CN108596475A - A kind of PMU data restoration methods based on interpolation section dynamic change - Google Patents
A kind of PMU data restoration methods based on interpolation section dynamic change Download PDFInfo
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Abstract
The invention discloses a kind of PMU data restoration methods based on interpolation section dynamic change for belonging to PMU data recovery technology field.The method includes：The actual scene that data are lost according to PMU defines one point data and loses scene and continuous multipoint data loss scene；Determine the recovery sequence for losing data, it is proposed that a kind of priority restoration methods based on interpolation section dynamic change；Restore to lose data, it is proposed that improved cubic spline functions, by proposing constraints to variable so that spline curve is more flat.The present invention can effectively restore different types of loss data under different conditions at system, solves conventional method and loses the problem of dtmf distortion DTMF under scene in continuous multipoint data, for ensureing that PMU data quality has great significance and larger value.
Description
Technical field
The invention belongs to PMU data recovery technology field more particularly to a kind of PMU numbers based on interpolation section dynamic change
According to restoration methods.
Background technology
As extensive regenerative resource develops and uses the development with intelligent grid, China is currently completed and services in the world
Most populous, coverage area is most wide, transmission voltage grade highest, accommodates the most ultra-large complicated interconnection electricity of regenerative resource
Force system.Essence variation occurs for mechanism characteristic, analysis method and the operation control method of electric system.Electric system is whole
Property become increasingly conspicuous, trans-regional, different voltage grade systemic cascading failure is increasingly becoming a kind of normality, and closed loop Precise control needs
Ask apparent.Synchronous phasor measurement unit (Phasor Measurement Units, PMUs) is because of its synchronism, rapidity and accurate
Property, make it possible that Electrical Power System Dynamic monitors in real time, data basis can be provided for system protection and closed-loop control.In currently,
State's 3000 or so PMU devices of installation and operation, cover whole 220kV and the above substation, main force power plant and new energy
It is grid-connected to collect station.In addition, about 2000 bussiness class PMU have been mounted on north America region.However, due to site environment complexity, by
To the influence of the factors such as synchronizing signal loss, communication protocol mistake, system overload, transmission delay, PMU is inevitably present number
The problems such as according to losing, seriously affects its application in dynamic monitoring and closed-loop control etc., or even threat power grid security.In electricity
Net topology is unknown, and only under the background of PMU measurement informations, PMU data loss can cause power grid fragile and inconsiderable, be vulnerable to and disturb
Dynamic attack even causes large-scale blackout.Therefore, PMU data restores to have become the critical issue for ensureing power system security.
In the prior art, time series method, matrix low-rank method, state estimate etc. are mostly used greatly.These methods can effectively be restored
Single-point loses data, however there has been no preferable recovery effects for continuous multipoint data loss.
Invention content
In view of the above-mentioned problems, the present invention proposes a kind of PMU data restoration methods based on interpolation section dynamic change,
It is characterized in that, includes the following steps：
Step 1, two kinds of basic scenes for establishing PMU data loss, including one point data lose scene and continuous multiple spot number
According to loss scene；
Step 2, the loss type for analyzing data, determine loss of data scene；
Step 3 determines the recovery sequence for losing data, if in the case where continuous multipoint data loses scene, considers that data are restored
Priority distribution, according to lose data amount check parity, calculate lose data recovery sequence；If being lost in one point data
Under scene, then it is not necessarily to consider that priority is distributed；
Step 4, determine lose data recovery sequence on the basis of, using improved standard cubic spline functions,
Loss data under different scenes are restored.
It refers to whithin a period of time, obtaining in one group of PMU metric data that there is only lists that the one point data, which loses scene,
The scene of one loss of data.
It refers to whithin a period of time, obtaining and existing in one group of PMU metric data that the continuous multipoint data, which loses scene,
The scene that continuous multipoint data is lost.
