CN105281326A - Slow coherency partition method considering damping influence of stator - Google Patents

Abstract

The invention discloses a slow coherency partition method considering a damping influence of a stator. The method comprises the following steps: step (1), establishing a linearized model of an electric power system; step (2), solving a characteristic root and a characteristic vector of a characteristic matrix K of the linearized model of the electric power system; step (3), selecting decision thresholds ep1 and ep2 and performing first partition; step (4), calculating a partition matrix L of each pre-partition and performing second partition. The slow coherency partition method considering the damping influence of the stator provided by the invention overcomes the problem of increasing space-time complexity of an algorithm when considering the damping effect of the stator, improves the accuracy of slow coherency partition and makes the calculation speed have a certain improvement.

Description

Consider the slow people having the same aspiration and interest partition method of stator damping effect

Technical field

The present invention relates to Simulating technique in Electric Power System, more particularly, relate to a kind of slow people having the same aspiration and interest partition method considering stator damping effect.

Background technology

In electric system simulation process, use dynamic equivalent technology can effectively reduce Transient-State Analysis of Power System calculate spent by time and internal memory.External system while reservation built-in system, can be divided into some subsystems, and replace with low dimension module by dynamic equivalent technology; It not only requires that the initial trend that must keep built-in system is constant, and must retain the original main behavioral characteristics of built-in system.

At present, dynamic equivalent technology can be divided into two large classes: coherency method and mode method method.Coherency method mainly contains Coherent Generator Group differentiation and people having the same aspiration and interest generator is polymerized two steps, and mode method method mainly contains model selection, model decoupling and sets up Equivalent Model.

The slow people having the same aspiration and interest zone method proposed based on singular perturbation principle belongs to the one of coherency method, and it need the characteristic value of computing system and characteristic vector, and the division in region and fault point have nothing to do.But this existing slow people having the same aspiration and interest method is when modeling, solves difficulty to reduce and calculate consuming time, have ignored the stator damping effect of generator.And real system is between age at failure, the stator damping effect of generator directly can affect oscillation amplitude and the frequency of oscillation of rotor angle swing curve, when the damping coefficient of each unit differs greatly, inherently affects the same tone between unit.

Summary of the invention

The object of the invention is to: a kind of slow people having the same aspiration and interest partition method considering stator damping effect is provided, solves the problem affecting same tone between unit when the damping coefficient of generating set differs greatly.

To achieve these goals, the invention provides a kind of slow people having the same aspiration and interest partition method considering stator damping effect, it comprises the steps:

A, set up electric power system inearized model

In power system modeling, generator adopts classical model, linearisation Jacobian matrix form after the Mathematical Modeling of electric power system adopts meritorious and reactive power flow decoupling zero represents, with power increment simulated disturbance, the second order differential equations that the Mathematical Modeling of electric power system is is unknown quantity with rotor angle deviation;

B, the characteristic root solving eigenmatrix K and characteristic vector

For solving system-wide Mathematical Modeling, need the characteristic value solving its eigenmatrix, but direct solution being more difficult, by adopting twice variable substitution method to second order differential equations, can indirectly being tried to achieve the solution of rotor angle deviation by the solution solving dummy argument.

C, selected decision threshold ep1 and ep2 value, carry out first time subregion

According to aforementioned modeling, D/M is only had just to have identical oscillation mode than identical unit.In practice, network system is between age at failure, and the oscillation mode that each unit has is all generally different, the oscillation characteristics of the more realistic electrical network of conclusion of improving one's methods.But this feature makes the method for the slow people having the same aspiration and interest method subdivision matrix subregion of tradition no longer applicable.In order to the energy continuation method subregion of subdivision matrix L, before asking for subdivision matrix, first can carry out once pre-subregion, set a certain threshold value ep1 and ep2, if generator i and generator j belongs to same pre-subregion, so should meet:

For the first time after subregion, think that the unit belonging to same pre-subregion has identical oscillation mode.

D, calculate each pre-subregion subdivision matrix L and carry out second time subregion

Utilizing the slow subdivision matrix L with readjusting the distribution of tradition to carry out secondary to each pre-subregion to hive off, obtaining final division result.

