CN104699964A - Order determination method of frequency dependence network equivalence applied to simulation of power system - Google Patents

Abstract

The invention relates to an order determination method of frequency dependence network equivalence applied to simulation of a power system and belongs to the technical field of dispatching automation of the power system and simulation of a power grid. The method comprises the following steps: carrying out rough model solution for one time according to the number of peaks of frequency domain sampling values of the frequency dependence network equivalence, converting the modified frequency domain sampling values to a time domain, and determining the order through a Prony analysis method. By adopting the method, the problem that the order is hard to select when the current frequency dependence network equivalence is applied to the simulation of the power system is solved; the method is quick and accurate, and is adjustable in accuracy and excellent in engineering practice effect.

Description

For the exponent number defining method of the frequency dependent network equivalence of electric system simulation

Technical field

The present invention relates to a kind of exponent number defining method of the frequency dependent network equivalence for electric system simulation, belong to dispatching automation of electric power systems and grid simulation technical field.

Background technology

Electric system simulation is one of important method of research electrical power system transient characteristic.According to investigate dynamic process different, electric system simulation can be divided into electromagnetic transient simulation, electromechanical transient simulation and long term dynamics to emulate.Wherein electromagnetic transient simulation precision is the highest, is mainly used in the transient state process studying power system network element Microsecond grade, as thunder and lighting process, wave process and direct-current commutation failure process etc.But high precision take intensive as cost, because calculated amount is too large, electromagnetic transient simulation is not suitable for the emulation being directly used in large-scale electrical power system.Usually for whole Iarge-scale system, retain the network element being concerned about part (referring to the part wishing to understand transient state process in detail), other subnetwork element Equivalent Networks represent, then carry out Electromagnetic Simulation, reach the object reducing calculated amount.

Traditional Equivalent Network adopts promise Equivalent Model of pausing to represent, as shown in Figure 1.Right side square frame is for being concerned about subnetwork; Left side square frame is adopt promise to pause the Equivalent Network of Equivalent Model, namely to pause equal currents I with a promise _abcto pause equivalent bus admittance matrix Y with a promise _abcrepresent the Equivalent Network of other subnetwork elements.

The bus admittance matrix that promise is paused in equivalent circuit is formed under fundamental frequency, therefore can only represent network element fundamental frequency characteristic.In order to more accurately represent network element frequency characteristic at respective frequencies, pull-in frequency network of relation equivalence (Frequency Dependent Network Equivalent, hereinafter referred to as FDNE) represents the Equivalent Network of other subnetwork elements.

Based on the Equivalent Network method of FDNE, as shown in Figure 2.Right side square frame is for being concerned about subnetwork; Left side square frame is Equivalent Network based on FDNE, namely to pause equal currents I with a promise _abcthe Equivalent Network of other parts is used as with a FDNE.

The bus admittance matrix of the essence of FDNE to be one with frequency be function.The mathematical expression that N × N ties up FDNE is:

Wherein, s=j2 π f, f is frequency, and j is imaginary unit, lower same;

Arbitrary element representation in FDNE is a frequency-domain function:

$y\left(s\right)=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\frac{c_i}{s-a_i}+d+\mathrm{sh},$

Wherein, limit { a _iand residual { c _ior are all real numbers, or respectively with complex conjugate to appearance, constant term d and once item h are real number, and n is limit number; These are unknown parameter.In practical application, all elements of FDNE one group of public limit { a _i, therefore the limit number n of each element is all identical, this n is also referred to as the exponent number of FDNE.

After a given exponent number n, limit { a _i, residual { c _i, constant term d and once item h according to the frequency domain sample value of Y (s), can solve by vector fitting method (vector fitting).About exponent number n, have need to illustrate at following 2: 1) exponent number of a suitable FDNE is very important, if exponent number is too low, cannot ensure simulation accuracy, if exponent number is too high, can affect simulation efficiency; 2) there is no the exponent number defining method of a kind of rational FDNE at present, still with the mode determination exponent number soundd out in practical application.

Summary of the invention

The object of the invention is the exponent number defining method proposing a kind of frequency dependent network equivalence for electric system simulation, first carry out once rough model solution according to the frequency domain sample value spike number of frequency dependent network equivalence, then the frequency domain sample value revised is transformed into time domain, carries out exponent number by Prony analytical approach and determine.

