CN107390022A - Electric energy gauging method based on discrete spectrum correction - Google Patents
Electric energy gauging method based on discrete spectrum correction Download PDFInfo
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- G01R22/06—Arrangements for measuring time integral of electric power or current, e.g. electricity meters by electronic methods
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Abstract
The invention discloses a kind of electric energy gauging method based on discrete spectrum correction, including the voltage and current signal of digital quantity is converted into using a length of N of window tetra- three rank windows progress time domain truncations of Nuttall；The spectrum barycenter and fundamental frequency of fundamental wave are calculated using spectrum barycenter formula；Harmonic spike position is estimated, calculates harmonic spectrum barycenter and the maximum spectrum peak position and offset of fundamental wave and each harmonic；Principal wave harmonic wave amplitude correction coefficient is determined, and calculates tested voltage, the fundamental wave of electric current, harmonic amplitude and phase；The electrical parameter of fundamental wave harmonic is calculated, completes electric energy metrical.Therefore the inventive method need not carry out peak value searching, offset need not be calculated according to the type of institute's windowed function, and mutually eliminate zero-crossing examination, it is directly calculated using fft analysis method, eliminate the window spectrum computing of complexity, calculate and analyze obtained frequency accuracy to greatly improve, and program realizes that simply real-time is good.
Description
Technical field
Present invention relates particularly to a kind of electric energy gauging method based on discrete spectrum correction.
Background technology
With the development and the improvement of people's living standards of economic technology, electric energy has become the daily production of people and life
Essential secondary energy sources in work, production and life to people bring endless facility.
Harmonious Waves in Power Systems has significant effect to the accuracy of electric energy metrical, using metering fundamental energy harmonic respectively
The metering of electric energy is a kind of relatively rational mode, and with the development of technology, requirement of the market to principal wave harmonic wave measuring accuracy is more next
It is higher.According to the current development in electric energy metrical field, the design of harmonic wave metering mainly has two kinds：A kind of is special metering
Chip, another kind are the special AD+MCU of DSP+.Former scheme cost is relatively low, is mainly used in the design of common list, three-phase meter
In；The latter's cost is of a relatively high, and main application is mainly used in regional grid, provincial power network, light with Source of Gateway Meter platform, Source of Gateway Meter
The stoichiometric point that volt, wind-powered electricity generation, water power and electric railway even load frequently change, the field changeable in face of the big load of this harmonic content
Close, the program is more flexible compared to the former function, it is easier to meets the needs of complicated.
Source of Gateway Meter does not require nothing more than higher electric energy metrical precision, and require lower fortune as a ripe product
Row power consumption.And many algorithms have been proposed currently for the high-precision measuring of fundamental wave, the amplitude of harmonic wave, phase and frequency, this its
In have quite a few algorithm because realizing complicated difficult to accomplish requirement of real-time in embedded systems, and realize it is more complicated,
System operation power consumption can be improved accordingly, thus finds a kind of measuring accuracy height, realized simply, and time and spatial complexity
It can meet that the algorithm of existing hardware platform is particularly important.
The content of the invention
It is an object of the invention to provide a kind of precision is of a relatively high, real-time is good and algorithm is simply based on discrete spectrum
The electric energy gauging method of correction.
This electric energy gauging method based on discrete spectrum correction provided by the invention, comprises the following steps：
S1. it is digital quantity by sample conversion by voltage and current signal, using a length of N of window tetra- three ranks of Nuttall
Window carries out time domain truncation to the digital quantity after conversion, obtains blocking the spectrum signal Y (k) of rear signal；The spectrum signal Y (k)
Including voltage spectrum value YuAnd current spectrum value Y (k)i(k)；
S2. the voltage spectrum value Y obtained according to step S1u(k) the spectrum barycenter of fundamental wave, is calculated using spectrum barycenter formula
ksc1With fundamental frequency f0；
S3. the fundamental frequency f obtained using step S20Estimate harmonic spike positionAnd calculated using spectrum barycenter formula
Obtain harmonic spectrum barycenter ksch, and the maximum spectrum peak position k of fundamental wave and each harmonic is further calculatedhWith offset λh；
S4. principal wave harmonic wave amplitude correction coefficient g (λ are determined according to the offset obtained in step S3h), and be calculated by
Survey voltage, the fundamental wave of electric current, harmonic amplitude and phase；
S5. tested voltage, the fundamental wave of electric current, harmonic amplitude and the phase calculation fundamental wave harmonic obtained according to step S4
Electrical parameter, so as to complete the metering of electric energy.
