CN108170885B - Method for identifying multiple harmonic sources in power distribution network - Google Patents

Method for identifying multiple harmonic sources in power distribution network Download PDF

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CN108170885B
CN108170885B CN201711214893.XA CN201711214893A CN108170885B CN 108170885 B CN108170885 B CN 108170885B CN 201711214893 A CN201711214893 A CN 201711214893A CN 108170885 B CN108170885 B CN 108170885B
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景明玉
王林信
王利平
李浩峰
王胤添
段明
马鹏涛
蔡晓成
郭海涛
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Qingyang Power Supply Company State Grid Gansu Electric Power Co
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Abstract

The invention relates to a method for identifying multiple harmonic sources in a power distribution network, which comprises the following steps: the method includes the steps that a PMU (power management unit) is placed in a power distribution network; secondly, carry out the optimal configuration of PMU to the distribution network: determining a mathematical model of PMU optimization configuration; solving a mathematical model of PMU optimal configuration by using a binary empire competition algorithm to obtain an optimal configuration scheme of the PMU in the power distribution network; obtaining harmonic voltage at a node configured with PMU in the power distribution network within a period of time
Figure DEST_PATH_IMAGE001
Data; harmonic voltage is obtained with mobile filter
Figure 409071DEST_PATH_IMAGE001
Rapidly changing component in
Figure 776598DEST_PATH_IMAGE002
(ii) a Fifth pair
Figure 126546DEST_PATH_IMAGE001
Carrying out preprocessing, namely centralization processing and whitening processing; sixthly, quickly changing components
Figure 667249DEST_PATH_IMAGE002
In the improved independent component analysis algorithm, a separation matrix is determined and then applied to harmonic voltage
Figure 248403DEST_PATH_IMAGE001
The harmonic currents injected into the distribution network are obtained by separation
Figure DEST_PATH_IMAGE003
. The method has the characteristics of systematization realization and accurate estimation result, and can be used for multi-harmonics when harmonic impedance is unknown in an actual power distribution networkAnd (5) in the identification process of the wave source.

Description

Method for identifying multiple harmonic sources in power distribution network
Technical Field
The invention relates to the field of power quality analysis and control, in particular to a multi-harmonic source identification method in a power distribution network.
Background
Electric energy is one of the indispensable important energy sources of modern human society because of its advantages of economy, practicality, cleanness, controllability, convenience in transmission and the like. As a special commodity, the electric energy also demands quality, and the high-quality electric energy supply not only ensures the safe, economic and efficient operation of an electric power system, but also ensures the normal production of enterprises, thereby being an important premise for improving the living standard of people. Since the 21 st century, the demand for electric power has been increasing, and new electric loads have been developed at a rapid pace, which brings unprecedented opportunities to the development of modern electric networks and also brings great challenges: on one hand, novel nonlinear loads are rapidly developed and widely applied to a power grid, and due to the nonlinear characteristics of the loads, a large amount of harmonic waves are generated in the power grid, so that the power quality is seriously polluted; on the other hand, with the vigorous development of the high and new technology industry, the degree of dependence on the power quality is continuously improved, and the requirement standard for the power quality is increased day by day. Under the large environment, the quality of electric energy is increasingly attracting attention of people.
The harmonic problem is an important component of the power quality problem. With the wide application of power electronic devices in the power grid and the large-scale access of various nonlinear loads, a large amount of harmonic waves are injected into the power grid, so that the power grid is seriously polluted by the harmonic waves. Due to the existence of harmonic waves, vibration and noise of the electrical equipment are increased, the electric energy utilization efficiency is reduced, the insulation of the electrical equipment and the electric transmission line is rapidly aged due to excessive heating, and the electric energy transmission efficiency is reduced, so that the operation cost of a power grid is increased. Therefore, in order to improve the quality of electric energy, quickly, economically and effectively treat harmonic waves and solve the problem of harmonic pollution, harmonic sources in the power grid must be identified first, and the magnitude of harmonic current injected into the power grid by each harmonic source is determined. Harmonic sources in the power grid come from the power grid itself on one hand, and ferromagnetic saturation devices such as transformers and reactors; on the other hand, the harmonic current generated by various nonlinear loads connected to the power grid, such as rectifiers, inverters, electronic switching type devices and the like, mainly depends on the characteristics of the nonlinear loads, the operating conditions and other factors, has little relation with system parameters, and is generally regarded as a harmonic constant current source. The power grid mainly comprises a transmission network and a distribution network, nonlinear loads are regarded as main harmonic sources in the power grid because the generated harmonics are the most, and therefore, the identification process of the harmonic sources in the power grid is mainly put on the identification of the nonlinear loads serving as harmonic constant current sources in the distribution network. The existing identification method of multiple harmonic sources in the power distribution network mainly comprises the following three methods:
harmonic source identification method based on harmonic state estimation
Under the condition that the harmonic source information is unknown, a harmonic state estimation module is established through harmonic measurement data acquired from the measurement nodes and by combining a network topological structure and element parameters of the system, the harmonic voltage and harmonic current states of the whole network are estimated according to a certain estimation criterion, and the harmonic source in the power grid is analyzed and identified. The method needs to know detailed network parameters and an accurate topological structure, but in actual engineering, due to the approximation of a system model and the lack of the network parameters, a large error is generated in an estimation result.