The step 3 is extensive using the priority based on difference section dynamic change in the case where continuous multipoint data loses scene
Compound method calculates the recovery sequence for losing data, and circular is：
(1) when it is odd number continuously to lose data amount check
Assuming that whithin a period of time, obtaining the data continuously lost there are 5 in one group of PMU metric data, respectively
Xn-2, Xn-1, Xn, Xn+1, Xn+2；
Step 1, the whole PMU data X of input1, X2..., Xm, lose data amount check N, restore number M, adjacent spaces Z,
In, M=N；
Step 2, the Chosen Point adjacent spaces Z for calculating first stage data to be restored1, calculation formula is as follows：
Step 3 determines first stage data X to be restoredn, whereinSelect XnFront and back each 4 adjacent spaces are Z1
Point, utilize improved standard cubic spline functions to restore data Xn；
Step 4, the Chosen Point adjacent spaces Z for calculating second stage data to be restored2, calculation formula is as follows：
Z2=Z1-1
Step 5 determines second stage data X to be restoredn-2And Xn+2, utilize the number of data with existing and first stage recovery
According to Xn, restore data X using improved standard cubic spline functionsn-2And Xn+2；
Step 6, the Chosen Point adjacent spaces Z for calculating phase III data to be restored3, calculation formula is as follows：
Z3=Z2-1
Step 7 determines phase III data X to be restoredn-1And Xn+1, utilize the number of data with existing and the recovery of the first two stage
According to Xn、Xn-2And Xn+2, restore data X using improved standard cubic spline functionsn-1And Xn+1；
(2) when it is even number continuously to lose data amount check
Assuming that whithin a period of time, obtaining the data continuously lost there are 6 in one group of PMU metric data, respectively
Xn-3, Xn-2, Xn-1, Xn, Xn+1, Xn+2；
Step a, whole PMU data X are inputted1, X2..., Xm, lose data amount check N, restore number M, adjacent spaces Z,
In, M=N；
Step b, the Chosen Point adjacent spaces Z of first stage data to be restored is calculated1, calculation formula is as follows：
Step c, first stage data X to be restored is determinedn-1And Xn, whereinBefore and after selection and data to be restored
Each 4 adjacent spaces are Z1Point, utilize improved standard cubic spline functions to restore data Xn-1And Xn；
Step d, the Chosen Point adjacent spaces Z of second stage data to be restored is calculated2, calculation formula is as follows：
Z2=Z1-1
Step e, second stage data X to be restored is determinedn-3And Xn+2, utilize the number of data with existing and first stage recovery
According to Xn-1And Xn, restore data X using improved standard cubic spline functionsn-3And Xn+2；
Step f, the Chosen Point adjacent spaces Z of phase III data to be restored is calculated3, calculation formula is as follows：
Z3=Z2-1
Step g, phase III data X to be restored is determinedn-2And Xn+1, utilize the number of data with existing and the recovery of the first two stage
According to Xn-1、Xn、Xn-3And Xn+2, restore data X using improved standard cubic spline functionsn-2And Xn+1。
The modeling method of the improved standard cubic spline functions is：
(1) cubic spline functions are constructed
Given function
yi=f (xi), i=1,2 ..., n (1)
Wherein,
A=x0＜ x1＜ x2＜ ... ＜ xn=b, [a, b]
If S (x)=y is in each subinterval [xk, xk+1] it is multinomial no more than three times on (k=1,2 ..., n-1)
Formula, and S (xi)=yi, i=1,2 ..., n；And S (x), S ' (x), S " (x) are continuous on [a, b], then S (x) is referred to as that f (x) exists
Node x0, x1, x2... xnOn cubic spline functions；
(2) M is enabledi=S " (xi), in section [xi, xi+1] on, S (x)=Si(x) second dervative is represented by：
Wherein,
hi=xi+1-xi
(3) formula (1) is integrated twice in succession, is obtained：
By continuity S ' (xi-)=S ' (xi+), it can obtain：
μiMi-1+2Mi+λiMi=di(i=1,2 ..., n-1) (5)
Wherein,
(4) according to boundary condition S ' (x0)=y0', S ' (xn)=yn', formula (5) is expressed as following matrix form：
Equation (7) coefficient matrix strictly diagonal dominant, there is unique solution,
S (x) is in each section [xi, xi+1] on Si(x) it is：
(5) improved cubic spline functions are constructed
Assuming that Si(x) in section [xi-1, xi] (i=1,2 ..., n) on maximum value minimum be respectively SimaxWith
Simin, then extreme value differences of the S (x) on section [a, b] be：
Assuming that S ' (x0)=y0', S ' (xn)=yn' unknown, it is obtained by the extreme value difference of S (x)：
In formula, f (xi) it is arbitrary function；A, b is independent variable x intervals；MiIt is led for the second order of cubic spline functions
Number.
