CN105977969B - Extensive stability of muilt-timelag electric power system method of discrimination based on SOD LMS - Google Patents
Extensive stability of muilt-timelag electric power system method of discrimination based on SOD LMS Download PDFInfo
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Abstract
The invention discloses the extensive stability of muilt-timelag electric power system method of discrimination based on SOD LMS, time-lag power system model is set up；According to the mapping relations between time-lag power system characteristic value and Solution operator characteristic value, the eigenvalue problem for solving time-lag power system is converted into the spectrum problem for solving Solution operator T (h)；Discretization is carried out to Solution operator T (h) using linear multistep method, step-length h is shifted by reasonable selection, obtains accurately differentiating the discretization matrix T of time-lag power system stabilityN；Discretization matrix T is calculated using sequential method or subspace method (such as implicit restarted Arnoldi algorithm)NThe maximum setting number of modulus value characteristic value；According to spectrum mapping relations, by discretization matrix TNCharacteristic value be converted to time-lag power system be located at the complex plane rightmost side characteristic value, the small signal stability for differentiating extensive muilt-timelag electric power system.When SOD LMS methods proposed by the present invention are used for the stability for the critical eigenvalue and judgement system for calculating real system, taken into full account the scale of real system, and communication delay influence.
Description
Technical field
The present invention relates to stability of power system analysis field, and in particular to during a kind of extensive many based on SOD-LMS
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
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 initial stage of interconnection, complicated electrical structure and weak transmission of electricity link cause interconnected network more
Low-frequency oscillation between easy region.For local oscillation, the coverage of inter-area oscillations is wide, participates in the machine of vibration
Electrical link between group is sufficiently complex, and the influence to the stability of extensive interconnected network is more prominent.Using local signal to be defeated
The power system stabilizer, PSS (Power System Stabilizer, PSS) entered can preferably calm local oscillation pattern, but
It is to be difficult to calm down inter-area oscillation mode, so as to be difficult to ensure that the stability of extensive interconnected network.
The appearance and development of WAMS (Wide-Area Measurement System, WAMS) so that use
The information realization electric power system stability control of global, distal end is possibly realized, to suppress the interregional low of extensive interconnected network
Frequency vibration, which is swung, brings opportunity.WAMS is mainly made up of three parts：Phasor measurement unit (Phasor Measurement Unit,
PMU), communication network, and monitoring system.PMU positioned at plant stand utilizes global positioning system (Global Positioning
System, GPS) high accurate clock signal, the quantity of state of each pivot point of synchro measure power network.Pass through the height in communication system
Target metric data is sent to monitoring system when fast information channel will be posted, and realizes the real-time monitoring, protection and control of power system
System.Metric data in the real-time data base handled by analysis, can not only be used for detecting the low-frequency oscillation letter in power system
Breath, moreover it is possible to which the wide area feedback signal of low frequency oscillation mode between effective reflecting regional is provided for damping controller.And then, optimal control
The performance of device, the ability of the gentle long-distance and large-capacity power transmission of damping water of lifting system.
However, wide area measurement data are in leading to for being made up of different communication medias (such as optical fiber, digital microwave, power line)
When transmitting and handle in letter system, there is the communication delay changed between tens to hundreds of milliseconds.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 PMU collection, the conveying of communication network and monitoring system
Time lag is often bigger than theoretical value.Time lag is to cause one kind weight of the failure of system control law, operation conditions deterioration and system unstability
Want inducement.When time lag constant is larger, relatively large deviation can occur for system features value, or even can change the small disturbance stability of system completely
Property.In summary, when modern extensive interconnected network carries out power system closed-loop control using wide area measurement information, it is necessary to count and
The influence of time lag.
Consider after time-delay, the state of power system is not only relevant with the state at current time, additionally depends on system mistake
The state gone.Therefore, the model of time-lag power system can be described 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, when
The corresponding characteristic equation of stagnant power system, exists and surmounts item, there is infinite multiple solutions (characteristic value).Accordingly, it is considered to after time-delay,
The difficulty of stability of power system research is greatly increased.
