CN107104430A - A kind of bilingual coupling method for estimating state of power distribution network - Google Patents
A kind of bilingual coupling method for estimating state of power distribution network Download PDFInfo
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- CN107104430A CN107104430A CN201710315211.8A CN201710315211A CN107104430A CN 107104430 A CN107104430 A CN 107104430A CN 201710315211 A CN201710315211 A CN 201710315211A CN 107104430 A CN107104430 A CN 107104430A
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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
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
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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
- H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
- H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
- Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
Abstract
The invention discloses a kind of bilingual coupling method for estimating state of power distribution network.The present invention estimates that model carries out the alternate decoupling under phase coordinates using compensation current model to the asymmetric three-phase distribution net state of line parameter circuit value first, realizes and independent state estimation is carried out to A, B, C three-phase；Then cause the problem of traditional fast decoupled is no longer applicable for R/X ratios in power distribution network are excessive, introduce references angle, impedance is integrally subjected to phase shift using complex field standardization, reduces R/X ratios, realizes the fast decoupled in power distribution network phase.The inventive method realize simultaneously it is alternate with mutually in decouple, realize that three-phase is decoupled by alternate compensation, reduce the scale of Jacobian matrix, improve the computational efficiency of large-scale distribution network, simultaneously, the selection principle of optimal power reference angle is drawn using optimal method, and branch current magnitudes measurement type is effectively converted into branch power and is measured, filtering accuracy is further improved.
Description
Technical field
The present invention relates to a kind of bilingual coupling method for estimating state of power distribution network, belong to power system monitoring, analysis and control and lead
Domain.
Technical background
With the fast development of intelligent distribution network, the scale of power distribution network constantly increases.And wind-powered electricity generation, photovoltaic decile in power distribution network
A large amount of accesses of cloth power supply, the network structure of power distribution network is increasingly complicated, more exacerbates power distribution network three-phase line parameter not
Symmetry so that the complexity increase of state of electric distribution network estimation.Simultaneously because resistance and the ratio of reactance are higher in power distribution network, make
The condition of P-Q fast decoupleds in power transmission network can not be met by obtaining the state estimation of power distribution network, it is therefore desirable to find the complexity that is easy to implement
Degree is low and can be good at being applied to the method for estimating state of large-scale distribution network.
Traditional the least square estimation method based on Newton method is different from, the Fast decomposition algorithms of state estimation are with it
Calculating is quick, convergence is good, the low feature of EMS memory occupation amount is widely used in power transmission network.With complex field standardization technology with
Introduction in power network so that application of the fast decoupled technology in state of electric distribution network estimation is possibly realized.Complex field standardization skill
Branch impedance is carried out phase shift by art, and branch impedance ratio can be reduced by phase shift, so as to meet state estimation fast decoupled condition.But
It is that this method is still progress complex field standardization direct to three-phase network, when the reasons such as distribution network line parameter, transformer cause
When power distribution network asymmetrical three-phase is larger, computation complexity can be multiplied.Therefore, it is necessary to study a kind of implementation complexity
Low, calculating is quick, can be applied to the efficient method for estimating state of large-scale distribution network.
The content of the invention
Goal of the invention：The present invention provides a kind of power distribution network double decoupled states for the technical problem solved needed for prior art
Method of estimation.
Technical scheme：The present invention to achieve the above object, is adopted the following technical scheme that：
A kind of bilingual coupling method for estimating state of power distribution network, comprises the following steps：
1) letters such as the network parameter of power distribution network, including line parameter circuit value, transformer parameter, and network node numbering are obtained
Breath；
2) the polynary metric data in power distribution network is obtained, and is classified according to type is measured；
3) classification application of data：The metric data of A, B, C three-phase is classified respectively, it is determined that choosing A, B, C three-phase plural number
The optimal power reference angle of domain standardization, and realize three-phase metric data complex field standardization and branch current measure etc.
Effect conversion；
4) init state estimator：Counter is set to 0, and assigns initial value to quantity of state；
5) using the decoupling compensation for compensating current model and realizing respectively A, B, C three-phase, and constant Jacobian matrix pair is utilized
Active and idle progress cross-iteration solution, corrects quantity of state, plus 1 by counter；
6) judge whether to meet estimated accuracy：If it has not, then turning to step 5), terminate to follow if estimated accuracy requirement is met
Ring, and output result.
Further, the step 2) in polynary metric data source include：The metric data of SCADA system, micro- PMU dresses
Metric data, customer data base metric data for putting etc., measure type and are divided into the survey of voltage magnitude actual quantities, branch current magnitudes actual quantities
The types such as survey, the survey of branch power actual quantities, the measurement of node injecting power puppet and virtual measurement；
Further, the step 3) in the determination of complex field standardization power perspective a reference value use optimal method,
Initially setting up optimization object function is：
In formula, αiIt is the intrinsic angle of line impedance, is decided by resistance and the reactance of circuit, φsFor it needs to be determined that optimal take
The power reference angle of value, l is the branch road sum in power distribution network, and the principle for choosing optimized power reference angle is to enable to own
The impedance angle of branch road as close asSo thatRatio as close as in 0, so as to realize the quick solution of power distribution network
Coupling condition, therefore, by bounding method by object function to φsLocal derviation is sought, and makes local derviation be 0, it can obtain optimal power benchmark
Angle φsValue be：
Further, the step 3) in metric data complex field standardization according to selected optimal power benchmark
Angle by the metric data of each phase, it is necessary to first carry out complex field standardization, wherein selecting power reference in complex fieldAnd electricity
Press benchmarkFor：
In formula, φvFor voltage reference angle, because voltage reference angle does not influence on impedance angle, so in order to simplify meter
Calculate, choose φvIt is equal with voltage magnitude before for the voltage magnitude after 0 degree, therefore complex field standardization；And power reference angle
φsFor the optimal value determined according to above-mentioned choosing method；
The complex field standardization of power measurement is measured suitable for power type, including node injecting power is measured, branch road work(
Rate measurement etc.；
It is if complex power is measured under real number fieldThen：
In formula, PmAnd QmRespectively active power is measured and reactive power is measured.It is rightComplex field standardization is carried out, is obtained
Complex power under complex field standardization is measured
Then have,
In formula,It is that active power and reactive power under complex field standardization is measured respectively；Respectively
It is that active power and reactive power under real number field standardization is measured；
Power measurement variance after complex field standardization is：
In formula,It is that active power under complex field standardization measures variance and reactive power measurement side respectively
Difference,It is the active power measurement variance and reactive power measurement variance under real number field standardization respectively；
It is φ to choose voltage reference anglev=0, voltage magnitude and real number field standardization voltage magnitude phase after complex field standardization
Deng.Now, the voltage magnitude measurement variance before and after complex field standardization is equal, i.e.,：
In formula,Variance is measured for the voltage magnitude under complex field standardization,For the electricity under real number field standardization
Pressure amplitude value measures variance；
There are most branch current magnitudes in power distribution network real system to measure, but these branch current magnitudes are measured not
Can directly it apply；The method converted using common equivalent measurement carries out the equivalent transformation of branch current magnitudes measurement；
Branch road direct-to-ground capacitance is neglected, then branch powerFor：
In formula,For the voltage magnitude of node i, θiFor the voltage phase angle of node i, IijFor branch road ij current amplitude, βij
For branch road ij current phase angle；
Then equivalent branch power, which is measured, is：
In formula,Respectively equivalent branch road is active and reactive power is measured,For branch road ij current amplitude；Need
It should be noted that Ui,θi,βijThe value of an iteration before being；The branch power of equivalent transformation is measured by the branch current magnitudes
Measure, it is necessary to be updated after each iteration, to ensure the accuracy of equivalent measurement conversion；
If branch current phasorFor：
Complex field current reference valueFor：
Through the branch current after complex field standardizationFor：
Branch current magnitudes i.e. after complex field standardization are equal with the branch current magnitudes after real number field standardization, its side
Difference is also equal：
In formula,For the variance after complex field standardization,For the variance after real number field standardization；
Equivalent branch road after complex field standardization, which is measured, is：
Equivalent branch road respectively after complex field standardization is active and reactive power is measured,For reality
Branch current after number field standardization.
