CN111679125A - Method and device for identifying oscillation of power system - Google Patents

Method and device for identifying oscillation of power system Download PDF

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CN111679125A
CN111679125A CN202010499817.3A CN202010499817A CN111679125A CN 111679125 A CN111679125 A CN 111679125A CN 202010499817 A CN202010499817 A CN 202010499817A CN 111679125 A CN111679125 A CN 111679125A
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frequency
component
sinusoidal component
frequency part
sinusoidal
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CN111679125B (en
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张放
刘军
王小君
和敬涵
许寅
吴翔宇
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Beijing Jiaotong University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R23/00—Arrangements for measuring frequencies; Arrangements for analysing frequency spectra
    • G01R23/16—Spectrum analysis; Fourier analysis
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R23/00—Arrangements for measuring frequencies; Arrangements for analysing frequency spectra
    • G01R23/02—Arrangements for measuring frequency, e.g. pulse repetition rate; Arrangements for measuring period of current or voltage
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R23/00—Arrangements for measuring frequencies; Arrangements for analysing frequency spectra
    • G01R23/02—Arrangements for measuring frequency, e.g. pulse repetition rate; Arrangements for measuring period of current or voltage
    • G01R23/06—Arrangements for measuring frequency, e.g. pulse repetition rate; Arrangements for measuring period of current or voltage by converting frequency into an amplitude of current or voltage

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Abstract

The embodiment of the invention provides a method and a device for identifying oscillation of a power system, wherein the method comprises the following steps: modeling an oscillation signal of a power system into a fundamental wave sinusoidal component with an offset frequency, a pair of subsynchronous sinusoidal components with coupled frequencies and a supersynchronous sinusoidal component; respectively synthesizing a positive frequency part and a negative frequency part of the oscillation component; calculating to obtain a positive frequency part and a negative frequency part in the fundamental wave sinusoidal component; constructing a synchronous phasor trajectory fitting equation set; solving the synchronous phasor trajectory fitting equation set to obtain the frequencies of a fundamental wave sinusoidal component, a subsynchronous sinusoidal component and a supersynchronous sinusoidal component, a positive frequency part and a negative frequency part in the fundamental wave sinusoidal component, and a positive frequency part and a negative frequency part in the oscillation component; calculating the amplitude and the phase of a fundamental wave sinusoidal component; and calculating the amplitude and the phase of the subsynchronous sinusoidal component and the supersynchronous sinusoidal component.

Description

Method and device for identifying oscillation of power system
Technical Field
The invention relates to the field of power systems, in particular to a method and a device for identifying oscillation of a power system.
Background
The oscillation process is one of the most common disturbance processes in power systems. Since severe oscillation will cause system instability, line overload, etc., and seriously threaten the grid safety, when the oscillation process occurs in the power system, the oscillation parameters need to be effectively monitored and identified. Because the power system is an alternating current power system operating at a rated frequency, when oscillation occurs, the oscillation signal mainly contains a fundamental wave sinusoidal component deviating from the rated frequency, a subsynchronous sinusoidal component and a supersynchronous sinusoidal component, the sum of which is twice the rated frequency, and a small amount of other frequency components. The frequency, amplitude and phase of the fundamental, subsynchronous and supersynchronous sinusoidal components are the most important oscillation parameters for power system operation management personnel.
With the increasing abundance of monitoring means, the wide-area measurement system of the power system becomes a new generation of dynamic monitoring system of the power system, and becomes an effective means for dynamic monitoring and control of the power system. The measurement terminal of the wide area measurement system is a phasor measurement terminal PMU, and the phasor measurement terminal uploads real-time measured synchronous phasor data at the highest double rated frequency. However, the synchronous phasor data is only the calculated fundamental phasor corresponding to the rated frequency, and the frequency offset fundamental component, the subsynchronous component and the supersynchronous component in the power system oscillation process are influenced by the frequency spectrum leakage and appear in the fundamental phasor of the synchronous phasor data, so that the synchronous phasor data contains oscillation information and can be used for oscillation identification, and a power system oscillation identification method based on the synchronous phasor is needed to effectively identify the frequency, the amplitude and the phase of the fundamental sinusoidal component, the subsynchronous sinusoidal component and the supersynchronous sinusoidal component.
The existing electric power system oscillation identification method based on the synchronous phasor is a Fourier transform spectrum analysis method, and the main technical problem is that when the synchronous phasor data is subjected to spectrum analysis, a large data window has to be adopted to avoid spectrum aliasing so as to ensure high enough spectrum resolution, so that the real-time performance of oscillation identification is poor; furthermore, poor real-time oscillation identification will lead to poor identification results, since the larger the data window length, the more likely the oscillation mode of the power system will change.
Disclosure of Invention
The embodiment of the invention provides a method and a device for identifying oscillation of a power system, which can overcome the defect of poor frequency resolution caused by small data window and spectrum aliasing in a spectrum analysis method.
A method of power system oscillation identification, comprising:
modeling an oscillation signal of a power system into a fundamental wave sinusoidal component with an offset frequency, a pair of subsynchronous sinusoidal components with coupled frequencies and a supersynchronous sinusoidal component, wherein the three components respectively have an amplitude value, a phase position and a frequency;
respectively synthesizing a positive frequency part and a negative frequency part of an oscillation component according to the positive frequency part and the negative frequency part of the subsynchronous sine component and the supersynchronous sine component; calculating to obtain a positive frequency part and a negative frequency part in the fundamental wave sinusoidal component;
constructing a synchronous phasor trajectory fitting equation set according to the positive frequency part and the negative frequency part of the oscillation component and the positive frequency part and the negative frequency part in the fundamental wave sinusoidal component;
solving the synchronous phasor track fitting equation set by adopting a nonlinear curve fitting numerical solving method to obtain the frequencies of a fundamental wave sinusoidal component, a subsynchronous sinusoidal component and a supersynchronous sinusoidal component, a positive frequency part and a negative frequency part in the fundamental wave sinusoidal component, and a positive frequency part and a negative frequency part of an oscillation component;
calculating the amplitude and the phase of the fundamental wave sinusoidal component according to the positive frequency part or the negative frequency part in the fundamental wave sinusoidal component;
calculating the amplitude and the phase of a subsynchronous sinusoidal component and a supersynchronous sinusoidal component according to the positive frequency part and the negative frequency part of the oscillation component;
and the amplitude, the phase and the frequency of the fundamental wave sinusoidal component, and the amplitude, the phase and the frequency of the subsynchronous sinusoidal component and the supersynchronous sinusoidal component are oscillation identification results of the power system.
