CN105977969A - Large-scale multi-time-lag power system stability judgment method based on SOD-LMS (Solution Operator Discretization-Linear MultiStep) - Google Patents

Abstract

The invention discloses a large-scale multi-time-lag power system stability judgment method based on SOD-LMS (Solution Operator Discretization-Linear MultiStep). The method comprises the following steps: establishing a time-lag power system model; converting an characteristic value problem of the time-lag power system during solving into a spectrum problem of a solved operator T(h) according to the mapping relation between a time-lag power system characteristic value and an operator characteristic value; carrying out discretization on the operator T(h) by using a linear multistep method, and reasonably selecting a transfer step length h to obtain a discretization matrix TN capable of accurately judging the stability of the time-lag power system; calculating a set number of characteristic values with the maximum modulus value of the discretization matrix TN by using a sequential method or a space method (such as an implicit restarted Arnoldi algorithm); and converting the characteristic value of the discretization matrix TN into the characteristic value when the time-lag power system is positioned on the rightmost side of a complex plane according to the mapping relation of the spectrum for judging the small-interference stability of a large-scale multi-time-lag power system. When the SOD-LMS method provided by the invention is used for calculating the key characteristic value of a real system and the stability of a judgment system, the scale of the real system and the influence of communication time-lag are fully taken into account.

Description

Extensive stability of muilt-timelag electric power system method of discrimination based on SOD-LMS

Technical field

The present invention relates to stability of power system analysis field, be specifically related to a kind of based on SOD-LMS extensive many time Stagnant stability of power system method of discrimination, SOD-LMS is " Solution Operator Discretization-Linear MultiStep " abbreviation, Chinese implication: Solution operator linear multi step discretization.

Background technology

Along with the continuous growth of the energy and electricity needs, set up since transregional, transnational large-scale interconnected power system is 21 century The new stage of electric power development.But at the interconnection initial stage, complicated electrical structure and weak transmission of electricity link make interconnected network more Easily low-frequency oscillation between region.Relatively for local oscillation, the coverage of inter-area oscillations is wide, participates in the machine of vibration Electrical link between Qun is sufficiently complex, and the impact on the stability of extensive interconnected network is the most prominent.It is defeated with local signal The power system stabilizer, PSS (Power System Stabilizer, PSS) entered can preferably be calmed local oscillation pattern, but It is to be difficult to calm down inter-area oscillation mode, thus is difficult to ensure that the stability of extensive interconnected network.

The appearance of WAMS (Wide-Area Measurement System, WAMS) and development so that use The overall situation, the information realization electric power system stability control of far-end be possibly realized, for suppress extensive interconnected network interregional low Frequency vibration is swung and is brought opportunity.WAMS is mainly made up of three parts: phasor measurement unit (Phasor Measurement Unit, PMU), communication network, and monitoring system.The PMU being positioned at plant stand utilizes global positioning system (Global Positioning System, GPS) high accurate clock signal, the quantity of state of synchro measure each pivot point of electrical network.By the height in communication system Speed communication channel when will post target metric data be sent to monitoring system, it is achieved the monitoring in real time, protect and control of power system System.Metric data in the real-time data base processed by analysis, can not only be used for the low-frequency oscillation letter detecting in power system Breath, moreover it is possible to provide the wide area feedback signal of low frequency oscillation mode between effective reflecting regional for damping controller.And then, optimal control The performance of device, promotes the ability of the gentle long-distance and large-capacity power transmission of damping water of system.

But, wide area measurement data are logical be made up of different communication medias (such as optical fiber, digital microwave, electric lines of force etc.) When communication system transmitting and processes, have tens and arrive the communication delay of change between hundreds of millisecond.Work as the complicated network structure, and transmission When data volume is big, Wide-area Measurement Information is actual present in the analyzing and processing of the collection of PMU, the conveying of communication network and monitoring system Time lag is often bigger than theoretical value.Time lag is to cause the inefficacy of system control law, operation conditions to deteriorate and a kind of weight of system unstability Want inducement.When time lag constant is bigger, system features value can occur relatively large deviation, even can change the small disturbance stability of system completely Property.In sum, when modern extensive interconnected network utilizes wide area measurement information to carry out power system closed loop control, it is necessary to meter and The impact of time lag.