As a modification of the present invention, steps A specifically comprises the steps:

A1, set up generator model, if system has n node, m platform generator, its median generatrix 1 to bus m is generator bus, and bus m+1 to bus n is load bus.The rotor dynamical equation of employing generator classical model is:

(i＝1，2…m)；

A2, suppose that the admittance matrix of this n node system is Y _{n × n}.The reactance of i generator transient state is X ' _id, and X ' _idnode admittance battle array can be incorporated to, and the load of each node be turned to equivalent impedance Z simultaneously _l, be incorporated to admittance battle array.Node admittance battle array becomes Y _{(n+m) × (n+m)}.Linearisation Jacobian matrix form after the Mathematical Modeling of electric power system adopts meritorious and reactive power flow decoupling zero represents:

Wherein E ', δ, U, θ all get Load flow calculation and are worth accordingly, then H battle array is permanent.When normal undisturbed, Δ P _m=0, Δ P _l=0, the rotor angle deviation of each unit is zero.When system has a large disturbances, use Δ P _mand Δ P _lcarry out simulated disturbance.

A3, set up system-wide Mathematical Modeling.Definition matrix M and D as follows:

E _nfor N ties up unit square formation.Simultaneous formula (1) and formula (2) depression of order, cancellation Δ θ and Δ P _gcan obtain:

In formula

Q ^T＝[C ^T0]

A＝-M ^-1D

B＝-M ^-1H _GG+M ^-1H _GLH _LL ^-1H _LG

C＝M ^-1ΔP _m-M ^-1H _GLH _LL ^-1ΔP _L

If the characteristic value of direct solution eigenmatrix P can make algorithm complex increase.

As a modification of the present invention, step B specifically comprises the steps:

B1, adopt a variable substitution method to system-wide Mathematical Modeling, doing distortion can obtain

Its homogeneous equation is

Here notice that A battle array is a strict diagonal angle linear array.E and F is as follows for definition matrix:

Wherein a _icorresponding to the diagonal element of A battle array i-th row.For solving first adopt variable substitution method:

Above formula is substituted into formula :

Wherein

B2, again variable substitution method is adopted to system-wide Mathematical Modeling, is provided with column vector:

Wherein g _k=f _kand then simultaneous above formula and have:

Wherein

B3, the characteristic root being solved eigenmatrix P by indirect method and characteristic vector thereof:

If feature value vector and the characteristic equation of H battle array are respectively:

λ ^T＝[λ ₁…λ _2N]

|H-λe _2N|＝|K-λ ²e _N|＝0

The characteristic root of N to opposite number is each other had, if i-th characteristic root λ by the known H battle array of above formula _icharacter pair vector is ζ _i ^t=[ζ _{1, i}ζ _{2N, i}].In addition, i-th characteristic root λ is defined _icorresponding shrinkage characteristic vector is

Formula formula formula general solution expression formula be respectively:

C _iit is the integral constant that i-th characteristic root is corresponding.Formula particular solution and general solution be respectively into:

Δδ _t＝-B ^-1C

Asking for i-th characteristic root λ _icharacteristic of correspondence vector is ζ _itime, need solve an equation (H-λ _ie _2N) ζ _i=0, ζ in formula _iit is 2N dimensional vector; Elementary transformation is done to this formula, can ζ be obtained _{k+N, i}=λ _iζ _{k, i}(i=1,2 ... 2N; K=1,2 ... N, wherein ζ k, i can be solved by equation K-λ i2eN ζ i '=0.Have the characteristic root of N to opposite number each other by known H battle array above, the characteristic vector corresponding to characteristic root of opposite number also has certain symmetry so each other, so the N stack features vector that need only solve wherein just directly can draw other N stack features vector.If λ _mwith λ _nbe the characteristic root of a pair opposite number each other, so both corresponding characteristic vectors have following relation:

ζ _i，m＝ζ _i，n，ζ _i+N，m＝-ζ _i+N，n(i＝1，2…N)

In summary, as long as solve characteristic root and the characteristic vector thereof of N rank eigenmatrix K, just can draw characteristic root and the characteristic vector thereof of corresponding 2N rank eigenmatrix P, its algorithm complex is suitable with tradition slow people having the same aspiration and interest method.

