CN1953291A - A method to realize high precision universal inverse time-limit protection - Google Patents

Abstract

The invention relates to a relay protective method, especially a relay protector and general reverse-time protection in controller. Wherein, said method comprises: the digit reverse-time protector samples the input value (current) to obtain its instant value; uses special algorism to calculate out the amplitude i of input value; when i is higher than the preset value i<SUB>s</SUB>, starting to accumulate time; calculating out the i/I<SUB>P</SUB> of general reverse-time function t=K<SUB>1</SUB>/(i/I<SUB>P</SUB>)<SUP>B</SUP>-K<SUB>2</SUB, while B and I<SUB>P</SUB>, K<SUB>1</SUB> and K<SUB>2</SUB> can be appointed by user, A= i/I<SUB>P</SUB>, the integer of B is N while decimal is M, calculating out A<SUP>N</SUP>; standardizing the radix number A into 2<SUP>M<SUB>1</SUP></SUB>*C, while M<SUB>1</SUB> is integer, 1<=C<2, calculating out M<SUB>1</SUB> and C, therefore, A<SUP>M</SUP>=2<SUP>M<SUB>1</SUP>M</SUB>*C<SUP>M</SUP>; based on A<SUP>B</SUP>=A<SUP>N</SUP>A<SUP>M</SUP>, calculating out A<SUP>B</SUP> as i/I<SUB>P</SUB>)<SUP>B</SUP>; calculating out the theory operation time t of reverse-time protection; when the accumulated time is higher than t, processing reverse-time protection.

Description

The implementation method of high precision universal inverse time protection

Technical field

The present invention relates to field of power, relate more specifically to the implementation method of relaying protection and controller.

Background technology

At first, according to briefly describing correlation technique of the present invention below with reference to document.

1.IEC 60255-3:1989 " relay. the 3rd part: the measuring relay of single input energizing quantity of on-fixed time limit or definite-time "

Protective device with inverse time lag principle is widely used in electric power system; ubiquitous in the protection of circuit, generator, transformer, capacitor, reactor, motor etc., the over-excitation protection of for example zero-sequence current inverse time protection of transmission line and grounding transformer, generator unit stator overload protection, generator negative phase-sequence overload protection, generator amature overload protection and generator and transformer etc. has all been used the inverse time lag element.

Most inverse time protections have general expression formula, and according to the regulation of the IEC of International Electrotechnical Commission, the expression formula of general anti-time limit characteristic is as follows:

$t=\frac{K_1}{{(i/I_P)}^B-K_2}---\left(1\right)$

Wherein:

T is the inverse time protection theoretical value of operate time;

I is a current measurement value;

I _PBe the fiducial value of electric current, be generally the rated current of protected element;

K ₁Time constant for inverse time protection;

K ₂Be a constant, general relevant with the long-time running permissible value;

B is an index.

The implementation method of existing inverse time protection all can only realize the anti-time limit characteristic of preset parameter, promptly requires the B parameter value in the inverse time lag function to fix, so underaction, can not satisfy the specific requirement of different objects.And mostly being of adopting tabled look-up and linear interpolation method, and the precision of tabling look-up depends on form length and step-length, also needs to determine data to be looked into according to preset parameter in advance, and this just requires extra hardware EEPROM resource to deposit a large amount of list datas.

The implementation method of the general inverse time protection that the present invention proposes does not need extra hardware resource storage list data, does not require that the B parameter value pre-determines, and can adjust according to actual in the different application occasion, has really realized general.This method not only amount of calculation is little, and the precision height: at i/I _PUnder=100 (input current reaches 100 times of fiducial value, and nargin is enough big) situation, (the n implication is seen below) blocks relative error ε when multinomial is got n=10 _r≤ 2.65 * 10 ^-12When getting n=5, relative error ε r≤1.15 * 10 ^-6Even when getting n=3, error ε _r≤ 1.02 * 10 ^-3Promptly be no more than 1.02 ‰.Generally get n=3 and can satisfy the requirement of engineering precision fully.

