CN108256274A - Based on the POWER SYSTEM STATE recognition methods for quick and precisely searching for attractor error algorithm - Google Patents

Based on the POWER SYSTEM STATE recognition methods for quick and precisely searching for attractor error algorithm Download PDF

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CN108256274A
CN108256274A CN201810194564.1A CN201810194564A CN108256274A CN 108256274 A CN108256274 A CN 108256274A CN 201810194564 A CN201810194564 A CN 201810194564A CN 108256274 A CN108256274 A CN 108256274A
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闵富红
李闯
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Nanjing Normal University
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Abstract

The invention discloses a kind of based on the POWER SYSTEM STATE recognition methods for quick and precisely searching for attractor error algorithm, one is initially set upkRank electric power system model changes with the two-parameter section of model, obtains distribution of the system motion state in section variation plane；Then it is solved according to numerical analysis methodkThe level system differential equation obtains the sequence of system, judges system motion track by calculating the first-order error of maximum in sequence of iterations, estimates chaotic systems or system unstability.Meanwhile the extreme value ERROR ALGORITHM analysis disturbance load that the present invention uses influences electric system chaotic model, has the characteristics that quick, efficient and accurate, has great importance in electric system chaotic dynamics characteristic research field.

Description

Based on the POWER SYSTEM STATE recognition methods for quick and precisely searching for attractor error algorithm
Technical field
The present invention relates to a kind of POWER SYSTEM STATE recognition methods, belong to electric system dynamics technology field.
Background technology
With the further investigation of stability of power system problem, system is found when by external disturbance, such as periodically Load disturbance, electromagnetic power disturbance, as long as disturbance amplitude and frequency meet certain condition, system will generate chaotic oscillation.It is grinding When studying carefully the chaotic dynamics characteristic of electric system, the bifurcation graphs for often making disturbance LOAD FREQUENCY or amplitude refer to Lyapunov Number spectrum, stability of the electric system in a certain parameter section is analyzed in conjunction with the two.Obviously, this be single dimension analysis System motion state, and if consider to disturb the influence to electric system of LOAD FREQUENCY and amplitude simultaneously, then bifurcation graphs and Lyapunov exponential spectrums traverse the parameter field.Therefore, it when considering the influence of disturbance LOAD FREQUENCY and amplitude to electric system, needs It wants a kind of new algorithm and is calculated to analyze.
At present, analysis disturbance load influences electric system chaotic model, and common method is each by computing system Sequence spectrum entropy complexity or maximum Lyapunov exponent under a Parameter Conditions judge the motion state of system.Wherein, it counts Sequence spectrum entropy complexity is calculated to search for attractor, although program operation speed is faster than calculating Lyapunov index program, is sentenced Disconnected is not very accurate and motion state differentiation is not apparent；And although calculating maximum Lyapunov exponent can accurately distinguish System period, chaos and stable trajectory, but the speed of service is excessively slow and cannot distinguish between period state.
Invention content
The technical problems to be solved by the invention are：The shortcomings that in order to overcome the prior art, the present invention propose that one kind can Making up algorithm mentioned above, there are the shortcomings such as arithmetic speed is slow, accuracy is poor, search efficiency is low, propose a kind of quick, clear, accurate The method that true algorithm solves two-parameter variation attractor condition adjudgement.Can rapidly judge the state of attractor for the period, Chaos or stable point and compartment system movement locus are for monocycle or multicycle, improve the electric power under disturbance System running state recognition efficiency.
The present invention uses following technical scheme to solve above-mentioned technical problem：
The present invention proposes a kind of POWER SYSTEM STATE recognition methods based on quick and precisely search attractor error algorithm,
First, it establishes a k rank electric power system model, chooses electromagnetic power disturbance amplitude and its frequency the two parameters, According to model with the constant interval of the two parameters, distribution of the system motion state in section variation plane is obtained；
Then, the k levels system differential equation is solved according to numerical analysis method and obtains the sequence of system, by calculating iteration sequence The first-order error of maximum judges system motion track in row, and it is period, chaos or stabilization to identify POWER SYSTEM STATE Point.