As a modification of the present invention, step C specifically comprises the steps:

C1, selected decision threshold ep1 and ep2 value.Land use models analytic approach identified region oscillation mode and the traditional slow people having the same aspiration and interest method of excitation Correlation oscillation pattern think that the same tone of generator is by the impact of position of failure point and fault type, and have ignored the effect of stator damping effect, in its conclusion, every platform generator all has identical oscillation mode.But from step B, in the conclusion of improving one's methods gained, the oscillation mode of each generator may be no longer identical, only has D/M just to have identical oscillation mode than identical unit.In practice, network system is between age at failure, and the oscillation mode that each unit has is all generally different, the oscillation characteristics of the more realistic electrical network of conclusion of improving one's methods.But this feature makes the method for the slow people having the same aspiration and interest method subdivision matrix subregion of tradition no longer applicable.In order to the energy continuation method subregion of subdivision matrix L, before asking for subdivision matrix, first can carry out once pre-subregion, set a certain threshold value ep1 and ep2;

If C2 generator i and generator j belongs to same pre-subregion, so should meet:

As a modification of the present invention, step D specifically comprises the steps:

After D1, for the first time subregion, think that the unit belonging to same pre-subregion has identical oscillation mode, so just the unit subdivision matrix method in same pre-subregion can be hived off when second time subregion again, just can obtain people having the same aspiration and interest unit division result finally.Suppose that the pre-subregion of kth group has s platform generator, need to be divided into r group people having the same aspiration and interest unit, V _scharacteristic vector corresponding to r the characteristic value minimum by eigenmatrix K absolute value formed, that is:

V _S＝[ζ′ ₁ζ′ ₂...ζ′ _r]＝[V ₁V ₂...V _S] ^T

V _irepresent V _sthe i-th every trade vector, be the Oscillatory mode shape vector that in this pre-subregion, i-th generator is corresponding.

The key of D2, second time subregion is from V _sin find out r group the most linear independence Oscillatory mode shape vector, as the reference vector of subregion, by V _sresequence as follows:

V _S＝[V _referenceV _{non-reference}] ^T

V _referencebe made up of the Oscillatory mode shape vector of r group linear independence the most, all the other vector compositions V _{non-reference}.To V _sdo distortion can obtain:

If positive element maximum in subdivision matrix L i-th row element is L _{i, j}, so i-th generator should be classified as one group with jth platform with reference to generator.

Compared with prior art, the present invention considers the problem that the Space Time complexity that the slow people having the same aspiration and interest partition method of stator damping effect overcomes the algorithm when considering stator damping effect increases, improve the accuracy of slow people having the same aspiration and interest subregion, and computational speed is improved.

Accompanying drawing explanation

Below in conjunction with the drawings and specific embodiments, structure of the present invention and Advantageous Effects thereof are described in detail.

Fig. 1 is the slow people having the same aspiration and interest partition method FB(flow block) that the present invention considers stator damping effect.

Fig. 2 is the topological diagram of embodiment of the present invention IEEE-39 node system.

Embodiment

In order to make goal of the invention of the present invention, technical scheme and Advantageous Effects thereof more clear, below in conjunction with the drawings and specific embodiments, the present invention is further elaborated.Should be understood that, the embodiment described in this specification is only used to explain the present invention, is not intended to limit the present invention.

Refer to Fig. 1 and Fig. 2, the present invention is with IEEE-39 node standard example system for example is demonstrated, and the present invention considers that the slow people having the same aspiration and interest partition method of stator damping effect comprises the steps:

A, set up electric power system inearized model

In power system modeling, generator adopts classical model, linearisation Jacobian matrix form after the Mathematical Modeling of electric power system adopts meritorious and reactive power flow decoupling zero represents, with power increment simulated disturbance, the second order differential equations that the Mathematical Modeling of electric power system is is unknown quantity with rotor angle deviation;

The concrete practice setting up system model is:

A1, set up generator model, system has 39 nodes, 10 generators, and its median generatrix 1 to bus 10 is generator bus, and bus 11 to bus 39 is load buses.The rotor dynamical equation of employing generator classical model is:

The admittance matrix of A2,39 node systems is Y _{39 × 39}.The reactance of i generator transient state is X ' _id, and X ' _idnode admittance battle array can be incorporated to, and the load of each node be turned to equivalent impedance Z simultaneously _l, be incorporated to admittance battle array.Node admittance battle array becomes Y _{(49) × (49)}.Linearisation Jacobian matrix form after the Mathematical Modeling of electric power system adopts meritorious and reactive power flow decoupling zero represents:

Wherein E ', δ, U, θ all get Load flow calculation and are worth accordingly, then H battle array is permanent.When normal undisturbed, Δ P _m=0, Δ P _l=0, the rotor angle deviation of each unit is zero.When system has a large disturbances, use Δ P _mand Δ P _lcarry out simulated disturbance.