After considering time-delay, the state of power system is not only relevant with the state of current time, additionally depends on system mistake The state gone.Therefore, the model of time-lag power system can describe with a Delay Differential-algebraic equation.With ordinary differential side System described by journey is different, and the solution space of the power system described by differential equations with delay is infinite dimensional.In a frequency domain, time Stagnant power system characteristic of correspondence equation, exists and surmounts item, has infinite multiple solution (eigenvalue).Accordingly, it is considered to after time-delay, The difficulty of stability of power system research is greatly increased.

At present, relate in the patent that time-lag power system small signal stability differentiates, Chinese invention patent one time lag electricity The stable method of discrimination .201010123345.8 [P] of Force system utilizes search method for tracing to determine the time lag stable region of system.So And, in said method, time lag eigenvalue solves bigger with the amount of calculation of search procedure.Chinese invention patent approximates based on Pad é Time-lag power system eigenvalue calculation and Convenient stable criterion .201210271783.8 [P]. approached by rational polynominal Time Delay, and then calculate the critical eigenvalue of the system rightmost side, and judge the time lag stability of system.But, said method The precision of accuracy and result of calculation need through analysing in depth and research.Chinese invention patent based on EIGD extensive time Stagnant power system eigenvalue calculation method .201510055743.3 [P]. propose a kind of discrete based on explicit infinitesimal generator Change the extensive time-lag power system of (Explicit Infinitesimal Generator Discretization, EIGD) Eigenvalue calculation method.Said method needs by Multiple-Scan [0.1,2.5] Hz low-frequency oscillation frequency range, near the imaginary axis Critical eigenvalue, the time lag stability of system could be judged.Chinese invention patent Power System Delay based on SOD-PS is steady Qualitative discrimination method .201510229738.X [P]. propose a kind of based on Solution operator puppet spectrum discretization (Solution Operator Discretization-Pseudospectral, SOD-PS) Power System Delay Convenient stable criterion.Should Method has only to calculate a maximum eigenvalue of Solution operator discretization matrix norm value or a pair Con-eigenvalue, it is possible to sentence Break the stability system under fixed time lag.But, the method, when calculating section critical eigenvalue, needs to ask for discretization Submatrix inverse, computationally intensive, to calculate the time long.

Summary of the invention

For solving the deficiency that prior art exists, the invention discloses extensive multiple time delay power train based on SOD-LMS System Convenient stable criterion, in order to quick and precisely to differentiate the small signal stability of extensive muilt-timelag electric power system.SOD-LMS side Method is not related to matrix inversion operation during calculating components of system as directed critical eigenvalue, and speed is fast, computational efficiency is high in calculating.With Time, the method only need to calculate the eigenvalue of the maximum setting number of Solution operator discretization matrix norm value, it becomes possible to accurately differentiates The stability of extensive muilt-timelag electric power system.

For achieving the above object, the concrete scheme of the present invention is as follows:

Extensive stability of muilt-timelag electric power system method of discrimination based on SOD-LMS, comprises the following steps:

S1: set up time-lag power system model；

S2: be the ordinary differential equation that Solution operator T (h) represents by the time-lag power system model conversion obtained in step S1 Initial-value problem；

S3: Solution operator T (h) in step S2 is carried out discretization, obtains the discretization matrix T of Solution operator_N；

S4: discretization matrix T in calculation procedure S3_NThe eigenvalue μ of the maximum setting number of modulus value；

S5: according to spectrum mapping relations, by the discretization matrix T in step S4_NEigenvalue μ be converted to time-lag power system Eigenvalue λ.

Further, in step one, the time-lag power system model of foundation: in the modeling of actual large-scale electrical power system During introduce Time Delay, obtain being applicable to the system model of time-lag power system analysis on Small Disturbance Stability, during with one group Stagnant differential equation group describes.