Further, POWER SYSTEM STATE recognition methods proposed by the invention, if model parameter electromagnetic power disturbs width Value μ and electromagnetic power forcing frequency η are respectively in section [μ1,μ2] and [η1,η2] variation, μ-η planes are subjected to gridding, it will Section [μ1,μ2] and [η1,η2] N equal portions are respectively classified into, obtain distribution of the system motion state in section variation plane.
Further, POWER SYSTEM STATE recognition methods proposed by the invention, it is described to be solved according to numerical analysis method Electric power system model obtains the sequence of system, judges system motion rail by calculating the first-order error of maximum in sequence of iterations Mark, in particular to：
Step 1), as μ=μ1+n1(μ2-μ1)/N, η=η1+n2(η2-η1During)/N, k is solved according to quadravalence Runge-Kutta Level system differential equation f (x1,x2,…,xk), the sequence of iterations for obtaining system is：
xin+1=xin+(Ki1+2Ki2+2Ki3+Ki4)/6, i=1,2 ..., k
In formula, Ki1=f (xi1,xi2,…,xik),Ki4 =f (xin+h,xin+1+hKi3), n1,2=1,2,3 ..., N；N=1,2,3 ..., N；
Step 2), from L × k rank sequences that step 1) calculates, take out the rank sequence X of l × 1={ x1,x2,…,xl, so Afterwards, the maximum point in this group of sequence is obtained, if
xm-1＜ xm＞ xm+1, m=2,3 ..., l-1
So, xmNew array T is just stored into, screened and data descending arrangement in array is stored in array T=again {t1,t2,…,tj}；Wherein, L represents the number of iterative numerical result, l ＜ ＜ L；
Step 3), to array T={ t1,t2,…,tjIn element make difference successively, i.e.,
es-1=ts-ts-1, s=2,3 ..., j
By element es-1Descending arranges, and obtains an error array E={ e1,e2,…,ej-1}；
Step 4) establishes two critical value ε1And ε2For judging system motion state, system motion condition adjudgement mode For：
Max if (abs (T))≤ε1, then fixed point is is stablized in system motion track；
If length (E (E ＞ ε2))=0 and max (abs (T)) ＞ ε1, then system motion track is the period 1；
If length (E (E ＞ ε2))=1 and max (abs (T)) ＞ ε1, then system motion track is the period 2；
If length (E (E ＞ ε2))=2 and max (abs (T)) ＞ ε1, then system motion track is the period 3；
And so on,
If length (E (E ＞ ε2))=H and max (abs (T)) ＞ ε1, then system motion track is cycle H+1；
If length (E (E ＞ ε2)) ＞ H and max (abs (T)) ＞ ε1, then just give tacit consent to the Operation of Electric Systems track To be chaos or system unstability；H is any one natural number in 8 to 15；
Step 5), the coordinate value for removing one group of μ-η plane net lattice point again, and step 1) is turned to, until all N × N grids The corresponding attractor of point has been searched for.
Further, POWER SYSTEM STATE recognition methods proposed by the invention, in step 4), ε1=ε2=τ eP,3≤τ ≤ 5, wherein ePThe difference of periodic sequence maxima and minima generated for k levels system.
Further, POWER SYSTEM STATE recognition methods proposed by the invention, the electric power system model are：
Wherein, t represents the time, and μ represents electromagnetic power disturbance amplitude；η represents electromagnetic power forcing frequency.
The present invention compared with prior art, has following technique effect using above technical scheme：
The present invention compared with the sequence of calculation composes entropy complexity or maximum Lyapunov exponent, in the present invention using sequence it Between first-order error, be no longer time-consuming multiple iteration operation, the speed of service and the suction of program also therefore greatly improved Introduction search capability.In addition, multi-motion track is distinguished, and represent by single numerical value using error relationship in algorithm Come, the abundant dynamic behavior of parameter field is presented as much as possible.Generally extract l maximum point sequence in the present invention, and l takes Value brings great simplification to Error processing below in this way much smaller than L (number of iterative numerical result).In short, this hair The algorithm of bright offer can fast and accurately judge the form of attractor, and the system for presenting two-parameter domain variation enriches dynamics Behavior.