The exponent number defining method of the frequency dependent network equivalence for electric system simulation that the present invention proposes, comprises the following steps:

(1) from the network model of electric system, N is obtained ₀the frequency domain sample value Y (s of individual equally distributed frequency dependent network equivalence _i), i=1,2 ..., p ... N ₀, wherein, Y (s _i) matrix of to be element be plural number, s=j2 π f, j are imaginary unit, and f is the frequency of each frequency domain sample value, and frequency range is 0 ~ F ₀hz;

(2) from above-mentioned N ₀the frequency domain sample value Y (s of individual frequency dependent network equivalence _i) the middle all frequency domain sample value y taking out first element ₁₁(s _i), i=1,2 ..., p ... N ₀, all frequency domain sample value y ₁₁(s _i) in each frequency domain sample value be plural number, to all frequency domain sample value y ₁₁(s _i) judge, if frequency domain sample value y ₁₁(s _p) meet following formula,

|y ₁₁(s _p-1)|＜|y ₁₁(s _p)|＞|y ₁₁(s _p+1)|，

Then judge y ₁₁(s _p) be a spike, travel through all frequency domain sample value y ₁₁(s _i), obtain frequency domain sample value y ₁₁(s _i) spike add up to n _peak, wherein | * | represent the amplitude of plural number;

(3) by above-mentioned spike sum n _peaktwice as the exponent number of original frequency network of relation equivalence, according to the frequency domain sample value y of above-mentioned first element ₁₁(s _i), i=1,2 ..., p ... N ₀, obtaining an initial frequency-domain function by vector fitting method is:

$y\left(s\right)=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\frac{c_i}{s-a_i}+d+\mathrm{sh},$

Wherein, s=j2 π f, a _ifor limit, d is constant term, and h is once item, travels through all a _i, obtain a _ifor the number n of real number _real;

(4) according to above-mentioned initial frequency-domain function, from the frequency domain sample value y of first element ₁₁(s _i) in delete real pole, constant term d and once item h, obtain revising frequency domain sample value, be designated as i=1,2 ..., p ... N ₀, frequency range be 0 ~ F ₀hz, for plural number;

(5) according to conjugation regular symmetric, p-F ₀frequency domain sample point between ~ 0Hz supplements, and obtains 2N ₀-1 frequency range is-F ₀~ F ₀the symmetrical complete frequency domain sample point of conjugation of Hz, is designated as k=1,2 ..., 2N ₀-1, adopt inverse fast fourier transform method, by frequency domain sample point be transformed to time-domain sampling point, obtain the sequence of real numbers in one group of time domain, be designated as x (m), m=1,2 ..., 2N ₀-1;

(6) utilize Prony analytical approach, determine the exponent number of frequency dependent network equivalence, detailed process is as follows:

(6-1) according to above-mentioned sequence of real numbers x (m), following matrix of coefficients R is built

(6-2) svd is carried out to R, obtain the N of R ₀-1 singular value, by N ₀-1 singular value is as follows by order arrangement from big to small:

${\mathrm{\σ}}_1\≥{\mathrm{\σ}}_2\≥...\≥{\mathrm{\σ}}_{N_0-1}\≥0,$

(6-3) set a judgment threshold λ, utilize judgment threshold λ to determine the order of matrix R, namely from 1, increase progressively parameter r, until following formula is set up:

${\left(\frac{{{\mathrm{\&sigma;}}_1}^2+{{\mathrm{\&sigma;}}_2}^2+...+{{\mathrm{\&sigma;}}_{r-1}}^2}{{{\mathrm{\&sigma;}}_1}^2+{{\mathrm{\&sigma;}}_2}^2+...+{{\mathrm{\&sigma;}}_{N_o-1}}^2}\right)}^{1/2}<\mathrm{\&lambda;}<{\left(\frac{{{\mathrm{\&sigma;}}_1}^2+{{\mathrm{\&sigma;}}_2}^2+...+{{\mathrm{\&sigma;}}_r}^2}{{{\mathrm{\&sigma;}}_1}^2+{{\mathrm{\&sigma;}}_2}^2+...+{{\mathrm{\&sigma;}}_{N_o-1}}^2}\right)}^{1/2},$

Then the order of trip current R is r;

(7) according to the n of above-mentioned steps (3) _realwith the order r of above-mentioned matrix R, obtaining for the exponent number of the frequency dependent network equivalence of electric system simulation is n _real+ r.

The exponent number defining method of the frequency dependent network equivalence for electric system simulation that the present invention proposes, solves exponent number when current frequency dependent network equivalence is applied to electric system simulation and is difficult to the problem selected, and the method fast, accurately, precision is adjustable; Engineering practice good results.

Accompanying drawing explanation

Fig. 1 is that existing employing promise is paused the Equivalent Network method schematic diagram of Equivalent Model.

Fig. 2 is the existing Equivalent Network method schematic diagram based on frequency dependent network equivalence (hereinafter referred to as FDNE).

