CN110308366A - A kind of harmonic source location method based on orthogonal matching pursuit algorithm - Google Patents
A kind of harmonic source location 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 harmonic source location method based on orthogonal matching pursuit algorithm that the invention discloses a kind of, the harmonic source location method are suitable for the effective position of real system harmonic source location, comprising steps of A, based on measurement information establishing measurement equation；B, the node harmonic electric current estimation based on orthogonal matching pursuit algorithm；C, major harmonic source is positioned based on estimation result.Measurement equation caused by being less likely to the present invention overcomes the configuration of existing measuring equipment owes problem fixed, that the non-overall situation of system is objective, in the case where obtaining the partial branch harmonic current of grid, can the harmonic electric current accurately to each node of network estimate, effective position is carried out to harmonic source in power distribution network, reduce cost of investment, it is divided for harmonic contributions and harmonic wave control provides foundation, for improving the power quality of power grid, economic loss is reduced, user satisfaction is improved and is of great significance.
Description
Technical field
The present invention relates to power quality analysis technical fields, more particularly to the harmonic source based on orthogonal matching pursuit algorithm
Localization method.
Background technique
As harmonic pollution is further prominent in the extensive use of all trades and professions, power grid for power electronic equipment.Power electronics
The meeting being difficult to avoid that in device operation injects a large amount of harmonic current to power grid, causes the voltage and current in power grid to generate abnormal
Become, influences the safe and stable operation of power grid and electrical equipment.In order to understand the harmonic pollution in power grid in time, reaches and distinguish harmonic wave
Responsibility, the purpose for effectively administering harmonic wave are correct to identify that the major harmonic source in power grid is vital.
Harmonic source location is the basis for dividing each harmonic source harmonic contributions and harmonic wave pollution control, and method can substantially be divided into
Positioning mode based on equivalent circuit and the positioning mode two major classes based on harmonic state estimation.
Equivalent-circuit model positioning mode is at points of common connection (point of common coupling, PCC) system
Two parts, i.e. system side S (system) and user side C (customer) are equivalent to, it is right then according to system equivalent-circuit model
Institute's measured data determines main harmonic source using respective algorithms and belongs to system side or load-side；Method based on state estimation,
The harmonic voltage, harmonic current or power that part of nodes is got generally by measuring equipment are used according to system electric network composition
The method of state estimation calculates the harmonic voltage of each node and the harmonic current of each branch, to determine harmonic source
Position, provides foundation for harmonic wave control.
Harmonic source location Method And Principle based on equivalent circuit is simple, is easily achieved, but mainly for the feelings in single harmonic source
Condition lacks globality, and does not consider the time variation of power network topology and branch parameters generally；Positioning based on harmonic state estimation method
As a result relatively accurate, there is whole ornamental, be suitble to Multi-harmonic Sources positioning, but required metric data is more, quantity of state is asked
Solve more complex, calculation amount is larger.
Therefore, in the case where measuring equipment is less, it is desirable to have a kind of harmonic source location method is able to solve the prior art
The problems in.
Summary of the invention
The invention discloses a kind of harmonic source location method based on orthogonal matching pursuit algorithm, the harmonic source location side
Method the following steps are included:
Step 1: measurement equation is established based on measurement information；
Step 2: the node harmonic electric current estimation based on orthogonal matching pursuit algorithm；
Step 3: major harmonic source being positioned based on estimation result.
Preferably, the step 1 passes through the harmonic wave of topological structure of electric and the branch for adding measuring device obtained electricity
Stream, obtains the h subharmonic current measurement matrix formula (1) of branch:
Wherein,For the rank matrix of M × 1, the h subharmonic branch current that measurement obtains is indicated, h is overtone order, and m is branch
Serial number, M is the circuitry number for adding measuring device, the transposition of subscript T representing matrix.
Preferably, the step 1 establishes the measurement according to the h subharmonic current measurement of topological structure of electric and branch
Equation formulations (2):
Wherein, Ih=[I1h,I2h,…,Inh,…,INh]TIt is state variable, is the rank matrix of N × 1, indicates unknown node
H subharmonic Injection Current, n indicate node ID, N indicate power grid number of nodes, A is measurement matrix, be M × N rank matrix, table
Show the incidence matrix between harmonic wave branch current and node harmonic injection electric current.