Further, obtain the characteristic equation of time-lag power system according to one group of time-delayed differential equations, and by time lag electricity The characteristic equation of Force system is expressed as augmentation form of equal value.

Further, in step 2, according to the mapping relations between time-lag power system eigenvalue and Solution operator eigenvalue, The eigenvalue problem solving time-lag power system is converted into the spectrum problem solving Solution operator T (h).

Further, Solution operator T (h): X → X is defined as the original state in the θ moment in space XWhen being mapped to h+ θ The linear operator of etching system state ψ；Wherein, h is transfer step-length, 0≤h≤τ_max；

Wherein: s is integration variable,WithIt is respectively the state of 0 and h+ θ moment time-lag power system；0<τ₁<τ₂ <…<τ_i…<τ_mFor the time lag constant of Time Delay, maximum of which time lag is τ_m=τ_max；For system mode matrix, It is a dense matrix,For system time lags state matrix, for sparse matrix；Δ x (s) is s moment system state variables Increment, Δ x (s-τ_i) it is s-τ_iThe increment of moment system state variables,Increasing for s moment system state variables derivative Amount.

Further, in step 3, utilize linear multistep method that Solution operator T (h) is carried out discretization, obtain accurately sentencing The discretization matrix T of other time-lag power system stability_N。

Further, corresponding with Solution operator T (h), discretization matrix T_NIt is expressed as follows:

T_NLast block row Γ be the coefficient matrix of polynomial eigenvalue problem, be specifically represented by:

$\mathrm{\&Gamma;}=R^{-1}\underset{i=0}{\overset{m}{\&Sigma;}}{w}_i\&CircleTimes;{\tilde{A}}_i$

In formula:K is the step number of linear multistep method, α_k, β_kFor the coefficient of linear multistep method,For Kronecker amasss computing,For system time lags state matrix, for sparse matrix,For middle and auxiliary vector.

Further, at the discretization matrix T that application Solution operator is corresponding_NSolve the eigenvalue of extensive time-lag power system Time, use sequential method or subspace method to calculate the eigenvalue of the maximum setting number of its modulus value.

Further, in step 4, particularly as follows: set the vector representation of k-th Krylov as q_K, then matrix-vector product q_K+1 =T_Nq_KFlow process as follows:

Step (4-1): from the direction of row, willBoil down to matrix WhereinJ=1 ..., L+k；L is discrete counting；

Step (4-2): q_K+1(1:(L+k-1) n, 1)=q_K((n+1):(L+k)n,1)；

Step (4-3): utilize the character of Kronecker product, calculates:

$\begin{array}{c}z=(\underset{i=0}{\overset{m}{\&Sigma;}}{w}_i\&CircleTimes;{\tilde{A}}_i)q_s=(\underset{i=0}{\overset{m}{\&Sigma;}}{w}_i\&CircleTimes;{\tilde{A}}_i)vec\left(P\right)\\ =vec\left(\underset{i=0}{\overset{m}{\&Sigma;}}{\tilde{A}}_i{\mathrm{Pw}}_i^T\right)\\ =vec(\underset{i=0}{\overset{m}{\&Sigma;}}{\tilde{A}}_i\&lsqb;p_1,\mathrm{...},p_{L+k}\&rsqb;w_i^T)\end{array}$

In formula: vec () is to be the computing of column vector by matrix compression；

Step (4-4): calculate q_K+1((L+k-1) n:(L+k) n, 1):

q_K+1((L+k-1) n+1:(L+k) n, 1)=(R)^-1z。

Further, discretization matrix T_NEigenvalue μ and the mapping relations of time-lag power system eigenvalue λ as follows:

$\mathrm{\&lambda;}=\frac{1}{h}ln\mathrm{\&mu;},\mathrm{\&mu;}\&Element;\mathrm{\&sigma;}\left(T\right(h\left)\right)\backslash \left\{0\right\}$

In formula: h for transfer step-length, σ () represents spectrum, represent eliminating.