Fig. 3 is the FB(flow block) of the exponent number defining method of the frequency dependent network equivalence for electric system simulation that the present invention proposes.

Embodiment

The exponent number defining method of the frequency dependent network equivalence for electric system simulation that the present invention proposes, its FB(flow block) as shown in Figure 3, comprises the following steps:

(1) from the network model of electric system, N is obtained ₀(N ₀usually 500 are got) the frequency domain sample value Y (s of individual equally distributed frequency dependent network equivalence _i), i=1,2 ..., p ... N ₀, wherein, Y (s _i) matrix of to be element be plural number, s=j2 π f, j are imaginary unit, and f is the frequency of each frequency domain sample value, and frequency range is 0 ~ F ₀hz (F ₀usually 2500 are got);

(2) from above-mentioned N ₀the frequency domain sample value Y (s of individual frequency dependent network equivalence _i) the middle all frequency domain sample value y taking out first element ₁₁(s _i), i=1,2 ..., p ... N ₀, all frequency domain sample value y ₁₁(s _i) in each frequency domain sample value be plural number, to all frequency domain sample value y ₁₁(s _i) judge, if frequency domain sample value y ₁₁(s _p) meet following formula,

|y ₁₁(s _p-1)|＜|y ₁₁(s _p)|＞|y ₁₁(s _p+1)|，

Then judge y ₁₁(s _p) be a spike, travel through all frequency domain sample value y ₁₁(s _i), obtain frequency domain sample value y ₁₁(s _i) spike add up to n _peak, wherein | * | represent the amplitude of plural number;

(3) by above-mentioned spike sum n _peaktwice as the exponent number of original frequency network of relation equivalence, according to the frequency domain sample value y of above-mentioned first element ₁₁(s _i), i=1,2 ..., p ... N ₀, obtaining an initial frequency-domain function by vector fitting method is:

$y\left(s\right)=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\frac{c_i}{s-a_i}+d+\mathrm{sh},$

Wherein, s=j2 π f, a _ifor limit, d is constant term, and h is once item, travels through all a _i, obtain a _ifor the number n of real number _real;

(4) according to above-mentioned initial frequency-domain function, from the frequency domain sample value y of first element ₁₁(s _i) in delete real pole, constant term d and once item h, obtain revising frequency domain sample value, be designated as i=1,2 ..., p ... N ₀, frequency range be 0 ~ F ₀hz, for plural number;

(5) according to conjugation regular symmetric, p-F ₀frequency domain sample point between ~ 0Hz supplements, and obtains 2N ₀-1 frequency range is-F ₀~ F ₀the symmetrical complete frequency domain sample point of conjugation of Hz, is designated as k=1,2 ..., 2N ₀-1, adopt inverse fast fourier transform method, by frequency domain sample point be transformed to time-domain sampling point, obtain the sequence of real numbers in one group of time domain, be designated as x (m), m=1,2 ..., 2N ₀-1;

(6) utilize Prony analytical approach, determine the exponent number of frequency dependent network equivalence, detailed process is as follows:

(6-1) according to above-mentioned sequence of real numbers x (m), following matrix of coefficients R is built

(6-2) svd is carried out to R, obtain the N of R ₀-1 singular value, by N ₀-1 singular value is as follows by order arrangement from big to small:

${\mathrm{\&sigma;}}_1\&GreaterEqual;{\mathrm{\&sigma;}}_2\&GreaterEqual;...\&GreaterEqual;{\mathrm{\&sigma;}}_{N_0-1}\&GreaterEqual;0,$

(6-3) set a judgment threshold λ, (threshold value λ elects 0.9999 as usually, can regulate according to required precision) utilizes judgment threshold λ to determine the order of matrix R, namely from 1, increases progressively parameter r, until following formula is set up:

${\left(\frac{{{\mathrm{\&sigma;}}_1}^2+{{\mathrm{\&sigma;}}_2}^2+...+{{\mathrm{\&sigma;}}_{r-1}}^2}{{{\mathrm{\&sigma;}}_1}^2+{{\mathrm{\&sigma;}}_2}^2+...+{{\mathrm{\&sigma;}}_{N_o-1}}^2}\right)}^{1/2}<\mathrm{\&lambda;}<{\left(\frac{{{\mathrm{\&sigma;}}_1}^2+{{\mathrm{\&sigma;}}_2}^2+...+{{\mathrm{\&sigma;}}_r}^2}{{{\mathrm{\&sigma;}}_1}^2+{{\mathrm{\&sigma;}}_2}^2+...+{{\mathrm{\&sigma;}}_{N_o-1}}^2}\right)}^{1/2},$

Then the order of trip current R is r;

(7) according to the n of above-mentioned steps (3) _realwith the order r of above-mentioned matrix R, obtaining for the exponent number of the frequency dependent network equivalence of electric system simulation is n _real+ r.