Summary of the invention

Inverse time protection algorithm in the past all requires the middle B parameter of formula (1) to fix.At B parameter is the situation of counting arbitrarily, the present invention proposes a kind of implementation method of high precision universal inverse time protection.This method comprises the steps:

A. sampling obtains the instantaneous value of input variable, calculates the amplitude i of input variable by fourier algorithm to input variable (being the magnitude of current generally speaking) in digital inverse time protection; When i greater than a certain predetermined startup value i _sThe time time started accumulation;

B. computer general inverse time lag function $t=\frac{K_1}{{(i/I_P)}^B-K_2}$ I/I in the denominator _P, wherein B and I _P, K ₁And K ₂Specify arbitrarily according to the needs of application scenario by the user, and make A=i/I _P

C. calculate the A in the denominator ^B

D. with A ^BI.e. (i/I _P) ^BSubstitution $t=\frac{K_1}{{(i/I_P)}^B-{\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="A20061014556800101.png"\; state="\{\{state\}\}">K</figure-callout>}}_2}$ Calculate theoretical operate time of the t of inverse time protection;

E. inverse time protection action when the time is accumulated greater than theory t operate time.

Step c of the present invention further comprises:

● ask integer part N and the fractional part M of index B;

● ask A ^N=A * A * ... * A, promptly N A even takes advantage of;

● A is normalized into the truth of a matter $A=2^{{\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="A20061014556800101.png"\; state="\{\{state\}\}">M</figure-callout>}}_1}\&times;C$ Form (M wherein ₁Be integer, 1≤C＜2), ask for M ₁With the value of C, then $A^M=2^{M_{1}M}\&times;C^M;$

● wherein 2 ^M1MCalculate according to following formula;

$2^{M_{1}M}=2^{4\&times;\frac{M_1\mathrm{<figure-callout\; id="4"\; label="M"\; filenames="A20061014556800101.png"\; state="\{\{state\}\}">M</figure-callout>}}{4}}=[{\left(2^{\frac{M}{4}}\right)}^4{]}^{{\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="A20061014556800101.png"\; state="\{\{state\}\}">M</figure-callout>}}_1}=[{\left({\mathrm{<figure-callout\; id="4"\; label="e\; M"\; filenames="A20061014556800101.png"\; state="\{\{state\}\}">e</figure-callout>}}^{\frac{M}{}}\right)}^4{]}^{{\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="A20061014556800101.png"\; state="\{\{state\}\}">M</figure-callout>}}_1}$

$e^x=1+x+\frac{1}{2!}{x}^2+\frac{1}{3!}{x}^3+\&hellip;\&hellip;+\frac{1}{n!}{x}^n+\&hellip;\&hellip;$

● C wherein ^MCalculate according to following four formula;

$C^M={(\frac{m+7}{8}+C_1)}^M=[\frac{m+7}{8}(1+\frac{8}{m+7}{C}_1){]}^M={\left(\frac{m+7}{8}\right)}^M{(1+\frac{8}{m+7}{C}_1)}^M$

${\left(\frac{m+7}{8}\right)}^M={\left(\frac{m+7}{8}\right)}^{4\&times;\frac{\mathrm{<figure-callout\; id="4"\; label="M"\; filenames="A20061014556800101.png"\; state="\{\{state\}\}">M</figure-callout>}}{4}}={\left({\mathrm{<figure-callout\; id="4"\; label="e\; M"\; filenames="A20061014556800101.png"\; state="\{\{state\}\}">e</figure-callout>}}^{\frac{M}{}}\right)}^4$

$e^x=1+x+\frac{1}{2!}{x}^2+\frac{1}{3!}{x}^3+\&hellip;\&hellip;+\frac{1}{n!}{x}^n+\&hellip;\&hellip;$

${(1+x)}^r=-+\mathrm{rx}\frac{r(r-1)}{2!}{x}^2+\frac{r(r-1)(r-2)}{3!}{x}^3+\&hellip;\&hellip;+\frac{r(r-1)\&hellip;\&hellip;(r-n+1)}{n!}{x}^n+\&hellip;\&hellip;$

● according to A ^B=A ^NA ^MAsk A ^B

Method of the present invention is by the low computational effort of special algorithm, limited number of time; just realized the high precision universal inverse time protection, do not required that each parameter fixes, can set flexibly; and have that not need eeprom chip to deposit list data, precision height, amount of calculation little, consuming time few, the advantage of fast convergence rate.

Description of drawings

Fig. 1 has shown the algorithm flow chart of high precision universal inverse time protection.