The beneficial effects of the present invention are：
(1) present invention can effectively restore data in the case where system is in different conditions to different types of loss data, this
The outer present invention is not constrained by topological structure of electric, only can be realized by inputting PMU real-time measurement data.Solves tradition side
Method loses the problem of dtmf distortion DTMF under scene in continuous multipoint data, to ensure that PMU data quality provides a kind of effective, feasible side
Method.
(2) a kind of priority recovery policy based on interpolation section dynamic change proposed by the present invention ensure that between sampling
Relationship between nyquist frequency, the periodic signal for avoiding PMU data is impaired, ensure that the accuracy of recovery.
(3) present invention improves cubic spline functions, provides about variable M0And MnConstraints, ensure that sample
The single order and second dervative of interpolating function are continuous.Avoid imperial lattice phenomenon simultaneously so that spline curve is more flat.
Description of the drawings
Attached drawing 1 is a kind of PMU data restoration methods flow chart based on interpolation section dynamic change；
Attached drawing 2 (a) is the basic scene that PMU one point datas are lost；
Attached drawing 2 (b) is the basic scene that the continuous multipoint datas of PMU are lost；
Attached drawing 3 (a) is that the discontinuous multipoint datas of PMU lose scene；
Attached drawing 3 (b) is that PMU complex datas lose scene；
Attached drawing 4 is the PMU data loss situation of odd number number；
Attached drawing 5 is the PMU data loss situation of even number number；
Attached drawing 6 is that two methods lose the comparison of data restoration result to different type；
The A phase voltages amplitude and phase angle measurement data that attached drawing 7 is certain PMU；
Attached drawing 8 is that single-point loses the TVE comparisons of data restoration result under stable state；
Attached drawing 9 is that single-point loses the TVE comparisons of Data Data restoration result under transient state；
Attached drawing 10 (a) is that continuous multiple spot loses data restoration result under stable state；
Attached drawing 10 (b) is that continuous multiple spot loses data restoration result under transient state；
Attached drawing 11 is surely, loses influence of the data amount check to conventional method TVE under transient state；
Attached drawing 12 (a) is that influence of the data amount check to the method for the present invention TVE is lost under stable state；
Attached drawing 12 (b) is that influence of the data amount check to the method for the present invention TVE is lost under transient state；
Specific implementation mode
The present invention is described in detail with reference to the accompanying drawings and examples.
Attached drawing 1 is a kind of PMU data restoration methods flow chart based on interpolation section dynamic change, as shown in Figure 1, described
Method includes the following steps：
Step 1：Two kinds of basic scenes of PMU data loss are established, including one point data loses scene and continuous multiple spot number
According to loss scene；
Step 2：The loss type for analyzing data, determines loss of data scene；
Step 3：It determines the recovery sequence for losing data, if in the case where continuous multipoint data loses scene, considers that data are restored
Priority distribution, according to lose data amount check parity, calculate lose data recovery sequence；If being lost in one point data
Under scene, then it is not necessarily to consider that priority is distributed；
Step 4：On the basis of determining loss data recovery sequence, by changing to standard cubic spline functions
Into restoring to the loss data under different scenes.
Specifically, in the step 1, problem model is lost in order to simplify PMU data, convenient for restoring data, the present invention
According to the actual conditions that the accuracy of PMU data, availability, real-time and field data are lost, loss of data is defined
Two kinds of basic scenes, respectively one point data lose scene and continuous multipoint data loses scene.Attached drawing 2 (a) is one point data
Scene is lost, attached drawing 2 (b) is that continuous multipoint data loses scene, and in Fig. 2 (a) -2 (b), square represented in a period of time
PMU metric data, wherein for white to lose data, black is given data.Other scenes can be equivalent to above two scene
Various combination.For example, discontinuous multipoint data, which loses scene, can be equivalent to multiple one point datas loss scenes, such as Fig. 3 (a) institutes
Show；Complex data, which loses scene, can be equivalent to the combination that one point data and continuous multipoint data are lost, as shown in Fig. 3 (b).According to
One point data can be lost scene and be defined as whithin a period of time, obtaining in one group of PMU metric data only by Fig. 2 (a), 3 (a)
There are the scenes of certain single loss of data；Continuous multipoint data can be lost scene and is defined as at one section by (b), 3 (b) according to fig. 2
In time, obtain in one group of PMU metric data that there are the scenes that continuous multipoint data is lost.
