CN111679125B - Method and device for identifying oscillation of power system - Google Patents
Method and device for identifying oscillation of power system Download PDFInfo
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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
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.
Drawings
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:
wherein the positive frequency part of the oscillation component isAnd a negative frequency part ofThe positive frequency part and the negative frequency part in the fundamental wave sinusoidal component are respectivelyAnd andsynchronous phasor results corresponding to the fundamental wave sinusoidal component, the subsynchronous sinusoidal component and the supersynchronous sinusoidal component respectively;
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,
is composed of two parts, the first partCorresponding to a frequency ofIs a negative frequency; the second partCorresponding to a frequency ofIs a positive frequency;
is composed of two parts, the first partCorresponding frequencyIs positive frequency andis the same; the second part isCorresponding frequencyIs of negative frequency andis identical;
is composed of two parts, the corresponding frequencies of the two parts are respectivelyAndwhen f is0>fNWhen the frequency is positive, the corresponding frequency of the two parts is negative; when f is0<fNAt the same time, two partsThe sub-corresponding frequencies are negative and positive frequencies, respectively.
Wherein step 13 comprises:
the synchronous phasor trajectory fitting equation set is as follows:
the number of equations of the synchrophasor trajectory fitting equation set is 2K +1,
the variables a and β are each, respectively,
wherein step 14 comprises:
solving the synchronous phasor trajectory fitting equation set by adopting a nonlinear curve fitting numerical solution method to obtain variables alpha and beta and a positive frequency part of the oscillation componentNegative frequency partPositive frequency part in fundamental wave sine componentNegative frequency part
Calculating the frequency of subsynchronous sine component according to the calculated alpha, beta and the following two formulasFrequency f of supersynchronous sinusoidal componentssup=2fN-fsubAnd assume f0<fNFrequency of fundamental sinusoidal component under condition
According to the positive frequency part in the obtained fundamental wave sinusoidal componentNegative frequency partDetermining the frequency f of the sinusoidal component of the fundamental wave0(ii) a The method specifically comprises the following steps:
wherein the content of the first and second substances,
step 15 comprises:
calculating the frequency f of the fundamental wave sinusoidal component according to the following formula0;
Q is calculated according to the following formula*(f0,+1);
Then according to the following formula, calculating to obtain the amplitude x of the fundamental wave sinusoidal component0And phase phi0;
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);
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
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,
for the kth power system synchronous phasor,andthe synchronous phasor results corresponding to the fundamental wave sinusoidal component, the subsynchronous sinusoidal component and the supersynchronous sinusoidal component respectively. Wherein the content of the first and second substances,andthe specific calculation results of (a) are shown in formulas (3), (4) and (5),
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
As can be seen from the formula (3),consisting of two parts, taking into account 0 < fsub<fNFirst partCorresponding to a frequency ofIs a negative frequency; the second partCorresponding to a frequency ofIs a positive frequency.
Similarly, as can be seen from formula (4),is composed of two parts, the first partCorresponding frequencyIs positive frequency andis the same; the second part isCorresponding frequencyIs of negative frequency andis identical.
