CN102542170B - Method for acquiring slip frequency difference of electric system - Google Patents

Abstract

A method for acquiring slip frequency difference of an electric system includes steps of firstly building a frequency variation model of the electric system, setting f(t)=f0e<lambda(t-tr)>, wherein f0 is a frequency at a reference time t=tr; sampling voltage signals of the electric system at the same interval Ts to obtain voltage sequence [x(n)]; searching time of crossing the zero points of the voltage signals in the sequence [x(n)], then storing time values corresponding to zero points from negative to positive into the sequence [tp(m)], and storing time values corresponding to zero points from positive to negative into the sequence [tn(m)]; then selecting N+1 data from tp(r) to tp(r+N) in the sequence [tp(m)] including the reference point t=tr and N data from tn(r) to tn(r+N-1) in the sequence [tn(m)], estimating an instant frequency fr+k, and building linear regression of N point two-dimension sequence to obtain parameters k and b, then acquiring parameters of a frequency model k=lambda, f0=e<b>, and finally acquiring differential at the time of t=tx of the frequency model, namely acquiring the slip frequency difference.

Description

A kind of method obtaining power system frequency slippage

One, technical field

The invention belongs to digital signal processing and field of electric power automation, be used for calculating power system frequency slippage.The present invention is applicable in higher UFLS, frequency urgent control device and the frequency recorder to slippage computational accuracy and requirement of real-time, and other utilize frequency slip frequency to realize the application scenario of locking or acceleration.

Two, background technology

Frequency slip frequency df/dt is defined as the pace of change of frequency, after referring to that network re-active power balance is destroyed, and the pace of change of system frequency.In the dynamic process of system power rebalancing, df/dt is constantly change.The function end of df/dt in frequency urgent control device gets up to have two: one to be accelerate function, namely when electric system active power vacancy (or superfluous) is larger, accelerate cutting load (or unit), the significantly change of blanketing frequency, prevents frequency stabilization malicious event as early as possible; Two is blocking functions, mainly in order to prevent the error action of device that may cause due to the abnormal condition such as system short-circuit, feedback loading from doing.Due to power system requirements rapid-action characteristic, therefore the calculating of slippage will be quick and precisely.When slippage is measured, it is generally acknowledged that frequency decrease is linear, then slippage is also constant relatively, and theoretical analysis and on-the-spot actual measurement ^{[6] [7] [8]}all show that the frequency of electric system exponentially changes, in starting stage of frequency departure normal value close to linear, but along with the decline of frequency, non-linear more and more obvious in the second half section, cause measuring error to strengthen.

The more method of current use is that hypothesis df/dt is linear among a small circle and frequency remains unchanged within a signal period, and conventional method mainly comprises following a few class:

1. the set time measures frequency-difference method

This method is in each period measurement frequency f of sinusoidal signal _n(n=0,1,2 ...), get the difference of the frequency being spaced apart 5 times as frequency departure, set the time interval as 100ms, then frequency slip frequency is calculated as simultaneously: df/dt=10 (f _n+5-f _n)

2. accumulated time measures frequency-difference method

If frequency is from initial value f ₁stop value f is changed to the speed change of df/dt=k _ntime, add up to need time t, then k=(f _n-f ₁)/t.This method ^[3]use the rising edge of hardware timer lock-on signal, the time of continuous two rising edges is got inverse and obtains frequency f _i(=1/T _i), obtain time t by accumulative multiple signal period, then calculated rate slippage.

Five cycles of above-mentioned first method supposition sinusoidal signal be spaced apart 100mS, and frequency departure 50hz more multiple error is larger.Second method, to this has been improvement, uses the time interval measurement between a hardware timer tracer signal zero crossing, eliminates the accumulated time error of first method, but need extra hardware supported.Above two kinds of methods all suppose that frequency is linear change, and during electric system emergent power vacancy accident, frequency is mainly by (may go back superposition and the little periodic component of some amplitudes) that exponential rule declines ^[7], due to system inertia after UFLS action, frequency can exponentially rise again.The incipient stage of frequency change is very linearly close, but along with time growth, non-linear meeting is more and more obvious, cannot ensure accuracy of measurement.Causing said method to measure inaccurate Another reason is that these algorithms all suppose that system frequency only just changes once when signal zero crossing ^{[1] [2]}(namely frequency meets " cycle increases progressively (subtracting) restrains "), and real system frequency is continually varying, the observational error of instantaneous frequency also will make whole frequency slip frequency measuring error strengthen.

