CN108429250A - A kind of equivalence method considering outer net static frequency characteristic - Google Patents

A kind of equivalence method considering outer net static frequency characteristic Download PDF

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CN108429250A
CN108429250A CN201810115476.8A CN201810115476A CN108429250A CN 108429250 A CN108429250 A CN 108429250A CN 201810115476 A CN201810115476 A CN 201810115476A CN 108429250 A CN108429250 A CN 108429250A
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matrix
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equivalent
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CN108429250B (en
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余娟
林伟
代伟
刘林虎
颜伟
赵霞
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Chongqing University
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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
    • 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]

Abstract

The invention discloses a kind of equivalence methods considering outer net static frequency characteristic, mainly include the following steps that：1) raw power network model is established.2) in the raw power network model input electric power network underlying parameter.3) equivalence method of trend and sensitivity consistency is utilized to establish equivalent power network model.4) according to the equivalent power network model, the static frequency characteristic of duty value is calculated.5) according to the equivalent power network model, the static frequency characteristic of equivalent generator is calculated.The present invention has not only been effectively retained trend and sensitivity consistency, while being effectively retained outer net static frequency characteristic, more truly reflects electric system actual motion characteristic.

Description

A kind of equivalence method considering outer net static frequency characteristic
Technical field
The present invention relates to Steady State Equivalents for Power System method field, specifically a kind of consideration outer net static frequency characteristic etc. Value method.
Background technology
Continuous with new energy permeability is risen, and systematic uncertainty gradually increases, frequency, branch work(in system load flow The out-of-limit risk such as rate and voltage becomes increasingly conspicuous.Therefore, be reflection electric system actual motion characteristic, should fall into a trap in tidal current analysis and Reflect the static frequency characteristic of load and generator frequency response.In addition, modern power systems have evolved into both layering and zonings The complex large power grid of tight contact again, overall size is huge and detailed data is difficult to real-time, interactive between subsystem, leads to one Body tidal current analysis is difficult to carry out, without considering that the tidal current analysis precision that outer net influences is not again good enough.Include quiet therefore, it is necessary to establish The Equivalent Model of state frequency characteristic, to improve the feasibility and computational accuracy of tidal current analysis.
Existing common static topological approach Equivalent Model, such as PV Equivalent Models, Thevenin's equivalence model, Ward Equivalent Models Deng, not in equivalent network consider the quiet distinct frequence characteristic of outer net.In the existing Equivalent Model for considering the quiet distinct frequence characteristic of outer net In research, it is typically based on DC flow model, the static frequency characteristic of outer net load and generator is united using Ward equivalent methods One is equivalent to boundary node, has ignored the significant difference between load and the static frequency characteristic of generator.Meanwhile Ward is equivalent Method can only ensure the consistency of trend before and after equivalence, can not retain the consistency of sensitivity before and after equivalence.Therefore, cause it can not True reflection electric system actual motion characteristic, it may be difficult to the tidal current analysis for being suitable for counting and frequency changes.
Invention content
Present invention aim to address problems of the prior art.
To realize the present invention purpose and the technical solution adopted is that such, it is a kind of consider outer net static frequency characteristic etc. Value method, mainly includes the following steps that：
1) raw power network model is established.
2) in the raw power network model input electric power network underlying parameter.
Further, the underlying parameter of the electric power networks includes mainly component parameters, original network topology in primitive network Structure and close on moment calculation of tidal current.
In the primitive network component parameters include mainly the admittance over the ground of all nodes, all nodes connected load work( Rate, the impedance of all circuits, the susceptance over the ground of all circuits, line transmission power constraints, transformer impedance, transformer pair Ground admittance, transformer voltage ratio, transformer transimission power constraints, generator output size, generator output constraints, hair The work(frequency static characteristic coefficient of motor and the work(frequency static characteristic coefficient of load.
The original network topology structure mainly includes the connection relation and network partition situation of all nodes.
It is described to close on moment calculation of tidal current mainly including node admittance matrix, node voltage matrix and node injection electricity Flow matrix.
3) equivalence method of trend and sensitivity consistency is utilized to establish equivalent power network model.
Further, the key step for establishing the equivalent power network model is as follows：
3.1) equivalence method of trend and sensitivity consistency is utilized to calculate the equivalence in the equivalent power network model Parameter.The equivalent parameters include mainly equivalent branch admittance yeqGij、yeqBiAnd yeqBij, equivalent branch admittance y over the groundeqBi0With Equivalent generator node voltage amplitude UGeqBi。
3.2) according to the equivalent parameters and raw power network model, equivalent power network model is established.
4) according to the equivalent power network model, the static frequency characteristic of duty value is calculated.
Further, the key step for calculating the static frequency characteristic of duty value is as follows：
4.1) duty value electric current I is calculatedLeq.Duty value electric current ILeqAs follows：
In formula, ILBFor the load current of original boundaries network.ILEFor the load current of pristine outside network.YLLIt is original The corresponding admittance submatrix of load bus in external network.LB is original boundaries load bus.LE is original outer net load bus.For the admittance submatrix YLLInverse matrix.
4.2) according to the duty value electric current ILeqCalculate duty value power SLeq.Duty value power SLeqFollowing institute Show：
In formula, SLBFor original boundaries load power.SLEFor original outer net load power.ULB_diagIndicate the elements in a main diagonal For boundary node voltage ULBDiagonal matrix.ULE_diagExpression the elements in a main diagonal is external load node voltage ULETo angular moment Battle array.For the admittance submatrix inverse matrixAdjoint matrix.For the admittance submatrix YLLAdjoint matrix.LB For original boundaries load bus.LE is original outer net load bus.
4.3) according to duty value power SLeqCalculate equivalent burden with power PLeqWith equivalent load or burden without work QLeq.Key step It is as follows：
4.3.1) setting intermediate parameters H：
In formula,For the admittance submatrix inverse matrixAdjoint matrix.For the admittance submatrix YLLCompanion With matrix.LB is original boundaries load bus.LE is original outer net load bus.ULE_diagIndicate that the elements in a main diagonal is outside Load bus voltage ULEDiagonal matrix.
4.3.2) equivalent burden with power PLeqAs follows：
In formula, PLBFor the burden with power of primitive network boundary.PLEFor original outer net burden with power.ULB_diag_realFor to angular moment Battle array ULB_diagThe matrix that the real part of element is constituted.ULB_diag_imagFor diagonal matrix ULB_diagThe matrix that the imaginary part of element is constituted.H For intermediate parameters.QLEFor original outer net load or burden without work.ULB_diagExpression the elements in a main diagonal is boundary node voltage ULBIt is diagonal Matrix.
4.3.3) equivalent load or burden without work QLeqAs follows：
In formula, QLBFor original boundaries load or burden without work.QLEFor original outer net load or burden without work.ULB_diag_realFor diagonal matrix ULB_diagThe matrix that the real part of element is constituted.ULB_diag_imagFor diagonal matrix ULB_diagThe matrix that the imaginary part of element is constituted.During H is Between parameter.ULB_diagExpression the elements in a main diagonal is boundary node voltage ULBDiagonal matrix.PLEFor original outer net burden with power.
4.4) setting new energy station.N is set as new energy station node set.L is set as the new energy field It stands load bus set.The new energy includes mainly wind and light.The new energy is set as negative load, i.e., the described new energy The burden with power in source transmits outward.
The burden with power P of the new energyLAs follows：
PL=PLN+KLP(f-fN)。 (6)
In formula, PLFor by the burden with power P of i-th of node under frequency fLiThe column vector of composition.F is frequency.fNIt is specified Frequency.KLPFor by the burden with power work(frequency static characteristic COEFFICIENT K of i-th of nodeLPiThe column vector of composition.PLNFor i-th node Specified burden with power PLNiThe column vector of composition.
Wheni∈LWhen, PLNiFor the specified burden with power of i-th of node.
As i ∈ N, PLNi=Pprei+ΔPprei。 (7)
In formula, PpreiFor the prediction active power of described i-th of node in new energy station.ΔPpreiFor the new energy field I-th of node of standing predicts active power error.I is the arbitrary node of the new energy station.N is the section of the new energy station Point set.L is search new energy station load bus set.
The load or burden without work Q of the new energyLAs follows：
QL=QLN+KLQ(f-fN)。 (8)
In formula, QLRespectively by the load or burden without work Q of i-th of node under frequency fLiThe column vector of composition.QLNFor i-th of node Nominal reactive load QLNiThe column vector of composition.KLQFor by the load or burden without work work(frequency static characteristic COEFFICIENT K of i-th of nodeLQiIt constitutes Column vector.fNFor rated frequency.F is frequency.
4.5) according to the division of original internal network, pristine outside network and original boundaries network node, by burden with power PLWith load or burden without work QLIt is respectively divided as follows：
In formula, LI represents original internal network load node.KLPFor by the burden with power work(frequency static characteristic system of i-th of node Number KLPiThe column vector of composition.PLNFor the specified burden with power P of i-th of nodeLNiThe column vector of composition.PLBFor primitive network side Boundary's burden with power.PLEFor pristine outside network burden with power.PLIFor original internal network burden with power.
In formula, LI represents original internal network load node.QLNFor the nominal reactive load Q of i-th of nodeLNiIt constitutes Column vector.KLQFor by the load or burden without work work(frequency static characteristic COEFFICIENT K of i-th of nodeLQiThe column vector of composition.QLBFor original boundaries net Network load or burden without work.QLEFor pristine outside network load or burden without work.QLIFor original internal network load or burden without work.
4.6) the pristine outside network load with static frequency characteristic in formula 9 and formula 10 is substituted into formula 5 and public affairs In the duty value of formula 6, to obtain the equivalent burden with power with static frequency characteristic and load or burden without work.Key step is such as Under：
4.6.1) setup parameter A1, parameter A2, parameter A3With parameter A4, and calculating parameter A successively1, parameter A2, parameter A3With Parameter A4。
A1=H_realPLN_LE-H_imagQLN_LE。 (11)
In formula, H_realFor the real part of the intermediate parameters H.PLN_LEFor the specified burden with power of equivalence of external network.QLN_LE For the equivalent nominal reactive load of external network.H_imagFor the imaginary part of the intermediate parameters H.
A2=H_imagPLN_LE+H_realQLN_LE。 (12)
In formula, H_imagFor the imaginary part of the intermediate parameters H.PLN_LEFor the specified burden with power of equivalence of external network.QLN_LE For the equivalent nominal reactive load of external network.H_realFor the real part of the intermediate parameters H.
A3=H_realKLP_LE-H_imagKLQ_LE。 (13)
In formula, H_realFor the real part of the intermediate parameters H.KLP_LEFor the burden with power work(of i-th of node in external network Frequency static characteristic COEFFICIENT KLPiThe column vector of composition.KLQ_LEFor the load or burden without work work(frequency static characteristic coefficient of i-th of node in external network KLQiThe column vector of composition.H_imagFor the imaginary part of the intermediate parameters H.
A4=H_imagKLP_LE+H_realKLQ_LE。 (14)
In formula, H_imagFor the imaginary part of the intermediate parameters H.KLP_LEFor the burden with power work(of i-th of node in external network Frequency static characteristic COEFFICIENT KLPiThe column vector of composition.KLQ_LEFor the load or burden without work work(frequency static characteristic coefficient of i-th of node in external network KLQiThe column vector of composition.H_realFor the imaginary part of the intermediate parameters H.
