CN113222095B - Fractional order prediction auxiliary state estimation method for power system based on evolutionary computation - Google Patents

Fractional order prediction auxiliary state estimation method for power system based on evolutionary computation Download PDF

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CN113222095B
CN113222095B CN202110378235.4A CN202110378235A CN113222095B CN 113222095 B CN113222095 B CN 113222095B CN 202110378235 A CN202110378235 A CN 202110378235A CN 113222095 B CN113222095 B CN 113222095B
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吴争光
陆康迪
刘妹琴
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Abstract

The invention discloses an electric power system fractional order prediction auxiliary state estimation method based on evolutionary computation, which is based on prediction auxiliary state estimation, establishes a fractional order state transition matrix to represent the dynamic characteristic of an electric power system through a fractional order calculus theory, adopts a fractional order expansion Kalman filter as a filtering method, then takes the average value of errors between a system estimation result and a reference value as an optimization objective function from the optimization angle, performs optimization solution by a genetic optimization solution method to overcome the problem of fractional order parameter setting, designs an optimal fractional order expansion Kalman filtering method, and realizes the electric power system fractional order auxiliary state estimation. The beneficial effects of the invention are as follows: compared with system modeling based on integer order, the method can more accurately establish the dynamic characteristic model of the power system and has higher state estimation accuracy; compared with the empirical rule setting method, the method can set fractional order more intelligently, is simpler to implement and has higher setting efficiency.

Description

Fractional order prediction auxiliary state estimation method for power system based on evolutionary computation
Technical Field
The invention belongs to the technical field of power system state estimation, and particularly relates to a power system fractional order prediction auxiliary state estimation method based on evolutionary computation.
Background
The main function of the power system state estimation filter is to provide accurate information for an Energy Management System (EMS), and the filter is a core part in the EMS, and an accurate state estimation result is an indispensable key part for maintaining safe, reliable, high-quality and economic operation of a modern power system. The basic principle of the prediction auxiliary state estimation is to analyze and utilize the state variables at the past moment so as to estimate the system state value at the next moment. Therefore, how to design an effective prediction auxiliary state estimation method to ensure stable operation of a modern power system has important engineering application value.
At present, mainstream technologies of a state estimation method of a prediction-aided technology mainly include an iterative least square method, extended kalman filtering, unscented kalman filtering and the like, and although good results are obtained under partial working conditions, the establishment of a model still has defects in consideration of the complex conditions of time-varying property, dynamic characteristic and the like of a modern power system. The prior art is designed based on a traditional integer order model, and is difficult to deal with the application of a modern power system in an environment with higher requirements on safe and stable operation. Therefore, for the complex characteristics of modern power systems, how to establish a more accurate model and design a more effective state estimation method is one of the important technical problems that must be solved in the field of power system state estimation.
The fractional calculus theory is an expansion of integral calculus, has been successfully applied in the system modeling fields of power electronics, chemical engineering process, wireless charging and the like, but has rarely been applied in the prediction auxiliary state estimation of the power system. However, how to determine the fractional order in the modeling process is also one of the key technical problems in building an accurate model.
Disclosure of Invention
The invention aims to provide a power system fractional order prediction auxiliary state estimation method based on evolutionary computation, aiming at the defects of the prior art.
The purpose of the invention is realized by the following technical scheme: a fractional order prediction auxiliary state estimation method of a power system based on evolutionary computation comprises the following steps:
(1) a power system prediction auxiliary state estimation model based on a fractional order state transition matrix is established through a mechanism analysis method and a fractional order calculus theory.
(2) And setting the parameter value of the evolutionary computation.
(3) A real number encoded population PG is randomly generated.
(4) And according to a fractional Kalman filtering method, performing fitness function evaluation on all individuals in the current population PG according to an optimization target, and sequencing the individuals from small to large according to fitness function values.
(5) Selecting operation: and selecting the individuals with half population scale with smaller fitness function value from the population PG, and copying the individuals to form a new population PS.
(6) And (3) cross operation: and (3) forming two individuals in the population PS into a group, generating random numbers between 0 and 1 for each group, and generating two new individuals in a crossed manner only when the random numbers are greater than the preset cross probability, otherwise, keeping the random numbers unchanged, and finally obtaining a new population PC.
