CN102608422B - Method for computing alternating current component fundamental amplitude value in microcomputer protection - Google Patents

Abstract

The invention discloses a method for computing alternating current component fundamental amplitude value in microcomputer protection, belonging to the microcomputer protection field of a power system, comprising the steps of obtaining the average value of the fundamental amplitude computed by Fourier series in the alternating current component 1/2 period, and then multiplying a coefficient related to frequency to obtain the actual fundamental amplitude value of the alternating current component. The method solves the problems in the prior art that as the alternating-current component fundamental amplitude value and the actual fundamental amplitude value of the alternating current component have a certain error caused by frequency shift, the more the frequency shift is, the bigger the error is, and the fundamental amplitude value error caused by the frequency shift can influence the protection action behavior of the microcomputer protection part. The method for computing alternating current component fundamental amplitude value in microcomputer protection can accurately compute the actual fundamental amplitude value of the alternating current component in the condition that the alternating current component fundamental frequency is not uniform with the rated frequency of the power system.

Description

The of ac fundamental voltage amplitude computing method used in a kind of Microcomputer Protection

Technical field

The invention belongs to electric system Microcomputer Protection field; relate to the of ac fundamental voltage amplitude computing method used in a kind of Microcomputer Protection, particularly use the fundamental voltage amplitude that calculates of Fourier series to average within of ac 1/2 cycle and be multiplied by one and ask the computing method of the actual fundamental voltage amplitude of of ac with the coefficient of frequency dependence.

Background technology

The general fundamental voltage amplitude using Fourier series to calculate of ac in current Microcomputer Protection.First calculate the coefficient of Fourier series according to the rated frequency of electric system and the sampling rate of device in Microcomputer Protection code and exist in a data form.These coefficients are always constant in the operational process of whole microcomputer protecting device.If the fundamental frequency of of ac and the rated frequency of electric system of input microcomputer protecting device have certain skew, so use these coefficient calculations fundamental voltage amplitude out will have certain error with actual fundamental voltage amplitude.

The first-harmonic composition of of ac can be expressed as x (t)=Msin (2 π ft+2 π fa), and wherein M, f, t, 2 π fa are respectively the fundamental voltage amplitude of of ac, the frequency of of ac, time, the initial phase angle of of ac.The computing formula utilizing Fourier series to ask for its fundamental voltage amplitude is:

$F=\left|2f_0\underset{-1/2f_0}{\overset{1/2f_0}{\∫}}M\sin (2\mathrm{\πft}+2\mathrm{\πfa})e^{-j2\mathrm{\π}{f}_{0}t}\mathrm{dt}\right|---\left(1\right)$

F in formula (1) ₀for the fundamental frequency chosen when calculating Fourier series.Abbreviation formula (1) can obtain:

$F=M|2f_0\sin (\mathrm{\πf}/f_0)/\mathrm{\π}/(f_0^2-f^2)|\sqrt{(f_0^2+f^2)/2+(f_0^2-f^2)/2*\cos \left(4\mathrm{\πfa}\right)}$

(2)

For moment t, the phase angle of of ac x (t) is 2 π ft+2 π fa, and therefore the pass of its fundamental voltage amplitude and time is:

$A(f,t)=M|2f_0\sin (\mathrm{\πf}/f_0)/\mathrm{\π}/(f_0^2-f^2)|\sqrt{(f_0^2+f^2)/2+(f_0^2-f^2)/2*\cos (4\mathrm{\πft}+4\mathrm{\πfa})}---\left(3\right)$

The fundamental voltage amplitude calculated with the ratio of actual fundamental voltage amplitude is:

$A_b(f,t)=A(f,t)/M$

$=|2f_0\sin (\mathrm{\πf}/f_0)/\mathrm{\π}/(f_0^2-f^2)|\sqrt{(f_0^2+f^2)/2+(f_0^2-f^2)/2*\cos (4\mathrm{\πft}+4\mathrm{\πfa})}---\left(4\right)$

As can be seen from formula (3); when the fundamental frequency of of ac and the rated frequency of electric system that input microcomputer protecting device have certain skew time; the fundamental voltage amplitude using Fourier series to calculate is not equal to the fundamental voltage amplitude of of ac reality; but one with the function of of ac frequency and time correlation, the ratio of the fundamental voltage amplitude calculated and actual fundamental voltage amplitude is such as formula shown in (4).

In Microcomputer Protection, some protection operates in very large frequency range, and the fundamental voltage amplitude error caused due to frequency shift (FS) will affect the action behavior of this part protection.

Summary of the invention

In order to the fundamental voltage amplitude solving of ac fundamental voltage amplitude and of ac reality in prior art has certain error; frequency shift (FS) is more; error is larger; and the fundamental voltage amplitude error caused due to frequency shift (FS) will affect the problem of this computer part protection act behavior; the invention provides the of ac fundamental voltage amplitude computing method used in a kind of Microcomputer Protection, can when of ac fundamental frequency and electric system rated frequency inconsistent correctly calculate the fundamental voltage amplitude of of ac reality.

In order to solve the problem, the technical solution used in the present invention is:

The of ac fundamental voltage amplitude computing method used in Microcomputer Protection, comprise the following steps, the fundamental frequency f chosen ₀when use Fourier series to calculate the fundamental voltage amplitude A (f, t) of of ac, t is sampled point; Adopt Frequency Measurement Algorithm to measure the frequency f of of ac, it is characterized in that: further comprising the steps of:

1), coefficient Coe (f) relevant to of ac frequency f is asked for;

1.1) ratio of the fundamental voltage amplitude that calculates of Fourier series and actual fundamental voltage amplitude is in theory:

$A_b(f,t)=|2f_0\sin (\mathrm{\πf}/f_0)/\mathrm{\π}/(f_0^2-f^2)|\sqrt{(f_0^2+f^2)/2+(f_0^2-f^2)/2*\cos (4\mathrm{\πft}+4\mathrm{\πfa})}---\left(5\right)$

Wherein f, t are respectively the frequency of of ac, the time, and 4 π fa+4 π ft are the twice of of ac x (t) at t phase angle, f ₀for the fundamental frequency chosen when calculating Fourier series,

1.2) A is asked for _b(f, t) mean value A within the 1/2f time _bmean(f),

$A_{\mathrm{bmean}}\left(f\right)=2f\underset{t}{\overset{t+1/2f}{\∫}}{A}_b(f,t)---\left(6\right)$

1.3) relevant to of ac frequency f coefficient Coe (f) is A _bmeanthe inverse of (f),

$\mathrm{Coe}\left(f\right)=1/A_{\mathrm{bmean}}\left(f\right)---\left(7\right);$

2) the fundamental voltage amplitude A (f, t), calculated Fourier series averages A within the 1/2f time _mean(f):

$A_{\mathrm{mean}}\left(f\right)=2f\underset{t}{\overset{t+1/2f}{\∫}}A(f,t)---\left(8\right);$

3), step 2) in the A that obtains _mean(f) and step 1.3) in the Coe (f) that obtains be multiplied and namely obtain the fundamental voltage amplitude M of of ac reality:

M＝A _mean(f)/A _bmean(f)＝A _mean(f)*Coe(f)(9)。

The invention has the beneficial effects as follows: by computing method of the present invention, can when of ac fundamental frequency and electric system rated frequency inconsistent correctly calculate the fundamental voltage amplitude of of ac reality.

Embodiment

In microcomputer protective relay device, data acquisition and processing (DAP) is all discrete, and each above-mentioned computation process all uses discrete method to process in protective relaying device.Frequency f and the fundamental voltage amplitude A (f, n) (n is current sampling point) of of ac has been tried to achieve in Microcomputer Protection.Therefore as follows to the computing method of of ac fundamental voltage amplitude in Microcomputer Protection:

1. suppose that the scope of the of ac fundamental frequency processed in Microcomputer Protection is between 5Hz ~ 70Hz; be that interval carry out discretize to frequency with 0.1Hz to this frequency range of 5Hz ~ 70Hz, ask for the Coe (f) at various discrete frequency place in advance and exist inside a data form.I-th data inside data form are the Coe (f) that frequency (5+0.1i) Hz is corresponding, and the computing method for the Coe (f) at each discrete frequency f place are as follows:

1.1) ratio of the fundamental voltage amplitude that calculates of Fourier series and actual fundamental voltage amplitude is in theory:

$A_b(f,t)=|2f_0\sin (\mathrm{\πf}/f_0)/\mathrm{\π}/(f_0^2-f^2)|\sqrt{(f_0^2+f^2)/2+(f_0^2-f^2)/2*\cos (4\mathrm{\πft}+4\mathrm{\πfa})}---\left(10\right)$

Wherein f, t, 4 π fa are respectively the frequency of of ac, time, the initial phase angle of twice of ac, f ₀for the fundamental frequency chosen when calculating Fourier series.

1.2) A is asked for _b(f, t) mean value A within the 1/2f time _bmean(f).

$A_{\mathrm{bmean}}\left(f\right)=2f\underset{t}{\overset{t+1/2f}{\∫}}{A}_b(f,t)---\left(11\right)$

1.3) relevant to of ac frequency f coefficient Coe (f) is A _bmeanthe inverse of (f).

Coe(f)＝1/A _bmean(f) (12)

2. ask for the mean value A of A (f, n) within the 1/2f time _mean(f)

$A_{\mathrm{mean}}\left(f\right)=\frac{1}{N_0}\underset{k=n-N_0+1}{\overset{n}{\mathrm{\Σ}}}A(f,k)---\left(13\right)$

N in formula ₀for the sampling number of Microcomputer Protection within the 1/2f time, n is current sampling point.

3. for the frequency f of of ac, solving equation (5+0.1i)=f obtains i=(f-5) * 10, carries out round obtain i to i ₀, in the form calculated in the 1st step i-th ₀individual data are Coe (f) corresponding to frequency f.

4. step 2) in the A that obtains _mean(f) and step 3) in the Coe (f) that inquires be multiplied and namely obtain the fundamental voltage amplitude M of of ac reality.

More than show and describe ultimate principle of the present invention, principal character and advantage.The technician of the industry should understand; the present invention is not restricted to the described embodiments; what describe in above-described embodiment and instructions just illustrates principle of the present invention; without departing from the spirit and scope of the present invention; the present invention also has various changes and modifications, and these changes and improvements all fall in the claimed scope of the invention.Application claims protection domain is defined by appending claims and equivalent thereof.

Claims (1)

1. the of ac fundamental voltage amplitude computing method used in Microcomputer Protection, comprise the following steps, the fundamental frequency f chosen ₀when use Fourier series to calculate the fundamental voltage amplitude A (f, t) of of ac, t is sampled point; Adopt Frequency Measurement Algorithm to measure the frequency f of of ac, it is characterized in that: further comprising the steps of:

1), coefficient Coe (f) relevant to of ac frequency f is asked for;

1.1) ratio of the fundamental voltage amplitude that calculates of Fourier series and actual fundamental voltage amplitude is in theory:

$A_b(f,t)=|2f_0\sin (\mathrm{\πf}/f_0)/\mathrm{\π}/(f_0^2-f^2)|\sqrt{(f_0^2+f^2)/2+(f_0^2-f^2)/2*\cos (4\mathrm{\πft}+4\mathrm{\πfa})}---\left(5\right)$

Wherein f, t are respectively the frequency of of ac, the time, and 4 π fa+4 π ft are the twice of of ac x (t) at t phase angle, f ₀for the fundamental frequency chosen when calculating Fourier series,

1.2) A is asked for _b(f, t) mean value A within the 1/2f time _bmean(f),

$A_{\mathrm{bmean}}\left(f\right)=2f\underset{t}{\overset{t+1/2f}{\∫}}{A}_b(f,t)---\left(6\right)$

1.3) relevant to of ac frequency f coefficient Coe (f) is A _bmeanthe inverse of (f),

Coe(f)＝1/A _bmean(f) (7)；

2) the fundamental voltage amplitude A (f, t), calculated Fourier series averages A within the 1/2f time _mean(f):

$A_{\mathrm{mean}}\left(f\right)=2f\underset{t}{\overset{t+1/2f}{\∫}}A(f,t)---\left(8\right)$

3), step 2) in the A that obtains _mean(f) and step 1.3) in the Coe (f) that obtains be multiplied and namely obtain the fundamental voltage amplitude M of of ac reality:

M＝A _mean(f)/A _bmean(f)＝A _mean(f)*Coe(f) (9)，

For the frequency f of of ac, solving equation (5+0.1i)=f obtains i=(f-5) * 10, carries out round obtain i to i ₀, in the form that formula (7) calculates i-th ₀individual data are Coe (f) corresponding to frequency f.