Further, as can be seen from the formula (5),is composed of two parts, the corresponding frequencies of the two parts are respectivelyAndtaking 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 componentAnd a negative frequency partThe positive frequency part and the negative frequency part in the fundamental wave sinusoidal component are respectivelyAndso as to obtain the compound with the characteristics of,
further, the step of constructing a synchronous phasor trajectory 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 of the fundamental sinusoidal component includes the step of obtaining a fitting value of a synchronous phasor trajectory in the oscillation process of the power system according to the formulas (2) and (7) to (10)Is composed of
Further, the modeling error of equation (1) is consideredSo as to obtain the compound with the characteristics of,
let the variables a and β be,
then, according to equations (7) to (10), equation (12) can be rewritten as the following equation system form,
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,
further, the above-mentioned method for solving the synchronous phasor trajectory fitting equations by using the nonlinear curve fitting numerical solution method obtains 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 subsynchronous sinusoidal component and the supersynchronous sinusoidal component, wherein in the synchronous phasor trajectory fitting equations shown in the formula (14), α and β to be quantified as real number domain, 0, α < pi, 0 < beta < pi, and the positive frequency part of the oscillation component in the complex number domainNegative frequency partPositive frequency part in fundamental wave sine componentNegative frequency partThe known quantity being a synchrophasor
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
And, from equation (14), an iterative Jacobian matrix can be determined analytically or numerically, and the variables α and β, and the positive frequency component of the oscillatory component can be determinedNegative frequency partPositive frequency part in fundamental wave sine componentNegative frequency partThe known quantity being a synchrophasor
From the obtained alpha and beta and the expressions (11) and (12), the frequency of the subsynchronous sinusoidal component can be calculatedFrequency f of supersynchronous sinusoidal componentssup=2fN-fsubAnd assume f0<fNFrequency of fundamental sinusoidal component under conditionSince when f is0<fNWhen the temperature of the water is higher than the set temperature,when f is0>fNWhen the temperature of the water is higher than the set temperature,therefore, according to the positive frequency part in the obtained fundamental wave sinusoidal componentNegative frequency partThe frequency f of the sinusoidal component of the fundamental wave can be finally judged0,
And
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,
solving the equation set to obtain the amplitude and phase of the subsynchronous sinusoidal component as xsubAnd phisubSuper synchronous sinusoidal componentAmplitude and phase x ofsupAnd 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 supersynchronous sineAmplitude, phase and frequency of the component, 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,
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,
the solution of the system of equations obtained by the solution is α -0.0465 and β -2.4988, and the positive frequency part of the oscillation componentNegative frequency partPositive frequency part in fundamental wave sine componentNegative frequency part
From the obtained alpha and beta, the frequency of the subsynchronous sinusoidal component can be calculated(Hz), frequency f of supersynchronous sinusoidal componentssup=2fN-fsub89.7700(Hz), and assume f0<fNFrequency of fundamental sinusoidal component under conditionSince when f is0<fNWhen the temperature of the water is higher than the set temperature,when f is0>fNWhen the temperature of the water is higher than the set temperature,according to the positive frequency part in the obtained fundamental wave sinusoidal componentNegative frequency partCan obtain the productThe frequency of the sine component of the fundamental wave can be finally judged And
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)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,
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、φ01.0000rad 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,fNThe rated frequency of the power system.
3. The method of claim 2, wherein the synthesizing of the positive and negative frequency portions of the oscillating component is based on the positive and negative frequency portions 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:
wherein the positive frequency part of the oscillation component isAnd a negative frequency part ofThe positive frequency part and the negative frequency part in the fundamental wave sinusoidal component are respectivelyAnd andsynchronous phasor results corresponding to the fundamental wave sinusoidal component, the subsynchronous sinusoidal component and the supersynchronous sinusoidal component respectively;
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,
is composed of two parts, the first partCorresponding to a frequency ofIs a negative frequency; the second partCorresponding to a frequency ofIs positiveFrequency;
is composed of two parts, the first partCorresponding frequencyIs positive frequency andis the same; the second part isCorresponding frequencyIs of negative frequency andis identical;
is composed of two parts, the corresponding frequencies of the two parts are respectivelyAndwhen 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:
the number of equations of the synchrophasor trajectory fitting equation set is 2K +1,
the variables a and β are each, respectively,
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 synchronous phasor trajectory fitting equation set by adopting a nonlinear curve fitting numerical solution method to obtain variables alpha and beta and a positive frequency part of the oscillation componentNegative frequency partPositive frequency part in fundamental wave sine componentNegative frequency part
Calculating the frequency of subsynchronous sine component according to the calculated alpha, beta and the following two formulasFrequency f of supersynchronous sinusoidal componentssup=2fN-fsubAnd assume f0<fNFrequency of fundamental sinusoidal component under condition
According to the positive frequency part in the obtained fundamental wave sinusoidal componentNegative frequency partDetermining the frequency f of the sinusoidal component of the fundamental wave0(ii) a The method specifically comprises the following steps:
wherein the content of the first and second substances,
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;
Q is calculated according to the following formula*(f0,+1);
Then according to the following formula, calculating to obtain the amplitude x of the fundamental wave sinusoidal component0And phase phi0;
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);
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
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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