At present, in the patent for being related to the differentiation of time-lag power system small signal stability, a kind of time lag electricity of Chinese invention patent
The stable method of discrimination .201010123345.8 [P] of Force system determines the time lag stable region of system using method for tracing is searched for.So
And, time lag characteristic value is solved in the above method and the amount of calculation of search procedure is larger.Chinese invention patent is based on Pad é approximate
Time-lag power system characteristic value is calculated and approached with Convenient stable criterion .201210271783.8 [P] by rational polynominal
Time Delay, and then the critical eigenvalue of the computing system rightmost side, and judge the time lag stability of system.However, the above method
Accuracy and result of calculation precision need through in-depth analysis with research.During extensive based on EIGD of Chinese invention patent
Stagnant power system feature value calculating method .201510055743.3 [P] proposes a kind of discrete based on explicit infinitesimal generator
Change the extensive time-lag power system of (Explicit Infinitesimal Generator Discretization, EIGD)
Feature value calculating method.The above method is needed by Multiple-Scan [0.1,2.5] Hz low-frequency oscillations frequency range, close to the imaginary axis
Critical eigenvalue, the time lag stability of system could be judged.Power System Delay of the Chinese invention patent based on SOD-PS is steady
Qualitative discrimination method .201510229738.X [P] proposes a kind of based on Solution operator puppet spectrum discretization (Solution
Operator Discretization-Pseudospectral, SOD-PS) Power System Delay Convenient stable criterion.Should
Method only needs to calculate a maximum characteristic value of Solution operator discretization matrix norm value or a pair of Con-eigenvalues, it is possible to sentence
Break the stability for system under fixed time lag.However, this method in calculating section critical eigenvalue, it is necessary to ask for discretization
Submatrix it is inverse, it is computationally intensive, calculate the time it is long.
The content of the invention
To solve the deficiency that prior art is present, the invention discloses the extensive multiple time delay power train based on SOD-LMS
System Convenient stable criterion, the small signal stability quick and precisely to differentiate extensive muilt-timelag electric power system.SOD-LMS side
Method is not related to matrix inversion operation during computing system Partial key characteristic value, and calculating speed is fast, computational efficiency is high.Together
When, this method need to only calculate the characteristic value of the maximum setting number of Solution operator discretization matrix norm value, it becomes possible to accurate to differentiate
The stability of extensive muilt-timelag electric power system.
To achieve the above object, concrete scheme of the 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：It is the ODE that Solution operator T (h) is represented by the time-lag power system model conversion obtained in step S1
Initial-value problem；
S3：Discretization is carried out to the Solution operator T (h) in step S2, the discretization matrix T of Solution operator is obtainedN；
S4：Discretization matrix T in calculation procedure S3NThe maximum setting number of modulus value characteristic value μ；
S5：According to spectrum mapping relations, by the discretization matrix T in step S4NCharacteristic value 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, the system model suitable for time-lag power system analysis on Small Disturbance Stability is obtained, during with one group
Stagnant differential equation group is described.
Further, the characteristic equation of time-lag power system is obtained according to one group of time-delayed differential equations, and time lag is electric
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 characteristic value and Solution operator characteristic value,
The eigenvalue problem for solving time-lag power system is converted into the spectrum problem for solving Solution operator T (h).
Further, Solution operator T (h)：X → X is defined as the original state at the θ moment in space XWhen being mapped to h+ θ
Etching system state ψ linear operator；Wherein, h is transfer step-length, 0≤h≤τmax；
Wherein：S is integration variable,WithThe state of respectively 0 and h+ θ moment time-lag power systems；0<τ1<τ2
<…<τi…<τmFor the time lag constant of Time Delay, maximum of which time lag is τm=τmax；For systematic observation matrix,
For a dense matrix,It is sparse matrix for system time lags state matrix；Δ x (s) is s moment system state variableses
Increment, Δ x (s- τi) it is s- τiThe increment of moment system state variables,For the increasing of s moment system state variables derivatives
Amount.
