CN108932215B - Low-frequency band multi-sinusoidal signal design method for power system linearization model identification - Google Patents

Low-frequency band multi-sinusoidal signal design method for power system linearization model identification Download PDF

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CN108932215B
CN108932215B CN201810486216.1A CN201810486216A CN108932215B CN 108932215 B CN108932215 B CN 108932215B CN 201810486216 A CN201810486216 A CN 201810486216A CN 108932215 B CN108932215 B CN 108932215B
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张俊勃
曾繁宏
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South China University of Technology SCUT
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Abstract

The invention discloses a low-frequency band multi-sine signal design method for multi-input multi-output linear model identification of a power system, which is implemented by specifying a of multi-sine signalsk、ωkAnd a sampling length N, using an algorithm to solve a set of parameters of the signal
Figure DDA0001666780650000011
Wherein k is 0,1, …, Nk‑1，NkN/2 or less, so that the maximum value of the amplitude u (t) of the low-frequency-band multi-sine signal time domain waveform is as small as possible, and the input signal which meets the requirements of time domain amplitude limitation and frequency domain energy concentration is obtained. The excitation signal designed by the invention can concentrate energy in the concerned frequency band, and the energy of the irrelevant frequency band is almost zero, so that the problem of low signal-to-noise ratio of the output response signal caused by unconcentration of the energy of the traditional small-amplitude excitation signal is solved, and the identification precision of the power system is improved. The low-frequency-band multi-sine signal generated by the invention is more beneficial to the identification of the multi-input multi-output linearization model of the power system.

Description

Low-frequency band multi-sinusoidal signal design method for power system linearization model identification
Technical Field
The invention relates to the technical field of intersection of electric power system identification and signal processing, in particular to a low-frequency band multi-sinusoidal signal design method for electric power system multi-input multi-output linear model identification.
Background
With the development of interconnected power networks, the problem of low-frequency oscillation of a power system in a frequency band range of 0.1 to 2.5 hertz is prominent, and the problem needs to be solved by installing a low-frequency oscillation controller of the power system. The design of the low-frequency oscillation controller of the power system depends on a multi-input multi-output linearization model of the power system, and the problem of multi-input multi-output linearization model identification needs to be solved firstly in the actual power system engineering design. In order to ensure that the power system can operate safely and stably in the identification process, the actual engineering usually adopts a small-amplitude disturbance signal to excite the power system, then collects excitation input and response output signals of the power system, and carries out corresponding linear model identification through a system identification algorithm. At this time, as a source of the identification work, the adopted small-amplitude disturbance signal becomes a key factor for determining whether the power system multiple-input multiple-output linearization model is successfully identified.
At present, the small-amplitude disturbance signals adopted by practical engineering include white noise signals passing through a low-pass filter and pseudo-random signals of a limited frequency band. The two types of signals have larger energy in a frequency band of 0.1 to 2.5 Hz which is concerned by low-frequency oscillation, but certain energy exists outside the concerned frequency band, so that when the multi-input multi-output linear model identification is carried out on the power system, the energy of the input signals is not concentrated enough, the signal-to-noise ratio of the output response signals of the system is reduced, and the accuracy of the multi-input multi-output linear model identification of the power system is influenced.
Disclosure of Invention
The invention aims to solve the defects in the prior art and provides a low-frequency-band multi-sinusoidal signal design method for power system multiple-input multiple-output linear model identification.
