CN111624441B - PMU measurement error analysis method under influence of low-frequency oscillation - Google Patents

PMU measurement error analysis method under influence of low-frequency oscillation Download PDF

Info

Publication number
CN111624441B
CN111624441B CN202010522982.6A CN202010522982A CN111624441B CN 111624441 B CN111624441 B CN 111624441B CN 202010522982 A CN202010522982 A CN 202010522982A CN 111624441 B CN111624441 B CN 111624441B
Authority
CN
China
Prior art keywords
oscillation
phasor
amplitude
phase angle
error
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN202010522982.6A
Other languages
Chinese (zh)
Other versions
CN111624441A (en
Inventor
李小鹏
冯世林
段翔兮
代宇涵
龙呈
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Electric Power Research Institute of State Grid Sichuan Electric Power Co Ltd
Original Assignee
Electric Power Research Institute of State Grid Sichuan Electric Power Co Ltd
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Electric Power Research Institute of State Grid Sichuan Electric Power Co Ltd filed Critical Electric Power Research Institute of State Grid Sichuan Electric Power Co Ltd
Priority to CN202010522982.6A priority Critical patent/CN111624441B/en
Publication of CN111624441A publication Critical patent/CN111624441A/en
Application granted granted Critical
Publication of CN111624441B publication Critical patent/CN111624441B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/08—Locating faults in cables, transmission lines, or networks
    • G01R31/088—Aspects of digital computing
    • 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
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/70—Smart grids as climate change mitigation technology in the energy generation sector
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
    • Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
    • Y04S10/00—Systems supporting electrical power generation, transmission or distribution
    • Y04S10/22—Flexible AC transmission systems [FACTS] or power factor or reactive power compensating or correcting units

Landscapes

  • Physics & Mathematics (AREA)
  • Mathematical Physics (AREA)
  • General Physics & Mathematics (AREA)
  • Engineering & Computer Science (AREA)
  • Theoretical Computer Science (AREA)
  • Measuring Phase Differences (AREA)
  • Tests Of Electronic Circuits (AREA)

Abstract

The invention discloses a PMU measurement error analysis method under the influence of low-frequency oscillation, which comprises the following steps of 1: establishing a power signal model under low-frequency oscillation; step 2: constructing a PMU (phasor measurement Unit) measuring method, wherein a phasor expression is obtained by a PMU (phasor measurement Unit) through Fourier transformation, the phasor form of a signal is transformed into a complex form through an Euler formula, and a real part error factor and an imaginary part error factor of a phasor measurement value under amplitude oscillation are calculated to obtain a phase measurement error expression under the condition of amplitude oscillation; and step 3: obtaining a phase angle oscillation condition phase measurement error expression; and 4, step 4: obtaining a measurement error expression under the condition that amplitude phase angles simultaneously oscillate; and 5: and calculating the measurement error of the quantitative PMU by using the obtained phasor measurement error expressions. The method solves the problems that the measurement error of the online PMU under the existing low-frequency oscillation cannot be calculated quantitatively and the mechanism analysis is insufficient, and obtains the error expression for calculation.