(7) Mutation operation: generating a random number between 0 and 1 for each individual in the population PC, carrying out mutation to generate a new individual only when the random number is greater than a preset mutation probability, and obtaining a new population PG finally if the random number is not changed; wherein, the new population PG keeps the individual with the minimum fitness function value in the previous generation of population PG.
(8) And (5) repeating the steps (4) to (7) until the iteration number of the genetic optimization solver reaches the preset maximum iteration number.
(9) And taking the individual with the minimum fitness function value obtained by the last iteration as the optimal order output of the fractional order state transition matrix of the power system, applying the optimal order output to an energy management system of the power system, and acquiring the state estimation values of the voltage amplitude and the voltage phase angle of all nodes in the power system in real time.
Further, in step (1), the power system prediction auxiliary state estimation model based on the fractional order state transition matrix specifically includes:
Figure BDA0003011675840000021
Figure BDA0003011675840000022
zk＝h(xk)+vk (3)
wherein the content of the first and second substances,
Figure BDA0003011675840000023
k denotes the sampling instant, w denotes the past sampling instant, w ═ 1, 2., k, n denote the number of state estimates, α ═ α [ [ α [ ]1,…,αn]The order of the fractional order is represented,
Figure BDA0003011675840000024
representing Hamiltonian, xkRepresents the system vector at time k (including all node voltage amplitudes and voltage phase angles), zkThe measured values (including the active and reactive power of the nodes, the active and reactive power of the branches), v representing the monitoring and data acquisition System (SCADA) at time kkRepresenting the observed noise at time k, ωk-1Representing the process noise at time k-1, fk-1(. h.) represents a relation function of the state variable and the measured variable.
Further, the air conditioner is provided with a fan,
Figure BDA0003011675840000025
fk-1(. h), h (. cndot.) are described in detail as follows:
Figure BDA0003011675840000026
Figure BDA0003011675840000031
Figure BDA0003011675840000032
wherein x isk,lDenotes the ith state estimate, x, at time kk-w，lRepresents the estimated value of the ith state at the time k-w, hm(xk) The mth measurement equation at the kth time is shown, M is 1,2, …, M represents the measured quantities obtained, the subscript s and the subscript j represent two different node numbers, VsAnd VjRepresenting the electricity of node s and node j, respectivelyMagnitude of pressure, θsRepresenting the phase angle of the voltage at node s, PsRepresenting the injected active power, Q, of node ssRepresenting the injected reactive power, P, of node ssjRepresenting the active power of the line between node s and node j, QsjRepresenting reactive power of the line between node s and node j, zmDenotes the m-th measured value at the k-th time, zVs,zθs,zPs,zQsThe voltage amplitude, the voltage phase angle, the measurement of the active injection power and the reactive injection power, z of the node s are representedPsjAnd zQsjRespectively representing the measurements of the active and reactive power of the line between node s and node j, ZV,Zθ,ZP,ZQRepresenting the measured set of the voltage amplitude, the voltage phase angle, the active injection power and the reactive injection power, ZPfAnd ZQfRespectively representing the measurement sets of the active power and the reactive power of the line, J representing the set of the node J, GsjAnd BsjRespectively representing the conductance and susceptance between node s and node j, thetasjRepresenting the phase angle difference between node s and node j, AkRepresenting a fractional order state transition matrix at time k, ΘkRepresents the set of voltage phase angles, Ω, at time kkRepresenting a set of voltage amplitude values at time k.
Further, in step (1), the time k is a fractional order state transition matrix AkSpecifically, the method can be calculated through the following substeps:
(1.1) combining the equations (1) to (2):
Figure BDA0003011675840000033
(1.2) setting up
Figure BDA0003011675840000034
Combined acquisition of power system front TtThe state estimation information of each moment can obtain:
Figure BDA0003011675840000035
wherein the content of the first and second substances,
Figure BDA0003011675840000036
(1.3) calculating to obtain a fractional order state transition matrix of the power system according to a least square estimation method:
Figure BDA0003011675840000037
further, in step (2), the parameter includes a maximum number of iterations GmaxPopulation size N, probability of crossover operation pcProbability p of mutation operationmVariation parameter mpA process noise covariance matrix Q, a measurement covariance matrix R, and an initial state covariance matrix P0。
Further, in step (3), the population PG is:
PG＝{I1,I2,…,IN}
Iμ＝αL+(αU-αL)×Ψμ,μ＝1,2,...,N (10)
wherein, the mu individual IμRepresenting the fractional order { alpha ] to be optimized1,α2,...,αn}，αLAnd alphaURespectively representing the lower and upper limits, Ψ, of the fractional orderμRepresenting a set of random numbers generated between 0 and 1.