The measurement variance of equivalent branch power after corresponding complex field standardizationWithFor：
Further, the step 5) in compensation current model be described as follows：
The relation of circuit head end and the voltage and current of end can be described as in power distribution network：
Wherein,For branch road head end voltage and the difference of terminal voltage,To flow through series connection branch
The electric current on road,Represent the three-phase admittance matrix of circuit：
In view of there is direct-to-ground capacitance, therefore the table of increase circuit first and last end node voltage and current in circuit first and last node
It is up to formula：
Wherein,WithThe voltage of branch road first and last end node is represented respectively,WithRepresent that branch road is first respectively
End and the node Injection Current of end,For the direct-to-ground capacitance matrix of circuit：
Wherein,
The alternate decoupling of the three-phase distribution net of asymmetry parameter is carried out using compensation current model；Therefore, by the electricity of circuit
Piezoelectricity flow relation is deployed, and the gaussian iteration form for obtaining A phases is as follows：
In formula, k is iterations；
Therefore, to flow into node direction as the injecting compensating electricity for just, obtaining A phase line first and last end nodes after decoupling accordingly
Flow Δ Ia,i(k+1)With Δ Ia,j(k+1)For：
In formula, k is counts；
The A phases that above formula is calculated finally are compensated into electric current and are converted into node injecting power, then the node injecting power after decoupling
For the algebraical sum of the original injecting power of node and compensation injecting power：
In formula, k is counts, and subscript * represents conjugation Δ Sa,i(k+1)With Δ Sa,j(k+1)Headed by end-node compensation injection
Power；
Similarly, it can be deduced that the injecting compensating power in B phases and C phases, the alternate full decoupled of ABC three-phases is realized.
Further, the step 5) in it is active and it is idle progress cross-iteration solve use below equation：
In formula, A be with active corresponding information matrix block, B be with idle corresponding information matrix block, α for correspondence it is active
Correction matrix block, β is the idle correction matrix block of correspondence, Δ θkWith Δ UkRespectively ABC three-phase voltages phase angle and voltage magnitude
The variable quantity of quantity of state, wherein, in order to improve constringency performance, balance node voltage is not involved in estimation；It is corresponding to measure vector
It is divided into active and idle two class, zαFor active measurement segment vector, including branch road effective power flow PijWith node active injection power
PiMeasurement, is set to mαDimension；zγFor idle measurement segment vector, including branch road reactive power flow Qij, node injection reactive power QiWith
Node voltage amplitude ViMeasurement, is set to mγDimension；hαFor correspondence zαPart measure function vector, mαDimension；hγFor correspondence zγPortion
Component surveys function vector, mγDimension.
Beneficial effect：The present invention is compared with prior art：A kind of bilingual coupling method for estimating state proposed by the present invention can be with
Realize that the three-phase line of power distribution network parameter unbalance is alternate full decoupled, so as to realize the state estimation of single phase networks independence, subtract
The complexity of algorithm is substantially reduced while the dimension for having lacked Jacobian matrix.Simultaneously resistance is realized using complex field standardization
The transfer at anti-angle, reduces the ratio of resistance/reactance so that fast decoupled technology can be applied smoothly in power distribution network, by having
Work(and idle iterative, shorten the time of each iteration, with traditional weighted least-squares based on Newton Algorithm
Method is compared, and Jacobian matrix constant can be accelerated convergence of algorithm by the inventive method while computational accuracy is ensured
Speed, has good applicability to the large-scale distribution network of the parameter unbalances such as access distributed power source.
Brief description of the drawings
The flow chart of the bilingual coupling state estimation of Fig. 1 power distribution networks；
Fig. 2 A phase decoupling compensation equivalent-circuit models；
The comparison diagram of IEEE13 nodes A phase voltage amplitude true value and filter value under two methods of Fig. 3；
The comparison diagram of IEEE13 nodes B phase voltage amplitude true value and filter value under two methods of Fig. 4；
The comparison diagram of IEEE13 nodes C phase voltage amplitude true value and filter value under two methods of Fig. 5.
Embodiment
The implementation of the present invention is illustrated below in conjunction with accompanying drawing and example, but the implementation of the present invention and comprising being not limited to
This.
A kind of bilingual coupling method for estimating state of power distribution network, comprises the following steps：
1) letters such as the network parameter of power distribution network, including line parameter circuit value, transformer parameter, and network node numbering are obtained
Breath；
2) the polynary metric data in power distribution network is obtained, and is classified according to type is measured；
3) classification application of data：The metric data of A, B, C three-phase is classified respectively, it is determined that choosing A, B, C three-phase plural number
The optimal power reference angle of domain standardization, and realize three-phase metric data complex field standardization and branch current measure etc.
Effect conversion；
4) init state estimator：Counter is set to 0, and assigns initial value to quantity of state；
5) using the decoupling compensation for compensating current model and realizing respectively A, B, C three-phase, and constant Jacobian matrix pair is utilized
Active and idle progress cross-iteration solution, corrects quantity of state, plus 1 by counter；
6) judge whether to meet estimated accuracy：If it has not, then turning to step 5), terminate to follow if estimated accuracy requirement is met
Ring, and output result.
Further, the step 2) in polynary metric data source include：The metric data of SCADA system, micro- PMU dresses
Metric data, customer data base metric data for putting etc., measure type and are divided into the survey of voltage magnitude actual quantities, branch current magnitudes actual quantities
The types such as survey, the survey of branch power actual quantities, the measurement of node injecting power puppet and virtual measurement；
Further, the step 3) in the determination of complex field standardization power perspective a reference value use optimal method,
Initially setting up optimization object function is：
In formula, αiIt is the intrinsic angle of line impedance, is decided by resistance and the reactance of circuit, φsFor it needs to be determined that optimal take
The power reference angle of value, l is the branch road sum in power distribution network, and the principle for choosing optimized power reference angle is to enable to own
The impedance angle of branch road as close asSo thatRatio as close as in 0, so as to realize the quick solution of power distribution network
Coupling condition, therefore, by bounding method by object function to φsLocal derviation is sought, and makes local derviation be 0, it can obtain optimal power benchmark
Angle φsValue be：
Further, the step 3) in metric data complex field standardization according to selected optimal power benchmark
Angle by the metric data of each phase, it is necessary to first carry out complex field standardization, wherein selecting power reference in complex fieldAnd electricity
Press benchmarkFor：
In formula, φvFor voltage reference angle, because voltage reference angle does not influence on impedance angle, so in order to simplify meter
Calculate, choose φvIt is equal with voltage magnitude before for the voltage magnitude after 0 degree, therefore complex field standardization；And power reference angle
φsFor the optimal value determined according to above-mentioned choosing method；
The complex field standardization of power measurement is measured suitable for power type, including node injecting power is measured, branch road work(
Rate measurement etc.；
It is if complex power is measured under real number fieldThen：
In formula, PmAnd QmRespectively active power is measured and reactive power is measured.It is rightComplex field standardization is carried out, is obtained
Complex power under complex field standardization is measured
Then have,
In formula,It is that active power and reactive power under complex field standardization is measured respectively；Respectively
It is that active power and reactive power under real number field standardization is measured；
Power measurement variance after complex field standardization is：
In formula,It is that active power under complex field standardization measures variance and reactive power measurement side respectively
Difference,It is the active power measurement variance and reactive power measurement variance under real number field standardization respectively；
It is φ to choose voltage reference anglev=0, voltage magnitude and real number field standardization voltage magnitude phase after complex field standardization
Deng.Now, the voltage magnitude measurement variance before and after complex field standardization is equal, i.e.,：
In formula,Variance is measured for the voltage magnitude under complex field standardization,For the electricity under real number field standardization
Pressure amplitude value measures variance；
There are most branch current magnitudes in power distribution network real system to measure, but these branch current magnitudes are measured not
Can directly it apply；The method converted using common equivalent measurement carries out the equivalent transformation of branch current magnitudes measurement；
Branch road direct-to-ground capacitance is neglected, then branch powerFor：
In formula,For the voltage magnitude of node i, θiFor the voltage phase angle of node i, IijFor branch road ij current amplitude, βij
For branch road ij current phase angle；
Then equivalent branch power, which is measured, is：
In formula,Respectively equivalent branch road is active and reactive power is measured,For branch road ij current amplitude；Need
It should be noted that Ui,θi,βijThe value of an iteration before being；The branch power of equivalent transformation is measured by the branch current magnitudes
Measure, it is necessary to be updated after each iteration, to ensure the accuracy of equivalent measurement conversion；
If branch current phasorFor：
Complex field current reference valueFor：
Through the branch current after complex field standardizationFor：
Branch current magnitudes i.e. after complex field standardization are equal with the branch current magnitudes after real number field standardization, its side
Difference is also equal：
In formula,For the variance after complex field standardization,For the variance after real number field standardization；
Equivalent branch road after complex field standardization, which is measured, is：
Equivalent branch road respectively after complex field standardization is active and reactive power is measured,For reality
Branch current after number field standardization.