The spectrum signal Y (k) for obtaining blocking rear signal described in step S1, after specially being blocked using fft analysis
The spectrum signal Y (k) of signal.
Tetra- three rank windows of Nuttall of a length of N of window described in step S1, the specially main lobe of tetra- three rank windows of Nuttall
Width isThere are 8 spectral lines in main lobe.
The a length of N of described window tetra- three rank windows of Nuttall meet following formula：
N=1,2 in formula ..., N-1；bmFor window function coefficient, meet
Fundamental wave spectrum barycenter k is calculated described in step S2sc1With fundamental frequency f0, specially calculated using following steps
Obtain：
A. fundamental wave spectrum barycenter k is calculated according to spectrum barycenter formulasc1：
In formulaAndFor downward bracket function, fmin is
The minimum value of signal fundamental frequency, fmax be signal fundamental frequency maximum, Δ f=fs/ N, fs are the sampling of analog-to-digital conversion
Frequency, N are that the analysis of fft algorithm is counted；
B. the fundamental wave obtained according to step A composes barycenter ksc1Measure fundamental frequency f0：
f0=ksc1*Δf。
Harmonic spectrum barycenter k is calculated described in step S3sch, fundamental wave and each harmonic maximum spectrum peak position khWith it is inclined
Shifting amount λh, specially it is calculated using following steps：
A. using following formula estimation harmonic spectrum peak
Wherein h value is 2,3 ..., M；M is the maximum overtone order of signal；
B. obtained according to step aHarmonic spectrum barycenter k is calculated using following formulasch：
C. the harmonic spectrum barycenter k obtained according to step bsch, fundamental wave and each harmonic are calculated most using equation below
Big spectrum peak position kh：
kh=round (ksch)
Round () is the function that rounds up in formula；
D. the maximum spectrum peak position k obtained according to step chOffset λ is calculatedh：
λh=kh-ksch。
Determination principal wave harmonic wave amplitude correction coefficient g (λ described in step S4h), specially calculated using equation below：
Wherein p1~p5It is constant.
Tested voltage, the fundamental wave of electric current, harmonic amplitude and phase is calculated described in step S4, specially using as follows
Updating formula is corrected to amplitude and phase：
A=| Y (kh)|g(λh)
A is revised amplitude in formula, and θ is revised phase, angle (Y (kh)) represent Y (kh) phase value.
The electrical parameter of calculating fundamental wave harmonic described in step S5, specially calculates fundamental wave harmonic using following formula
Electrical parameter：
Define principal wave harmonic wave voltage magnitude Uh, voltage-phase θ uh, current amplitude Ih, current phase θ ih, h=1,2 ...,
63；
Phase difference：θh=θ uh-θih
Principal wave harmonic wave active power：Ph=UhIh cos(θuh-θih)
Principal wave harmonic wave reactive power：Qh=UhIh sin(θuh-θih)
Full wave voltage：
Full-wave electric current：
All-wave is active：
All-wave is idle：
Fundamental active electric flux：EP=P1T, t are the time；
Fundamental wave reactive power electric flux：EQ=Q1T, t are the time；
Harmonic wave active energy amount：T is the time；
Harmonic wave reactive energy amount：T is the time；
All-wave active energy amount：EP=Pt, t are the time；
All-wave reactive energy amount：EQ=Qt, t are the time.