4.6.2) according to parameter A3With parameter A4Calculate the work(frequency static characteristic COEFFICIENT K of equivalent burden with powerLeq_PWith equivalent nothing The work(frequency static characteristic COEFFICIENT K of workloadLeq_Q。
The work(frequency static characteristic COEFFICIENT K of equivalent burden with powerLeq_PAs follows：
KLeq_p=KLP_LB-ULB_diag_realA3+ULB_diag_imagA4。 (15)
In formula, KLP_LBFor the burden with power work(frequency static characteristic COEFFICIENT K of i-th of node of border networksLPi_LBThe row of composition to Amount.ULB_diag_realExpression the elements in a main diagonal is boundary node voltage ULBDiagonal matrix ULB_diagWhat the real part of element was constituted Matrix.A3For the parameter of setting.A4For the parameter of setting.ULB_diag_imagExpression the elements in a main diagonal is boundary node voltage ULB Diagonal matrix ULB_diagThe matrix that the imaginary part of element is constituted.
The work(frequency static characteristic COEFFICIENT K of equivalent load or burden without workLeq_QAs follows：
KLeq_Q=KLQ_LB-ULB_diag_realA4-ULB_diag_imagA3。 (16)
In formula, KLQ_LBFor the load or burden without work work(frequency static characteristic COEFFICIENT K of i-th of node of border networksLQi_LBThe row of composition to Amount.ULB_diag_realExpression the elements in a main diagonal is boundary node voltage ULBDiagonal matrix ULB_diagWhat the real part of element was constituted Matrix.A3For the parameter of setting.A4For the parameter of setting.ULB_diag_imagExpression the elements in a main diagonal is boundary node voltage ULB Diagonal matrix ULB_diagThe matrix that the imaginary part of element is constituted.
4.6.3) according to parameter A1With parameter A2Calculate equivalent specified burden with power PLeq_LNWith equivalent nominal reactive load QLeq_LN。
Equivalent specified burden with power PLeq_LNAs follows：
PLeq_LN=PLN_LB-ULB_diag_realA1+ULB_diag_imagA2。 (17)
In formula, PLN_LBFor the specified burden with power of equivalence of border networks.A1For the parameter of setting.A2For the parameter of setting. ULB_diag_realExpression the elements in a main diagonal is boundary node voltage ULBDiagonal matrix ULB_diagThe square that the real part of element is constituted Battle array.ULB_diag_imagExpression the elements in a main diagonal is boundary node voltage ULBDiagonal matrix ULB_diagWhat the imaginary part of element was constituted Matrix.
Equivalent nominal reactive load QLeq_LNAs follows：
QLeq_LN=QLN_LB-ULB_diag_real A2-ULB_diag_imag A1。 (18)
In formula, QLN_LBFor the equivalent nominal reactive load of border networks.ULB_diag_realExpression the elements in a main diagonal is boundary Node voltage ULBDiagonal matrix ULB_diagThe matrix that the real part of element is constituted.ULB_diag_imagExpression the elements in a main diagonal is side Boundary node voltage ULBDiagonal matrix ULB_diagThe matrix that the imaginary part of element is constituted.A1For the parameter of setting.A2For the ginseng of setting Number.
4.6.4 equivalent burden with power P) is calculatedLeqWith equivalent load or burden without work QLeq。
Equivalent burden with power PLeqAs follows：
PLeq=PLeq_LN+KLeq_P(f-fN)。 (19)
In formula, PLeq_LNFor equivalent specified burden with power.F is frequency.fNFor rated frequency.KLeq_PFor equivalent burden with power Work(frequency static characteristic coefficient.
Equivalent load or burden without work QLeqAs follows：
QLeq=QLeq_LN+KLeq_Q(f-fN)。 (20)
In formula, QLeq_LNFor equivalent nominal reactive load.F is frequency.fNFor rated frequency.QLeq_PFor equivalent load or burden without work Work(frequency static characteristic coefficient.
5) according to the equivalent power network model, the static frequency characteristic of equivalent generator is calculated.
Further, the key step for calculating the static frequency characteristic of equivalent generator is as follows：
5.1) the electric current I of equivalent generator node Geq is calculatedGeq.Key step is as follows：
5.1.1 primitive network generator node Injection Current I) is calculatedG：
In formula, IGEFor pristine outside network power machine node current.IGIFor original internal network power machine node current.
UGEFor pristine outside network power machine node voltage.UGIFor pristine outside network power electromechanics pressure.ULEIt is original outer Portion's network voltage.ULBFor original boundaries network voltage.ULIFor original internal network voltage.
YGG(GE)(GE)For the corresponding admittance submatrix of generator node in pristine outside network.
YGG(GI)(GI)For the corresponding admittance submatrix of generator node in original internal network.
YGL(GE)(LE)For generator node in pristine outside network and the corresponding admittance submatrix of pristine outside network node.
YGL(GE)(LB)For in pristine outside network, with generator node be corresponding row, original boundaries network node is corresponding Row, to the admittance submatrix generated.
GE is pristine outside network power machine node.GI is original internal network power machine node.GL is original boundaries net Network generator node.LI is original internal network node.LB is original boundaries network node.LE is pristine outside network node.
5.1.2) according to formula 21, pristine outside network power machine node voltage U is obtainedGE.The pristine outside network hair Motor node voltage UGEAs follows：
In formula,For the corresponding admittance submatrix Y of generator node in pristine outside networkGG(GE)(GE)Inverse square Battle array.IGEFor generator node current in pristine outside network.ULEFor pristine outside network voltage.ULBFor original boundaries network electricity Pressure.YGL(GE)(LE)For in primitive network, the generator node with pristine outside network is corresponding row, pristine outside network node is Respective column, to the admittance submatrix generated.YGL(GE)(LB)In primitive network, to be with the generator node of pristine outside network Corresponding row, original boundaries network node are respective column, to the admittance submatrix generated.
5.1.3 equivalent generator node voltage) is obtained according to the static equivalence method based on trend and sensitivity consistency UGeq.The equivalence generator node voltage UGeqAs follows：
In formula, UGEFor pristine outside network power machine node voltage.In equivalent network, to be made with duty value node It is that corresponding row, equivalent generator node are used as respective column, to the admittance submatrix Y ' of generationLGInverse matrix.YLGFor original net In network, using load bus as corresponding row, generator node is as respective column, to the admittance submatrix generated.YLLIt is original The corresponding admittance submatrix of load bus in external network.For the admittance submatrix YLLInverse matrix.LB is original boundaries Load bus.LE is original outer net load bus.GE is pristine outside network power machine node.Gep is equivalent generator node.
5.1.4 generator node Injection Current I' in equivalent network) is calculatedG.Generator node is noted in the equivalent network Enter electric current I'GAs follows：
In formula, Y'GG(Geq)(Geq)For the corresponding admittance submatrix of generator node in equivalent external network.YGG(GI)(GI)For The corresponding admittance submatrix of generator node in original internal network.UGIFor pristine outside network power electromechanics pressure.UGeqFor equivalence Network power machine node voltage.Y'GL(Geq)(LB)It is corresponding row, equivalent side with equivalent generator node in equivalent external network Boundary's network node is respective column, to the admittance submatrix generated.Y'GL(GI)(LB)For in equivalent network, with equivalent internal network Generator node be corresponding row, equivalent boundary network node (BNN) is respective column, to the admittance submatrix generated.Y'GL(GI)(LI) For in equivalent network, the generator node using equivalent internal network is corresponding row, equivalent internal network nodes as respective column, to The admittance submatrix of generation.ULIFor original internal network voltage.ULBFor original boundaries network voltage.
5.1.5) according to formula 24, the electric current I of equivalent generator node Geq is obtainedGeq.The equivalence generator node Geq Electric current IGeqAs follows：
In formula, Y'GG(Geq)(Geq)For the corresponding admittance submatrix of generator node in equivalent external network.YLGFor original net In network, using load bus as corresponding row, generator node is as respective column, to the admittance submatrix generated.YLLIt is original The corresponding admittance submatrix of load bus in external network.For the admittance submatrix YLLInverse matrix.LB is original boundaries Load bus.LE is original outer net load bus.GE is pristine outside network power machine node.ULBFor original boundaries network electricity Pressure.EGEFor pristine outside network power machine node voltage.
5.2) the voltage U of equivalent generator node is calculatedGeq.Key step is as follows：
5.2.1) setting constant matrices C, constant matrices F and constant matrices D.
Constant matrices C is as follows：
In formula, YLLFor the corresponding admittance submatrix of load bus in pristine outside network.For the admittance submatrix YLL Inverse matrix.LB is original boundaries load bus.LE is original outer net load bus.GE is pristine outside network power machine section Point.YLGFor in primitive network, using load bus as corresponding row, generator node is as respective column, admittance to generate Matrix.
Constant matrices F is as follows：
In formula, YLLFor the corresponding admittance submatrix of load bus in pristine outside network.For the admittance submatrix YLL Inverse matrix.LB is original boundaries load bus.LE is original outer net load bus.GE is pristine outside network power machine section Point.YLGFor in primitive network, using load bus as corresponding row, generator node is as respective column, admittance to generate Matrix.
Constant matrices D is as follows：
In formula, YLLFor the corresponding admittance submatrix of load bus in pristine outside network.For the admittance submatrix YLL Inverse matrix.LB is original boundaries load bus.LE is original outer net load bus.GE is pristine outside network power machine section Point.YLGFor in primitive network, using load bus as corresponding row, generator node is as respective column, admittance to generate Matrix.
5.2.2) according to constant matrices C, constant matrices F and constant matrices D, the voltage U of the equivalence generator nodeGeq As follows：
In formula,For outer net generator power matrix SGEAdjoint matrix.Matrix C, matrix F and matrix D are respectively to set Constant matrices.ULBFor original boundaries network voltage.
5.3) equivalent generator output S is calculatedGeq.Equivalent generator output SGeqAs follows：
In formula, IGeq_diagFor by IGeqDiagonal matrix as the elements in a main diagonal.For the diagonal matrix IGeq_diagAdjoint matrix.UGEQFor the voltage of equivalent generator node.
5.4) according to equivalent generator output SGeqWith equivalent generator power SGE, obtain equivalent generator output SGeqWith etc. It is worth generator power SGEParsing relationship：
In formula, Matrix C, matrix F and matrix D are respectively the constant matrices set.For the diagonal matrix IGeq_diagAdjoint matrix.ULBFor original boundaries network voltage.For outer net generator power matrix SGEAdjoint matrix.
5.5) according to equivalent generator output SGeqWith equivalent generator power SGEParsing relationship, obtain equivalent generator Active-power PGeq.Key step is as follows：
5.5.1) setting intermediate parameters H1, intermediate parameters H2, intermediate parameters H21, intermediate parameters H22, intermediate parameters H23, it is intermediate Parameter H24, intermediate parameters H25With intermediate parameters H26。
The intermediate parameters H1As follows：
H1=IGeq_diag_realCreal+IGeq_diag_imagCimag。 (32)
In formula, IGeq_diag_realFor by IGeqDiagonal matrix I as the elements in a main diagonalGeq_diagThe real part of element is constituted Matrix.IGeq_diag_imagFor by IGeqDiagonal matrix I as the elements in a main diagonalGeq_diagThe matrix that the imaginary part of element is constituted. CrealThe matrix constituted for the real part of constant matrices C element.CimagThe matrix constituted for the imaginary part of constant matrices C element.