Further, in step 3, discretization is carried out to Solution operator T (h) using linear multistep method, obtains accurately sentencing
The discretization matrix T of other time-lag power system stabilityN。
Further, corresponding with Solution operator T (h), discretization matrix TNIt is expressed as follows：
TNLast block row Γ be polynomial eigenvalue problem coefficient matrix, be specifically represented by：
In formula：K is the step number of linear multistep method, αk, βkFor the coefficient of linear multistep method,For
Kronecker product operation,It is sparse matrix for system time lags state matrix,For middle and auxiliary vector.
Further, in the corresponding discretization matrix T of application Solution operatorNSolve the characteristic value of extensive time-lag power system
When, the characteristic value of the maximum setting number of its modulus value is calculated using sequential method or subspace method.
Further, in step 4, it is specially：If k-th Krylov vector representations are qK, then matrix-vector product qK+1
=TNqKFlow it is as follows：
Step (4-1)：, will from the direction of rowBoil down to matrix
WhereinJ=1 ..., L+k；L is discrete points；
Step (4-2)：qK+1(1:(L+k-1) n, 1)=qK((n+1):(L+k)n,1)；
Step (4-3)：Using the property of Kronecker product, calculate：
In formula：Vec () is by computing that matrix compression is column vector；
Step (4-4)：Calculate qK+1((L+k-1)n:(L+k)n,1)：
qK+1((L+k-1)n+1:(L+k) n, 1)=(R)-1z。
Further, discretization matrix TNCharacteristic value μ and time-lag power system eigenvalue λ mapping relations it is as follows：
In formula：H for transfer step-length, σ () represent spectrum, represent exclude.
Beneficial effects of the present invention：
Firstth, SOD-LMS proposed by the present invention is used to calculate the critical eigenvalue of real system and the stabilization of judgement system
During property, taken into full account the scale of real system, and communication delay influence.
Secondth, SOD-LMS proposed by the present invention is not related to Matrix Calculating during computing system Partial key characteristic value
Inverse operation, calculating speed is fast, computational efficiency is high.
3rd, the discretization matrix T that SOD-LMS proposed by the present invention is obtainedNStep-length h is shifted by reasonable selection, can
Ensure the accuracy of stability distinguishing result.
4th, SOD-LMS proposed by the present invention need to only calculate discretization matrix TNThe maximum setting number of modulus value spy
Value indicative, it is possible to differentiate the small signal stability of time-lag power system.
5th, SOD-LMS proposed by the present invention makes full use of the sparse characteristic of sytem matrix, and accurate calculate obtains 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.
Brief description of the drawings
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 the extensive stability of muilt-timelag electric power system method of discrimination based on SOD-LMS.
Embodiment：
The present invention is described in detail below in conjunction with the accompanying drawings：
As shown in Figure 1：Time Delay is introduced in the modeling process of actual large-scale electrical power system.Time-lag power system bag
Containing without time-lag power system, wide area Feedback Delays, wide area damping control and wide area output time lag four part, between each several part
Annexation is as shown in the figure.In Fig. 1, yfFor the output without time-lag power system, ydfTo consider the wide area feedback after Feedback Delays
Signal is simultaneously used as the input of damping controller, ycFor the output of wide area damping control, ydcTo consider wide area delayed during output
The output of damping controller, while also serving as the control input of no time-lag power system.
Time lag system is located at the characteristic value of left half complex plane and is mapped in Fig. 2 (b) Solution operator and is located at unit in Fig. 2 (a)
Characteristic value within circle, and time lag system is mapped as Solution operator in Fig. 2 (b) positioned at the characteristic value of right half complex plane in Fig. 2 (a)
Modulus value is more than 1 characteristic value, and outside unit circle.Therefore, the characteristic value of Solution operator is utilized, it is possible to judge former time lag system
The stability of system.If Solution operator at least has the characteristic value that a modulus value is more than 1, it is unstable for may determine that former time lag system
Fixed, if the modulus value of all characteristic values of Solution operator is respectively less than 1, former time lag system is asymptotically stability.