List of references

1. development Scientific and Technological Institutes Of Zhejiang journal in the June, 2003 of the digital am phase modulation voltage source of Pan Wen really with df/dt frequency slip frequency function

2. meter Zeng Qiang electric system low-frequency low-voltage load shedding device to test research North China Electric Power University's journal in October, 1998 is built in field

3. the same frequency collection based on DSP of Liu state and slippage calculate engineering and build in August, 2009

4. witch Ke Lixing source Li Qing rues a kind of design Sichuan Electric Power technology in April, 2009 of adaptive UFLS scheme

5. easy imperial strong basis is in the digital sinusoidal signal frequency measurement algorithm electrical measurement of one-variable linear regression theory and instrument the 3rd phase in 2011

6. the Qin become clear Yang Xiuchao expand in frequency urgent control device df/dt application discussion electric power network technique in June, 1998

7. Yang Guan city Power System Automation Equipment principle. Beijing: hydraulic and electric engineering publishing house, 1986.

8. the loyal Wang Bo of Meng Xiang edits Automation of Electric Systems China Forestry Publishing House August in 2006 the 1st edition.

Three, summary of the invention

The object of the invention is the methods and applications proposing a kind of accurate calculating power system frequency slippage, by quick and precisely calculating instantaneous frequency and frequency slip frequency, be applicable in higher UFLS, frequency urgent control device and the frequency recorder to slippage computational accuracy and requirement of real-time, and other utilize frequency slip frequency to realize the application scenario of locking or acceleration.

The present invention is realized by such scheme:

(1). first set up power system frequency variation model wherein f ₀for reference time t=t _rplace's frequency;

(2). by power system voltage signal with T _scarry out equal interval sampling, obtain voltage signal sampling sequence { x (n) } _;

(3). find by zero passage detection and method of interpolation the moment that in sequence { x (n) }, voltage over zero occurs, and put into sequence { t by by the time value (hereinafter referred to as positive zero point) born corresponding to zero point of just changing _p(m) } (following adopt positive xero-sequence as the time reference sequence of algorithm), by just to the time value (hereinafter referred to as negative zero point) corresponding to the negative zero point changed then stored in sequence { t _n(m) };

(4). selected positive xero-sequence { t _p(m) } in comprise reference point t=t _rinterior from t _pr () is to t _p(r+N) N+1 data and negative zero point sequence { t _n(m) } in from t _nr () is to t _n(r+N-1) N number of data, estimation t _p(r+k) the instantaneous frequency f in moment _r+k

$f_{r+k}=0.5(T_n^2-T_p^2+2T_p{T}_n)/T_p{T}_n(T_p+T_n),k=\mathrm{0,1},...N-1$

Wherein: T _p=t _n(r+k)-t _p(r+k), T _n=t _p(r+k+1)-t _n(r+k)

And build N point two-dimensional sequence according to the instantaneous frequency estimated and observation moment

{＜t _p(k+r)-t _p(r),lnf _r+k＞} (k＝0,1,...N-1)；

(5). to two-dimensional sequence { < t _p(k+r)-t _p(r), lnf _r+k> } by y=b+ λ (t-t _r) carry out simple regression, obtain parameter lambda and f ₀;

$\mathrm{\&lambda;}=\frac{\underset{k=1}{\overset{N}{\mathrm{\&Sigma;}}}(X_k-\stackrel{\&OverBar;}{X})(Y_k-\stackrel{\&OverBar;}{Y})}{\underset{k=1}{\overset{N}{\mathrm{\&Sigma;}}}{(X_k-\stackrel{\&OverBar;}{X})}^2},b=\stackrel{\&OverBar;}{y}-\mathrm{\&lambda;}\stackrel{\&OverBar;}{x},f_0=e^b$

Wherein: X _k=t _p(k+r)-t _p(r), Y _k=lnf _k+r, k=0,1 ... N-1

$\stackrel{\&OverBar;}{y}=\frac{1}{N}\underset{k=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{Y}_k,\stackrel{\&OverBar;}{X}=\frac{(t_p(N+r)-t_p\left(r\right))}{N}$

(6). to frequency model get differential and can obtain system at moment t=t _xfrequency slip frequency $\frac{\mathrm{df}}{\mathrm{dt}}{|}_{t=t_x}=\mathrm{\&lambda;}{f}_0{e}^{\mathrm{\&lambda;}(t_x-t_r)};$

The method above of utilization can also pick out two different system instantaneous frequency models, and then the frequency draft calculated between two systems and frequency draft acceleration, provides the prediction of more accurate switching angle for set grid-connection with for synchronizing close.