An apparatus of power system oscillation identification, comprising:
the modeling unit is used for modeling an oscillating signal of the power system into a fundamental wave sinusoidal component with an offset frequency, a pair of frequency-coupled subsynchronous sinusoidal components and a supersynchronous sinusoidal component, wherein the three components respectively have amplitude, phase and frequency;
a first calculation unit that synthesizes a positive frequency part and a negative frequency part of an oscillation component, respectively, from the subsynchronous sinusoidal component and the positive frequency part and the negative frequency part of the supersynchronous sinusoidal component; calculating to obtain a positive frequency part and a negative frequency part in the fundamental wave sinusoidal component;
the construction unit is used for constructing a synchronous phasor track fitting equation set according to the positive frequency part and the negative frequency part of the oscillation component and the positive frequency part and the negative frequency part in the fundamental wave sinusoidal component;
the second calculation unit is used for solving the synchronous phasor trajectory fitting equation set by adopting a nonlinear curve fitting numerical solving method to obtain the frequencies of a fundamental wave sinusoidal component, a subsynchronous sinusoidal component and a supersynchronous sinusoidal component, a positive frequency part and a negative frequency part in the fundamental wave sinusoidal component, and a positive frequency part and a negative frequency part of an oscillation component;
the third calculating unit is used for calculating the amplitude and the phase of the fundamental wave sinusoidal component according to the positive frequency part or the negative frequency part in the fundamental wave sinusoidal component;
the fourth calculating unit is used for calculating the amplitude and the phase of the subsynchronous sinusoidal component and the supersynchronous sinusoidal component according to the positive frequency part and the negative frequency part of the oscillation component;
and the identification result unit is used for identifying the amplitude, the phase and the frequency of the fundamental wave sinusoidal component, and the amplitude, the phase and the frequency of the subsynchronous sinusoidal component and the supersynchronous sinusoidal component as the result of identifying the oscillation of the power system.
The method provided by the invention adopts a nonlinear overdetermined equation system solving method, overcomes the defects of poor frequency resolution caused by small data window and spectrum aliasing in a spectrum analysis method, and can effectively identify the amplitude, phase and frequency of a frequency offset fundamental wave sinusoidal component, a pair of subsynchronous sinusoidal components and an oversynchronous sinusoidal component within twice rated frequency.
According to the technical scheme provided by the embodiment of the invention, the adopted data window is smaller in length and has better real-time performance, the nonlinear overdetermined equation system solving method is adopted to overcome the defect of poor frequency resolution caused by small data window and frequency spectrum aliasing in the frequency spectrum analysis method, and the amplitude, the phase and the frequency of the frequency offset fundamental wave sinusoidal component, the pair of subsynchronous sinusoidal components and the supersynchronous sinusoidal component within twice rated frequency can be effectively identified.
Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without inventive labor.
FIG. 1 is a flow chart of a method for identifying oscillation in an electrical power system according to the present invention;
FIG. 2 is a flowchart of a method for identifying oscillation in a power system based on synchrophasor trajectory fitting according to another embodiment of the present invention;
fig. 3 is a schematic diagram of a synchrophasor data sequence according to an embodiment of the method for identifying oscillation of a power system based on synchrophasor trajectory fitting provided by the present invention;
fig. 4 is a connection diagram of the oscillation identification device of the power system according to the present invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.
For the convenience of understanding the embodiments of the present invention, the following description will be further explained by taking several specific embodiments as examples in conjunction with the drawings, and the embodiments are not to be construed as limiting the embodiments of the present invention.
As shown in fig. 1, a method for identifying oscillation of an electric power system according to the present invention includes:
step 11, modeling an oscillation signal of the power system into a fundamental wave sinusoidal component with frequency offset, a pair of frequency-coupled subsynchronous sinusoidal components and supersynchronous sinusoidal components, wherein the three components respectively have amplitude, phase and frequency;
step 12, respectively synthesizing a positive frequency part and a negative frequency part of an oscillation component according to the positive frequency part and the negative frequency part of the subsynchronous sine component and the supersynchronous sine component; calculating to obtain a positive frequency part and a negative frequency part in the fundamental wave sinusoidal component;
step 13, constructing a synchronous phasor trajectory fitting equation set according to the positive frequency part and the negative frequency part of the oscillation component and the positive frequency part and the negative frequency part of the fundamental wave sinusoidal component;
step 14, solving the synchronous phasor trajectory fitting equation set by adopting a nonlinear curve fitting numerical solution method to obtain the frequencies of a fundamental wave sinusoidal component, a subsynchronous sinusoidal component and a supersynchronous sinusoidal component, a positive frequency part and a negative frequency part in the fundamental wave sinusoidal component, and a positive frequency part and a negative frequency part of an oscillation component;
step 15, calculating the amplitude and the phase of the fundamental wave sinusoidal component according to the positive frequency part or the negative frequency part in the fundamental wave sinusoidal component;
step 16, calculating the amplitudes and phases of the subsynchronous sinusoidal components and the supersynchronous sinusoidal components according to the positive frequency part and the negative frequency part of the oscillation components;
and step 17, the amplitude, the phase and the frequency of the fundamental wave sinusoidal component, and the amplitude, the phase and the frequency of the subsynchronous sinusoidal component and the supersynchronous sinusoidal component are oscillation identification results of the power system.