Harmonic source identification method based on neural network method
Under the condition that network parameters are unknown, harmonic real-time measurement data acquired from the measurement nodes are utilized to establish an estimator model, so that harmonic current in the network is estimated. Although the method does not need to solve the harmonic impedance of the network, the method has the defects of high dependence degree of a training model on pre-training, susceptibility to influence of a connection weight matrix by the operation condition of the power grid, lack of flexibility and the like.
C harmonic source identification method based on blind source separation method
Under the condition that network parameters and a topological structure are unknown, harmonic current injected into the network is estimated through a blind source separation algorithm by utilizing a harmonic voltage value measured on a measurement node. Although the method can identify the harmonic source in the network only by measuring the quantity under the condition that the network parameters and the topology structure are unknown, the amplitude and the sequence of the harmonic current obtained by separation are uncertain due to the characteristics of the blind source separation algorithm, and particularly, the separation performance of the algorithm is greatly influenced by the sequence of the separated harmonic currents. In addition, in the method, the measuring devices are placed at will, so long as the number of the measuring devices is not less than the number of the harmonic sources, and whether the network is observable or not can be guaranteed by considering the placement of the measuring devices is not considered, which inevitably causes deviation on a final estimation result.
Disclosure of Invention
The invention aims to provide a method for identifying multiple harmonic sources in a power distribution network, which is more systematic and has more accurate identification result.
In order to solve the above problems, the method for identifying multiple harmonic sources in a power distribution network comprises the following steps:
the method includes the steps that a PMU (power management unit) is placed in a power distribution network;
secondly, carry out the optimal configuration of PMU to the distribution network:
on the premise that the network harmonic state can be observed, configuring a mathematical model with the minimum number of measurement points and the maximum redundancy of each node as targets, and determining PMU (phasor measurement Unit) optimization configuration; solving the mathematical model of PMU optimal configuration by using Binary Imperial Competitive Algorithm (BICA), namely obtaining the optimal configuration scheme of PMU in the power distribution network; the mathematical model of the PMU optimization configuration is as follows:
Figure 434899DEST_PATH_IMAGE001
in the formula:
Figure 186954DEST_PATH_IMAGE002
is thatnA dimensional row vector, representing a PMU configuration,nis the number of nodes contained in the system, if a nodejDispose PMU, then
Figure 9416DEST_PATH_IMAGE003
=1, otherwise
Figure 214133DEST_PATH_IMAGE003
= 0; t represents vector transposition;
Figure 350716DEST_PATH_IMAGE004
and
Figure 19595DEST_PATH_IMAGE005
are weight coefficients, respectively
Figure 463825DEST_PATH_IMAGE006
、
Figure 218155DEST_PATH_IMAGE007
；mIs thatnA column vector of dimensions consisting of the number of times each node needs to be measured;Ais thatn*nAnd the incidence matrix of the dimension is used for describing the connection relation between the nodes and is defined as that:
Figure 158429DEST_PATH_IMAGE008
；
obtaining harmonic voltage at a node configured with PMU in the power distribution network within a period of time
Figure 619497DEST_PATH_IMAGE009
Data;
the harmonic voltage is obtained by the movable filter
Figure 783762DEST_PATH_IMAGE009
Rapidly changing component in
Figure 963071DEST_PATH_IMAGE010
；
Figure 503774DEST_PATH_IMAGE011
In the formula:
Figure 317884DEST_PATH_IMAGE010
and
Figure 856312DEST_PATH_IMAGE012
representing rapidly varying components in the harmonic voltage and harmonic current respectively,
Figure 319655DEST_PATH_IMAGE013
and
Figure 601732DEST_PATH_IMAGE014
representing slowly varying components in the harmonic voltage and harmonic current, respectively;
Figure 834130DEST_PATH_IMAGE015
representing a known measurement vector;
Figure 543460DEST_PATH_IMAGE016
represents a harmonic current;
fifthly to
Figure 933246DEST_PATH_IMAGE009
Carrying out preprocessing, namely centralization processing and whitening processing;
sixthly, dividing the quick change component
Figure 815752DEST_PATH_IMAGE010
For improving the independent component analysis algorithm, determining a separation matrix, and applying the separation matrix to the harmonic voltage
Figure 105919DEST_PATH_IMAGE009
The harmonic currents injected into the distribution network are obtained by separation
Figure 48467DEST_PATH_IMAGE016
。
Compared with the prior art, the invention has the following advantages:
1. the binary empire competition algorithm adopted when the mathematical model of the PMU optimal configuration is solved has the characteristics of high convergence speed and optimal global search, and can quickly and accurately obtain the optimal configuration scheme of the PMU.