Solid line represents the border that the absolute stability regions of 2 rank backward difference methods are formed after 1/h amplifies, border in Fig. 3
Interior is unstable region.Dotted line represents the characteristic value distributed areas of simple time-lag power system.According to the characteristic of linear multistep method,
Step-length h is shifted by reasonable selection so that the unstable region that solid line is surrounded, which is included, is located at complex plane in characteristic value distributed areas
The part of RHP.When the transfer step-length h of selection meets above-mentioned condition, the discretization matrix obtained by linear multistep method
It is capable of 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 following step
Suddenly：
S1：Set up time-lag power system model；
S2：The eigenvalue problem for solving time-lag power system is converted into the spectrum problem for solving Solution operator T (h)；
S3：By linear multi step discretization, Solution operator T (h) finite dimension discretization matrix T is obtainedN；
S4：The Solution operator discretization matrix T obtained using implicit restarted Arnoldi algorithm come calculation procedure S3NMould
It is worth the characteristic value μ of maximum setting number；
S5：After calculating obtains μ, according to spectrum mapping relations, the eigenvalue λ of time-lag power system is obtained.
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 be described 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<…<τi…<τmFor the time lag constant of Time Delay, maximum of which time lag is τm=τmax。For system shape
State matrix, is a dense matrix.It is sparse matrix for system time lags state matrix.Δ x (t) is
The increment of t system state variables, Δ x (t- τi) it is t- τiThe increment of moment system state variables,For t system
The increment of state variable derivative.Δ x (0) is the initial value (i.e. primary condition) of system state variables, and is abbreviated as
The characteristic equation for the time-lag power system that above formula is represented is：
In formula：λ is characterized value, and v is characterized the corresponding right characteristic vector of value.
The augmentation form of equal value of above formula is：
In formula：For middle and auxiliary vector.If InFor n rank unit matrixs, then A'(λ) and B'(λ) can specific table
It is shown as：
In formula：A0, B0, C0, D0, Ai, BiFor highly sparse linearisation coefficient matrix.
In step S2, Solution operator T (h):X → X is defined as the primary condition (state) at the θ moment in space XIt is mapped to
H+ θ moment system modes ψ linear operator；Wherein, h is transfer step-length, 0≤h≤τmax；
Wherein：S is integration variable,WithThe state of respectively 0 and h+ θ moment time-lag power systems.Time lag electricity
Relation between characteristic value and Solution operator T (h) spectrum of Force system model：
There is such as ShiShimonoseki between spectral mapping theorem, Solution operator T (h) characteristic value μ and the eigenvalue λ of time lag system
System：
In formula：H for transfer step-length, σ () represent spectrum, represent exclude.
T (h) is by the stable region of time-lag power system, i.e., left half s Planar Mappings are within the unit circle of z-plane.This causes
Several characteristic values that can be maximum only by calculating T (h) modulus value, you can judge the stability of time-lag power system.If | μ |>1,
Then corresponding λ real part 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 the Infinite Dimension Linear operator for describing X → X mappings., can from the spectrum map feature of Solution operator
With the spectrum by calculating Solution operator, the Partial key characteristic value of time-lag power system is obtained.However, calculating T (h) characteristic value is
One Infinite-dimensional eigenvalue problem.Therefore, it is necessary to first to T (h) carry out discretization, then by calculate corresponding finite dimension from
The characteristic value of dispersion matrix, using the partial feature value as time lag system.
The step of step S3, is as follows：
, discretization matrix T corresponding with Solution operator T (h)NIt is expressed as follows：
TNLast block row Γ be polynomial eigenvalue problem coefficient matrix, be specifically represented by：
In formula：K is the step number of linear multistep method,For Kronecker product operation, especially, when
When system is integer only containing a time lag and N=τ/h, Γ can be explicitly expressed as follows：
Γ=[Γ0,0n×n(N-k-1),Γ1]
In formula：αj,βj(j=0 ..., it is k) coefficient of linear k footworks
In step S4, discretization matrix TNExponent number be (L+k) n.For large-scale electrical power system, matrix TNExponent number will
It is very huge.Therefore, in the corresponding discretization matrix T of application Solution operatorNWhen solving the time lag characteristic value of large-scale electrical power system,
The characteristic value of the maximum setting number of its modulus value must be calculated using sparse features value-based algorithm.