Wherein, step 11 comprises:
the instantaneous value x (t) of the power system oscillation signal is expressed as the following formula,
x(t)＝x0cos(2πf0t+φ0)+xsubcos(2πfsubt+φsub)+xsupcos(2πfsupt+φsup)
wherein f is0、x0、φ0The frequency, amplitude and phase of the fundamental wave sinusoidal component respectively;
xsub、φsub、fsubamplitude, phase and frequency of subsynchronous sinusoidal components;
xsup、φsup、fsupamplitude, phase and frequency of the supersynchronous sinusoidal components; f. ofsub+fsup＝2fN。
Wherein step 12 comprises:
Figure BDA0002524373580000061
Figure BDA0002524373580000062
Figure BDA0002524373580000063
Figure BDA0002524373580000064
wherein the positive frequency part of the oscillation component is
Figure BDA0002524373580000065
And a negative frequency part of
Figure BDA0002524373580000066
The positive frequency part and the negative frequency part in the fundamental wave sinusoidal component are respectively
Figure BDA0002524373580000067
And
Figure BDA0002524373580000068
Figure BDA0002524373580000069
and
Figure BDA00025243735800000610
synchronous phasor results corresponding to the fundamental wave sinusoidal component, the subsynchronous sinusoidal component and the supersynchronous sinusoidal component respectively;
Figure BDA0002524373580000071
Figure BDA0002524373580000072
n is the number of data points in the fast Fourier transform synchrophasor calculation data window, fSUploading frequency and f for synchronous phasor dataS＝2fNThe "+" notation denotes the conjugate of the complex number,
Figure BDA0002524373580000073
Figure BDA0002524373580000074
is composed of two parts, the first part
Figure BDA0002524373580000075
Corresponding to a frequency of
Figure BDA0002524373580000076
Is a negative frequency; the second part
Figure BDA0002524373580000077
Corresponding to a frequency of
Figure BDA0002524373580000078
Is a positive frequency;
Figure BDA0002524373580000079
is composed of two parts, the first part
Figure BDA00025243735800000710
Corresponding frequency
Figure BDA00025243735800000711
Is positive frequency and
Figure BDA00025243735800000712
is the same; the second part is
Figure BDA00025243735800000713
Corresponding frequency
Figure BDA00025243735800000714
Is of negative frequency and
Figure BDA00025243735800000715
is identical;
Figure BDA00025243735800000716
is composed of two parts, the corresponding frequencies of the two parts are respectively
Figure BDA00025243735800000717
And
Figure BDA00025243735800000718
when f is0＞fNWhen the frequency is positive, the corresponding frequency of the two parts is negative; when f is0＜fNWhen the frequency of the two parts is negative frequency and positive frequency respectively.
Wherein step 13 comprises:
the synchronous phasor trajectory fitting equation set is as follows:
Figure BDA0002524373580000081
the number of equations of the synchrophasor trajectory fitting equation set is 2K +1,
the variables a and β are each, respectively,
Figure BDA0002524373580000082
Figure BDA0002524373580000083
wherein step 14 comprises:
solving the synchrophasor trajectory fitting equation set by using a nonlinear curve fitting numerical solution method to obtain variables α and β and a positive frequency part of an oscillation component
Figure BDA0002524373580000084
Negative frequency part
Figure BDA0002524373580000085
Positive frequency part in fundamental wave sine component
Figure BDA0002524373580000086
Negative frequency part
Figure BDA0002524373580000087
Calculating the frequency of subsynchronous sine component according to the obtained α and β and the following two formulas
Figure BDA0002524373580000088
Frequency f of supersynchronous sinusoidal componentssup＝2fN-fsubAnd assume f0＜fNFrequency of fundamental sinusoidal component under condition
Figure BDA0002524373580000089
Figure BDA0002524373580000091
Figure BDA0002524373580000092
Wherein the modeling error is
Figure BDA0002524373580000093
According to the positive frequency part in the obtained fundamental wave sinusoidal component
Figure BDA0002524373580000094
Negative frequency part
Figure BDA0002524373580000095
Determining the frequency f of the sinusoidal component of the fundamental wave0(ii) a The method specifically comprises the following steps:
Figure BDA0002524373580000096
wherein,
Figure BDA0002524373580000097
step 15 comprises:
calculating the frequency f of the fundamental wave sinusoidal component according to the following formula0；
Figure BDA0002524373580000098
Q is calculated according to the following formula*(f0,+1)；
Figure BDA0002524373580000099
Then according to the following formula, calculating to obtain the amplitude x of the fundamental wave sinusoidal component0And phase phi0；
Figure BDA00025243735800000910
Wherein step 16 comprises:
according to the frequency f of the subsynchronous sinusoidal componentssubAnd frequency f of the supersynchronous sinusoidal componentsupAnd the following formula, calculate Q (f)sub,-1)、Q(fsup,-1)、Q*(fsub, +1) and Q*(fsup,+1)；
Figure BDA0002524373580000101
Solving the following equation set to obtain the amplitude and phase of the subsynchronous sinusoidal component as xsubAnd phisub，
Amplitude and phase x of the supersynchronous sinusoidal componentssupAnd phisup
Figure BDA0002524373580000102
The idea of the present invention is described below.
The invention provides a synchronous phasor trajectory fitting-based electric power system oscillation identification method, which comprises the steps of modeling an electric power system oscillation signal into a fundamental wave sinusoidal component with frequency deviation possible to offset, and a pair of frequency-coupled subsynchronous sinusoidal component and supersynchronous sinusoidal component; the positive frequency part and the negative frequency part of the synchrophasor are subjected to equation fitting according to the constructed synchrophasor trajectory; solving a synchronous phasor trajectory fitting equation set by adopting a nonlinear curve fitting numerical solving method to obtain the frequency of each component; calculating the amplitude and the phase of the fundamental wave sinusoidal component according to the positive frequency part or the negative frequency part in the fundamental wave sinusoidal component, and calculating the amplitude and the phase of the subsynchronous sinusoidal component and the supersynchronous sinusoidal component according to the positive frequency part and the negative frequency part of the oscillation component; compared with a synchronous phasor spectrum analysis method in the prior art, the method provided by the invention has the advantages that the length of the data window adopted is smaller, the real-time performance is better, the defect of poor frequency resolution caused by spectrum aliasing due to the small data window in the spectrum analysis method is overcome by adopting a nonlinear overdetermined equation system solving method, and the amplitude, the phase and the frequency of the frequency offset fundamental wave sinusoidal component, the pair of subsynchronous sinusoidal components and the supersynchronous sinusoidal component within twice rated frequency can be effectively identified.