Preferably, the step 2 the following steps are included:
Step 2.1: initialization introduces dictionary subset S, indicates the set of the column serial number of measurement matrix A, introduces the rank of M × 1
Residual vector e, by initial dictionary subset S0It is set as empty set, initial residual vector e0It is set as measuring vectorEnable the number of iterations k=
1；
Step 2.2: identification calculates residual vector ek-1With the inner product of column column vector each in measurement matrix A, select absolutely
Be worth it is maximum one column, as in current iteration operation with ek-1The column α of strongest correlationλ, the column serial number λ of the column is added to word
In allusion quotation subset S, αλIt is added to set ASIn, the repetition selection of column is avoided, the locally optimal solution of iteration is obtained, improves
Computational accuracy, reduces the number of iterations, expression formula such as formula (3) and (4):
Wherein αjIndicate the jth column of measurement matrix A, ASIndicate the column vector by the dictionary subset S measurement matrix A elected
Set, is M × k rank matrix, and subscript k is indicated currently as kth time iteration；
Step 2.3: estimation solves minimization problem by formula (5):
Available formula (6):
The wherein conjugation of subscript H representing matrix, -1 representing matrix of subscript are inverted；
Step 2.4: iteration is updated, updated residual error is formula (7):
K=k+1 is enabled, judges whether to meet stopping criterion, is returned if iterative steps are not up to preset fixed value
Step 2.2, stop iteration if reaching and enter step 2.5；
Step 2.5: obtain final estimation result formula (8):
Ih=[I1h,I2h,…,Inh,…,INh]T(8),
Wherein, IhIndicate h harmonic current value of each node of estimation, InhIndicate the h note for the node n that estimation obtains
Enter harmonic current.
Preferably, the step 2.3 only need to be to the column vector of the measurement matrix A elected by the dictionary subset S
Set is inverted, and when measuring equipment causes the non-global viewable of system less in real system, leads to the measurement equationIt owes
Calmly, when the measurement matrix A is irreversible, the effective position of harmonic source can still be carried out.
Preferably, the specific steps that the step 3 positions major harmonic source based on estimation result include:
Step 3.1: according to the estimation result I of h harmonic current value of each node in the step 2hTo harmonic source
It is positioned, Ih=[I1h,I2h,…,Inh,…,INh]TIf h harmonic electric current estimated value I of n-th of nodenhIt is positive
Value, then it represents that contain h subharmonic source at the node, and the size of estimated value is the h subharmonic that the harmonic source is injected to power grid
Size of current；Otherwise it indicates at the node without containing h subharmonic source；
Step 3.2: the small harmonic source of harmonic content being judged as major harmonic source in order to prevent, to step 3.1
In the harmonic source that estimates carry out the differentiation in major harmonic source；
If certain node number is the injection h subharmonic current estimated value I of nnhFor positive value, then the h subharmonic of node n is injected into electricity
The size of stream is set as Inh+ΔInhIf the h subharmonic changes of contents for having more than the node of p% in power grid is more than q% Δ Inh,
Then judge that wherein the occurrence of p and q is according to the structure of power grid, capacity, voltage class etc. containing h major harmonic source at node n
Parameter is configured.
The harmonic source location method based on orthogonal matching pursuit algorithm that the invention discloses a kind of, the present invention overcomes existing
Measurement equation caused by measuring equipment configuration is less likely to owes problem fixed, that the non-overall situation of system is objective, in the part for obtaining power grid
In the case where branch harmonic current, can the harmonic electric current accurately to each node estimate, to humorous in power distribution network
Wave source carries out effective position, reduces cost of investment, divides for harmonic contributions and harmonic wave control provides foundation.
Detailed description of the invention
Fig. 1 is the flow chart of the harmonic source location method based on orthogonal matching pursuit algorithm.
Fig. 2 is the IEEE14 node power grid topological graph of emulation experiment in invention specific embodiment.
Specific embodiment
To keep the purposes, technical schemes and advantages of the invention implemented clearer, below in conjunction in the embodiment of the present invention
Attached drawing, technical solution in the embodiment of the present invention is further described in more detail.In the accompanying drawings, identical from beginning to end or class
As label indicate same or similar element or element with the same or similar functions.Described embodiment is the present invention
A part of the embodiment, instead of all the embodiments.The embodiments described below with reference to the accompanying drawings are exemplary, it is intended to use
It is of the invention in explaining, and be not considered as limiting the invention.Based on the embodiments of the present invention, ordinary skill people
Member's every other embodiment obtained without creative efforts, shall fall within the protection scope of the present invention.