The intermediate parameters H21As follows：
H21=-IGeq_diag_realCimag-IGeq_diag_imagCreal。 (33)
In formula, IGeq_diag_realFor by IGeqDiagonal matrix I as the elements in a main diagonalGeq_diagThe real part of element is constituted Matrix.IGeq_diag_imagFor by IGeqDiagonal matrix I as the elements in a main diagonalGeq_diagThe matrix that the imaginary part of element is constituted. CrealThe matrix constituted for the real part of constant matrices C element.CimagThe matrix constituted for the imaginary part of constant matrices C element.
The intermediate parameters H22As follows：
In formula, YGG(GE)(GE)_realFor the real part of the corresponding admittance block matrix elements of generator node in pristine outside network The matrix of composition.YGG(GE)(GE)_imagFor the imaginary part structure of the corresponding admittance block matrix elements of generator node in pristine outside network At matrix.UGE_imagFor pristine outside network power machine node voltage UGEImaginary part.UGE_realFor pristine outside network power Machine node voltage UGEReal part.ULE_realFor pristine outside network node voltage ULEReal part.ULE_imagFor pristine outside network Node voltage ULEImaginary part.YGL(GE)(LE)_imagFor admittance submatrix YGL(GE)(LE)The matrix that the imaginary part of element is constituted. YGL(GE)(LE)_realFor admittance submatrix YGL(GE)(LE)The matrix that the real part of element is constituted.
The intermediate parameters H23As follows：
In formula, YGG(GE)(GE)_realFor the corresponding admittance submatrix Y of generator node in pristine outside networkGG(GE)(GE)Member The matrix that the real part of element is constituted.YGG(GE)(GE)_imagFor the corresponding admittance submatrix of generator node in pristine outside network YGG(GE)(GE)The matrix that the imaginary part of element is constituted.UGE_imagFor pristine outside network power machine node voltage UGEImaginary part.UGE_real For pristine outside network power machine node voltage UGEReal part.ULE_realFor pristine outside network node voltage ULEReal part. ULE_imagFor pristine outside network node voltage ULEImaginary part.YGL(GE)(LE)_imagFor admittance submatrix YGL(GE)(LE)The void of element The matrix that portion is constituted.YGL(GE)(LE)_realFor admittance submatrix YGL(GE)(LE)The matrix that the real part of element is constituted.
The intermediate parameters H24As follows：
H24=-IGeq_diag_realFreal+IGeq_diag_imagFimag。 (36)
In formula, IGeq_diag_realFor by IGeqDiagonal matrix I as the elements in a main diagonalGeq_diagThe real part of element is constituted Matrix.IGeq_diag_imagFor by IGeqDiagonal matrix I as the elements in a main diagonalGeq_diagThe matrix that the imaginary part of element is constituted. FrealThe matrix constituted for the real part of constant matrices F elements.FimagThe matrix constituted for the imaginary part of constant matrices F elements.
The intermediate parameters H25As follows：
H25=IGeq_diag_realFimag-IGeq_diag_imagFreal。 (37)
In formula, IGeq_diag_realFor by IGeqDiagonal matrix I as the elements in a main diagonalGeq_diagThe real part of element is constituted Matrix.IGeq_diag_imagFor by IGeqDiagonal matrix I as the elements in a main diagonalGeq_diagThe matrix that the imaginary part of element is constituted. FrealThe matrix constituted for the real part of constant matrices F elements.FimagThe matrix constituted for the imaginary part of constant matrices F elements.
The intermediate parameters H26As follows：
H26=-IGeq_diag_realDreal-IGeq_diag_imagDimag。 (38)
In formula, IGeq_diag_realFor by IGeqDiagonal matrix I as the elements in a main diagonalGeq_diagThe real part of element is constituted Matrix.IGeq_diag_imagFor by IGeqDiagonal matrix I as the elements in a main diagonalGeq_diagThe matrix that the imaginary part of element is constituted. DrealThe matrix constituted for the real part of constant matrices D elements.DimagThe matrix constituted for the imaginary part of constant matrices D elements.
In formula, H21、H22、H23、H24、H25And H26The intermediate parameters respectively set.YGL(GE)(LB)_imagFor admittance submatrix YGL(GE)(LB)The matrix that the imaginary part of element is constituted.YGL(GE)(LB)_realFor admittance submatrix YGL(GE)(LB)The square that the real part of element is constituted Battle array.UGE_diag_realExpression the elements in a main diagonal is external network generator node voltage UGEDiagonal matrix UGE_diagElement The matrix that real part is constituted.UGE_diag_imagExpression the elements in a main diagonal is external network generator node voltage UGEDiagonal matrix UGE_diagThe matrix that the imaginary part of element is constituted.ULB_imagFor original boundaries network node voltage ULBImaginary part.ULB_realFor original side Boundary network node voltage ULBReal part.
5.5.2) according to the intermediate parameters H of setting1, intermediate parameters H2, intermediate parameters H21, intermediate parameters H22, intermediate parameters H23, intermediate parameters H24, intermediate parameters H25With intermediate parameters H26, obtain equivalent generator active power PGeq。
The equivalence generator active power PGeqAs follows：
PGeq=H1PGE+H2。 (40)
In formula, H1And H2The intermediate parameters respectively set.PGEFor equivalent external network node active power.
5.6) generator active power PGStatic frequency characteristic it is as follows：
PG=PGmax-KG_diag(f-fGmax)。 (41)
In formula, PGFor by the active power output P of i-th of node generator under frequency fGiThe column vector of composition.PGmaxIt serves as reasons The maximum active power output P of i-th of node generatorGmaxiThe column vector of composition.KGFor by the work(frequency Jing Te of i-th of node generator Property coefficient KGiThe column vector of composition.fGmaxFor the frequency inflection point for no longer having when Primary frequency control ability by i-th of node generator fGmaxiThe column vector of composition.F is frequency.KG_diagFor by work(frequency static characteristic COEFFICIENT KGMatrix as the elements in a main diagonal.
5.7) according to the division of internal network and external network, by generator active power PGIt divides as follows：
In formula, PGmax_GIFor the maximum active power output P of i-th of node generator of internal networkGmaxiThe column vector of composition. PGmax_GEFor the maximum active power output P of i-th of node generator of external networkGmaxiThe column vector of composition.KG_GIFor internal network The work(frequency static characteristic COEFFICIENT K of i-th of node generatorGiThe column vector of composition.KG_GEFor i-th of node generator of external network Work(frequency static characteristic COEFFICIENT KGiThe column vector of composition.fGmax_GINo longer there is primary frequency modulation for i-th of node generator of internal network Frequency inflection point f when abilityGmaxiThe column vector of composition.fGmax_GEIndicate that no longer there is primary frequency modulation energy by external network generator The column vector that frequency inflection point when power is constituted.F is frequency.PGIFor equivalent internal network generator active power.PGEOutside for equivalence Portion's network power machine active power.
5.8) by the outer net generator active power P with static frequency characteristicGEIt substitutes into equivalent generator active power, To obtain the equivalent generated power output P with static frequency characteristicGeq。
The equivalent generated power output P with static frequency characteristicGeqAs follows：
PGeq=PGmax_eq-KGeqf'。 (43)
In formula, column vector f' be made of state variable, that is, frequency f and PGeqSame dimensional vector.KGeqIt is sent out for equivalent network Motor work(frequency static characteristic coefficient.PGmax_eqFor original outer net generator maximum active power output information PGmax_GEEquivalent information inside
Wherein, original outer net generator maximum active power output information PGmax_GEEquivalent information P insideGmax_eqAs follows：
PGmax_eq=H1PGmax_GE+H2+KGeqfGmax_GE。 (44)
In formula, H1And H2The intermediate parameters respectively set.fGmax_GEFor no longer there is primary frequency modulation energy by external generator The column vector that frequency inflection point when power is constituted.KGeqFor equivalent network generator work(frequency static characteristic coefficient.
Equivalent network generator work(frequency static characteristic COEFFICIENT KGeqAs follows：
KGeq=H1KG_GE。 (45)
In formula, KG_GEFor the work(frequency static characteristic COEFFICIENT K of i-th of node generator of external networkGiThe column vector of composition.H1For The intermediate parameters of setting.KG_GEFor outer net generator work(frequency static characteristic coefficient.
The solution have the advantages that unquestionable.The present invention is directed to the deficiency of existing static topological method equivalence, proposes A kind of equivalence method considering outer net static frequency characteristic.Present invention utilizes the equivalence sides of trend and sensitivity consistency Method is also improved the equivalence of outer net load, outer net generator, introduced in equivalence outer net load, outer net generator it is quiet State frequency characteristic it is equivalent.The present invention has not only been effectively retained trend and sensitivity consistency, while it is quiet to be effectively retained outer net State frequency characteristic more truly reflects electric system actual motion characteristic.
Description of the drawings
Fig. 1 is equivalent network figure.
Specific implementation mode
With reference to embodiment, the invention will be further described, but should not be construed the above-mentioned subject area of the present invention only It is limited to following embodiments.Without departing from the idea case in the present invention described above, according to ordinary skill knowledge and used With means, various replacements and change are made, should all include within the scope of the present invention.
Embodiment 1：
Referring to Fig. 1, a kind of equivalence method considering outer net static frequency characteristic mainly includes the following steps that：
1) raw power network model is established.
Further, the raw power network model includes mainly pristine outside network E, primitive network boundary and original interior Portion's network.
There is E outer net node in the pristine outside network.
There is B boundary node in the primitive network boundary.
There is I Intranet node in the original internal network.I Intranet node includes 1 balance Intranet node and I-1 A non-equilibrium Intranet node.Total element number is N in the original internal network.State available components number in original internal network For Nf。
The underlying parameter of the electric power networks mainly including component parameters, original network topology structure in primitive network and faces Nearly moment calculation of tidal current.
2) in the raw power network model input electric power network underlying parameter.
Further, the underlying parameter of the electric power networks includes mainly component parameters, original network topology in primitive network Structure and close on moment calculation of tidal current.
In the primitive network component parameters include mainly the admittance over the ground of all nodes, all nodes connected load work( Rate, the impedance of all circuits, the susceptance over the ground of all circuits, line transmission power constraints, transformer impedance, transformer pair Ground admittance, transformer voltage ratio, transformer transimission power constraints, generator output size, generator output constraints, hair The work(frequency static characteristic coefficient of motor and the work(frequency static characteristic coefficient of load.
The original network topology structure mainly includes the connection relation and network partition situation of all nodes.
It is described to close on moment calculation of tidal current mainly including node admittance matrix, node voltage matrix and node injection electricity Flow matrix.
3) equivalence method of trend and sensitivity consistency is utilized to establish equivalent power network model.
Further, the key step for establishing the equivalent power network model is as follows：
3.1) equivalence method of trend and sensitivity consistency is utilized to calculate the equivalence in the equivalent power network model Parameter.The equivalent parameters include mainly equivalent branch admittance yeqGij、yeqBiAnd yeqBij, equivalent branch admittance y over the groundeqBi0With Equivalent generator node voltage amplitude UGeqBi。
yeqGijIndicate equivalent branch admittance of the pristine outside network between equivalent generator node.
yeqBijIndicate the branch admittance of pristine outside network and generator between equivalent boundary node.
yeqBiIndicate equivalent branch admittance of the pristine outside network between boundary node and equivalent generator.
After calculating equivalent parameters, equivalent network figure is drawn according to equivalent parameters.
3.2) according to the equivalent parameters and raw power network model, equivalent power network model is established.
4) according to the equivalent power network model, the static frequency characteristic of duty value is calculated.