In the invention, an electric power system oscillation signal is modeled into a fundamental wave sinusoidal component with frequency offset possible to offset, a pair of frequency-coupled subsynchronous sinusoidal components and a supersynchronous sinusoidal component, wherein the three components respectively have undetermined amplitude, phase and frequency;
constructing a synchronous phasor trajectory fitting equation set according to a positive frequency part and a negative frequency part of an oscillation component respectively synthesized by a positive frequency part and a negative frequency part of a subsynchronous sinusoidal component and a supersynchronous sinusoidal component, and a positive frequency part and a negative frequency part in a fundamental sinusoidal component;
solving a synchronous phasor trajectory fitting equation set by adopting a nonlinear curve fitting numerical solution method to obtain the frequencies of a fundamental wave sinusoidal component, a subsynchronous sinusoidal component and a supersynchronous sinusoidal component, a positive frequency part and a negative frequency part in the fundamental wave sinusoidal component, and a positive frequency part and a negative frequency part of the subsynchronous sinusoidal component and the supersynchronous sinusoidal component;
and calculating the amplitude and the phase of the fundamental wave sinusoidal component according to the positive frequency part or the negative frequency part in the fundamental wave sinusoidal component, and calculating the amplitude and the phase of the subsynchronous sinusoidal component and the supersynchronous sinusoidal component according to the positive frequency part and the negative frequency part of the oscillation component.
Further, the power system oscillation signal is modeled as a fundamental wave sinusoidal component with a frequency offset which can be shifted, a pair of frequency-coupled subsynchronous sinusoidal components and supersynchronous sinusoidal components, the three components respectively have undetermined amplitude, phase and frequency, and the instantaneous value x (t) of the power system oscillation signal is expressed as the following formula,
x(t)＝x0cos(2πf0t+φ0)+xsubcos(2πfsubt+φsub)+xsupcos(2πfsupt+φsup) (1)
which comprises the following steps: fundamental sinusoidal component, f0、x0、φ0Is the frequency, amplitude and phase of the sinusoidal component of the fundamental wave, and the frequency f of the sinusoidal component of the fundamental wave0Rated frequency f of power systemNMay not be equal; a pair of subsynchronous sinusoidal components and supersynchronous sinusoidal components, xsub、φsub、fsubAmplitude, phase and frequency, x, of subsynchronous sinusoidal componentssup、φsup、fsupIs the amplitude, phase and frequency of the supersynchronous sinusoidal components, and fsub+fsup＝2fN(ii) a The amplitudes, phases and frequencies of the fundamental sinusoidal component, the subsynchronous sinusoidal component and the supersynchronous sinusoidal component are undetermined.
The synchrophasor in the power system is obtained by a fast fourier transform synchrophasor calculation method, since the fast fourier transform is a linear transform, there is,
Figure BDA0002524373580000121
Figure BDA0002524373580000122
for the kth power system synchronous phasor,
Figure BDA0002524373580000123
and
Figure BDA0002524373580000124
the synchronous phasor results corresponding to the fundamental wave sinusoidal component, the subsynchronous sinusoidal component and the supersynchronous sinusoidal component respectively. Wherein,
Figure BDA0002524373580000125
and
Figure BDA0002524373580000126
the specific calculation results of (a) are shown in formulas (3), (4) and (5),
Figure BDA0002524373580000127
Figure BDA0002524373580000128
Figure BDA0002524373580000129
wherein, the length of the fast Fourier transform synchronous phasor calculation data window is a cycle corresponding to the rated frequency of a power system, N is the number of data points in the fast Fourier transform synchronous phasor calculation data window, fSUploading frequency and f for synchronous phasor dataS＝2fNDue to fS＝2fNAnd the fast Fourier transform synchrophasor calculation data window is a rated frequency cycle, so (e) existsjkπ) One, the "+" symbol denotes a complex conjugate, and has
Figure BDA00025243735800001210
As can be seen from the formula (3),
Figure BDA0002524373580000131
consisting of two parts, taking into account 0 < fsub＜fNFirst part
Figure BDA0002524373580000132
Corresponding to a frequency of
Figure BDA0002524373580000133
Is a negative frequency; the second part
Figure BDA0002524373580000134
Corresponding to a frequency of
Figure BDA0002524373580000135
Is a positive frequency.
Similarly, as can be seen from formula (4),
Figure BDA00025243735800001322
is composed of two parts, the first part
Figure BDA0002524373580000136
Corresponding frequency
Figure BDA0002524373580000137
Is positive frequency and
Figure BDA0002524373580000138
is the same; the second part is
Figure BDA0002524373580000139
Corresponding frequency
Figure BDA00025243735800001310
Is of negative frequency and
Figure BDA00025243735800001311
is identical.