Description

PMU measurement error analysis method under influence of low-frequency oscillation
Technical Field
The invention relates to the technical field of dynamic phasor measurement of a power system, in particular to a PMU measurement error analysis method under the influence of low-frequency oscillation.
Background
With the large-scale expansion of internet engineering in various regions in China and the large-scale grid connection of various distributed power supplies, China forms an exponentially very large-scale complex power grid in the world. When the interconnection of power grids brings remarkable benefits, due to the large-scale access of novel power electronic devices and the wide use of high-amplification-factor and rapid excitation technologies, some abnormal dynamic behaviors of the power grids, which are not reported before at home and abroad, gradually appear. The low-frequency band oscillation is a ubiquitous extreme condition, so that the amplitude and phase angle of the power signal are dynamically changed, and meanwhile, serious frequency deviation is also caused, and a series of new challenges are brought to a power grid wide-area measurement system and a phasor measurement unit, so that the effective dynamic security monitoring of a power grid is threatened.
When the system generates low-frequency oscillation, the traditional DFT method can not represent the dynamic characteristics of the signal any more, and especially when the system fundamental frequency shifts or serious amplitude and phase angle oscillation occurs, the traditional DFT method is difficult to keep the signal synchronization, thereby causing serious spectrum leakage.
Disclosure of Invention
The invention aims to solve the technical problems that the PMU measurement error under the existing low-frequency oscillation cannot be calculated quantitatively, and the mechanism analysis is insufficient; the invention provides a PMU measurement error analysis method under the influence of low-frequency oscillation, which solves the problems, utilizes the advantages of discrete Fourier transform in terms of lower operation amount and harmonic suppression as a synchronous phasor measurement method applied to PMU measurement under the influence of low-frequency oscillation, clarifies the PMU measurement error generation mechanism under the influence of low-frequency oscillation, solves the problems that the PMU measurement error under the existing low-frequency oscillation cannot be calculated quantitatively and the mechanism analysis is insufficient, and obtains an error expression. The method has important significance for improving the applicability and the fault handling capability of the conventional PMU under the condition of low-frequency oscillation.
The invention is realized by the following technical scheme:
a PMU measurement error analysis method under the influence of low-frequency oscillation comprises the following steps:
step 1: establishing a power signal model under low-frequency oscillation, wherein the power signal model comprises an amplitude oscillation model xAm(t), phase angle oscillation model xPm(t) Simultaneous oscillation model xAm&Pm(t); wherein the model x is oscillated simultaneouslyAm&Pm(t) is a model of simultaneous oscillation of amplitude phase angles;
step 2: construction of PMU measurement method and phasor measurement device PMUObtaining a phasor expression by Fourier transform, transforming the phasor form of the signal into a complex form by an Euler formula, and calculating a real part error factor of a phasor measurement value under amplitude oscillation according to the amplitude oscillation model in the step 1
Figure BDA0002532820930000011
With imaginary error factor
Figure BDA0002532820930000012
Obtaining a measurement error expression under the condition of amplitude oscillation
Figure BDA0002532820930000021
And step 3: obtaining a phasor expression by utilizing Fourier transform, transforming the phasor form of the signal into a complex form by an Euler formula, and calculating a real part error factor of a phasor measured value under phase angle oscillation according to the phase angle oscillation model in the step 1
Figure BDA0002532820930000022
With imaginary error factor
Figure BDA0002532820930000023
Obtaining a measurement error expression under the condition of phase angle oscillation
Figure BDA0002532820930000024
And 4, step 4: obtaining a complex representation form of Fourier transform by utilizing Euler formula transformation, and obtaining real part error factors of phasor measurement values under the condition of amplitude and phase angle simultaneous oscillation according to the simultaneous oscillation model in the step 1
Figure BDA0002532820930000025
With imaginary error factor
Figure BDA0002532820930000026
Obtaining a measurement error expression under the condition that the amplitude and the phase angle simultaneously oscillate
Figure BDA0002532820930000027
And 5: and calculating the measurement error of the quantitative PMU by using the phasor measurement error expressions obtained in the steps.
Based on the problems that PMU measurement errors under the existing low-frequency oscillation cannot be calculated quantitatively and mechanism analysis is insufficient; the invention adopts the scheme that the discrete Fourier transform is used as a synchronous phasor measurement method due to the advantages of lower operation quantity and harmonic suppression of the discrete Fourier transform, the method is applied to PMU measurement under the influence of low-frequency oscillation, amplitude oscillation, phase angle oscillation and amplitude phase angle simultaneous oscillation can occur under the low-frequency oscillation, and in order to analyze the PMU measurement error generation mechanism when the low-frequency oscillation occurs, a plurality of power signal models under the low-frequency oscillation are established, and an amplitude oscillation model xAm(t), phase angle oscillation model xPm(t) Simultaneous oscillation model xAm&Pm(t), the PMU measurement error production mechanism under the influence of low-frequency oscillation is further clarified, the problems that the PMU measurement error under the existing low-frequency oscillation cannot be quantitatively calculated and the mechanism analysis is insufficient are solved, and an error expression is obtained. The method has important significance for improving the applicability and the fault handling capability of the conventional PMU under the condition of low-frequency oscillation.
Further, amplitude oscillation, phase angle oscillation, and simultaneous oscillation of amplitude and phase angles may occur under low-frequency oscillation, and in order to analyze a PMU measurement error generation mechanism when low-frequency oscillation occurs, the step 1 includes the following steps:
step 11: establishing an amplitude oscillation model under low-frequency oscillation, and modulating a coefficient k through an amplitudeAmAnd amplitude modulation frequency omegaAmCharacterizing the oscillation condition of the amplitude of the power signal under low-frequency oscillation; the amplitude oscillation model formula is as follows:
Figure BDA0002532820930000028
in the formula: a. themRepresenting the effective value of the fundamental frequency component, ω0Which represents the fundamental frequency of the wave,
Figure BDA0002532820930000029
representing the initial phase angle of the fundamental frequency; k is a radical ofAmRepresenting the amplitude modulation factor, ωAmRepresenting amplitude modulation frequency, delta t representing sampling interval time, and n representing discrete sampling point number;
step 12: in order to analyze the condition of phase angle oscillation, a phase angle oscillation model under low-frequency oscillation is established, and the phase angle oscillation model is modulated by a phase angle modulation coefficient kPmAnd phase angle modulation frequency omegaPmCharacterizing the phase angle oscillation condition of the electric power signal under low-frequency oscillation; the phase angle oscillation case is formulated as follows:
Figure BDA00025328209300000210
in the formula: k is a radical ofPmRepresenting the phase angle modulation factor, ωPmRepresents the phase angle modulation frequency, Δ t represents the sampling interval time; a. themRepresenting the effective value of the fundamental frequency component, ω0Which represents the fundamental frequency of the wave,
Figure BDA0002532820930000031
representing the initial phase angle of the fundamental frequency, and n represents the discrete sampling point number;
step 13: in order to analyze the condition of amplitude and phase angle simultaneous oscillation, an amplitude and phase angle simultaneous oscillation model under low-frequency oscillation is established, and an amplitude modulation coefficient k is usedAmAmplitude modulation frequency omegaAmPhase angle modulation factor kPmAnd phase angle modulation frequency omegaPmRepresenting the simultaneous oscillation condition of the amplitude and the phase angle of the electric power signal under low-frequency oscillation; the formula of the amplitude and phase angle simultaneous oscillation model is as follows:
Figure BDA0002532820930000032
in the formula: a. themRepresenting the effective value of the fundamental frequency component, ω0Which represents the fundamental frequency of the wave,
Figure BDA0002532820930000033
representing the initial phase angle of the fundamental frequency; k is a radical ofAmRepresenting amplitudeModulation factor, omegaAmRepresenting amplitude modulation frequency, delta t representing sampling interval time, and n representing discrete sampling point number; k is a radical ofPmRepresenting the phase angle modulation factor, ωPmRepresenting the phase angle modulation frequency.
Further, the step 2 comprises the following steps:
step 21: the phasor measurement unit PMU adopts discrete Fourier transform to measure, and the current measurement phasor value is:
Figure BDA0002532820930000034
in the formula:
Figure BDA0002532820930000035
representing a current measured phasor value; n represents the number of sampling points in one period; x (n) represents a sampling signal; n represents the number of discrete sampling points; omega0Represents the filtering frequency; Δ t represents a sampling interval time; j is the complex imaginary unit. Hereinafter, each j is a complex imaginary unit, and is not described in detail.
Step 22: according to the Euler formula expansion, the phasor at the current moment is transformed into a complex form represented by an imaginary part and a real part:
Figure BDA0002532820930000036
wherein:
C(n)＝Re(L)＝x(n)cos(ω0nΔt)
S(n)＝Im(L)＝x(n)sin(ω0nΔt)
Figure BDA0002532820930000037
step 23: when amplitude oscillation occurs, the power signal model (i.e. amplitude oscillation model x) is modeledAm(t)) substituting phasors
Figure BDA0002532820930000038
In the real and imaginary parts of (a), we get:
Figure BDA0002532820930000039
Figure BDA0002532820930000041
wherein the expression of the real part terms is:
Figure BDA0002532820930000042
Figure BDA0002532820930000043
Figure BDA0002532820930000044
Figure BDA0002532820930000045
the expression for the imaginary terms is:
Figure BDA0002532820930000046
Figure BDA0002532820930000047
Figure BDA0002532820930000048
Figure BDA0002532820930000049
wherein,
Figure BDA00025328209300000410
the error part is an integral multiple of the fundamental frequency, is 0 in summation in a period and can be eliminated naturally;
Figure BDA00025328209300000411
after a period of accumulation, the phasor is a true value; the other entries are not 0 after a period of accumulation, and are the part of error that cannot be eliminated except the measured true value; the phase measurement error under amplitude oscillation is obtained and defined as the real error factor
Figure BDA00025328209300000412
And imaginary error factor
Figure BDA00025328209300000413
Their values are respectively:
Figure BDA00025328209300000414
Figure BDA00025328209300000415
from this, the analysis yields the PMU phasor measurement error under amplitude oscillation:
Figure BDA0002532820930000051
wherein,
Figure BDA0002532820930000052
is the phasor true value at the time of amplitude oscillation,
Figure BDA0002532820930000053
is a phasor measurement at the time of amplitude oscillation,
Figure BDA0002532820930000054
is the phasor measurement error of the PMU at amplitude oscillations.
As can be seen from the phasor error expression, the DFT measurement method commonly used by PMU is influenced by the amplitude modulation coefficient k when the amplitude oscillation occurs in the low-frequency oscillation conditionAmAmplitude modulation frequency omegaAmAffecting the occurrence of a calculation misalignment. When k isAm、ωAmThe phasor measurement error is 0, namely when oscillation does not occur, the measurement error is 0 according to the PMU phasor measurement error expression provided by the method of the invention; when k isAm、ωAmWhen the phasor measurement error is not 0, as can be known from the expression of PMU phasor measurement error,
Figure BDA0002532820930000055
the imaginary and real error expressions are sinusoidal functions of time, with amplitude and kAmCorrelation, frequency and ωAmAnd (4) correlating. When k isAmWhen the amplitude of oscillation increases and the oscillation condition becomes more serious, the modulus of PMU phasor measurement error
Figure BDA0002532820930000056
Increasing along with the increase of the total weight of the particles to present positive correlation; when ω isAmWhen the amplitude increases, i.e. the oscillation frequency increases, the signal fluctuation is larger, and the modulus value of PMU phasor measurement error
Figure BDA0002532820930000057
The frequency of change is increased, and positive correlation is also shown.
Further, the step 3 comprises the following steps:
step 31: the phasor measurement unit PMU adopts discrete Fourier transform to measure, and the current measurement phasor value is:
Figure BDA0002532820930000058
in the formula:
Figure BDA0002532820930000059
representing a current measured phasor value; n represents the number of sampling points in one period; x (n) represents a sampling signal; n represents the number of discrete sampling points; omega0Represents the filtering frequency; Δ t represents the sampling interval time.
Step 32: and (3) expanding the exponential part according to an Euler formula, and transforming the phasor at the current moment into a complex form represented by an imaginary part and a real part:
Figure BDA00025328209300000510
wherein
C(n)＝Re(L)＝x(n)cos(ω0nΔt)
S(n)＝Im(L)＝x(n)sin(ω0nΔt)
Figure BDA00025328209300000511
Step 33: when phase angle oscillation occurs, its power signal model (i.e. phase angle oscillation model x)Pm(t)) into the phasor at the current time
Figure BDA00025328209300000512
In the real and imaginary parts of (a), we get:
Figure BDA0002532820930000061
Figure BDA0002532820930000062
wherein the expression of the real part terms is:
Figure BDA0002532820930000063
Figure BDA0002532820930000064
Figure BDA0002532820930000065
Figure BDA0002532820930000066
the expression for the imaginary terms is:
Figure BDA0002532820930000067
Figure BDA0002532820930000068
Figure BDA0002532820930000069
Figure BDA00025328209300000610
wherein
Figure BDA00025328209300000611
The error part is an integral multiple of the fundamental frequency, is 0 in summation in a period and can be eliminated naturally;
Figure BDA00025328209300000612
after a period of accumulation, the phasor is a true value; the other entries are not 0 after a period of accumulation, and are the part of error that cannot be eliminated except the measured true value; thus, a real part error factor is obtained
Figure BDA00025328209300000613
And imaginary error factor
Figure BDA00025328209300000614
Their values are respectively:
Figure BDA00025328209300000615
Figure BDA0002532820930000071
from this analysis the phasor measurement error under phase angle oscillation is obtained:
Figure BDA0002532820930000072
wherein,
Figure BDA0002532820930000073
is the phasor true value at phase angle oscillation,
Figure BDA0002532820930000074
is a measure of when the phase angle is oscillating,
Figure BDA0002532820930000075
is the phasor measurement error at phase angle oscillation.
According to the phasor error expression, when the phase angle oscillation occurs in the low-frequency oscillation condition, the phase angle modulation coefficient k is applied to the DFT measurement method commonly used by PMUPmPhase angle modulation frequency omegaPmAffecting the occurrence of a calculation misalignment. When k isPm、ωPmThe phasor measurement error is 0, namely when oscillation does not occur, the measurement error is 0 according to the PMU phasor measurement error expression provided by the method of the invention; with kPmAugmentation, PMU phasor measurement error modulus
Figure BDA0002532820930000076
Exhibits a sine-like wave variation in maximum value of (c); with omegaPmAugmentation, PMU phasor measurement error modulus
Figure BDA0002532820930000077
Shows a gradually decreasing trend, showing a negative correlation.
Further, the step 4 comprises the following steps:
step 41: the phasor measurement unit PMU adopts discrete Fourier transform to measure, and the current measurement phasor value is:
Figure BDA0002532820930000078
in the formula:
Figure BDA0002532820930000079
representing a current measured phasor value; n represents the number of sampling points in one period; x (n) represents a sampling signal; n represents the number of discrete sampling points; omega0Represents the filtering frequency; Δ t represents the sampling interval time.
Step 42: and (3) expanding the exponential part according to an Euler formula, and transforming the phasor at the current moment into a complex form represented by an imaginary part and a real part:
Figure BDA00025328209300000710
wherein
C(n)＝Re(L)＝x(n)cos(ω0nΔt)
S(n)＝Im(L)＝x(n)sin(ω0nΔt)
Figure BDA00025328209300000711
Step 43: when the amplitude and phase angle simultaneously oscillate, the power signal model (i.e. the simultaneous oscillation model x) is usedAm&Pm(t)) into the phasor at the current time
Figure BDA00025328209300000712
In the real and imaginary parts of (a), we get:
Figure BDA0002532820930000081
Figure BDA0002532820930000082
wherein the expression of the real part terms is:
Figure BDA0002532820930000083
Figure BDA0002532820930000084