Description of the drawings
Fig. 1 is one machine infinity bus system model.
X when Fig. 2 is parameter μ=1.14 and η=0.61-x2Plane phasor.
X when Fig. 3 is parameter μ=1.18 and η=0.81-x2Plane phasor.
X when Fig. 4 is parameter μ=1.22 and η=0.81-x2Plane phasor.
X when Fig. 5 is parameter μ=1.26 and η=0.71-x2Plane phasor.
Symbol explanation in wherein Fig. 1：The equivalent generator of 1- systems I；The equivalent generator of 2- systems II；3- systems I's Equivalent main transformer；The equivalent main transformer of 4- systems II；5- load pieces；6- breakers；7- system interconnections.
Specific embodiment
Technical scheme of the present invention is described in further detail below in conjunction with the accompanying drawings：
Those skilled in the art of the present technique are it is understood that unless otherwise defined, all terms used herein are (including skill Art term and scientific terminology) there is the meaning identical with the general understanding of the those of ordinary skill in fields of the present invention.Also It should be understood that those terms such as defined in the general dictionary should be understood that with in the context of the prior art The consistent meaning of meaning, and unless defined as here, will not be explained with the meaning of idealization or too formal.
The present invention relates to a kind of ERROR ALGORITHMs for quick and precisely searching for attractor, know to solve the state of electric system Not.The algorithm composes entropy complicated dynamic behaviour or maximum by calculating the first-order error of maximum in sequence of iterations come alternative sequence Lyapunov indexes calculate so that the efficiency of algorithm of the algorithm is far above now there are two types of conventional method, and also is able to distinguish more The abundant dynamic behavior that system is generated with two-parameter variation is presented in kind attractor state.
Algorithm the specific steps are：
Assuming that a k ranks electric power system model is analyzed with model parameter μ and η respectively in section [μ1,μ2] and [η1,η2] Variation, distribution of the system motion state in μ-η planes.
1. μ-η planes are subjected to gridding, i.e., by section [μ1,μ2] and [η1,η2] it is respectively classified into N equal portions.It thus can be with It discusses as μ=μ1+n(μ2-μ1)/N, η=η1+n(η2-η1)/N, system motion track state when (n=1,2,3 ..., N).
2. as μ=μ1+n1(μ2-μ1)/N, η=η1+n2(η2-η1)/N,(n1,2=1,2,3 ..., N) when, according to quadravalence Runge-Kutta solves k levels system differential equation f (x1,x2,L xk), the sequence for obtaining system is
xin+1=xin+(Ki1+2Ki2+2Ki3+Ki4)/6, i=1,2 ..., k
In formula, Ki1=f (xi1,xi2,…,xik), Ki4=f (xin+h,xin+1+hKi3)。
3. in the L × k rank sequences calculated from step 2, the rank sequence X of l × 1={ x is taken out1,x2,…,xl}.Then, this is obtained Maximum point in group sequence, if
xm-1＜ xm＞ xm+1, m=2,3 ..., l-1
So, xmJust it is stored into new array T.It has screened and data descending arrangement in array is stored in array T=again {t1,t2,…,tj}。
4. couple array T={ t1,t2,…,tjIn element make difference successively, i.e.,
es-1=ts-ts-1, s=2,3 ..., j
By element es-1Descending arranges, and obtains an error array E={ e1,e2,…,ej-1}.There is also the need to establish two Critical value ε1And ε2For judging system motion state.Under normal circumstances, ε1=ε2=τ eP, 3≤τ≤5, wherein ePIt unites for k levels The difference of the periodic sequence maxima and minima of generation.