Beneficial effects of the present invention:

The first, the SOD-LMS that the present invention proposes is for calculating the critical eigenvalue of real system and stablizing of judgement system During property, the scale of real system, and the impact of communication delay are taken into full account.

The second, the SOD-LMS that the present invention proposes is not related to Matrix Calculating during calculating components of system as directed critical eigenvalue Inverse operation, speed is fast, computational efficiency is high in calculating.

3rd, the discretization matrix T that the SOD-LMS that the present invention proposes obtains_NBy rationally selecting transfer step-length h, it is possible to Ensure the accuracy of stability distinguishing result.

4th, the SOD-LMS that the present invention proposes only need to calculate discretization matrix T_NThe spy of the maximum setting number of modulus value Value indicative, it is possible to differentiate the small signal stability of time-lag power system.

5th, the SOD-LMS that the present invention proposes makes full use of the sparse characteristic of sytem matrix, is accurately calculated Solution operator The critical eigenvalue of modulus value maximum (successively decreasing), the stability of the extensive muilt-timelag electric power system of Quick in discretization matrix.

Accompanying drawing explanation

Fig. 1 is time-lag power system schematic diagram；

Fig. 2 (a) and Fig. 2 (b) is the graph-based of spectral mapping theorem；

Fig. 3 is the graph-based of transfer step-length h basis for selecting；

Fig. 4 is the flow chart of extensive stability of muilt-timelag electric power system method of discrimination based on SOD-LMS.

Detailed description of the invention:

The present invention is described in detail below in conjunction with the accompanying drawings:

As shown in Figure 1: in the modeling process of actual large-scale electrical power system, introduce Time Delay.Time-lag power system bag Time lag four part is exported, between each several part containing without time-lag power system, wide area Feedback Delays, wide area damping control and wide area Annexation is as shown in the figure.In Fig. 1, y_fFor the output without time-lag power system, y_dfFeed back for the wide area after considering Feedback Delays Signal the input as damping controller, y_cFor the output of wide area damping control, y_dcWide area delayed during for considering to export The output of damping controller, also serves as inputting without the control of time-lag power system simultaneously.

In Fig. 2 (a), time lag system is positioned at the eigenvalue of left half complex plane and is mapped to Solution operator in Fig. 2 (b) and is positioned at unit Eigenvalue within circle, and in Fig. 2 (a), time lag system is positioned at the eigenvalue of right half complex plane and is mapped as Solution operator in Fig. 2 (b) The modulus value eigenvalue more than 1, and be positioned at outside unit circle.Therefore, the eigenvalue of Solution operator is utilized, it is possible to judge former time lag system The stability of system.If Solution operator at least exists the modulus value eigenvalue more than 1, then may determine that former time lag system is unstable Fixed, if the modulus value of all eigenvalues of Solution operator is respectively less than 1, the most former time lag system is asymptotically stability.

In Fig. 3, solid line represents the border that the absolute stability regions of 2 rank backward difference methods is formed after 1/h amplifies, border Interior is unstable region.Dotted line represents the eigenvalue distributed areas of simple time-lag power system.According to the characteristic of linear multistep method, By rationally selecting transfer step-length h so that the unstable region that solid line surrounds comprises in eigenvalue distributed areas and is positioned at complex plane The part of RHP.When transfer step-length h chosen meets above-mentioned condition, the discretization matrix obtained by linear multistep method Can the small signal stability of accurate judgement system.

As shown in Figure 4: extensive stability of muilt-timelag electric power system method of discrimination based on SOD-LMS, including walking as follows Rapid:

S1: set up time-lag power system model；

S2: the eigenvalue problem solving time-lag power system is converted into the spectrum problem solving Solution operator T (h)；

S3: by linear multi step discretization, obtain the finite dimension discretization matrix T of Solution operator T (h)_N；

S4: use implicit restarted Arnoldi algorithm to carry out the Solution operator discretization matrix T that calculation procedure S3 obtains_NMould The eigenvalue μ of the setting number that value is maximum；

S5: after being calculated μ, according to spectrum mapping relations, obtains the eigenvalue λ of time-lag power system.