As shown in Figure 1, the harmonic source location method in embodiment of the present invention based on orthogonal matching pursuit algorithm include with
Lower step:
A, measurement equation is established based on measurement information；
B, the node harmonic electric current estimation based on orthogonal matching pursuit algorithm；
C, major harmonic source is positioned based on estimation result.
A kind of harmonic source location method based on orthogonal matching pursuit algorithm through the invention, can be effectively to reality
Harmonic source in system is accurately positioned.
In step A, establishing measurement equation based on measurement information includes:
A1, it obtains topological structure of electric and adds the branch harmonic current of measuring device, obtain the h subharmonic electricity of branch
Flow measurement matrixWhereinFor the rank matrix of M × 1, the h subharmonic that measurement obtains is indicated
Branch current, h are overtone order, and m is the serial number of branch, and M is the circuitry number for adding measuring device, subscript T representing matrix
Transposition；
A2, measurement equation is established according to the h subharmonic current measurement of topological structure of electric and branch:
Wherein Ih=[I1h,I2h,…,Inh,…,INh]TIt is state variable, is the rank matrix of N × 1, indicates unknown node
H subharmonic Injection Current, n indicate that node ID, N indicate the number of nodes of power grid, and A is measurement matrix, is M × N rank matrix, indicates
Incidence matrix between harmonic wave branch current and node harmonic injection electric current.
In step B, the node harmonic electric current estimation based on orthogonal matching pursuit algorithm includes:
B1, initialization: introducing dictionary subset S, indicates the set of the column serial number of measurement matrix A, introduces the residual error of the rank of M × 1
Vector e, by initial dictionary subset S0It is set as empty set, initial residual vector e0It is set as measuring vectorEnable the number of iterations k=1.
B2, identification: residual vector e is calculatedk-1With the inner product of column column vector each in measurement matrix A, maximum absolute value is selected
A column, as in current iteration operation with ek-1The column α of strongest correlationλ, the column serial number λ of the column is added to dictionary subset S
In, αλIt is added to set ASIn, the repetition selection of column is avoided, the locally optimal solution of iteration is obtained, improves calculating essence
Degree, reduces the number of iterations, expression formula is as follows:
Wherein αjIndicate the jth column of measurement matrix A, ASIndicate the column vector by the dictionary subset S measurement matrix A elected
Set, is M × k rank matrix, and subscript k is indicated currently as kth time iteration.
B3, estimation: minimization problem is solved:
It is available:
The wherein conjugation of subscript H representing matrix, -1 representing matrix of subscript are inverted.
The non-global viewable of system is caused when measuring equipment is less in real system, leads to measurement equationOwe fixed, amount
Survey matrix A it is irreversible when, due to the present invention in each iterative process only need to select in measurement matrix A with residual vector ek-1
The column α of strongest correlationλ, step B2 still can be used when measurement matrix A is irreversible and step B3 solves underdetermined equation.
B4, iteration: updated residual error is updated are as follows:
K=k+1 is enabled, judges whether to meet stopping criterion, is returned if iterative steps are not up to preset fixed value
Step B2 stops iteration if reaching and enters next step.
B5, final estimation result I is obtainedh=[I1h,I2h,…,Inh,…,INh]T, wherein IhIndicate each node h of estimation
Secondary harmonic current value, InhIndicate the h harmonic electric current for the node n that estimation obtains.
In step C, harmonic source is positioned based on estimation result:
C1, harmonic source is positioned according to the estimation result Ih of h harmonic current value of each node in step B,
Ih=[I1h,I2h,…,Inh,…,INh]TIf h harmonic electric current estimated value I of n-th of nodenhFor positive value, then it represents that should
Contain h subharmonic source at node, and the size of estimated value is the h subharmonic current size that the harmonic source is injected to power grid；It is no
It then indicates at the node without containing h subharmonic source.
C2, since there are the harmonic sources that harmonic content is small in real system, influenced caused by power grid smaller, be
Prevent from the small harmonic source of harmonic content being judged as major harmonic source, can to the harmonic source estimated in step C1 into
The differentiation in row major harmonic source.