Specifically, in the step 3, according to two kinds of basic scenes of the PMU loss data that step 1 is established, determination is lost
The recovery sequence of data is lost, if in the case where one point data loses scene, without considering that priority is distributed.If in continuous multipoint data
It loses under scene, since existing method needs are largely calculated, and resultant error is larger, therefore the present invention proposes a kind of base
In the priority restoration methods of interpolation section dynamic change, the method considers the priority distribution that data are restored, according to continuous
The parity of data amount check is lost, the recovery sequence for losing data is calculated, computational accuracy can be effectively improved.Number is lost for continuous
According to the parity of number, it is divided into following two situations and discusses：
(1) it is odd number when continuously losing data amount check
Attached drawing 4 is the PMU data loss situation of odd number number, it is assumed that Xn-2, Xn-1, Xn, Xn+1, Xn+2It is 5
A continuous loss data, remaining is given data, and in this case, the priority restoration methods of use are as follows：
Step 1, the whole PMU data X of input1, X2..., Xm, lose data amount check N, restore number M, adjacent spaces Z,
In, M=N；
Step 2, the Chosen Point adjacent spaces Z for calculating first stage data to be restored1, calculation formula is as follows：
Step 3 determines first stage data X to be restoredn, whereinSelect XnFront and back each 4 adjacent spaces are Z1
Point, utilize improved standard cubic spline functions to restore data Xn；
Step 4, the Chosen Point adjacent spaces Z for calculating second stage data to be restored2, calculation formula is as follows：
Z2=Z1-1
Step 5 determines second stage data X to be restoredn-2And Xn+2, utilize the number of data with existing and first stage recovery
According to Xn, restore data X using improved standard cubic spline functionsn-2And Xn+2；
Step 6, the Chosen Point adjacent spaces Z for calculating phase III data to be restored3, calculation formula is as follows：
Z3=Z2-1
Step 7 determines phase III data X to be restoredn-1And Xn+1, utilize the number of data with existing and the recovery of the first two stage
According to Xn、Xn-2And Xn+2, restore data X using improved standard cubic spline functionsn-1And Xn+1。
(2) it is even number when continuously losing data amount check
Attached drawing 5 is the PMU data loss situation of even number number, as shown in fig. 5, it is assumed that Xn-3, Xn-2, Xn-1, Xn, Xn+1, Xn+2
For 6 continuous loss data, remaining is given data, and in this case, the priority restoration methods specific steps of use are such as
Under：
Step a, whole PMU data X are inputted1, X2..., Xm, lose data amount check N, restore number M, adjacent spaces Z,
In, M=N；
Step b, the Chosen Point adjacent spaces Z of first stage data to be restored is calculated1, calculation formula is as follows：
Step c, first stage data X to be restored is determinedn-1And Xn, whereinBefore and after selection and data to be restored
Each 4 adjacent spaces are Z1Point, utilize improved standard cubic spline functions to restore data Xn-1And Xn；
Step d, the Chosen Point adjacent spaces Z of second stage data to be restored is calculated2, calculation formula is as follows：
Z2=Z1-1
Step e, second stage data X to be restored is determinedn-3And Xn+2, utilize the number of data with existing and first stage recovery
According to Xn-1And Xn, restore data X using improved standard cubic spline functionsn-3And Xn+2；
Step f, the Chosen Point adjacent spaces Z of phase III data to be restored is calculated3, calculation formula is as follows：
Z3=Z2-1
Step g, phase III data X to be restored is determinedn-2And Xn+1, utilize the number of data with existing and the recovery of the first two stage
According to Xn-1、Xn、Xn-3And Xn+2, restore data X using improved standard cubic spline functionsn-2And Xn+1。
According to sampling thheorem, the interval Z of use meet interval and point to be restored between each Chosen Point be spaced it is equal, to protect
Demonstrate,prove the relationship between sampling interval and nyquist frequency.Compared to other algorithms, PMU data will not be made using the restoration methods
Periodic signal is impaired.