Further, in the step (4), fitness function evaluation is performed on all individuals in the current population PG according to optimization targets shown in formulas (11) to (18), and the obtained N fitness function values F are ranked from small to large
Figure BDA0003011675840000041
Wherein
Figure BDA0003011675840000042
Is an index number of the sort.
Figure BDA0003011675840000043
Figure BDA0003011675840000044
Figure BDA0003011675840000045
Figure BDA0003011675840000046
Figure BDA0003011675840000047
Figure BDA0003011675840000048
Figure BDA0003011675840000049
Pk＝Pk|k-1-KkHKPk|k-1 (18)
Wherein, TNThe time window is represented by a time window,
Figure BDA00030116758400000410
indicating the l-th system state estimate, l-1, 2, …, n,
Figure BDA00030116758400000411
a true value representing the estimated value of the ith system state;
Figure BDA00030116758400000412
the predicted value of the state at the moment k is shown,
Figure BDA00030116758400000413
represents the state estimate at time k-1, Pk|k-1Representing the state prediction covariance matrix at time k, HkRepresenting the Jacobian matrix derived from the state vector and the measurement vector at time k,
Figure BDA00030116758400000414
represents the predicted measurement value at time K, KkRepresenting the Kalman filter gain at time k, PkRepresenting the state estimate covariance matrix at time k, Qk-1Representing the process noise covariance matrix, R, at time k-1kRepresenting the measured covariance matrix at time k, vkRepresenting the observed noise at time k.
Further, in step (5), the new population PS is:
Figure BDA00030116758400000415
wherein, the population scale N is even number, I represents individual,
Figure BDA00030116758400000416
and
Figure BDA00030116758400000417
denotes an index number of
Figure BDA00030116758400000418
And
Figure BDA00030116758400000419
the corresponding individual.
Further, in step (6), a population PC ═ PS is set, for the i-th individual PS in the PSiWherein i represents an odd number of 1 to N, to generate a random number r uniformly distributed from 0 to 1pcIf r ispcIs less than pcUpdating the ith individual and the (i + 1) th individual PCs in the population PC according to the real number intersection operation shown in the formulas (20) to (21)iAnd PCi+1Else PCiAnd PCi+1Remain unchanged.
PCi＝rpc×PSi+1+(1-rpc)×PSi (20)
PCi+1＝rpc×PSi+(1-rpc)×PSi+1 (21)
Wherein r ispcRepresenting a set of uniformly distributed random numbers from 0 to 1.
Further, in step (7), the population PM is set to PC for the μ -th individual PC among PCsμGenerating a random number r in the range of 0 to 1pmIf r ispmIs less than pmGenerating new individuals according to the real number variation operation shown in the formula (22), otherwise, generating the mu-th individual PM in the PMsμKeeping unchanged until the whole population PC is traversed, and ensuring that the optimal individual is not damaged
Figure BDA0003011675840000052
And sets the current population PG ═ PM.
Figure BDA0003011675840000051
Where μ ═ 1,2, …, N, PM (μ, d) and PC (μ, d) denote the d-th variable of the μ -th individual in the population PM and PC, respectively, and αL(d) And alphaU(d) Respectively represent the lower limit and the upper limit of the d-th variable, r1And r2Represents a uniform random number, k, generated in the range of 0 to 1gRepresenting the current number of iterations, mpRepresenting a variation parameter.
The invention has the beneficial effects that:
1. compared with system modeling based on an integer order, the dynamic characteristic of a modern power system can be more accurately represented, higher state estimation accuracy is obtained, and safe and reliable operation of a power grid is guaranteed;
2. the invention intelligently sets the fractional order through the evolutionary algorithm, and compared with a setting method based on the empirical rule, the method is simpler to implement and more efficient.