The application of the inventive method in electric system UFLS, frequency urgent control device and frequency recorder.

Beneficial effect of the present invention:

1. adopt simple regression estimated frequency model parameter, always utilize the observation moment information of N number of observation station, noise inhibiting ability is good, can change by adaptive system;

The temporal information of 2.N observation station, need not additional hardware loop by searching for zero point and interpolation generation;

3. the instantaneous frequency of observation station is estimated by short-run model and obtains, and method is closer to actual value than ever;

4. adopt exponential model as system frequency variation model, obtain model parameter by linear regression, calculate simple

5. overcome the shortcoming that the error of fitting of the slippage measurement of linear frequency model when system low frequency is in the past large;

6. final frequency is provided by the exponential model estimated, and can draw system instantaneous frequency.

Four, accompanying drawing explanation

Frequency change period observation schematic diagram when Fig. 1 is system emergent power vacancy.

Fig. 2 is that system voltage signal zero detects schematic diagram.

Five, specific implementation

1. frequency model builds

Research shows that electric system is an inertia system, and the frequency jitter that load variations will cause, exponentially changes ^{[7] [8]}(as accompanying drawing 1), is approximately in each smaller time period frequency change trend:

wherein f ₀for reference time t=t _rfrequency lambda--system inertia (1) frequency slip frequency is then expressed as at place:

$\frac{\mathrm{df}}{\mathrm{dt}}=f_0\&CenterDot;{\mathrm{\&lambda;e}}^{\mathrm{\&lambda;}(t_x-t_r)}---\left(2\right)$

Get natural logarithm to formula 1 both sides to have:

lnf(t)＝lnf ₀+λ(t-t _r) (3)

Make y (t)=lnf (t), b=lnf ₀, x=t-t _r, the linear model of a frequency change can be obtained

y＝b+λ(t-t _r) (4)

2. zero crossing search

The acquisition frequency slip frequency method that the present invention provides is that concrete steps are as follows by carrying out search at zero point to { x (n) } and linear interpolation obtains the exact time at each zero point of signal:

(1). search sequence { x (n) }, if x (n) is different with the symbol of x (n+1), then at sampling instant t _nand t _n+1between there is the accurate location that zero crossing went to step for 2 calculating zero points, otherwise continue the next sampling point data of search; (2). the moment t of current zero crossing is obtained on a timeline by Lagrange's interpolation _i(t _n≤ t _i≤ t _n+1);

T _i=t _n-x _n[(t _n+1-t _n)/(x _n+1-x _n)]=[n-x _n/ (x _n+1-x _n)] T _swherein T _s-sampling interval (3) if. x (n)≤0 and x (n+1) > 0, then current zero point is positive zero point, by moment t _ibe recorded to sequence { t _p(m) }, otherwise be recorded to negative zero point sequence { t _n(m) };

(4). go to step 1 and carry out new search at zero point.

3. the reference time is chosen

The data length N determining to participate in returning was needed before determining time reference.If need to calculate t _xthe system frequency slippage in moment, by positive xero-sequence { t _p(m) } in find and to satisfy condition t _p(i) < t _x< t _p(i+1) point, then recursion N-1 point forward, make r=i-N+1, then moment t _r(=t _p(r)) correspond to the reference point needing to find.

4. the estimation of instantaneous frequency

As the phase angle of voltage signal (t in as accompanying drawing 2 in [0,2 π] during change _r-1to t _r), according to formula 1, can think that frequency linearly changes among a small circle.For accompanying drawing 2, if the time that signal is greater than 0 is T _p, the time being less than 0 is T _n, at t _r-1to t _rin time, frequency is from frequency f _st(corresponding moment t _r-1) meet Equation f (t)=f with slope α consecutive variations _st+ α t, again because voltage signal is at T _pand T _ntime period internal phase angle change is identical is π, then have following system of equations:

$\left\{\begin{array}{c}{\&Integral;}_0^{T_p}2\mathrm{\&pi;}(f_{\mathrm{st}}+\mathrm{\&alpha;t})\mathrm{dt}=\mathrm{\&pi;}\\ {\&Integral;}_0^{T_p+T_n}=2\mathrm{\&pi;}(f_{\mathrm{st}}+\mathrm{\&alpha;t})\mathrm{dt}=2\mathrm{\&pi;}\end{array}\right.---\left(6\right)$

Separate above-mentioned system of equations to have

$\mathrm{\&alpha;}=\frac{(T_p-T_n)}{T_p{T}_n(T_p+T_n)}---\left(7\right)$

$f_{\mathrm{st}}=0.5\frac{T_n^2-T_p^2+2T_p{T}_n}{T_p{T}_n(T_p+T_n)}---\left(8\right)$

According to formula 8, if must T be had when system frequency is stablized constant _p=T _n, then frequency f _stcalculation expression can abbreviation as follows:

f _st＝1/(T _p+T _n)＝1/(t _r-t _r-1) (9)

The instantaneous frequency f at place at each positive zero point can be estimated with said method _r+k(t _rfor reference zero, k=0,1...N-1).

5. Recursive sequence builds

At positive xero-sequence { t _p(m) } in t _rfor the time reference of model, choose data t _p(r), t _p(r+1) ..., t _p(r+N-1) two-dimensional sequence { <X is built _k, Y _k>}, wherein X _k=t _p(k+r)-t _p(r), Y _k=lnf _k+r(k=0,1...N-1).

To this sequence { <X _k, Y _k>} does the linear regression of N point by the model that formula 4 defines, and obtains parameter b and λ is as follows,

$\mathrm{\&lambda;}=\frac{\underset{k=1}{\overset{N}{\mathrm{\&Sigma;}}}(X_k-\stackrel{\&OverBar;}{X})(Y_k-\stackrel{\&OverBar;}{Y})}{\underset{k=1}{\overset{N}{\mathrm{\&Sigma;}}}{(X_k-\stackrel{\&OverBar;}{X})}^2}---\left(10\right)$

$b=\stackrel{\&OverBar;}{y}-\mathrm{\&lambda;}\stackrel{\&OverBar;}{x}---\left(11\right)$

Wherein: $\stackrel{\&OverBar;}{y}=\frac{1}{N}\underset{k=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{Y}_k,\stackrel{\&OverBar;}{X}=\frac{(t_p(N+r)-t_p\left(r\right))}{N}(k=\mathrm{0,1,2}...N-1)$

According to parameter b, obtain the parameter f in the model of formula 1 description ₀=e ^b.

6. frequency and slippage calculate

Calculating frequency model parameter f ₀after λ, moment t should be calculated by formula 1 _xthe system instantaneous frequency values in moment

$f_{\mathrm{sys}}{|}_{t=t_x}=f_0{e}^{\mathrm{\&lambda;}(t_x-t_r)}---\left(12\right)$

Differential is got to formula 12 and can obtain moment t _xthe frequency slip frequency in moment, as shown in the formula:

$\frac{\mathrm{df}}{\mathrm{dt}}{|}_{t=t_x}=\mathrm{\&lambda;}{f}_0{e}^{\mathrm{\&lambda;}(t_x-t_r)}---\left(13\right)$

7. apply

For improving noise inhibiting ability, zero point, detection also can use document ^[5]described simple regression method.According to the feature of sinusoidal signal, sampling rate is higher, and voltage signal is linearly more close at zero crossings, obtains temporal information more accurate when zero point is detected.But sampling rate increase can cause the increase storing increase and calculated amount, and noise and harmonic wave all can affect the zero crossing of signal, so need choose reasonable sampling rate and carry out bandpass filtering to sequence.Participate in returning counting of calculating in theory more, the parameter estimated is more accurate, and operand is also larger simultaneously, and the dynamic response time of algorithm is longer.And the uncertainty of power system load change causes the model parameter in formula 1 not to immobilize, and the calculation requirement of slippage is quick and precisely, gets the parameter estimation that up-to-date 6 groups of observation datas (corresponding N=5) carry out model during actual computation and just can obtain satisfied result.

More than analyze for sake of convenience, the sequence of employing is infinite sequence, and actual algorithm program timing sequence row should adopt fifo queue as the data window of sequence, and ensures the data on correct process data window border.

The UFLS that the method for power system frequency slippage is applied to electric system controls, in frequency urgent control device and frequency record.The Selecting parameter that UFLS controls, frequency urgent control protective device is all prior art of electric system, the inventive method can improve the level of electric power system control and protection greatly.