This electric energy gauging method based on discrete spectrum correction provided by the invention, is accurately looked for using spectrum centroid method first
Go out signal spectrum peak value, to eliminate caused spectral leakage and fence response under non-synchronous sampling；Further to voltage, electric current
Spectrum value be corrected using amplitude correction formula and phase only pupil filter formula, finally try to achieve all-wave, fundamental wave harmonic electric parameter
And electric flux；Therefore the inventive method need not carry out peak value searching, it is not necessary to calculated and offset according to the type of institute's windowed function
Amount, and zero-crossing examination is mutually eliminated, it is directly calculated using fft analysis method, eliminates the window spectrum computing of complexity, meter
Calculate and analyze obtained frequency accuracy to greatly improve, and program realizes that simply real-time is good.
Brief description of the drawings
Fig. 1 is the method flow diagram of the inventive method.
Fig. 2 is the spectrum centroid calculation schematic diagram of the inventive method.
Fig. 3 is the correction coefficient matched curve of the inventive method.
Fig. 4 is the harmonic frequency error precision of the inventive method.
Fig. 5 is the harmonic amplitude error precision of the inventive method.
Fig. 6 is the harmonic phase error precision of the inventive method.
Embodiment
It is the method flow diagram of the inventive method as shown in Figure 1：It is provided by the invention it is this based on discrete spectrum correction
Electric energy gauging method, comprise the following steps：
S1. it is digital quantity by sample conversion by voltage and current signal, using a length of N of window tetra- three ranks of Nuttall
Window carries out time domain truncation to the digital quantity after conversion, obtains blocking the spectrum signal Y (k) of rear signal using fft analysis；The frequency
Spectrum signal Y (k) includes voltage spectrum value YuAnd current spectrum value Y (k)i(k)；
In the specific implementation, the main lobe width of preferably tetra- three rank windows of Nuttall isThere are 8 spectral lines in main lobe；
The a length of N of described window tetra- three rank windows of Nuttall meet following formula：
N=1,2 in formula ..., N-1；bmFor window function coefficient, meetb0=
0.338946, b1=0.481973, b2=0.161054, b3=0.018027；
Described application window function is to do following processing to discrete voltage u (n), current signal i (n)：U ' (n)=u (n) * w
(n), i ' (n)=i (n) * w (n)；U ' (n) and i ' (n) obtains discrete spectrum Y after fft analysisuAnd Y (k)i(k), for ease of point
Analysis, it is used uniformly Y (k) expressions；
S2. the voltage spectrum value Y obtained according to step S1u(k), using spectrum barycenter formula to calculate, (Fig. 2 is the inventive method
Spectrum centroid calculation schematic diagram) obtain the spectrum barycenter k of fundamental wavesc1With fundamental frequency f0；Specially calculated using following steps
Arrive：
A. fundamental wave spectrum barycenter k is calculated according to spectrum barycenter formulasc1：
In formulaAndFor downward bracket function, fmin is
The minimum value of signal fundamental frequency, specially 45Hz；Fmax be signal fundamental frequency maximum, specially 65Hz；Δ f=
fs/ N, fs are the sample frequency of analog-to-digital conversion, and N is that the analysis of fft algorithm is counted；
B. the fundamental wave obtained according to step A composes barycenter ksc1Measure fundamental frequency f0：
f0=ksc1*Δf
S3. the fundamental frequency f obtained using step S20Estimate harmonic spike positionAnd calculated using spectrum barycenter formula
Obtain harmonic spectrum barycenter ksch, and the maximum spectrum peak position k of fundamental wave and each harmonic is further calculatedhWith offset λh；Tool