The measurement variance of equivalent branch power after corresponding complex field standardizationWithFor：
Further, the step 5) in compensation current model be described as follows：
The relation of circuit head end and the voltage and current of end can be described as in power distribution network：
Wherein,For branch road head end voltage and the difference of terminal voltage,To flow through series connection branch
The electric current on road,Represent the three-phase admittance matrix of circuit：
In view of there is direct-to-ground capacitance, therefore the table of increase circuit first and last end node voltage and current in circuit first and last node
It is up to formula：
Wherein,WithThe voltage of branch road first and last end node is represented respectively,WithRepresent that branch road is first respectively
End and the node Injection Current of end,For the direct-to-ground capacitance matrix of circuit：
Wherein,
The alternate decoupling of the three-phase distribution net of asymmetry parameter is carried out using compensation current model；Therefore, by the electricity of circuit
Piezoelectricity flow relation is deployed, and the gaussian iteration form for obtaining A phases is as follows：
In formula, k is iterations；
Therefore, to flow into node direction as the injecting compensating electricity for just, obtaining A phase line first and last end nodes after decoupling accordingly
Flow Δ Ia,i(k+1)With Δ Ia,j(k+1)For：
In formula, k is counts；
The A phases that above formula is calculated finally are compensated into electric current and are converted into node injecting power, then the node injecting power after decoupling
For the algebraical sum of the original injecting power of node and compensation injecting power：
In formula, k is counts, and subscript * represents conjugation Δ Sa,i(k+1)With Δ Sa,j(k+1)Headed by end-node compensation injection
Power；
Similarly, it can be deduced that the injecting compensating power in B phases and C phases, the alternate full decoupled of ABC three-phases is realized.
Further, the step 5) in it is active and it is idle progress cross-iteration solve use below equation：
In formula, A be with active corresponding information matrix block, B be with idle corresponding information matrix block, α for correspondence it is active
Correction matrix block, β is the idle correction matrix block of correspondence, Δ θkWith Δ UkRespectively ABC three-phase voltages phase angle and voltage magnitude
The variable quantity of quantity of state, wherein, in order to improve constringency performance, balance node voltage is not involved in estimation；It is corresponding to measure vector
It is divided into active and idle two class, zαFor active measurement segment vector, including branch road effective power flow PijWith node active injection power
PiMeasurement, is set to mαDimension；zγFor idle measurement segment vector, including branch road reactive power flow Qij, node injection reactive power QiWith
Node voltage amplitude ViMeasurement, is set to mγDimension；hαFor correspondence zαPart measure function vector, mαDimension；hγFor correspondence zγPortion
Component surveys function vector, mγDimension.State of electric distribution network is estimated
In the case of known network structure, line parameter circuit value and measurement mechanism, non-linear measurement equation can be represented
It is as follows：
Z=h (x)+v
In formula, x is state variable, and z is measurement, and h () is nonlinear function, and v is residual error.
The object function that quantity of state can be obtained accordingly is：
J (x)=[z-h (x)]TR-1[z-h(x)]
In formula, R-1To measure weight matrix, then the value of optimal quantity of state is the state for causing object function minimum
The value of amount.Generally solved using Newton iteration method.The inventive method first passes through alternate decoupling separation three-phase data, then by fast
Speed, which is decomposed, decoupled in phase, and the same optimal objective function using above formula is solved, most by active and idle cross-iteration
The approximation of optimum state amount is obtained afterwards.
Sample calculation analysis
The example test of the present invention is based on IEEE13, IEEE34 and IEEE123 three-phase imbalance distribution system,
The inventive method is designated as method 1, three-phase is not decoupled and the method for estimating state based on Newton method is designated as method 2, will
The filtering performance of two kinds of algorithms is contrasted.Selection three-phase is not decoupled simultaneously and the power flow solutions based on Newton method calculating are as shape
The true value of state estimation.
Table 1 be method 1 with method 2 in three kinds of different test systems, the contrast of the iterations of two methods, and
Fixed convergence precision is 10-6In the case of compared for two kinds of algorithms calculating take.As can be seen from Table 1, compared to method 2,
The inventive method sacrifices partial convergence, and iterations is more, about twice of method 2.But sent out from time-consuming contrast is calculated
Existing, context of methods calculating speed in three different test systems is faster than method 2, and the scale of system is bigger, calculates consumption
When advantage it is more obvious, this is due to that the inventive method has carried out three-phase to decouple in alternate and phase respectively, active reactive repeatedly
In generation, solves, and constant Jacobian matrix does not need variations and modifications in iteration, therefore greatly improves calculating speed.By
Data in table are visible, and context of methods greatly improves calculating speed under the requirement of identical filtering accuracy, in extensive distribution
Had a good application prospect in the state estimation of net system.
Accompanying drawing 3-5 is respectively method 1 and 2 times three-phase voltage amplitudes of method and Three-phase Power Flow true value in IEEE13 node systems
Error amount contrast.Final result is used as using the average value of 100 independent tests.As seen from the figure, the inventive method and method 2
There is close filtering accuracy, the error amount of 2 kinds of methods and trend true value is about 10-3, illustrate that the inventive method can be protected
Filtering accuracy is demonstrate,proved, simultaneously because its quick computing capability, makes it have good in the state estimation of large-scale power distribution network
Engineering practice is worth.
The iterations of the two methods of table 1 is with calculating time-consuming contrast
Claims (6)
1. a kind of bilingual coupling method for estimating state of power distribution network, it is characterised in that：Comprise the following steps：
1) information such as the network parameter of power distribution network, including line parameter circuit value, transformer parameter, and network node numbering are obtained；
2) the polynary metric data in power distribution network is obtained, and is classified according to type is measured；
3) classification application of data：The metric data of A, B, C three-phase is classified respectively, it is determined that choosing A, B, C three-phase complex field mark
The optimal power reference angle of youngestization, and realize three-phase metric data complex field standardization and branch current measure equivalent turn
Change；
4) init state estimator：Counter is set to 0, and assigns initial value to quantity of state；
5) using the decoupling compensation for compensating current model and realizing respectively A, B, C three-phase, and using constant Jacobian matrix to active
With idle progress cross-iteration solution, quantity of state is corrected, counter plus 1；
6) judge whether to meet estimated accuracy：If it has not, then turning to step 5), the end loop if estimated accuracy requirement is met,
And output result.
2. the bilingual coupling method for estimating state of power distribution network according to claim 1, it is characterised in that：The step 2) in it is polynary
Metric data source includes metric data, the metric data of micro- PMU devices, customer data base metric data of SCADA system etc.,
Measure type and be divided into the survey of voltage magnitude actual quantities, the survey of branch current magnitudes actual quantities, the survey of branch power actual quantities, node injecting power puppet amount
Survey and virtual measurement.