5. system motion condition adjudgement mode is：
Max if (abs (T))≤ε1, then fixed point is is stablized in system motion track；
If length (E (E ＞ ε2))=0 and max (abs (T)) ＞ ε1, then system motion track is the period 1；
If length (E (E ＞ ε2))=1 and max (abs (T)) ＞ ε1, then system motion track is the period 2；
If length (E (E ＞ ε2))=2 and max (abs (T)) ＞ ε1, then system motion track is the period 3；
If length (E (E ＞ ε2))=14 and max (abs (T)) ＞ ε1, then system motion track is the period 15；
If length (E (E ＞ ε2))=15 and max (abs (T)) ＞ ε1, then system motion track is the period 16；
Generally speaking, if length (E (E ＞ ε2)) ＞ 15 and max (abs (T)) ＞ ε1, then the Operation of Electric Systems Track is just defaulted as being chaos or system unstability.
Certainly, another situation as the present invention, if be not for the required precision of recognition result it is very stringent, can be with If it is arranged to length (E (E ＞ ε2)) ＞ 8 and max (abs (T)) ＞ ε1, then the Operation of Electric Systems track is just defaulted as It is chaos or system unstability.I.e.：
Max if (abs (T))≤ε1, then fixed point is is stablized in system motion track；
If length (E (E ＞ ε2))=0 and max (abs (T)) ＞ ε1, then system motion track is the period 1；
If length (E (E ＞ ε2))=1 and max (abs (T)) ＞ ε1, then system motion track is the period 2；
If length (E (E ＞ ε2))=2 and max (abs (T)) ＞ ε1, then system motion track is the period 3；
If length (E (E ＞ ε2))=8 and max (abs (T)) ＞ ε1, then system motion track is the period 9；
If length (E (E ＞ ε2)) ＞ 8 and max (abs (T)) ＞ ε1, then just give tacit consent to the Operation of Electric Systems track To be chaos or system unstability.
The judgment mode of system above motion state can require to be adjusted, to judge according to the accuracy of identification of system The chaos or instability status of electric system.
6. parameter μ and η remove the coordinate value of one group of μ-η plane net lattice point again, and turn to step 2, until all N × N nets The corresponding attractor of lattice point has been searched for.
Specific implementation process：
Model about electric system chaos study is mostly based on the Infinite bus power system system using synchronous motor as capital equipment System, as shown in Figure 1, system I and system II includes equivalent generator, equivalent main transformer, load piece, breaker；System II packets Include equivalent generator, equivalent main transformer, load piece, breaker；System I is connected with system II by system interconnection 7.
Consider electromagnetic power disturbance, obtaining a second order mathematical models of power system that t changes at any time is：
Wherein μ represents electromagnetic power disturbance amplitude, and η represents electromagnetic power forcing frequency, is that can embody electric system work( Two important parameters of rate shock wave.
The section of parameter μ and η are subjected to five deciles, are utilized respectively sequence spectrum entropy product complexity theory, maximum Lyapunov refers to Number method and ERROR ALGORITHM provided by the invention obtain movement of the above-mentioned second order one machine infinity bus system under corresponding Parameter Conditions State, as shown in table 1, table 2 and table 3.
Wherein, 0.5,0.6,0.7,0.8,0.9,1 expression parameter η in table 1- tables 3 can value；7.5,7.7,7.9, 8.1,8.3,8.5 expression parameter μ's can value.
In table 1, spectrum entropy complexity is more than 0.39, then it represents that system is in chaotic motion state；Conversely, system is in the period Motion state.
In table 2, maximum Lyapunov exponent is less than 0.1, then it represents that system is in periodic motion state；Conversely, at system In chaotic motion state.
In table 3,17 expression systems are in chaotic motion state or system is in instability status；I (i=1,2 ..., 16) Expression system is in period i motion state.
Can be seen that spectrum entropy product complexity theory from three tables cannot distinguish period and chaos substantially, can not distinguish not With the movement locus of periodicity；Largest Lyapunov exponent method distinguishes the period and the effect comparison entropy product complexity theory of chaos is good, But it cannot equally identify that movement locus is a few periods；ERROR ALGORITHM provided by the invention accurately identifies the movement of different cycles number Track and chaotic motion track.