The purpose of the invention can be achieved by adopting the following technical scheme:
a low-frequency band multi-sinusoidal signal design method for power system multiple-input multiple-output linear model identification comprises the following steps:
an initial starting stage:
s1, determining the time domain length of the low-frequency band multi-sine signal to be N and the expected crest factor to be Cr,setThe corresponding Fourier coefficient recording variable is FS, the amplitude recording variable is Mag, the phase recording variable is Pha, and the initial FS, Mag and Pha are zero vectors with the length of N;
s2, determining the harmonic component frequency omega of the low-frequency-band multi-sine signalkAnd frequency domain amplitude akWhere k is 0,1, …, Nk-1，NkN/2 or less, and then the amplitude a is calculatedkAccording to harmonic component frequency omegakFilling the amplitude recording variable Mag in a position corresponding to the amplitude recording variable Mag so as to obtain the amplitude-frequency characteristic of the initial low-frequency-band multi-sine signal;
s3, settingDetermining initial phase of harmonic component of low-frequency band multi-sinusoidal signal
Figure GDA0002944074680000021
Is a set of random numbers uniformly distributed in the range of-pi to pi, wherein k is 0,1, …, Nk-1, then phase
Figure GDA0002944074680000022
According to harmonic component frequency omegakFilling the phase recording variable Pha into a position corresponding to the phase recording variable Pha, thereby obtaining the phase characteristic of the initial low-frequency multi-sinusoidal signal;
s4, carrying out complex synthesis on the amplitude recording variable Mag and the phase recording variable Pha to obtain the frequency domain characteristic FS of the initial low-frequency multi-sinusoidal signal, wherein the frequency band omega is concernedkCorresponding Fourier coefficients are
Figure GDA0002944074680000023
k＝0,1,…,Nk-1；
S5, carrying out Fourier inverse transformation on the frequency domain characteristic FS of the initial low-frequency multi-sine Signal to obtain an initial time domain waveform u (t) of the low-frequency multi-sine Signal, and storing the initial time domain waveform u (t) in a variable Signal, wherein the length of the variable Signal is N;
s6, calculating crest factor C of variable SignalrAnd storing it in the variable CF if it is less than the expected crest factor Cr,setThen, the process proceeds to step S13 after Signal _ min is counted as Signal; otherwise, setting the number Num of iterative loop times as 0, and setting the maximum iterative times as Num _ max and Num _ max>1, entering the following iterative cycle stage;
and (3) an iterative cycle stage:
s7, if the iteration cycle number Num is smaller than the maximum iteration number Num _ max, adding 1 to the iteration cycle number Num, and then switching to the step S8, otherwise, directly switching to the step S13;
s8, setting the low-frequency multi-sine signal waveform value with the absolute value exceeding 90% of the maximum value max (abs (u (t))) in the time domain waveform as 90% of the maximum value max (abs (u (t))), keeping the sign unchanged,obtaining an updated time-domain waveform u (t)*And replacing and updating a variable Signal, wherein abs () represents an absolute value taking operation, and max () represents a maximum value taking operation;
s9, carrying out Fourier transformation on the updated variable Signal to obtain a Fourier coefficient FS*The phase characteristic is Pha*Recording the variable Mag and the phase characteristic Pha by amplitude*Synthesizing as an updated frequency domain characteristic FS;
s10, performing Fourier inverse transformation on the updated frequency domain characteristic FS to obtain an updated time domain waveform u (t), and replacing and updating a variable Signal;
s11, calculating crest factor C of updated variable SignalrIf crest factor CrLess than the expected crest factor Cr,setThen, the process proceeds to step S13 after Signal _ min is counted as Signal; otherwise, go to step S12;
s12, f crest factor CrIf the variable CF is smaller than the variable CF of the last iteration process, the variable CF is counted as CrSignal _ min is Signal, and the process returns to step S7; otherwise, directly returning to the step S7;
exiting the iteration loop;
and S13, taking the variable Signal _ min as a finally obtained time domain waveform.
Further, the expression of the time domain waveform of the low-frequency band multi-sine signal is
Figure GDA0002944074680000031
Figure GDA0002944074680000041
Where t is the sampling time, Ak、ωkAnd
Figure GDA0002944074680000042
time domain amplitude, frequency and phase, N, of the kth sinusoidal harmonic component, respectivelykThe number of sinusoidal harmonic frequency components; the crest factor of the variable Signal is according to the crest factor CrIs calculated by the formula (1), wherein the crest factor CrIs defined as follows:
Figure GDA0002944074680000043
where N is the total number of samples of the low band multi-sinusoidal signal (i.e., the total length of the signal), and max () represents the maximum value of the array taken between brackets. Obviously, CrThe size of (2) reflects the fluctuation condition of the signal in the time domain: given the frequency domain characteristics of signal u (t), the smaller the time domain fluctuation of signal u (t), the lower its CrThe smaller.