A3, set up system-wide Mathematical Modeling.Definition matrix M and D as follows:

E _nfor N ties up unit square formation.Simultaneous formula (1) and formula (2) depression of order, cancellation Δ θ and Δ P _gcan obtain:

In formula

Q ^T＝[C ^T0]

A＝-M ^-1D

B＝-M ^-1H _GG+M ^-1H _GLH _LL ^-1H _LG

C＝M ^-1ΔP _m-M ^-1H _GLH _LL ^-1ΔP _L

If the characteristic value of direct solution eigenmatrix P can make algorithm complex increase.

B, the characteristic root solving eigenmatrix K and characteristic vector

For solving system-wide Mathematical Modeling, need the characteristic value solving its eigenmatrix, but direct solution being more difficult, by adopting twice variable substitution method to second order differential equations, can indirectly being tried to achieve the solution of rotor angle deviation by the solution solving dummy argument.

Solve characteristic root and the characteristic vector of eigenmatrix K, the concrete practice is as follows:

B1, adopt a variable substitution method to system-wide Mathematical Modeling, doing distortion can obtain

Its homogeneous equation is

Here notice that A battle array is a strict diagonal angle linear array.E and F is as follows for definition matrix:

Wherein a _icorresponding to the diagonal element of A battle array i-th row.For solving first adopt variable substitution method:

Above formula is substituted into formula :

Wherein

B2, again variable substitution method is adopted to system-wide Mathematical Modeling, is provided with column vector:

Wherein g _k=f _kand then simultaneous above formula and have:

Wherein

B3, the characteristic root being solved eigenmatrix P by indirect method and characteristic vector thereof:

If feature value vector and the characteristic equation of H battle array are respectively:

λ ^T＝[λ ₁…λ _2N]

|H-λe _2N|＝|K-λ ²e _N|＝0

The characteristic root of N to opposite number is each other had, if i-th characteristic root λ by the known H battle array of above formula _icharacter pair vector is ζ _i ^t=[ζ _{1, i}ζ _{2N, i}].In addition, i-th characteristic root λ is defined _icorresponding shrinkage characteristic vector is

Formula formula formula general solution expression formula be respectively:

C _iit is the integral constant that i-th characteristic root is corresponding.Formula particular solution and general solution be respectively into:

Δδ _t＝-B ^-1C

Asking for i-th characteristic root λ _icharacteristic of correspondence vector is ζ _itime, need solve an equation (H-λ _ie _2N) ζ _i=0, ζ in formula _iit is 2N dimensional vector; Elementary transformation is done to this formula, can ζ be obtained _{k+N, i}=λ _iζ _{k, i}(i=1,2 ... 2N; K=1,2 ... N, wherein ζ k, i can be solved by equation K-λ i2eN ζ i '=0.Have the characteristic root of N to opposite number each other by known H battle array above, the characteristic vector corresponding to characteristic root of opposite number also has certain symmetry so each other, so the N stack features vector that need only solve wherein just directly can draw other N stack features vector.If λ _mwith λ _nbe the characteristic root of a pair opposite number each other, so both corresponding characteristic vectors have following relation:

ζ _i，m＝ζ _i，n，ζ _i+N，m＝-ζ _i+N，n(i＝1，2…N)

In summary, as long as solve characteristic root and the characteristic vector thereof of N rank eigenmatrix K, just can draw characteristic root and the characteristic vector thereof of corresponding 2N rank eigenmatrix P, its algorithm complex is suitable with tradition slow people having the same aspiration and interest method.