Further, the key step for calculating the static frequency characteristic of duty value is as follows：
4.1) duty value electric current I is calculatedLeq.Duty value electric current ILeqAs follows：
In formula, ILBFor the load current of original boundaries network.ILEFor the load current of pristine outside network.YLLIt is original The corresponding admittance submatrix of load bus in external network.LB is original boundaries load bus.LE is original outer net load bus.For the admittance submatrix YLLInverse matrix.
4.2) according to the duty value electric current ILeqCalculate duty value power SLeq.Duty value power SLeqFollowing institute Show：
In formula, SLBFor original boundaries load power.SLEFor original outer net load power.ULB_diagIndicate the elements in a main diagonal For boundary node voltage ULBDiagonal matrix.ULE_diagExpression the elements in a main diagonal is external load node voltage ULETo angular moment Battle array.For the admittance submatrix inverse matrixAdjoint matrix.For the admittance submatrix YLLAdjoint matrix.LB For original boundaries load bus.LE is original outer net load bus.
4.3) according to duty value power SLeqCalculate equivalent burden with power PLeqWith equivalent load or burden without work QLeq.Key step It is as follows：
4.3.1) setting intermediate parameters H：
In formula,For the admittance submatrix inverse matrixAdjoint matrix.For the admittance submatrix YLLCompanion With matrix.LB is original boundaries load bus.LE is original outer net load bus.ULE_diagIndicate that the elements in a main diagonal is outside Load bus voltage ULEDiagonal matrix.
4.3.2) equivalent burden with power PLeqAs follows：
In formula, PLBFor the burden with power of primitive network boundary.PLEFor original outer net burden with power.ULB_diag_realFor to angular moment Battle array ULB_diagThe matrix that the real part of element is constituted.ULB_diag_imagFor diagonal matrix ULB_diagThe matrix that the imaginary part of element is constituted.H For intermediate parameters.QLEFor original outer net load or burden without work.ULB_diagExpression the elements in a main diagonal is boundary node voltage ULBIt is diagonal Matrix.
4.3.3) equivalent load or burden without work QLeqAs follows：
In formula, QLBFor original boundaries load or burden without work.QLEFor original outer net load or burden without work.ULB_diag_realFor diagonal matrix ULB_diagThe matrix that the real part of element is constituted.ULB_diag_imagFor diagonal matrix ULB_diagThe matrix that the imaginary part of element is constituted.During H is Between parameter.ULB_diagExpression the elements in a main diagonal is boundary node voltage ULBDiagonal matrix.PLEFor original outer net burden with power.
4.4) setting new energy station.N is set as new energy station node set.L is set as the new energy field It stands load bus set.The new energy includes mainly wind and light.The new energy is set as negative load, i.e., the described new energy The burden with power in source transmits outward.
The burden with power P of the new energyLAs follows：
PL=PLN+KLP(f-fN)。 (6)
In formula, PLFor by the burden with power P of i-th of node under frequency fLiThe column vector of composition.F is frequency.fNIt is specified Frequency.KLPFor by the burden with power work(frequency static characteristic COEFFICIENT K of i-th of nodeLPiThe column vector of composition.PLNFor i-th node Specified burden with power PLNiThe column vector of composition.
As i ∈ L, PLNiFor the specified burden with power of i-th of node.
As i ∈ N, PLNi=Pprei+ΔPprei。 (7)
In formula, PpreiFor the prediction active power of described i-th of node in new energy station.ΔPpreiFor the new energy field I-th of node of standing predicts active power error.I is the arbitrary node of the new energy station.N is the section of the new energy station Point set.L is search new energy station load bus set.
The load or burden without work Q of the new energyLAs follows：
QL=QLN+KLQ(f-fN)。 (8)
In formula, QLRespectively by the load or burden without work Q of i-th of node under frequency fLiThe column vector of composition.QLNFor i-th of node Nominal reactive load QLNiThe column vector of composition.KLQFor by the load or burden without work work(frequency static characteristic COEFFICIENT K of i-th of nodeLQiIt constitutes Column vector.fNFor rated frequency.F is frequency.
4.5) according to the division of original internal network, pristine outside network and original boundaries network node, by burden with power PLWith load or burden without work QLIt is respectively divided as follows：
In formula, LI represents original internal network load node.KLPFor by the burden with power work(frequency static characteristic system of i-th of node Number KLPiThe column vector of composition.PLNFor the specified burden with power P of i-th of nodeLNiThe column vector of composition.PLBFor primitive network side Boundary's burden with power.PLEFor pristine outside network burden with power.PLIFor original internal network burden with power.
In formula, LI represents original internal network load node.QLNFor the nominal reactive load Q of i-th of nodeLNiIt constitutes Column vector.KLQFor by the load or burden without work work(frequency static characteristic COEFFICIENT K of i-th of nodeLQiThe column vector of composition.QLBFor original boundaries net Network load or burden without work.QLEFor pristine outside network load or burden without work.QLIFor original internal network load or burden without work.
4.6) the pristine outside network load with static frequency characteristic in formula 9 and formula 10 is substituted into formula 5 and public affairs In the duty value of formula 6, to obtain the equivalent burden with power with static frequency characteristic and load or burden without work.Key step is such as Under：
4.6.1) calculating parameter A1, parameter A2, parameter A3With parameter A4。
A1=H_realPLN_LE-H_imagQLN_LE。 (11)
In formula, H_realFor the real part of the intermediate parameters H.PLN_LEFor the specified burden with power of equivalence of external network.QLN_LE For the equivalent nominal reactive load of external network.
A2=H_imagPLN_LE+H_realQLN_LE。 (12)
In formula, H_imagFor the imaginary part of the intermediate parameters H.PLN_LEFor the specified burden with power of equivalence of external network.QLN_LE For the equivalent nominal reactive load of external network.
A3=H_realKLP_LE-H_imagKLQ_LE。 (13)
In formula, H_realFor the real part of the intermediate parameters H.KLP_LEFor the burden with power work(of i-th of node in external network Frequency static characteristic COEFFICIENT KLPiThe column vector of composition.KLQ_LEFor the load or burden without work work(frequency static characteristic coefficient of i-th of node in external network KLQiThe column vector of composition.H_imagFor the imaginary part of the intermediate parameters H.
A4=H_imagKLP_LE+H_realKLQ_LE。 (14)
In formula, H_imagFor the imaginary part of the intermediate parameters H.KLP_LEFor the burden with power work(of i-th of node in external network Frequency static characteristic COEFFICIENT KLPiThe column vector of composition.KLQ_LEFor the load or burden without work work(frequency static characteristic coefficient of i-th of node in external network KLQiThe column vector of composition.H_realFor the imaginary part of the intermediate parameters H.
4.6.2) according to parameter A3With parameter A4Calculate the work(frequency static characteristic COEFFICIENT K of equivalent burden with powerLeq_PWith equivalent nothing The work(frequency static characteristic COEFFICIENT K of workloadLeq_Q。
The work(frequency static characteristic COEFFICIENT K of equivalent burden with powerLeq_PAs follows：
KLeq_p=KLP_LB-ULB_diag_realA3+ULB_diag_imagA4。 (15)
In formula, KLP_LBFor the burden with power work(frequency static characteristic COEFFICIENT K of i-th of node of border networksLPi_LBThe row of composition to Amount.ULB_diag_realExpression the elements in a main diagonal is boundary node voltage ULBDiagonal matrix ULB_diagWhat the real part of element was constituted Matrix.A3For the parameter of setting.A4For the parameter of setting.
The work(frequency static characteristic COEFFICIENT K of equivalent load or burden without workLeq_QAs follows：
KLeq_Q=KLQ_LB-ULB_diag_realA4-ULB_diag_imagA3。 (16)
In formula, KLQ_LBFor the load or burden without work work(frequency static characteristic COEFFICIENT K of i-th of node of border networksLQi_LBThe row of composition to Amount.ULB_diag_realExpression the elements in a main diagonal is boundary node voltage ULBDiagonal matrix ULB_diagWhat the real part of element was constituted Matrix.A3For the parameter of setting.A4For the parameter of setting.
4.6.3) according to parameter A1With parameter A2Calculate equivalent specified burden with power PLeq_LNWith equivalent nominal reactive load QLeq_LN。
Equivalent specified burden with power PLeq_LNAs follows：
PLeq_LN=PLN_LB-ULB_diag_realA1+ULB_diag_imagA2。 (17)
In formula, PLN_LBFor the specified burden with power of equivalence of border networks.A1For the parameter of setting.A2For the parameter of setting. ULB_diag_realExpression the elements in a main diagonal is boundary node voltage ULBDiagonal matrix ULB_diagThe square that the real part of element is constituted Battle array.ULB_diag_imagExpression the elements in a main diagonal is boundary node voltage ULBDiagonal matrix ULB_diagWhat the imaginary part of element was constituted Matrix.
Equivalent nominal reactive load QLeq_LNAs follows：
QLeq_LN=QLN_LB-ULB_diag_real A2-ULB_diag_imag A1。 (18)
In formula, QLN_LBFor the equivalent nominal reactive load of border networks.ULB_diag_realExpression the elements in a main diagonal is boundary Node voltage ULBDiagonal matrix ULB_diagThe matrix that the real part of element is constituted.ULB_diag_imagExpression the elements in a main diagonal is side Boundary node voltage ULBDiagonal matrix ULB_diagThe matrix that the imaginary part of element is constituted.A1For the parameter of setting.A2For the ginseng of setting Number.
4.6.4 equivalent burden with power P) is calculatedLeqWith equivalent load or burden without work QLeq。
Equivalent burden with power PLeqAs follows：
PLeq=PLeq_LN+KLeq_P(f-fN)。 (19)
In formula, PLeq_LNFor equivalent specified burden with power.F is frequency.fNFor rated frequency.KLeq_PFor equivalent burden with power Work(frequency static characteristic coefficient.
Equivalent load or burden without work QLeqAs follows：
QLeq=QLeq_LN+KLeq_Q(f-fN)。 (20)
In formula, QLeq_LNFor equivalent nominal reactive load.F is frequency.fNFor rated frequency.QLeq_PFor equivalent load or burden without work Work(frequency static characteristic coefficient.
5) according to the equivalent power network model, the static frequency characteristic of equivalent generator is calculated.
Further, the key step for calculating the static frequency characteristic of equivalent generator is as follows：
5.1) the electric current I of equivalent generator node Geq is calculatedGeq.Key step is as follows：
5.1.1 primitive network generator node Injection Current I) is calculatedG：
In formula, IGEFor pristine outside network power machine node current.IGIFor original internal network power machine node current.
UGEFor pristine outside network power machine node voltage.UGIFor pristine outside network power electromechanics pressure.ULEIt is original outer Portion's network voltage.ULBFor original boundaries network voltage.ULIFor original internal network voltage.
YGG(GE)(GE)For the corresponding admittance submatrix of generator node in pristine outside network.YGG(GI)(GI)For original internal The corresponding admittance submatrix of generator node in network.YGL(GE)(LE)For generator node and pristine outside in pristine outside network The corresponding admittance submatrix of network node.YGL(GE)(LB)It is corresponding row, original side with generator node in pristine outside network Boundary's network node is respective column, to the admittance submatrix generated.
GE is pristine outside network power machine node.GI is original internal network power machine node.GL is original boundaries net Network generator node.LI is original internal network node.LB is original boundaries network node.LE is pristine outside network node.