Figure BDA0002532820930000085
Figure BDA0002532820930000086
Figure BDA0002532820930000087
Figure BDA0002532820930000088
Figure BDA0002532820930000089
Figure BDA00025328209300000810
Figure BDA00025328209300000811
the expression for the imaginary terms is:
Figure BDA00025328209300000812
Figure BDA00025328209300000813
Figure BDA00025328209300000814
Figure BDA00025328209300000815
Figure BDA0002532820930000091
Figure BDA0002532820930000092
Figure BDA0002532820930000093
Figure BDA0002532820930000094
Figure BDA0002532820930000095
wherein,
Figure BDA0002532820930000096
the sum is an integral multiple of the fundamental frequency, is 0 in a period summation, and is an erasable error term;
Figure BDA0002532820930000097
after a period of accumulation, the phasor is a true value; the other term, which is not 0 in one cycle, is an irresolvable error component other than the measured true value. Thus, a real part error factor is obtained
Figure BDA0002532820930000098
And imaginary error factor
Figure BDA0002532820930000099
Their values are respectively:
Figure BDA00025328209300000910
Figure BDA00025328209300000911
the phasor measurement errors under simultaneous oscillation of amplitude and phase angle are obtained through analysis:
Figure BDA00025328209300000912
wherein,
Figure BDA00025328209300000913
is the phasor true value under the condition of simultaneous oscillation of amplitude value and phase angle,
Figure BDA00025328209300000914
is a measurement value under the condition that the amplitude and the phase angle synchronously oscillate,
Figure BDA00025328209300000915
is the phasor measurement error under simultaneous oscillation of amplitude and phase angle.
By error of phasorThe difference expression shows that when the amplitude and the phase angle in the low-frequency oscillation condition oscillate simultaneously, the DFT measurement method commonly used by PMU is influenced by the amplitude modulation coefficient kAmAmplitude modulation frequency omegaAmPhase angle modulation factor kPmPhase angle modulation frequency omegaPmThe combined effect is that a calculation misalignment occurs. When all parameters are 0, namely oscillation does not occur, calculating the measurement error to be 0 according to the expression of the phasor measurement error of the PMU provided by the method of the invention; when k isAmModulus of Phasor Measurement Unit (PMU) phasor measurement error at increasing time
Figure BDA00025328209300000916
Increasing along with the increase of the total weight of the particles to present positive correlation; when ω isAmWhen increasing, the modulus of the phasor measurement error of the PMU
Figure BDA00025328209300000917
The change frequency is increased, and positive correlation is also presented; with kPmAugmentation, PMU phasor measurement error modulus
Figure BDA0002532820930000101
Exhibits a sine-like wave variation in maximum value of (c); with omegaPmAugmentation, PMU phasor measurement error modulus
Figure BDA0002532820930000102
Shows a gradually decreasing trend, showing a negative correlation.
Compared with the prior art, the invention has the following advantages and beneficial effects:
1. the invention relates to a PMU measurement error analysis method under the influence of low-frequency oscillation, which finds a PMU measurement device error generation mechanism under the low-frequency band oscillation from PMU measurement error generation mechanism analysis; the method starts from the essence of DFT, carries out deep theoretical analysis on the error generated by the prior PMU under the condition of low-frequency band oscillation, and finds out an error factor;
2. the method obtains the PMU measurement error expression under the influence of low-frequency band oscillation, quantitatively and definitely determines the measurement errors of the measurement device under the conditions of amplitude oscillation, phase angle oscillation and simultaneous oscillation of amplitude and phase angles; the error analysis method provided by the invention is suitable for the PMU error measurement method under low-frequency oscillation, and has important significance for improving the applicability and the fault handling capability of the conventional PMU under the low-frequency oscillation condition.
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 embodiments will be briefly described below, it should be understood that the following drawings only illustrate some embodiments of the present invention and therefore should not be considered as limiting the scope, and for those skilled in the art, other related drawings can be obtained according to the drawings without inventive efforts. In the drawings:
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a graph showing the effect of the present invention in amplitude oscillation;
FIG. 3 is a diagram illustrating the effect of the present invention in phase angle oscillation;
FIG. 4 is a diagram illustrating the effect of the present invention in the simultaneous phase and amplitude oscillation;
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the detailed description and specific examples, while indicating the preferred embodiment of the invention, are intended for purposes of illustration only and are not intended to limit the scope of the invention. The components of embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations.
Thus, the following detailed description of the embodiments of the present invention, presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present invention without making any creative effort, shall fall within the protection scope of the present invention.
It is noted that relational terms such as "first" and "second," and the like, may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other identical elements in a process, method, article, or apparatus that comprises the element.
Examples
As shown in fig. 1 to 4, a PMU measurement error analysis method under the influence of low-frequency oscillation includes the following steps:
step 1: establishing a power signal model under low-frequency oscillation, wherein the power signal model comprises an amplitude oscillation model xAm(t), phase angle oscillation model xPm(t) Simultaneous oscillation model xAm&Pm(t); wherein the model x is oscillated simultaneouslyAm&Pm(t) is a model of simultaneous oscillation of amplitude phase angles;
amplitude oscillation, phase angle oscillation and amplitude phase angle simultaneous oscillation may occur under low-frequency oscillation, and in order to analyze a PMU measurement error generation mechanism when the low-frequency oscillation occurs, specifically: the step 1 comprises the following steps:
step 11: establishing an amplitude oscillation model under low-frequency oscillation, and modulating a coefficient k through an amplitudeAmAnd amplitude modulation frequency omegaAmCharacterizing the oscillation condition of the amplitude of the power signal under low-frequency oscillation; the amplitude oscillation model formula is as follows:
Figure BDA0002532820930000111
in the formula: a. themRepresenting fundamental frequency componentsEffective value, ω0Which represents the fundamental frequency of the wave,
Figure BDA0002532820930000112
representing the initial phase angle of the fundamental frequency; k is a radical ofAmRepresenting the amplitude modulation factor, ωAmRepresenting amplitude modulation frequency, delta t representing sampling interval time, and n representing discrete sampling point number;
step 12: in order to analyze the condition of phase angle oscillation, a phase angle oscillation model under low-frequency oscillation is established, and the phase angle oscillation model is modulated by a phase angle modulation coefficient kPmAnd phase angle modulation frequency omegaPmCharacterizing the phase angle oscillation condition of the electric power signal under low-frequency oscillation; the phase angle oscillation case is formulated as follows:
Figure BDA0002532820930000113
in the formula: k is a radical ofPmRepresenting the phase angle modulation factor, ωPmRepresents the phase angle modulation frequency, Δ t represents the sampling interval time; a. themRepresenting the effective value of the fundamental frequency component, ω0Which represents the fundamental frequency of the wave,
Figure BDA0002532820930000114
representing the initial phase angle of the fundamental frequency, and n represents the discrete sampling point number;
step 13: in order to analyze the condition of amplitude and phase angle simultaneous oscillation, an amplitude and phase angle simultaneous oscillation model under low-frequency oscillation is established, and an amplitude modulation coefficient k is usedAmAmplitude modulation frequency omegaAmPhase angle modulation factor kPmAnd phase angle modulation frequency omegaPmRepresenting the simultaneous oscillation condition of the amplitude and the phase angle of the electric power signal under low-frequency oscillation; the formula of the amplitude and phase angle simultaneous oscillation model is as follows:
Figure BDA0002532820930000115
in the formula: a. themRepresenting the effective value of the fundamental frequency component, ω0Which represents the fundamental frequency of the wave,
Figure BDA0002532820930000116