In addition, in order to which the validity of the algorithm is presented, the present embodiment provides some phase path figures, respectively such as Fig. 2 to Fig. 5 institutes Show.Wherein, x when Fig. 2 is parameter μ=1.14 and η=0.61-x2Plane phasor；X when Fig. 3 is parameter μ=1.18 and η=0.81- x2Plane phasor；X when Fig. 4 is parameter μ=1.22 and η=0.81-x2Plane phasor；When Fig. 5 is parameter μ=1.26 and η=0.7 x1-x2Plane phasor.
Table 1 composes the system motion state that entropy product complexity theory obtains
0.6 0.7 0.8 0.9 1 1.1
1.10 0.1218 0.2328 0.1253 0.1967 0.1837 0.0118
1.14 0.2119 0.3372 0.0606 0.0181 0.1358 0.0770
1.18 0.2090 0.2377 0.1246 0.1683 0.1916 0.0796
1.22 0.2241 0.1663 0.2308 0.2031 0.1436 0.0436
1.26 0.1625 0.2079 0.2915 0.2066 0.0944 0.0316
1.30 0.1494 0.2060 0.3320 0.1130 0.0303 0.1896
The system motion state that 2 maximum Lyapunov exponent algorithm of table obtains
0.6 0.7 0.8 0.9 1 1.1
1.10 0 0.0544 0 0 0 0
1.14 0 0.0434 0 0 0 0
1.18 0 0.0516 0 0 0 0
1.22 0 0.0528 0.0543 0 0 0
1.26 0 0.0639 0.0522 0 0 0
1.30 0.0422 0.0533 0.0546 0 0 0
The system motion state that 3 ERROR ALGORITHM of table obtains
0.6 0.7 0.8 0.9 1 1.1
1.10 2 17 1 1 1 1
1.14 2 17 1 1 1 1
1.18 2 17 2 1 1 1
1.22 2 17 17 1 1 1
1.26 2 17 17 1 1 1
1.30 17 17 17 1 1 1
Obtain table 1, table 2 and table 3 as a result, time for being used respectively under the conditions of equal allocation of computer of three kinds of algorithms such as Shown in table 4.From table 4, it can be seen that largest Lyapunov exponent method run time longest；ERROR ALGORITHM operation provided by the invention Time is close with spectrum entropy product complexity theory run time.
4 three kinds of algorithm speed of service comparisons of table
Compose entropy complexity Maximum Lyapunov exponent Error
Run time 7.037366 the second 168.696677 the second 7.097847 the second
In conclusion ERROR ALGORITHM provided by the invention is a kind of to be used for searching for two-parameter domain attractor, quickly and efficiently Method, play an important role in terms of electric system chaotic characteristic is analyzed.The present invention is by calculating maximum in sequence of iterations First-order error judge system motion track, and a variety of attractor states can be distinguished, system is presented with two-parameter variation The abundant dynamic behavior generated.Simple first-order error is pertained only to using extreme value ERROR ALGORITHM, is answered with existing sequence spectrum entropy Miscellaneous degree calculates or Lyapunov exponent calculation is compared, and the present invention is capable of the movement locus of identifying system very well, is counting on an equal basis Under calculation machine configuration condition, computational efficiency is far above existing conventional method.
The above is only some embodiments of the present invention, it is noted that for the ordinary skill people of the art For member, various improvements and modifications may be made without departing from the principle of the present invention, these improvements and modifications also should It is considered as protection scope of the present invention.

Claims (5)

  1. It is 1. a kind of based on the POWER SYSTEM STATE recognition methods for quick and precisely searching for attractor error algorithm, which is characterized in that
    First, it establishes a k rank electric power system model, chooses electromagnetic power disturbance amplitude and its frequency the two parameters, according to Model obtains distribution of the system motion state in section variation plane with the constant interval of the two parameters；
    Then, the k levels system differential equation is solved according to numerical analysis method and obtains the sequence of system, by calculating in sequence of iterations The first-order error of maximum judges system motion track, and it is period, chaos or stable point to identify POWER SYSTEM STATE.
  2. 2. according to the method described in claim 1, it is characterized in that, set model parameter electromagnetic power disturbance amplitude μ and electromagnetic work Rate forcing frequency η is respectively in section [μ1,μ2] and [η1,η2] variation, μ-η planes are subjected to gridding, i.e., by section [μ1,μ2] and [η1,η2] N equal portions are respectively classified into, obtain distribution of the system motion state in section variation plane.