The packet count of selected each pre-subregion is 2, and calculated characteristics matrix K also solves its feature value vector and is:

λ ^T＝[-0.6144-0.3125-0.2145-0.1171-0.1109

-0.0582-0.0251-0.0282-0.0884]

C, selected decision threshold ep1 and ep2 value, carry out first time subregion

The concrete practice of carrying out first time subregion is as follows:

C1, selected decision threshold ep1 and ep2 value, choose ep1 and ep2 according to operating experience and be respectively 0.0001,0.04.Land use models analytic approach identified region oscillation mode and the traditional slow people having the same aspiration and interest method of excitation Correlation oscillation pattern think that the same tone of generator is by the impact of position of failure point and fault type, and have ignored the effect of stator damping effect, in its conclusion, every platform generator all has identical oscillation mode.But from step B, in the conclusion of improving one's methods gained, the oscillation mode of each generator may be no longer identical, only has D/M just to have identical oscillation mode than identical unit.In practice, network system is between age at failure, and the oscillation mode that each unit has is all generally different, the oscillation characteristics of the more realistic electrical network of conclusion of improving one's methods.But this feature makes the method for the slow people having the same aspiration and interest method subdivision matrix subregion of tradition no longer applicable.In order to the energy continuation method subregion of subdivision matrix L, before asking for subdivision matrix, first can carry out once pre-subregion, set a certain threshold value ep1 and ep2;

The D/M when Δ δ of each unit of table 1 _t

If C2 generator i and generator j belongs to same pre-subregion, so should meet:

The result of subregion is as shown in table 2 for the first time.

The pre-partitioning scenario of table 2

D, calculate each pre-subregion subdivision matrix L and carry out second time subregion

Utilizing the slow subdivision matrix L with readjusting the distribution of tradition to carry out secondary to each pre-subregion to hive off, obtaining final division result.

The concrete practice of carrying out second time subregion is as follows:

After D1, for the first time subregion, think that the unit belonging to same pre-subregion has identical oscillation mode, so just the unit subdivision matrix method in same pre-subregion can be hived off when second time subregion again, just can obtain people having the same aspiration and interest unit division result finally.Suppose that the pre-subregion of kth group has s platform generator, need to be divided into r group people having the same aspiration and interest unit, V _scharacteristic vector corresponding to r the characteristic value minimum by eigenmatrix K absolute value formed, that is:

V _S＝[ζ′ ₁ζ′ ₂...ζ′ _r]＝[V ₁V ₂...V _S] ^T

V _irepresent V _sthe i-th every trade vector, be the Oscillatory mode shape vector that in this pre-subregion, i-th generator is corresponding.

The key of D2, second time subregion is from V _sin find out r group the most linear independence Oscillatory mode shape vector, as the reference vector of subregion, by V _sresequence as follows:

V _S＝[V _referenceV _{non-reference}] ^T

V _referencebe made up of the Oscillatory mode shape vector of r group linear independence the most, all the other vector compositions V _{non-reference}.To V _sdo distortion can obtain:

If positive element maximum in subdivision matrix L i-th row element is L _{i, j}, so i-th generator should be classified as one group with jth platform with reference to generator.

In value indicative vector

λ ^T＝[-0.6144-0.3125-0.2145-0.1171-0.1109

-0.0582-0.0251-0.0282-0.0884]

Minimum two characteristic values of absolute value are-0.0251 and-0.0282 respectively, and it corresponds respectively to two of original system oscillation modes at a slow speed: with the V that first pre-subregion is corresponding _sfor:

Analyze the linear dependence of each unit Oscillatory mode shape vector, final selected BUS1 and BUS8 unit, as reference unit, can obtain corresponding subdivision matrix as follows:

Visible, in the row vector that BUS2 and BUS3 unit is corresponding, maximum positive element is respectively 0.8701 and 0.8182, and it is all corresponding to BUS8 reference unit, and namely BUS2 and BUS3 unit should be classified as same subregion with BUS8 reference unit.The V that second pre-subregion is corresponding _sfor:

In like manner, BUS4 and BUS9 unit can be selected as reference unit, corresponding subdivision matrix can be obtained as follows:

In like manner, known through contrasting, BUS5 and BUS6 unit should be classified as same subregion with BUS4 reference unit, and BUS6 unit should be classified as same subregion with BUS9 reference unit.So far, second time division result is as shown in table 3, is consistent with the result obtained by Based on Power System Analysis Software Package (PSD-BPA) simulation calculation.