representing the initial phase angle of the fundamental frequency; k is a radical ofAmRepresenting the amplitude modulation factor, ωAmRepresenting amplitude modulation frequency, delta t representing sampling interval time, and n representing discrete sampling point number; k is a radical ofPmRepresenting the phase angle modulation factor, ωPmRepresenting the phase angle modulation frequency.
Step 2: constructing a PMU measuring method, obtaining a phasor expression by a phasor measuring device PMU through Fourier transformation, transforming the phasor form of a signal into a complex form through an Euler formula, and calculating a real part error factor of a phasor measured value under amplitude oscillation according to an amplitude oscillation model in the step 1
Figure BDA0002532820930000121
With imaginary error factor
Figure BDA0002532820930000122
Obtaining a measurement error expression under the condition of amplitude oscillation
Figure BDA0002532820930000123
Specifically, the step 2 includes the following steps:
step 21: the phasor measurement unit PMU adopts discrete Fourier transform to measure, and the current measurement phasor value is:
Figure BDA0002532820930000124
in the formula:
Figure BDA0002532820930000125
representing a current measured phasor value; n represents the number of sampling points in one period; x (n) represents a sampling signal; n represents the number of discrete sampling points; omega0Represents the filtering frequency; Δ t represents the sampling interval time.
Step 22: according to the Euler formula expansion, the phasor at the current moment is transformed into a complex form represented by an imaginary part and a real part:
Figure BDA0002532820930000126
wherein:
C(n)＝Re(L)＝x(n)cos(ω0nΔt)
S(n)＝Im(L)＝x(n)sin(ω0nΔt)
Figure BDA0002532820930000127
step 23: when amplitude oscillation occurs, the power signal model (i.e. amplitude oscillation model x) is modeledAm(t)) substituting phasors
Figure BDA0002532820930000128
In the real and imaginary parts of (a), we get:
Figure BDA0002532820930000129
Figure BDA00025328209300001210
wherein the expression of the real part terms is:
Figure BDA0002532820930000131
Figure BDA0002532820930000132
Figure BDA0002532820930000133
Figure BDA0002532820930000134
the expression for the imaginary terms is:
Figure BDA0002532820930000135
Figure BDA0002532820930000136
Figure BDA0002532820930000137
Figure BDA0002532820930000138
wherein,
Figure BDA0002532820930000139
the error part is an integral multiple of the fundamental frequency, is 0 in summation in a period and can be eliminated naturally;
Figure BDA00025328209300001310
after a period of accumulation, the phasor is a true value; the other entries are not 0 after a period of accumulation, and are the part of error that cannot be eliminated except the measured true value; the phase measurement error under amplitude oscillation is obtained and defined as the real error factor
Figure BDA00025328209300001311
And imaginary error factor
Figure BDA00025328209300001312
Their values are respectively:
Figure BDA00025328209300001313
Figure BDA00025328209300001314
from this, the analysis yields the PMU phasor measurement error under amplitude oscillation:
Figure BDA00025328209300001315
wherein,
Figure BDA00025328209300001316
is the phasor true value at the time of amplitude oscillation,
Figure BDA00025328209300001317
is a phasor measurement at the time of amplitude oscillation,
Figure BDA00025328209300001318
is the phasor measurement error of the PMU at amplitude oscillations.
As can be seen from the phasor error expression, the DFT measurement method commonly used by PMU is influenced by the amplitude modulation coefficient k when the amplitude oscillation occurs in the low-frequency oscillation conditionAmAmplitude modulation frequency omegaAmAffecting the occurrence of a calculation misalignment. When k isAm、ωAmThe phasor measurement error is 0, namely when oscillation does not occur, the measurement error is 0 according to the PMU phasor measurement error expression provided by the method of the invention; when k isAm、ωAmWhen the phasor measurement error is not 0, as can be known from the expression of PMU phasor measurement error,
Figure BDA0002532820930000141
the imaginary and real error expressions are sinusoidal functions of time, with amplitude and kAmCorrelation, frequency and ωAmAnd (4) correlating. When k isAmWhen the amplitude of oscillation increases and the oscillation condition becomes more serious, the modulus of PMU phasor measurement error
Figure BDA0002532820930000142
Increasing along with the increase of the total weight of the particles to present positive correlation; when ω isAmWhen increased, i.e. the oscillation frequency increases, the signal waveLarger moving, modular value of PMU phasor measurement error
Figure BDA0002532820930000143
The frequency of change is increased, and positive correlation is also shown.
And step 3: obtaining a phasor expression by utilizing Fourier transform, transforming the phasor form of the signal into a complex form by an Euler formula, and calculating a real part error factor of a phasor measured value under phase angle oscillation according to the phase angle oscillation model in the step 1
Figure BDA0002532820930000144
With imaginary error factor
Figure BDA0002532820930000145
Obtaining a measurement error expression under the condition of phase angle oscillation
Figure BDA0002532820930000146
Specifically, the step 3 includes the following steps:
step 31: the phasor measurement unit PMU adopts discrete Fourier transform to measure, and the current measurement phasor value is:
Figure BDA0002532820930000147
in the formula:
Figure BDA0002532820930000148
representing a current measured phasor value; n represents the number of sampling points in one period; x (n) represents a sampling signal; n represents the number of discrete sampling points; omega0Represents the filtering frequency; Δ t represents the sampling interval time.
Step 32: and (3) expanding the exponential part according to an Euler formula, and transforming the phasor at the current moment into a complex form represented by an imaginary part and a real part:
Figure BDA0002532820930000149
wherein
C(n)＝Re(L)＝x(n)cos(ω0nΔt)
S(n)＝Im(L)＝x(n)sin(ω0nΔt)
Figure BDA00025328209300001410
Step 33: when phase angle oscillation occurs, its power signal model (i.e. phase angle oscillation model x)Pm(t)) into the phasor at the current time
Figure BDA00025328209300001411
In the real and imaginary parts of (a), we get:
Figure BDA0002532820930000151
Figure BDA0002532820930000152
wherein the expression of the real part terms is:
Figure BDA0002532820930000153
Figure BDA0002532820930000154
Figure BDA0002532820930000155
Figure BDA0002532820930000156
the expression for the imaginary terms is:
Figure BDA0002532820930000157
Figure BDA0002532820930000158
Figure BDA0002532820930000159
Figure BDA00025328209300001510
wherein
Figure BDA00025328209300001511
The error part is an integral multiple of the fundamental frequency, is 0 in summation in a period and can be eliminated naturally;
Figure BDA00025328209300001512
after a period of accumulation, the phasor is a true value; the other entries are not 0 after a period of accumulation, and are the part of error that cannot be eliminated except the measured true value; thus, a real part error factor is obtained
Figure BDA00025328209300001513
And imaginary error factor
Figure BDA00025328209300001514
Their values are respectively:
Figure BDA00025328209300001515
Figure BDA0002532820930000161
from this analysis the phasor measurement error under phase angle oscillation is obtained:
Figure BDA0002532820930000162
wherein,
Figure BDA0002532820930000163
is the phasor true value at phase angle oscillation,
Figure BDA0002532820930000164
is a measure of when the phase angle is oscillating,
Figure BDA0002532820930000165
is the phasor measurement error at phase angle oscillation.
According to the phasor error expression, when the phase angle oscillation occurs in the low-frequency oscillation condition, the phase angle modulation coefficient k is applied to the DFT measurement method commonly used by PMUPmPhase angle modulation frequency omegaPmAffecting the occurrence of a calculation misalignment. When k isPm、ωPmThe phasor measurement error is 0, namely when oscillation does not occur, the measurement error is 0 according to the PMU phasor measurement error expression provided by the method of the invention; with kPmAugmentation, PMU phasor measurement error modulus
Figure BDA0002532820930000166
Exhibits a sine-like wave variation in maximum value of (c); with omegaPmAugmentation, PMU phasor measurement error modulus
Figure BDA0002532820930000167
Shows a gradually decreasing trend, showing a negative correlation.
And 4, step 4: obtaining a complex representation form of Fourier transform by utilizing Euler formula transformation, and obtaining real part error factors of phasor measurement values under the condition of amplitude and phase angle simultaneous oscillation according to the simultaneous oscillation model in the step 1
Figure BDA0002532820930000168
Error from imaginary partFactor(s)
Figure BDA0002532820930000169
Obtaining a measurement error expression under the condition that the amplitude and the phase angle simultaneously oscillate