3. the bilingual coupling method for estimating state of power distribution network according to claim 1, it is characterised in that：The step 3) in plural number
The determination of domain standardization power perspective a reference value uses optimal method, and initially setting up optimization object function is：
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In formula, αiIt is the intrinsic angle of line impedance, is decided by resistance and the reactance of circuit, φsFor it needs to be determined that optimal value
Power reference angle, l is the branch road sum in power distribution network, and the principle for choosing optimized power reference angle is to enable to all branch roads
Impedance angle as close asSo thatRatio as close as in 0, so as to realize the quick decoupling bar of power distribution network
Part, therefore, by bounding method by object function to φsLocal derviation is sought, and makes local derviation be 0, it can obtain optimal power reference angle φs
Value be：
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<mo>.</mo>
</mrow>
4. the bilingual coupling method for estimating state of power distribution network according to claim 1, it is characterised in that：The step 3) middle measurement
The complex field standardization of data is according to selected optimal power reference angle, it is necessary to which the metric data of each phase first is carried out into complex field
Standardization, wherein selecting power reference in complex fieldAnd voltage referenceFor：
<mrow>
<msub>
<mover>
<mi>S</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>b</mi>
<mi>a</mi>
<mi>s</mi>
<mi>e</mi>
</mrow>
</msub>
<mo>=</mo>
<msub>
<mi>S</mi>
<mrow>
<mi>b</mi>
<mi>a</mi>
<mi>s</mi>
<mi>e</mi>
</mrow>
</msub>
<mo>&CenterDot;</mo>
<msup>
<mi>e</mi>
<mrow>
<mo>-</mo>
<msub>
<mi>j&phi;</mi>
<mi>s</mi>
</msub>
</mrow>
</msup>
</mrow>
<mrow>
<msub>
<mover>
<mi>U</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>b</mi>
<mi>a</mi>
<mi>s</mi>
<mi>e</mi>
</mrow>
</msub>
<mo>=</mo>
<msub>
<mi>U</mi>
<mrow>
<mi>b</mi>
<mi>a</mi>
<mi>s</mi>
<mi>e</mi>
</mrow>
</msub>
<mo>&CenterDot;</mo>
<msup>
<mi>e</mi>
<mrow>
<msub>
<mi>j&phi;</mi>
<mi>v</mi>
</msub>
</mrow>
</msup>
</mrow>
In formula, φvFor voltage reference angle, because voltage reference angle does not influence on impedance angle, so in order to simplify calculating, choosing
Take φvIt is equal with voltage magnitude before for the voltage magnitude after 0 degree, therefore complex field standardization；And power reference angle φsFor
The optimal value determined according to above-mentioned choosing method；
The complex field standardization of power measurement is measured suitable for power type, including node injecting power is measured, branch power amount
Survey etc.；
It is if complex power is measured under real number fieldThen：
<mrow>
<msup>
<mover>
<mi>S</mi>
<mo>&CenterDot;</mo>
</mover>
<mi>m</mi>
</msup>
<mo>=</mo>
<msup>
<mi>P</mi>
<mi>m</mi>
</msup>
<mo>+</mo>
<msup>
<mi>jQ</mi>
<mi>m</mi>
</msup>
</mrow>
In formula, PmAnd QmRespectively active power is measured and reactive power is measured.It is rightComplex field standardization is carried out, plural number is obtained
Complex power under the standardization of domain is measured
<mrow>
<msubsup>
<mover>
<mi>S</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>c</mi>
<mi>p</mi>
<mi>u</mi>
</mrow>
<mi>m</mi>
</msubsup>
<mo>=</mo>
<mfrac>
<msup>
<mover>
<mi>S</mi>
<mo>&CenterDot;</mo>
</mover>
<mi>m</mi>
</msup>
<msub>
<mover>
<mi>S</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>b</mi>
<mi>a</mi>
<mi>s</mi>
<mi>e</mi>
</mrow>
</msub>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<msup>
<mi>P</mi>
<mi>m</mi>
</msup>
<mo>+</mo>
<msup>
<mi>jQ</mi>
<mi>m</mi>
</msup>
</mrow>
<mrow>
<msub>
<mi>S</mi>
<mrow>
<mi>b</mi>
<mi>a</mi>
<mi>s</mi>
<mi>e</mi>
</mrow>
</msub>
<mo>&CenterDot;</mo>
<msup>
<mi>e</mi>
<mrow>
<mo>-</mo>
<msub>
<mi>j&phi;</mi>
<mi>s</mi>
</msub>
</mrow>
</msup>
</mrow>
</mfrac>
<mo>=</mo>
<mrow>
<mo>(</mo>
<msubsup>
<mi>P</mi>
<mrow>
<mi>p</mi>
<mi>u</mi>
</mrow>
<mi>m</mi>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>jQ</mi>
<mrow>
<mi>p</mi>
<mi>u</mi>
</mrow>
<mi>m</mi>
</msubsup>
<mo>)</mo>
</mrow>
<mo>&CenterDot;</mo>
<msup>
<mi>e</mi>
<mrow>
<msub>
<mi>j&phi;</mi>
<mi>s</mi>
</msub>
</mrow>
</msup>
<mo>=</mo>
<msubsup>
<mi>P</mi>
<mrow>
<mi>c</mi>
<mi>p</mi>
<mi>u</mi>
</mrow>
<mi>m</mi>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>jQ</mi>
<mrow>
<mi>c</mi>
<mi>p</mi>
<mi>u</mi>
</mrow>
<mi>m</mi>
</msubsup>
</mrow>
Then have,
<mrow>
<msubsup>
<mi>P</mi>
<mrow>
<mi>c</mi>
<mi>p</mi>
<mi>u</mi>
</mrow>
<mi>m</mi>
</msubsup>
<mo>=</mo>
<mi>r</mi>
<mi>e</mi>
<mi>a</mi>
<mi>l</mi>
<mrow>
<mo>(</mo>
<mo>(</mo>
<msubsup>
<mi>P</mi>
<mrow>
<mi>p</mi>
<mi>u</mi>
</mrow>
<mi>m</mi>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>jQ</mi>
<mrow>
<mi>p</mi>
<mi>u</mi>
</mrow>
<mi>m</mi>
</msubsup>
<mo>)</mo>
</mrow>
<mo>&CenterDot;</mo>
<msup>
<mi>e</mi>
<mrow>
<msub>
<mi>j&phi;</mi>
<mi>s</mi>
</msub>
</mrow>
</msup>
<mo>)</mo>
<mo>=</mo>
<msubsup>
<mi>P</mi>
<mrow>
<mi>p</mi>
<mi>u</mi>
</mrow>
<mi>m</mi>
</msubsup>
<msub>
<mi>cos&phi;</mi>
<mi>s</mi>
</msub>
<mo>-</mo>
<msubsup>
<mi>Q</mi>
<mrow>
<mi>p</mi>
<mi>u</mi>
</mrow>
<mi>m</mi>
</msubsup>
<msub>
<mi>sin&phi;</mi>
<mi>s</mi>
</msub>
</mrow>
<mrow>
<msubsup>
<mi>Q</mi>
<mrow>
<mi>c</mi>
<mi>p</mi>
<mi>u</mi>
</mrow>
<mi>m</mi>
</msubsup>
<mo>=</mo>
<mi>i</mi>
<mi>m</mi>
<mi>a</mi>
<mi>g</mi>
<mrow>
<mo>(</mo>
<mo>(</mo>
<msubsup>
<mi>P</mi>
<mrow>
<mi>p</mi>
<mi>u</mi>
</mrow>
<mi>m</mi>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>jQ</mi>
<mrow>
<mi>p</mi>
<mi>u</mi>
</mrow>
<mi>m</mi>
</msubsup>
<mo>)</mo>
</mrow>
<mo>&CenterDot;</mo>
<msup>
<mi>e</mi>
<mrow>
<msub>
<mi>j&phi;</mi>
<mi>s</mi>
</msub>
</mrow>
</msup>
<mo>)</mo>
<mo>=</mo>
<msubsup>
<mi>P</mi>
<mrow>
<mi>p</mi>
<mi>u</mi>
</mrow>
<mi>m</mi>
</msubsup>
<msub>
<mi>sin&phi;</mi>
<mi>s</mi>
</msub>
<mo>+</mo>
<msubsup>
<mi>Q</mi>
<mrow>
<mi>p</mi>
<mi>u</mi>
</mrow>
<mi>m</mi>
</msubsup>
<msub>
<mi>cos&phi;</mi>
<mi>s</mi>
</msub>
</mrow>
In formula,It is that active power and reactive power under complex field standardization is measured respectively；It is real respectively
Active power and reactive power under number field standardization are measured；
Power measurement variance after complex field standardization is：
<mrow>
<msubsup>
<mi>&sigma;</mi>
<mrow>
<mi>p</mi>
<mo>,</mo>
<mi>c</mi>
<mi>p</mi>
<mi>u</mi>
</mrow>
<mn>2</mn>
</msubsup>
<mo>=</mo>
<msubsup>
<mi>&sigma;</mi>
<mrow>
<mi>p</mi>
<mo>,</mo>
<mi>p</mi>
<mi>u</mi>
</mrow>
<mn>2</mn>
</msubsup>
<msup>
<mi>cos</mi>
<mn>2</mn>
</msup>
<msub>
<mi>&phi;</mi>
<mi>s</mi>
</msub>
<mo>-</mo>
<msubsup>
<mi>&sigma;</mi>
<mrow>
<mi>q</mi>
<mo>,</mo>
<mi>p</mi>
<mi>u</mi>
</mrow>
<mn>2</mn>
</msubsup>
<msup>
<mi>sin</mi>
<mn>2</mn>
</msup>
<msub>
<mi>&phi;</mi>
<mi>s</mi>
</msub>
</mrow>
<mrow>
<msubsup>
<mi>&sigma;</mi>
<mrow>
<mi>q</mi>
<mo>,</mo>
<mi>c</mi>
<mi>p</mi>
<mi>u</mi>
</mrow>
<mn>2</mn>
</msubsup>
<mo>=</mo>
<msubsup>
<mi>&sigma;</mi>
<mrow>
<mi>p</mi>
<mo>,</mo>
<mi>p</mi>
<mi>u</mi>