Claims (5)

1. obtain a method for power system frequency slippage, it is characterized in that step is as follows:

(1) power system frequency variation model is first set up, if wherein f ₀for reference time t=t _rplace's frequency;

(2) pass through power system voltage signal with T _scarry out equal interval sampling, obtain contact potential series { x (n) };

(3) find by zero passage detection and method of interpolation the moment that in sequence { x (n) }, voltage signal zero crossing occurs, and put into sequence { t positive zero point by being called for short by the time value born corresponding to zero point of just changing _p(m) }, below adopt positive xero-sequence as the time reference sequence of algorithm, by being just called for short negative zero point then stored in sequence { t to the time value corresponding to the negative zero point changed _n(m) };

(4) selected positive xero-sequence { t _p(m) } in comprise reference point t=t _rinterior from t _pr () is to t _p(r+N) N+1 data and negative zero point sequence { t _n(m) } in from t _nr () is to t _n(r+N-1) N number of data, estimation t _p(r+k) the instantaneous frequency f in moment _r+k

$f_{r+k}=0.5(T_n^2-T_p^2+2T_p{T}_n)/T_p{T}_n(T_p+T_n),k=\mathrm{0,1},...N$

Wherein: T _p=t _n(r+k)-t _p(r+k), T _n=t _p(r+k+1)-t _n(r+k)

And build N point two-dimensional sequence according to the instantaneous frequency estimated and observation moment

{＜t _p(k+r)-t _p(r),lnf _r+k＞} k＝0,1,...N-1；

(5) to two-dimensional sequence { < t _p(k+r)-t _p(r), lnf _r+k> } by y=b+ λ (t-t _r) carry out simple regression, obtain parameter lambda and f ₀;

$\begin{array}{ccc}\mathrm{\&lambda;}=\frac{\underset{k=1}{\overset{N}{\mathrm{\&Sigma;}}}(X_k-\stackrel{\&OverBar;}{X})(Y_k-\stackrel{\&OverBar;}{Y})}{\underset{k=1}{\overset{N}{\mathrm{\&Sigma;}}}{(X_k-\stackrel{\&OverBar;}{X})}^2}& b=\stackrel{\&OverBar;}{Y}-\mathrm{\&lambda;}\stackrel{\&OverBar;}{X}& f_0=e^b\end{array}$

Wherein: X _k=t _p(k+r)-t _p(r), Y _k=lnf _k+r, k=0,1 ... N-1

$\stackrel{\&OverBar;}{Y}=\frac{1}{N}\underset{k=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{Y}_k,\stackrel{\&OverBar;}{X}=\frac{(t_p(N+r)-t_p\left(r\right))}{N}$

(6) to frequency model get differential and can obtain system at moment t=t _xfrequency slip frequency ${\frac{\mathrm{df}}{\mathrm{dt}}|}_{t=t_x}=\mathrm{\&lambda;}{f}_0{e}^{\mathrm{\&lambda;}(t_x-t_r)}.$

2. the method obtaining power system frequency slippage according to claim 1, is characterized in that: corresponding moment t=t _xthe time reference t of Recursive sequence _rby at the positive xero-sequence { t of voltage signal _p(m) } in find and to satisfy condition t _p(i) < t _x< t _p(i+1) point, then forward recursion N-1 point after obtain t _r=t _p(r), wherein r=i-N+1.

3. the method obtaining power system frequency slippage according to claim 1, is characterized in that: according to returning the frequency model parameter lambda and f that obtain ₀, electric system is at t=t _xthe instantaneous frequency in moment is by formula calculate, and moment t=t _xfrequency slip frequency be calculated as follows:

${\frac{\mathrm{df}}{\mathrm{dt}}|}_{t=t_x}=\mathrm{\&lambda;}{f}_0{e}^{\mathrm{\&lambda;}(t_x-t_r)}.$

4. the method obtaining power system frequency slippage according to claim 1, it is characterized in that getting 6 groups of up-to-date observation datas when calculating, corresponding N=5 carries out parameter estimation; The sequence adopted is infinite sequence, and actual algorithm program timing sequence row should adopt fifo queue as the data window of sequence, and ensures the data on correct process data window border.

5. control at the UFLS of electric system according to the method obtaining power system frequency slippage one of Claims 1-4 Suo Shu, application in frequency urgent control device and frequency record.