The final partitioning scenario of table 3

The announcement of book and instruction according to the above description, those skilled in the art in the invention can also carry out suitable change and amendment to above-mentioned execution mode.Therefore, the present invention is not limited to embodiment disclosed and described above, also should fall in the protection range of claim of the present invention modifications and changes more of the present invention.In addition, although employ some specific terms in this specification, these terms just for convenience of description, do not form any restriction to the present invention.

Claims (5)

1. consider a slow people having the same aspiration and interest partition method for stator damping effect, it is characterized in that, the method comprises the steps:

(1) electric power system inearized model is set up;

(2) characteristic root and the characteristic vector of the eigenmatrix K of described electric power system inearized model is solved;

(3) selected decision threshold ep1 and ep2 value, carry out first time subregion;

(4) calculate the subdivision matrix L of each pre-subregion and carry out second time subregion.

2. the slow people having the same aspiration and interest partition method of consideration stator damping effect according to claim 1, is characterized in that, described step (1) comprises the steps:

(101) generator model is set up, if system has n node, m platform generator, its median generatrix 1 to bus m is generator bus, and bus m+1 to bus n is load bus, and the rotor dynamical equation of employing generator classical model is:

$M_i\mathrm{\Δ}{\stackrel{\·\·}{\mathrm{\δ}}}_i={\mathrm{\ΔP}}_{mi}-{\mathrm{\ΔP}}_{Gi}-D_i\mathrm{\Δ}{\stackrel{\·}{\mathrm{\δ}}}_i$

(i＝1,2…m)；

(102) suppose that the admittance matrix of this n node system is Y _{n × n}, the reactance of i generator transient state is X ' _id, and X ' _idnode admittance battle array can be incorporated to, and the load of each node be turned to equivalent impedance Z simultaneously _l, be incorporated to admittance battle array, node admittance battle array becomes Y _{(n+m) × (n+m)}, the linearisation Jacobian matrix form after the Mathematical Modeling of electric power system adopts meritorious and reactive power flow decoupling zero represents:

$\left[\begin{array}{c}{\mathrm{\ΔP}}_G\\ {\mathrm{\ΔP}}_L\end{array}\right]\≈\left[\begin{array}{cc}\frac{\∂P_G}{\∂\mathrm{\δ}}& \frac{\∂P_G}{\∂\mathrm{\θ}}\\ \frac{\∂P_L}{\∂\mathrm{\δ}}& \frac{\∂P_L}{\∂\mathrm{\θ}}\end{array}\right]\left[\begin{array}{c}\mathrm{\Δ}\mathrm{\δ}\\ \mathrm{\Δ}\mathrm{\θ}\end{array}\right]\stackrel{def}{=}\left[\begin{array}{cc}{H}_{GG}& H_{GL}\\ H_{LG}& H_{LL}\end{array}\right]\left[\begin{array}{c}\mathrm{\Δ}\mathrm{\δ}\\ \mathrm{\Δ}\mathrm{\θ}\end{array}\right]$

Wherein E ', δ, U, θ all get Load flow calculation and are worth accordingly, then H battle array is permanent, when normal undisturbed, and Δ P _m=0, Δ P _l=0, the rotor angle deviation of each unit is zero, when system has a large disturbances, uses Δ P _mand Δ P _lcarry out simulated disturbance;

(103) set up system-wide Mathematical Modeling, definition matrix M and D as follows:

E _nfor N ties up unit square formation, cancellation Δ θ and Δ P _gcan obtain:

$\stackrel{\·}{X}=PX+Q$

In formula $P=\left[\begin{array}{cc}A& B\\ E_N& 0\end{array}\right]$

Q ^T＝[C ^T0]

A＝-M ^-1D

B＝-M ^-1H _GG+M ^-1H _GLH _LL ^-1H _LG

C＝M ^-1ΔP _m-M ^-1H _GLH _LL ^-1ΔP _L

${\stackrel{\·}{X}}^T=\left(\begin{array}{cccccc}\stackrel{\·\·}{{\mathrm{\Δ\δ}}_1}& \mathrm{...}& \stackrel{\·\·}{{\mathrm{\Δ\δ}}_N}& \stackrel{\·}{{\mathrm{\Δ\δ}}_1}& \mathrm{...}& \stackrel{\·}{{\mathrm{\Δ\δ}}_N}\end{array}\right)$