Specifically, in the step 4, on the basis of priority recovery policy, the present invention is using interpolation method to losing
Data are restored.Cubic spline functions are sought using given data, make it that there is higher degree of fitting with given data, into
And it seeks losing data.Imperial lattice phenomenon caused by order to avoid using higher order polynomial, the present invention is to cubic spline functions
It is improved, is finding out the improvement cubic spline functions met under extreme value difference constraints, restore to lose data, it is described
Improved cubic spline functions be on the basis of the single order of spline interpolation function for ensureing to acquire is continuous with second dervative,
Constraints is proposed to variable so that line smoothing is good, has stronger linear approximation ability, and can Efficient Characterization data
Situation of change, modeling method are as described below：
(1) cubic spline functions are constructed
Given function
yi=f (xi), i=1,2 ..., n (1)
Wherein,
A=x0＜ x1＜ x2＜ ... ＜ xn=b, [a, b]
If S (x)=y is in each subinterval [xk, xk+1] it is multinomial no more than three times on (k=1,2 ..., n-1)
Formula, and S (xi)=yi, i=1,2 ..., n；And S (x), S ' (x), S " (x) are continuous on [a, b], then S (x) is referred to as that f (x) exists
Node x0, x1, x2... xnOn cubic spline functions.
(2) M is enabledi=S " (xi), since the interpolation formula that cubic spline interpolation obtains can ensure on every section of section and side
First derivative at boundary is smooth, while second dervative is continuous.Therefore in [xi, xi+1] on, S (x)=Si(x) second dervative can table
It is shown as：
Wherein,
hi=xi+1-xi
(3) continuous integral twice is carried out to formula (1), obtained：
By continuity S ' (xi-)=S ' (xi+), it can obtain：
μiMi-1+2Mi+λiMi=di(i=1,2 ..., n-1) (5)
Wherein,
(4) according to boundary condition S ' (x0)=y0', S ' (xn)=yn', formula (5) is expressed as following matrix form：
(5) improved cubic spline functions are constructed
Since cubic spline functions are the functions about boundary condition, in order to keep spline curve more flat, this hair
It is minimum to acquire extreme value difference for the bright actual conditions changed according to electric system.
Assuming that Si(x) in section [xi-1, xi] (i=1,2 ..., n) on extreme value be respectively SimaxAnd Simin, then S (x) exist
Extreme value difference on section [a, b] is：
Assuming that S ' (x0)=y0', S ' (xn)=yn' unknown, then the extreme value difference of S (x) is about M0And MnFunction, obtain
About M0And MnWithout constraint Non-Linear Programming object function be：
Formula (9) is about M0And MnUnconstrained non-linear programming problem, since object function contains extreme value operation, and
Parameter is determined by equation group, simple form method of substitution can be used to solve.
Embodiment 1
In order to which the present invention is described in more detail, the present embodiment is using Matlab in systematic steady state and transient state two states
Lower carry out emulation testing, and verified using PMU measured datas, it is compared with the restoration result of existing algorithm.Synchronized phasor is surveyed
It measures error to weigh using total vector error (Total vector error, TVE), calculation formula is as follows：
In formula, Xr(n) and Xi(n) real and imaginary parts of input signal theoretical value, X ' are indicated respectivelyr(n) and X 'i(n) respectively
Indicate the real and imaginary parts of input signal estimated value.
1, emulation testing
Power system mesomeric state signal expression is as follows：
In formula, XmFor phasor amplitude, f0For power frequency,For initial phase angle, and Xm=57.73V, f0=50Hz,
Under ideal conditions, any variation, output knot will not occur for the phasor, frequency of above-mentioned signal and frequency change rate
Fruit is constant, therefore is easy to restore in loss of data.When system occurrence frequency deviates, then electrical power system transient signal expression is such as
Under：
In formula, Δ f is frequency offset, and Δ f=5Hz.