Drawings
FIG. 1 is a block diagram of an IEEE-14 node power system embodying the present invention;
FIG. 2 is a schematic diagram of an implementation process of power system fractional order prediction aided state estimation based on evolutionary computation;
FIG. 3 is a graph comparing the voltage amplitude state estimation absolute error results at each node using the Extended Kalman (EKF) method according to an embodiment of the present invention;
FIG. 4 is a graph comparing the voltage phase angle state estimation absolute error results at each node using the EKF method and the method of the present invention.
Detailed Description
The purpose and effect of the present invention will be more apparent from the following further description of the present invention with reference to the accompanying drawings.
Taking the IEEE 14 node power system shown in fig. 1 as an example, acquiring parameters and corresponding measurement values of the power system through MATPOWER software, the method for estimating the fractional order prediction aided state of the power system based on the evolutionary computation of the invention, as shown in fig. 2, includes the following steps:
(1) establishing a prediction auxiliary state estimation model based on a fractional order state transition matrix power system through a mechanism analysis method and a fractional order calculus theory:
Figure BDA0003011675840000061
Figure BDA0003011675840000062
zk＝h(xk)+vk (3)
wherein the content of the first and second substances,
Figure BDA0003011675840000063
k denotes a sampling time, w denotes a past sampling time, w is 1,2, and k, w is 1, which denotes a 1 st time; x is the number ofkRepresenting a system vector at the k moment, including the voltage amplitude and the voltage phase angle of all nodes;zkthe measurement values of a monitoring and data acquisition System (SCADA) at the moment k are represented, and comprise active power and reactive power of nodes and active power and reactive power of branches; v. ofkRepresenting the observed noise at time k, ωk-1Representing the process noise at time k-1;
Figure BDA0003011675840000064
α＝[α1,…,αn]representing the fractional order, n represents the number of state estimates,
Figure BDA0003011675840000065
representing a hamiltonian; f. ofk-1(. h.) represents a relation function of the state variable and the measured variable.
Figure BDA0003011675840000066
fk-1(. h), h (. cndot.) are described in detail as follows:
Figure BDA0003011675840000067
Figure BDA0003011675840000068
wherein
Figure BDA0003011675840000071
Figure BDA0003011675840000072
Wherein, l is 1,2, … n; m is 1,2, …, M represents the number of measurements taken; x is the number ofk,lDenotes the ith state estimate, x, at time kk-w，lRepresenting the estimated value of the ith state at the k-w moment; h ism(xk) An mth measurement equation representing a kth time; subscript s and subscript j denote two different node numbers, VsAnd VjRepresenting the voltage amplitudes, θ, of nodes s and j, respectivelysRepresenting the phase angle of the voltage at node s, PsRepresenting the injected active power, Q, of node ssRepresenting the injected reactive power, P, of node ssjRepresenting the active power of the line between node s and node j, QsjRepresenting the reactive power of the line between node s and node j; z is a radical ofmRepresents the m-th measurement value at the k-th time; z is a radical ofVs,zθs,zPs,zQsThe measurement of the voltage amplitude, the voltage phase angle, the active injection power and the reactive injection power of the node s, zPsjAnd zQsjRespectively representing the measurement of the active power and the reactive power of the line between the node s and the node j; zV,Zθ,ZP,ZQRepresenting a measurement set of voltage amplitude, voltage phase angle, active injection power and reactive injection power; zPfAnd ZQfRespectively measuring and collecting the active power and the reactive power of the line; j represents a set of nodes J; gsjAnd BsjRespectively representing the conductance and susceptance between node s and node j, thetasjRepresenting the phase angle difference between node s and node j. A. thekRepresenting a fractional order state transition matrix at time k, ΘkRepresents the set of voltage phase angles, Ω, at time kkRepresenting a set of voltage amplitude values at time k.