Compared with the prior art, the invention has the following advantages and effects:
the invention provides a low-frequency band multi-sinusoidal signal design method for power system multiple-input multiple-output linear model identification, which is characterized in that a of a designated signal is usedk、ωkAnd a sampling length N, using an algorithm to solve a set of parameters of the signal
Figure GDA0002944074680000044
Wherein k is 0,1, …, Nk-1，NkN/2 is less than or equal to, the maximum value of u (t) is as small as possible, so that the input signal can meet the requirement of time domain amplitude limitation, the disturbance to a system is small, the energy of the input signal can be concentrated in the concerned frequency band, and the energy of the careless frequency band is almost zero. Compared with the traditional small-amplitude excitation signal design method, the method solves the problems of non-centralized input signal energy and low signal-to-noise ratio of output response signals, and compared with other low-frequency-band multi-sinusoidal signals, the designed low-frequency-band multi-sinusoidal signal is more suitable for multi-input multi-output linear model identification of the power system.
Drawings
FIG. 1 is a time domain waveform of three low band input signals in one embodiment of the invention;
FIG. 2 is a frequency domain waveform of three low band input signals in one embodiment of the invention;
FIG. 3 is a wiring diagram of a power system according to an embodiment of the present invention;
FIG. 4 is a frequency domain waveform of an output signal corresponding to three input signals in an embodiment of the present invention;
FIG. 5 is a flowchart illustrating a low-band multi-sinusoidal signal design method for electric power system MIMO linearized model identification according to the present disclosure.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Examples
The invention provides a low-frequency band multi-sinusoidal signal design method for power system multiple-input multiple-output linear model identification, as shown in fig. 5, comprising the following steps:
initial start-up
(1) Determining the time domain length of the low-frequency band multi-sine signal to be N and the expected crest factor to be Cr,setThe corresponding fourier coefficient recording variable is FS, the amplitude recording variable is Mag, the phase recording variable is Pha, and the initial FS, Mag, and Pha are zero vectors with length N.
(2) Determining harmonic component frequency omega of low-frequency multi-sinusoidal signalkAnd frequency domain amplitude akWhere k is 0,1, …, Nk-1，NkN/2 or less, and then the amplitude a is calculatedkAccording to harmonic component frequency omegakAnd filling the amplitude recording variable Mag in a position corresponding to the amplitude recording variable Mag so as to obtain the amplitude-frequency characteristic of the initial low-frequency-band multi-sinusoidal signal.
(3) Setting initial phase of harmonic component of low-frequency-band multi-sinusoidal signal
Figure GDA0002944074680000051
Is a set of random numbers uniformly distributed in the range of-pi to pi, wherein k is 0,1, …, Nk-1, then phase
Figure GDA0002944074680000052
According to harmonic component frequency omegakThe phase recording variable Pha is filled in a position corresponding to the phase recording variable Pha, thereby obtaining the phase characteristics of the initial low frequency band multi-sinusoidal signal.
(4) Carrying out complex synthesis on the amplitude recording variable Mag and the phase recording variable Pha to obtain the frequency domain characteristic FS of the initial low-frequency multi-sinusoidal signal, wherein the frequency range omega is concernedkCorresponding Fourier coefficients are
Figure GDA0002944074680000061
k＝0,1,…,Nk-1。
(5) And carrying out inverse Fourier transform on the frequency domain characteristic FS of the initial low-frequency multi-sine Signal to obtain an initial time domain waveform u (t) of the low-frequency multi-sine Signal, and storing the initial time domain waveform u (t) in a variable Signal, wherein the length of the variable Signal is N.
(6) According to crest factor CrThe crest factor C of the variable Signal is calculated by the formularAnd storing it in the variable CF if it is less than the expected crest factor Cr,setCounting Signal _ min as Signal, and then entering the step (13); otherwise, setting the number Num of iterative loop times as 0, and setting the maximum iterative times as Num _ max and Num _ max>1, entering the following circulation process.
Circulation process
(7) If the iteration cycle number Num is less than the maximum iteration number Num _ max, adding 1 to the iteration cycle number Num, and then turning to the step (8); otherwise, directly entering the step (13).
(8) Setting the low-frequency multi-sinusoidal signal waveform value of 90% of the maximum value max (abs (u (t))) in the time domain waveform as 90% of the maximum value max (abs (u (t))), and keeping the symbol unchanged to obtain an updated time domain waveform u (t))*And replacing and updating a variable Signal, wherein abs () represents an absolute value operation, and max () represents a maximum value operation.