So far, the critical eigenvalue of the setting number of judgement system stability has been obtained.

In step S1, it is considered to after time-delay, power system can describe with one group of following time-delayed differential equations:

In formula:For the state variable vector of power system, n is system state variables sum.T is current time.0 <τ₁<τ₂<…<τ_i…<τ_mFor the time lag constant of Time Delay, maximum of which time lag is τ_m=τ_max。For system shape State matrix, is a dense matrix.For system time lags state matrix, for sparse matrix.Δ x (t) is The increment of t system state variables, Δ x (t-τ_i) it is t-τ_iThe increment of moment system state variables,For t system The increment of state variable derivative.Δ x (0) is the initial value (i.e. initial condition) of system state variables, and is abbreviated as

The characteristic equation of the time-lag power system that above formula represents is:

$({\tilde{A}}_0+\underset{i=1}{\overset{m}{\&Sigma;}}{\tilde{A}}_i{e}^{-{\mathrm{\&lambda;\&tau;}}_i})v=\mathrm{\&lambda;}v$

In formula: λ is characterized value, v is characterized the right characteristic vector that value is corresponding.

The augmentation form of equal value of above formula is:

$\left[\begin{array}{cc}{A}^{\&prime;}\left(\mathrm{\&lambda;}\right)& B^{\&prime;}\left(\mathrm{\&lambda;}\right)\\ C_0& D_0\end{array}\right]\left[\begin{array}{c}v\\ w\end{array}\right]=0$

In formula:For middle and auxiliary vector.If I_nFor n rank unit matrix, then A'(λ) and B'(λ) can concrete table It is shown as:

$A^{\&prime;}\left(\mathrm{\&lambda;}\right)=A_0-{\mathrm{\&lambda;I}}_n+\underset{i=1}{\overset{m}{\&Sigma;}}{A}_i{e}^{-{\mathrm{\&lambda;\&tau;}}_i}$

$B^{\&prime;}\left(\mathrm{\&lambda;}\right)=B_0+\underset{i=1}{\overset{m}{\&Sigma;}}{B}_i{e}^{-{\mathrm{\&lambda;\&tau;}}_i}$

In formula: A₀, B₀, C₀, D₀, A_i, B_iFor the linearisation coefficient matrix that height is sparse.

In step S2, Solution operator T (h): X → X is defined as the initial condition (state) in the θ moment in space XIt is mapped to The linear operator of h+ θ moment system mode ψ；Wherein, h is transfer step-length, 0≤h≤τ_max；

Wherein: s is integration variable,WithIt is respectively the state of 0 and h+ θ moment time-lag power system.Time lag electricity Relation between the eigenvalue of Force system model and Solution operator T (h) spectrum:

From spectral mapping theorem, have such as ShiShimonoseki between eigenvalue μ and the eigenvalue λ of time lag system of Solution operator T (h) System:

$\mathrm{\&lambda;}=\frac{1}{h}ln\mathrm{\&mu;},\mathrm{\&mu;}\&Element;\mathrm{\&sigma;}\left(T\right(h\left)\right)\backslash \left\{0\right\}$

In formula: h for transfer step-length, σ () represents spectrum, represent eliminating.

T (h) is by the stable region of time-lag power system, within the most left half s Planar Mapping is the unit circle of z-plane.This makes The stability of time-lag power system can be i.e. can determine whether only by calculating several eigenvalues of T (h) modulus value maximum.If | μ | > 1, The real part of then corresponding λ is more than zero, i.e. Re (λ) > 0, system is unstable.If | μ | < 1, then Re (λ) < 0, system asymptotically stability.If | μ |=1, then Re (λ)=0, system neutrality.

