CN108932215A - A kind of more sinusoidal signal design methods of low-frequency range for the identification of electric system multiple-input and multiple-output inearized model - Google Patents
A kind of more sinusoidal signal design methods of low-frequency range for the identification of electric system multiple-input and multiple-output inearized model Download PDFInfo
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Abstract
The invention discloses a kind of more sinusoidal signal design methods of low-frequency range for the identification of electric system multiple-input and multiple-output inearized model, by a for specifying more sinusoidal signalsk、ωkAnd sampling length N, one group of parameter of signal is solved with algorithmWherein k=0,1 ..., Nk- 1, Nk≤ N/2, so that the maximum value of the amplitude u (t) of the more sinusoidal signal time domain waveforms of low-frequency range is as small as possible, so that not only having been met Time Domain Amplitude limitation requires but also meet the input signal that frequency domain energy concentrates requirement.The pumping signal that the present invention designs can will measure the frequency range for concentrating on being concerned about, it is almost nil without concern for band energy, solving the problems, such as that traditional small size pumping signal energy is not concentrated causes output response signal signal-to-noise ratio low, improves the identification precision of electric system.The more sinusoidal signals of the low-frequency range that the present invention generates are more advantageous to the identification of electric system multiple-input and multiple-output inearized model.
Description
Technical field
The present invention relates to the interleaving techniques fields of electric system identification and signal processing, and in particular to one kind is used for power train
The more sinusoidal signal design methods of low-frequency range that multiple-input and multiple-output inearized model of uniting recognizes.
Background technique
With the development of interconnected network, low-frequency oscillation problem of the electric system in 0.1 to 2.5 hertz of band limits is prominent
Out, it needs to solve by installing low-frequency oscillation of electric power system controller.Low-frequency oscillation of electric power system controller design relies on
How defeated electric system multiple-input and multiple-output inearized model need to solve multi input first in practical power systems engineering design
Identification problems of model is linearized out.In order to ensure, electric system energy safe and stable operation, Practical Project are usually adopted in identification process
Electric system is motivated with small size disturbing signal, electric system excitation input and response output signal is then acquired, passes through
System Discrimination algorithm carries out corresponding inearized model identification.At this point, the source as identification work, the small size disturbance letter of use
Number just become determine electric system multiple-input and multiple-output inearized model identification success or not key factor.
Currently, the small size disturbing signal that Practical Project uses has white noise signal and limited frequency band by low-pass filter
Pseudo-random signal.Two class signals are larger in 0.1 to 2.5 hertz of frequency range self-energy that low-frequency oscillation is concerned about, but in the care
There are certain energy other than frequency range, when leading to carry out electric system the identification of multiple-input and multiple-output inearized model, input letter
Number energy is not enough concentrated, and the signal-to-noise ratio of system output response signal reduces, to affect electric system multiple-input and multiple-output line
The precision of property Model Distinguish.
Summary of the invention
The purpose of the present invention is to solve drawbacks described above in the prior art, provide a kind of for electric system multi input
The more sinusoidal signal design methods of low-frequency range of multi output inearized model identification.