2. The invention improves the ICA algorithm, solves the problem that the separation performance of the algorithm is greatly influenced by the original ICA algorithm due to the fact that each independent component in the source signal is extracted out of order, and enables each independent component in the source signal to be output in order according to the magnitude of the negative entropy.
3. Compared with the existing multi-harmonic source identification method, the method provided by the invention can estimate each harmonic current injected into the power distribution network only by the harmonic voltage obtained at the measurement node under the condition that the harmonic impedance is unknown, and the estimated harmonic current is more accurate through the optimal configuration of PMU and the improvement of ICA algorithm.
4. The method provided by the invention systematically completes the identification process of the multiple harmonic sources in the power distribution network from the selection of the measuring device to the configuration of the measuring device and then to the identification of each harmonic current injected into the power distribution network, and meanwhile, the method is simple in algorithm and suitable for the practical engineering problem and can be used for solving the identification problem of the multiple harmonic sources in the practical power distribution network.
Drawings
The following describes embodiments of the present invention in further detail with reference to the accompanying drawings.
FIG. 1 is a flow chart of the binary empire competition algorithm of the present invention.
FIG. 2 is a linear model of the independent component analysis algorithm of the present invention.
Fig. 3 is a flow chart of the improved independent component analysis algorithm of the present invention.
Fig. 4 is a block diagram of an IEEE14 node standard power distribution network of the present invention.
FIG. 5 is a comparison graph of the convergence effect of the binary empire competition algorithm and the binary particle swarm algorithm.
FIG. 6 is a graph of the actual 5 harmonic current for each harmonic source node normalization of the present invention. Wherein: a is the normalized 5 th harmonic current at node 3, b is the normalized 5 th harmonic current at node 6, and c is the normalized 5 th harmonic current at node 13.
FIG. 7 is a plot of the estimated 5 th harmonic current for the normalized ordered output of the present invention.
FIG. 8 is a graph of the actual 7 harmonic currents for each harmonic source node normalization of the present invention. Wherein: a is the normalized 7 th harmonic current at node 3, b is the normalized 7 th harmonic current at node 6, and c is the normalized 7 th harmonic current at node 13.
FIG. 9 is a graph of the estimated 7 th harmonic current for the normalized ordered output of the present invention.
FIG. 10 is a graph of the actual 11 th harmonic current normalized by the harmonic source nodes of the present invention. Wherein: a is the normalized 11 th harmonic current at node 3, b is the normalized 11 th harmonic current at node 6, and c is the normalized 11 th harmonic current at node 13.
FIG. 11 is a plot of the estimated 11 th harmonic current for the normalized ordered output of the present invention.
Detailed Description
A method for identifying multiple harmonic sources in a power distribution network comprises the following steps:
the method includes the steps that a PMU (power management unit) is placed in a power distribution network.
A Phasor Measurement Unit (PMU) is a Phasor Measurement device based on GPS technology, and has been used as a collection device for harmonic Measurement information because of its function of synchronous Measurement at multiple Measurement points, but PMU is expensive in cost, and only when PMU is reasonably configured in a power distribution network, the system can be observed under the condition of installation of less PMU.
Secondly, carry out the optimal configuration of PMU to the distribution network:
on the premise that the network harmonic state can be observed, configuring a mathematical model with the minimum number of measurement points and the maximum redundancy of each node as targets, and determining PMU (phasor measurement Unit) optimization configuration; solving a mathematical model of PMU optimal configuration by using a Binary Imperial Competitive Algorithm (BICA), namely obtaining an optimal configuration scheme of the PMU in the power distribution network; the mathematical model of PMU optimization configuration is as follows:
Figure 424084DEST_PATH_IMAGE001
in the formula:
Figure 110281DEST_PATH_IMAGE002
is thatnA dimensional row vector, representing a PMU configuration,nis the number of nodes contained in the system, if a nodejDispose PMU, then
Figure 254954DEST_PATH_IMAGE003
=1, otherwise
Figure 804622DEST_PATH_IMAGE003
= 0; t represents vector transposition;
Figure 729853DEST_PATH_IMAGE004
and
Figure 891844DEST_PATH_IMAGE005
are weight coefficients, respectively
Figure 218920DEST_PATH_IMAGE006
、
Figure 175375DEST_PATH_IMAGE007
；mIs thatnA column vector of dimensions consisting of the number of times each node needs to be measured;Ais thatn*nAnd the incidence matrix of the dimension is used for describing the connection relation between the nodes and is defined as that:
Figure 525585DEST_PATH_IMAGE008
。
on the basis of analyzing an ICA optimization mechanism, an integer coding mode is adopted, and meanwhile, an ICA is improved by using an optimization idea of a Binary Particle Swarm Optimization (BPSO) to obtain the BICA. As shown in fig. 1, the specific steps of solving the PMU optimization configuration problem by using BICA are as follows:
first, an initial empire is generated.