Further, as can be seen from the formula (5),
Figure BDA00025243735800001312
is composed of two parts, the corresponding frequencies of the two parts are respectively
Figure BDA00025243735800001313
And
Figure BDA00025243735800001314
taking into account the possible presence of f0＜fN、f0＝fNAnd f0＞fNIn this case, the two corresponding frequencies are positive and negative frequencies or negative and positive frequencies, respectively. Since the frequency of the power system does not strictly exist f0＝fNSo that the first assumption f without loss of generality0＜fNAnd performing subsequent calculation, and judging that the final result is f according to the subsequent calculation result0＜fNOr f0＞fN。
According to the derivation, the positive frequency part and the negative frequency part of the subsynchronous sinusoidal component and the supersynchronous sinusoidal component are respectively set to be synthesized into the positive frequency part of the oscillation component
Figure BDA00025243735800001315
And a negative frequency part
Figure BDA00025243735800001316
The positive frequency part and the negative frequency part in the fundamental wave sinusoidal component are respectively
Figure BDA00025243735800001317
And
Figure BDA00025243735800001318
so as to obtain the compound with the characteristics of,
Figure BDA00025243735800001319
Figure BDA00025243735800001320
Figure BDA00025243735800001321
Figure BDA0002524373580000141
further, the oscillation components are synthesized from the positive frequency part and the negative frequency part of the subsynchronous sinusoidal component and the supersynchronous sinusoidal component, respectivelyThe positive frequency part and the negative frequency part, and the positive frequency part and the negative frequency part in the fundamental wave sinusoidal component, and the construction of a synchronous phasor track fitting equation set comprises the steps of obtaining a fitting value of a synchronous phasor track in the oscillation process of the power system according to the formula (2) and the formulas (7) to (10)
Figure BDA0002524373580000142
Is composed of
Figure BDA0002524373580000143
Further, the modeling error of equation (1) is considered
Figure BDA0002524373580000144
So as to obtain the compound with the characteristics of,
Figure BDA0002524373580000145
let the variables a and β be,
Figure BDA0002524373580000146
Figure BDA0002524373580000147
then, according to equations (7) to (10), equation (12) can be rewritten as the following equation system form,
Figure BDA0002524373580000148
for simplifying the calculation, equation (13) is rewritten into a synchrophasor trajectory fitting equation set shown in equation (14) with the number of equations being 2K +1,
Figure BDA0002524373580000151
further, the method for solving the synchronous phasor trajectory fitting equation by adopting the nonlinear curve fitting numerical solution methodThe set of synchronous phasor trajectory fitting equations shown in equation (14) including α and β to be quantified in the real number domain, 0, α < pi, 0 < β < pi, and the positive frequency part of the oscillation component in the complex number domain
Figure BDA0002524373580000158
Negative frequency part
Figure BDA0002524373580000159
Positive frequency part in fundamental wave sine component
Figure BDA00025243735800001511
Negative frequency part
Figure BDA00025243735800001512
The known quantity being a synchrophasor
Figure BDA00025243735800001510
The synchronous phasor trajectory fitting equation set shown in the solving formula (14) can be solved by adopting a general nonlinear curve fitting numerical solving method, and the initial value of the solution can be set as
Figure BDA0002524373580000152
The iterative Jacobian matrix can be determined analytically or numerically from equation (14), and the variables α and β, and the positive frequency component of the oscillation component can be determined
Figure BDA0002524373580000153
Negative frequency part
Figure BDA0002524373580000154
Positive frequency part in fundamental wave sine component
Figure BDA0002524373580000155
Negative frequency part
Figure BDA0002524373580000156
The known quantity being a synchrophasor
Figure BDA0002524373580000157
From the obtained α and β and equations (11) and (12), the frequency of the subsynchronous sinusoidal component can be calculated
Figure BDA0002524373580000161
Frequency f of supersynchronous sinusoidal componentssup＝2fN-fsubAnd assume f0＜fNFrequency of fundamental sinusoidal component under condition
Figure BDA0002524373580000162
Since when f is0＜fNWhen the temperature of the water is higher than the set temperature,
Figure BDA0002524373580000163
when f is0＞fNWhen the temperature of the water is higher than the set temperature,
Figure BDA0002524373580000164
therefore, according to the positive frequency part in the obtained fundamental wave sinusoidal component
Figure BDA0002524373580000165
Negative frequency part
Figure BDA0002524373580000166
The frequency f of the sinusoidal component of the fundamental wave can be finally judged0，
Figure BDA0002524373580000167
And
Figure BDA0002524373580000168
further, the amplitude and phase of the fundamental sinusoidal component are calculated from the positive frequency part or the negative frequency part of the fundamental sinusoidal component, and the amplitude and phase of the subsynchronous sinusoidal component and the supersynchronous sinusoidal component are calculated from the positive frequency part and the negative frequency part of the oscillation component, including,
calculating the amplitude and phase of the fundamental sinusoidal component according to the positive frequency part or the negative frequency part in the fundamental sinusoidal component, and calculating the frequency f of the fundamental sinusoidal component according to the formula (15)0And equation (6) calculating Q*(f0, +1), and then the amplitude x of the fundamental wave sinusoidal component is calculated according to the formula (16)0And phase phi0。
Similarly, the frequency f of the subsynchronous sinusoidal components is dependent onsubAnd frequency f of the supersynchronous sinusoidal componentsupAnd equation (6) calculates Q (f)sub,-1)、Q(fsup,-1)、Q*(fsub, +1) and Q*(fsup, +1), and further, according to the simultaneous equation set of the formula (7) and the formula (8), since k is set as the reference point, it can be obtained by substituting the formula (7) and the formula (8) with k being 0,
Figure BDA0002524373580000169
solving the equation set to obtain the amplitude and phase of the subsynchronous sinusoidal component as xsubAnd phisubAmplitude and phase x of the supersynchronous sinusoidal componentssupAnd phisup。
In summary, the amplitude, phase and frequency of the fundamental sinusoidal component, the subsynchronous sinusoidal component and the supersynchronous sinusoidal component to be determined in equation (1) are obtained.
The present invention also provides a practical embodiment for exemplarily showing a process of performing oscillation identification of a power system by using the method provided by the present invention, and the steps are shown in fig. 2.
Let instantaneous value x (t) in the power system oscillation contain 3 components, which are:
1. the fundamental wave sinusoidal component has the frequency of 50.74Hz, the amplitude of 100 and the phase of 1rad at the moment when k is 0;
2. subsynchronous sinusoidal components, frequency 10.23Hz, amplitude 40, phase 2rad at time k 0;
3. supersynchronous sinusoidal components, frequency 89.77Hz, amplitude 60, phase 0.5rad at time k-0.
The corresponding synchrophasor for this instantaneous value is shown in fig. 3.