$X^T=\left(\begin{array}{cccccc}\stackrel{\·}{{\mathrm{\Δ\δ}}_1}& \mathrm{...}& \stackrel{\·}{{\mathrm{\Δ\δ}}_N}& {\mathrm{\Δ\δ}}_1& \mathrm{...}& {\mathrm{\Δ\δ}}_N\end{array}\right).$

3. the slow people having the same aspiration and interest partition method of consideration stator damping effect according to claim 2, is characterized in that, described step (2) comprises the steps:

(201) adopt a variable substitution method to system-wide Mathematical Modeling, doing distortion can obtain

$\stackrel{\·\·}{\mathrm{\Δ}\mathrm{\δ}}-A\·\stackrel{\·}{\mathrm{\Δ}\mathrm{\δ}}-B.\mathrm{\Δ}\mathrm{\δ}-C=0$

Its homogeneous equation is

$\stackrel{\·\·}{\mathrm{\Δ}\mathrm{\δ}}-A\·\stackrel{\·}{\mathrm{\Δ}\mathrm{\δ}}-B\·\mathrm{\Δ}\mathrm{\δ}=0$

A battle array is a strict diagonal angle linear array, E and F is as follows for definition matrix:

Wherein a _icorresponding to the diagonal element of A battle array i-th row, for solving first adopt variable substitution method:

$\left\{\begin{array}{c}\mathrm{\Δ}\mathrm{\δ}=EF\\ \stackrel{\·\·}{\mathrm{\Δ}\mathrm{\δ}}==E\stackrel{\·}{F}+\frac{1}{2}AEF\\ \stackrel{\·\·}{\mathrm{\Δ}\mathrm{\δ}}=E\stackrel{\·\·}{F}+AE\stackrel{\·}{F}+\frac{1}{4}{A}^{2}EF\end{array}\right.$

Above formula is substituted into formula $\stackrel{\·\·}{\mathrm{\Δ}\mathrm{\δ}}-A\·\stackrel{\·}{\mathrm{\Δ}\mathrm{\δ}}-B\·\mathrm{\Δ}\mathrm{\δ}=0$ :

$\stackrel{\·\·}{F}=KF$

Wherein $K=\frac{1}{4}{A}^2-B;$

(202) again variable substitution method is adopted to system-wide Mathematical Modeling, is provided with column vector:

$\left\{\begin{array}{c}G=\left(\begin{array}{ccc}{g}_1& \mathrm{...}& g_{2N}\end{array}\right)\\ \stackrel{\·}{G}=\left(\begin{array}{ccc}{\stackrel{\·}{g}}_1& \mathrm{...}& {\stackrel{\·}{g}}_{2N}\end{array}\right)\end{array}\right.$

Wherein g _k=f _kand ${\stackrel{\·}{g}}_k={\stackrel{\·}{f}}_k=g_{k+N},(k=1,2...N),$ Then simultaneous above formula and $\stackrel{\·\·}{F}=KF$ Have:

$\stackrel{\·}{G}=HG$

Wherein $H=\left[\begin{array}{cc}0& e_N\\ K& 0\end{array}\right];$

(203) characteristic root and the characteristic vector thereof of eigenmatrix P is solved by indirect method:

If feature value vector and the characteristic equation of H battle array are respectively:

λ ^T＝[λ ₁…λ _2N]

|H-λe _2N|＝|K-λ ²e _N|＝0

The characteristic root of N to opposite number is each other had, if i-th characteristic root λ by the known H battle array of above formula _icharacter pair vector is ζ _i ^t=[ζ _{1, i}ζ _{2N, i}], meanwhile, define i-th characteristic root λ _icorresponding shrinkage characteristic vector is ζ ' _i ^t=[ζ _{1, i}ζ _n,i],