(1) best interpolation point number is tested
The present invention restores data using interpolation method, and interpolation point number directly affects accuracy of data recovery and calculating speed.Cause
This tests best interpolation point number by taking above-mentioned frequency offset signals as an example.
It randomly chooses single-point and loses data, restore to lose data using different interpolation points, repeat 100 experiments, and record
As a result, test result is as shown in table 1, TVE indicates mean value in table 1, the results showed that 8 adjacent point datas are restored before and after loss data
As a result optimal.
1 best interpolation point number of table
| Interpolation is counted | 2 | 4 | 6 | 8 | 10 |
| TVE() | 4.89% | 0.16 | 0.06 | 0.07 | 0.07 |
(2) data restoration result when frequency shift (FS)
Different types of loss data in frequency offset signals are carried out using data reconstruction method proposed by the present invention extensive
Multiple, and compared with existing method, comparing result is as shown in fig. 6, when attached drawing 6 indicates frequency shift (FS), inhomogeneity in complex plane
Type loses the recovery effects of data, and in figure, transverse and longitudinal coordinate axis indicates that real and imaginary parts, PS and LS are the method for the present invention and show respectively
There is method to lose the restoration result of data to single-point, PM and LS is that the method for the present invention and existing method lose data to continuous multiple spot
Restoration result.It will be appreciated from fig. 6 that method using the present invention restores single-point to lose the TVE of data to be 0.07%, it is better than existing side
The 3.06% of method.When continuous multipoint data is lost, there is serious distortion in existing method, and method proposed by the present invention can be compared with
Restore frequency offset signals well, keeps the variation tendency of data.The TVE comparing results of two methods are as shown in table 2, by table 2
It is found that TVELM increases gradual increase with data are lost, TVEPM nonlinear changes can effectively be restored to lose data.
2 two methods TVE comparisons of table
2, PMU measured datas are tested
The present invention analyzes PMU monitorings institute total when western part of China new energy collects certain sub-synchronous oscillation in area
According to, and carried out data and restored verification.The A phase voltages amplitude of PMU and phase angle measurement data such as Fig. 7 institutes when certain sub-synchronous oscillation
Show.
(1) system one point data loss recovery Comparative result under steady, transient state
When system is in stable state, the method for the present invention is respectively adopted and existing method restores randomly selected single-point and loses number
According to.Data restoration result TVE comparisons are lost as shown in figure 8, as seen from Figure 8,80% TVEPS is less than 1% under stable state, only
30% TVELS is less than 1%, and restoration result error change is larger, it is difficult to apply in practice.
When system is in transient state, restores randomly selected single-point using same two methods and lose data.Lose number
According to restoration result TVE comparisons as shown in figure 9, in Fig. 9, PS corresponds to main longitudinal axis coordinate, and LS corresponds to time ordinate of orthogonal axes.It follows that
When sub-synchronous oscillation occurs for system, 90% TVEPS is less than 3%, and recovery effects are preferable, and only minority TVELS is less than 5%, restores
Data serious distortion.Due to voltage oscillation, if losing data is located at wave crest or wave trough position, this method only passes through Primary Stage Data hardly possible
To restore variation tendency.
(2) system is steady, continuous multipoint data loss recovery Comparative result under transient state
When system is in steady, transient state, it is respectively adopted and continuous multiple spot is restored using the method for the present invention and existing method loses
Data, shown in result such as Figure 10 (a) -10 (b), test result when attached drawing 10 (a) is stable state can be obtained by Figure 10 (a), under stable state
The ability that the method for the present invention restores continuous loss data is more excellent, and TVELM increases gradual increase with loss data, with emulation testing
As a result consistent.Test result when attached drawing 10 (b) is transient state, can be obtained by Figure 10 (b), when system is in transient state, TVELM situations of change
Identical when with stable state, restoration result deviation is larger, and TVEPM is 1% hereinafter, restoration result accuracy is high.