5.1.2) according to formula 21, pristine outside network power machine node voltage U is obtainedGE.The pristine outside network hair Motor node voltage UGEAs follows：
In formula,For the corresponding admittance submatrix Y of generator node in pristine outside networkGG(GE)(GE)Inverse square Battle array.IGEFor generator node current in pristine outside network.ULEFor pristine outside network voltage.ULBFor original boundaries network electricity Pressure.YGL(GE)(LE)For in primitive network, the generator node with pristine outside network is corresponding row, pristine outside network node is Respective column, to the admittance submatrix generated.YGL(GE)(LB)In primitive network, to be with the generator node of pristine outside network Corresponding row, original boundaries network node are respective column, to the admittance submatrix generated.
5.1.3 equivalent generator node voltage) is obtained according to the static equivalence method based on trend and sensitivity consistency UGeq.The equivalence generator node voltage UGeqAs follows：
In formula, UGEFor pristine outside network power machine node voltage.In equivalent network, to be made with duty value node It is that corresponding row, equivalent generator node are used as respective column, to the admittance submatrix Y ' of generationLGInverse matrix.YLGFor original net In network, using load bus as corresponding row, generator node is as respective column, to the admittance submatrix generated.YLLIt is original The corresponding admittance submatrix of load bus in external network.For the admittance submatrix YLLInverse matrix.LB is original boundaries Load bus.LE is original outer net load bus.GE is pristine outside network power machine node.Gep is equivalent generator node.
5.1.4 generator node Injection Current I' in equivalent network) is calculatedG.Generator node is noted in the equivalent network Enter electric current I'GAs follows：
In formula, Y'GG(Geq)(Geq)For the corresponding admittance submatrix of generator node in equivalent external network.YGG(GI)(GI)For The corresponding admittance submatrix of generator node in original internal network.UGIFor pristine outside network power electromechanics pressure.UGeqFor equivalence Network power machine node voltage.Y'GL(Geq)(LB)It is corresponding row, equivalent side with equivalent generator node in equivalent external network Boundary's network node is respective column, to the admittance submatrix generated.Y'GL(GI)(LB)For in equivalent network, with equivalent internal network Generator node be corresponding row, equivalent boundary network node (BNN) is respective column, to the admittance submatrix generated.Y'GL(GI)(LI) For in equivalent network, the generator node using equivalent internal network is corresponding row, equivalent internal network nodes as respective column, to The admittance submatrix of generation.ULIFor original internal network voltage.ULBFor original boundaries network voltage.
5.1.5) according to formula 24, the electric current I of equivalent generator node Geq is obtainedGeq.The equivalence generator node Geq Electric current IGeqAs follows：
In formula, Y'GG(Geq)(Geq)For the corresponding admittance submatrix of generator node in equivalent external network.YLGFor original net In network, using load bus as corresponding row, generator node is as respective column, to the admittance submatrix generated.YLLIt is original The corresponding admittance submatrix of load bus in external network.For the admittance submatrix YLLInverse matrix.LB is original boundaries Load bus.LE is original outer net load bus.GE is pristine outside network power machine node.ULBFor original boundaries network electricity Pressure.EGEFor pristine outside network power machine node voltage.
5.2) the voltage U of equivalent generator node is calculatedGeq.Key step is as follows：
5.2.1) setting constant matrices C, constant matrices F and constant matrices D.
Constant matrices C is as follows：
In formula, YLLFor the corresponding admittance submatrix of load bus in pristine outside network.For the admittance submatrix YLL Inverse matrix.LB is original boundaries load bus.LE is original outer net load bus.GE is pristine outside network power machine section Point.YLGFor in primitive network, using load bus as corresponding row, generator node is as respective column, admittance to generate Matrix.
Constant matrices F is as follows：
In formula, YLLFor the corresponding admittance submatrix of load bus in pristine outside network.For the admittance submatrix YLL Inverse matrix.LB is original boundaries load bus.LE is original outer net load bus.GE is pristine outside network power machine section Point.YLGFor in primitive network, using load bus as corresponding row, generator node is as respective column, admittance to generate Matrix.
Constant matrices D is as follows：
In formula, YLLFor the corresponding admittance submatrix of load bus in pristine outside network.For the admittance submatrix YLL Inverse matrix.LB is original boundaries load bus.LE is original outer net load bus.GE is pristine outside network power machine section Point.YLGFor in primitive network, using load bus as corresponding row, generator node is as respective column, admittance to generate Matrix.
5.2.2) according to constant matrices C, constant matrices F and constant matrices D, the voltage U of the equivalence generator nodeGeq As follows：
In formula,For outer net generator power matrix SGEAdjoint matrix.Matrix C, matrix F and matrix D are respectively to set Constant matrices.ULBFor original boundaries network voltage.
5.3) equivalent generator output S is calculatedGeq.Equivalent generator output SGeqAs follows：
In formula, IGeq_diagFor by IGeqDiagonal matrix as the elements in a main diagonal.For the diagonal matrix IGeq_diagAdjoint matrix.UGEQFor the voltage of equivalent generator node.
5.4) according to equivalent generator output SGeqWith equivalent generator power SGE, obtain equivalent generator output SGeqWith etc. It is worth generator power SGEParsing relationship：
In formula, Matrix C, matrix F and matrix D are respectively the constant matrices set.For the diagonal matrix IGeq_diagAdjoint matrix.ULBFor original boundaries network voltage.For outer net generator power matrix SGEAdjoint matrix.
5.5) according to equivalent generator output SGeqWith equivalent generator power SGEParsing relationship, obtain equivalent generator Active-power PGeq.Key step is as follows：
5.5.1) setting intermediate parameters H1, intermediate parameters H2, intermediate parameters H21, intermediate parameters H22, intermediate parameters H23, it is intermediate Parameter H24, intermediate parameters H25With intermediate parameters H26。
The intermediate parameters H1As follows：
H1=IGeq_diag_realCreal+IGeq_diag_imagCimag。 (32)
In formula, IGeq_diag_realFor by IGeqDiagonal matrix I as the elements in a main diagonalGeq_diagThe real part of element is constituted Matrix.IGeq_diag_imagFor by IGeqDiagonal matrix I as the elements in a main diagonalGeq_diagThe matrix that the imaginary part of element is constituted. CrealThe matrix constituted for the real part of constant matrices C element.CimagThe matrix constituted for the imaginary part of constant matrices C element.
The intermediate parameters H21As follows：
H21=-IGeq_diag_realCimag-IGeq_diag_imagCreal。 (33)
In formula, IGeq_diag_realFor by IGeqDiagonal matrix I as the elements in a main diagonalGeq_diagThe real part of element is constituted Matrix.IGeq_diag_imagFor by IGeqDiagonal matrix I as the elements in a main diagonalGeq_diagThe matrix that the imaginary part of element is constituted. CrealThe matrix constituted for the real part of constant matrices C element.CimagThe matrix constituted for the imaginary part of constant matrices C element.
The intermediate parameters H22As follows：
In formula, YGG(GE)(GE)_realFor the real part of the corresponding admittance block matrix elements of generator node in pristine outside network The matrix of composition.YGG(GE)(GE)_imagFor the imaginary part structure of the corresponding admittance block matrix elements of generator node in pristine outside network At matrix.UGE_imagFor pristine outside network power machine node voltage UGEImaginary part.UGE_realFor pristine outside network power Machine node voltage UGEReal part.ULE_realFor pristine outside network node voltage ULEReal part.ULE_imagFor pristine outside network Node voltage ULEImaginary part.YGL(GE)(LE)_imagFor admittance submatrix YGL(GE)(LE)The matrix that the imaginary part of element is constituted. YGL(GE)(LE)_realFor admittance submatrix YGL(GE)(LE)The matrix that the real part of element is constituted.
The intermediate parameters H23As follows：
In formula, YGG(GE)(GE)_realFor the corresponding admittance submatrix Y of generator node in pristine outside networkGG(GE)(GE)Member The matrix that the real part of element is constituted.YGG(GE)(GE)_imagFor the corresponding admittance submatrix of generator node in pristine outside network YGG(GE)(GE)The matrix that the imaginary part of element is constituted.UGE_imagFor pristine outside network power machine node voltage UGEImaginary part.UGE_real For pristine outside network power machine node voltage UGEReal part.ULE_realFor pristine outside network node voltage ULEReal part. ULE_imagFor pristine outside network node voltage ULEImaginary part.YGL(GE)(LE)_imagFor admittance submatrix YGL(GE)(LE)The void of element The matrix that portion is constituted.YGL(GE)(LE)_realFor admittance submatrix YGL(GE)(LE)The matrix that the real part of element is constituted.
The intermediate parameters H24As follows：
H24=-IGeq_diag_realFreal+IGeq_diag_imagFimag。 (36)
In formula, IGeq_diag_realFor by IGeqDiagonal matrix I as the elements in a main diagonalGeq_diagThe real part of element is constituted Matrix.IGeq_diag_imagFor by IGeqDiagonal matrix I as the elements in a main diagonalGeq_diagThe matrix that the imaginary part of element is constituted. FrealThe matrix constituted for the real part of constant matrices F elements.FimagThe matrix constituted for the imaginary part of constant matrices F elements.
The intermediate parameters H25As follows：
H25=IGeq_diag_realFimag-IGeq_diag_imagFreal。 (37)
In formula, IGeq_diag_realFor by IGeqDiagonal matrix I as the elements in a main diagonalGeq_diagThe real part of element is constituted Matrix.IGeq_diag_imagFor by IGeqDiagonal matrix I as the elements in a main diagonalGeq_diagThe matrix that the imaginary part of element is constituted. FrealThe matrix constituted for the real part of constant matrices F elements.FimagThe matrix constituted for the imaginary part of constant matrices F elements.
The intermediate parameters H26As follows：
H26=-IGeq_diag_realDreal-IGeq_diag_imagDimag。 (38)
In formula, IGeq_diag_realFor by IGeqDiagonal matrix I as the elements in a main diagonalGeq_diagThe real part of element is constituted Matrix.IGeq_diag_imagFor by IGeqDiagonal matrix I as the elements in a main diagonalGeq_diagThe matrix that the imaginary part of element is constituted. DrealThe matrix constituted for the real part of constant matrices D elements.DimagThe matrix constituted for the imaginary part of constant matrices D elements.
In formula, H21、H22、H23、H24、H25And H26The intermediate parameters respectively set.YGL(GE)(LB)_imagFor admittance submatrix YGL(GE)(LB)The matrix that the imaginary part of element is constituted.YGL(GE)(LB)_realFor admittance submatrix YGL(GE)(LB)The square that the real part of element is constituted Battle array.UGE_diag_realExpression the elements in a main diagonal is external network generator node voltage UGEDiagonal matrix UGE_diagElement The matrix that real part is constituted.UGE_diag_imagExpression the elements in a main diagonal is external network generator node voltage UGEDiagonal matrix UGE_diagThe matrix that the imaginary part of element is constituted.ULB_imagFor original boundaries network node voltage ULBImaginary part.ULB_realFor original side Boundary network node voltage ULBReal part.
5.5.2) according to the intermediate parameters H of setting1, intermediate parameters H2, intermediate parameters H21, intermediate parameters H22, intermediate parameters H23, intermediate parameters H24, intermediate parameters H25With intermediate parameters H26, obtain equivalent generator active power PGeq。
The equivalence generator active power PGeqAs follows：
PGeq=H1PGE+H2。 (40)
In formula, H1And H2The intermediate parameters respectively set.PGEFor equivalent external network node active power.