Body is to be calculated using following steps：
A. using following formula estimation harmonic spectrum peak
Wherein h value is 1,2,3 ..., M；M is the maximum overtone order of signal；
B. obtained according to step aHarmonic spectrum barycenter k is calculated using following formulasch：
C. the harmonic spectrum barycenter k obtained according to step bsch, fundamental wave and each harmonic are calculated most using equation below
Big spectrum peak position kh：
kh=round (ksch)
Round () is the function that rounds up in formula；
D. offset λ is calculated in the maximum spectrum peak position kh obtained according to step ch：
λh=kh-ksch
S4. principal wave harmonic wave amplitude correction coefficient g (λ are determined according to the offset obtained in step S3h), and be calculated by
Survey voltage, the fundamental wave of electric current, harmonic amplitude and phase；
Calculating g (λ are carried out using equation belowh)：
Wherein p1~p5It is constant；Preferable p1=0.2073, p2=-0.01546, p3=0.9941, p4=-
0.000251, p5=2.9503；
Amplitude and phase are corrected using following updating formula：
A=| Y (kh)|g(λh)
A is revised amplitude in formula, and θ is revised phase, angle (Y (kh)) represent Y (kh) phase value；
The derivation of above-mentioned amplitude correction coefficient described briefly below, amplitude correction formula and phase only pupil filter formula：
Consider single-frequency signals y (n) with sample frequency f firstsThe discrete-time signal that uniform sampling obtains is：
A is amplitude in formula, f0For frequency,For initial phase；
Y is obtained to y (n) plus tetra- three rank windows of Nuttallw(n)=y (n) w (n), yw(n) continuous fourier transform is
Discrete sampling is carried out to above formula, and ignores negative frequency point-f0Going out the secondary lobe at frequency peak influences, and obtains signal after adding window
The expression formula of discrete Fourier transform is：
Make f0=kscΔ f, then kscFor the spectrum barycenter of signal；As shown in Fig. 2 k*For close to spectrum barycenter kscMaximum spectral peak
Position, therefore can obtain：
Make λ=k*-ksc, λ is offset, λ ∈ [- 0.5,0.5]；
Further derive that the discrete spectrum approximation to function of tetra- three rank windows of Nuttall is as follows：
Amplitude correction formula, which can to sum up be obtained, is：
In formulaFor window function offset amplitude；Curve map it is as shown in Figure 3；Therefrom
It can be seen that the curve can use fitting of a polynomial, to reduce operand, first approached using fourth order polynomial fitting formulaCurve, fitting formula are as follows：
G (λ)=p1λ4+p2|λ|3+p3λ2+p4|λ|+p5
Wherein p1=0.2073, p2=-0.01546, p3=0.9941, p4=-0.000251, p5=2.9503；
Therefore amplitude formula can be obtained is：
A=| Y (k*)|g(λ)
Phase only pupil filter formula is：
S5. tested voltage, the fundamental wave of electric current, harmonic amplitude and the phase calculation fundamental wave harmonic obtained according to step S4
Electrical parameter, so as to complete the metering of electric energy；The electrical parameter of fundamental wave harmonic is specially calculated using following formula：
Define principal wave harmonic wave voltage magnitude Uh, voltage-phase θ uh, current amplitude Ih, current phase θ ih, h=1,2 ...,
63；
Phase difference：θh=θ uh-θih
Principal wave harmonic wave active power：Ph=UhIh cos(θuh-θih)
Principal wave harmonic wave reactive power：Qh=UhIh sin(θuh-θih)
Full wave voltage：
Full-wave electric current：
All-wave is active：
All-wave is idle：
Fundamental active electric flux：EP=P1T, t are the time；
Fundamental wave reactive power electric flux：EQ=Q1T, t are the time；
Harmonic wave active energy amount：T is the time；
Harmonic wave reactive energy amount：T is the time；
All-wave active energy amount：EP=Pt, t are the time；
All-wave reactive energy amount：EQ=Qt, t are the time.