</mrow>
<mn>2</mn>
</msubsup>
<msup>
<mi>sin</mi>
<mn>2</mn>
</msup>
<msub>
<mi>&phi;</mi>
<mi>s</mi>
</msub>
<mo>+</mo>
<msubsup>
<mi>&sigma;</mi>
<mrow>
<mi>q</mi>
<mo>,</mo>
<mi>p</mi>
<mi>u</mi>
</mrow>
<mn>2</mn>
</msubsup>
<msup>
<mi>cos</mi>
<mn>2</mn>
</msup>
<msub>
<mi>&phi;</mi>
<mi>s</mi>
</msub>
</mrow>
In formula,It is the active power measurement variance and reactive power measurement variance under complex field standardization respectively,It is the active power measurement variance and reactive power measurement variance under real number field standardization respectively；
It is φ to choose voltage reference anglev=0, voltage magnitude is equal with real number field standardization voltage magnitude after complex field standardization.This
When, it is equal that the voltage magnitude before and after complex field standardization measures variance, i.e.,：
<mrow>
<msubsup>
<mi>&sigma;</mi>
<mrow>
<mi>v</mi>
<mo>,</mo>
<mi>c</mi>
<mi>p</mi>
<mi>u</mi>
</mrow>
<mn>2</mn>
</msubsup>
<mo>=</mo>
<msubsup>
<mi>&sigma;</mi>
<mrow>
<mi>v</mi>
<mo>,</mo>
<mi>p</mi>
<mi>u</mi>
</mrow>
<mn>2</mn>
</msubsup>
</mrow>
In formula,Variance is measured for the voltage magnitude under complex field standardization,For the voltage magnitude under real number field standardization
Measure variance；
There are most branch current magnitudes in power distribution network real system to measure, but the measurement of these branch current magnitudes can not be straight
Scoop out use；The method converted using common equivalent measurement carries out the equivalent transformation of branch current magnitudes measurement；
Branch road direct-to-ground capacitance is neglected, then branch powerFor：
<mrow>
<msub>
<mover>
<mi>S</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>=</mo>
<msub>
<mover>
<mi>U</mi>
<mo>&CenterDot;</mo>
</mover>
<mi>i</mi>
</msub>
<msup>
<mrow>
<mo>(</mo>
<msub>
<mover>
<mi>I</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>*</mo>
</msup>
<mo>=</mo>
<msub>
<mi>U</mi>
<mi>i</mi>
</msub>
<msup>
<mi>e</mi>
<mrow>
<msub>
<mi>j&theta;</mi>
<mi>i</mi>
</msub>
</mrow>
</msup>
<mo>&CenterDot;</mo>
<msup>
<mrow>
<mo>(</mo>
<msub>
<mi>I</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<msup>
<mi>e</mi>
<mrow>
<msub>
<mi>j&beta;</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
</mrow>
</msup>
<mo>)</mo>
</mrow>
<mo>*</mo>
</msup>
<mo>=</mo>
<msub>
<mi>U</mi>
<mi>i</mi>
</msub>
<msub>
<mi>I</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>&CenterDot;</mo>
<msup>
<mi>e</mi>
<mrow>
<mi>j</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>&theta;</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<msub>
<mi>&beta;</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</msup>
</mrow>
In formula,For the voltage magnitude of node i, θiFor the voltage phase angle of node i, IijFor branch road ij current amplitude, βijFor branch
Road ij current phase angle；
Then equivalent branch power, which is measured, is：
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<msubsup>
<mi>P</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
<mi>e</mi>
</msubsup>
<mo>=</mo>
<msub>
<mi>U</mi>
<mi>i</mi>
</msub>
<msubsup>
<mi>I</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
<mi>m</mi>
</msubsup>
<mi>c</mi>
<mi>o</mi>
<mi>s</mi>
<mo>(</mo>
<msub>
<mi>&theta;</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<msub>
<mi>&beta;</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>)</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<msubsup>
<mi>Q</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
<mi>e</mi>
</msubsup>
<mo>=</mo>
<msub>
<mi>U</mi>
<mi>i</mi>
</msub>
<msubsup>
<mi>I</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
<mi>m</mi>
</msubsup>
<mi>s</mi>
<mi>i</mi>
<mi>n</mi>
<mo>(</mo>
<msub>
<mi>&theta;</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<msub>
<mi>&beta;</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>)</mo>
</mtd>
</mtr>
</mtable>
</mfenced>
In formula,Respectively equivalent branch road is active and reactive power is measured,For branch road ij current amplitude；Need note
Meaning, Ui,θi,βijThe value of an iteration before being；The branch power for measuring equivalent transformation by the branch current magnitudes is measured,
Need to be updated after each iteration, to ensure the accuracy of equivalent measurement conversion；
If branch current phasorFor：
<mrow>
<msub>
<mover>
<mi>I</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>=</mo>
<msub>
<mi>I</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>&CenterDot;</mo>
<msup>
<mi>e</mi>
<mrow>
<msub>
<mi>j&beta;</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
</mrow>
</msup>
</mrow>
Complex field current reference valueFor：
<mrow>
<msub>
<mover>
<mi>I</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>b</mi>
<mi>a</mi>
<mi>s</mi>
<mi>e</mi>
</mrow>
</msub>
<mo>=</mo>
<msup>
<mrow>
<mo>(</mo>
<mfrac>
<msub>
<mover>
<mi>S</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>b</mi>
<mi>a</mi>
<mi>s</mi>
<mi>e</mi>
</mrow>
</msub>
<msub>
<mover>
<mi>U</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>b</mi>
<mi>a</mi>
<mi>s</mi>
<mi>e</mi>
</mrow>
</msub>
</mfrac>
<mo>)</mo>
</mrow>
<mo>*</mo>
</msup>
<mo>=</mo>
<msup>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<msub>
<mi>S</mi>
<mrow>
<mi>b</mi>
<mi>a</mi>
<mi>s</mi>
<mi>e</mi>
</mrow>
</msub>
<mo>&CenterDot;</mo>
<msup>
<mi>e</mi>
<mrow>
<mo>-</mo>
<msub>
<mi>j&phi;</mi>
<mi>s</mi>
</msub>
</mrow>
</msup>
</mrow>
<mrow>
<msub>
<mi>U</mi>
<mrow>
<mi>b</mi>
<mi>a</mi>
<mi>s</mi>
<mi>e</mi>
</mrow>
</msub>
<mo>&CenterDot;</mo>
<msup>
<mi>e</mi>
<mrow>
<mi>j</mi>
<mn>0</mn>
</mrow>
</msup>
</mrow>
</mfrac>
<mo>)</mo>
</mrow>
<mo>*</mo>
</msup>
<mo>=</mo>
<msub>
<mi>I</mi>
<mrow>
<mi>b</mi>
<mi>a</mi>
<mi>s</mi>
<mi>e</mi>
</mrow>
</msub>
<mo>&CenterDot;</mo>
<msup>
<mi>e</mi>
<mrow>
<msub>
<mi>j&phi;</mi>
<mi>s</mi>
</msub>
</mrow>
</msup>
</mrow>
Through the branch current after complex field standardizationFor：
<mrow>
<msub>
<mover>
<mi>I</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>i</mi>
<mi>j</mi>
<mo>,</mo>
<mi>c</mi>
<mi>p</mi>
<mi>u</mi>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<msub>
<mover>
<mi>I</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<msub>
<mover>
<mi>I</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>b</mi>
<mi>a</mi>
<mi>s</mi>
<mi>e</mi>
</mrow>
</msub>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mi>I</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>&CenterDot;</mo>
<msup>
<mi>e</mi>
<mrow>
<msub>
<mi>j&beta;</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
</mrow>
</msup>
</mrow>
<mrow>
<msub>
<mi>I</mi>
<mrow>
<mi>b</mi>
<mi>a</mi>
<mi>s</mi>
<mi>e</mi>
</mrow>
</msub>
<mo>&CenterDot;</mo>
<msup>
<mi>e</mi>
<mrow>
<msub>
<mi>j&phi;</mi>
<mi>s</mi>
</msub>
</mrow>
</msup>
</mrow>
</mfrac>
<mo>=</mo>
<msub>
<mi>I</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
<mo>,</mo>
<mi>p</mi>
<mi>u</mi>
</mrow>
</msub>
<mo>&CenterDot;</mo>
<msup>
<mi>e</mi>
<mrow>
<mi>j</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>&beta;</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>&phi;</mi>