Solution operator T (h) is to describe the Infinite Dimension Linear operator that X → X maps.From the spectrum map feature of Solution operator, can With the spectrum by calculating Solution operator, obtain the Partial key eigenvalue of time-lag power system.But, the eigenvalue calculating T (h) is One Infinite-dimensional eigenvalue problem.Therefore, it is necessary to first T (h) is carried out discretization, then by calculate corresponding finite dimension from The eigenvalue of dispersion matrix, using the partial feature value as time lag system.

The step of step S3 is as follows:

Corresponding with Solution operator T (h), discretization matrix T_NIt is expressed as follows:

T_NLast block row Γ be the coefficient matrix of polynomial eigenvalue problem, be specifically represented by:

$\mathrm{\&Gamma;}=R^{-1}\underset{i=0}{\overset{m}{\&Sigma;}}{w}_i\&CircleTimes;{\tilde{A}}_i$

In formula:K is the step number of linear multistep method,Computing is amassed for Kronecker, especially, when System contains only a time lag and time N=τ/h is integer, and Γ can explicitly be expressed as follows:

Γ=[Γ₀,0_n×n(N-k-1),Γ₁]

${\mathrm{\&Gamma;}}_0=h({\mathrm{\&beta;}}_0,...,{\mathrm{\&beta;}}_k)\&CircleTimes;\left(R^{-1}{\tilde{A}}_1\right)$

${\mathrm{\&Gamma;}}_1=-({\mathrm{\&alpha;}}_0,...,{\mathrm{\&alpha;}}_{k-1})\&CircleTimes;R^{-1}+h({\mathrm{\&beta;}}_0,...,{\mathrm{\&beta;}}_{k-1})\&CircleTimes;\left(R^{-1}{\tilde{A}}_0\right)$

In formula: α_j,β_j(j=0 ..., k) it is the coefficient of linear k footwork

In step S4, discretization matrix T_NExponent number be (L+k) n.For large-scale electrical power system, matrix T_NExponent number will The hugest.Therefore, at the discretization matrix T that application Solution operator is corresponding_NWhen solving the time lag eigenvalue of large-scale electrical power system, Sparse features value-based algorithm must be used to calculate the eigenvalue of the maximum setting number of its modulus value.

The step of step S4 is as follows:

If the vector representation of k-th Krylov is q_K, then matrix-vector product q_K+1=T_Nq_KFlow process as follows:

Step (4-1): from the direction of row, willBoil down to matrix WhereinJ=1 ..., L+k；L is discrete counting.

Step (4-2): q_K+1(1:(L+k-1) n, 1)=q_K((n+1):(L+k)n,1)；

Step (4-3): utilize the character of Kronecker product, calculates:

$\begin{array}{c}z=(\underset{i=0}{\overset{m}{\&Sigma;}}{w}_i\&CircleTimes;{\tilde{A}}_i)q_s=(\underset{i=0}{\overset{m}{\&Sigma;}}{w}_i\&CircleTimes;{\tilde{A}}_i)vec\left(P\right)\\ =vec\left(\underset{i=0}{\overset{m}{\&Sigma;}}{\tilde{A}}_i{\mathrm{Pw}}_i^T\right)\\ =vec(\underset{i=0}{\overset{m}{\&Sigma;}}{\tilde{A}}_i\&lsqb;p_1,\mathrm{...},p_{L+k}\&rsqb;w_i^T)\end{array}$

In formula: vec () is to be the computing of column vector by matrix compression.

Step (4-4): calculate q_K+1((L+k-1) n:(L+k) n, 1):

q_K+1((L+k-1) n+1:(L+k) n, 1)=(R)^-1z

By above-mentioned flow process it can be seen that in step (4-3)With in step (44) (R)^-1The calculating of z Amount is maximum, the longest.Such that it is able to deduce, the amount of calculation of whole flow process is approximately equal to carry out L+k+1 general characteristics value and divides The amount of calculation of analysis.It should be noted that in step (4-3) and step (4-4) two of computationally intensive time-consuming length can be with sparse reality Existing, thus reduce amount of calculation, improve computational efficiency.