(9) Fourier transformation is carried out on the updated variable Signal to obtain a Fourier coefficient FS*The phase characteristic is Pha*Then classRecording the variable Mag and the phase characteristic Pha by amplitude in a manner similar to that in step (4)*Synthesized as the updated frequency domain characteristic FS.
(10) And performing inverse Fourier transform on the updated frequency domain characteristic FS to obtain an updated time domain waveform u (t), and replacing and updating the variable Signal.
(11) Calculating crest factor C of updated variable SignalrIf crest factor CrLess than the expected crest factor Cr,setCounting Signal _ min as Signal, and then entering the step (13); otherwise, entering the step (12).
(12) If crest factor CrIf the variable CF is smaller than the variable CF of the last iteration process, the variable CF is counted as CrReturning to the step (7) if Signal _ min is equal to Signal; otherwise, directly returning to the step (7).
Loop out
(13) The variable Signal _ min is the time domain waveform finally obtained.
Example two
An embodiment of the method of the present invention is described below.
The method of the invention is used for generating a low-frequency band multi-sinusoidal signal with the frequency domain energy concentrated at 0.1-2.5 Hz, and a white noise signal passing through a low-pass filter and a pseudo-random signal of a limited frequency band are generated by a traditional method. The white noise signal passing through the low-pass filter is obtained by filtering the white noise signal by a 5-order Butterworth filter with the cut-off frequency of 2.5 Hz, and the pseudo-random signal with the limited frequency band is obtained by reassigning the amplitude of the white noise signal passing through the low-pass filter to +/-1 p.u. according to the positive and negative signs. The lengths of the three low-frequency band input signals are all 100s, the sampling rates are all 100Hz, and the amplitude of the signals in the time domain is limited to +/-0.1 p.u.
FIG. 1 is a time domain waveform of three low band input signals; fig. 2 is a frequency domain waveform of three low-band input signals, the ordinate of which is the magnitude of fourier coefficients. It can be seen from fig. 2 that the energy of the low band multi-sinusoidal signal is almost concentrated in the frequency band of interest (0.1-2.5 hz), whereas the white noise signal passing through the low pass filter and the band limited pseudo-random signal have a part of energy exceeding the frequency band of interest. The low band multi-sinusoidal signal and the band limited pseudorandom signal have comparable energy in the frequency band of interest, both of which have higher energy in the frequency band of interest than the low pass filtered white noise signal.
Fig. 3 is a 39-node standard test system of the new england 10 machine according to the present embodiment, which includes 10 generators, 39 buses, 19 loads and 34 transmission lines. The rated frequency of the system is 60Hz, the main voltage level is 345kV, wherein the machine No. 1 is an equivalent machine of an external power grid, and the machine No. 2 is a balancing machine. And respectively adding the three low-frequency-band input signals to an excitation voltage reference end of the No. 9 generator, taking the frequency of the No. 38 bus of the No. 9 generator connecting bus as an output signal, and comparing the frequency domain energy distribution of the output signal under three conditions.
Fig. 4 shows frequency domain waveforms corresponding to the output signals in three cases. It can be seen that the output signal corresponding to the low band multi-sinusoidal signal and the limited band pseudo-random signal has higher energy in the frequency band of interest than the output signal corresponding to the white noise signal passing through the low pass filter. In addition, the energy of the output signal corresponding to the limited-band pseudo-random signal and the low-band multi-sinusoidal signal in the concerned frequency band is basically equal, but the energy of the output signal corresponding to the limited-band pseudo-random signal in the irrelevant 0-0.1 Hz frequency band is also quite large, which brings noise effect and affects the system identification precision. In summary, the output signal-to-noise ratio corresponding to the multi-sine signal of the low frequency band is the highest, which is most beneficial to the identification of the power system.
The above embodiments are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments, and any other changes, modifications, substitutions, combinations, and simplifications which do not depart from the spirit and principle of the present invention should be construed as equivalents thereof, and all such changes, modifications, substitutions, combinations, and simplifications are intended to be included in the scope of the present invention.