First of all produce
Figure 553583DEST_PATH_IMAGE017
AnNThe countries of the dimension, each representing a PMU configuration scheme. The text uses integer coding to generate countriesiThe individual countries can be represented as:
Figure 174314DEST_PATH_IMAGE018
the variables of each dimension in the formula are respectively expressed inNThe configuration of PMUs in the power system of an individual node,
Figure 629566DEST_PATH_IMAGE019
，
Figure 201493DEST_PATH_IMAGE020
is represented at a nodejThe PMU is not configured,
Figure 705287DEST_PATH_IMAGE021
is represented at a nodejConfiguring a PMU;
then calculate the cost of each country, secondiThe cost of each country is:
Figure 6955DEST_PATH_IMAGE022
in the formula:
Figure 570791DEST_PATH_IMAGE023
as a function of fitnessI.e. the objective function. The smaller the cost is, the greater the momentum of the corresponding country is, the countries are arranged in ascending order according to the cost, and before the cost is taken
Figure 692331DEST_PATH_IMAGE024
One country as the empire nationality, the rest
Figure 498351DEST_PATH_IMAGE025
（
Figure 654526DEST_PATH_IMAGE026
) One country acts as a colonial country.
Finally, an initial empire is generated. An empire country is composed of an empire country and the colonial countries occupied by the empire country, and the number of colonial countries owned by the empire country is in direct proportion to the potential of the empire country, i.e. the greater the potential, the more colonial countries are occupied. First, thenThe number of colonial sites owned by each empire state is:
Figure 389264DEST_PATH_IMAGE027
in the formula:
Figure 935782DEST_PATH_IMAGE028
is as followsnThe standard strength of an empire nationality can be determined by the following equation:
Figure 843696DEST_PATH_IMAGE029
Figure 792060DEST_PATH_IMAGE030
in the formula:
Figure 760016DEST_PATH_IMAGE031
is as followsnThe cost of the individual empire state is,
Figure 295296DEST_PATH_IMAGE032
is as followsnStandard cost of an empire state.
② assimilation process.
After the initial empire was formed, empire-minded countries in each empire achieved assimilation of colonial countries by spreading their own thoughts, cultures and customs to colonial countries. Different from ICA, the assimilation process is simulated by controlling the moving distance and angle of the colonial countries to the empire country, in BICA, most colonial countries are firstly enabled to accept assimilation and move to the empire country, then the rest colonial countries are enabled to conduct self exploration to seek development and develop greatly under the influence of assimilation, the exploration speed concept is introduced according to the BPSO optimization idea, and finally the colonial countries are updated through the exploration speed, so that the local optimal problem can be effectively avoided. The countries in the colonial area that are fully assimilated or self-developed are determined by the following formula:
Figure 944583DEST_PATH_IMAGE033
in the formula: imp is the empire country in the empire,
Figure 809771DEST_PATH_IMAGE034
is the first in the empireiThe country of the individual colonial area,yis subject to [0,1]Uniformly distributed random variables in between. The process of seeking development of national exploration of colonial regions is as follows:
Figure 886311DEST_PATH_IMAGE035
in the formula:
Figure 469739DEST_PATH_IMAGE036
is a colonial place in the empireiIn the first placekOn the second iteration it explores the first of the velocity vectorsjThe number of the elements is one,wis the weight coefficient of the weight of the image,ris between [0,1 ]]A random number in between, and a random number,
Figure 922718DEST_PATH_IMAGE037
is the first of the empire State in the empire StatejThe number of the elements is one,
Figure 642412DEST_PATH_IMAGE038
representing a new country of the colonial region. The new colonial countries are:
Figure 388389DEST_PATH_IMAGE039
the empire state in this case is composed of an empire state, a fully assimilated colonial country, and a progressively developing colonial country.
③ exchange the positions of the empire country and the colonial country
After the assimilation process is over, when the development (momentum) of a colonial country exceeds the empire nationality, the colonial country becomes the empire nationality in this empire, and the total empire cost is:
Figure 396796DEST_PATH_IMAGE040
in the formula:
Figure 450203DEST_PATH_IMAGE041
is as followsnThe total cost of the empire state,
Figure 227666DEST_PATH_IMAGE042
is as followsnThe empire state of the individual empire states,
Figure 708326DEST_PATH_IMAGE043
a positive number less than 1, for weakening the contribution of the colonial country to the empire's total cost, usually takes 0.1.
Empire competition
Each empire state competes with each other to predate the colonial land of the weakest empire state according to the strength of the own momentum, thereby achieving the purpose of enhancing the own momentum. Standard forces of empire availabletcReplacement ofcCalculated, the greater the force of the empire, the more colonial land is occupied, and the weaker empireThe colonial areas continue to decrease until all of their colonial areas are lost, the empire goes out.
Fifth convergence judgment
With the continuation of empire competition, the Weak and small empires are continuously extinguished, only one empire is left in the end under ideal conditions, the algorithm is terminated at the moment, and the empire principal country in the empire is the optimal allocation scheme of the PMU; under general conditions, a plurality of empires cannot be classified as one empire through empire competition, so that the empire-derived country in the empire with the minimum total cost can be taken as the optimal allocation scheme of the PMU after the set iteration times are reached.