In step S5, after being calculated μ, obtain time-lag power system through spectrum mapping and be positioned at the complex plane rightmost side Set the eigenvalue λ of number, thus judge the stability of system.Discretization matrix T_NEigenvalue μ and time-lag power system special The mapping relations of value indicative λ are as follows:

$\mathrm{\&lambda;}=\frac{1}{h}ln\mathrm{\&mu;},\mathrm{\&mu;}\&Element;\mathrm{\&sigma;}\left(T\right(h\left)\right)\backslash \left\{0\right\}$

In formula: h for transfer step-length, σ () represents spectrum, represent eliminating.

The present invention sets up the model of electric power system model and the wide area damping control not considering time-delay respectively, passes through Introduce Time Delay, set up the mathematical model of the closed loop power system considering time-delay.By time-lag power system model at it Linearisation near steady-state operation point, obtains can be used for the system model of time-lag power system analysis on Small Disturbance Stability.

By means of Solution operator T (h), by initial condition (state)It is mapped as Account Dept and decomposes (state) ψ, obtain sign and reflect Penetrate the expression formula of relation.In order to obtain the spectrum of Solution operator, Solution operator T (h) of described time-lag power system is carried out linear multi step Discretization, obtains the finite dimension Solution operator discretization matrix T with explicit expression_N。

Use implicit restarted Arnoldi algorithm, calculate discretization matrix T_NThe eigenvalue of the setting number that modulus value is maximum μ.After being calculated μ, obtain time-lag power system according to spectrum mapping relations and be positioned at the eigenvalue λ of the complex plane rightmost side, use Stability in judgement system.

The SOD-LMS method of the present invention only need to be by an eigenvalue calculation, it is possible to quickly obtain for judgement system The critical eigenvalue being positioned at the complex plane rightmost side of stability.

Although the detailed description of the invention of the present invention is described by the above-mentioned accompanying drawing that combines, but not the present invention is protected model The restriction enclosed, one of ordinary skill in the art should be understood that on the basis of technical scheme, and those skilled in the art are not Need to pay various amendments or deformation that creative work can make still within protection scope of the present invention.

Claims (10)

1. extensive stability of muilt-timelag electric power system method of discrimination based on SOD-LMS, is characterized in that, comprise the following steps:

S1: set up time-lag power system model；

S2: the initial value that time-lag power system model conversion is the ordinary differential equation that Solution operator T (h) represents that will obtain in step S1 Problem；

S3: Solution operator T (h) in step S2 is carried out discretization, obtains the discretization matrix T of Solution operator_N；

S4: discretization matrix T in calculation procedure S3_NThe eigenvalue μ of the maximum setting number of modulus value；

S5: according to spectrum mapping relations, by the discretization matrix T in step S4_NEigenvalue μ be converted to the spy of time-lag power system Value indicative λ.

2. extensive stability of muilt-timelag electric power system method of discrimination based on SOD-LMS as claimed in claim 1, its feature It is, in step one, the time-lag power system model of foundation: introduce time lag in the modeling process of actual large-scale electrical power system Link, obtains being applicable to the system model of time-lag power system analysis on Small Disturbance Stability, comes with one group of time-delayed differential equations Describe.

3. extensive stability of muilt-timelag electric power system method of discrimination based on SOD-LMS as claimed in claim 2, its feature It is to obtain the characteristic equation of time-lag power system according to one group of time-delayed differential equations, and by the feature side of time-lag power system Journey is expressed as augmentation form of equal value.

4. extensive stability of muilt-timelag electric power system method of discrimination based on SOD-LMS as claimed in claim 1, its feature It is, in step 2, according to the mapping relations between time-lag power system eigenvalue and Solution operator eigenvalue, time lag electric power will to be solved The eigenvalue problem of system is converted into the spectrum problem solving Solution operator T (h).