<mi>s</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</msup>
</mrow>
Branch current magnitudes i.e. after complex field standardization are equal with the branch current magnitudes after real number field standardization, and its variance is also
It is equal：
<mrow>
<msubsup>
<mi>&sigma;</mi>
<mrow>
<mi>I</mi>
<mo>,</mo>
<mi>c</mi>
<mi>p</mi>
<mi>u</mi>
</mrow>
<mn>2</mn>
</msubsup>
<mo>=</mo>
<msubsup>
<mi>&sigma;</mi>
<mrow>
<mi>I</mi>
<mo>,</mo>
<mi>p</mi>
<mi>u</mi>
</mrow>
<mn>2</mn>
</msubsup>
</mrow>
In formula,For the variance after complex field standardization,For the variance after real number field standardization；
Equivalent branch road after complex field standardization, which is measured, is：
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<msubsup>
<mi>P</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
<mo>,</mo>
<mi>c</mi>
<mi>p</mi>
<mi>u</mi>
</mrow>
<mi>e</mi>
</msubsup>
<mo>=</mo>
<msub>
<mi>U</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>p</mi>
<mi>u</mi>
</mrow>
</msub>
<msubsup>
<mi>I</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
<mo>,</mo>
<mi>p</mi>
<mi>u</mi>
</mrow>
<mi>m</mi>
</msubsup>
<mi>c</mi>
<mi>o</mi>
<mi>s</mi>
<mo>(</mo>
<msub>
<mi>&theta;</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<msub>
<mi>&beta;</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>&phi;</mi>
<mi>s</mi>
</msub>
<mo>)</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<msubsup>
<mi>Q</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
<mo>,</mo>
<mi>c</mi>
<mi>p</mi>
<mi>u</mi>
</mrow>
<mi>e</mi>
</msubsup>
<mo>=</mo>
<msub>
<mi>U</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>p</mi>
<mi>u</mi>
</mrow>
</msub>
<msubsup>
<mi>I</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
<mo>,</mo>
<mi>p</mi>
<mi>u</mi>
</mrow>
<mi>m</mi>
</msubsup>
<mi>s</mi>
<mi>i</mi>
<mi>n</mi>
<mo>(</mo>
<msub>
<mi>&theta;</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<msub>
<mi>&beta;</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>&phi;</mi>
<mi>s</mi>
</msub>
<mo>)</mo>
</mtd>
</mtr>
</mtable>
</mfenced>
Equivalent branch road respectively after complex field standardization is active and reactive power is measured,For real number field
Branch current after standardization.
The measurement variance of equivalent branch power after corresponding complex field standardizationWithFor：
<mrow>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>&sigma;</mi>
<mrow>
<msup>
<mi>p</mi>
<mi>e</mi>
</msup>
<mo>,</mo>
<mi>c</mi>
<mi>p</mi>
<mi>u</mi>
</mrow>
<mn>2</mn>
</msubsup>
<mo>=</mo>
<msubsup>
<mi>&sigma;</mi>
<mrow>
<mi>I</mi>
<mo>,</mo>
<mi>p</mi>
<mi>u</mi>
</mrow>
<mn>2</mn>
</msubsup>
<msup>
<mi>cos</mi>
<mn>2</mn>
</msup>
<mrow>
<mo>(</mo>
<msub>
<mi>&theta;</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<msub>
<mi>&beta;</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>&phi;</mi>
<mi>s</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>&sigma;</mi>
<mrow>
<msup>
<mi>q</mi>
<mi>e</mi>
</msup>
<mo>,</mo>
<mi>c</mi>
<mi>p</mi>
<mi>u</mi>
</mrow>
<mn>2</mn>
</msubsup>
<mo>=</mo>
<msubsup>
<mi>&sigma;</mi>
<mrow>
<mi>I</mi>
<mo>,</mo>
<mi>p</mi>
<mi>u</mi>
</mrow>
<mn>2</mn>
</msubsup>
<msup>
<mi>sin</mi>
<mn>2</mn>
</msup>
<mrow>
<mo>(</mo>
<msub>
<mi>&theta;</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<msub>
<mi>&beta;</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>&phi;</mi>
<mi>s</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>.</mo>
</mrow>
5. the bilingual coupling method for estimating state of power distribution network according to claim 1, it is characterised in that：The step 5) in benefit
Current model is repaid to be described as follows：
The relation of circuit head end and the voltage and current of end can be described as in power distribution network：
<mrow>
<msubsup>
<mi>Y</mi>
<mrow>
<mi>a</mi>
<mi>b</mi>
<mi>c</mi>
</mrow>
<mi>z</mi>
</msubsup>
<mi>&Delta;</mi>
<msub>
<mover>
<mi>U</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>a</mi>
<mi>b</mi>
<mi>c</mi>
<mo>,</mo>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>=</mo>
<msub>
<mover>
<mi>I</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>a</mi>
<mi>b</mi>
<mi>c</mi>
<mo>,</mo>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
</mrow>
Wherein,For branch road head end voltage and the difference of terminal voltage,To flow through series arm
Electric current,Represent the three-phase admittance matrix of circuit：
<mrow>
<msubsup>
<mi>Y</mi>
<mrow>
<mi>a</mi>
<mi>b</mi>
<mi>c</mi>
</mrow>
<mi>z</mi>
</msubsup>
<mo>=</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<msubsup>
<mi>y</mi>
<mrow>
<mi>a</mi>
<mi>a</mi>
</mrow>
<mi>z</mi>
</msubsup>
</mtd>
<mtd>
<msubsup>
<mi>y</mi>
<mrow>
<mi>a</mi>
<mi>b</mi>
</mrow>
<mi>z</mi>
</msubsup>
</mtd>
<mtd>
<msubsup>
<mi>y</mi>
<mrow>
<mi>a</mi>
<mi>c</mi>
</mrow>
<mi>z</mi>
</msubsup>
</mtd>
</mtr>
<mtr>
<mtd>
<msubsup>
<mi>y</mi>
<mrow>
<mi>b</mi>
<mi>a</mi>
</mrow>
<mi>z</mi>
</msubsup>
</mtd>
<mtd>
<msubsup>
<mi>y</mi>
<mrow>
<mi>b</mi>
<mi>b</mi>
</mrow>
<mi>z</mi>
</msubsup>
</mtd>
<mtd>
<msubsup>
<mi>y</mi>
<mrow>
<mi>b</mi>
<mi>c</mi>
</mrow>
<mi>z</mi>
</msubsup>
</mtd>
</mtr>
<mtr>
<mtd>
<msubsup>
<mi>y</mi>
<mrow>
<mi>c</mi>
<mi>a</mi>
</mrow>
<mi>z</mi>
</msubsup>
</mtd>
<mtd>
<msubsup>
<mi>y</mi>
<mrow>
<mi>c</mi>
<mi>b</mi>
</mrow>
<mi>z</mi>
</msubsup>
</mtd>
<mtd>
<msubsup>
<mi>y</mi>
<mrow>
<mi>c</mi>
<mi>c</mi>
</mrow>
<mi>z</mi>
</msubsup>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
In view of there is direct-to-ground capacitance, therefore the expression formula of increase circuit first and last end node voltage and current in circuit first and last node
For：
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<msubsup>
<mi>Y</mi>
<mrow>
<mi>a</mi>
<mi>b</mi>
<mi>c</mi>
</mrow>
<mi>c</mi>
</msubsup>
<msub>
<mover>
<mi>U</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>a</mi>
<mi>b</mi>
<mi>c</mi>
<mo>,</mo>
<mi>i</mi>
</mrow>
</msub>
<mo>=</mo>
<msub>
<mover>
<mi>I</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>a</mi>
<mi>b</mi>
<mi>c</mi>
<mo>,</mo>
<mi>i</mi>
<mi>i</mi>
</mrow>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>Y</mi>
<mrow>
<mi>a</mi>
<mi>b</mi>
<mi>c</mi>
</mrow>
<mi>c</mi>
</msubsup>
<msub>
<mover>
<mi>U</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>a</mi>
<mi>b</mi>
<mi>c</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<mo>=</mo>
<msub>
<mover>
<mi>I</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>a</mi>
<mi>b</mi>
<mi>c</mi>
<mo>,</mo>
<mi>j</mi>
<mi>j</mi>
</mrow>
</msub>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
Wherein,WithThe voltage of branch road first and last end node is represented respectively,WithBranch road head end and end are represented respectively
The node Injection Current at end,For the direct-to-ground capacitance matrix of circuit：
Wherein,
<mrow>
<msubsup>
<mi>Y</mi>
<mrow>
<mi>a</mi>
<mi>b</mi>
<mi>c</mi>
</mrow>
<mi>c</mi>
</msubsup>
<mo>=</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<msubsup>
<mi>y</mi>
<mrow>
<mi>a</mi>
<mi>a</mi>
</mrow>
<mi>c</mi>
</msubsup>
</mtd>
<mtd>
<msubsup>
<mi>y</mi>
<mrow>
<mi>a</mi>
<mi>b</mi>
