each harmonic active power value. This process not only takes into account the injection of multiple harmonic sources, thus providing a new solution for the harmonic distribution calculation of large-scale AC power grids, but also can achieve accurate calculation of harmonic distribution by acquiring measurement data from a small number of broadband measurement devices without relying on simulation software. In addition, the present application can also be used in uncertain harmonic power flow calculations, as an intermediate step in uncertain harmonic power flow calculations, to participate in iterations and achieve real-time display of harmonic power flows.

In one embodiment, the present application also provides a computer-readable storage medium, in which computer-readable instructions are stored. When the computer-readable instructions are executed by one or more processors, the one or more processors execute the steps of the power grid harmonic distribution calculation method as described in any of the above embodiments.

In one embodiment, the present application also provides a computer device, including: one or more processors, and a memory.

The memory stores computer-readable instructions, and when the computer-readable instructions are executed by the one or more processors, the steps of the method for calculating power grid harmonic distribution as described in any one of the above embodiments are performed.

Schematically, as shown in FIG6 , FIG6 is a schematic diagram of the internal structure of a computer device provided in an embodiment of the present application, and the computer device 300 can be provided as a server. Referring to FIG6 , the computer device 300 includes a processing component 302, which further includes one or more processors, and a memory resource represented by a memory 301, for storing instructions that can be executed by the processing component 302, such as an application. The application stored in the memory 301 may include one or more modules, each of which corresponds to a set of instructions. In addition, the processing component 302 is configured to execute instructions to execute the power grid harmonic distribution calculation method of any of the above-mentioned embodiments.

The computer device 300 may further include a power supply component 303 configured to perform power management of the computer device 300, a wired or wireless network interface 304 configured to connect the computer device 300 to a network, and an input/output (I/O) interface 305. The computer device 300 may operate based on an operating system stored in the memory 301, such as Windows Server TM, Mac OS X TM, Unix TM, Linux TM, Free BSD TM, or the like.

Those skilled in the art will understand that the structure shown in FIG. 6 is merely a block diagram of a partial structure related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components than shown in the figure, or combine certain components, or have a different arrangement of components.

Finally, it should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the sentence "comprise a ..." do not exclude the presence of other identical elements in the process, method, article or device including the elements.

The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The various embodiments can be combined as needed, and the same or similar parts can refer to each other.

The above description of the disclosed embodiments enables those skilled in the art to implement or use the present application. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application will not be limited to the embodiments shown herein, but will conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims (10)