5.6) generator active power PGStatic frequency characteristic it is as follows：
PG=PGmax-KG_diag(f-fGmax)。 (41)
In formula, PGFor by the active power output P of i-th of node generator under frequency fGiThe column vector of composition.PGmaxIt serves as reasons The maximum active power output P of i-th of node generatorGmaxiThe column vector of composition.KGFor by the work(frequency Jing Te of i-th of node generator Property coefficient KGiThe column vector of composition.fGmaxFor the frequency inflection point for no longer having when Primary frequency control ability by i-th of node generator fGmaxiThe column vector of composition.F is frequency.KG_diagFor by work(frequency static characteristic COEFFICIENT KGMatrix as the elements in a main diagonal.
5.7) according to the division of internal network and external network, by generator active power PGIt divides as follows：
In formula, PGmax_GIFor the maximum active power output P of i-th of node generator of internal networkGmaxiThe column vector of composition. PGmax_GEFor the maximum active power output P of i-th of node generator of external networkGmaxiThe column vector of composition.KG_GIFor internal network The work(frequency static characteristic COEFFICIENT K of i-th of node generatorGiThe column vector of composition.KG_GEFor i-th of node generator of external network Work(frequency static characteristic COEFFICIENT KGiThe column vector of composition.fGmax_GINo longer there is primary frequency modulation for i-th of node generator of internal network Frequency inflection point f when abilityGmaxiThe column vector of composition.fGmax_GEIndicate that no longer there is primary frequency modulation energy by external network generator The column vector that frequency inflection point when power is constituted.F is frequency.PGIFor equivalent internal network generator active power.PGEOutside for equivalence Portion's network power machine active power.
5.8) by the outer net generator active power P with static frequency characteristicGEIt substitutes into equivalent generator active power, To obtain the equivalent generated power output P with static frequency characteristicGeq。
The equivalent generated power output P with static frequency characteristicGeqAs follows：
PGeq=PGmax_eq-KGeqf'。 (43)
In formula, column vector f' be made of state variable, that is, frequency f and PGeqSame dimensional vector.KGeqIt is sent out for equivalent network Motor work(frequency static characteristic coefficient.PGmax_eqFor original outer net generator maximum active power output information PGmax_GEEquivalent information inside.
Wherein, original outer net generator maximum active power output information PGmax_GEEquivalent information P insideGmax_eqAs follows：
PGmax_eq=H1PGmax_GE+H2+KGeqfGmax_GE。 (44)
In formula, H1And H2The intermediate parameters respectively set.fGmax_GEFor no longer there is primary frequency modulation energy by external generator The column vector that frequency inflection point when power is constituted.KGeqFor equivalent network generator work(frequency static characteristic coefficient.
Equivalent network generator work(frequency static characteristic COEFFICIENT KGeqAs follows：
KGeq=H1KG_GE。 (45)
In formula, KG_GEFor the work(frequency static characteristic COEFFICIENT K of i-th of node generator of external networkGiThe column vector of composition.H1For The intermediate parameters of setting.KG_GEFor outer net generator work(frequency static characteristic coefficient.
Embodiment 2：
A kind of experiment of the equivalence method of verification consideration outer net static frequency characteristic, mainly includes the following steps that：
1) test system is established.
In IEEE9 node systems, system is divided into external network, boundary node and internal network：External node：Section Point 2, node 3, node 6 and node 7.Boundary node：Node 5 and node 9.Internal node：Node 1 and node 4, wherein 1 node For balance nodes.In IEEE118 node systems, system is equally divided into external network, boundary node and internal network：Outside Portion's node：Node 80, node 83 to node 112.Boundary node：Node 81 and node 82.Internal node：Node 1 to node 79, Node 113 is to node 118, wherein 69 nodes are balance nodes.
In two test systems, related coefficient takes 0.1 between outer net load.Conventional burden with power and conventional load or burden without work Work(frequency static characteristic coefficient perunit value takes 2 and -1.5 respectively.The work(frequency of generator is static special at non-equilibrium node and balance nodes Property coefficient perunit value takes 20 and 25 respectively.System nominal frequency is taken as 50Hz, and frequency limits take 50.2Hz and 49.8Hz respectively.
2) different comparison models
The correctness and validity that the equivalence method for considering outer net static frequency characteristic is carried for the verification present invention, using such as Lower 4 kinds of tidal current computing methods carry out static security analysis comparison：
M0：Tidal current computing method (reference method) based on primitive network.
M1：The present invention carries equivalent tidal current computing method.
M2：Equivalence method (i.e. " StaticEquivalentMethodBasedonC based on trend and sensitivity consistency OmponentParticularityRepresentationandSensitivityConsist ency ") in only consider outer net spirit The equivalent tidal current computing method of sensitivity.
M3：Based on by external network equivalent be balance nodes, PV node or PQ nodal methods tidal current computing method.Using absolute Error criterion e1With relative error index e2Weigh the error of M1-M3 methods and M0 methods.
3) simulating, verifying of equivalence method static frequency characteristic
12% and 8% are increased in proportion to the Intranet load of IEEE9 node systems and IEEE118 node systems respectively, profit Static security analysis is carried out respectively with M0-M3.
Table 1 lists the error analysis result of system frequency and worst error branch active power.
As seen from Table 1, when Intranet load growth, the frequency of M0 methods and the carried M1 methods of this paper based on primitive network Rate is not out-of-limit, and the difference of the two is smaller, maximum absolute error e1Only 0.03HZ.However the frequency of M2 and M3 models is Through out-of-limit, maximum absolute error e1Respectively up to 0.06Hz and 1.11Hz.The branch with maximum active power error is chosen simultaneously Road is compared (9 node systems are 1-4 branches, and 118 node systems are 77-82 branches).For the carried M1 models of the present invention, The maximum relative error e of branch active power2Only 2.5%, and the maximum relative error e of M2, M3 method2Up to it is respectively 18.4%, 430.92%.It follows that this paper institutes extracting method can be effectively retained outer net static frequency characteristic information, improve static Safety analysis precision.Value and e in table 11Unit it is corresponding with unit Hz, MW of f, P respectively.e2Unit be %.
The error analysis of table 1IEEE9 node systems, IEEE118 node systems frequency and worst error branch active power As a result
It can be seen that the present invention has not only been effectively retained trend and sensitivity consistency, while it is quiet to be effectively retained outer net State frequency characteristic more truly reflects electric system actual motion characteristic.

Claims (5)

1. a kind of equivalence method considering outer net static frequency characteristic, which is characterized in that mainly include the following steps that：
1) the raw power network model is established；
2) in the raw power network model input electric power network underlying parameter.
3) equivalence method of trend and sensitivity consistency is utilized to establish equivalent power network model；
5) according to the equivalent power network model, the static frequency characteristic of duty value is calculated；
5) according to the equivalent power network model, the static frequency characteristic of equivalent generator is calculated.
2. a kind of equivalence method considering outer net static frequency characteristic according to claim 1, it is characterised in that：The electricity The underlying parameter of power network mainly including component parameters, original network topology structure in primitive network and closes on moment Load flow calculation As a result；
In the primitive network component parameters include mainly the admittance over the ground of all nodes, all nodes connected load power, The impedance of all circuits, the susceptance over the ground of all circuits, line transmission power constraints, transformer impedance, transformer are over the ground Admittance, transformer voltage ratio, transformer transimission power constraints, generator output size, generator output constraints, power generation The work(frequency static characteristic coefficient of machine and the work(frequency static characteristic coefficient of load；
The original network topology structure mainly includes the connection relation and network partition situation of all nodes；
It is described to close on moment calculation of tidal current mainly including node admittance matrix, node voltage matrix and node Injection Current square Battle array.
3. a kind of equivalence method considering outer net static frequency characteristic according to claim 1, it is characterised in that：Establish institute The key step for stating equivalent power network model is as follows：
1) equivalence method of trend and sensitivity consistency is utilized to calculate the equivalent parameters in the equivalent power network model；Institute It includes equivalent branch admittance y to state equivalent parameters mainlyeqGij、yeqBiAnd yeqBij, equivalent branch admittance y over the groundeqBi0It generates electricity with equivalence Machine node voltage amplitude UGeqBi；
2) according to the equivalent parameters and raw power network model, equivalent power network model is established.