Specific embodiments

Use a large amount of dissimilar inverse time protections in the electric power system, according to the regulation of the IEC of International Electrotechnical Commission, the expression formula of general anti-time limit characteristic is seen formula (1).Under different application scenarios, because the difference of index B in the formula (1), the characteristic of inverse time lag has nothing in common with each other.Inverse time protection algorithm in the past all requires the middle B parameter of formula (1) to fix.Now, the present invention proposes a kind of implementation method of high precision universal inverse time protection at B parameter arbitrarily.

Method of the present invention comprises the steps:

Sampling obtains the instantaneous value of input variable, calculates the amplitude i of input variable by fourier algorithm to input variable (being the magnitude of current generally speaking) in digital inverse time protection; When i greater than a certain predetermined startup value i _sThe time time started accumulation, decision logic is seen Fig. 1.

Make A=i/I _P, calculate A as follows ^B

Can get function f (x)=(1+x) according to Taylor's mean value theorem ^r, and f (x)=e ^xThe Maclaurin expansion on n rank:

${(1+x)}^r=1+\mathrm{rx}+\frac{r(r-1)}{2!}{x}^2+\frac{r(r-1)(r-2)}{3!}{x}^3+\&hellip;\&hellip;+\frac{r(r-1)\&hellip;\&hellip;(r-n+1)}{n!}{x}^n+\&hellip;\&hellip;---\left(2\right)$

$e^x=1+x+\frac{1}{2!}{x}^2+\frac{1}{3!}{x}^3+\&hellip;\&hellip;+\frac{1}{n!}{x}^n+\&hellip;\&hellip;---\left(3\right)$

For improving computational accuracy to greatest extent, reducing amount of calculation, directly will not ask A ^B=[1+ (A-1)] ^BSubstitution formula (2) is calculated, but adopts following method.

1.. press shown in Fig. 1 (1) part, ask N and M, ask only .A ^N:

Ask for A ^BInteger part N and the fractional part M of middle index B, wherein 0≤M＜1.

Because Gu=N+M, then A ^B=A ^N+M=A ^NA ^M

Calculate A ^N: be easy to realize that N A even takes advantage of and get final product.

2.. press shown in Fig. 1 (2) part, ask M ₁And C:

With A ^BIn truth of a matter A be normalized into $A=2^{{\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="A20061014556800101.png"\; state="\{\{state\}\}">M</figure-callout>}}_1}\&times;C$ Form (M wherein _lBe integer, 1≤c＜2), ask for M ₁Value with C.As A=4.2, specification turns to A=2 ²* 1.05, then corresponding M ₁=2, c=1.05.The normalization back:

$A^M={(2^{{\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="A20061014556800101.png"\; state="\{\{state\}\}">M</figure-callout>}}_1}\&times;C)}^M=2^{M_{1}M}\&times;C^M---\left(4\right)$

3.. press shown in Fig. 1 (3) part, ask 2 in the formula (4) ^M1M:

To 2 ^M1MDo to calculate as through type behind the down conversion (3).

$2^{M_{1}M}=2^{4\&times;\frac{M_{1}M}{4}}[{\left(2^{\frac{M}{4}}\right)}^4{]}^{{\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="A20061014556800101.png"\; state="\{\{state\}\}">M</figure-callout>}}_1}=[{\left({\mathrm{<figure-callout\; id="4"\; label="e\; M"\; filenames="A20061014556800101.png"\; state="\{\{state\}\}">e</figure-callout>}}^{\frac{M}{}}\right)}^4{]}^{M_1}---\left(5\right)$

Following formula is with index M ₁* M dwindles 4 times earlier, is in order to incite somebody to action $e^{\frac{M}{}}$ ${\frac{}{4}\mathrm{In}2}^{}$ The e of substitution formula (3) ^xMake x approach zero during calculating, accelerate convergence rate, reduce truncated error.Use in the formula ${\left[{\left({\mathrm{<figure-callout\; id="4"\; label="e\; M"\; filenames="A20061014556800101.png"\; state="\{\{state\}\}">e</figure-callout>}}^{\frac{M}{}}\right)}^4\right]}^{{\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="A20061014556800101.png"\; state="\{\{state\}\}">M</figure-callout>}}_1}$ But not ${\left({\mathrm{<figure-callout\; id="4"\; label="e\; M"\; filenames="A20061014556800101.png"\; state="\{\{state\}\}">e</figure-callout>}}^{\frac{M}{}}\right)}^{4M_1}$ (M wherein ₁Be integer), be in order to reduce the multiplying number of times: the former is M ₁+ 1 time, the latter is 4 * M ₁-1 time.

4.. press shown in Fig. 1 (4) part, ask C ₁And m, ask C ^MA factor ${(1+\frac{8}{m+7}{C}_1)}^M:$

In the formula (4) span of C be C ∈ [1,2).By change step 0.125 will [1,2) scope is divided into eight sections, C ^MOn every section [1+ (m-1) * 0.125]≤C＜(1+m * 0.125), have:

$C^M={(\frac{m+7}{8}+C_1)}^M=[\frac{m+7}{8}(1+\frac{8}{m+7}{C}_1){]}^M={\left(\frac{m+7}{8}\right)}^M{(1+\frac{8}{m+7}{C}_1)}^M---\left(6\right)$

Integer m=1～8,0≤C in the formula ₁＜0.125. ${(1+\frac{8}{m+7}{C}_1)}^M$ Through type (2) is tried to achieve.

Step-length is got 0.125 reason: because of 0≤C ₁＜0.125 approaches zero, $\frac{8}{M+7}{\mathrm{<figure-callout\; id="1"\; label="C"\; filenames="A20061014556800101.png"\; state="\{\{state\}\}">C</figure-callout>}}_1$ More approach zero, so have very little error when calculating with formula (2).Divide multistage calculating to avoid repeatedly iteration, approached zero process one by one, significantly reduced amount of calculation and computing time.

5.. press shown in Fig. 1 (5) part, ask in the formula (6) ${\left(\frac{m+7}{8}\right)}^M,$ Be C ^MAnother factor:

Right ${\left(\frac{m+7}{8}\right)}^M$ Do to calculate as through type behind the down conversion (3).Following formula dwindles 4 times to index M earlier, also is in order to incite somebody to action $e^{\frac{M}{}}$ ${\frac{}{4}\ln \frac{m+7}{8}}^{}$ The e of substitution formula (3) ^xMake x approach zero during calculating, convergence reduces error fast.

${\left(\frac{m+7}{8}\right)}^M={\left(\frac{m+7}{8}\right)}^{4\&times;\frac{\mathrm{<figure-callout\; id="4"\; label="M"\; filenames="A20061014556800101.png"\; state="\{\{state\}\}">M</figure-callout>}}{4}}={\left({\mathrm{<figure-callout\; id="4"\; label="e\; M"\; filenames="A20061014556800101.png"\; state="\{\{state\}\}">e</figure-callout>}}^{\frac{M}{}}\right)}^4---\left(7\right)$

6.. press shown in Fig. 1 (6) part, ask C according to formula (6) ^M, ask A according to formula (4) ^M, again according to A ^B=A ^NA ^MAsk A ^B

With what in 4., calculated ${(1+\frac{8}{m+7}{C}_1)}^M$ Value, in 5., calculated ${\left(\frac{m+7}{8}\right)}^M$ Value substitution formula (6) can be obtained C ^M

Again with C ^MIn 3., calculated 2 ^M1MSubstitution formula (4) can be obtained A ^M

Again according to A ^B=A ^NA ^MThereby, can ask A ^BI.e. (i/I _P) ^B

Then, by logic shown in Figure 1, with (i/I _P) ^BSubstitution formula (1) is calculated theoretical operate time of the t of inverse time protection, B and I in the formula (1) _P, K ₁And K ₂Specify arbitrarily according to the needs of application scenario by the user.Inverse time protection action when the time is accumulated greater than theory t operate time.

The computational accuracy of this algorithm is very high, and the value of n and x is relevant in its computational accuracy and formula (2) and the formula (3): x approaches zero more, n is big more, and then error is more little.In the algorithm of the present invention, try hard to make the x of two formulas in the substitution to be in close proximity to zero, fast convergence rate so not only, and under the situation that does not increase n value (polynomial item number), can reach very high computational accuracy.

At i/I _PUnder=100 (input current reaches 100 times of fiducial value, nargin enough big) situation, by analysis, when getting different numerical value, several n block relative error such as following table:

Relative error when table 1 n gets different value

	?n＝2	?n＝3	?n＝4	?n＝5
					Relative error ε r	?≤2.36×10 -2Promptly 2.36%	?≤1.02×10 -3Promptly 1.02 ‰	?≤3.60×10 -5	?≤1.15×10 -6
	?n＝6	?n＝8	?n＝10
					Relative error ε r	?≤4.12×10 -8	?≤2.17×10 -10	?≤2.65×10 -12

As seen the precision of this algorithm is very high, even the n value is very little, error is also very little, also is no more than 2.36% such as the relative error when the n=2, and the relative error during n=3 is no more than 1.02 ‰, can satisfy the requirement of engineering precision.This is because when algorithm for design, and the conversion process through special makes that the x numerical value of each substitution formula (2) and formula (3) is all very little, approaches very much zero.

Can realize the high precision universal inverse time protection by above method, this method has the precision height, amount of calculation is little, consuming time few, does not have repeatedly the characteristics of iteration.

Claims (2)

1. the implementation method of a high precision universal inverse time protection, this method comprises the steps:

A. sampling obtains the instantaneous value of input variable, calculates the amplitude i of input variable by fourier algorithm to input variable (being the magnitude of current generally speaking) in digital inverse time protection; When i greater than a certain predetermined startup value i _sThe time time started accumulation:

B. computer general inverse time lag function $t=\frac{K_1}{{(i/I_P)}^B-K_2}$ I/I in the denominator _P, wherein:

T is the inverse time protection theoretical value of operate time;

I is a current measurement value;

I _PBe the fiducial value of electric current, be generally the rated current of protected element;

K ₁, be the time constant of inverse time protection;

K ₂Be a constant, general relevant with the long-time running permissible value;

B is an index,

Wherein B and I _P, K ₁And K ₂Specify arbitrarily according to the needs of application scenario by the user, and order ends A=i/I _P

C. calculate the A in the denominator ^B

D. with A ^BI.e. (i/I _P) ^BSubstitution $t=\frac{K_1}{{(i/I_P)}^B-K_2}$ Calculate theoretical operate time of the t of inverse time protection;

E. inverse time protection action when the time is accumulated greater than theory t operate time.

2. according to the process of claim 1 wherein that step c further comprises:

Ask the integer part N and the fractional part M of index cutter;

Ask only A ^N=A * A * ... * A, promptly N A even takes advantage of;

A is normalized into the truth of a matter $A=2^{M_1}\&times;C$ Form, wherein M ₁Be integer, M is asked in 1≤C＜2 ₁With the value of C, then $A^M=2^{M_{1}M}\&times;C^M;$

Wherein 2 ^M1MCalculate according to following formula;

$2^{M_{1}M}=2^{4\&times;\frac{M_{1}M}{4}}=[{\left(2^{\frac{M}{4}}\right)}^4{]}^{M_1}=[{\left(e^{\frac{M}{4}\ln 2}\right)}^4{]}^{M_1}$

$e^x=1+x+\frac{1}{2!}{x}^2+\frac{1}{3!}{x}^3+\&hellip;\&hellip;\frac{1}{n!}{x}^n+\&hellip;\&hellip;$

C wherein ^MCalculate according to following four formula;

$\begin{array}{c}{C}^M={(\frac{m+7}{8}+C_1)}^M=[\frac{m+7}{8}(1+\frac{8}{m+7}{C}_1){]}^M={\left(\frac{m+7}{8}\right)}^M{(1+\frac{8}{m+7}{C}_1)}^M\\ {\left(\frac{m+7}{8}\right)}^M={\left(\frac{m+7}{8}\right)}^{4\&times;\frac{M}{4}}={\left(e^{\frac{M}{4}\ln \frac{m+7}{8}}\right)}^4\end{array}$

$e^x=1+x+\frac{1}{2!}{x}^2+\frac{1}{3!}{x}^3+\&hellip;\&hellip;+\frac{1}{n!}{x}^n+\&hellip;\&hellip;$

${(1+x)}^r=1+\mathrm{rx}+\frac{r(r-1)}{2!}{x}^2+\frac{r(r-1)(r-2)}{3!}{x}^3+\&hellip;\&hellip;+\frac{r(r-1)\&hellip;\&hellip;(r-n+1)}{n!}{x}^n+\&hellip;\&hellip;$

According to A ^B=A ^NA ^MAsk A ^B

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