The purpose of the present invention can be reached by adopting the following technical scheme that：
A kind of more sinusoidal signal design methods of low-frequency range for the identification of electric system multiple-input and multiple-output inearized model,
The more sinusoidal signal design methods of the low-frequency range include the following steps：
Initial start up phase：
S1, determine the more sinusoidal signals of low-frequency range time domain length be N, it is contemplated that crest factor be Cr,set, in corresponding Fu
Leaf system number record variable is FS, and amplitude record variable is Mag, phase recording variable is Pha, and initial FS, Mag, Pha are length
Degree is the null vector of N；
S2, the frequencies of harmonic components ω for determining the more sinusoidal signals of low-frequency rangekAnd frequency domain amplitude ak, wherein k=0,1 ...,
Nk- 1, Nk≤ N/2, then by amplitude akAccording to frequencies of harmonic components ωkWidth is inserted in position corresponding to amplitude record variable Mag
It is worth record variable Mag, to obtain the amplitude-frequency characteristic of the more sinusoidal signals of initial low frequency section；
S3, the harmonic component initial phase for setting the more sinusoidal signals of low-frequency rangeIt is uniform between-π to π for one group of range
The random number of distribution, wherein k=0,1 ..., Nk- 1, then by phaseAccording to frequencies of harmonic components ωkCorresponding to phase recording
Phase recording variable Pha is inserted in the position of variable Pha, to obtain the phase characteristic of the more sinusoidal signals of initial low frequency section；
S4, amplitude record variable Mag and phase recording variable Pha is subjected to plural synthesis, obtains initial low frequency Duan Duozheng
The frequency domain characteristic FS of string signal, wherein being concerned about frequency range ωkCorresponding Fourier coefficient is
S5, inverse fourier transform is carried out to the frequency domain characteristic FS of the more sinusoidal signals of initial low frequency section, obtains low-frequency range mostly just
The initial time domain waveform u (t) of string signal, and initial time domain waveform u (t) is stored in variable Signal, variable Signal's
Length is N；
S6, the crest factor C for calculating variable Signalr, and store it in variable CF, if variable CF is less than expected
Crest factor Cr,set, Signal_min=Signal is counted, step S13 is then transferred to；Otherwise, set iterative cycles times N um as
0, setting maximum number of iterations is Num_max, Num_max>1, into the following iterative cycles stage；
The iterative cycles stage：
If S7, iterative cycles times N um are less than maximum number of iterations Num_max, iterative cycles times N um is added 1, so
After be transferred to step S8, otherwise, be directly entered step S13；
S8, be more than by absolute value in time domain waveform maximum value max (abs (u (t))) the more sinusoidal signals of 90% low-frequency range
Waveform values are set as the 90% of maximum value max (abs (u (t))), and keep symbol constant, obtain updated time domain waveform u
(t)*, and update is replaced to variable Signal, wherein abs () indicates that the operation that takes absolute value, max () expression are maximized
Operation；
S9, Fourier transform is carried out to updated variable Signal, obtains fourier coefficient FS*, phase characteristic is
Pha*, with amplitude record variable Mag and phase characteristic Pha*Synthesis is used as updated frequency domain characteristic FS；
S10, inverse fourier transform is carried out to updated frequency domain characteristic FS, obtains updated time domain waveform u (t), and
Update is replaced to variable Signal；
S11, the crest factor C for calculating the variable Signal updatedrIf crest factor CrLess than expected crest factor
Cr,set, Signal_min=Signal is counted, subsequently into step S13；Otherwise S12 is entered step；
If S12, crest factor CrLess than the variable CF of last iterative process, then variable CF=C is countedr, Signal_min
=Signal, return step S7；Otherwise direct return step S7；
Iterative cycles exit；
S13, using variable Signal_min as finally obtained time domain waveform.
Further, the time domain waveform expression formula of the more sinusoidal signals of the low-frequency range is Wherein t is sampling time, Ak、ωkWithRespectively k-th multifrequency sinusoid component
Time Domain Amplitude, frequency and phase, NkFor the number of sinusoidal harmonics frequency component；The crest factor of the variable Signal according to
Crest factor CrDefinition calculate, wherein crest factor CrDefinition it is as follows：Wherein N is that total sampling number of the more sinusoidal signals of low-frequency range (is believed
Number total length), max (), which is represented, takes the maximum value of array in bracket.Obviously, CrSize reflect signal in the fluctuation of time domain
Situation：Hour is got in the time domain fluctuation of the frequency domain characteristic of Setting signal u (t), signal u (t), then its CrIt is smaller.
The present invention has the following advantages and effects with respect to the prior art：
How sinusoidal a kind of low-frequency range for the identification of electric system multiple-input and multiple-output inearized model proposed by the present invention is
Design of Signal method, by a for specifying signalk、ωkAnd sampling length N, one group of parameter of signal is solved with algorithmWherein k=0,1 ..., Nk- 1, Nk≤ N/2, so that the maximum value of u (t) is as small as possible, to make to input
Signal had both been able to satisfy Time Domain Amplitude limitation and had required, and kept it smaller to the disturbance of system, and can concentrate on the energy of input signal
The frequency range of care, the energy without concern for frequency range are almost nil.Compared with traditional small size pumping signal design method, this method
It solves input signal energy not concentrate, the low problem of the signal-to-noise ratio of output response signal, how sinusoidal the designed low-frequency range is
Signal compares other low-frequency range pumping signals and is more suitable for the identification of electric system multiple-input and multiple-output inearized model.
Detailed description of the invention
Fig. 1 is the time domain waveform of three kinds of low-frequency range input signals in one embodiment of the present of invention；
Fig. 2 is the frequency-domain waveform of three kinds of low-frequency range input signals in one embodiment of the present of invention；
Fig. 3 is electric system wiring diagram based on one embodiment of the present of invention；
Fig. 4 is the frequency-domain waveform of the corresponding output signal of three kinds of input signals in one embodiment of the present of invention；
Fig. 5 is that a kind of low-frequency range for the identification of electric system multiple-input and multiple-output inearized model disclosed by the invention is more
The process step figure of sinusoidal signal design method.
Specific embodiment
In order to make the object, technical scheme and advantages of the embodiment of the invention clearer, below in conjunction with the embodiment of the present invention
In attached drawing, technical scheme in the embodiment of the invention is clearly and completely described, it is clear that described embodiment is
A part of the embodiment of the present invention, instead of all the embodiments.Based on the embodiments of the present invention, those of ordinary skill in the art
Every other embodiment obtained without making creative work, shall fall within the protection scope of the present invention.
Embodiment
How sinusoidal a kind of low-frequency range for the identification of electric system multiple-input and multiple-output inearized model proposed by the present invention is
Design of Signal method, as shown in figure 5, including the following steps：
Initial start
(1) determine the more sinusoidal signals of low-frequency range time domain length be N, it is contemplated that crest factor be Cr,set, in corresponding Fu
Leaf system number record variable is FS, and amplitude record variable is Mag, phase recording variable is Pha, and initial FS, Mag, Pha are length
Degree is the null vector of N.
(2) the frequencies of harmonic components ω of the more sinusoidal signals of low-frequency range is determinedkAnd frequency domain amplitude ak, wherein k=0,1 ...,
Nk- 1, Nk≤ N/2, then by amplitude akAccording to frequencies of harmonic components ωkWidth is inserted in position corresponding to amplitude record variable Mag
It is worth record variable Mag, to obtain the amplitude-frequency characteristic of the more sinusoidal signals of initial low frequency section.
(3) the harmonic component initial phase of the more sinusoidal signals of low-frequency range is setIt is uniform between-π to π for one group of range
The random number of distribution, wherein k=0,1 ..., Nk- 1, then by phaseAccording to frequencies of harmonic components ωkCorresponding to phase recording
Phase recording variable Pha is inserted in the position of variable Pha, to obtain the phase characteristic of the more sinusoidal signals of initial low frequency section.
(4) amplitude record variable Mag and phase recording variable Pha is subjected to plural synthesis, obtains initial low frequency Duan Duozheng
The frequency domain characteristic FS of string signal, wherein being concerned about frequency range ωkCorresponding Fourier coefficient is
(5) inverse fourier transform is carried out to the frequency domain characteristic FS of the more sinusoidal signals of initial low frequency section, obtains low-frequency range mostly just
The initial time domain waveform u (t) of string signal, and initial time domain waveform u (t) is stored in variable Signal, variable Signal's
Length is N.
(6) according to crest factor CrDefinition calculate variable Signal crest factor Cr, and store it in variable CF
In, if variable CF is less than expected crest factor Cr,set, Signal_min=Signal is counted, subsequently into (13) step；It is no
Then, iterative cycles times N um is set as 0, and setting maximum number of iterations is Num_max, Num_max>1, into being circulated throughout as follows
Journey.
Cyclic process
(7) if iterative cycles times N um is less than maximum number of iterations Num_max, iterative cycles times N um is added 1, so
After turn (8) step；Otherwise, it is directly entered (13) step.
(8) be more than by absolute value in time domain waveform maximum value max (abs (u (t))) the more sinusoidal signals of 90% low-frequency range
Waveform values are set as the 90% of maximum value max (abs (u (t))), and keep symbol constant, obtain updated time domain waveform u
(t)*, and update is replaced to variable Signal, wherein abs () indicates that the operation that takes absolute value, max () expression are maximized
Operation.
(9) Fourier transform is carried out to updated variable Signal, obtains fourier coefficient FS*, phase characteristic is
Pha*, then similar to the method for (4) step, with amplitude record variable Mag and phase characteristic Pha*Synthesis is used as updated frequency domain
Characteristic FS.
(10) inverse fourier transform is carried out to updated frequency domain characteristic FS, obtains updated time domain waveform u (t), and
Update is replaced to variable Signal.
(11) the crest factor C of the variable Signal updated is calculatedrIf crest factor CrLess than expected crest factor
Cr,set, Signal_min=Signal is counted, subsequently into (13) step；Otherwise enter (12) step.
(12) if crest factor CrLess than the variable CF of last iterative process, then variable CF=C is countedr, Signal_min
=Signal returns to (7) step；Otherwise (7) step is directly returned.
Circulation exits
(13) variable Signal_min is finally obtained time domain waveform.
Embodiment two
One embodiment of the method for the present invention introduced below.
The more sinusoidal signals of low-frequency range that a frequency domain energy concentrates on 0.1-2.5 hertz are generated with the method for the present invention, are used in combination
Conventional method generates the pseudo-random signal of the white noise signal and limited frequency band Jing Guo low-pass filter.Wherein, by low pass filtered
The white noise signal of wave device is to be filtered white noise signal with the 5 rank Butterworth filters that cutoff frequency is 2.5 hertz
It obtains, the pseudo-random signal of limited frequency band is will to pass through the amplitude of the white noise signal of low-pass filter according to the positive weight bearing of symbol
± 1p.u. is newly assigned a value of to obtain.Three kinds of low-frequency range input signal length are 100s, and sample rate is 100Hz, and by signal
It is limited between ± 0.1p.u. in the amplitude of time domain.
Fig. 1 is the time domain waveform of three kinds of low-frequency range input signals；Fig. 2 is the frequency-domain waveform of three kinds of low-frequency range input signals,
Its ordinate is the amplitude of fourier coefficient.Figure it is seen that the energy of the more sinusoidal signals of low-frequency range nearly all concentrates on closing
The frequency range (0.1-2.5 hertz) of the heart, however the pseudo-random signal of white noise signal and limited frequency band Jing Guo low-pass filter has
Part energy has exceeded the frequency range of care.The more sinusoidal signals of low-frequency range and the pseudo-random signal of limited frequency band are being concerned about frequency range
Energy be it is comparable, the two is all higher than the white noise signal of low-pass filtering in the energy for being concerned about frequency range.
Fig. 3 is 10 machine of New England, the 39 node standard test system of the present embodiment foundation, it includes 10 generators,
39 buses, load and 34 transmission lines of electricity at 19.The rated frequency of the system is 60Hz, and mains voltage grade is 345kV,
In No. 1 machine be external electrical network equal check-ins, No. 2 machines are balancing machine.Above-mentioned three kinds of low-frequency range input signals are attached to No. 9 respectively
The excitation voltage reference end of generator, and taking the frequency of No. 9 machine connection No. 38 buses of bus is output signal, compares three kinds of situations
The frequency domain energy of lower output signal is distributed.
Fig. 4 is frequency-domain waveform corresponding to output signal in the case of three kinds.As can be seen that the more sinusoidal signals of low-frequency range and having
The corresponding output signal of the pseudo-random signal of frequency limit band is higher than in the energy for being concerned about frequency range to be believed by the white noise of low-pass filter
The energy of number corresponding output signal.In addition, the corresponding output of the more sinusoidal signals of pseudo-random signal and low-frequency range of limited frequency band
Signal is of substantially equal in the energy for being concerned about frequency range, but the corresponding output signal of pseudo-random signal of limited frequency band is in unconcerned 0-
The energy of 0.1 hertz of frequency range is also quite large, will bring noise effect, influences System Identification Accuracy.In conclusion low-frequency range is mostly just
The corresponding output signal-noise ratio highest of string signal is recognized most useful for electric system.
The above embodiment is a preferred embodiment of the present invention, but embodiments of the present invention are not by above-described embodiment
Limitation, other any changes, modifications, substitutions, combinations, simplifications made without departing from the spirit and principles of the present invention,
It should be equivalent substitute mode, be included within the scope of the present invention.
Claims (2)
1. a kind of more sinusoidal signal design methods of low-frequency range for the identification of electric system multiple-input and multiple-output inearized model,
It is characterized in that, the more sinusoidal signal design methods of the low-frequency range include the following steps：
Initial start up phase：
S1, determine the more sinusoidal signals of low-frequency range time domain length be N, it is contemplated that crest factor be Cr,set, corresponding Fourier system
Number record variable is FS, and amplitude record variable is Mag, phase recording variable is Pha, and initial FS, Mag, Pha are that length is
The null vector of N；
S2, the frequencies of harmonic components ω for determining the more sinusoidal signals of low-frequency rangekAnd frequency domain amplitude ak, wherein k=0,1 ..., Nk- 1,
Nk≤ N/2, then by amplitude akAccording to frequencies of harmonic components ωkPosition filling amplitude record corresponding to amplitude record variable Mag
Variable Mag, to obtain the amplitude-frequency characteristic of the more sinusoidal signals of initial low frequency section；
S3, the harmonic component initial phase for setting the more sinusoidal signals of low-frequency rangeIt is uniformly distributed between-π to π for one group of range
Random number, wherein k=0,1 ..., Nk- 1, then by phaseAccording to frequencies of harmonic components ωkCorresponding to phase recording variable
Phase recording variable Pha is inserted in the position of Pha, to obtain the phase characteristic of the more sinusoidal signals of initial low frequency section；
S4, amplitude record variable Mag and phase recording variable Pha is subjected to plural synthesis, obtains the more sinusoidal letters of initial low frequency section
Number frequency domain characteristic FS, wherein be concerned about frequency range ωkCorresponding Fourier coefficient is
S5, inverse fourier transform is carried out to the frequency domain characteristic FS of the more sinusoidal signals of initial low frequency section, obtains the more sinusoidal letters of low-frequency range
Number initial time domain waveform u (t), and initial time domain waveform u (t) is stored in variable Signal, the length of variable Signal
For N；
S6, the crest factor C for calculating variable Signalr, and store it in variable CF, if variable CF is less than expected wave crest
Factor Cr,set, Signal_min=Signal is counted, step S13 is then transferred to；Otherwise, iterative cycles times N um is set as 0, if
Setting maximum number of iterations is Num_max, Num_max>1, into the following iterative cycles stage；
The iterative cycles stage：
If S7, iterative cycles times N um are less than maximum number of iterations Num_max, iterative cycles times N um is added 1, is then turned
Enter step S8, otherwise, is directly entered step S13；
S8, be more than by absolute value in time domain waveform maximum value max (abs (u (t))) the more sinusoidal signal waveforms of 90% low-frequency range
Value is set as the 90% of maximum value max (abs (u (t))), and keeps symbol constant, obtains updated time domain waveform u (t)*,
And update is replaced to variable Signal, wherein abs () indicates that the operation that takes absolute value, max () expression are maximized operation；
S9, Fourier transform is carried out to updated variable Signal, obtains fourier coefficient FS*, phase characteristic Pha*,
With amplitude record variable Mag and phase characteristic Pha*Synthesis is used as updated frequency domain characteristic FS；
S10, inverse fourier transform is carried out to updated frequency domain characteristic FS, obtains updated time domain waveform u (t), and to change
Amount Signal is replaced update；
S11, the crest factor C for calculating the variable Signal updatedrIf crest factor CrLess than expected crest factor Cr,set, meter
Signal_min=Signal, subsequently into step S13；Otherwise S12 is entered step；
If S12, crest factor CrLess than the variable CF of last iterative process, then variable CF=C is countedr, Signal_min=
Signal, return step S7；Otherwise direct return step S7；
Iterative cycles exit；
S13, using variable Signal_min as finally obtained time domain waveform.
2. a kind of low-frequency range for the identification of electric system multiple-input and multiple-output inearized model according to claim 1 is more
Sinusoidal signal design method, which is characterized in that the time domain waveform expression formula of the more sinusoidal signals of the low-frequency range isWherein t is sampling time, Ak、ωkWithRespectively k-th of multifrequency sinusoid
Time Domain Amplitude, frequency and the phase of component, NkFor the number of sinusoidal harmonics frequency component；The wave crest of the variable Signal because
Son is according to crest factor CrDefinition calculate, wherein crest factor CrDefinition it is as follows： Wherein N is total sampling number of the more sinusoidal signals of low-frequency range, i.e., signal is total
Length, max () represent the maximum value for taking array in bracket.
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