Claims (1)

1., for an exponent number defining method for the frequency dependent network equivalence of electric system simulation, it is characterized in that the method comprises the following steps:

(1) from the network model of electric system, N is obtained ₀the frequency domain sample value Y (s of individual equally distributed frequency dependent network equivalence _i), i=1,2 ..., p ... N ₀, wherein, Y (s _i) matrix of to be element be plural number, s=j2 π f, j are imaginary unit, and f is the frequency of each frequency domain sample value, and frequency range is 0 ~ F ₀hz;

(2) from above-mentioned N ₀the frequency domain sample value Y (s of individual frequency dependent network equivalence _i) the middle all frequency domain sample value y taking out first element ₁₁(s _i), i=1,2 ..., p ... N ₀, all frequency domain sample value y ₁₁(s _i) in each frequency domain sample value be plural number, to all frequency domain sample value y ₁₁(s _i) judge, if frequency domain sample value y ₁₁(s _p) meet following formula,

|y ₁₁(s _p-1)|＜|y ₁₁(s _p)|＞|y ₁₁(s _p+1)|，

Then judge y ₁₁(s _p) be a spike, travel through all frequency domain sample value y ₁₁(s _i), obtain frequency domain sample value y ₁₁(s _i) spike add up to n _peak, wherein | * | represent the amplitude of plural number;

(3) by above-mentioned spike sum n _peaktwice as the exponent number of original frequency network of relation equivalence, according to the frequency domain sample value y of above-mentioned first element ₁₁(s _i), i=1,2 ..., p ... N ₀, obtaining an initial frequency-domain function by vector fitting method is:

$\left(s\right)=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\frac{c_i}{s-a_i}+d+\mathrm{sh},$

Wherein, s=j2 π f, a _ifor limit, d is constant term, and h is once item, travels through all a _i, obtain a _ifor the number n of real number _real;

(4) according to above-mentioned initial frequency-domain function, from the frequency domain sample value y of first element ₁₁(s _i) in delete real pole, constant term d and once item h, obtain revising frequency domain sample value, be designated as i=1,2 ..., p ... N ₀, frequency range be 0 ~ F ₀hz, for plural number;

(5) according to conjugation regular symmetric, p-F ₀frequency domain sample point between ~ 0Hz supplements, and obtains 2N ₀-1 frequency range is-F ₀~ F ₀the symmetrical complete frequency domain sample point of conjugation of Hz, is designated as k=1,2 ..., 2N ₀-1, adopt inverse fast fourier transform method, by frequency domain sample point be transformed to time-domain sampling point, obtain the sequence of real numbers in one group of time domain, be designated as x (m), m=1,2 ..., 2N ₀-1;

(6) utilize Prony analytical approach, determine the exponent number of frequency dependent network equivalence, detailed process is as follows:

(6-1) according to above-mentioned sequence of real numbers x (m), following matrix of coefficients R is built

(6-2) svd is carried out to R, obtain the N of R ₀-1 singular value, by N ₀-1 singular value is as follows by order arrangement from big to small:

${\mathrm{\&sigma;}}_1\&GreaterEqual;{\mathrm{\&sigma;}}_2\&GreaterEqual;...\&GreaterEqual;{\mathrm{\&sigma;}}_{N_0-1}\&GreaterEqual;0,$

(6-3) set a judgment threshold λ, utilize judgment threshold λ to determine the order of matrix R, namely from 1, increase progressively parameter r, until following formula is set up:

${\left(\frac{{{\mathrm{\&sigma;}}_1}^2+{{\mathrm{\&sigma;}}_2}^2+...+{{\mathrm{\&sigma;}}_{r-1}}^2}{{{\mathrm{\&sigma;}}_1}^2+{{\mathrm{\&sigma;}}_2}^2+...+{{\mathrm{\&sigma;}}_{N_o-1}}^2}\right)}^{1/2}<\mathrm{\&lambda;}<{\left(\frac{{{\mathrm{\&sigma;}}_1}^2+{{\mathrm{\&sigma;}}_2}^2+...+{{\mathrm{\&sigma;}}_r}^2}{{{\mathrm{\&sigma;}}_1}^2+{{\mathrm{\&sigma;}}_2}^2+...+{{\mathrm{\&sigma;}}_{N_o-1}}^2}\right)}^{1/2},$

Then the order of trip current R is r;

(7) according to the n of above-mentioned steps (3) _realwith the order r of above-mentioned matrix R, obtaining for the exponent number of the frequency dependent network equivalence of electric system simulation is n _real+ r.