Figure BDA00025328209300001610
Specifically, the step 4 includes the following steps:
step 41: the phasor measurement unit PMU adopts discrete Fourier transform to measure, and the current measurement phasor value is:
Figure BDA00025328209300001611
in the formula:
Figure BDA00025328209300001612
representing a current measured phasor value; n represents the number of sampling points in one period; x (n) represents a sampling signal; n represents the number of discrete sampling points; omega0Represents the filtering frequency; Δ t represents the sampling interval time.
Step 42: and (3) expanding the exponential part according to an Euler formula, and transforming the phasor at the current moment into a complex form represented by an imaginary part and a real part:
Figure BDA00025328209300001613
wherein
C(n)＝Re(L)＝x(n)cos(ω0nΔt)
S(n)＝Im(L)＝x(n)sin(ω0nΔt)
Figure BDA0002532820930000171
Step 43: when the amplitude and phase angle simultaneously oscillate, the power signal model (i.e. the simultaneous oscillation model x) is usedAm&Pm(t)) into the phasor at the current time
Figure BDA0002532820930000172
In the real and imaginary parts of (a), we get:
Figure BDA0002532820930000173
Figure BDA0002532820930000174
wherein the expression of the real part terms is:
Figure BDA0002532820930000175
Figure BDA0002532820930000176
Figure BDA0002532820930000177
Figure BDA0002532820930000178
Figure BDA0002532820930000179
Figure BDA00025328209300001710
Figure BDA00025328209300001711
Figure BDA00025328209300001712
Figure BDA00025328209300001713
the expression for the imaginary terms is:
Figure BDA00025328209300001714
Figure BDA0002532820930000181
Figure BDA0002532820930000182
Figure BDA0002532820930000183
Figure BDA0002532820930000184
Figure BDA0002532820930000185
Figure BDA0002532820930000186
Figure BDA0002532820930000187
Figure BDA0002532820930000188
wherein,
Figure BDA0002532820930000189
the sum is an integral multiple of the fundamental frequency, is 0 in a period summation, and is an erasable error term;
Figure BDA00025328209300001810
after a period of accumulation, the phasor is a true value; the other term, which is not 0 in one cycle, is an irresolvable error component other than the measured true value. Thus, a real part error factor is obtained
Figure BDA00025328209300001811
And imaginary error factor
Figure BDA00025328209300001812
Their values are respectively:
Figure BDA00025328209300001813
Figure BDA00025328209300001814
the phasor measurement errors under simultaneous oscillation of amplitude and phase angle are obtained through analysis:
Figure BDA00025328209300001815
wherein,
Figure BDA00025328209300001816
is the phasor true value under the condition of simultaneous oscillation of amplitude value and phase angle,
Figure BDA00025328209300001817
is a measurement value under the condition that the amplitude and the phase angle synchronously oscillate,
Figure BDA00025328209300001818
is the phasor measurement error under simultaneous oscillation of amplitude and phase angle.
As can be known from phasor error expression, when the amplitude and phase angle in the low-frequency oscillation condition oscillate simultaneously, the DFT measurement method commonly used by PMU is subjected to the amplitude modulation coefficient kAmAmplitude modulation frequency omegaAmPhase angle modulation factor kPmPhase angle modulation frequency omegaPmThe combined effect is that a calculation misalignment occurs. When all parameters are 0, namely oscillation does not occur, calculating the measurement error to be 0 according to the expression of the phasor measurement error of the PMU provided by the method of the invention; when k isAmModulus of Phasor Measurement Unit (PMU) phasor measurement error at increasing time
Figure BDA0002532820930000191
Increasing along with the increase of the total weight of the particles to present positive correlation; when ω isAmWhen increasing, the modulus of the phasor measurement error of the PMU
Figure BDA0002532820930000192
The change frequency is increased, and positive correlation is also presented; with kPmAugmentation, PMU phasor measurement error modulus
Figure BDA0002532820930000193
Exhibits a sine-like wave variation in maximum value of (c); with omegaPmAugmentation, PMU phasor measurement error modulus
Figure BDA0002532820930000194
Shows a gradually decreasing trend, showing a negative correlation.
And 5: and calculating the measurement error of the quantitative PMU by using the phasor measurement error expressions obtained in the steps.
As shown in fig. 2, in specific implementation, when the system is analyzed for amplitude oscillation in a low-frequency oscillation condition, according to the method of the present invention, an error expression of PMU phasor measurement under amplitude oscillation is proposed:
Figure BDA0002532820930000195
Figure BDA0002532820930000196
modulated by amplitude factor kAmCoefficient of influence, gradually increasing kAmTo obtain
Figure BDA0002532820930000197
As shown in fig. 2. It can be seen that when k isAmWhen the amplitude of oscillation increases and the oscillation condition becomes more serious, the modulus of PMU phasor measurement error
Figure BDA0002532820930000198
With the increase, a positive correlation is exhibited.
As shown in fig. 3, in the specific implementation, the phase angle oscillation condition in the low-frequency oscillation condition of the system is analyzed, and the PMU phasor measurement error expression under the phase angle oscillation is provided according to the method of the present invention:
Figure BDA0002532820930000199
Figure BDA00025328209300001910
maximum value phase angle modulation frequency omegaPmInfluence, increasing ω graduallyPmTo obtain
Figure BDA00025328209300001911
A maximum value. As shown in fig. 3. It can be seen that with ωPmAugmentation, PMU phasor measurement error modulus
Figure BDA00025328209300001912
Shows a gradually decreasing trend, showing a negative correlation.
As shown in fig. 4, in specific implementation, the condition that the phase angle and the amplitude oscillate simultaneously in the low-frequency oscillation condition of the system is analyzed, and according to the method of the present invention, a PMU phasor measurement error expression under the condition that the phase angle and the amplitude oscillate simultaneously is provided:
Figure BDA00025328209300001913
as shown in fig. 4. It can be seen that with kPmAugmentation, PMU phasor measurement error modulus
Figure BDA0002532820930000201
Exhibits a sine-like wave variation in maximum value of (c).
The working principle is as follows: based on the problems that PMU measurement errors under the existing low-frequency oscillation cannot be calculated quantitatively and mechanism analysis is insufficient; the invention adopts the scheme that the discrete Fourier transform is used as a synchronous phasor measurement method due to the advantages of lower operation quantity and harmonic suppression of the discrete Fourier transform, the method is applied to PMU measurement under the influence of low-frequency oscillation, amplitude oscillation, phase angle oscillation and amplitude phase angle simultaneous oscillation can occur under the low-frequency oscillation, and in order to analyze the PMU measurement error generation mechanism when the low-frequency oscillation occurs, a plurality of power signal models under the low-frequency oscillation are established, and an amplitude oscillation model xAm(t), phase angle oscillation model xPm(t) Simultaneous oscillation model xAm&Pm(t); the method can obtain real part error factors and imaginary part error factors in phasor measurement values under low-frequency oscillation, thereby obtaining PMU measurement error expression under the influence of low-frequency band oscillation, and quantitatively determining measurement errors of the phasor measurement device under the conditions of amplitude oscillation, phase angle oscillation and simultaneous oscillation of amplitude and phase angle. And furthermore, a PMU measurement error production mechanism under the influence of low-frequency oscillation is clarified, the problems that the PMU measurement error under the existing low-frequency oscillation cannot be quantitatively calculated and the mechanism analysis is insufficient are solved, and an error expression is obtained.
The error analysis method provided by the invention is suitable for a PMU measurement error method under low-frequency oscillation, and solves the problems that the PMU measurement error under the existing low-frequency oscillation cannot be calculated quantitatively and the mechanism analysis is insufficient; the method has important significance for improving the applicability and the fault handling capability of the conventional PMU under the condition of low-frequency oscillation.
The above-mentioned embodiments are intended to illustrate the objects, technical solutions and advantages of the present invention in further detail, and it should be understood that the above-mentioned embodiments are merely exemplary embodiments of the present invention, and are not intended to limit the scope of the present invention, and any modifications, equivalent substitutions, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (5)

