CN109709378A - The frequency and amplitude adaptive algorithm of transition electric signal - Google Patents
The frequency and amplitude adaptive algorithm of transition electric signal Download PDFInfo
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Abstract
The invention discloses a kind of frequency of transition electric signal and amplitude adaptive algorithms, the following steps are included: first carrying out cubic spline interpolation to the electric signal of sampling in the time domain, data truncation is carried out according to the sampling interval after acquisition interpolating sequence, reconstructed sample is constructed, the frequency amplitude of each reconstructed sample is finally estimated using Prony algorithm.Experiment show, the algorithm rapidly and accurately realize the synchronous self-adapting tracking of grid frequency amplitude；The present invention adapts to the synchronous detection of the electrical parameter when frequency changes over time simultaneously with amplitude in power network signal, and algorithm accuracy is high, accurately measures for power grid three elements and analysis provides a kind of reliable, effective technical support.
Description
Technical field
The present invention relates to varying electrical signals analysis field when electric system, a kind of frequency more particularly to transition electric signal and
Amplitude adaptive algorithm.
Background technique
The frequency and amplitude of electric system are to measure the important parameter index of power quality, are not only to realize electric power system stability
The feedback quantity of qualitative contrlol, while the benchmark also as protective relaying device precision maneuver, thus to mains frequency and amplitude into
Row is accurately measured to be of great significance with analysis.
With the proposition of smart grid concept, the access of large-scale distributed power supply and nonlinear load causes power grid electric
Pressure and power frequency amplitude are in time-varying characteristics, are non-stable time-varying electric power signals.
It is real about frequency power signal under the conditions of unstable time varying signal from the point of view of the paper published both at home and abroad at present
When tracking have many research achievements, main method has: wavelet analysis method, least square method, Taylor formula rule, Kalman filtering
Method etc..However above-mentioned algorithm is established in the standard sine basis of signals of constant amplitude, and when amplitude varies widely, meter
Calculating precision will be substantially reduced, and cannot achieve effective tracking in frequency time-varying synchronous with amplitude.
Under the conditions of the grid-connected generated unstable state time varying signal of distributed energy, frequency amplitude synchronous real-time trace is ground
Study carefully also in blank stage, be badly in need of it is theoretical and in terms of carry out fruitful exploration, and provide effective solution.
Summary of the invention
Technical problem to be solved by the invention is to provide a kind of frequency of transition electric signal and amplitude adaptive algorithm, energy
Enough synchronous self-adapting tracking for rapidly and accurately realizing grid frequency amplitude.
In order to solve the above technical problems, one technical scheme adopted by the invention is that: a kind of frequency of transition electric signal is provided
Rate and amplitude adaptive algorithm, comprising the following steps:
S1: power system signal x (t) after the filtering of anti-aliasing analog filter, is f with sample frequencys, sampling when it is a length of
tsIt is sampled, obtains N point discrete electric signals x (n), wherein N=fs*ts, sampling interval Ts=1/fs；
S2: cubic spline functions are established, interpolation is carried out to discrete electric signals x (n), obtain the interpolation containing interpolation point
Sequence x'(k), k=1,2, ┄, (M-2) (N-1), interpolation points of the M between two neighboring sampled point；
S3: interpolating sequence x'(k) is truncated to obtain (N-1) a reconstructed sample at equal intervals according to the sampling interval, is denoted as xi
(m), wherein i=1,2, ┄, N-1, m=1,2, ┄, M；
S4: (N-1) a reconstructed sample sequence x is estimated using Prony algorithmi(m) frequency and amplitude.