  3. 3. according to the method described in claim 2, it is characterized in that, described solve electric power system model according to numerical analysis method Obtain the sequence of system, by calculate the first-order error of maximum in sequence of iterations judge system motion track, in particular to：
    Step 1), as μ=μ1+n1(μ2-μ1)/N, η=η1+n2(η2-η1During)/N, k levels are solved according to quadravalence Runge-Kutta Unite differential equation f (x1,x2,…,xk), the sequence of iterations for obtaining system is：
    xin+1=xin+(Ki1+2Ki2+2Ki3+Ki4)/6, i=1,2 ..., k
    In formula, Ki1=f (xi1,xi2,…,xik), Ki4=f (xin+h,xin+1+hKi3), n1,2=1,2,3 ..., N；N=1,2,3 ..., N；
    Step 2), from L × k rank sequences that step 1) calculates, take out the rank sequence X of l × 1={ x1,x2,…,xl, then, ask Go out the maximum point in this group of sequence, if
    xm-1＜ xm＞ xm+1, m=2,3 ..., l-1
    So, xmNew array T is just stored into, screened and data descending arrangement in array is stored in array T={ t again1, t2,…,tj}；Wherein, L represents the number of iterative numerical result, l ＜ ＜ L；
    Step 3), to array T={ t1,t2,…,tjIn element make difference successively, i.e.,
    es-1=ts-ts-1, s=2,3 ..., j
    By element es-1Descending arranges, and obtains an error array E={ e1,e2,…,ej-1}；
    Step 4) establishes two critical value ε1And ε2For judging system motion state, system motion condition adjudgement mode is：
    Max if (abs (T))≤ε1, then fixed point is is stablized in system motion track；
    If length (E (E ＞ ε2))=0 and max (abs (T)) ＞ ε1, then system motion track is the period 1；
    If length (E (E ＞ ε2))=1 and max (abs (T)) ＞ ε1, then system motion track is the period 2；
    If length (E (E ＞ ε2))=2 and max (abs (T)) ＞ ε1, then system motion track is the period 3；
    ●
    ●
    ●
    And so on,
    If length (E (E ＞ ε2))=H and max (abs (T)) ＞ ε1, then system motion track is cycle H+1；
    If length (E (E ＞ ε2)) ＞ H and max (abs (T)) ＞ ε1, then the Operation of Electric Systems track be just defaulted as be Chaos or system unstability；H is any one natural number in 8 to 15；
    Step 5), the coordinate value for removing one group of μ-η plane net lattice point again, and step 1) is turned to, until all N × N mesh points pair The attractor answered has been searched for.
  4. 4. according to the method described in claim 3, it is characterized in that, in step 4), ε1=ε2=τ eP, 3≤τ≤5, wherein ePFor k The difference of periodic sequence maxima and minima that level system generates.
  5. 5. according to the method described in claim 1, it is characterized in that, electric power system model is：
    Wherein, t represents the time, and μ represents electromagnetic power disturbance amplitude；η represents electromagnetic power forcing frequency.
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CN110910271A (en) * 2019-09-29 2020-03-24 浙江大学 Power terminal fingerprint construction method based on power consumption and EMI
CN110910271B (en) * 2019-09-29 2021-07-06 浙江大学 Power terminal fingerprint construction method based on power consumption and EMI
CN111683369A (en) * 2020-06-04 2020-09-18 重庆邮电大学 Hierarchical digital chaotic encryption method for body area network data transmission
CN111683369B (en) * 2020-06-04 2023-02-17 重庆邮电大学 Hierarchical digital chaotic encryption method for body area network data transmission
CN113642119A (en) * 2021-07-13 2021-11-12 武汉理工大学 Method for rapidly determining discontinuous system Lyapunov exponential spectrum
CN113642119B (en) * 2021-07-13 2023-10-27 武汉理工大学 Method for rapidly determining Lyapunov index spectrum of discontinuous system

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