1. A method for calculating harmonic distribution of a power grid, characterized in that the method comprises: Obtaining, by means of a broadband measuring device installed in the power system, node harmonic voltages of key nodes at different harmonic orders, branch harmonic currents of branches connected to the broadband measuring device at different harmonic orders, and measurement errors of the broadband measuring device when measuring at different harmonic orders; Based on the node harmonic voltage, branch harmonic current and measurement error at different harmonic orders, the measurement equations at different harmonic orders are constructed; The measurement equation is solved using a weighted least square method to obtain branch harmonic currents of various nodes in the power system at different harmonic orders; The harmonic active power value injected by each node into the power system is calculated according to the branch harmonic current of each node, and the location of the harmonic source in the power system is determined according to the numerical value of each harmonic active power value. 2. The method for calculating harmonic distribution of a power grid according to claim 1, characterized in that before obtaining the node harmonic voltages of key nodes at different harmonic orders by a broadband measurement device installed in the power system, it also includes: Based on the harmonic distribution calculation requirements of the power system, a 0-1 integer programming model is constructed; After solving the 0-1 integer programming model, the location where the broadband measurement device is installed in the power system is determined according to the solution result. 3. The method for calculating the harmonic distribution of a power grid according to claim 1, characterized in that the measurement equations under different harmonic orders are constructed based on the node harmonic voltages, branch harmonic currents and measurement errors under different harmonic orders, comprising: According to the node harmonic voltage, branch harmonic current and measurement error under different harmonic orders, the node voltage measurement equation and branch injection current measurement equation under different harmonic orders are constructed; Determine a measurement matrix corresponding to node harmonic voltages and branch harmonic currents at different harmonic orders in the power system; According to the node voltage measurement equations under different harmonic orders, the branch injection current measurement equations and the corresponding measurement matrices, the synchronous phasor measurement equations are constructed. 4. The method for calculating the harmonic distribution of a power grid according to claim 3, wherein the node voltage measurement equation is: In the above formula, the subscript M represents the quantity measurement, and the subscript S represents the state quantity. It represents the hth node harmonic voltage measurement of node i, represents the h-order node harmonic voltage state quantity of node i, I represents the unit matrix with the same dimension as the node harmonic voltage measurement quantity, η _i represents the node harmonic voltage measurement error at node i in the case of h-order harmonic; The branch injection current measurement equation is: In the above formula, It represents the measurement of the harmonic current of the hth branch injected into the node i, It represents the node harmonic voltage state quantity of node j under the condition of h-order harmonic, represents the matrix element related to the hth harmonic of node i and node j in the node admittance matrix under the condition of hth harmonic, and n represents the total number of nodes in the power system; It represents the measurement of the amount of current injected between nodes i and j under the condition of harmonic h. represents the self-admittance in the admittance matrix of node i in the case of hth harmonic, represents the admittance between nodes i and j in the case of hth harmonic; The synchronized phasor measurement equation is: In the above formula, Indicates the node harmonic voltage measurement of key nodes where broadband measurement devices are installed. It indicates the measurement of branch harmonic current connected to the key node where the broadband measurement device is installed. represents the branch harmonic current state quantity of each node to be determined, The quantity measured is the measurement matrix of node harmonic voltage, The measured quantity is the measurement matrix of branch harmonic current. 5. The method for calculating the harmonic distribution of a power grid according to claim 4, characterized in that the method of using a weighted least square method to solve the measurement equation to obtain branch harmonic currents of each node in the power system at different harmonic orders comprises: Constructing a harmonic distribution calculation model according to the node voltage measurement equation and the branch injection current measurement equation under different harmonic orders, and the synchronous phasor measurement equation; The harmonic distribution calculation model is solved using a weighted least square method to obtain branch harmonic currents of various nodes in the power system at different harmonic orders. 6. The method for calculating the harmonic distribution of a power grid according to claim 5, wherein the harmonic distribution calculation model is: Z＝HX+ε Wherein, Z is the m×1-dimensional measurement phasor, X is the n×1-dimensional state quantity phasor to be determined, Z and X are determined according to the selected measurement and state quantity and phasor measurement equations, H is the m×n-dimensional measurement matrix, the measurement matrix is mainly determined by the network topology structure and component harmonic parameters in the power system, ε represents the m×1-dimensional measurement error phasor, m represents the number of measurement, and n represents the number of state quantities to be determined; The objective function of the weighted least squares method is: J(x)＝(Z-HX) ^T W(Z-HX) In the above formula, Represents the estimated value of the state quantity X; when When , the objective function reaches the minimum value, that is: minJ(x)＝Z-HX) ^T W(Z-HX) Differentiate the residual sum of squares to find the maximum value, and obtain the harmonic distribution calculation equation based on the weighted least squares principle: Wherein, W=R ^-1 , W is the m-th order measurement weight matrix, and R is the diagonal matrix of the measurement error variance of each measurement data; Solving the above equation, we can get the weighted least squares solution of the harmonic distribution calculation model: 7. The method for calculating the harmonic distribution of a power grid according to any one of claims 1 to 6, characterized in that the step of determining the location of the harmonic source in the power system according to the numerical values of each harmonic active power value comprises: If the value of at least one harmonic active power value is positive and exceeds a preset value, the node of the at least one harmonic active power value injected into the power system is determined to be the location of the harmonic source. 8. A power grid harmonic distribution calculation device, comprising: A data acquisition module, used to acquire, through a broadband measurement device installed in the power system, node harmonic voltages of key nodes at different harmonic orders, branch harmonic currents of branches connected to the broadband measurement device at different harmonic orders, and measurement errors of the broadband measurement device when measuring at different harmonic orders; A measurement equation construction module is used to construct measurement equations under different harmonic orders based on node harmonic voltages, branch harmonic currents and measurement errors under different harmonic orders; A harmonic current determination module, used to solve the measurement equation using a weighted least square method to obtain branch harmonic currents of various nodes in the power system at different harmonic orders; The harmonic source positioning module is used to calculate the harmonic active power value injected by each node into the power system according to the branch harmonic current of each node, and determine the location of the harmonic source in the power system according to the numerical value of each harmonic active power value. 9. A computer-readable storage medium, characterized in that: the computer-readable storage medium stores computer-readable instructions, and when the computer-readable instructions are executed by one or more processors, the one or more processors execute the steps of the power grid harmonic distribution calculation method as described in any one of claims 1 to 7. 10. A computer device, comprising: one or more processors, and a memory; The memory stores computer-readable instructions, and when the computer-readable instructions are executed by the one or more processors, the steps of the method for calculating power grid harmonic distribution as claimed in any one of claims 1 to 7 are performed.