In a preferred embodiment of the present invention, in step s 2, the establishment step of the cubic spline functions are as follows:
Function f and a group node a=x on given section [a, b]0<x1<┄<xq=b, then the cubic spline of function f is inserted
Value S is the function for meeting following condition:
Condition 1: for subinterval [xj,xj+1], (j=0,1,2, ┄, q-1), S (x) is the multinomial three times of the subinterval
Formula is denoted as Sj(x)；
Condition 2:S (xj)=f (xj), (j=0,1,2, ┄, q-1)；
Condition 3:Sj+1(xj+1)=Sj+1(xj+1), (j=0,1,2, ┄, q-2)；
Condition 4:S 'j+1(xj+1)=S 'j(xj+1), (j=0,1,2, ┄, q-2)；
Condition 5:S "j+1(xj+1)=S "j(xj+1), (j=0,1,2, ┄, q-2)；
Meet one of boundary condition, 1. S " (x0)=S " (xq)=0；②S′(x0)=f ' (x0) and S ' (xq)=f ' (xq)。
In a preferred embodiment of the present invention, the specific steps of step S2 include:
S2.1: the function f being interpolated corresponds to the signal x (t) of electric system, the function point f (x being interpolatedj) correspond to electric power
Discrete electric signals x (n) obtained by the sampling of system；
S2.2: difference h between arbitrary cellsj=xj+1-xj, (j=1,2, ┄, q-1), corresponding sampling interval Ts；
S2.3: the interpolation points M between two neighboring sampled point is determined；
S2.4: after finding out cubic spline functions, enabling its independent variable x, successively value is 0, Ts, 2Ts, 3Ts, ┄, (N-
1) MTs obtains new interpolating sequence x'(k).
In a preferred embodiment of the present invention, the specific steps of step S4 include:
S4.1: set the power system signal of transition asBy sample interpolation weight
Reconstructed sample x after structure and truncationi(m) contain the p harmonic wave letters with any amplitude, phase and frequency for one group
Number, building extension Prony detection model, discrete time function form are as follows:
Wherein, m=0,1,2 ..., M-1, p are the order of model matrix, AjFor amplitude, fjFor frequency, θjFor phase, αjDecaying
The factor；
S4.2:Prony algorithm utilizes error sum of squares minimum principle implementation model parameter Estimation, constructs cost function, it may be assumed that
S4.3: calculating Prony detection model, the amplitude and frequency carved when solving transition electric signal；
S4.4: repeating step S4.1 to S4.3, solves the amplitude and frequency at transition electric signal each moment.
Further, the calculating process of step S4.3 includes:
S4.3.1: calculating reconstructed sample function r (i, j), constructs extended matrix Ri, determine RiEffective order p；
peFor linear prediction model order；
S4.3.2: establishing formula linear matrix equation, solves parameter aj: Ri[1,a1,…,ap]T=[ξi,0,…,0]T, wherein
εpiFor least error energy:
S4.3.3: polynomial characteristic root z is solvedj: 1+a1z-1+…+apz-p=0；
S4.3.4: the amplitude and frequency of transient signal: A are solvedj=2 | aj|, fj=arctan [Im (zj)/Re(zj)]/(2π
Ts)。
Further, in step S4.4, the amplitude and frequency at transition electric signal each moment are A=[A1 Ai …
AN-1], f=[f1 fi … fN-1], wherein Ai=[2 | a1| 2|aj| … 2|ap|],
The beneficial effects of the present invention are:
(1) present invention first carries out cubic spline interpolation to the electric signal of sampling in the time domain, obtain after interpolating sequence according to
Sampling interval carries out data truncation, constructs reconstructed sample, and the frequency width of each reconstructed sample is finally estimated using Prony algorithm
Value.Experiment show, the algorithm rapidly and accurately realize the synchronous self-adapting tracking of grid frequency amplitude；
(2) present invention adapts to the synchronous inspection of the electrical parameter when frequency changes over time simultaneously with amplitude in power network signal
It surveys, algorithm accuracy is high, accurately measures for power grid three elements and analysis provides a kind of reliable, effective technical support.
Detailed description of the invention
Fig. 1 is the frequency of transition electric signal of the present invention and the flow chart of amplitude adaptive algorithm；
Fig. 2 is the schematic diagram of the reconstructed sample；
Fig. 3 is the amplitude tracking curve graph of the embodiment of the present invention one；
Fig. 4 is the frequency-tracking curve graph of the embodiment of the present invention one；
Fig. 5 is the amplitude tracking error curve diagram of the embodiment of the present invention one；
Fig. 6 is the frequency tracking error curve graph of the embodiment of the present invention one；
Fig. 7 is the amplitude tracking curve graph of the embodiment of the present invention two；
Fig. 8 is the frequency-tracking curve graph of the embodiment of the present invention two；
Fig. 9 is the amplitude tracking error curve diagram of the embodiment of the present invention two；
Figure 10 is the frequency tracking error curve graph of the embodiment of the present invention two.
Specific embodiment
The preferred embodiments of the present invention will be described in detail with reference to the accompanying drawing, so that advantages and features of the invention energy
It is easier to be readily appreciated by one skilled in the art, so as to make a clearer definition of the protection scope of the present invention.
Referring to Fig. 1, the embodiment of the present invention includes:
A kind of frequency and amplitude adaptive algorithm of transition electric signal, comprising the following steps:
S1: power system signal x (t) before AD sampling module, installs anti-aliasing analog filter additional and reduces to greatest extent and adopts
The leakage of sample signal spectrum, is f with sample frequencys(unit: Hz), when sampling a length of ts(unit: s) is to power system signal x (t)
(unit: V or A) is sampled, and obtains N point discrete electric signals x (n), wherein N=fs*ts, sampling interval Ts=1/fs；
S2: cubic spline functions are established, interpolation is carried out to discrete electric signals x (n), obtain the interpolation containing interpolation point
Sequence x'(k), k=1,2, ┄, (M-2) (N-1), interpolation points of the M between two neighboring sampled point；
Wherein, the establishment step of the cubic spline functions are as follows:
Function f and a group node a=x on given section [a, b]0<x1<┄<xq=b, then the cubic spline of function f is inserted
Value S is the function for meeting following condition:
Condition 1: for subinterval [xj,xj+1], (j=0,1,2, ┄, q-1), S (x) is the multinomial three times of the subinterval
Formula is denoted as Sj(x)；
Condition 2:S (xj)=f (xj), (j=0,1,2, ┄, q-1)；
Condition 3:Sj+1(xj+1)=Sj+1(xj+1), (j=0,1,2, ┄, q-2)；
Condition 4:S 'j+1(xj+1)=S 'j(xj+1), (j=0,1,2, ┄, q-2)；
Condition 5:S "j+1(xj+1)=S "j(xj+1), (j=0,1,2, ┄, q-2)；
Meet one of boundary condition, 1. S " (x0)=S " (xq)=0；②S′(x0)=f ' (x0) and S ' (xq)=f ' (xq)。
Cubic spline interpolation specific steps for applying in the reconstruct of electric power signal sample include:
S2.1: the function f being interpolated corresponds to the signal x (t) of electric system, the function point f (x being interpolatedj) correspond to electric power
Discrete electric signals x (n) obtained by the sampling of system；
S2.2: difference h between arbitrary cellsj=xj+1-xj, (j=1,2, ┄, q-1), corresponding sampling interval Ts；
Since power system signal uses real-time sampling and equivalent time sampling, the sampling interval, Ts was fixed, therefore hjValue also
It immobilizes；
S2.3: the interpolation points M between two neighboring sampled point is determined；
S2.4: after finding out cubic spline functions, enabling its independent variable x, successively value is 0, Ts, 2Ts, 3Ts, ┄, (N-
1) MTs obtains new interpolating sequence x'(k).
S3: interpolating sequence x'(k) is truncated to obtain (N-1) a reconstructed sample at equal intervals according to the sampling interval, is denoted as xi
(m), wherein i=1,2, ┄, N-1, m=1,2, ┄, M；Specific steps are as follows:
Successively by sampled point two neighboring in new interpolating sequence x'(k) (as shown in Fig. 2 intermediate cam shape) and two neighboring
(M-2) a interpolation point (as shown in five-pointed star in Fig. 2) is combined into a reconstructed sample (except initial samples point and end between sampled point
Sampled point is held, remaining sampled point uses twice), finally substantially interpolating sequence x'(k) is truncated to obtain according to the sampling interval
(N-1) a reconstructed sample at equal intervals, and it is denoted as xi(m), wherein i=1,2, ┄, N-1, m=1,2, ┄, M.
S4: (N-1) a reconstructed sample sequence x is estimated using Prony algorithmi(m) frequency and amplitude.The step includes inspection
Survey the building and calculating of model, the specific steps are as follows:
S4.1: set the power system signal of transition asBy sample interpolation weight
Reconstructed sample x after structure and truncationi(m) contain the p harmonic wave letters with any amplitude, phase and frequency for one group
Number, building extension Prony detection model, discrete time function form are as follows:
Wherein, m=0,1,2 ..., M-1, p are the order of model matrix, AjFor amplitude, fjFor frequency, θjFor phase, αjDecaying
The factor；
S4.2:Prony algorithm utilizes error sum of squares minimum principle implementation model parameter Estimation, constructs cost function, it may be assumed that
S4.3: calculating Prony detection model, the amplitude and frequency carved when solving transition electric signal；
Further, the calculating process of step S4.3 includes:
S4.3.1: calculating reconstructed sample function r (i, j), constructs extended matrix Ri, determine RiEffective order p；
Pe is linear prediction model order；
S4.3.2: establishing formula linear matrix equation, solves parameter aj: Ri[1,a1,…,ap]T=[ξi,0,…,0]T, wherein
εpiFor least error energy:
S4.3.3: polynomial characteristic root z is solvedj: 1+a1z-1+…+apz-p=0；
S4.3.4: the amplitude and frequency of transient signal: A are solvedj=2 | aj|, fj=arctan [Im (zj)/Re(zj)]/(2π
Ts)。
S4.4: repeating step S4.1 to S4.3, solves the amplitude and frequency at transition electric signal each moment: A=[A1 Ai
… AN-1], f=[f1 fi … fN-1], wherein Ai=[2 | a1| 2|aj| … 2|ap|],
In field of power system control, transmission function general type is
M and n is positive integer in formula, and n > m, without repeated root in the case where pass the forms of time and space of letter are as follows:Therefore in structure
The frequency and amplitude for making signal are given at the tracking of algorithm under MATLAB emulation platform according to e-t and te-t rule transition
Performance.
The present invention illustrates the algorithm to the frequency of transition electric signal and the tracking performance of amplitude with two embodiments:
Signal 1 are as follows: x (t)=A1(t)cos(2πf1(t)t+45°)+A2(t)cos(2πf2(t) t+45 °), amplitude A1, A2
It is respectively as follows:Frequency f1, f2 are respectively as follows:Sampling interval is
0.001s, sampling length N=100, reconstructed sample length M=1000.Rendering algorithm frequency and amplitude tracking curve and error
Curve is as seen in figures 3-6.
Signal 2 are as follows:: x (t)=A1(t)cos(2πf1(t)t+45°)+A2(t)cos(2πf2(t) t+45 °), amplitude A1, A2
It is respectively as follows:Frequency f1, f2 are respectively as follows:Sampling interval
For 0.001s, sampling length N=200, reconstructed sample length M=1000.Rendering algorithm frequency and amplitude tracking curve and mistake
Poor curve is as is seen in figs 7-10.
Can be seen that the algorithm well from test frequency twice, amplitude tracking curve and error curve realized to wink
The frequency amplitude synchronized tracking of varying signal.Comparative example one and embodiment two, for the effect of different signal algorithm tracking
Different: (1) the overall tracking effect of embodiment two is better than embodiment one, and reason is embodiment binary signal amplitude of variation than real
It is big to apply example one；(2) tracking effect of two frequency of embodiment one and embodiment is better than amplitude tracking effect, and reason is
Prony algorithm is more sensitive to frequency.
This algorithm carries out after time domain carries out cubic spline interpolation reconstruct to electric system sampled signal according to the sampling interval
Data truncation, there are three advantages for gained reconstructed sample: cutting first, the data sequence at equal intervals after truncation is not only the stringent period
It is disconnected, and include integer reconstruction point in each period；Second, cubic spline interpolation is small to signal reconstruction error, frequency spectrum and amplitude
Leakage is hardly generated, is provided the foundation to realize that Prony parameter accurately detects；Third, can be by being reconstructed after reducing truncation
Sample length guarantees that time interval is sufficiently small to realize that software reduces the sampling interval, improves algorithm accuracy, while reducing and adopting
Sample equipment cost.The frequency amplitude of each reconstructed sample is finally estimated using Prony algorithm.Experiment show, the algorithm are fast
Speed has been accurately realized the synchronous self-adapting tracking of grid frequency amplitude.
The above description is only an embodiment of the present invention, is not intended to limit the scope of the invention, all to utilize this hair
Equivalent structure or equivalent flow shift made by bright specification and accompanying drawing content is applied directly or indirectly in other relevant skills
Art field, is included within the scope of the present invention.