(3) influence of the data amount check to TVE is lost in analysis
Data amount check is lost by change, compares two methods recovery effects under steady, transient state, i.e. TVE situations of change, than
Shown in result such as Figure 11,12 (a), 12 (b), wherein attached drawing 11 is loss data amount check under steady, transient state to existing method TVE
Influence, Tu11Zhong, Lst indicate that TVE changes under stable state, corresponding main longitudinal axis coordinate；Ltt indicates that TVE changes under transient state, corresponding time
Ordinate of orthogonal axes.As shown in Figure 11, TVELst, TVELtt are linear to increase with the increase for losing data amount check.However this method is only
Using lose point before data, can not each restoration result of precise calibration, to make error gradually increase.
Attached drawing 12 (a) -12 (b) is surely, loses influence of the data amount check to the method for the present invention TVE under transient state, by Figure 12
(a) -12 (b) can be obtained, and the method for the present invention can effectively restore data under steady, transient state two states.Surely, precision is far high under transient state
It loses data under existing method, stable state to be easier to restore, TVE is no more than 1.1% under transient state.Meanwhile it is a with data are lost
Several increases, according to priority restoration methods, recovery sequence be also not quite similar, therefore TVE variation with lose data amount check without
Obvious relation still needs to further probe into.
By above-mentioned test, system has been separately verified in temporary, stable state, has been restored in the case where single-point, continuous multiple spot lose scene
Data are lost, test result shows that this method has good recovery effects.
This embodiment is merely preferred embodiments of the present invention, but scope of protection of the present invention is not limited thereto,
Any one skilled in the art in the technical scope disclosed by the present invention, the change or replacement that can be readily occurred in,
It should be covered by the protection scope of the present invention.Therefore, protection scope of the present invention should be with scope of the claims
Subject to.
Claims (5)
1. a kind of PMU data restoration methods based on interpolation section dynamic change, which is characterized in that include the following steps：
Step 1, two kinds of basic scenes for establishing PMU data loss, including one point data loses scene and continuous multipoint data is lost
Lose scene；
Step 2, the loss type for analyzing data, determine loss of data scene；
Step 3 determines the recovery sequence for losing data, if in the case where continuous multipoint data loses scene, considers that data restore excellent
First grade distribution calculates the recovery sequence for losing data according to the parity for losing data amount check；If losing scene in one point data
Under, then it is not necessarily to consider that priority is distributed；
Step 4, determine lose data recovery sequence on the basis of, using improved standard cubic spline functions, to not
Restored with the loss data under scene.
2. a kind of PMU data restoration methods based on interpolation section dynamic change according to claim 1, feature exist
It refers to whithin a period of time, obtaining in one group of PMU metric data that there is only single data to lose scene in, the one point data
The scene of loss.
3. a kind of PMU data restoration methods based on interpolation section dynamic change according to claim 1, feature exist
In it refers to whithin a period of time, obtaining in one group of PMU metric data in the presence of continuous more that the continuous multipoint data, which loses scene,
The scene that point data is lost.
4. a kind of PMU data restoration methods based on interpolation section dynamic change according to claim 1, feature exist
In the step 3 is in the case where continuous multipoint data loses scene, using the priority restoration methods based on difference section dynamic change
The recovery sequence for losing data is calculated, circular is：
(1) when it is odd number continuously to lose data amount check
Assuming that whithin a period of time, obtaining the data continuously lost there are 5 in one group of PMU metric data, respectively Xn-2,
Xn-1,Xn,Xn+1,Xn+2；
Step 1, the whole PMU data X of input1,X2,...,Xm, lose data amount check N, restore number M, adjacent spaces Z, wherein M
=N；
Step 2, the Chosen Point adjacent spaces Z for calculating first stage data to be restored1, calculation formula is as follows：