If certain node number is the injection h subharmonic current estimated value I of nnhFor positive value, then the h subharmonic of node n is injected into electricity
The size of stream is set as Inh+ΔInhIf the h subharmonic changes of contents for having more than the node of p% in power grid is more than q% Δ Inh,
Then judge to contain h major harmonic source at node n.
Wherein the occurrence of p and q is configured according to parameters such as the structure of power grid, capacity, voltage class.
In order to verify reliability and accuracy of the invention, following emulation experiment has been carried out to above method.
Emulation experiment:
Emulation experiment is the emulation estimation carried out in IEEE14 node system, and power grid topological graph is as shown in Fig. 2, therein
Number designation indicates the node number of power grid, such as 3 indicate node 3, which includes node 1-14, is contained in the power grid
2 harmonic sources are located at node 4 and node 5, the overtone order and harmonic wave current value size such as table 1 of harmonic electric current
Shown in middle actual value, the value of p and q are respectively 20 and 5.
The simulation experiment result is as follows:
It is respectively adopted and is estimated based on least square method and method proposed by the present invention, obtain 5 times and 7 subharmonic inject
The results are shown in Table 1 for current estimation.
Table 1
Wherein PE indicates the harmonic current actual value of node harmonic electric current estimated value and node of the invention
Accuracy errors, unit %, calculation formula are as follows:
Wherein, PEnhIndicate the accuracy errors of the h harmonic electric current of node n, InhrIndicate the h injection of node n
Harmonic current actual value；InhIndicate the h subharmonic Injection Current estimated value of node n.
From table 1 it follows that being compared with the harmonic source location method based on least square method, estimated using the method for the present invention
The node harmonic electric current of calculating is closer with actual value, and accuracy errors are smaller, being capable of effective position egress 4 and node
Contain harmonic source at 5.When only increasing by 5 subharmonic current 1A of node 4 and node 5 respectively, have 3 in remaining 13 node
5 subharmonic contents of a node have increased above 0.05A, thus can determine whether node 4 and node 5 is major harmonic source.
Therefore, it can accurately the node harmonic electric current to system be carried out using harmonic source location method of the invention
Estimation carries out effective position to the major harmonic source in power grid.
In view of economic factor, the measuring equipment configured in real system is less, and metric data is less, and system cannot reach
Global viewable, therefore, injection size is 5 subharmonic currents of 1+j1A at node 11,12,13, changes the number of measuring equipment
Amount and installation site, it is as shown in table 2 to obtain positioning result:
Table 2
√ indicates that effective position can be carried out to harmonic source in table, and × expression cannot.
Wherein only when node 2,6,7,9,12 is configured with measuring equipment, system is global viewable, measurement equation Ib
=AI is non-to owe fixed.Table 2 shows that measuring equipment is less in the real system and causes the non-global viewable of system, leads to measurement equation Ib=
AI owes timing, and method of the invention still is able to effectively determine harmonic source.
By above description, the present invention is based on the basic functions of the harmonic source location method of orthogonal matching pursuit algorithm to obtain
It illustrates.A kind of harmonic source location method based on orthogonal matching pursuit algorithm of the invention, realizes to Distribution Network Harmonics source
Effective position, overcome the deficiency in existing appraisal procedure, for improve power grid power quality, reduce economic loss, mention
High user satisfaction is of great significance.
Finally it is noted that the above embodiments are merely illustrative of the technical solutions of the present invention, rather than its limitations.To the greatest extent
Present invention has been described in detail with reference to the aforementioned embodiments for pipe, those skilled in the art should understand that: it is still
It is possible to modify the technical solutions described in the foregoing embodiments, or part of technical characteristic is equally replaced
It changes；And these are modified or replaceed, the essence for technical solution of various embodiments of the present invention that it does not separate the essence of the corresponding technical solution
Mind and range.
Claims (6)
1. a kind of harmonic source location method based on orthogonal matching pursuit algorithm, which is characterized in that the harmonic source location method
The following steps are included:
Step 1: measurement equation is established based on measurement information；
Step 2: the node harmonic electric current estimation based on orthogonal matching pursuit algorithm；
Step 3: major harmonic source being positioned based on estimation result.