Performing said first step of modeling the power system oscillation signal as a fundamental sinusoidal component with a possible frequency offset, a pair of frequency-coupled subsynchronous sinusoidal components and supersynchronous sinusoidal components, the three components having respectively undetermined amplitude, phase and frequency comprising, expressing the instantaneous value x (t) of the power system oscillation signal as the following formula,
x(t)＝x0cos(2πf0t+φ0)+xsubcos(2πfsubt+φsub)+xsupcos(2πfsupt+φsup) (1)
which comprises the following steps: fundamental sinusoidal component, f0、x0、φ0Is the frequency, amplitude and phase of the sinusoidal component of the fundamental wave, and the frequency f of the sinusoidal component of the fundamental wave0Rated frequency f of power systemNMay not be equal; a pair of subsynchronous sinusoidal components and supersynchronous sinusoidal components, xsub、φsub、fsubAmplitude, phase and frequency, x, of subsynchronous sinusoidal componentssup、φsup、fsupIs the amplitude, phase and frequency of the supersynchronous sinusoidal components, and fsub+fsup＝2fN(ii) a The amplitudes, phases and frequencies of the fundamental sinusoidal component, the subsynchronous sinusoidal component and the supersynchronous sinusoidal component are undetermined. N is the number of data points of a Fourier transform data window in the synchronous phasor calculation, and N is 256; f. ofNFor rating the frequency, f, of the power systemN＝50Hz；fSIs the sampling frequency of the synchrophasor data and fS＝2fN，fS＝100Hz。
And executing the second step, and constructing a synchronous phasor track fitting equation set according to the positive frequency part and the negative frequency part of the oscillation component respectively synthesized by the positive frequency part and the negative frequency part of the subsynchronous sinusoidal component and the supersynchronous sinusoidal component, and the positive frequency part and the negative frequency part in the fundamental sinusoidal component.
In this embodiment, K is 3, that is, the number of equations is 2K +1 is 7, and K is 0. The established system of fitting equations for constructing the synchrophasor trajectory is as follows,
Figure BDA0002524373580000181
wherein,
Figure BDA0002524373580000182
and executing the third step, solving a synchronous phasor trajectory fitting equation set by adopting a nonlinear curve fitting numerical solution method, and obtaining the frequencies of a fundamental wave sinusoidal component, a subsynchronous sinusoidal component and a supersynchronous sinusoidal component, a positive frequency part and a negative frequency part in the fundamental wave sinusoidal component, and a positive frequency part and a negative frequency part of the subsynchronous sinusoidal component and the supersynchronous sinusoidal component.
In this embodiment, a nonlinear newton-raphson iteration number solving method is adopted as a nonlinear curve fitting numerical value solving method to solve the synchronous phasor trajectory fitting equation set. The initial value of the numerical solution method is taken as,
Figure BDA0002524373580000191
the solution to the system of equations is α -0.0465, β -2.4988, and the positive frequency portion of the oscillating component
Figure BDA0002524373580000192
Negative frequency part
Figure BDA0002524373580000193
Positive frequency part in fundamental wave sine component
Figure BDA0002524373580000194
Negative frequency partIs divided into
Figure BDA0002524373580000195
From the obtained α and β, the frequency of the subsynchronous sinusoidal component is calculated
Figure BDA0002524373580000196
(Hz), frequency f of supersynchronous sinusoidal componentssup＝2fN-fsub89.7700(Hz), and assume f0＜fNFrequency of fundamental sinusoidal component under condition
Figure BDA0002524373580000197
Since when f is0＜fNWhen the temperature of the water is higher than the set temperature,
Figure BDA0002524373580000198
when f is0＞fNWhen the temperature of the water is higher than the set temperature,
Figure BDA0002524373580000199
according to the positive frequency part in the obtained fundamental wave sinusoidal component
Figure BDA00025243735800001910
Negative frequency part
Figure BDA00025243735800001911
Can obtain the product
Figure BDA00025243735800001912
The frequency of the sine component of the fundamental wave can be finally judged
Figure BDA00025243735800001913
Figure BDA00025243735800001914
And
Figure BDA00025243735800001915
performing the fourth step of calculating the amplitude and phase of the fundamental sinusoidal component from the positive frequency part or the negative frequency part of the fundamental sinusoidal component, calculating the amplitude and phase of the subsynchronous sinusoidal component and the supersynchronous sinusoidal component from the positive frequency part and the negative frequency part of the oscillation component, including,
calculating the amplitude and phase of the fundamental sinusoidal component according to the positive frequency part or the negative frequency part in the fundamental sinusoidal component, and calculating the frequency f of the fundamental sinusoidal component according to the formula (15)0Q (f) is calculated by formula (6) at 50.7400Hz0-1) 255.63+11.848i, further according to formula (16)
Figure BDA0002524373580000201
Calculating to obtain the amplitude x of the sine component of the fundamental wave0And phase phi0To obtain the amplitude x0100.00 and phase phi0＝1.0000rad。
Similarly, the frequency f of the subsynchronous sinusoidal components is dependent onsubAnd frequency f of the supersynchronous sinusoidal componentsupAnd the calculation of equation (6)
Q(fsub,-1)＝-48.7933-37.2881i
Q(fsup,-1)＝-48.7933+37.2881i
Q*(fsub,+1)＝32.8135-23.8238i
Q*(fsup,+1)＝-13.6215-10.9494i
Furthermore, since k is set as a reference point in the simultaneous equation set of equations (7) and (8), it can be obtained by substituting equation (7) and (8) with k equal to 0,
Figure BDA0002524373580000202
solving the equation set to obtain the amplitude and phase of the subsynchronous sinusoidal component as xsub60.0000 and phisub2.0000rad, amplitude and phase x of the supersynchronous sinusoidal componentssup40.0000 and phisup＝0.5000rad。
The amplitude, phase and frequency of the fundamental wave sinusoidal component to be determined in equation (1) are not found to be x0＝100.00、φ0＝1.0000rad and f050.7400(Hz), the subsynchronous sinusoidal components have amplitude, phase and frequency xsub＝60.0000、φsub2.0000rad and fsub10.2300(Hz), the supersynchronous sinusoidal components have amplitude, phase and frequency xsup＝40.0000、φsup0.5000rad and fsup89.7700 (Hz); completely matched with the actual set value in a one-to-one correspondence manner.
From the above, it can be seen that the method of the present invention is accurate and practical.