</mrow>
<mi>c</mi>
</msubsup>
</mtd>
<mtd>
<msubsup>
<mi>y</mi>
<mrow>
<mi>a</mi>
<mi>c</mi>
</mrow>
<mi>c</mi>
</msubsup>
</mtd>
</mtr>
<mtr>
<mtd>
<msubsup>
<mi>y</mi>
<mrow>
<mi>b</mi>
<mi>a</mi>
</mrow>
<mi>c</mi>
</msubsup>
</mtd>
<mtd>
<msubsup>
<mi>y</mi>
<mrow>
<mi>b</mi>
<mi>b</mi>
</mrow>
<mi>c</mi>
</msubsup>
</mtd>
<mtd>
<msubsup>
<mi>y</mi>
<mrow>
<mi>b</mi>
<mi>c</mi>
</mrow>
<mi>c</mi>
</msubsup>
</mtd>
</mtr>
<mtr>
<mtd>
<msubsup>
<mi>y</mi>
<mrow>
<mi>c</mi>
<mi>a</mi>
</mrow>
<mi>c</mi>
</msubsup>
</mtd>
<mtd>
<msubsup>
<mi>y</mi>
<mrow>
<mi>c</mi>
<mi>b</mi>
</mrow>
<mi>c</mi>
</msubsup>
</mtd>
<mtd>
<msubsup>
<mi>y</mi>
<mrow>
<mi>c</mi>
<mi>c</mi>
</mrow>
<mi>c</mi>
</msubsup>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
The alternate decoupling of the three-phase distribution net of asymmetry parameter is carried out using compensation current model；Therefore, by the voltage electricity of circuit
Flow relation is deployed, and the gaussian iteration form for obtaining A phases is as follows：
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<msubsup>
<mi>y</mi>
<mrow>
<mi>a</mi>
<mi>a</mi>
</mrow>
<mi>z</mi>
</msubsup>
<mo>(</mo>
<msub>
<mover>
<mi>U</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>a</mi>
<mo>,</mo>
<mi>i</mi>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>+</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mover>
<mi>U</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>a</mi>
<mo>,</mo>
<mi>j</mi>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>+</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
</msub>
<mo>)</mo>
<mo>=</mo>
<msub>
<mover>
<mi>I</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>a</mi>
<mo>,</mo>
<mi>i</mi>
<mi>j</mi>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>+</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
</msub>
<mo>-</mo>
<mo>&lsqb;</mo>
<msubsup>
<mi>y</mi>
<mrow>
<mi>a</mi>
<mi>b</mi>
</mrow>
<mi>z</mi>
</msubsup>
<mo>(</mo>
<msub>
<mover>
<mi>U</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>b</mi>
<mo>,</mo>
<mi>i</mi>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mover>
<mi>U</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>b</mi>
<mo>,</mo>
<mi>j</mi>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
</mrow>
</msub>
<mo>)</mo>
<mo>+</mo>
<msubsup>
<mi>y</mi>
<mrow>
<mi>a</mi>
<mi>c</mi>
</mrow>
<mi>z</mi>
</msubsup>
<mo>(</mo>
<msub>
<mover>
<mi>U</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>c</mi>
<mo>,</mo>
<mi>i</mi>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mover>
<mi>U</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>c</mi>
<mo>,</mo>
<mi>j</mi>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
</mrow>
</msub>
<mo>)</mo>
<mo>&rsqb;</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<msubsup>
<mi>y</mi>
<mrow>
<mi>a</mi>
<mi>a</mi>
</mrow>
<mi>c</mi>
</msubsup>
<msub>
<mover>
<mi>U</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>a</mi>
<mo>,</mo>
<mi>i</mi>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>+</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
</msub>
<mo>=</mo>
<msub>
<mover>
<mi>I</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>a</mi>
<mo>,</mo>
<mi>i</mi>
<mi>i</mi>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>+</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
</msub>
<mo>-</mo>
<mo>(</mo>
<msubsup>
<mi>y</mi>
<mrow>
<mi>a</mi>
<mi>b</mi>
</mrow>
<mi>c</mi>
</msubsup>
<msub>
<mover>
<mi>U</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>b</mi>
<mo>,</mo>
<mi>i</mi>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
</mrow>
</msub>
<mo>+</mo>
<msubsup>
<mi>y</mi>
<mrow>
<mi>a</mi>
<mi>c</mi>
</mrow>
<mi>c</mi>
</msubsup>
<msub>
<mover>
<mi>U</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>c</mi>
<mo>,</mo>
<mi>i</mi>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
</mrow>
</msub>
<mo>)</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<msubsup>
<mi>y</mi>
<mrow>
<mi>a</mi>
<mi>a</mi>
</mrow>
<mi>c</mi>
</msubsup>
<msub>
<mover>
<mi>U</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>a</mi>
<mo>,</mo>
<mi>j</mi>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>+</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
</msub>
<mo>=</mo>
<msub>
<mover>
<mi>I</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>a</mi>
<mo>,</mo>
<mi>j</mi>
<mi>j</mi>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>+</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
</msub>
<mo>-</mo>
<mo>(</mo>
<msubsup>
<mi>y</mi>
<mrow>
<mi>a</mi>
<mi>b</mi>
</mrow>
<mi>c</mi>
</msubsup>
<msub>
<mover>
<mi>U</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>b</mi>
<mo>,</mo>
<mi>j</mi>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
</mrow>
</msub>
<mo>+</mo>
<msubsup>
<mi>y</mi>
<mrow>
<mi>a</mi>
<mi>c</mi>
</mrow>
<mi>c</mi>
</msubsup>
<msub>
<mover>
<mi>U</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>c</mi>
<mo>,</mo>
<mi>j</mi>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
</mrow>
</msub>
<mo>)</mo>
</mtd>
</mtr>
</mtable>
</mfenced>
In formula, k is iterations；
Therefore, to flow into node direction as the injecting compensating electric current Δ for just, obtaining A phase line first and last end nodes after decoupling accordingly
Ia,i(k+1)With Δ Ia,j(k+1)For：
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>&Delta;I</mi>
<mrow>
<mi>a</mi>
<mo>,</mo>
<mi>i</mi>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>+</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
</msub>
<mo>=</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<msubsup>
<mi>y</mi>
<mrow>
<mi>a</mi>
<mi>b</mi>
</mrow>
<mi>c</mi>
</msubsup>
<msub>
<mover>
<mi>U</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>b</mi>
<mo>,</mo>
<mi>i</mi>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
</mrow>
</msub>
<mo>+</mo>
<msubsup>
<mi>y</mi>
<mrow>
<mi>a</mi>
<mi>c</mi>
</mrow>
<mi>c</mi>
</msubsup>
<msub>
<mover>
<mi>U</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>c</mi>
<mo>,</mo>
<mi>i</mi>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mrow>
<mo>(</mo>
<msubsup>
<mi>y</mi>
<mrow>
<mi>a</mi>
<mi>b</mi>
</mrow>
<mi>z</mi>
</msubsup>
<mo>(</mo>
<msub>
<mover>
<mi>U</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>b</mi>
<mo>,</mo>
<mi>i</mi>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mover>
<mi>U</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>b</mi>
<mo>,</mo>
<mi>j</mi>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msubsup>
<mi>y</mi>
<mrow>
<mi>a</mi>
<mi>c</mi>
</mrow>
<mi>z</mi>
</msubsup>
<mrow>
<mo>(</mo>
<msub>
<mover>
<mi>U</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>c</mi>
<mo>,</mo>
<mi>i</mi>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mover>
<mi>U</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>c</mi>
<mo>,</mo>
<mi>j</mi>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>)</mo>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>&Delta;I</mi>
<mrow>
<mi>a</mi>
<mo>,</mo>
<mi>j</mi>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>+</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
</msub>
<mo>=</mo>
<mo>-</mo>
<msubsup>
<mi>y</mi>
<mrow>