2. the harmonic source location method according to claim 1 based on orthogonal matching pursuit algorithm, it is characterised in that: described
Step 1 obtains the h subharmonic of branch by the harmonic current of topological structure of electric and the branch for adding measuring device obtained
Current measurement Matrix Formula (1):
Wherein,For the rank matrix of M × 1, indicate that the h subharmonic branch current that measurement obtains, h are overtone order, m is the sequence of branch
Number, M is the circuitry number for adding measuring device, the transposition of subscript T representing matrix.
3. the harmonic source location method according to claim 2 based on orthogonal matching pursuit algorithm, it is characterised in that: described
Step 1 establishes the measurement equation formula (2) according to the h subharmonic current measurement of topological structure of electric and branch:
Wherein, Ih=[I1h,I2h,…,Inh,…,INh]TIt is state variable, is the rank matrix of N × 1, indicates h times of unknown node
Harmonic injection electric current, n indicate that node ID, N indicate the number of nodes of power grid, and A is measurement matrix, is M × N rank matrix, indicates humorous
Incidence matrix between wave branch current and node harmonic injection electric current.
4. the harmonic source location method according to claim 3 based on orthogonal matching pursuit algorithm, it is characterised in that: described
Step 2 the following steps are included:
Step 2.1: initialization introduces dictionary subset S, indicates the set of the column serial number of measurement matrix A, introduces the residual error of the rank of M × 1
Vector e, by initial dictionary subset S0It is set as empty set, initial residual vector e0It is set as measuring vectorEnable the number of iterations k=1；
Step 2.2: identification calculates residual vector ek-1With the inner product of column column vector each in measurement matrix A, absolute value is selected most
A big column, as in current iteration operation with ek-1The column α of strongest correlationλ, the column serial number λ of the column is added to dictionary
Collect in S, αλIt is added to set ASIn, such as formula (3) and (4):
Wherein αjIndicate the jth column of measurement matrix A, ASIndicate the column vector set by the dictionary subset S measurement matrix A elected,
For M × k rank matrix, subscript k is indicated currently as kth time iteration；
Step 2.3: estimation solves minimization problem by formula (5):
Available formula (6):
The wherein conjugation of subscript H representing matrix, -1 representing matrix of subscript are inverted；
Step 2.4: iteration is updated, updated residual error is formula (7):
K=k+1 is enabled, judges whether to meet stopping criterion, the return step if iterative steps are not up to preset fixed value
2.2, stop iteration if reaching and enters step 2.5；
Step 2.5: obtain final estimation result formula (8):
Ih=[I1h,I2h,…,Inh,…,INh]T (8)
Wherein, IhIndicate h harmonic current value of each node of estimation, InhIndicate that the h injection for the node n that estimation obtains is humorous
Wave electric current.
5. the harmonic source location method according to claim 4 based on orthogonal matching pursuit algorithm, it is characterised in that: described
Step 2.3 need to only invert to the column vector set of the measurement matrix A elected by the dictionary subset S, when the measurement
EquationOwe fixed, the described measurement matrix A it is irreversible when, can still carry out the effective position of harmonic source.
6. the harmonic source location method according to claim 5 based on orthogonal matching pursuit algorithm, it is characterised in that: described
Step 3 includes: based on the specific steps that estimation result positions major harmonic source
Step 3.1: according to the estimation result I of h harmonic current value of each node in the step 2hHarmonic source is determined
Position, if h harmonic electric current estimated value I of n-th of nodenhFor positive value, then it represents that contain h subharmonic source at the node, and
The size of estimated value is the h subharmonic current size that the harmonic source is injected to power grid；Otherwise it indicates at the node without containing h times
Harmonic source；
Step 3.2: the small harmonic source of harmonic content being judged as major harmonic source in order to prevent, is estimated in step 3.1
The harmonic source of calculating carries out the differentiation in major harmonic source；
If certain node number is the injection h subharmonic current estimated value I of nnhFor positive value, then by the h subharmonic Injection Current of node n
Size is set as Inh+ΔInhIf the h subharmonic changes of contents for having more than the node of p% in power grid is more than q% Δ Inh, then sentence
Contain h major harmonic source at disconnected node n, wherein the occurrence of p and q is according to parameters such as the structure of power grid, capacity, voltage class
It is configured.
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