Obtaining harmonic voltage at a node configured with PMU in the power distribution network within a period of time
Figure 204029DEST_PATH_IMAGE009
And (4) data.
Harmonic voltage is obtained with mobile filter
Figure 222977DEST_PATH_IMAGE009
Rapidly changing component in
Figure 917263DEST_PATH_IMAGE010
。
Figure 772087DEST_PATH_IMAGE011
In the formula:
Figure 489507DEST_PATH_IMAGE010
and
Figure 884716DEST_PATH_IMAGE012
representing rapidly varying components in the harmonic voltage and harmonic current respectively,
Figure 636772DEST_PATH_IMAGE013
and
Figure 459234DEST_PATH_IMAGE014
representing slowly varying divisions in harmonic voltages and currents, respectivelyAn amount;
Figure 162486DEST_PATH_IMAGE015
representing a known measurement vector;
Figure 299069DEST_PATH_IMAGE016
representing harmonic currents.
The purpose of obtaining a rapidly varying component in a harmonic voltage using a moving filter is to satisfy the preconditions of an Independent Component Analysis (ICA) algorithm. Because the harmonic current is estimated by the ICA algorithm, the estimated harmonic current is limited by the precondition of the ICA algorithm, and the estimated harmonic current needs to meet the requirements of mutual statistical independence and non-Gaussian property. While harmonic currents generated by non-linear loads typically contain slowly varying components as well as rapidly varying components. The slow change component is mainly caused by external factors such as environment, climate and the like, and has slow speed and small amplitude along with the time change; the fast varying component is mainly caused by the temporal variation of the specific non-linear load. Since the variation trends of the slowly varying components of the nonlinear loads are relatively similar, it can be considered that a strong correlation exists between the slowly varying components; the fast-changing components of the nonlinear loads are different from each other, so that the fast-changing components can be considered to be independent from each other.
Measured harmonic voltage
Figure 967948DEST_PATH_IMAGE009
Using linear filters to reject them
Figure 898995DEST_PATH_IMAGE013
Then obtain
Figure 591007DEST_PATH_IMAGE010
To do so
Figure 767167DEST_PATH_IMAGE010
Correspond to
Figure 290552DEST_PATH_IMAGE012
Due to individual harmonic wavesThe fast-changing components in the flow are statistically independent and non-gaussian distributed, and the linear filtering of the measured harmonic voltages does not affect the admittance matrix, and will therefore
Figure 658080DEST_PATH_IMAGE009
The rapidly varying component of (a) is applied to improve the independent component analysis algorithm.
Fifth pair
Figure 899705DEST_PATH_IMAGE009
Preprocessing, namely centralizing processing and whitening processing, is carried out.
Sixthly, quickly changing components
Figure 112512DEST_PATH_IMAGE010
In the improved independent component analysis algorithm, a separation matrix is determined and then applied to harmonic voltage
Figure 693666DEST_PATH_IMAGE009
The harmonic currents injected into the distribution network are obtained by separation
Figure 28832DEST_PATH_IMAGE016
。
FIG. 2 shows a linear model of ICA, where the relationship between the signal data is:
Figure 193972DEST_PATH_IMAGE044
Figure 210469DEST_PATH_IMAGE045
in the formula:Xin order to be able to observe the signal as known,Ain the case of an unknown mixing matrix,Sin order for the source signal to be unknown,
Figure 708447DEST_PATH_IMAGE046
is a gaussian noise, and is a noise,Yin order to estimate the resulting source signal(s),Wis a separation matrix. The basic idea of ICA isAt the source signalSMixing with source signalAUnder unknown conditions, from known observed signalsXObtaining an optimal separation matrix by iterative optimizationWIn aWUnder the action of (1) make fromXObtained by separation inYApproximating to the actual source signal to the maximumS. While ignoring the measurement noise of the harmonic voltage, the harmonic current injected into the node can be expressed in the form of the following linear equation, namely:
Figure 417777DEST_PATH_IMAGE047
in the formula:
Figure 306099DEST_PATH_IMAGE048
is composed oftThe harmonic current vector injected into the node at the moment, the voltage distortion caused by the harmonic current can cause the linear load to inject the harmonic current into the node, which increases the number of the harmonic sources to be estimated except the linear load, but the harmonic current injected into the node by the nonlinear load is not greatly influenced by whether the linear load is contained on the node or not, so the harmonic current is injected into the node by the nonlinear load
Figure 188604DEST_PATH_IMAGE049
Only represents the harmonic current injected by the nonlinear load as a harmonic source to a node;
Figure 980236DEST_PATH_IMAGE050
in order to be a system admittance matrix,
Figure 860467DEST_PATH_IMAGE051
is composed oftThe harmonic voltage vector of the instant in time,hare harmonic orders. Due to the difficulty in obtaining accurate system parameters
Figure 298402DEST_PATH_IMAGE050
Especially at high frequency harmonics, and therefore
Figure 656702DEST_PATH_IMAGE050
Is unknown;
Figure 129271DEST_PATH_IMAGE052
can be derived from PMU measurements configured at the node, then
Figure 180404DEST_PATH_IMAGE052
Are known; the harmonic sources in the power distribution network are unknown, and harmonic currents injected into the power distribution network by the harmonic sources
Figure 541853DEST_PATH_IMAGE049
Are unknown and are also desirable. From the above analysis, it can be seen that:Ycorrespond to
Figure 766161DEST_PATH_IMAGE049
，WCorrespond to
Figure 765341DEST_PATH_IMAGE050
，XCorrespond to
Figure 49692DEST_PATH_IMAGE052
Then is at
Figure 399902DEST_PATH_IMAGE050
When unknown, the estimation of harmonic current from measured harmonic voltage can be solved by independent component analysis algorithm.
