CN110308366B - Harmonic source positioning method based on orthogonal matching pursuit algorithm - Google Patents
Harmonic source positioning method based on orthogonal matching pursuit algorithm Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
- G01R31/08—Locating faults in cables, transmission lines, or networks
- G01R31/081—Locating faults in cables, transmission lines, or networks according to type of conductors
- G01R31/086—Locating faults in cables, transmission lines, or networks according to type of conductors in power transmission or distribution networks, i.e. with interconnected conductors
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J13/00—Circuit arrangements for providing remote indication of network conditions, e.g. an instantaneous record of the open or closed condition of each circuitbreaker in the network; Circuit arrangements for providing remote control of switching means in a power distribution network, e.g. switching in and out of current consumers by using a pulse code signal carried by the network
Abstract
The invention discloses a harmonic source positioning method based on an orthogonal matching pursuit algorithm, which is suitable for effective positioning of actual system harmonic source positioning and comprises the following steps: A. establishing a measurement equation based on the measurement information; B. estimating node injection harmonic current based on an orthogonal matching pursuit algorithm; C. and positioning the main harmonic source based on the estimation result. The method and the device solve the problems of underdetermined measurement equation and non-global objective system possibly caused by less configuration of the conventional measurement device, can accurately estimate the injected harmonic current of each node of the network under the condition of obtaining partial branch harmonic current of a system network, effectively position a harmonic source in the power distribution network, reduce the investment cost, provide a basis for harmonic responsibility division and harmonic treatment, and have important significance for improving the power quality of the power grid, reducing the economic loss and improving the user satisfaction.
Description
Technical Field
The invention relates to the technical field of power quality analysis, in particular to a harmonic source positioning method based on an orthogonal matching pursuit algorithm.
Background
With the wide application of power electronic devices in various industries, harmonic pollution in power grids is increasingly prominent. A large amount of harmonic current is injected into a power grid in the operation of a power electronic device, which is difficult to avoid, so that the voltage and the current in the power grid are distorted, and the safe and stable operation of the power grid and electric equipment is influenced. In order to know the harmonic pollution in the power grid in time and achieve the purposes of clearing harmonic responsibility and effectively treating harmonic, it is vital to correctly identify the main harmonic source in the power grid.
Harmonic source positioning is the basis for dividing harmonic responsibility and harmonic pollution control of each harmonic source, and the method can be roughly divided into two categories, namely a positioning method based on an equivalent circuit and a positioning method based on harmonic state estimation.
The equivalent circuit model positioning method is characterized in that a system is equivalent into two parts, namely a system side S (system) and a user side C (customer), at a Point of Common Coupling (PCC), and then according to a system equivalent circuit model, a corresponding algorithm is adopted for measured data to judge whether a main harmonic source belongs to the system side or the load side; the method based on state estimation generally obtains harmonic voltage, harmonic current or power of partial nodes through a measuring device, and calculates the harmonic voltage of each node and the harmonic current of each branch circuit by using the state estimation method according to the system power grid structure, thereby positioning a harmonic source and providing a basis for harmonic treatment.
The harmonic source positioning method based on the equivalent circuit is simple in principle and easy to implement, but mainly aims at the condition of a single harmonic source, is lack of integrity, and generally does not consider the time-varying property of power grid topology and branch parameters; the positioning result based on the harmonic wave state estimation method is relatively accurate, has integral observability and is suitable for positioning multiple harmonic wave sources, but the required measurement data is more, the state quantity solving is more complex and the calculated quantity is larger.
Therefore, in the case of fewer measuring devices, a method for locating a harmonic source is desired to solve the problems in the prior art.
Disclosure of Invention
The invention discloses a harmonic source positioning method based on an orthogonal matching pursuit algorithm, which comprises the following steps:
step 1: establishing a measurement equation based on the measurement information;
step 2: estimating node injection harmonic current based on an orthogonal matching pursuit algorithm;
and step 3: and positioning the main harmonic source based on the estimation result.
Preferably, in step 1, an h-th harmonic current measurement matrix formula (1) of the branch is obtained through the power grid topology and the obtained harmonic current of the branch with the measuring device:
wherein the content of the first and second substances,
the harmonic measurement device is an Mx 1-order matrix and represents h harmonic branch current obtained through measurement, h is the harmonic frequency, M is the serial number of a branch, M is the number of the branches provided with the measurement device, and superscript T represents the transposition of the matrix.