1. A PMU measurement error analysis method under the influence of low-frequency oscillation is characterized by comprising the following steps:
step 1: establishing a power signal model under low-frequency oscillation, wherein the power signal model comprises an amplitude oscillation model xAm(t), phase angle oscillation model xPm(t) Simultaneous oscillation model xAm&Pm(t)；
Step 2: constructing a PMU measuring method, obtaining a phasor expression by a phasor measuring device PMU through Fourier transformation, transforming the phasor form of a signal into a complex form through an Euler formula, and calculating a real part error factor of a phasor measured value under amplitude oscillation according to an amplitude oscillation model in the step 1
Figure FDA0003428373990000011
With imaginary error factor
Figure FDA0003428373990000012
Obtaining a measurement error expression under the condition of amplitude oscillation
Figure FDA0003428373990000013
And step 3: obtaining a phasor expression by utilizing Fourier transform, transforming the phasor form of the signal into a complex form by an Euler formula, and calculating a real part error factor of a phasor measured value under phase angle oscillation according to the phase angle oscillation model in the step 1
Figure FDA0003428373990000014
Error from imaginary partFactor(s)
Figure FDA0003428373990000015
Obtaining a measurement error expression under the condition of phase angle oscillation
Figure FDA0003428373990000016
And 4, step 4: obtaining a complex representation form of Fourier transform by utilizing Euler formula transformation, and obtaining real part error factors of phasor measurement values under the condition of amplitude and phase angle simultaneous oscillation according to the simultaneous oscillation model in the step 1
Figure FDA0003428373990000017
With imaginary error factor
Figure FDA0003428373990000018
Obtaining a measurement error expression under the condition that the amplitude and the phase angle simultaneously oscillate
Figure FDA0003428373990000019
And 5: and calculating the measurement error of the quantitative PMU by using the phasor measurement error expressions obtained in the steps.
2. The method according to claim 1, wherein said step 1 comprises the steps of:
step 11: establishing an amplitude oscillation model under low-frequency oscillation, and modulating a coefficient k through an amplitudeAmAnd amplitude modulation frequency omegaAmCharacterizing the oscillation condition of the amplitude of the power signal under low-frequency oscillation; the amplitude oscillation model formula is as follows:
Figure FDA00034283739900000110
in the formula: a. themRepresenting the effective value of the fundamental frequency component, ω0Which represents the fundamental frequency of the wave,
Figure FDA00034283739900000111
representing the initial phase angle of the fundamental frequency; k is a radical ofAmRepresenting the amplitude modulation factor, ωAmRepresenting amplitude modulation frequency, delta t representing sampling interval time, and n representing discrete sampling point number;
step 12: establishing a phase angle oscillation model under low-frequency oscillation, and modulating a coefficient k through a phase anglePmAnd phase angle modulation frequency omegaPmCharacterizing the phase angle oscillation condition of the electric power signal under low-frequency oscillation; the phase angle oscillation case is formulated as follows:
Figure FDA00034283739900000112
in the formula: a. themRepresenting the effective value of the fundamental frequency component, ω0Which represents the fundamental frequency of the wave,
Figure FDA00034283739900000113
representing the initial phase angle of the fundamental frequency; k is a radical ofPmRepresenting the phase angle modulation factor, ωPmRepresenting phase angle modulation frequency, delta t representing sampling interval time, and n representing discrete sampling point number;
step 13: establishing an amplitude and phase angle simultaneous oscillation model under low-frequency oscillation, and modulating a coefficient k through an amplitudeAmAmplitude modulation frequency omegaAmPhase angle modulation factor kPmAnd phase angle modulation frequency omegaPmRepresenting the simultaneous oscillation condition of the amplitude and the phase angle of the electric power signal under low-frequency oscillation; the formula of the amplitude and phase angle simultaneous oscillation model is as follows:
Figure FDA0003428373990000021
in the formula: a. themRepresenting the effective value of the fundamental frequency component, ω0Which represents the fundamental frequency of the wave,
Figure FDA0003428373990000022
representing the initial phase of the fundamental frequencyAn angle; k is a radical ofAmRepresenting the amplitude modulation factor, ωAmRepresenting amplitude modulation frequency, delta t representing sampling interval time, and n representing discrete sampling point number; k is a radical ofPmRepresenting the phase angle modulation factor, ωPmRepresenting the phase angle modulation frequency.
3. The method according to claim 2, wherein said step 2 comprises the steps of:
step 21: the phasor measurement unit PMU adopts discrete Fourier transform to measure, and the current measurement phasor value is:
Figure FDA0003428373990000023
in the formula:
Figure FDA0003428373990000024
representing a current measured phasor value; n represents the number of sampling points in one period; x (n) represents a sampling signal; n represents the number of discrete sampling points; omega0Represents the fundamental frequency; Δ t represents a sampling interval time; j is the complex imaginary unit;
step 22: according to the Euler formula expansion, the phasor at the current moment is transformed into a complex form represented by an imaginary part and a real part:
Figure FDA0003428373990000025
wherein:
C(n)＝Re(L)＝x(n)cos(ω0nΔt)
S(n)＝Im(L)＝x(n)sin(ω0nΔt)
Figure FDA0003428373990000026
step 23: substituting its power signal model into phasor when amplitude oscillation occurs
Figure FDA0003428373990000029
In the real and imaginary parts of (a), we get:
Figure FDA0003428373990000027
Figure FDA0003428373990000028
wherein the expression of the real part terms is:
Figure FDA0003428373990000031
Figure FDA0003428373990000032
Figure FDA0003428373990000033
Figure FDA0003428373990000034
the expression for the imaginary terms is:
Figure FDA0003428373990000035
Figure FDA0003428373990000036
Figure FDA0003428373990000037
Figure FDA0003428373990000038
wherein,
Figure FDA0003428373990000039
the error part is an integral multiple of the fundamental frequency, is 0 in summation in a period and can be eliminated naturally;
Figure FDA00034283739900000310
after a period of accumulation, the phasor is a true value; the other entries are not 0 after a period of accumulation, and are the part of error that cannot be eliminated except the measured true value; the phase measurement error under amplitude oscillation is obtained and defined as the real error factor
Figure FDA00034283739900000311
And imaginary error factor
Figure FDA00034283739900000312
Their values are respectively:
Figure FDA00034283739900000313
Figure FDA00034283739900000314
from this, the analysis yields the PMU phasor measurement error under amplitude oscillation:
Figure FDA00034283739900000315
wherein,
Figure FDA00034283739900000316
is the phasor true value at the time of amplitude oscillation,
Figure FDA00034283739900000317
is a phasor measurement at the time of amplitude oscillation,
Figure FDA00034283739900000318
is the phasor measurement error of the PMU at amplitude oscillations.
4. The method according to claim 2, wherein said step 3 comprises the steps of:
step 31: the phasor measurement unit PMU adopts discrete Fourier transform to measure, and the current measurement phasor value is:
Figure FDA0003428373990000041
in the formula:
Figure FDA0003428373990000042
representing a current measured phasor value; n represents the number of sampling points in one period; x (n) represents a sampling signal; n represents the number of discrete sampling points; omega0Represents the fundamental frequency; Δ t represents a sampling interval time;
step 32: and (3) expanding the exponential part according to an Euler formula, and transforming the phasor at the current moment into a complex form represented by an imaginary part and a real part:
Figure FDA0003428373990000043
wherein
C(n)＝Re(L)＝x(n)cos(ω0nΔt)
S(n)＝Im(L)＝x(n)sin(ω0nΔt)
Figure FDA0003428373990000044
Step 33: when phase angle oscillation occurs, substituting the power signal model into the phasor at the current moment
Figure FDA00034283739900000410
In the real and imaginary parts of (a), we get:
Figure FDA0003428373990000045
Figure FDA0003428373990000046
wherein the expression of the real part terms is:
Figure FDA0003428373990000047
Figure FDA0003428373990000048
Figure FDA0003428373990000049
Figure FDA0003428373990000051
the expression for the imaginary terms is:
Figure FDA0003428373990000052
Figure FDA0003428373990000053
Figure FDA0003428373990000054
Figure FDA0003428373990000055
wherein
Figure FDA0003428373990000056
The error part is an integral multiple of the fundamental frequency, is 0 in summation in a period and can be eliminated naturally;
Figure FDA0003428373990000057
after a period of accumulation, the phasor is a true value; the other entries are not 0 after a period of accumulation, and are the part of error that cannot be eliminated except the measured true value; thus, a real part error factor is obtained
Figure FDA0003428373990000058
And imaginary error factor
Figure FDA0003428373990000059
Their values are respectively:
Figure FDA00034283739900000510
Figure FDA00034283739900000511
from this analysis the phasor measurement error under phase angle oscillation is obtained:
Figure FDA00034283739900000512
wherein,
Figure FDA00034283739900000513
is the phasor true value at phase angle oscillation,
Figure FDA00034283739900000514
is a measure of when the phase angle is oscillating,
Figure FDA00034283739900000515
is the phasor measurement error at phase angle oscillation.
5. The method according to claim 2, wherein said step 4 comprises the steps of:
step 41: the phasor measurement unit PMU adopts discrete Fourier transform to measure, and the current measurement phasor value is:
Figure FDA00034283739900000516
in the formula:
Figure FDA0003428373990000061
representing a current measured phasor value; n represents the number of sampling points in one period; x (n) represents a sampling signal; n represents the number of discrete sampling points; omega0Represents the fundamental frequency; Δ t represents a sampling interval time;
step 42: and (3) expanding the exponential part according to an Euler formula, and transforming the phasor at the current moment into a complex form represented by an imaginary part and a real part:
Figure FDA0003428373990000062
wherein
C(n)＝Re(L)＝x(n)cos(ω0nΔt)
S(n)＝Im(L)＝x(n)sin(ω0nΔt)
Figure FDA0003428373990000063
Step 43: when the amplitude and the phase angle simultaneously oscillate, the power signal model is substituted into the phasor at the current moment
Figure FDA00034283739900000611
In the real and imaginary parts of (a), we get:
Figure FDA0003428373990000064
Figure FDA0003428373990000065
wherein the expression of the real part terms is:
Figure FDA0003428373990000066
Figure FDA0003428373990000067
Figure FDA0003428373990000068
Figure FDA0003428373990000069
Figure FDA00034283739900000610
Figure FDA0003428373990000071
Figure FDA0003428373990000072
the expression for the imaginary terms is:
Figure FDA0003428373990000073
Figure FDA0003428373990000074
Figure FDA0003428373990000075
Figure FDA0003428373990000076
Figure FDA0003428373990000077
Figure FDA0003428373990000078
Figure FDA0003428373990000079
wherein,
Figure FDA00034283739900000710
the sum is an integral multiple of the fundamental frequency, is 0 in a period summation, and is an erasable error term;
Figure FDA00034283739900000711
after a period of accumulation, the phasor is a true value; the other entries are not 0 in one period, and are the part of the error that cannot be eliminated except the measured true value; thus, a real part error factor is obtained
Figure FDA00034283739900000712
And imaginary error factor
Figure FDA00034283739900000713
Their values are respectively:
Figure FDA0003428373990000081
Figure FDA0003428373990000082
the phasor measurement errors under simultaneous oscillation of amplitude and phase angle are obtained through analysis:
Figure FDA0003428373990000083
wherein,
Figure FDA0003428373990000084
is the phasor true value under the condition of simultaneous oscillation of amplitude value and phase angle,
Figure FDA0003428373990000085
is a measurement value under the condition that the amplitude and the phase angle synchronously oscillate,
Figure FDA0003428373990000086
is the phasor measurement error under simultaneous oscillation of amplitude and phase angle.
CN202010522982.6A 2020-06-10 2020-06-10 PMU measurement error analysis method under influence of low-frequency oscillation Active CN111624441B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202010522982.6A CN111624441B (en) 2020-06-10 2020-06-10 PMU measurement error analysis method under influence of low-frequency oscillation