The improved independent component analysis algorithm is used for solving the problem of disordered output of each component when the independent component analysis algorithm estimates each component in a source signal. Because the sequence of extracting each independent component in the source signal has a great influence on the separation performance of the algorithm, if each independent component in the source signal can be extracted according to a certain sequence, the separation precision is increased, and the algorithm is more stable. Therefore, the air extraction unit is used for eliminating the influence of the extracted components on the original mixed signal to obtain a new mixed signal, and then the new mixed signal is brought into the iterative process of the ICA algorithm. In the alternate process of extraction and air extraction, the components in the separated source signals are output in a descending order according to the magnitude of the negative entropy of the components.
Fig. 3 is a flow chart of the improved independent component analysis algorithm, which includes the following specific steps:
i preprocessing the observed signal to obtain
Figure 365584DEST_PATH_IMAGE053
；
Ii selecting the number of components contained in the source signal to be separatednAnd make an orderp=1；
Iii is
Figure 547166DEST_PATH_IMAGE054
Assigning a random vectorw；
Iv set up
Figure 175987DEST_PATH_IMAGE054
：
Figure 75810DEST_PATH_IMAGE055
；
V will get
Figure 579604DEST_PATH_IMAGE054
Respectively orthogonalizing and normalizing by the following formula
Figure 818955DEST_PATH_IMAGE056
After the representation treatment
Figure 179529DEST_PATH_IMAGE054
；
Figure 504331DEST_PATH_IMAGE057
Figure 874133DEST_PATH_IMAGE058
；
Vi calculation
Figure 200947DEST_PATH_IMAGE056
Convergence of if
Figure 998001DEST_PATH_IMAGE056
Do not converge, order
Figure 544520DEST_PATH_IMAGE059
And simultaneously returning to the step iv; if it is not
Figure 655696DEST_PATH_IMAGE056
Convergence, then use
Figure 666377DEST_PATH_IMAGE056
De-separating to obtain a component of the source signal
Figure 572016DEST_PATH_IMAGE060
（kIs the number of components in the source signal that have been separated);
vii is the vector of the blood-extracting weight
Figure 668148DEST_PATH_IMAGE061
Assigning a random vector;
ⅷ
Figure 830619DEST_PATH_IMAGE061
the iterative update is carried out by the following formula to obtain
Figure 633490DEST_PATH_IMAGE062
；
Figure 772347DEST_PATH_IMAGE063
In the formula:
Figure 293459DEST_PATH_IMAGE064
represents a learning rate;
ix calculation
Figure 543174DEST_PATH_IMAGE065
Convergence of (2)
Figure 466131DEST_PATH_IMAGE066
If, if
Figure 212108DEST_PATH_IMAGE065
Returning to the step viii when convergence does not occur; if it is not
Figure 282832DEST_PATH_IMAGE065
Converge, then will
Figure 273922DEST_PATH_IMAGE067
Bringing in
Figure 113702DEST_PATH_IMAGE068
To eliminate
Figure 469728DEST_PATH_IMAGE069
To pair
Figure 201317DEST_PATH_IMAGE070
Is influenced by
Figure 58414DEST_PATH_IMAGE071
；
Xi ling
Figure 690384DEST_PATH_IMAGE072
Simultaneously orderp=p+1 andk=k+1, if
Figure 279628DEST_PATH_IMAGE073
Then, return to step iii.
The method comprises the following steps: and step i-vi is an extraction process, and step vii-ix is an air extraction process, wherein in the alternate process of extraction and air extraction, each component in the separated source signal is output in a descending order according to the magnitude of the negative entropy.
The algorithm analysis results given below show that the novel method for identifying the multiple harmonic sources in the power distribution network is practical and effective. The harmonic currents injected into the power distribution network are identified from the selection of the measuring device to the configuration of the measuring device, the identification of multiple harmonic sources in the power distribution network is systematically realized, and meanwhile, the change trend of the harmonic currents can be more accurately reflected by utilizing an improved independent component analysis algorithm.
Calculation example: an IEEE14 node standard power distribution network shown in figure 4 is built in PSCAD (Power System Computer aid design) software, harmonic current sources are located at nodes 3, 6 and 13, and the geographic positions and the electrical distances of the harmonic sources are far away, so that the power distribution network accords with the actual situation of the power grid. The harmonic current data injected into the three nodes is generated by a model built in the PSCAD software: the Harmonic current of the injection node 3 is generated by a Harmonic current module, the Harmonic current of the injection node 6 is generated by an SVC (static var compensator) module, the Harmonic current of the injection node 13 is generated by a 6 pulse rectifier module, and each group of data comprises 321 sampling points; harmonic current data generated by PSCAD software is led into Matlab software, and random signals which have the mean value of 0 and the variance of 0.002 and meet Laplace distribution are added to the harmonic current data, so that the random signals in the Laplace distribution strengthen the rapid change of non-Gaussian distribution, and the independence of harmonic currents is enhanced; and introducing the obtained harmonic current data into PSCAD software to be used as harmonic current injected into the appointed node of the IEEE14 node standard power distribution network. The binary empire state competition algorithm is adopted to carry out PMU optimization configuration on the IEEE14 node standard distribution network, so that PMU configuration at least at nodes 2, 6, 7 and 9 can enable the state of the whole system to be observable, FIG. 5 is a comparison graph of convergence effects of two algorithms when the BICA and BPSO algorithms are adopted to carry out PMU optimization configuration on the IEEE14 node standard distribution network, and the graph shows that: compared with the BPSO algorithm, the BICA is more excellent in search directionality and convergence rate, and is beneficial to rapidly and accurately obtaining the optimal configuration scheme of the PMU.
Harmonic voltage data can be obtained directly from PMU measurements, and harmonic currents are estimated using the improved independent component analysis algorithm herein. Because the harmonic current obtained by estimation has uncertainty of amplitude, the harmonic current obtained by estimation and the actual harmonic current are subjected to normalization processing; meanwhile, the harmonic current source model built in PSCAD software is generated
Figure 324945DEST_PATH_IMAGE074
And
Figure 657837DEST_PATH_IMAGE075
（mis an integer) order, so only odd harmonics need to be considered, and since the magnitude of the injected harmonic current is inversely proportional to the frequency of the harmonic, higher harmonics can also be ignored, so that the major harmonic currents to be identified are 5, 7, 11 orders. The normalized actual and estimated harmonic currents are shown in fig. 6 to 11.
In the actual harmonic current diagram, the three waveforms are the harmonic currents injected into nodes 3, 6, 13 in sequence. And (3) estimating the harmonic current by using an improved independent component analysis algorithm, and arranging the harmonic currents obtained by estimation in a descending order according to the magnitude of the negative entropy of the harmonic currents. In order to indicate that the estimated harmonic currents are arranged according to the descending order of the negative entropy, the negative entropy of each estimated harmonic current needs to be calculated, however, the accurate value of the negative entropy is not easy to be obtained, so the following processing is performed: the negative entropy is a measure for measuring non-gaussian property, the stronger the non-gaussian property is, the larger the corresponding negative entropy is, in other words, the estimated harmonic currents are arranged in descending order of the non-gaussian property, the kurtosis is easy to calculate as a measure for measuring non-gaussian property, and the absolute value of the kurtosis corresponding to the stronger the non-gaussian property is, the absolute value of the kurtosis is larger, and the negative entropy is calculated instead of the absolute value of the kurtosis. The kurtosis of the 5 th harmonic current actually injected into nodes 3, 6, 13 in FIG. 6 is sequentiallyk(3)=6.4938，k(6)=3.3821，k(13) =3.3010, so the order in which the harmonic currents are estimated to be unchanged; the kurtosis of the 7 th harmonic current actually injected into nodes 3, 6, 13 in FIG. 8 is in turnk(3)=5.5119，k(6)=3.1432，k(13) =4.6173, so the harmonic current order exchange of nodes 6 and 13 is estimated; the kurtosis of the 11 th harmonic current actually injected into nodes 3, 6, 13 in FIG. 10 is in turnk(3)=4.7695，k(6)=3.1432，k(13) =4.6592, therefore the estimate results in node 6 and 13 harmonic current order exchange.
The above analysis shows that: the harmonic currents obtained by estimation can be arranged in a descending order according to the magnitude of the negative entropy by using an improved independent component analysis algorithm.
By normalised offset error
Figure 206630DEST_PATH_IMAGE076
Using correlation coefficient as error evaluation index
Figure 730890DEST_PATH_IMAGE077
As a measure of the degree of correlation.
Wherein: subscriptkRepresenting estimated harmonic current vectors
Figure 935607DEST_PATH_IMAGE078
To (1) akThe value of the one or more of,Nis the total number of the sample points,
Figure 134507DEST_PATH_IMAGE079
in order to calculate the covariance,
Figure 475489DEST_PATH_IMAGE080
as the actual harmonic current vectorIStandard deviation of (2).
Figure 672115DEST_PATH_IMAGE081
The smaller the representative result, the more accurate the method performance is;
Figure 426445DEST_PATH_IMAGE082
larger means more closely related. The indexes of the improved independent component analysis algorithm and the estimation effect of the existing independent component analysis algorithm are shown in table 1.