As shown in fig. 4, the apparatus for identifying oscillation in an electrical power system according to the present invention includes:
the modeling unit is used for modeling an oscillating signal of the power system into a fundamental wave sinusoidal component with an offset frequency, a pair of frequency-coupled subsynchronous sinusoidal components and a supersynchronous sinusoidal component, wherein the three components respectively have amplitude, phase and frequency;
a first calculation unit that synthesizes a positive frequency part and a negative frequency part of an oscillation component, respectively, from the subsynchronous sinusoidal component and the positive frequency part and the negative frequency part of the supersynchronous sinusoidal component; calculating to obtain a positive frequency part and a negative frequency part in the fundamental wave sinusoidal component;
the construction unit is used for constructing a synchronous phasor track fitting equation set according to the positive frequency part and the negative frequency part of the oscillation component and the positive frequency part and the negative frequency part in the fundamental wave sinusoidal component;
the second calculation unit is used for solving the synchronous phasor trajectory fitting equation set by adopting a nonlinear curve fitting numerical solving method to obtain the frequencies of a fundamental wave sinusoidal component, a subsynchronous sinusoidal component and a supersynchronous sinusoidal component, a positive frequency part and a negative frequency part in the fundamental wave sinusoidal component, and a positive frequency part and a negative frequency part of an oscillation component;
the third calculating unit is used for calculating the amplitude and the phase of the fundamental wave sinusoidal component according to the positive frequency part or the negative frequency part in the fundamental wave sinusoidal component;
the fourth calculating unit is used for calculating the amplitude and the phase of the subsynchronous sinusoidal component and the supersynchronous sinusoidal component according to the positive frequency part and the negative frequency part of the oscillation component;
and the identification result unit is used for identifying the oscillation result of the power system according to the amplitude, the phase and the frequency of the fundamental wave sinusoidal component, and the amplitude, the phase and the frequency of the subsynchronous sinusoidal component and the supersynchronous sinusoidal component.
From the above description of the embodiments, it is clear to those skilled in the art that the present invention can be implemented by software plus necessary general hardware platform. Based on such understanding, the technical solutions of the present invention may be embodied in the form of a software product, which may be stored in a storage medium, such as ROM/RAM, magnetic disk, optical disk, etc., and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute the method according to the embodiments or some parts of the embodiments.
The embodiments in the present specification are described in a progressive manner, and the same and similar parts among the embodiments are referred to each other, and each embodiment focuses on the differences from the other embodiments. In particular, for apparatus or system embodiments, since they are substantially similar to method embodiments, they are described in relative terms, as long as they are described in partial descriptions of method embodiments. The above-described embodiments of the apparatus and system are merely illustrative, and the units described as separate parts may or may not be physically separate, and the parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of the present embodiment. One of ordinary skill in the art can understand and implement it without inventive effort.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (8)

1. A method for identifying oscillation in a power system, comprising:
modeling an oscillation signal of a power system into a fundamental wave sinusoidal component with frequency offset, a pair of frequency-coupled subsynchronous sinusoidal components and supersynchronous sinusoidal components, wherein the amplitudes, phases and frequencies of the three components are parameters to be identified;
respectively synthesizing a positive frequency part and a negative frequency part of an oscillation component according to the positive frequency part and the negative frequency part of the subsynchronous sine component and the supersynchronous sine component; calculating to obtain a positive frequency part and a negative frequency part in the fundamental wave sinusoidal component;
constructing a synchronous phasor trajectory fitting equation set according to the positive frequency part and the negative frequency part of the oscillation component and the positive frequency part and the negative frequency part in the fundamental wave sinusoidal component;
solving the synchronous phasor track fitting equation set by adopting a nonlinear curve fitting numerical solving method to obtain the frequencies of a fundamental wave sinusoidal component, a subsynchronous sinusoidal component and a supersynchronous sinusoidal component, a positive frequency part and a negative frequency part in the fundamental wave sinusoidal component, and a positive frequency part and a negative frequency part of an oscillation component;
calculating the amplitude and the phase of the fundamental wave sinusoidal component according to the positive frequency part or the negative frequency part in the fundamental wave sinusoidal component;
calculating the amplitude and the phase of a subsynchronous sinusoidal component and a supersynchronous sinusoidal component according to the positive frequency part and the negative frequency part of the oscillation component;
and the amplitude, the phase and the frequency of the fundamental wave sinusoidal component, and the amplitude, the phase and the frequency of the subsynchronous sinusoidal component and the supersynchronous sinusoidal component are oscillation identification results of the power system.
2. The method of claim 1, wherein the step of modeling the power system oscillation signal as a fundamental sinusoidal component with a possible offset in frequency, a pair of frequency-coupled subsynchronous sinusoidal components, and a supersynchronous sinusoidal component, the three components each having a pending amplitude, phase, and frequency specifically comprises:
the instantaneous value x (t) of the power system oscillation signal is expressed as the following formula,
x(t)＝x0cos(2πf0t+φ0)+xsubcos(2πfsubt+φsub)+xsupcos(2πfsupt+φsup)
wherein f is0、x0、φ0The frequency, amplitude and phase of the fundamental wave sinusoidal component respectively;
xsub、φsub、fsubamplitude, phase and frequency of subsynchronous sinusoidal components;
xsup、φsup、fsupamplitude, phase and frequency of the supersynchronous sinusoidal components; f. ofsub+fsup＝2fN。
3. The method of claim 2, wherein the meter synthesizes a positive frequency portion and a negative frequency portion of an oscillation component from the positive frequency portion and the negative frequency portion of the subsynchronous sinusoidal component and the supersynchronous sinusoidal component, respectively; the step of calculating the positive frequency part and the negative frequency part in the fundamental wave sinusoidal component comprises the following steps:
Figure FDA0002524373570000021
Figure FDA0002524373570000022
Figure FDA0002524373570000023
Figure FDA0002524373570000024
wherein the positive frequency part of the oscillation component is
Figure FDA0002524373570000025
And a negative frequency part of
Figure FDA0002524373570000026
The positive frequency part and the negative frequency part in the fundamental wave sinusoidal component are respectively
Figure FDA0002524373570000027
And
Figure FDA0002524373570000028
Figure FDA0002524373570000029
and
Figure FDA00025243735700000210
synchronous phasor results corresponding to the fundamental wave sinusoidal component, the subsynchronous sinusoidal component and the supersynchronous sinusoidal component respectively;
Figure FDA0002524373570000031
Figure FDA0002524373570000032
n is the number of data points in the fast Fourier transform synchrophasor calculation data window, fSUploading frequency and f for synchronous phasor dataS＝2fNThe "+" notation denotes the conjugate of the complex number,
Figure FDA0002524373570000033
Figure FDA0002524373570000034
is composed of two parts, the first part
Figure FDA0002524373570000035
Corresponding to a frequency of
Figure FDA0002524373570000036
Is a negative frequency; the second part
Figure FDA0002524373570000037
Corresponding to a frequency of
Figure FDA0002524373570000038
Is a positive frequency;
Figure FDA0002524373570000039
is composed of two parts, the first part
Figure FDA00025243735700000310
Corresponding frequency
Figure FDA00025243735700000311
Is positive frequency and
Figure FDA00025243735700000312
is the same; the second part is
Figure FDA00025243735700000313
Corresponding frequency
Figure FDA00025243735700000314
Is of negative frequency and
Figure FDA00025243735700000315
is identical;
Figure FDA00025243735700000316
is composed of two parts, the corresponding frequencies of the two parts are respectively
Figure FDA00025243735700000317
And
Figure FDA00025243735700000318
when f is0＞fNWhen the frequency is positive, the corresponding frequency of the two parts is negative; when f is0＜fNWhen the frequency of the two parts is negative frequency and positive frequency respectively.