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202010522982.6A CN111624441B (en) 2020-06-10 2020-06-10 PMU measurement error analysis method under influence of low-frequency oscillation

Publications (2)

Publication Number Publication Date
CN111624441A CN111624441A (en) 2020-09-04
CN111624441B true CN111624441B (en) 2022-02-18

Family

ID=72270188

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202010522982.6A Active CN111624441B (en) 2020-06-10 2020-06-10 PMU measurement error analysis method under influence of low-frequency oscillation

Country Status (1)

Country Link
CN (1) CN111624441B (en)

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114113898B (en) * 2021-11-29 2023-11-14 大连海事大学 Power distribution network loss analysis method and system based on multi-source measurement data

Citations (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103033789A (en) * 2012-12-26 2013-04-10 华北电力大学 Static and dynamic test system of synchronous phasor measurement unit pressure measuring unit (PMU)
CN103606113A (en) * 2013-12-02 2014-02-26 东北石油大学 Static state estimation method for electrical power system based on PMU device
CN104049144A (en) * 2014-06-27 2014-09-17 福州大学 Synchronous phasor measurement implementing method with filtered-out attenuation direct current components
CN104502877A (en) * 2014-12-22 2015-04-08 国家电网公司 Automatic detection system and method of synchronous phasor measurement device
CN106850496A (en) * 2017-03-02 2017-06-13 北京邮电大学 A kind of quadrature amplitude modulation signal phase recovery method and device
CN109298284A (en) * 2018-09-18 2019-02-01 四川大学 The method and system of island effect detection are carried out using PMU measurement phasor angle-data
CN110244151A (en) * 2019-07-05 2019-09-17 南方电网科学研究院有限责任公司 Synchronous phasor measurement method and system and related components
CN110414787A (en) * 2019-06-24 2019-11-05 北京交通大学 Power system state estimation method, device, equipment and storage medium
CN110543720A (en) * 2019-09-03 2019-12-06 北京交通大学 State estimation method based on SDAE-ELM pseudo-measurement model

Patent Citations (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103033789A (en) * 2012-12-26 2013-04-10 华北电力大学 Static and dynamic test system of synchronous phasor measurement unit pressure measuring unit (PMU)
CN103606113A (en) * 2013-12-02 2014-02-26 东北石油大学 Static state estimation method for electrical power system based on PMU device
CN104049144A (en) * 2014-06-27 2014-09-17 福州大学 Synchronous phasor measurement implementing method with filtered-out attenuation direct current components
CN104502877A (en) * 2014-12-22 2015-04-08 国家电网公司 Automatic detection system and method of synchronous phasor measurement device
CN106850496A (en) * 2017-03-02 2017-06-13 北京邮电大学 A kind of quadrature amplitude modulation signal phase recovery method and device
CN109298284A (en) * 2018-09-18 2019-02-01 四川大学 The method and system of island effect detection are carried out using PMU measurement phasor angle-data
CN110414787A (en) * 2019-06-24 2019-11-05 北京交通大学 Power system state estimation method, device, equipment and storage medium
CN110244151A (en) * 2019-07-05 2019-09-17 南方电网科学研究院有限责任公司 Synchronous phasor measurement method and system and related components
CN110543720A (en) * 2019-09-03 2019-12-06 北京交通大学 State estimation method based on SDAE-ELM pseudo-measurement model

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
一种计及零注入电流的PMU 量测线性状态估计方法;陈亮灯;《电力科学与工程》;20160228;第32卷(第2期);全文 *
一种适用于配电网的同步相量测量改进算法;蔡云峰等;《电力系统自动化》;20191110;第43卷(第21期);全文 *
同步相量测量技术研究;林彬;《冶金丛刊》;20160831(第4期);全文 *

Also Published As

Publication number Publication date
CN111624441A (en) 2020-09-04

Similar Documents

Publication Publication Date Title
Macii et al. Accuracy analysis and enhancement of DFT-based synchrophasor estimators in off-nominal conditions
Huang et al. Frequency estimation of distorted power system signals using a robust algorithm
US7701090B2 (en) Active filter
CN108155643B (en) A kind of robust estimation method of the single-phase mains voltage parameter based on sliding mode observer
CN106970264B (en) Improved phase difference correction method considering power grid frequency change rate
CN104635094A (en) Method for improving PMU (power management unit) synchronous phasor measurement precision
CN111624441B (en) PMU measurement error analysis method under influence of low-frequency oscillation
CN105825289A (en) Prediction method for wind power time sequence
CN109861296B (en) Inertia and damping identification method for island virtual synchronous generator system
CN104993501A (en) On-line evaluation method of low-frequency oscillation suppression performance of excitation regulator
Wang et al. Real-time subsynchronous control interaction monitoring using improved intrinsic time-scale decomposition
CN105738772A (en) Compulsory disturbance source positioning method based on power and frequency fluctuation phase
CN106250904A (en) Based on Power Disturbance analyser and the sorting technique of improving S-transformation
Borkowski et al. Interpolated-DFT-based fast and accurate amplitude and phase estimation for the control of power
CN111311021A (en) Theoretical power prediction method, device, equipment and storage medium for wind power plant
CN105243187B (en) A kind of parameter influence degree analysis method based on transient stability measurement index
CN113629729A (en) Wind power-containing power system area inertia estimation method based on frequency measurement point selection
Donnini et al. On the Estimation of Power System Inertia accounting for Renewable Generation Penetration
CN112511056A (en) Robust generator dynamic state estimation method based on phasor measurement
CN109444539B (en) Synchronous phasor measurement method based on Clark transformation
CN101656421B (en) Simulation method of electricity grid oscillating signal
Kamwa et al. Computer software to automate the graphical analysis of sudden-short-circuit oscillograms of large synchronous machines
CN112485522B (en) Electric energy data perception-based flat-top window function synchronous phasor measurement method and device
CN115952394A (en) Multi-machine power system robust dynamic state estimation method considering sensor faults
CN114792984A (en) Quick positioning method for subsynchronous/supersynchronous oscillation source

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant