CN1375702A - Reactive power measuring method based on digital filtering - Google Patents

Abstract

The present invention relates to a method for measuring reactive power based on digital filtration, which is characterized by that firstly, the analogue voltage signal and analogue current signal measured from electric network for measuring reactive power are undergone the process of A/D conversion to obtain discrete digital voltage signal and digital current signal. Said digital voltage signal is passed through the digital phase shift filter to obtain signal u'(n), and the digital current signal i(n) is passed through the digital phase shift filter to obtain signal i'(n), said signals of u'(n) and i'(n) are multiplied to obtain signal q(n), q(n)=u'(n)X i'(n), the signal q (n) is undergone the process of D.C. filtration so as to obtain its D.C. component Q(n), i.e. reactive powder.

Description

A kind of reactive power measuring method based on digital filtering

Technical field

The present invention relates to a kind of reactive power measuring method based on digital filtering, this method obtains the total reactive power data to fundamental wave reactive power power and the summation of each harmonic reactive power according to a pair of power-frequency voltage and the current input signal that comprises harmonic wave.The invention belongs to the electric parameter measurement technical field.

Background technology

In electric system, reactive power and reactive energy are crucial electrical parameters, idle size has very large influence to transfer efficiency, the quality of power supply of electric system, by accurately calculating the idle of system, just can take appropriate measures and carry out the allocation schedule of electric network reactive-load, perhaps reactive load is compensated, suppress idle transmission line loss that causes and voltage sag, thereby reach the effect of improving the quality of power supply.Therefore, be one of important topic of studying of people to idle measurement always.

If the port voltage of a two-port network is a frequency is f, effective value is the AC signal of U, and then its transient expression formula is: $u\left(t\right)=\sqrt{2}\mathrm{<figure-callout\; id="2"\; label="U\; sin"\; filenames="A02116443.600091.png,A02116443.600131.png"\; state="\{\{state\}\}">U</figure-callout>}\sin 2\mathrm{\&pi;ft}$ If the current signal of port also is a frequency is the AC signal of f, its transient expression formula is:

Wherein, the current reference direction is that the anode with Voltage Reference flows into two port direction for just, and I is an effective value, and- is the phasing degree of current signal.According to the definition of AC signal reactive power, the reactive power that this two-port network absorbs is:

Q=UIsin following formula also is equal to: Wherein,

It is the one-period of AC signal.If following formula explanation is with the voltage signal of single-frequency

Time-delay

The gained signal In one-period T, carry out integration with the product of current signal, then to cycle length T average, can obtain the reactive power of being asked.According to this principle, a kind of numerical approach of traditional power frequency component wattless power measurement as shown in Figure 1.With reference to figure 1, a pair of analog voltage signal u (t) and the current signal i (t) that measure at first enter the analog to digital conversion part, are converted to the voltage signal sequence u (n) and the current signal sequence i (n) of digital sample respectively.Then, if the primitive period of power-frequency voltage is T ₁, then voltage signal will be delayed time

Obtain signal u ' (n).Signal u ' (n) and i (n) carry out multiplication process, obtain signal q (n), promptly q (n)=u ' (n) * i (n).At last, q (n) is carried out filtering, obtain its flip-flop Q (n), Q (n) is the reactive power of asking.Consider the periodicity of power frequency component,, then can adopt the numerical computation method of integral mean the DC filtering process of q (n) if one-period has N sampled point, as the following formula shown in: $Q\left(n\right)=\frac{1}{N}\underset{i=n-N+1}{\overset{n}{\mathrm{\&Sigma;}}}q\left(i\right)$

But classic method can not be handled the power system reactive power problems of measurement that comprises harmonic wave well.If suppose the voltage signal and the current signal that comprise 2～M time (M 〉=2) harmonic components be: $u\left(t\right)=\underset{k=1}{\overset{M}{\mathrm{\&Sigma;}}}\sqrt{2}{U}_k\sin (2\mathrm{\&pi;k}{f}_{1}t+{\mathrm{\&theta;}}_k)$

Wherein, f ₁Be the fundamental frequency of electrical network, U ₁Be the fundamental voltage effective value, θ ₁Be the phase place of fundamental voltage, U ₂～U _MBe the effective value of each harmonic voltage composition, θ ₂～θ _MBe the phase place of each harmonic voltage composition, I ₁Be the fundamental current effective value, (θ ₁- ₁) be the phase place of fundamental current, I ₂～I _MBe the effective value of each harmonic electric current composition, (θ ₂- ₂)～(θ _M- _M) be the phase place of each harmonic voltage composition.Reactive power for first-harmonic or a certain subharmonic voltage and electric current generation should be:

Q _k=U _kI _kSin _kK=1,2 ... if the summation that M calculates fundamental wave reactive power power and each harmonic reactive power is:

Yet, if adopt shown in Figure 1 traditional according to primitive period T ₁Voltage signal is delayed time The reactive power data result that reactive power measuring method obtained be: Wherein, P _k=U _kI _kCos _kObviously, the Q ' as a result that records like this is not equal to the summation Q of fundamental wave reactive power power and each harmonic reactive power.Though classic method to the fundamental voltage phase shift 90 the degree, for second harmonic with regard to phase shift 180 the degree, the third harmonic phase shift 270 the degree, the four-time harmonic phase shift 360 the degree ...Therefore, this method does not only add 2,6,1 ... etc. the reactive power that even harmonics produced, deducted the active power that these even-order harmonics produce on the contrary; Not only do not add 3,7,11 ... etc. the reactive power that odd harmonics produced, deducted the reactive power that these odd harmonics produced on the contrary; For 4,8,12 ... then added the active power that they produced etc. even harmonics.In view of this, in the electrical network that has harmonic wave to exist, it is irrational utilizing classic method to measure reactive power, and its result can not reflect the summation of being concerned about the each harmonic reactive power in the frequency band.

Summary of the invention

The objective of the invention is to overcome the deficiency of above-mentioned reactive power measuring method, a kind of reactive power measuring method based on digital filtering is proposed, with the sum data of 2～M subharmonic reactive power of real acquisition fundamental wave reactive power power and major concern, and with it as measured reactive power data.Thereby solve under the situation that harmonic wave exists the problems of measurement of power system reactive power.

The reactive power measuring method based on digital filtering that the present invention proposes may further comprise the steps:

1, a pair of analog voltage signal u (t) and the analog current signal i (t) that are used to measure reactive power to recording from electrical network, carry out analog to digital conversion, digital voltage signal u (n) that obtains dispersing and digital current signal i (n) by identical fixing sample frequency respectively.The sample frequency of choosing should be to measure more than the twice of higher hamonic wave (M time) frequency be concerned about, and should be able to satisfy the requirement of computational accuracy.

2, above-mentioned the 1st digital voltage signal u (n) that obtains of step through first group of digital phase shift filtering F1 after, obtain signal u ' (n).Above-mentioned the 1st digital current signal i (n) that obtains of step through second group of digital phase shift filtering F2 after, obtain signal i ' (n).The frequency domain transport property of above-mentioned two groups of digital phase shift filtering F1 and F2 is used H respectively _F1(e ^{J ω}) and H _F2(e ^{J ω}) expression, then at the frequency band (ω that comprises first-harmonic and 2～M subharmonic ₁, ω ₂) in, the frequency domain transport property of phase-shift filtering F1 and F2 should satisfy following relation:

Satisfying under the condition of accuracy requirement, can there be certain error in the constraint of above-mentioned transport property.

3, with above-mentioned the 2nd signal u ' that obtains of step (n) and i ' (n) multiply each other, obtain signal q (n), that is:

q(n)＝u′(n)×i′(n)

4, the signal q (n) that above-mentioned the 3rd step is obtained passes through DC filtering, obtains its flip-flop Q (n), and Q (n) is exactly the reactive power data that need measurement.

The reactive power measuring method that the present invention proposes has overcome the deficiency of traditional reactive power measuring method.The reactive power data that obtain by the inventive method are fundamental wave reactive power power and the summation of measuring 2～M subharmonic reactive power of being concerned about.The work of treatment that this method is carried out after the aanalogvoltage current signal is converted into digital sampled signal all is digitized, and its project organization is simple, and implementation method is easy.The present invention by the control to filtering order and data bits, is easy to realize high-precision measurement owing to used the digital filtering phase-moving method.

In addition, after the total reactive power data that obtain based on aforementioned inventive method to first-harmonic and the summation of each harmonic reactive power, with it at t ₁To t ₂(t ₂＞t ₁) time range in get discrete integration, the reactive energy data that circuit-under-test absorbs or produces in just can obtaining during this period of time.

Description of drawings

Fig. 1 is the theory diagram of traditional reactive power measuring method.

Fig. 2 is the theory diagram that the present invention is based on the reactive power measuring method of digital phase shift filtering.

Fig. 3 is the amplitude versus frequency characte of first group of digital phase shift filtering F1 among the embodiment | H _F1(e ^{J ω}) |.

Fig. 4 is the amplitude versus frequency characte of second group of digital phase shift filtering F2 among the embodiment | H _F2(e ^{J ω}) |.

Fig. 5 is the ratio of second group of digital phase shift filtering F2 frequency domain transport property and first group of digital phase shift filtering F1 frequency domain transport property among the embodiment

Amplitude versus frequency characte

Fig. 6 is the ratio of second group of digital phase shift filtering F2 frequency domain transport property and first group of digital phase shift filtering F1 frequency domain transport property among the embodiment

Phase-frequency characteristic.

Fig. 7 is among the embodiment The amplitude-versus-frequency curve that in care frequency band 37.5～962.5Hz interval, amplifies.

Fig. 8 is among the embodiment

The phase-frequency characteristic curve that in care frequency band 37.5～962.5Hz interval, amplifies.

Fig. 9 be input single-frequency sinusoidal signal x and respectively through the output signal y1 that obtains after F1 and the F2 filtering and the waveform of y2.

Figure 10 is the harmonic components table of a pair of voltage and current signal of the input embodiment of the invention

Embodiment

The present invention is based on digital phase shift filtering reactive power measuring method theory diagram as shown in Figure 2.With reference to Fig. 2, the course of work of reactive power measuring method that the present invention is based on digital phase shift filtering is as follows:

1. a pair of analog voltage signal u (t) that at first will record from the 50Hz common frequency power network and analog current signal i (t) are respectively according to identical fixed sampling frequency F _SCarry out the A/D conversion, digital voltage signal u (n) that obtains dispersing and digital current signal i (n).Be concerned about high reps M=18 time of harmonic wave, higher hamonic wave respective frequencies is 900Hz, the sample frequency F of selection _S=8000Hz, it is greater than 2 times of higher hamonic wave frequency.

2. after the digital voltage signal u (n) that above-mentioned the 1st step is obtained handles through first group of digital phase shift filtering F1, obtain signal u ' (n).After above-mentioned the 1st digital current signal i (n) that obtains of step handled through second group of digital phase shift filtering F2, obtain signal i ' (n).

The digital phase shift filtering F1 that embodiment selects is an infinite-duration impulse response IIR type, its frequency domain transport property H _F1(e ^{J ω}) have a following form: $H_{F1}\left(e^{\mathrm{j\&omega;}}\right)=\frac{\underset{i=1}{\overset{29}{\mathrm{\&Sigma;}}}B1\left(i\right)e^{-j(i-1)\mathrm{\&omega;}}}{\underset{k=1}{\overset{25}{\mathrm{\&Sigma;}}}\mathrm{Al}\left(k\right)e^{-j(k-1)\mathrm{\&omega;}}}=\frac{B1\left(1\right)+B1\left(2\right)e^{-\mathrm{j\&omega;}}+B1\left(3\right)e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="A02116443.600091.png,A02116443.600131.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&omega;}}+\&hellip;+B1\left(29\right)e^{-j28\mathrm{\&omega;}}}{A1\left(1\right)+A1\left(2\right)e^{-\mathrm{j\&omega;}}+A1\left(3\right)e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="A02116443.600091.png,A02116443.600131.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&omega;}}+\&hellip;+A1\left(25\right)e^{-j24\mathrm{\&omega;}}}$ Concrete coefficient is as follows:

B1＝[0，0，0，0，1，0，0，0，0，0，0，0，-6.64335708964449，0，0，0，0，0，0，0，12.1534183893028，0，0，0，

0，0，0，0，-6.61890164586758]

A1＝[6.61890164586758，0，0，0，0，0，0，0，-12.1534183893028，0，0，0，0，0，0，0，

6.64335708964449，0，0，0，0，0，0，0，-1]

According to the digital filtering design theory as can be known, digital filtering F1 is a cause and effect, and is just attainable.And further analyze as can be known that this Filtering Processing is stable.H _F1(e ^{J ω}) amplitude versus frequency characte as shown in Figure 3.As can be seen from the figure, in frequency band 50～900Hz scope of being concerned about, 20log|H is arranged basically _F1(e ^{J ω}) |=0dB, promptly | H _F1(e ^{J ω}) |=1.

The digital phase shift filtering F2 that embodiment selects is an infinite-duration impulse response IIR type, its frequency domain transport property H _F2(e ^{J ω}) have a following form: $H_{F2}\left(e^{\mathrm{j\&omega;}}\right)=\frac{\underset{i=1}{\overset{25}{\mathrm{\&Sigma;}}}B2\left(i\right)e^{-j(i-1)\mathrm{\&omega;}}}{\underset{k=1}{\overset{25}{\mathrm{\&Sigma;}}}A2\left(k\right)e^{-j(k-1)\mathrm{\&omega;}}}=\frac{B2\left(1\right)+B2\left(2\right)e^{-\mathrm{j\&omega;}}+B2\left(3\right)e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="A02116443.600091.png,A02116443.600131.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&omega;}}+\&hellip;+B2\left(25\right)e^{-j24\mathrm{\&omega;}}}{A2\left(1\right)+A2\left(2\right)e^{-\mathrm{j\&omega;}}+2\left(3\right)e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="A02116443.600091.png,A02116443.600131.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&omega;}}+\&hellip;+A2\left(25\right)e^{-j24\mathrm{\&omega;}}}$ Concrete coefficient is as follows:

B2＝[0.0261621603509115，0，0，0，0，0，0，0，-0.460053043476611，0，0，0，0，0，0，0，

1.3370805244134，0，0，0，0，0，0，0，-1]

A2＝[1，0，0，0，0，0，0，0，-1.3370805244134，0，0，0，0，0，0，0，0.460053043476611，0，0，0，

0，0，0，0，-0.0261621603509115]

According to the digital filtering design theory as can be known, digital filtering F2 also is a cause and effect, can realize.And further analyze as can be known that this Filtering Processing is stable.H _F2(e ^{J ω}) amplitude versus frequency characte as shown in Figure 4.As can be seen from the figure, in frequency band 50～900Hz scope of being concerned about, 20log|H is arranged basically _F1(e ^{J ω}) |=0dB, promptly | H _F2(e ^{J ω}) |=1.

Further analyze

Characteristic, its amplitude versus frequency characte in 0～4000Hz scope and phase-frequency characteristic family curve are respectively as Fig. 5, shown in Figure 6.It is amplified in the 0～1000Hz frequency band range that comprises first-harmonic and 2～M subharmonic,

Amplitude versus frequency characte and phase-frequency characteristic respectively as Fig. 7, shown in Figure 8.In frequency band 40～960Hz scope, Amplitude versus frequency characte extremely be close to 0dB, promptly the passband gain characteristic is 1; And in frequency band 40～960Hz scope, Phase-frequency characteristic be about 90 °.So two groups of digital filter system F1 and F2 are satisfied substantially in 40～960Hz scope: $\frac{H_{F2}\left(e^{\mathrm{j\&omega;}}\right)}{H_{F1}\left(e^{\mathrm{j\&omega;}}\right)}=j$

If amplitude is 1, frequency is sinusoidal fundamental wave signal x (t)=sin (2 π * 50 * t) (volt) of 50Hz, through after the sampling of 8000Hz, handle through the F1 digital filtering again and obtain output signal y1, processing obtains output signal y2 through the F2 digital filtering, and then the actual waveform curve of x, y1 in the 100th to 150 sampled point scope and y2 as shown in Figure 9.As can be seen from the figure, 90 ° of just in time leading y1 signals of y2 signal on phase relation.

3. above-mentioned the 2nd signal u ' that obtains of step (n) and i ' (n) multiply each other, obtain signal q (n).

4. the signal q (n) that above-mentioned the 3rd step is obtained obtains its flip-flop by DC filtering, and the gained result is the reactive power Q (n) that will measure.Because sample frequency is F _S=8000Hz, corresponding 160 sampled points of the primitive period of power frequency 50Hz are so can adopt following average treatment to carry out DC filtering.Promptly $Q\left(n\right)=\frac{1}{160}\underset{i=n-159}{\overset{n}{\mathrm{\&Sigma;}}}q\left(i\right)$

The embodiment of the wattless power measurement that utilization obtains based on step of the present invention handles comprising shown in Figure 10 form a pair of voltage and current signal of harmonic components.In the harmonic components table shown in Figure 10 explanation this voltage and current signal is comprised the harmonic components of first-harmonic and 2～18 times, and provided the voltage effective value U of first-harmonic and each harmonic components correspondence _k(volt), current effective value I _k(peace), the phase angle of the leading harmonic current of harmonic voltage _k(degree).And the following formula of foundation:

Q _k=U _kI _kSin _kK=1,2 ..., 18 have provided the reactive power Q of first-harmonic and each harmonic composition correspondence _k(lacking).The reactive power of first-harmonic generation and the reactive power of each harmonic generation are carried out total reactive power that addition obtains For-0.54236 weary.

After the embodiment system with this a pair of voltage and current signal input wattless power measurement of the present invention, the total reactive power Q that measures ' for-0.54249 weary.

According to following relative error computing method:

The reactive power data Q ' that the inventive method obtains has only 0.23 ‰ with the relative error of actual reactive power summation Q.As seen measured value and actual value are very approaching.

Claims (1)

1, a kind of reactive power measuring method based on digital filtering is characterized in that this method comprises the steps:

(1) a pair of analog voltage signal u (t) and the analog current signal i (t) that are used to measure reactive power to recording from electrical network, carry out analog to digital conversion by identical fixed sampling frequency respectively, digital voltage signal u (n) that obtains dispersing and digital current signal i (n), the sample frequency of choosing is more than the twice of the highest M subfrequency be concerned about of measurement, and satisfies the requirement of computational accuracy;

(2) with above-mentioned the 1st digital voltage signal u (n) that obtains of step through first group of digital phase shift filtering F1 after, obtain signal u ' (n), the digital current signal i (n) that above-mentioned the 1st step is obtained through second group of digital phase shift filtering F2 after, obtain signal i ' (n); The frequency domain transport property of above-mentioned two groups of digital phase shift filtering F1 and F2 is used H respectively _F1(e ^{J ω}) and H _F2(e ^{J ω}) expression, then at the frequency band (ω that comprises first-harmonic and 2～M subharmonic ₁, ω ₂) in, the frequency domain transport property of phase-shift filtering F1 and F2 satisfies following relation:

(3) with above-mentioned the 2nd signal u ' that obtains of step (n) and i ' (n) multiply each other, obtain signal q (n), that is:

q(n)＝u′(n)×i′(n)

(4) the signal q (n) that above-mentioned the 3rd step is obtained passes through DC filtering, obtains its flip-flop Q (n), and Q (n) is exactly the reactive power that needs measurement.

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