4. The method of claim 3, wherein the step of constructing a synchrophasor trajectory fitting equation set from the positive and negative frequency portions of the oscillating component and the positive and negative frequency portions of the fundamental sinusoidal component comprises:
the synchronous phasor trajectory fitting equation set is as follows:
Figure FDA0002524373570000041
the number of equations of the synchrophasor trajectory fitting equation set is 2K +1,
the variables a and β are each, respectively,
Figure FDA0002524373570000042
Figure FDA0002524373570000043
5. the method of claim 4, wherein the step of solving the synchronous phasor trajectory fitting equations using a non-linear curve fitting numerical solution method to obtain the frequencies of the fundamental sinusoidal component, the subsynchronous sinusoidal component, and the supersynchronous sinusoidal component, the positive frequency part and the negative frequency part in the fundamental sinusoidal component, and the positive frequency part and the negative frequency part of the oscillation component comprises:
solving the synchrophasor trajectory fitting equation set by using a nonlinear curve fitting numerical solution method to obtain variables α and β and a positive frequency part of an oscillation component
Figure FDA0002524373570000051
Negative frequency part
Figure FDA0002524373570000052
Positive frequency part in fundamental wave sine component
Figure FDA0002524373570000053
Negative frequency part
Figure FDA0002524373570000054
Calculating the frequency of subsynchronous sine component according to the obtained α and β and the following two formulas
Figure FDA0002524373570000055
Frequency f of supersynchronous sinusoidal componentssup＝2fN-fsubAnd assume f0＜fNFrequency of fundamental sinusoidal component under condition
Figure FDA0002524373570000056
Figure FDA0002524373570000057
Figure FDA0002524373570000058
Wherein the modeling error is
Figure FDA0002524373570000059
According to the positive frequency part in the obtained fundamental wave sinusoidal component
Figure FDA00025243735700000510
Negative frequency part
Figure FDA00025243735700000511
Determining the frequency f of the sinusoidal component of the fundamental wave0(ii) a The method specifically comprises the following steps:
Figure FDA00025243735700000512
wherein,
Figure FDA00025243735700000513
6. the method of claim 5, wherein the step of calculating the amplitude and phase of the fundamental sinusoidal component from the positive or negative frequency component of the fundamental sinusoidal component comprises:
calculating the frequency f of the fundamental wave sinusoidal component according to the following formula0；
Figure FDA0002524373570000061
Q is calculated according to the following formula*(f0,+1)；
Figure FDA0002524373570000062
Then according to the following formula, calculating to obtain the amplitude x of the fundamental wave sinusoidal component0And phase phi0；
Figure FDA0002524373570000063
7. The method of claim 6, wherein the step of calculating the amplitudes and phases of the subsynchronous sinusoidal components and the supersynchronous sinusoidal components based on the positive frequency component and the negative frequency component of the oscillating component comprises:
according to the frequency f of the subsynchronous sinusoidal componentssubAnd frequency f of the supersynchronous sinusoidal componentsupAnd the following formula, calculate Q (f)sub,-1)、Q(fsup,-1)、Q*(fsub, +1) and Q*(fsup,+1)；
Figure FDA0002524373570000064
Solving the following equation set to obtain the amplitude and phase of the subsynchronous sinusoidal component as xsubAnd phisubAmplitude and phase x of the supersynchronous sinusoidal componentssupAnd phisup
Figure FDA0002524373570000065
8. An apparatus for power system oscillation identification, comprising:
the modeling unit is used for modeling an oscillating signal of the power system into a fundamental wave sinusoidal component with an offset frequency, a pair of frequency-coupled subsynchronous sinusoidal components and a supersynchronous sinusoidal component, wherein the three components respectively have amplitude, phase and frequency;
a first calculation unit that synthesizes a positive frequency part and a negative frequency part of an oscillation component, respectively, from the subsynchronous sinusoidal component and the positive frequency part and the negative frequency part of the supersynchronous sinusoidal component; calculating to obtain a positive frequency part and a negative frequency part in the fundamental wave sinusoidal component;
the construction unit is used for constructing a synchronous phasor track fitting equation set according to the positive frequency part and the negative frequency part of the oscillation component and the positive frequency part and the negative frequency part in the fundamental wave sinusoidal component;
the second calculation unit is used for solving the synchronous phasor trajectory fitting equation set by adopting a nonlinear curve fitting numerical solving method to obtain the frequencies of a fundamental wave sinusoidal component, a subsynchronous sinusoidal component and a supersynchronous sinusoidal component, a positive frequency part and a negative frequency part in the fundamental wave sinusoidal component, and a positive frequency part and a negative frequency part of an oscillation component;
the third calculating unit is used for calculating the amplitude and the phase of the fundamental wave sinusoidal component according to the positive frequency part or the negative frequency part in the fundamental wave sinusoidal component;
the fourth calculating unit is used for calculating the amplitude and the phase of the subsynchronous sinusoidal component and the supersynchronous sinusoidal component according to the positive frequency part and the negative frequency part of the oscillation component;
and the identification result unit is used for identifying the amplitude, the phase and the frequency of the fundamental wave sinusoidal component, and the amplitude, the phase and the frequency of the subsynchronous sinusoidal component and the supersynchronous sinusoidal component as the result of identifying the oscillation of the power system.
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