The step of step S4, is as follows：
If k-th Krylov vector representations are qK, then matrix-vector product qK+1=TNqKFlow it is as follows：
Step (4-1)：, will from the direction of rowBoil down to matrix
WhereinJ=1 ..., L+k；L is discrete points.
Step (4-2)：qK+1(1:(L+k-1) n, 1)=qK((n+1):(L+k)n,1)；
Step (4-3)：Using the property of Kronecker product, calculate：
In formula：Vec () is by computing that matrix compression is column vector.
Step (4-4)：Calculate qK+1((L+k-1)n:(L+k)n,1)：
qK+1((L+k-1)n+1:(L+k) n, 1)=(R)-1z
In step (4-3) it can be seen from above-mentioned flowIn step (44) (R)-1Z calculating
Amount is maximum, time-consuming most long.So as to deduce, the amount of calculation of whole flow process is approximately equal to L+k+1 general characteristics value point of progress
The amount of calculation of analysis.It is worth noting that, computationally intensive two that time-consuming can be with sparse reality in step (4-3) and step (4-4)
It is existing, so as to reduce amount of calculation, improve computational efficiency.
In step S5, after calculating obtains μ, time-lag power system is obtained positioned at the complex plane rightmost side by spectrum mapping
The eigenvalue λ of number is set, so as to judge the stability of system.Discretization matrix TNCharacteristic value μ and time-lag power system it is special
Value indicative λ mapping relations are as follows：
In formula：H for transfer step-length, σ () represent spectrum, represent exclude.
The present invention sets up the model of the electric power system model and wide area damping control that do not consider time-delay respectively, passes through
Time Delay is introduced, the mathematical modeling for the closed loop power system for considering time-delay is set up.By time-lag power system model at it
Linearized near steady-state operation point, obtain the system model available for time-lag power system analysis on Small Disturbance Stability.
By means of Solution operator T (h), by primary condition (state)It is mapped as Account Dept and decomposes (state) ψ, obtains sign and reflect
Penetrate the expression formula of relation.In order to obtain the spectrum of Solution operator, linear multi step is carried out to the Solution operator T (h) of the time-lag power system
Discretization, obtains the finite dimension Solution operator discretization matrix T with explicit expressionN。
Using implicit restarted Arnoldi algorithm, discretization matrix T is calculatedNThe characteristic value of the maximum setting number of modulus value
μ.After calculating obtains μ, the eigenvalue λ that time-lag power system is located at the complex plane rightmost side is obtained according to spectrum mapping relations, is used
In the stability of judgement system.
The SOD-LMS methods of the present invention need to only be calculated by a sub-eigenvalue, it is possible to quick to obtain being used for judgement system
The critical eigenvalue positioned at the complex plane rightmost side of stability.
Although above-mentioned the embodiment of the present invention is described with reference to accompanying drawing, not to present invention protection model
The limitation enclosed, one of ordinary skill in the art should be understood that on the basis of technical scheme those skilled in the art are not
Need to pay various modifications or deform still within protection scope of the present invention that creative work can make.
Claims (8)
1. the extensive stability of muilt-timelag electric power system method of discrimination based on SOD-LMS, it is characterized in that, comprise the following steps：
S1：Set up time-lag power system model；
S2：By the initial value that the time-lag power system model conversion obtained in step S1 is the ODE that Solution operator T (h) is represented
Problem；
S3：Discretization is carried out to the Solution operator T (h) in step S2, the discretization matrix T of Solution operator is obtainedN；
S4：Discretization matrix T in calculation procedure S3NThe maximum setting number of modulus value characteristic value μ；
S5：According to spectrum mapping relations, by the discretization matrix T in step S4NCharacteristic value μ be converted to the spy of time-lag power system
Value indicative λ；
In step 3, discretization is carried out to Solution operator T (h) using linear multistep method, obtains accurately differentiating time lag power train
The discretization matrix T for stability of unitingN；
, discretization matrix T corresponding with Solution operator T (h)NIt is expressed as follows：
TNLast block row Γ be polynomial eigenvalue problem coefficient matrix, be specifically represented by：
<mrow>
<mi>&Gamma;</mi>
<mo>=</mo>
<msup>
<mi>R</mi>
<mrow>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msup>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mi>m</mi>
</munderover>
<msub>
<mi>w</mi>
<mi>i</mi>
</msub>
<mo>&CircleTimes;</mo>
<msub>
<mover>
<mi>A</mi>
<mo>~</mo>
</mover>
<mi>i</mi>
</msub>
</mrow>
In formula：K is the step number of linear multistep method,For Kronecker product operation,For system
Hangover state matrix, is sparse matrix,For middle and auxiliary vector.