Preferably, the step 1 establishes the measurement equation formula (2) according to the power grid topology and the h-harmonic current measurement of the branch:
wherein, Ih＝[I1h,I2h,…,Inh,…,INh]TThe state variable is an NxN order matrix which represents h-order harmonic injection current of an unknown node, N represents a node serial number, N represents the node number of a power grid, and A is a measurement matrix which is an MxN order matrix and represents a correlation matrix between harmonic branch current and node harmonic injection current.
Preferably, the step 2 comprises the steps of:
step 2.1: initializing, introducing a dictionary subset S, representing a set of column sequence numbers of a measurement matrix A, introducing a residual vector e of M multiplied by 1 order, and initially performing dictionary subset S0Set to empty set, initial residual vector e0Set as the measurement vector
Making the iteration number k equal to 1;
step 2.2: identifying and calculating residual vector ek-1The inner product of the column vector of each column in the measurement matrix A is used to select the column with the maximum absolute value, i.e. the column with e in the current iteration operationk-1The most strongly correlated column αλAdding the column sequence number lambda of the column to the dictionary subset S, and adding alphaλAdding to set ASIn the method, repeated selection of columns is avoided, iterative local optimal solution is obtained, calculation precision is improved, and reduction of the number of columns is reducedThe number of iterations is expressed as in equations (3) and (4):
wherein alpha isjRepresents the jth column, A, of the measurement matrix ASRepresenting a column vector set of a measurement matrix A selected according to the dictionary subset S, wherein the column vector set is an M multiplied by k order matrix, and a subscript k represents that the current iteration is the kth iteration;
step 2.3: estimation, the minimization problem is solved by equation (5):
equation (6) can be obtained:
wherein the superscript H represents the conjugate of the matrix and the superscript-1 represents the inversion of the matrix;
step 2.4: updating iteration, and the updated residual is formula (7):
if the iteration step number does not reach a preset fixed value, returning to the step 2.2, and if the iteration step number reaches the preset fixed value, stopping iteration and entering the step 2.5;
step 2.5: obtaining the final estimation result formula (8):
Ih＝[I1h,I2h,…,Inh,…,INh]T (8)，
wherein, IhRepresenting the estimated value of the h-th injected harmonic current, I, at each nodenhRepresenting the estimated h-order injected harmonic current at node n.
Preferably, the step 2.3 only needs to invert the column vector set of the measurement matrix a selected according to the dictionary subset S, and when the number of measurement devices in the actual system is small, the system is not globally observable, resulting in the measurement equation
Under-determining and the measurement matrix A is irreversible, the effective positioning of the harmonic source can still be carried out.
Preferably, the step 3 of locating the main harmonic source based on the estimation result includes the following specific steps:
step 3.1: according to the estimation result I of h-order injection harmonic current value of each node in the step 2hPositioning of harmonic sources, Ih＝[I1h,I2h,…,Inh,…,INh]TIf the h-order injection harmonic current estimation value I of the nth nodenhIf the value is positive, the node contains an h-order harmonic source, and the estimated value is the h-order harmonic current injected into the power grid by the harmonic source; otherwise, the node does not contain the h-order harmonic source;
step 3.2: in order to prevent the injected harmonic source with the small harmonic content from being judged as the main harmonic source, the main harmonic source is judged for the harmonic source estimated in the step 3.1;
if a certain node number is n, injecting h-order harmonic current estimation value InhSetting the h-th harmonic injection current of the node n as I when the voltage is positivenh+ΔInhIf the h-order harmonic content of nodes in the power grid exceeding p% changes by more than q% delta InhAnd judging that the node n contains h times of main harmonic sources, wherein the specific values of p and q are set according to parameters such as the structure, the capacity, the voltage level and the like of the power grid.
The invention discloses a harmonic source positioning method based on an orthogonal matching pursuit algorithm, which solves the problems of underdetermined measurement equation and non-global objective system caused by less configuration of the existing measurement device, can accurately estimate the injected harmonic current of each node under the condition of obtaining partial branch harmonic current of a power grid, effectively positions a harmonic source in a power distribution network, reduces the investment cost and provides a basis for harmonic responsibility division and harmonic governance.