Step 3 determines first stage data X to be restoredn, whereinSelect XnFront and back each 4 adjacent spaces are Z1's
Point restores data X using improved standard cubic spline functionsn；
Step 4, the Chosen Point adjacent spaces Z for calculating second stage data to be restored2, calculation formula is as follows：
Z2=Z1-1
Step 5 determines second stage data X to be restoredn-2And Xn+2, utilize the data X of data with existing and first stage recoveryn,
Restore data X using improved standard cubic spline functionsn-2And Xn+2；
Step 6, the Chosen Point adjacent spaces Z for calculating phase III data to be restored3, calculation formula is as follows：
Z3=Z2-1
Step 7 determines phase III data X to be restoredn-1And Xn+1, utilize the data X of data with existing and the recovery of the first two stagen、
Xn-2And Xn+2, restore data X using improved standard cubic spline functionsn-1And Xn+1；
(2) when it is even number continuously to lose data amount check
Assuming that whithin a period of time, obtaining the data continuously lost there are 6 in one group of PMU metric data, respectively Xn-3,
Xn-2,Xn-1,Xn,Xn+1,Xn+2；
Step a, whole PMU data X are inputted1,X2,...,Xm, lose data amount check N, restore number M, adjacent spaces Z, wherein M
=N；
Step b, the Chosen Point adjacent spaces Z of first stage data to be restored is calculated1, calculation formula is as follows：
Step c, first stage data X to be restored is determinedn-1And Xn, whereinEach 4 before and after selection and data to be restored
Adjacent spaces are Z1Point, utilize improved standard cubic spline functions to restore data Xn-1And Xn；
Step d, the Chosen Point adjacent spaces Z of second stage data to be restored is calculated2, calculation formula is as follows：
Z2=Z1-1
Step e, second stage data X to be restored is determinedn-3And Xn+2, utilize the data of data with existing and first stage recovery
Xn-1And Xn, restore data X using improved standard cubic spline functionsn-3And Xn+2；
Step f, the Chosen Point adjacent spaces Z of phase III data to be restored is calculated3, calculation formula is as follows：
Z3=Z2-1
Step g, phase III data X to be restored is determinedn-2And Xn+1, utilize the data of data with existing and the recovery of the first two stage
Xn-1、Xn、Xn-3And Xn+2, restore data X using improved standard cubic spline functionsn-2And Xn+1。
5. a kind of PMU data restoration methods based on interpolation section dynamic change according to claim 1, feature exist
In the modeling method of the improved standard cubic spline functions is：
(1) cubic spline functions are constructed
Given function
yi=f (xi), i=1,2 ..., n (1)
Wherein,
A=x0＜ x1＜ x2＜ ... ＜ xn=b, [a, b]
If S (x)=y is in each subinterval [xk,xk+1] on (k=1,2 ..., n-1), for no more than multinomial three times, and S
(xi)=yi, i=1,2 ..., n；And S (x), S ' (x), S " (x) are continuous on [a, b], then S (x) is referred to as f (x) in node
x0,x1,x2,…xnOn cubic spline functions；
(2) M is enabledi=S " (xi), in section [xi,xi+1] on, S (x)=Si(x) second dervative is represented by：
Wherein,
hi=xi+1-xi
(3) formula (1) is integrated twice in succession, is obtained：
By continuity S ' (xi-)=S ' (xi+), it can obtain：
μiMi-1+2Mi+λiMi=di(i=1,2 ..., n-1) (5)
Wherein,
(4) according to boundary condition S ' (x0)=y0′,S′(xn)=yn', formula (5) is expressed as following matrix form：
Equation (7) coefficient matrix strictly diagonal dominant, there is unique solution,
S (x) is in each section [xi,xi+1] on Si(x) it is：
(5) improved cubic spline functions are constructed
Assuming that Si(x) in section [xi-1,xi] the maximum value minimum on (i=1,2 ..., n) is respectively SimaxAnd Simin, then S
(x) the extreme value difference on section [a, b] is：
Assuming that S ' (x0)=y0′,S′(xn)=yn' unknown, it is obtained by the extreme value difference of S (x)：
In formula, f (xi) it is arbitrary function；A, b is independent variable x intervals；MiFor the second dervative of cubic spline functions.
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| CN116737451A (en) * | 2023-05-26 | 2023-09-12 | 珠海妙存科技有限公司 | Data recovery method and device of flash memory, solid state disk and storage medium |
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| US20080228435A1 (en) * | 2007-03-14 | 2008-09-18 | Korea Advanced Institute Of Science And Technology | Measurement system for correcting overlay measurement error |
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| US10983492B1 (en) * | 2020-08-07 | 2021-04-20 | North China Electric Power University | Adaptive PMU missing data recovery method |
| CN116737451A (en) * | 2023-05-26 | 2023-09-12 | 珠海妙存科技有限公司 | Data recovery method and device of flash memory, solid state disk and storage medium |
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