In the step (1), a k moment fractional order state transition matrix AkSpecifically, the method can be calculated through the following substeps:
(1.1) combining the equations (1) to (2):
Figure BDA0003011675840000073
(1.2) setting up
Figure BDA0003011675840000074
Combined acquisition of power system front TtThe state estimation information of each moment can obtain:
Figure BDA0003011675840000075
wherein the content of the first and second substances,
Figure BDA0003011675840000076
(1.3) calculating to obtain a fractional order state transition matrix of the power system according to a least square estimation method:
Figure BDA0003011675840000081
(2) setting parameter values: maximum number of iterations Gmax30, population size N30, probability of crossover operation pc0.8, probability of mutation operation pm0.1, variation parameter m p3, the process noise covariance matrix Q10-4×I28×28，I28×28Denotes a 28 × 28 identity matrix, and the measured covariance matrix R is 10-4×I119×119，I119×119An identity matrix representing 119 x 119, and an initial state covariance matrix P0＝10-2×I28×28；
(3) Randomly generating a real number coded population PG ═ I1,I2,…,INH, wherein the μ th individual IμRepresenting the fractional order { alpha ] to be optimized1,α2,...,αnThe specific process is as follows:
Iμ＝αL+(αU-αL)×Ψμ,μ＝1,2,...,N (10)
wherein alpha isLAnd alphaURespectively representing the lower and upper limits, alpha, of the fractional orderL＝0.1×I1×28，αU＝1.9×I1×28，I1×281 x 28 vector with all 1 elements, ΨiRepresenting a set of random numbers generated between 0 and 1.
(4) According to a fractional Kalman filtering method, carrying out fitness function evaluation on all individuals in the current population PG according to optimization targets shown in formulas (11) to (18), and according to N obtained fitness functionsThe response function values F are sorted from small to large
Figure BDA0003011675840000082
Smaller F value indicates better individual, wherein
Figure BDA0003011675840000083
Is a sorting index number; the sequence is shown in parentheses for the purpose of sorting,
Figure BDA0003011675840000084
is an index.
Figure BDA0003011675840000085
Figure BDA0003011675840000086
Figure BDA0003011675840000087
Figure BDA0003011675840000088
Figure BDA0003011675840000089
Figure BDA00030116758400000810
Figure BDA00030116758400000811
Pk＝Pk|k-1-KkHKPk|k-1 (18)
Wherein, TNWhen it is indicatedIntermediate window, TN＝55；
Figure BDA0003011675840000091
Represents the estimated value of the l-th system state,
Figure BDA0003011675840000092
a true value indicating the estimated value of the l-th system state, l-1, 2, … n,
Figure BDA0003011675840000093
the predicted value of the state at the moment k is shown,
Figure BDA0003011675840000094
representing the state estimate at time k-1; gamma ray1Represents γ corresponding to when w is 1wA value; pk|k-1Representing the state prediction covariance matrix at time k, HkRepresenting the Jacobian matrix derived from the state vector and the measurement vector at time k,
Figure BDA0003011675840000095
represents the predicted measurement value at time K, KkRepresenting the Kalman filter gain at time k, PkRepresenting the state estimate covariance matrix at time k, Qk-1Representing the process noise covariance matrix, R, at time k-1kRepresenting the measured covariance matrix at time k, vkRepresenting the observed noise at time k.
(5) Selecting operation: selecting the better individual from the population PG according to the formula (19), namely selecting the rank number in the population PG according to the fitness function value F
Figure BDA0003011675840000096
To
Figure BDA0003011675840000097
For the individual of (2), then the sorting index number is
Figure BDA0003011675840000098
To
Figure BDA0003011675840000099
To obtain a new population PS:
Figure BDA00030116758400000910
wherein the population size N is an even number; i represents the number of individuals,
Figure BDA00030116758400000911
and
Figure BDA00030116758400000912
denotes an ordering index number of
Figure BDA00030116758400000913
And
Figure BDA00030116758400000914
the corresponding individual.
(6) And (3) cross operation: first, a population PC ═ PS is set, and PS is designated for the i-th individual in PSiWherein i represents an odd number of 1 to N, to generate a random number r uniformly distributed from 0 to 1pcIf r ispcIs less than pcUpdating the ith individual and the (i + 1) th individual PCs in the population PC according to the real number intersection operation of the formulas (20) to (21)iAnd PCi+1Else PCiAnd PCi+1Remain unchanged.
PCi＝rpc×PSi+1+(1-rpc)×PSi (20)
PCi+1＝rpc×PSi+(1-rpc)×PSi+1 (21)
Wherein r ispcRepresenting a set of uniformly distributed random numbers from 0 to 1.
(7) Mutation operation: first, a population PM is set to PC, for the μ th individual PC among PCsμGenerating a random number r in the range of 0 to 1pmIf r ispmIs less than pmA new individual is generated according to the real number mutation operation of equation (22), otherwise in PMμ individual PMμKeeping unchanged until the whole population PC is traversed, and ensuring that the optimal individual is not damaged
Figure BDA00030116758400000915
And sets the current population PG ═ PM.
Figure BDA00030116758400000916
Wherein PM (μ, d) and PC (μ, d) represent the d variable of the μ individual in the population PM and PC, respectively, αL(d) And alphaU(d) Respectively represent the lower limit and the upper limit of the d-th variable, r1And r2Represents a uniform random number, k, generated in the range of 0 to 1gRepresenting the current number of iterations, mpRepresenting a variation parameter.
(8) Repeating the steps (4) to (7) until the iteration number k of the genetic optimization solvergTo reach Gmax＝30；
(9) Obtained by the last iteration
Figure BDA0003011675840000101
And the state estimation values of the voltage amplitude values and the voltage phase angles of all nodes in the power system can be obtained in real time by the EMS through a monitoring computer according to the formula (12) to the formula (16).
Table 1 shows the comparison of the mean absolute error results of voltage amplitude and voltage phase angle state estimation at all nodes using the EKF method and the method of the present invention. As can be seen from FIGS. 3, 4 and Table 1, smaller voltage magnitude estimation errors and voltage phase angle estimation errors were obtained with the method of the present invention than with the EKF method. Through the comparison and analysis of the power system operation experimental results of the EKF and the technology, the method can obtain higher state estimation precision than the EKF, verifies that the method has higher precision on the auxiliary prediction state estimation of the power system, and can better meet the requirements of the analysis and control of the power system.
Table 1: mean absolute error result comparison
Method Average absolute error of voltage amplitude (pu) Mean absolute error of voltage phase angle (rad)
EKF 6.40×10-4 1.42×10-3
The invention relates to an estimation method 5.03×10-4 1.28×10-3
In summary, the power system fractional order prediction aided state estimation can be realized by adopting the invention, and the invention has the following advantages that the prior art does not have: the nonlinear characteristic and the dynamic characteristic of a modern power system can be more accurately represented, the state estimation accuracy is improved, and the safe and reliable operation of a power grid is ensured; the fractional order is intelligently set, the implementation is simpler, and the setting efficiency is higher.

Claims (9)

1. A power system fractional order prediction auxiliary state estimation method based on evolutionary computation is characterized by comprising the following steps:
(1) establishing a prediction auxiliary state estimation model based on a fractional order state transition matrix power system through a mechanism analysis method and a fractional order calculus theory, and specifically comprising the following steps of:
▽αxk＝fk-1(xk-1)+ωk-1 (1)
Figure FDA0003397144150000011
zk＝h(xk)+vk (3)
wherein the content of the first and second substances,
Figure FDA0003397144150000012
k denotes the sampling instant, w denotes the past sampling instant, w ═ 1, 2., k, n denote the number of state estimates, α ═ α [ [ α [ ]1,…,αn]Represents a fractional order, and ∑ represents a hamiltonian; x is the number ofkRepresenting a system vector at the k moment, including voltage amplitudes and voltage phase angles of all nodes; z is a radical ofkThe measured values of the monitoring and data acquisition system at the moment k are represented, and comprise active power and reactive power of the nodes and active power and reactive power of the branches; v. ofkRepresenting the observed noise at time k, ωk-1Representing the process noise at time k-1, fk-1(. h) represents a relation function of the state variable and the measured variable;
(2) setting a parameter value of the evolutionary computation;
(3) randomly generating a real number coded population PG;
(4) according to a fractional Kalman filtering method, all individuals in the current population PG are subjected to fitness function evaluation according to an optimization target, and the individuals are sorted from small to large according to fitness function values;
(5) selecting operation: selecting individuals with half population scale with smaller fitness function value from the population PG, and copying the individuals to form a new population PS;
(6) and (3) cross operation: all individuals in the population PS are in a group, random numbers between 0 and 1 are generated for each group, two new individuals are generated in a crossed mode only when the random numbers are larger than the preset crossed probability, otherwise, the two new individuals are not changed, and finally a new population PC is obtained;
(7) mutation operation: generating a random number between 0 and 1 for each individual in the population PC, carrying out mutation to generate a new individual only when the random number is greater than a preset mutation probability, and obtaining a new population PG finally if the random number is not changed; wherein, the new population PG reserves the individual with the minimum fitness function value in the previous generation of population PG;
(8) repeating the steps (4) to (7) until the iteration number of the genetic optimization solver reaches a preset maximum iteration number;
(9) and taking the individual with the minimum fitness function value obtained by the last iteration as the optimal order output of the fractional order state transition matrix of the power system, applying the optimal order output to an energy management system of the power system, and acquiring the state estimation values of the voltage amplitude and the voltage phase angle of all nodes in the power system in real time.
2. The evolutionary-computing-based power system fractional order prediction aided state estimation method of claim 1, wherein v &, f &k-1(. h), h (. cndot.) are described in detail as follows:
Figure FDA0003397144150000021
wherein
Figure FDA0003397144150000022
Figure FDA0003397144150000023
Wherein
Figure FDA0003397144150000024
fk-1(xk-1)＝Akxk-1Wherein
Figure FDA0003397144150000025
Wherein x isk,lDenotes the ith state estimate, x, at time kk-w，lRepresents the estimated value of the ith state at the time k-w, hm(xk) The mth measurement equation at the kth time is shown, M is 1,2, …, M represents the measured quantities obtained, the subscript s and the subscript j represent two different node numbers, VsAnd VjRepresenting the voltage amplitudes, θ, of nodes s and j, respectivelysRepresenting the phase angle of the voltage at node s, PsRepresenting the injected active power, Q, of node ssRepresenting the injected reactive power, P, of node ssjRepresenting the active power of the line between node s and node j, QsjRepresenting reactive power of the line between node s and node j, zmDenotes the m-th measured value at the k-th time, zVs,zθs,zPs,zQsThe voltage amplitude, the voltage phase angle, the measurement of the active injection power and the reactive injection power, z of the node s are representedPsjAnd zQsjRespectively representing the measurements of the active and reactive power of the line between node s and node j, ZV,Zθ,ZP,ZQRepresenting the measured set of the voltage amplitude, the voltage phase angle, the active injection power and the reactive injection power, ZPfAnd ZQfRespectively representing the measurement sets of the active power and the reactive power of the line, J representing the set of the node J, GsjAnd BsjRespectively representing the conductance and susceptance between node s and node j, thetasjRepresenting the phase angle difference between node s and node j, AkRepresenting a fractional order state transition matrix at time k, ΘkRepresents the set of voltage phase angles, Ω, at time kkRepresenting a set of voltage amplitude values at time k.
3. The evolutionary computing-based power system fractional order prediction aided state estimation method according to claim 2, wherein in the step (1), the time k fractional order state transition matrix AkSpecifically, the method can be calculated through the following substeps:
(1.1) combining the equations (1) to (2):
Figure FDA0003397144150000026
(1.2) setting up
Figure FDA0003397144150000027
Combined acquisition of power system front TtThe state estimation information of each moment can obtain:
Figure FDA0003397144150000031
wherein the content of the first and second substances,
Figure FDA0003397144150000032
(1.3) calculating to obtain a fractional order state transition matrix of the power system according to a least square estimation method:
Figure FDA0003397144150000033
4. the evolutionary computing-based fractional order prediction aided state estimation method for the power system according to claim 3, wherein in the step (2), the parameter comprises a maximum iteration number GmaxPopulation size N, probability of crossover operation pcProbability p of mutation operationmVariation parameter mpA process noise covariance matrix Q, a measurement covariance matrix R, and an initial state covariance matrix P0。
5. The method for estimating the power system fractional order prediction aided state based on the evolutionary computation of claim 4, wherein in the step (3), the population PG is as follows:
PG＝{I1,I2,…,IN}
Iμ＝αL+(αU-αL)×Ψμ,μ＝1,2,...,N (10)
wherein, the mu individual IμRepresenting the fractional order { alpha ] to be optimized1,α2,...,αn}，αLAnd alphaURespectively representing the lower and upper limits, Ψ, of the fractional orderμRepresenting a set of random numbers generated between 0 and 1.
6. The method for estimating the auxiliary state of fractional order prediction of the power system based on the evolutionary computation of claim 5, wherein in the step (4), fitness function evaluation is performed on all individuals in the current population PG according to optimization targets shown in formulas (11) to (18), and the obtained N fitness function values F are ranked from small to large according to the obtained N fitness function values F
Figure FDA0003397144150000034
Wherein
Figure FDA0003397144150000035
Is a sorting index number;
Figure FDA0003397144150000036
Figure FDA0003397144150000037
Figure FDA0003397144150000038
Figure FDA0003397144150000039
Figure FDA00033971441500000310
Figure FDA00033971441500000311
Figure FDA00033971441500000312
Pk＝Pk|k-1-KkHKPk|k-1 (18)
wherein, TNThe time window is represented by a time window,
Figure FDA00033971441500000313
indicating the l-th system state estimate, l-1, 2, …, n,
Figure FDA00033971441500000314
a true value representing the estimated value of the ith system state;
Figure FDA0003397144150000041
the predicted value of the state at the moment k is shown,
Figure FDA0003397144150000042
represents the state estimate at time k-1, Pk|k-1Representing the state prediction covariance matrix at time k, HkRepresenting the Jacobian matrix derived from the state vector and the measurement vector at time k,
Figure FDA0003397144150000043
represents the predicted measurement value at time K, KkRepresenting the Kalman filter gain at time k, PkRepresenting the state estimate covariance matrix at time k, Qk-1Representing the process noise covariance matrix, R, at time k-1kRepresenting the measured covariance matrix at time k, vkRepresenting the observed noise at time k.
7. The method for estimating the power system fractional order prediction aided state based on the evolutionary computation of claim 6, wherein in the step (5), the new population PS is:
Figure FDA0003397144150000044
wherein, the population scale N is even number, I represents individual,
Figure FDA0003397144150000045
and
Figure FDA0003397144150000046
denotes an index number of
Figure FDA0003397144150000047
And
Figure FDA0003397144150000048
the corresponding individual.
8. The method for estimating the power system fractional order prediction aided state based on the evolutionary computation of claim 7, wherein in the step (6), a population (PC-PS) is set, and an ith individual (PS) in the PS is selectediWherein i represents an odd number of 1 to N, to generate a random number r uniformly distributed from 0 to 1pcIf r ispcIs less than pcUpdating the ith individual and the (i + 1) th individual PCs in the population PC according to the real number intersection operation shown in the formulas (20) to (21)iAnd PCi+1Else PCiAnd PCi+1Keeping the same;
PCi＝rpc×PSi+1+(1-rpc)×PSi (20)
PCi+1＝rpc×PSi+(1-rpc)×PSi+1 (21)
wherein r ispcRepresenting a set of uniformly distributed random numbers from 0 to 1.
9. The method for estimating the power system fractional order prediction aided state based on the evolutionary computation of claim 8, wherein in the step (7), a population PM (PM) ═ PC (PC) is set, and the PC is targeted at the mu-th individual PC in the PCμGenerating a random number r in the range of 0 to 1pmIf r ispmIs less than pmGenerating new individuals according to the real number variation operation shown in the formula (22), otherwise, generating the mu-th individual PM in the PMsμKeeping unchanged until the whole population PC is traversed, and ensuring that the optimal individual is not damaged
Figure FDA0003397144150000049
Setting the current population PG as PM;
Figure FDA00033971441500000410
where μ ═ 1,2, …, N, PM (μ, d) and PC (μ, d) denote the d-th variable of the μ -th individual in the population PM and PC, respectively, and αL(d) And alphaU(d) Respectively represent the lower limit and the upper limit of the d-th variable, r1And r2Represents a uniform random number, k, generated in the range of 0 to 1gRepresenting the current number of iterations, mpRepresenting a variation parameter.
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