The electric energy gauging method provided below by way of verification experimental verification invention：
The inventive method be applied to Source of Gateway Meter (ammeter specifications and models are DTSD341-MA2,3 × 57.7V, 3 × 1.5 (6) A,
20000imp/kWh, 50Hz), program is implemented in meter platform Blackfin BF533 DSP process chips.
The fundamental active pulse elementary error precision of this method is as shown in Figure 1：
The fundamental active pulse elementary error precision of table 1
Harmonic pulse Setup Experiments：
Fundamental voltage Un=57.7V；Fundamental current In is 0.5*Imax, as In=2*Ib=3A；Phasor power factor
For 1.0；Fundamental frequency is 50Hz；Single harmonic component is superimposed on the basis of fundamental wave, overtone order highest is added to 48 times；Harmonic voltage
Amplitude 0.05*Un；Harmonic current 0.4*In；Harmonic power factor is 0.5L；Harmonic pulse constant 1000000imp/kWh；
It is superimposed below for Source of Gateway Meter under single harmonic component, the error that harmonic wave goes out pulse is as shown in table 2：
The harmonic wave of table 2 goes out the error signal table of pulse
From upper table it can be found that Source of Gateway Meter measured data greatly differs from each other with theoretical value, this is due to that experiment condition is limited, is made
Obtaining experimental data can not reach best, and nonetheless, upper table error information has met GB/T17215.302-2013 pair harmonic wave
Electric energy metrical precision peak demand, and entered every strict test, fully meet standard requirement.Harmonic pulse error is main
Influenceed by caused by hardware sample circuit and transformer than difference and difference, in table harmonic error data be ammeter through amplitude and
Data are surveyed after phasing.After experiment condition permission, above-mentioned data precision will have the lifting of matter.
MATLAB simulation results as shown in Fig. 3~Fig. 6, respectively correction coefficient matched curve, harmonic frequency error precision,
Harmonic amplitude error precision harmonic phase error precision；It can be seen that the present invention, which carries algorithm, can realize that harmonic wave is believed
Number high-precision measuring.
Claims (9)
1. a kind of electric energy gauging method based on discrete spectrum correction, comprises the following steps：
S1. it is digital quantity by sample conversion by voltage and current signal, using a length of N of window tetra- three rank windows pair of Nuttall
Digital quantity after conversion carries out time domain truncation, obtains blocking the spectrum signal Y (k) of rear signal；The spectrum signal Y (k) includes
Voltage spectrum value YuAnd current spectrum value Y (k)i(k)；
S2. the voltage spectrum value Y obtained according to step S1u(k) the spectrum barycenter k of fundamental wave, is calculated using spectrum barycenter formulasc1With
Fundamental frequency f0；
S3. the fundamental frequency f obtained using step S20Estimate harmonic spike positionAnd it is calculated using spectrum barycenter formula
Harmonic spectrum barycenter ksch, and the maximum spectrum peak position k of fundamental wave and each harmonic is further calculatedhWith offset λh；
S4. principal wave harmonic wave amplitude correction coefficient g (λ are determined according to the offset obtained in step S3h), and tested electricity is calculated
Pressure, the fundamental wave of electric current, harmonic amplitude and phase；
S5. the electricity ginseng of tested voltage, the fundamental wave of electric current, harmonic amplitude and the phase calculation fundamental wave harmonic obtained according to step S4
Number, so as to complete the metering of electric energy.
2. the electric energy gauging method according to claim 1 based on discrete spectrum correction, it is characterised in that described in step S1
The spectrum signal Y (k) for obtaining blocking rear signal, specially obtain blocking the spectrum signal Y (k) of rear signal using fft analysis.
3. the electric energy gauging method according to claim 2 based on discrete spectrum correction, it is characterised in that described in step S1
The a length of N of window tetra- three rank windows of Nuttall, the main lobe width of specially tetra- three rank windows of Nuttall isHave in main lobe
8 spectral lines.