Claims (1)

1. A low-frequency band multi-sinusoidal signal design method for power system multiple-input multiple-output linear model identification is characterized by comprising the following steps:
an initial starting stage:
s1, determining the time domain length of the low-frequency band multi-sine signal to be N and the expected crest factor to be Cr,setThe corresponding Fourier coefficient recording variable is FS, the amplitude recording variable is Mag, the phase recording variable is Pha, and the initial FS, Mag and Pha are zero vectors with the length of N;
s2, determining the harmonic component frequency omega of the low-frequency-band multi-sine signalkAnd frequency domain amplitude akWhere k is 0,1, …, Nk-1，NkN/2 or less, and then the amplitude a is calculatedkAccording to harmonic component frequency omegakFilling the amplitude recording variable Mag in a position corresponding to the amplitude recording variable Mag so as to obtain the amplitude-frequency characteristic of the initial low-frequency-band multi-sine signal;
s3, setting the initial phase of the harmonic component of the low-frequency multi-sine signal
Figure FDA0002944074670000011
Is a set of random numbers uniformly distributed in the range of-pi to pi, wherein k is 0,1, …, Nk-1, then phase
Figure FDA0002944074670000012
According to harmonic component frequency omegakFilling the phase recording variable Pha into a position corresponding to the phase recording variable Pha, thereby obtaining the phase characteristic of the initial low-frequency multi-sinusoidal signal;
s4, carrying out complex synthesis on the amplitude recording variable Mag and the phase recording variable Pha to obtain the frequency domain characteristic FS of the initial low-frequency multi-sinusoidal signal, wherein the frequency band omega is concernedkCorresponding Fourier coefficients are
Figure FDA0002944074670000013
S5, carrying out Fourier inverse transformation on the frequency domain characteristic FS of the initial low-frequency multi-sine Signal to obtain an initial time domain waveform u (t) of the low-frequency multi-sine Signal, and storing the initial time domain waveform u (t) in a variable Signal, wherein the length of the variable Signal is N;
s6, calculating variablesCrest factor C of SignalrAnd storing it in the variable CF if it is less than the expected crest factor Cr,setThen, the process proceeds to step S13 after Signal _ min is counted as Signal; otherwise, setting the number Num of iterative loop times as 0, and setting the maximum iterative times as Num _ max and Num _ max>1, entering the following iterative cycle stage;
and (3) an iterative cycle stage:
s7, if the iteration cycle number Num is smaller than the maximum iteration number Num _ max, adding 1 to the iteration cycle number Num, and then switching to the step S8, otherwise, directly switching to the step S13;
s8, setting the low-frequency multi-sine signal waveform value with the absolute value exceeding 90% of the maximum value max (abs (u (t))) in the time domain waveform as 90% of the maximum value max (abs (u (t))), keeping the sign unchanged, and obtaining the updated time domain waveform u (t))*And replacing and updating a variable Signal, wherein abs () represents an absolute value taking operation, and max () represents a maximum value taking operation;
s9, carrying out Fourier transformation on the updated variable Signal to obtain a Fourier coefficient FS*The phase characteristic is Pha*Recording the variable Mag and the phase characteristic Pha by amplitude*Synthesizing as an updated frequency domain characteristic FS;
s10, performing Fourier inverse transformation on the updated frequency domain characteristic FS to obtain an updated time domain waveform u (t), and replacing and updating a variable Signal;
s11, calculating crest factor C of updated variable SignalrIf crest factor CrLess than the expected crest factor Cr,setThen, the process proceeds to step S13 after Signal _ min is counted as Signal; otherwise, go to step S12;
s12, f crest factor CrIf the variable CF is smaller than the variable CF of the last iteration process, the variable CF is counted as CrSignal _ min is Signal, and the process returns to step S7; otherwise, directly returning to the step S7;
exiting the iteration loop;
s13, taking the variable Signal _ min as a finally obtained time domain waveform;
wherein, the expression of the time domain waveform of the low-frequency band multi-sine signal is
Figure FDA0002944074670000021
Figure FDA0002944074670000022
Where t is the sampling time, Ak、ωkAnd
Figure FDA0002944074670000023
time domain amplitude, frequency and phase, N, of the kth sinusoidal harmonic component, respectivelykThe number of sinusoidal harmonic frequency components; the crest factor of the variable Signal is according to the crest factor CrIs calculated by the formula (1), wherein the crest factor CrIs defined as follows:
Figure FDA0002944074670000031
where N is the total number of samples of the low band multi-sinusoidal signal, i.e. the total length of the signal, and max () represents the maximum value of the array in parentheses.
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