TABLE 1 Performance comparison of an improved independent component analysis algorithm with an existing independent component analysis algorithm
Figure 602605DEST_PATH_IMAGE083
As can be seen from Table 1, the normalized offset error of the improved independent component analysis algorithm is 8.19% at the maximum, but still less than 10%, which meets the engineering requirements. Through comparison, the normalized offset error of the harmonic current estimated by the improved independent component analysis algorithm is smaller and the correlation coefficient is larger than that of the harmonic current estimated by the existing independent component analysis algorithm, and the fact that the change trend of the harmonic current can be reflected more accurately by the improved independent component analysis algorithm is shown.
Therefore, the method provided by the invention realizes the accurate estimation of the variation trend of the multi-harmonic current injected into the power distribution network, and shows that the novel method for identifying the multi-harmonic source in the power distribution network provided by the invention has the characteristics of systematization realization and accurate estimation result, and can be used in the identification process of the multi-harmonic source when the harmonic impedance in the actual power distribution network is unknown, thereby having certain engineering practical value.

Claims (1)

1. A method for identifying multiple harmonic sources in a power distribution network comprises the following steps:
the method includes the steps that a PMU (power management unit) is placed in a power distribution network;
secondly, carry out the optimal configuration of PMU to the distribution network:
on the premise that the network harmonic state can be observed, configuring a mathematical model with the minimum number of measurement points and the maximum redundancy of each node as targets, and determining PMU (phasor measurement Unit) optimization configuration; solving the mathematical model of the PMU optimal configuration by using a binary empire competition algorithm to obtain an optimal configuration scheme of the PMU in the power distribution network; the mathematical model of the PMU optimization configuration is as follows:
Figure FDF0000009586980000011
in the formula: x ═ x1，Λ，xj，Λ，xn]For representing a PMU configuration scheme, n is the number of nodes in the system, and if a PMU is configured at node j, x isj1, otherwise xjT denotes vector transpose, 0; w is a1And w2Are weight coefficients, respectively w1＝36，w20.8; m is a column vector of n dimensions, which is formed by the number of times each node needs to be measured; a is an n-by-n-dimensional incidence matrix used for describing the connection relation between nodes, and is defined as:
Figure FDF0000009586980000012
obtaining a node configured with PMU in the power distribution network within a period of timeOf the harmonic voltage vhData;
the harmonic voltage v is obtained by a movable filterhOf the rapidly changing component Vh.fast；
Vh＝ZhIh＝Zh(Ih.fast+Ih.slow)＝Vh.fast+Vh.slow
In the formula: vh.fastAnd Ih.fastRespectively representing rapidly varying components, V, in harmonic voltages and currentsh.slowAnd Ih.slowRepresenting slowly varying components in the harmonic voltage and harmonic current, respectively; z is a radical ofhRepresenting a known measurement vector; i ishRepresents a harmonic current;
fifthly, carrying out the fifth stephCarrying out preprocessing, namely centralization processing and whitening processing;
sixthly, dividing the rapidly-changed component V into a plurality of partsh.fastFor improving the independent component analysis algorithm, determining a separation matrix, and applying the separation matrix to the harmonic voltage vhThe harmonic currents I injected into the power distribution network are obtained by separationh；
The specific steps of improving the independent component analysis algorithm are as follows:
i preprocessing the observed signal to obtain xk(t)；
Ii, selecting the number n of components contained in the source signal to be separated, and making p equal to 1;
iii is wpAssigning a random vector w;
iv setting wp：wp＝E[xg(wTx)]-E[g(wTx)]w；
V. w topRespectively orthogonalizing and normalizing by the following formula
Figure FDF0000009586980000021
Indicating after the treatment;
Figure FDF0000009586980000022
Figure FDF0000009586980000023
vi calculation
Figure FDF0000009586980000024
Convergence of if
Figure FDF0000009586980000025
Do not converge, order
Figure FDF0000009586980000026
And simultaneously returning to the step iv; if it is not
Figure FDF0000009586980000027
Convergence, then use
Figure FDF0000009586980000028
Separating to obtain a component y in the source signalk(t), where k is the number of components in the separated source signal;
vii is the vector v of the blood-drawing weightk(t) assigning a random vector;
ⅷvk(t) obtaining v by iterative updating using the following formulak(t+1)；
vk(t+1)＝vk(t)+η(t)yk(t)xk+1(t), wherein η represents a learning rate;
ix calculation vkConvergence of (t +1), let vk(t)＝vk(t +1) if vk(t +1) not converging, and returning to the step viii; if v isk(t +1) converge, then v will bek(t) substitution of xk+1(t)＝xk(t)-vk(t)yk(t) to eliminate yk(t) to xkThe influence of (t) gives xk+1(t)；
x is order xk(t)＝xk+1(t) and if p ≦ n, returning to step iii, while making p ≦ p +1 and k ≦ k + 1.
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