<mi>a</mi>
<mi>b</mi>
</mrow>
<mi>c</mi>
</msubsup>
<msub>
<mover>
<mi>U</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>b</mi>
<mo>,</mo>
<mi>j</mi>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
</mrow>
</msub>
<mo>-</mo>
<msubsup>
<mi>y</mi>
<mrow>
<mi>a</mi>
<mi>c</mi>
</mrow>
<mi>c</mi>
</msubsup>
<msub>
<mover>
<mi>U</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>c</mi>
<mo>,</mo>
<mi>j</mi>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
</mrow>
</msub>
<mo>+</mo>
<msubsup>
<mi>y</mi>
<mrow>
<mi>a</mi>
<mi>b</mi>
</mrow>
<mi>z</mi>
</msubsup>
<mrow>
<mo>(</mo>
<msub>
<mover>
<mi>U</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>b</mi>
<mo>,</mo>
<mi>i</mi>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mover>
<mi>U</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>b</mi>
<mo>,</mo>
<mi>j</mi>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msubsup>
<mi>y</mi>
<mrow>
<mi>a</mi>
<mi>c</mi>
</mrow>
<mi>z</mi>
</msubsup>
<mrow>
<mo>(</mo>
<msub>
<mover>
<mi>U</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>c</mi>
<mo>,</mo>
<mi>i</mi>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mover>
<mi>U</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>c</mi>
<mo>,</mo>
<mi>j</mi>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
</mrow>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
In formula, k is counts；
The A phases that above formula is calculated finally are compensated into electric current and are converted into node injecting power, then the node injecting power after decoupling is section
The algebraical sum of the original injecting power of point and compensation injecting power：
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mi>&Delta;</mi>
<msub>
<mi>S</mi>
<mrow>
<mi>a</mi>
<mo>,</mo>
<mi>i</mi>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>+</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
</msub>
<mo>=</mo>
<msub>
<mi>U</mi>
<mrow>
<mi>a</mi>
<mo>,</mo>
<mi>i</mi>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>+</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
</msub>
<mo>&CenterDot;</mo>
<mi>&Delta;</mi>
<msubsup>
<mi>I</mi>
<mrow>
<mi>a</mi>
<mo>,</mo>
<mi>i</mi>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>+</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
<mo>*</mo>
</msubsup>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>&Delta;S</mi>
<mrow>
<mi>a</mi>
<mo>,</mo>
<mi>j</mi>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>+</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
</msub>
<mo>=</mo>
<msub>
<mi>U</mi>
<mrow>
<mi>a</mi>
<mo>,</mo>
<mi>j</mi>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>+</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
</msub>
<mo>&CenterDot;</mo>
<msubsup>
<mi>&Delta;I</mi>
<mrow>
<mi>a</mi>
<mo>,</mo>
<mi>j</mi>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>+</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
<mo>*</mo>
</msubsup>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
In formula, k is counts, and subscript * represents conjugation Δ Sa,i(k+1)With Δ Sa,j(k+1)Headed by end-node compensation injecting power；
Similarly, it can be deduced that the injecting compensating power in B phases and C phases, the alternate full decoupled of ABC three-phases is realized.
6. the bilingual coupling method for estimating state of power distribution network according to claim 1, it is characterised in that：The step 5) in having
Work(and idle carry out cross-iteration, which are solved, uses below equation：
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mi>A</mi>
<mi>&Delta;</mi>
<msup>
<mi>&theta;</mi>
<mi>k</mi>
</msup>
<mo>=</mo>
<mi>&alpha;</mi>
<mo>&lsqb;</mo>
<msub>
<mi>z</mi>
<mi>&alpha;</mi>
</msub>
<mo>-</mo>
<msub>
<mi>h</mi>
<mi>&alpha;</mi>
</msub>
<mo>(</mo>
<msup>
<mi>&theta;</mi>
<mi>k</mi>
</msup>
<mo>,</mo>
<msup>
<mi>U</mi>
<mi>k</mi>
</msup>
<mo>)</mo>
<mo>&rsqb;</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<msup>
<mi>&theta;</mi>
<mrow>
<mi>k</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msup>
<mo>=</mo>
<msup>
<mi>&theta;</mi>
<mi>k</mi>
</msup>
<mo>+</mo>
<mi>&Delta;</mi>
<msup>
<mi>&theta;</mi>
<mi>k</mi>
</msup>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msup>
<mi>B&Delta;U</mi>
<mi>k</mi>
</msup>
<mo>=</mo>
<mi>&beta;</mi>
<mo>&lsqb;</mo>
<msub>
<mi>z</mi>
<mi>&gamma;</mi>
</msub>
<mo>-</mo>
<msub>
<mi>h</mi>
<mi>&gamma;</mi>
</msub>
<mrow>
<mo>(</mo>
<msup>
<mi>&theta;</mi>
<mi>k</mi>
</msup>
<mo>,</mo>
<msup>
<mi>U</mi>
<mi>k</mi>
</msup>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<msup>
<mi>U</mi>
<mrow>
<mi>k</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msup>
<mo>=</mo>
<msup>
<mi>U</mi>
<mi>k</mi>
</msup>
<mo>+</mo>
<mi>&Delta;</mi>
<msup>
<mi>U</mi>
<mi>k</mi>
</msup>
</mtd>
</mtr>
</mtable>
</mfenced>
In formula, A be with active corresponding information matrix block, B active is repaiied for correspondence with idle corresponding information matrix block, α
Positive matrices block, β is the idle correction matrix block of correspondence, Δ θkWith Δ UkRespectively ABC three-phase voltages phase angle and voltage magnitude state
The variable quantity of amount, wherein, in order to improve constringency performance, balance node voltage is not involved in estimation；The corresponding vector that will measure is divided into
Active and idle two class, zαFor active measurement segment vector, including branch road effective power flow PijWith node active injection power PiAmount
Measurement, is set to mαDimension；zγFor idle measurement segment vector, including branch road reactive power flow Qij, node injection reactive power QiAnd section
Point voltage magnitude ViMeasurement, is set to mγDimension；hαFor correspondence zαPart measure function vector, mαDimension；hγFor correspondence zγPart
Measure function vector, mγDimension.
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| CN108964047A (en) * | 2018-08-07 | 2018-12-07 | 河海大学 | A kind of State Estimation for Distribution Network |
| CN109787268A (en) * | 2017-11-10 | 2019-05-21 | 国网青海省电力公司 | It is a kind of meter and photovoltaic injecting power method for estimating state |
| CN112448403A (en) * | 2020-11-16 | 2021-03-05 | 国网四川省电力公司经济技术研究院 | Decoupling configuration method for energy storage of power distribution network |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN109787268A (en) * | 2017-11-10 | 2019-05-21 | 国网青海省电力公司 | It is a kind of meter and photovoltaic injecting power method for estimating state |
| CN108964047A (en) * | 2018-08-07 | 2018-12-07 | 河海大学 | A kind of State Estimation for Distribution Network |
| CN112636325A (en) * | 2020-11-11 | 2021-04-09 | 广东电网有限责任公司广州供电局 | Power distribution network robust state calculation method and device, terminal and storage medium |
| CN112636325B (en) * | 2020-11-11 | 2023-04-18 | 广东电网有限责任公司广州供电局 | Power distribution network robust state calculation method and device, terminal and storage medium |
| CN112448403A (en) * | 2020-11-16 | 2021-03-05 | 国网四川省电力公司经济技术研究院 | Decoupling configuration method for energy storage of power distribution network |
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