4. the electric energy gauging method according to claim 3 based on discrete spectrum correction, it is characterised in that described window length
Meet following formula for N tetra- three rank windows of Nuttall：
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5. the electric energy gauging method according to claim 4 based on discrete spectrum correction, it is characterised in that described in step S2
Fundamental wave spectrum barycenter k is calculatedsc1With fundamental frequency f0, specially it is calculated using following steps：
A. fundamental wave spectrum barycenter k is calculated according to spectrum barycenter formulasc1：
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The minimum value of wave frequency rate, fmax be signal fundamental frequency maximum, Δ f=fs/ N, fs be analog-to-digital conversion sample frequency, N
Counted for the analysis of fft algorithm；
B. the fundamental wave obtained according to step A composes barycenter ksc1Measure fundamental frequency f0：
f0=ksc1*Δf。
6. the electric energy gauging method according to claim 5 based on discrete spectrum correction, it is characterised in that described in step S3
Harmonic spectrum barycenter k is calculatedsch, fundamental wave and each harmonic maximum spectrum peak position khWith offset λh, specially using such as
Lower step is calculated：
A. using following formula estimation harmonic spectrum peak
Wherein h value is 2,3 ..., M；M is the maximum overtone order of signal；
B. obtained according to step aHarmonic spectrum barycenter k is calculated using following formulasch：
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C. the harmonic spectrum barycenter k obtained according to step bsch, fundamental wave is calculated using equation below and the maximum of each harmonic is composed
Peak position kh：
kh=round (ksch)
Round () is the function that rounds up in formula；
D. the maximum spectrum peak position k obtained according to step chOffset λ is calculatedh：
λh=kh-ksch。
7. the electric energy gauging method according to claim 6 based on discrete spectrum correction, it is characterised in that described in step S4
Determination principal wave harmonic wave amplitude correction coefficient g (λh), specially calculated using equation below：
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Wherein p1~p5It is constant.
8. the electric energy gauging method according to claim 7 based on discrete spectrum correction, it is characterised in that described in step S4
Tested voltage, the fundamental wave of electric current, harmonic amplitude and phase is calculated, specially using following updating formula to amplitude and phase
Position is corrected：
A=| Y (kh)|g(λh)
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<mi>a</mi>
<mi>n</mi>
<mi>g</mi>
<mi>l</mi>
<mi>e</mi>
<mrow>
<mo>(</mo>
<mi>Y</mi>
<mo>(</mo>
<msub>
<mi>k</mi>
<mi>h</mi>
</msub>
<mo>)</mo>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mi>&lambda;</mi>
<mi>h</mi>
</msub>
<mi>&pi;</mi>
<mo>+</mo>
<mfrac>
<mi>&pi;</mi>
<mn>2</mn>
</mfrac>
</mrow>
A is revised amplitude in formula, and θ is revised phase, angle (Y (kh)) represent Y (kh) phase value.
9. the electric energy gauging method according to claim 8 based on discrete spectrum correction, it is characterised in that described in step S5
Calculating fundamental wave harmonic electrical parameter, specially using following formula calculate fundamental wave harmonic electrical parameter：
Define principal wave harmonic wave voltage magnitude Uh, voltage-phase θ uh, current amplitude Ih, current phase θ ih, h=1,2 ..., 63；
Phase difference：θh=θ uh-θih
Principal wave harmonic wave active power：Ph=UhIhcos(θuh-θih)
Principal wave harmonic wave reactive power：Qh=UhIhsin(θuh-θih)
Full wave voltage：
Full-wave electric current：
All-wave is active：
All-wave is idle：
Fundamental active electric flux：EP=P1T, t are the time；
Fundamental wave reactive power electric flux：EQ=Q1T, t are the time；
Harmonic wave active energy amount：T is the time；
Harmonic wave reactive energy amount：T is the time；
All-wave active energy amount：EP=Pt, t are the time；
All-wave reactive energy amount：EQ=Qt, t are the time.
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