Claims (6)
1. the frequency and amplitude adaptive algorithm of a kind of transition electric signal, comprising the following steps:
S1: power system signal x (t) after the filtering of anti-aliasing analog filter, is f with sample frequencys, sampling when a length of tsInto
Row sampling, obtains N point discrete electric signals x (n), wherein N=fs*ts, sampling interval Ts=1/fs；
S2: cubic spline functions are established, interpolation is carried out to discrete electric signals x (n), obtain the interpolating sequence containing interpolation point
X'(k), k=1,2, ┄, (M-2) (N-1), interpolation points of the M between two neighboring sampled point；
S3: interpolating sequence x'(k) is truncated to obtain (N-1) a reconstructed sample at equal intervals according to the sampling interval, is denoted as xi(m), wherein
I=1,2, ┄, N-1, m=1,2, ┄, M；
S4: (N-1) a reconstructed sample sequence x is estimated using Prony algorithmi(m) frequency and amplitude.
2. the frequency and amplitude adaptive algorithm of transition electric signal according to claim 1, which is characterized in that in step S2
In, the establishment step of the cubic spline functions are as follows:
Function f and a group node a=x on given section [a, b]0<x1<┄<xq=b, then the cubic spline interpolation S of function f be
Meet the function of following condition:
Condition 1: for subinterval [xj,xj+1], (j=0,1,2, ┄, q-1), S (x) is the cubic polynomial in the subinterval, is denoted as
Sj(x)；
Condition 2:S (xj)=f (xj), (j=0,1,2, ┄, q-1)；
Condition 3:Sj+1(xj+1)=Sj+1(xj+1), (j=0,1,2, ┄, q-2)；
Condition 4:S 'j+1(xj+1)=S 'j(xj+1), (j=0,1,2, ┄, q-2)；
Condition 5:S "j+1(xj+1)=S "j(xj+1), (j=0,1,2, ┄, q-2)；
Meet one of boundary condition, 1. S " (x0)=S " (xq)=0；②S′(x0)=f ' (x0) and S ' (xq)=f ' (xq)。
3. the frequency and amplitude adaptive algorithm of transition electric signal according to claim 1, which is characterized in that step S2's
Specific steps include:
S2.1: the function f being interpolated corresponds to the signal x (t) of electric system, the function point f (x being interpolatedj) correspond to electric system
Sampling gained discrete electric signals x (n)；
S2.2: difference h between arbitrary cellsj=xj+1-xj, (j=1,2, ┄, q-1), corresponding sampling interval Ts；
S2.3: the interpolation points M between two neighboring sampled point is determined；
S2.4: after finding out cubic spline functions, enabling its independent variable x, successively value is 0, Ts, 2Ts, 3Ts, ┄, (N-1)
MTs obtains new interpolating sequence x'(k).
4. the frequency and amplitude adaptive algorithm of transition electric signal according to claim 1, which is characterized in that step S4's
Specific steps include:
S4.1: set the power system signal of transition asBy sample interpolation reconstruct with
And the reconstructed sample x after truncationi(m) contain the p harmonic signals with any amplitude, phase and frequency, structure for one group
Build extension Prony detection model, discrete time function form are as follows:
Wherein, m=0,1,2 ..., M-1, p are the order of model matrix, AjFor amplitude, fjFor frequency, θjFor phase, αjDecay factor；
S4.2:Prony algorithm utilizes error sum of squares minimum principle implementation model parameter Estimation, constructs cost function, it may be assumed that
S4.3: calculating Prony detection model, the amplitude and frequency carved when solving transition electric signal；
S4.4: repeating step S4.1 to S4.3, solves the amplitude and frequency at transition electric signal each moment.
5. the frequency and amplitude adaptive algorithm of transition electric signal according to claim 4, which is characterized in that step S4.3
Calculating process include:
S4.3.1: calculating reconstructed sample function r (i, j), constructs extended matrix Ri, determine RiEffective order p；
peFor linear prediction model order；
S4.3.2: establishing formula linear matrix equation, solves parameter aj: Ri[1,a1,…,ap]T=[ξi,0,…,0]T, wherein εpiFor
Least error energy:
S4.3.3: polynomial characteristic root z is solvedj: 1+a1z-1+…+apz-p=0；
S4.3.4: the amplitude and frequency of transient signal: A are solvedj=2 | aj|, fj=arctan [Im (zj)/Re(zj)]/(2πTs)。
6. the frequency and amplitude adaptive algorithm of transition electric signal according to claim 5, which is characterized in that in step
In S4.4, the amplitude and frequency at transition electric signal each moment are A=[A1 Ai…AN-1], f=[f1 fi…fN-1], wherein Ai=
[2|a1| 2|aj|…2|ap|],
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