4. a kind of equivalence method considering outer net static frequency characteristic according to claim 1, it is characterised in that：Calculate etc. The key step of the static frequency characteristic of duty value is as follows：
1) duty value electric current I is calculatedLeq；Duty value electric current ILeqAs follows：
In formula, ILBFor the load current of original boundaries network；ILEFor the load current of pristine outside network；YLLFor pristine outside The corresponding admittance submatrix of load bus in network；LB is original boundaries load bus；LE is original outer net load bus；For The admittance submatrix YLLInverse matrix；
2) according to the duty value electric current ILeqCalculate duty value power SLeq；Duty value power SLeqAs follows：
In formula, SLBFor original boundaries load power；SLEFor original outer net load power；ULB_diagExpression the elements in a main diagonal is side Boundary node voltage ULBDiagonal matrix；ULE_diagExpression the elements in a main diagonal is external load node voltage ULEDiagonal matrix；For the admittance submatrix inverse matrixAdjoint matrix；For the admittance submatrix YLLAdjoint matrix；LB is original Initial line circle load bus；LE is original outer net load bus；
3) according to duty value power SLeqCalculate equivalent burden with power PLeqWith equivalent load or burden without work QLeq；Key step is as follows：
3.1) setting intermediate parameters H：
In formula,For the admittance submatrix inverse matrixAdjoint matrix；For the admittance submatrix YLLAdjoint matrix Battle array；LB is original boundaries load bus；LE is original outer net load bus；ULE_diagExpression the elements in a main diagonal is external load Node voltage ULEDiagonal matrix；
3.2) equivalent burden with power PLeqAs follows：
In formula, PLBFor the burden with power of primitive network boundary；PLEFor original outer net burden with power；ULB_diag_realFor diagonal matrix ULB_diagThe matrix that the real part of element is constituted；ULB_diag_imagFor diagonal matrix ULB_diagThe matrix that the imaginary part of element is constituted；H is Intermediate parameters；QLEFor original outer net load or burden without work；ULB_diagExpression the elements in a main diagonal is boundary node voltage ULBTo angular moment Battle array；
3.3) equivalent load or burden without work QLeqAs follows：
In formula, QLBFor original boundaries load or burden without work；QLEFor original outer net load or burden without work；ULB_diag_realFor diagonal matrix ULB_diag The matrix that the real part of element is constituted；ULB_diag_imagFor diagonal matrix ULB_diagThe matrix that the imaginary part of element is constituted；H is intermediate joins Number；ULB_diagExpression the elements in a main diagonal is boundary node voltage ULBDiagonal matrix；PLEFor original outer net burden with power；
4) setting new energy station；N is set as new energy station node set；L is set as new energy station load Node set；The new energy includes mainly wind and light；The new energy is set as negative load, i.e., the described new energy has Workload transmits outward；
The burden with power P of the new energyLAs follows：
PL=PLN+KLP(f-fN)； (6)
In formula, PLFor by the burden with power P of i-th of node under frequency fLiThe column vector of composition；F is frequency；fNFor rated frequency； KLPFor by the burden with power work(frequency static characteristic COEFFICIENT K of i-th of nodeLPiThe column vector of composition；PLNHave for i-th of the specified of node Workload PLNiThe column vector of composition；
As i ∈ L, PLNiFor the specified burden with power of i-th of node；
As i ∈ N, PLNi=Pprei+ΔPprei； (7)
In formula, PpreiFor the prediction active power of described i-th of node in new energy station；ΔPpreiFor the new energy station i-th A node predicts active power error；I is the arbitrary node of the new energy station；N is the set of node of the new energy station It closes；L is search new energy station load bus set；
The load or burden without work Q of the new energyLAs follows：
QL=QLN+KLQ(f-fN)； (8)
In formula, QLRespectively by the load or burden without work Q of i-th of node under frequency fLiThe column vector of composition；QLNFor the volume of i-th of node Determine load or burden without work QLNiThe column vector of composition；KLQFor by the load or burden without work work(frequency static characteristic COEFFICIENT K of i-th of nodeLQiThe row of composition Vector；fNFor rated frequency；F is frequency；
5) according to the division of original internal network, pristine outside network and original boundaries network node, by burden with power PLWith it is idle Load QLIt is respectively divided as follows：
In formula, LI represents original internal network load node；KLPFor by the burden with power work(frequency static characteristic coefficient of i-th of node KLPiThe column vector of composition；PLNFor the specified burden with power P of i-th of nodeLNiThe column vector of composition；PLBFor primitive network boundary Burden with power；PLEFor pristine outside network burden with power；PLIFor original internal network burden with power；
In formula, LI represents original internal network load node；QLNFor the nominal reactive load Q of i-th of nodeLNiThe row of composition to Amount；KLQFor by the load or burden without work work(frequency static characteristic COEFFICIENT K of i-th of nodeLQiThe column vector of composition；QLBFor original boundaries network without Workload；QLEFor pristine outside network load or burden without work；QLIFor original internal network load or burden without work；
6) by the pristine outside network load with static frequency characteristic in formula 9 and formula 10 substitute into formula 5 and formula 6 etc. In duty value, to obtain the equivalent burden with power with static frequency characteristic and load or burden without work；Key step is as follows：
6.1) setup parameter A1, parameter A2, parameter A3With parameter A4, and A is calculated successively1, parameter A2, parameter A3With parameter A4；
A1=H_realPLN_LE-H_imagQLN_LE； (11)
In formula, H_realFor the real part of the intermediate parameters H；PLN_LEFor the specified burden with power of equivalence of external network；QLN_LEIt is outer The equivalent nominal reactive load of portion's network；H_imagFor the imaginary part of the intermediate parameters H；
A2=H_imagPLN_LE+H_realQLN_LE； (12)
In formula, H_imagFor the imaginary part of the intermediate parameters H；PLN_LEFor the specified burden with power of equivalence of external network；QLN_LEIt is outer The equivalent nominal reactive load of portion's network；H_realFor the real part of the intermediate parameters H；
A3=H_realKLP_LE-H_imagKLQ_LE； (13)
In formula, H_realFor the real part of the intermediate parameters H；KLP_LEBurden with power work(frequency for i-th of node in external network is quiet Characteristic coefficient KLPiThe column vector of composition；KLQ_LEFor the load or burden without work work(frequency static characteristic COEFFICIENT K of i-th of node in external networkLQi The column vector of composition；H_imagFor the imaginary part of the intermediate parameters H；
A4=H_imagKLP_LE+H_realKLQ_LE； (14)
In formula, H_imagFor the imaginary part of the intermediate parameters H；KLP_LEBurden with power work(frequency for i-th of node in external network is quiet Characteristic coefficient KLPiThe column vector of composition；KLQ_LEFor the load or burden without work work(frequency static characteristic COEFFICIENT K of i-th of node in external networkLQi The column vector of composition；H_realFor the imaginary part of the intermediate parameters H；
6.2) according to parameter A3With parameter A4Calculate the work(frequency static characteristic COEFFICIENT K of equivalent burden with powerLeq_PWith equivalent load or burden without work Work(frequency static characteristic COEFFICIENT KLeq_Q；
The work(frequency static characteristic COEFFICIENT K of equivalent burden with powerLeq_PAs follows：
KLeq_p=KLP_LB-ULB_diag_realA3+ULB_diag_imagA4； (15)
In formula, KLP_LBFor the burden with power work(frequency static characteristic COEFFICIENT K of i-th of node of border networksLPi_LBThe column vector of composition； ULB_diag_realExpression the elements in a main diagonal is boundary node voltage ULBDiagonal matrix ULB_diagThe square that the real part of element is constituted Battle array；A3For the parameter of setting；A4For the parameter of setting；ULB_diag_imagExpression the elements in a main diagonal is boundary node voltage ULB's Diagonal matrix ULB_diagThe matrix that the imaginary part of element is constituted；
The work(frequency static characteristic COEFFICIENT K of equivalent load or burden without workLeq_QAs follows：
KLeq_Q=KLQ_LB-ULB_diag_realA4-ULB_diag_imagA3； (16)
In formula, KLQ_LBFor the load or burden without work work(frequency static characteristic COEFFICIENT K of i-th of node of border networksLQi_LBThe column vector of composition； ULB_diag_realExpression the elements in a main diagonal is boundary node voltage ULBDiagonal matrix ULB_diagThe square that the real part of element is constituted Battle array；A3For the parameter of setting；A4For the parameter of setting；ULB_diag_imagExpression the elements in a main diagonal is boundary node voltage ULB's Diagonal matrix ULB_diagThe matrix that the imaginary part of element is constituted；
6.3) according to parameter A1With parameter A2Calculate equivalent specified burden with power PLeq_LNWith equivalent nominal reactive load QLeq_LN；
Equivalent specified burden with power PLeq_LNAs follows：
PLeq_LN=PLN_LB-ULB_diag_realA1+ULB_diag_imagA2； (17)
In formula, PLN_LBFor the specified burden with power of equivalence of border networks；A1For the parameter of setting；A2For the parameter of setting； ULB_diag_realExpression the elements in a main diagonal is boundary node voltage ULBDiagonal matrix ULB_diagThe square that the real part of element is constituted Battle array；ULB_diag_imagExpression the elements in a main diagonal is boundary node voltage ULBDiagonal matrix ULB_diagWhat the imaginary part of element was constituted Matrix；
Equivalent nominal reactive load QLeq_LNAs follows：
QLeq_LN=QLN_LB-ULB_diag_realA2-ULB_diag_imagA1； (18)
In formula, QLN_LBFor the equivalent nominal reactive load of border networks；ULB_diag_realExpression the elements in a main diagonal is boundary node Voltage ULBDiagonal matrix ULB_diagThe matrix that the real part of element is constituted；ULB_diag_imagIndicate that the elements in a main diagonal saves for boundary Point voltage ULBDiagonal matrix ULB_diagThe matrix that the imaginary part of element is constituted；A1For the parameter of setting；A2For the parameter of setting；
6.4) equivalent burden with power P is calculatedLeqWith equivalent load or burden without work QLeq；
Equivalent burden with power PLeqAs follows：
PLeq=PLeq_LN+KLeq_P(f-fN)； (19)
In formula, PLeq_LNFor equivalent specified burden with power；F is frequency；fNFor rated frequency；KLeq_PFor the work(of equivalent burden with power Frequency static characteristic coefficient；
Equivalent load or burden without work QLeqAs follows：
QLeq=QLeq_LN+KLeq_Q(f-fN)； (20)
In formula, QLeq_LNFor equivalent nominal reactive load；F is frequency；fNFor rated frequency；QLeq_PFor the work(of equivalent load or burden without work Frequency static characteristic coefficient.
5. a kind of equivalence method considering outer net static frequency characteristic according to claim 1, it is characterised in that：Calculate etc. The key step for being worth the static frequency characteristic of generator is as follows：
1) the electric current I of equivalent generator node Geq is calculatedGeq；Key step is as follows：
1.1) primitive network generator node Injection Current I is calculatedG：
In formula, IGEFor pristine outside network power machine node current；IGIFor original internal network power machine node current；
UGEFor pristine outside network power machine node voltage；UGIFor pristine outside network power electromechanics pressure；ULEFor pristine outside net Network voltage；ULBFor original boundaries network voltage；ULIFor original internal network voltage；
YGG(GE)(GE)For the corresponding admittance submatrix of generator node in pristine outside network；
YGG(GI)(GI)For the corresponding admittance submatrix of generator node in original internal network；
YGL(GE)(LE)For generator node in pristine outside network and the corresponding admittance submatrix of pristine outside network node；
YGL(GE)(LB)It is corresponding row, original boundaries network node as respective column using generator node in pristine outside network, from And the admittance submatrix generated；
GE is pristine outside network power machine node；GI is original internal network power machine node；GL sends out for original boundaries network Motor node；LI is original internal network node；LB is original boundaries network node；LE is pristine outside network node；
1.2) according to formula 21, pristine outside network power machine node voltage U is obtainedGE；The pristine outside network power machine section Point voltage UGEAs follows：
In formula,For the corresponding admittance submatrix Y of generator node in pristine outside networkGG(GE)(GE)Inverse matrix； IGEFor generator node current in pristine outside network；ULEFor pristine outside network voltage；ULBFor original boundaries network voltage； YGL(GE)(LE)For in primitive network, the generator node with pristine outside network is corresponding row, pristine outside network node is pair Ying Lie, to the admittance submatrix generated；YGL(GE)(LB)It is pair with the generator node of pristine outside network in primitive network Ying Hang, original boundaries network node are respective column, to the admittance submatrix generated；
1.3) equivalent generator node voltage U is obtained according to the static equivalence method based on trend and sensitivity consistencyGeq；Institute State equivalent generator node voltage UGeqAs follows：
In formula, UGEFor pristine outside network power machine node voltage；For in equivalent network, using duty value node as pair Ying Hang, equivalent generator node are as respective column, to the admittance submatrix Y generatedL′GInverse matrix；YLGFor primitive network In, using load bus as corresponding row, generator node is as respective column, to the admittance submatrix generated；YLLIt is original outer The corresponding admittance submatrix of load bus in portion's network；For the admittance submatrix YLLInverse matrix；LB is negative for original boundaries Lotus node；LE is original outer net load bus；GE is pristine outside network power machine node；Gep is equivalent generator node；