2. the extensive stability of muilt-timelag electric power system method of discrimination as claimed in claim 1 based on SOD-LMS, its feature
It is, in step one, the time-lag power system model of foundation：Time lag is introduced in the modeling process of actual large-scale electrical power system
Link, obtains the system model suitable for time-lag power system analysis on Small Disturbance Stability, is come with one group of time-delayed differential equations
Description.
3. the extensive stability of muilt-timelag electric power system method of discrimination as claimed in claim 2 based on SOD-LMS, its feature
It is that the characteristic equation of time-lag power system is obtained 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. the extensive stability of muilt-timelag electric power system method of discrimination as claimed in claim 1 based on SOD-LMS, its feature
It is that in step 2, according to the mapping relations between time-lag power system characteristic value and Solution operator characteristic value, time lag electric power will be solved
The eigenvalue problem of system is converted into the spectrum problem for solving Solution operator T (h).
5. the extensive stability of muilt-timelag electric power system method of discrimination based on SOD-LMS as described in claim 1 or 4, its
It is characterized in, Solution operator T (h)：X → X is defined as the original state at the θ moment in space XIt is mapped to h+ θ moment system modes ψ
Linear operator；Wherein, h is transfer step-length, 0≤h≤τmax；
Wherein：S is integration variable,WithThe state of respectively 0 and h+ θ moment time-lag power systems；0<τ1<τ2<…<
τi…<τmFor the time lag constant of Time Delay, maximum of which time lag is τm=τmax；It is one for systematic observation matrix
Individual dense matrix,It is sparse matrix for system time lags state matrix；Δ x (s) is the increasing of s moment system state variableses
Amount, Δ x (s- τi) it is s- τiThe increment of moment system state variables,For the increment of s moment system state variables derivatives.
6. the extensive stability of muilt-timelag electric power system method of discrimination as claimed in claim 1 based on SOD-LMS, its feature
It is, in the corresponding discretization matrix T of application Solution operatorNWhen solving the characteristic value of extensive time-lag power system, using sequential method
Or subspace method calculates the characteristic value of the maximum setting number of its modulus value.
7. the extensive stability of muilt-timelag electric power system method of discrimination based on SOD-LMS as described in claim 1 or 6, its
It is characterized in step 4, to be specially：If k-th Krylov vector representations are qK, then matrix-vector product qK+1=TNqKFlow
It is as follows：
Step (4-1)：, will from the direction of rowBoil down to matrixWhereinJ=1 ..., L+k；L is discrete points；
Step (4-2)：qK+1(1:(L+k-1) n, 1)=qK((n+1):(L+k)n,1)；
Step (4-3)：Using the property of Kronecker product, calculate
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In formula：Vec () is by computing that matrix compression is column vector；
Step (4-4)：Calculate qK+1((L+k-1)n:(L+k)n,1)：
qK+1((L+k-1)n+1:(L+k) n, 1)=(R)-1z。
8. the extensive stability of muilt-timelag electric power system method of discrimination as claimed in claim 1 based on SOD-LMS, its feature
It is, discretization matrix TNCharacteristic value μ and time-lag power system eigenvalue λ mapping relations it is as follows：
<mrow>
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In formula：H for transfer step-length, σ () represent spectrum, represent exclude.
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