5. based on SOD-LMS the extensive stability of muilt-timelag electric power system method of discrimination as described in claim 1 or 4, its Feature is, Solution operator T (h): X → X is defined as being mapped to original state υ in the θ moment in space X h+ θ moment system mode ψ Linear operator；Wherein, h is transfer step-length, 0≤h≤τ_max；

Wherein: s is integration variable,WithIt is respectively the state of 0 and h+ θ moment time-lag power system；0<τ₁<τ₂<…< τ_i…<τ_mFor the time lag constant of Time Delay, maximum of which time lag is τ_m=τ_max；For system mode matrix, it is one Individual dense matrix,For system time lags state matrix, for sparse matrix；Δ x (s) is the increasing of s moment system state variables Amount, Δ x (s-τ_i) it is s-τ_iThe increment of moment system state variables,Increment for s moment system state variables derivative.

6. extensive stability of muilt-timelag electric power system method of discrimination based on SOD-LMS as claimed in claim 1, its feature It is, in step 3, to utilize linear multistep method that Solution operator T (h) is carried out discretization, obtains can accurately differentiating time-lag power system The discretization matrix T of stability_N；

Corresponding with Solution operator T (h), discretization matrix T_NIt is expressed as follows:

7. extensive stability of muilt-timelag electric power system method of discrimination based on SOD-LMS as claimed in claim 6, its feature It is, T_NLast block row Γ be the coefficient matrix of polynomial eigenvalue problem, be specifically represented by:

$\mathrm{\&Gamma;}=R^{-1}\underset{i=0}{\overset{m}{\&Sigma;}}{w}_i\&CircleTimes;{\tilde{A}}_i$

In formula:K is the step number of linear multistep method,Computing is amassed for Kronecker,For system Hangover state matrix, for sparse matrix,For middle and auxiliary vector.

8. extensive stability of muilt-timelag electric power system method of discrimination based on SOD-LMS as claimed in claim 1, its feature It is, at the discretization matrix T that application Solution operator is corresponding_NWhen solving the eigenvalue of extensive time-lag power system, use sequential method Or subspace method calculates the eigenvalue of the maximum setting number of its modulus value.

9. based on SOD-LMS the extensive stability of muilt-timelag electric power system method of discrimination as described in claim 1 or 8, its Feature is, in step 4, particularly as follows: set the vector representation of k-th Krylov as q_K, then matrix-vector product q_K+1=T_Nq_KFlow process As follows:

Step (4-1): from the direction of row, willBoil down to matrixWhereinJ=1 ..., L+k；L is discrete counting；

Step (4-2): q_K+1(1:(L+k-1) n, 1)=q_K((n+1):(L+k)n,1)；

Step (4-3): utilize the character of Kronecker product, calculates

$\begin{array}{c}z=(\underset{i=0}{\overset{m}{\&Sigma;}}{w}_i\&CircleTimes;{\tilde{A}}_i)q_s=(\underset{i=0}{\overset{m}{\&Sigma;}}{w}_i\&CircleTimes;{\tilde{A}}_i)vec\left(P\right)\\ =vec\left(\underset{i=0}{\overset{m}{\&Sigma;}}{\tilde{A}}_i{\mathrm{Pw}}_i^T\right)\\ =vec(\underset{i=0}{\overset{m}{\&Sigma;}}{\tilde{A}}_i\&lsqb;p_1,\mathrm{...},p_{L+k}\&rsqb;w_i^T)\end{array}$

In formula: vec () is to be the computing of column vector by matrix compression；

Step (4-4): calculate q_K+1((L+k-1) n:(L+k) n, 1):

q_K+1((L+k-1) n+1:(L+k) n, 1)=(R)^-1z。

10. extensive stability of muilt-timelag electric power system method of discrimination based on SOD-LMS as claimed in claim 1, it is special Levy and be, discretization matrix T_NEigenvalue μ and the mapping relations of time-lag power system eigenvalue λ as follows:

$\mathrm{\&lambda;}=\frac{1}{h}ln\mathrm{\&mu;},\mathrm{\&mu;}\&Element;\mathrm{\&sigma;}\left(T\right(h\left)\right)\backslash \left\{0\right\}$

In formula: h for transfer step-length, σ () represents spectrum, represent eliminating.