Drawings
FIG. 1 is a flow chart of a method for locating a harmonic source based on an orthogonal matching pursuit algorithm.
Fig. 2 is a power grid topology diagram of an IEEE14 node of a simulation experiment in the embodiment of the present invention.
Detailed Description
In order to make the implementation objects, technical solutions and advantages of the present invention clearer, the technical solutions in the embodiments of the present invention will be described in more detail below with reference to the accompanying drawings in the embodiments of the present invention. In the drawings, the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The described embodiments are only some, but not all embodiments of the invention. The embodiments described below with reference to the drawings are illustrative and intended to be illustrative of the invention and are not to be construed as limiting the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As shown in fig. 1, the method for locating a harmonic source based on an orthogonal matching pursuit algorithm in the embodiment of the present invention includes the following steps:
A. establishing a measurement equation based on the measurement information;
B. estimating node injection harmonic current based on an orthogonal matching pursuit algorithm;
C. and positioning the main harmonic source based on the estimation result.
The method for positioning the harmonic source based on the orthogonal matching pursuit algorithm can effectively and accurately position the harmonic source in an actual system.
In step a, establishing a measurement equation based on the measurement information includes:
a1, obtaining a power grid topological structure and a branch harmonic current with a measuring device, and obtaining an h-harmonic current measuring matrix of the branch
Wherein
The harmonic measurement device is an Mx 1-order matrix and represents h harmonic branch current obtained by measurement, h is the harmonic frequency, M is the serial number of a branch, M is the number of the branches provided with the measurement device, and a superscript T represents the transposition of the matrix;
a2, establishing a measurement equation according to the power grid topological structure and h-harmonic current measurement of the branch circuit:
wherein Ih＝[I1h,I2h,…,Inh,…,INh]TThe state variable is an NxN order matrix which represents h-order harmonic injection current of an unknown node, N represents a node serial number, N represents the node number of a power grid, and A is a measurement matrix which is an MxN order matrix and represents a correlation matrix between harmonic branch current and node harmonic injection current.
In step B, the node injection harmonic current estimation based on the orthogonal matching pursuit algorithm includes:
b1, initialization: introducing a dictionary subset S, representing a set of column sequence numbers of a measurement matrix A, introducing a residual vector e of M multiplied by 1 order, and initially performing dictionary subset S0Set to empty set, initial residual vector e0Set as the measurement vector
Let the iteration number k equal to 1.
B2, identification: computing residual vector ek-1The inner product of the column vector of each column in the measurement matrix A is used to select the column with the maximum absolute value, i.e. the column with e in the current iteration operationk-1Strongest powerAssociated column alphaλAdding the column sequence number lambda of the column to the dictionary subset S, and adding alphaλAdding to set ASIn the method, repeated selection of columns is avoided, an iterative local optimal solution is obtained, the calculation precision is improved, and the iteration times are reduced, wherein the expression is as follows:
wherein alpha isjRepresents the jth column, A, of the measurement matrix ASThe column vector set of the measurement matrix a selected according to the dictionary subset S is represented as an M × k order matrix, and the subscript k represents the current kth iteration.
B3, estimating: solving a minimization problem:
it is possible to obtain:
where the superscript H represents the conjugate of the matrix and the superscript-1 represents the inversion of the matrix.
When the number of measurement devices in the actual system is less, the system is not globally observable, resulting in measurement equation
When the underdetermined measurement matrix A is not reversible, the invention only needs to select the measurement matrix A and the residual vector e in each iteration processk-1The most strongly correlated column αλWhen the measurement matrix A is not reversible, the underdetermined equation can still be solved by adopting the step B2 and the step B3.
B4, updating iteration: the updated residuals are:
and c, judging whether the stop criterion is met or not by setting k to be k +1, returning to the step B2 if the iteration step number does not reach a preset fixed value, and stopping iteration and entering the next step if the iteration step number reaches the preset fixed value.
B5, obtaining the final estimation result Ih＝[I1h,I2h,…,Inh,…,INh]TIn which IhRepresenting the estimated value of the h-th injected harmonic current, I, at each nodenhRepresenting the estimated h-order injected harmonic current at node n.