1.4) generator node Injection Current I' in equivalent network is calculatedG；Generator node Injection Current in the equivalent network I'GAs follows：
In formula, Y'GG(Geq)(Geq)For the corresponding admittance submatrix of generator node in equivalent external network；YGG(GI)(GI)It is original interior The corresponding admittance submatrix of generator node in portion's network；UGIFor pristine outside network power electromechanics pressure；UGeqIt is sent out for equivalent network Motor node voltage；Y'GL(Geq)(LB)It is corresponding row, equivalent border networks with equivalent generator node in equivalent external network Node is respective column, to the admittance submatrix generated；Y'GL(GI)(LB)For in equivalent network, with the power generation of equivalent internal network Machine node is corresponding row, equivalent boundary network node (BNN) is respective column, to the admittance submatrix generated；Y'GL(GI)(LI)For equivalence In network, the generator node using equivalent internal network is corresponding row, equivalent internal network nodes as respective column, to what is generated Admittance submatrix；ULIFor original internal network voltage；ULBFor original boundaries network voltage；
1.5) according to formula 24, the electric current I of equivalent generator node Geq is obtainedGeq；The electric current of the equivalence generator node Geq IGeqAs follows：
In formula, Y'GG(Geq)(Geq)For the corresponding admittance submatrix of generator node in equivalent external network；YLGFor in primitive network, Using load bus as corresponding row, generator node is as respective column, to the admittance submatrix generated；YLLFor pristine outside net The corresponding admittance submatrix of load bus in network；For the admittance submatrix YLLInverse matrix；LB is original boundaries load section Point；LE is original outer net load bus；GE is pristine outside network power machine node；ULBFor original boundaries network voltage；EGEFor Pristine outside network power machine node voltage；
2) the voltage U of equivalent generator node is calculatedGeq；Key step is as follows：
2.1) setting constant matrices C, constant matrices F and constant matrices D；
Constant matrices C is as follows：
In formula, YLLFor the corresponding admittance submatrix of load bus in pristine outside network；For the admittance submatrix YLLIt is inverse Matrix；LB is original boundaries load bus；LE is original outer net load bus；GE is pristine outside network power machine node；YLG For in primitive network, using load bus as corresponding row, generator node is as respective column, to the admittance submatrix generated；
Constant matrices F is as follows：
In formula, YLLFor the corresponding admittance submatrix of load bus in pristine outside network；For the admittance submatrix YLLIt is inverse Matrix；LB is original boundaries load bus；LE is original outer net load bus；GE is pristine outside network power machine node；YLG For in primitive network, using load bus as corresponding row, generator node is as respective column, to the admittance submatrix generated；
Constant matrices D is as follows：
In formula, YLLFor the corresponding admittance submatrix of load bus in pristine outside network；For the admittance submatrix YLLIt is inverse Matrix；LB is original boundaries load bus；LE is original outer net load bus；GE is pristine outside network power machine node；YLG For in primitive network, using load bus as corresponding row, generator node is as respective column, to the admittance submatrix generated；
2.2) according to constant matrices C, constant matrices F and constant matrices D, the voltage U of the equivalence generator nodeGeqFollowing institute Show：
In formula,For outer net generator power matrix SGEAdjoint matrix；Matrix C, matrix F and matrix D are respectively the normal of setting Matrix number；ULBFor original boundaries network voltage；
3) equivalent generator output S is calculatedGeq；Equivalent generator output SGeqAs follows：
In formula, IGeq_diagFor by IGeqDiagonal matrix as the elements in a main diagonal；For the diagonal matrix IGeq_diag Adjoint matrix；UGEQFor the voltage of equivalent generator node；
4) according to equivalent generator output SGeqWith equivalent generator power SGE, obtain equivalent generator output SGeqIt generates electricity with equivalence Acc power SGEParsing relationship：
In formula, Matrix C, matrix F and matrix D are respectively the constant matrices set；For the diagonal matrix IGeq_diag Adjoint matrix；ULBFor original boundaries network voltage；For outer net generator power matrix SGEAdjoint matrix；
5) according to equivalent generator output SGeqWith equivalent generator power SGEParsing relationship, obtain equivalent generated power work( Rate PGeq；Key step is as follows：
5.1) setting intermediate parameters H1, intermediate parameters H2, intermediate parameters H21, intermediate parameters H22, intermediate parameters H23, intermediate parameters H24, intermediate parameters H25With intermediate parameters H26；
The intermediate parameters H1As follows：
H1=IGeq_diag_realCreal+IGeq_diag_imagCimag； (32)
In formula, IGeq_diag_realFor by IGeqDiagonal matrix I as the elements in a main diagonalGeq_diagThe square that the real part of element is constituted Battle array；IGeq_diag_imagFor by IGeqDiagonal matrix I as the elements in a main diagonalGeq_diagThe matrix that the imaginary part of element is constituted；Creal The matrix constituted for the real part of constant matrices C element；CimagThe matrix constituted for the imaginary part of constant matrices C element；
The intermediate parameters H21As follows：
H21=-IGeq_diag_realCimag-IGeq_diag_imagCreal； (33)
In formula, IGeq_diag_realFor by IGeqDiagonal matrix I as the elements in a main diagonalGeq_diagThe square that the real part of element is constituted Battle array；IGeq_diag_imagFor by IGeqDiagonal matrix I as the elements in a main diagonalGeq_diagThe matrix that the imaginary part of element is constituted；Creal The matrix constituted for the real part of constant matrices C element；CimagThe matrix constituted for the imaginary part of constant matrices C element；
The intermediate parameters H22As follows：
In formula, YGG(GE)(GE)_realIt is constituted for the real part of the corresponding admittance block matrix elements of generator node in pristine outside network Matrix；YGG(GE)(GE)_imagFor the corresponding admittance block matrix elements of generator node in pristine outside network imaginary part constitute Matrix；UGE_imagFor pristine outside network power machine node voltage UGEImaginary part；UGE_realFor pristine outside network power machine section Point voltage UGEReal part；ULE_realFor pristine outside network node voltage ULEReal part；ULE_imagFor pristine outside network node Voltage ULEImaginary part；YGL(GE)(LE)_imagFor admittance submatrix YGL(GE)(LE)The matrix that the imaginary part of element is constituted；YGL(GE)(LE)_real For admittance submatrix YGL(GE)(LE)The matrix that the real part of element is constituted；
The intermediate parameters H23As follows：
In formula, YGG(GE)(GE)_realFor the corresponding admittance submatrix Y of generator node in pristine outside networkGG(GE)(GE)The reality of element The matrix that portion is constituted；YGG(GE)(GE)_imagFor the corresponding admittance submatrix Y of generator node in pristine outside networkGG(GE)(GE)Member The matrix that the imaginary part of element is constituted；UGE_imagFor pristine outside network power machine node voltage UGEImaginary part；UGE_realIt is original outer Portion network power machine node voltage UGEReal part；ULE_realFor pristine outside network node voltage ULEReal part；ULE_imagFor original Beginning external network node voltage ULEImaginary part；YGL(GE)(LE)_imagFor admittance submatrix YGL(GE)(LE)The square that the imaginary part of element is constituted Battle array；YGL(GE)(LE)_realFor admittance submatrix YGL(GE)(LE)The matrix that the real part of element is constituted；
The intermediate parameters H24As follows：
H24=-IGeq_diag_realFreal+IGeq_diag_imagFimag； (36)
In formula, IGeq_diag_realFor by IGeqDiagonal matrix I as the elements in a main diagonalGeq_diagThe square that the real part of element is constituted Battle array；IGeq_diag_imagFor by IGeqDiagonal matrix I as the elements in a main diagonalGeq_diagThe matrix that the imaginary part of element is constituted；Freal The matrix constituted for the real part of constant matrices F elements；FimagThe matrix constituted for the imaginary part of constant matrices F elements；
The intermediate parameters H25As follows：
H25=IGeq_diag_realFimag-IGeq_diag_imagFreal； (37)
In formula, IGeq_diag_realFor by IGeqDiagonal matrix I as the elements in a main diagonalGeq_diagThe square that the real part of element is constituted Battle array；IGeq_diag_imagFor by IGeqDiagonal matrix I as the elements in a main diagonalGeq_diagThe matrix that the imaginary part of element is constituted；Freal The matrix constituted for the real part of constant matrices F elements；FimagThe matrix constituted for the imaginary part of constant matrices F elements；
The intermediate parameters H26As follows：
H26=-IGeq_diag_realDreal-IGeq_diag_imagDimag； (38)
In formula, IGeq_diag_realFor by IGeqDiagonal matrix I as the elements in a main diagonalGeq_diagThe square that the real part of element is constituted Battle array；IGeq_diag_imagFor by IGeqDiagonal matrix I as the elements in a main diagonalGeq_diagThe matrix that the imaginary part of element is constituted；Dreal The matrix constituted for the real part of constant matrices D elements；DimagThe matrix constituted for the imaginary part of constant matrices D elements；
In formula, H21、H22、H23、H24、H25And H26The intermediate parameters respectively set；YGL(GE)(LB)_imagFor admittance submatrix YGL(GE)(LB)The matrix that the imaginary part of element is constituted；YGL(GE)(LB)_realFor admittance submatrix YGL(GE)(LB)The square that the real part of element is constituted Battle array；UGE_diag_realExpression the elements in a main diagonal is external network generator node voltage UGEDiagonal matrix UGE_diagElement The matrix that real part is constituted；UGE_diag_imagExpression the elements in a main diagonal is external network generator node voltage UGEDiagonal matrix UGE_diagThe matrix that the imaginary part of element is constituted；ULB_imagFor original boundaries network node voltage ULBImaginary part；ULB_realFor original side Boundary network node voltage ULBReal part；
5.2) according to the intermediate parameters H of setting1, intermediate parameters H2, intermediate parameters H21, intermediate parameters H22, intermediate parameters H23, it is intermediate Parameter H24, intermediate parameters H25With intermediate parameters H26, obtain equivalent generator active power PGeq；
The equivalence generator active power PGeqAs follows：
PGeq=H1PGE+H2； (40)
In formula, H1And H2The intermediate parameters respectively set；PGEFor equivalent external network node active power；
6) generator active power PGStatic frequency characteristic it is as follows：
PG=PGmax-KG_diag(f-fGmax)； (41)
In formula, PGFor by the active power output P of i-th of node generator under frequency fGiThe column vector of composition；PGmaxFor by i-th The maximum active power output P of node generatorGmaxiThe column vector of composition；KGFor by the work(frequency static characteristic system of i-th of node generator Number KGiThe column vector of composition；fGmaxFor the frequency inflection point f for no longer having when Primary frequency control ability by i-th of node generatorGmaxi The column vector of composition；F is frequency；KG_diagFor by work(frequency static characteristic COEFFICIENT KGMatrix as the elements in a main diagonal；
7) according to the division of internal network and external network, by generator active power PGIt divides as follows：
In formula, PGmax_GIFor the maximum active power output P of i-th of node generator of internal networkGmaxiThe column vector of composition；PGmax_GE For the maximum active power output P of i-th of node generator of external networkGmaxiThe column vector of composition；KG_GIFor i-th of section of internal network The work(frequency static characteristic COEFFICIENT K of point generatorGiThe column vector of composition；KG_GEIt is quiet for the work(frequency of i-th of node generator of external network Characteristic coefficient KGiThe column vector of composition；fGmax_GIWhen no longer there is Primary frequency control ability for i-th of node generator of internal network Frequency inflection point fGmaxiThe column vector of composition；fGmax_GEWhen indicating that no longer there is Primary frequency control ability by external network generator The column vector that frequency inflection point is constituted；F is frequency；PGIFor equivalent internal network generator active power；PGEFor equivalent external network Generator active power；
8) by the outer net generator active power P with static frequency characteristicGEIt substitutes into equivalent generator active power, to To the equivalent generated power output P with static frequency characteristicGeq；
The equivalent generated power output P with static frequency characteristicGeqAs follows：
PGeq=PGmax_eq-KGeqf'； (43)
In formula, column vector f' be made of state variable, that is, frequency f and PGeqSame dimensional vector；KGeqFor equivalent network generator Work(frequency static characteristic coefficient；PGmax_eqFor original outer net generator maximum active power output information PGmax_GEEquivalent information inside
Wherein, original outer net generator maximum active power output information PGmax_GEEquivalent information P insideGmax_eqAs follows：
PGmax_eq=H1PGmax_GE+H2+KGeqfGmax_GE； (44)
In formula, H1And H2The intermediate parameters respectively set；fGmax_GEWhen no longer to have Primary frequency control ability by external generator Frequency inflection point constitute column vector；KGeqFor equivalent network generator work(frequency static characteristic coefficient；
Equivalent network generator work(frequency static characteristic COEFFICIENT KGeqAs follows：
KGeq=H1KG_GE； (45)
In formula, KG_GEFor the work(frequency static characteristic COEFFICIENT K of i-th of node generator of external networkGiThe column vector of composition；H1For setting Intermediate parameters；KG_GEFor outer net generator work(frequency static characteristic coefficient.
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