Formula $\stackrel{\·}{G}=HG,$ Formula $\stackrel{\·\·}{F}=KF,$ Formula $\stackrel{\·\·}{\mathrm{\Δ}\mathrm{\δ}}-A\·\stackrel{\·}{\mathrm{\Δ}\mathrm{\δ}}-B\·\mathrm{\Δ}\mathrm{\δ}=0$ General solution expression formula be respectively:

$G=\underset{i=1}{\overset{2N}{\Σ}}{C}_i{\mathrm{\ζ}}_i{e}^{{\mathrm{\λ}}_{i}t}$

$F=\underset{i=1}{\overset{N}{\Σ}}{C}_i{\mathrm{\ζ}}_i^{\′}{e}^{{\mathrm{\λ}}_{i}t}$

$\mathrm{\Δ}\mathrm{\δ}=E\underset{i=1}{\overset{2N}{\Σ}}{C}_i{\mathrm{\ζ}}_i^{\′}{e}^{{\mathrm{\λ}}_{i}t}$

C _ibe the integral constant that i-th characteristic root is corresponding, formula particular solution and general solution be respectively:

Δδ _t＝-B ^-1C

$\mathrm{\Δ}\mathrm{\δ}=E\underset{i=1}{\overset{2N}{\Σ}}{C}_i{\mathrm{\ζ}}_i^{\′}{e}^{{\mathrm{\λ}}_{i}t}{\mathrm{\Δ\δ}}_t$

Asking for i-th characteristic root λ _icharacteristic of correspondence vector is ζ _itime, solve an equation (H-λ _ie _2N) ζ _i=0, ζ in formula _iit is 2N dimensional vector; Elementary transformation is done to this formula, can ζ be obtained _{k+N, i}=λ _iζ _k,i(i=1,2 ... 2N; K=1,2 ... N, wherein ζ k, i can be solved by equation K-λ i2eN ζ i '=0, if λ m and λ n is the characteristic root of a pair opposite number each other, so both corresponding characteristic vectors have following relation:

ζ _i,m＝ζ _i,n，ζ _i+N,m＝-ζ _i+N,n(i＝1,2…N)

Solve characteristic root and the characteristic vector thereof of N rank eigenmatrix K, just can draw characteristic root and the characteristic vector thereof of corresponding 2N rank eigenmatrix P.

4. the slow people having the same aspiration and interest partition method of consideration stator damping effect according to claim 3, is characterized in that, described step (3) comprises the steps:

(301) before asking for subdivision matrix, first carry out once pre-subregion, set a certain threshold value ep1 and ep2;

(302) if generator i and generator j belongs to same pre-subregion, so should meet:

$\{\begin{array}{c}\left|a_i-a_j\right|\≤ep1\\ \left|{\mathrm{\δ}}_{ti}-{\mathrm{\δ}}_{tj}\right|\≤ep2\end{array}.$

5. the slow people having the same aspiration and interest partition method of consideration stator damping effect according to claim 4, is characterized in that, described step (4) comprises the steps:

(401), after first time subregion, think that the unit belonging to same pre-subregion has identical oscillation mode, when second time subregion, the unit subdivision matrix method in same pre-subregion is hived off again; Suppose that the pre-subregion of kth group has s platform generator, need to be divided into r group people having the same aspiration and interest unit, V _scharacteristic vector corresponding to r the characteristic value minimum by eigenmatrix K absolute value formed, that is:

V _S＝[ζ′ ₁ζ′ ₂...ζ′ _r]＝[V ₁V ₂...V _s] ^T

V _irepresent V _sthe i-th every trade vector, be the Oscillatory mode shape vector that in this pre-subregion, i-th generator is corresponding;

(402) from V _sin find out r group the most linear independence Oscillatory mode shape vector, as the reference vector of subregion, by V _sresequence as follows:

V _S＝[V _referenceV _{non-reference}] ^T

V _referencebe made up of the Oscillatory mode shape vector of r group linear independence the most, all the other vector compositions V _{non-reference}, to V _sdo distortion can obtain:

$\left[\begin{array}{c}{V}_{reference}\\ V_{non-reference}\end{array}\right]V_{reference}^{-1}=\left[\begin{array}{c}I\\ L\end{array}\right]$

If positive element maximum in subdivision matrix L i-th row element is L _i,j, so i-th generator and jth platform are classified as one group with reference to generator.