In step C, the harmonic source is positioned based on the estimation result:
c1, positioning the harmonic source according to the estimation result Ih of the h-th order injection harmonic current value of each node in the step B, Ih＝[I1h,I2h,…,Inh,…,INh]TIf the h-order injection harmonic current estimation value I of the nth nodenhIf the value is positive, the node contains an h-order harmonic source, and the estimated value is the h-order harmonic current injected into the power grid by the harmonic source; otherwise, the node does not contain the h-order harmonic source.
And C2, because the injected harmonic source with the small harmonic content exists in the actual system, the influence on the power grid is small, and in order to prevent the injected harmonic source with the small harmonic content from being judged as the main harmonic source, the main harmonic source can be judged for the harmonic source estimated in the step C1.
If a certain node number is n, injecting h-order harmonic current estimation value InhSetting the h-th harmonic injection current of the node n as I when the voltage is positivenh+ΔInhIf the h-order harmonic content of nodes in the power grid exceeding p% changes by more than q% delta InhAnd judging that the node n contains h times of main harmonic sources.
The specific values of p and q are set according to parameters such as the structure, the capacity, the voltage level and the like of the power grid.
To verify the reliability and accuracy of the present invention, the following simulation experiments were performed on the above method.
Simulation experiment:
the simulation experiment is a simulation estimation performed in an IEEE14 node system, a grid topology diagram of the simulation experiment is shown in fig. 2, wherein a number label indicates a node number of a grid, for example, 3 indicates a node 3, the grid topology diagram includes nodes 1 to 14, the grid includes 2 harmonic sources, which are respectively located at a node 4 and a node 5, the harmonic times and the harmonic current values of the injected harmonic currents are shown in an actual value in table 1, and the values of p and q are respectively 20 and 5.
The simulation experiment results are as follows:
the estimation is carried out by adopting a method based on least square and the method provided by the invention, and the estimation results of 5 th harmonic injection current and 7 th harmonic injection current are shown in table 1.
TABLE 1
Wherein, PE represents the accuracy error between the estimated value of the node injection harmonic current and the actual value of the node injection harmonic current, and the unit is% as follows:
wherein, PEnhAccuracy error, I, of the h-th injected harmonic current representing node nnhrRepresenting the actual value of the h-order injection harmonic current of the node n; i isnhRepresenting the h-th harmonic injection current estimate of node n.
As can be seen from Table 1, compared with the harmonic source positioning method based on the least square method, the node injection harmonic current estimated by the method of the invention is closer to the actual value, the accuracy error is smaller, and the harmonic sources contained in the nodes 4 and 5 can be effectively positioned. When only the 5 th harmonic current 1A of the node 4 and the node 5 is increased, respectively, the 5 th harmonic content of 3 nodes of the remaining 13 nodes is increased by more than 0.05A, and thus it can be judged that the node 4 and the node 5 are both main harmonic sources.
Therefore, the harmonic source positioning method can accurately estimate the node injection harmonic current of the system and effectively position the main harmonic source in the power grid.
Considering economic factors, the actual system has fewer measuring devices, less measuring data, and the system cannot achieve global observability, therefore, 5 th harmonic currents with the magnitude of 1+ j1A are injected at the nodes 11, 12 and 13, the number and the installation positions of the measuring devices are changed, and the positioning results are shown in table 2:
TABLE 2
In the table, √ indicates that the harmonic source can be effectively located, and x indicates that it cannot.
Wherein, only when the nodes 2, 6, 7, 9 and 12 are all configured with the measuring device, the system is the overall observable measuring equation IbAI is not underdetermined. Table 2 shows that when the number of measurement devices in the actual system is small, the system is not globally observable, resulting in measurement equation IbThe method of the present invention still enables an efficient determination of the source of the harmonics when AI is under-timed.
Through the above description, the basic functions of the harmonic source positioning method based on the orthogonal matching pursuit algorithm are explained. The harmonic source positioning method based on the orthogonal matching pursuit algorithm realizes effective positioning of the harmonic source of the power distribution network, overcomes the defects in the existing evaluation method, and has important significance for improving the power quality of the power grid, reducing the economic loss and improving the user satisfaction.
Finally, it should be pointed out that: the above examples are only for illustrating the technical solutions of the present invention, and are not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.
Claims (3)
1. A harmonic source positioning method based on an orthogonal matching pursuit algorithm is characterized by comprising the following steps:
step 1: establishing a measurement equation based on the measurement information;
in the step 1, an h-order harmonic current measurement matrix formula (1) of the branch is obtained through a power grid topological structure and the obtained harmonic current of the branch with the measuring device:
wherein the content of the first and second substances,
the harmonic measurement device is an Mx 1-order matrix and represents h harmonic branch current obtained by measurement, h is the harmonic frequency, M is the serial number of a branch, M is the number of the branches provided with the measurement device, and a superscript T represents the transposition of the matrix;
the step 1 establishes the measurement equation formula (2) according to the power grid topological structure and the h-harmonic current measurement of the branch circuit:
wherein, Ih＝[I1h,I2h,…,Inh,…,INh]TThe state variable is an NxN order matrix and represents h-order harmonic injection current of an unknown node, N represents a node serial number, N represents the node number of a power grid, A is a measurement matrix and is an MxN order matrix and represents a correlation matrix between harmonic branch current and node harmonic injection current;
step 2: estimating node injection harmonic current based on an orthogonal matching pursuit algorithm;
the step 2 comprises the following steps:
step 2.1: initializing, introducing a dictionary subset S, representing a set of column sequence numbers of a measurement matrix A, introducing a residual vector e of M multiplied by 1 order, and initially performing dictionary subset S0Set to empty set, initial residual vector e0Set as the measurement vector
Making the iteration number k equal to 1;
step 2.2: identifying and calculating residual vector ek-1The inner product of the column vector of each column in the measurement matrix A is used to select the column with the maximum absolute value, i.e. the column with e in the current iteration operationk-1The most strongly correlated column αλAdding the column sequence number lambda of the column to the dictionary subset S, and adding alphaλAdding to set ASAs in formulas (3) and (4):
wherein alpha isjRepresents the jth column, A, of the measurement matrix ASRepresenting a column vector set of a measurement matrix A selected according to the dictionary subset S, wherein the column vector set is an M multiplied by k order matrix, and a subscript k represents that the current iteration is the kth iteration;
step 2.3: estimation, the minimization problem is solved by equation (5):
equation (6) can be obtained:
wherein the superscript H represents the conjugate of the matrix and the superscript-1 represents the inversion of the matrix;
step 2.4: updating iteration, and the updated residual is formula (7):
if the iteration step number does not reach a preset fixed value, returning to the step 2.2, and if the iteration step number reaches the preset fixed value, stopping iteration and entering the step 2.5;
step 2.5: obtaining the final estimation result formula (8):
Ih＝[I1h,I2h,…,Inh,…,INh]T (8)
wherein, IhRepresenting the estimated value of the h-th injected harmonic current, I, at each nodenhRepresenting the estimated h-order injection harmonic current of the node n;
and step 3: and positioning the main harmonic source based on the estimation result.
2. The method for locating a harmonic source based on an orthogonal matching pursuit algorithm according to claim 1, characterized in that: step 2.3 is to invert the column vector set of the measurement matrix a selected according to the dictionary subset S, and then to apply the measurement equation
Under-determining and the measurement matrix A is irreversible, the effective positioning of the harmonic source can still be carried out.
3. The method for locating a harmonic source based on an orthogonal matching pursuit algorithm according to claim 2, characterized in that: the step 3 of positioning the main harmonic source based on the estimation result specifically includes:
step 3.1: according to the estimation result I of h-order injection harmonic current value of each node in the step 2hPositioning the harmonic source, and if the h-order injection harmonic current estimation value I of the nth nodenhIf the value is positive, the node contains an h-order harmonic source, and the estimated value is the h-order harmonic current injected into the power grid by the harmonic source; otherwise, the node does not contain the h-order harmonic source;
step 3.2: in order to prevent the injected harmonic source with the small harmonic content from being judged as the main harmonic source, the main harmonic source is judged for the harmonic source estimated in the step 3.1;
if a certain node number is n, injecting h-order harmonic current estimation value InhSetting the h-th harmonic injection current of the node n as I when the voltage is positivenh+ΔInhIf the h-order harmonic content of nodes in the power grid exceeding p% changes by more than q% delta InhAnd judging that the node n contains h times of main harmonic sources, wherein the specific values of p and q are set according to the structure, capacity and voltage level parameters of the power grid.
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