CN105809294A - PRONY analysis method and device for low-frequency oscillation of electric system - Google Patents

Abstract

The invention provides a PRONY analysis method and device for low-frequency oscillation of an electric system.The method includes the steps that a discrete linear prediction model is established based on discrete signals of the electric system; multiple discrete modes are calculated according to a characteristic polynomial of the discrete linear prediction model; energy values corresponding to the discrete modes are calculated; multiple modes are screened out from the discrete modes by comparing the energy values and serve as first dominant oscillation modes, and the low-frequency oscillation property of the electric system is analyzed according to the first dominant oscillation modes.The probability of erroneous judgment occurring when dominant modes are screened in a traditional PRONY analysis method can be reduced.

Description

The PRONY of low-frequency oscillation of electric power system analyzes method and device

Technical field

The present invention relates to power system safety and stability analysis technical field, the PRONY particularly relating to a kind of low-frequency oscillation of electric power system analyzes method and device.

Background technology

PRONY algorithm is the mathematical model that the linear combination of a kind of exponential function describes equal interval sampling data.Apply it in the research of low-frequency oscillation of electric power system, it is possible to from simulation curve and measured data, analyze the frequency of oscillator signal, damped coefficient, amplitude and phase place.And, can when electric power system model be unknown, measured data is analyzed, obtain the transmission function design for controller of depression of order, such as, for the parameter setting etc. of PSS (power electronic system regulator) parameter tuning, HVDC (HVDC) small signal modulation.

In order to improve the accuracy of model estimation, traditional PRONY method employs the linear prediction model of high-order, and the pattern count therefore estimated is more than in esse pattern count, and unnecessary pattern can be described as ordinary pattern.But, the ordinary pattern with underdamping or negative damping may be erroneously interpreted as dominant pattern when analyzing, and therefore tradition PRONY method exists the possibility of erroneous judgement when estimating dominant pattern, and then can cause the mistake that predicts the outcome.

Summary of the invention

The present invention provides the PRONY of a kind of low-frequency oscillation of electric power system to analyze method and device, to reduce tradition PRONY analysis method probability of appearance erroneous judgement when screening dominant pattern.

The present invention provides the PRONY of a kind of low-frequency oscillation of electric power system to analyze method, including: the discrete signal of electrically-based system sets up Discrete Linear forecast model；Proper polynomial according to described Discrete Linear forecast model calculates multiple discrete modes；Calculate the energy value corresponding to each described discrete mode；From the plurality of discrete mode, filter out multiple pattern as the first control oscillation modes by relatively each described energy value, and according to described first control oscillation modes, the low-frequency oscillation characteristic of power system is analyzed.

In one embodiment, the method also includes: calculate the amplitude corresponding to described discrete mode, phase place, frequency and damped coefficient；According to described amplitude, phase place, frequency and damped coefficient, described first control oscillation modes is done screening further, obtain the second control oscillation modes, and according to described second control oscillation modes, the low-frequency oscillation characteristic of power system is analyzed.

In one embodiment, calculate the energy value corresponding to each described discrete mode, including: utilize the characteristic root corresponding to described discrete signal and described discrete mode to calculate the residual obtained corresponding to described discrete mode；By Real Number Roots pattern and conjugate complex number root mode, described discrete mode is classified；According to type belonging to described discrete mode, the characteristic root corresponding to described discrete mode and corresponding described residual is utilized to calculate the energy value obtained corresponding to described discrete mode.

In one embodiment, calculate the amplitude corresponding to described discrete mode, phase place, frequency and damped coefficient, including: calculate described frequency and damped coefficient according to described residual, the characteristic root corresponding to described discrete mode calculates and obtains described amplitude and phase place.

In one embodiment, the discrete signal of electrically-based system sets up Discrete Linear forecast model, including: the signal data point in described discrete signal is fitted, obtains multiple signal estimation value；Described Discrete Linear forecast model is set up according to the plurality of signal estimation value, wherein, the number of the plurality of signal estimation value is identical with the exponent number of described Discrete Linear forecast model, and the number of equation corresponding to described Discrete Linear forecast model is the number difference with described exponent number of described signal data point.

In one embodiment, affiliated type is the energy value corresponding to the discrete mode of Real Number Roots pattern is:

$E_i=\underset{k=1}{\overset{N}{\Σ}}\[{\left(real\right(c_i{z}_i^k)\]}^2,$

Wherein, E_iFor the energy value corresponding to i-th discrete mode, N is the data point number of described discrete signal, and real () represents treating excess syndrome portion, c_iFor the residual corresponding to discrete mode i, z_iFor the characteristic root corresponding to discrete mode i, k≤N, i, k and N are positive integer.

In one embodiment, affiliated type is the energy value corresponding to the discrete mode of conjugate complex number root mode is:

$E_i=\underset{k=1}{\overset{N}{\Σ}}{\[2real\left(c_i{z}_i^k\right)\]}^2,$

Wherein, E_iFor the energy value corresponding to i-th discrete mode, N is the data point number of described discrete signal, and real () represents treating excess syndrome portion, c_iFor the residual corresponding to discrete mode i, z_iFor the characteristic root corresponding to discrete mode i, k≤N, k and N is positive integer.

The present invention also provides for the PRONY analytical equipment of a kind of low-frequency oscillation of electric power system, including: linear prediction model sets up unit, and the discrete signal for electrically-based system sets up Discrete Linear forecast model；Discrete mode generates unit, calculates multiple discrete modes for the proper polynomial according to described Discrete Linear forecast model；Energy value generates unit, for calculating the energy value corresponding to each described discrete mode；First Low Frequency Oscillation Analysis unit, for filtering out multiple pattern from the plurality of discrete mode as the first control oscillation modes by relatively each described energy value, and is analyzed the low-frequency oscillation characteristic of power system according to described first control oscillation modes.

In one embodiment, also include: discrete mode parameter generating unit, for calculating amplitude corresponding to described discrete mode, phase place, frequency and damped coefficient；Second Low Frequency Oscillation Analysis unit, for described first control oscillation modes being done screening further according to described amplitude, phase place, frequency and damped coefficient, obtain the second control oscillation modes, and according to described second control oscillation modes, the low-frequency oscillation characteristic of power system is analyzed.

In one embodiment, described energy value generates unit and includes: residual generation module, for utilizing the characteristic root corresponding to described discrete signal and described discrete mode to calculate the residual obtained corresponding to described discrete mode；Discrete mode sort module, for classifying to described discrete mode by Real Number Roots pattern and conjugate complex number root mode；Energy value generation module, for according to type belonging to described discrete mode, utilizing the characteristic root corresponding to described discrete mode and corresponding described residual to calculate the energy value obtained corresponding to described discrete mode.

In one embodiment, described discrete mode parameter generating unit includes: discrete mode parameter generation module, and for calculating described frequency and damped coefficient according to described residual, the characteristic root corresponding to described discrete mode calculates and obtains described amplitude and phase place.

In one embodiment, described linear prediction model is set up unit and is included: signal estimation value generation module, for the signal data point in described discrete signal is fitted, obtains multiple signal estimation value；Linear prediction model sets up module, for setting up described Discrete Linear forecast model according to the plurality of signal estimation value, wherein, the number of the plurality of signal estimation value is identical with the exponent number of described Discrete Linear forecast model, and the number of equation corresponding to described Discrete Linear forecast model is the number difference with described exponent number of described signal data point.

The PRONY of the low-frequency oscillation of electric power system of the embodiment of the present invention analyzes method and device, on tradition PRONY analysis foundation, consider that different patterns has different energy values, calculate the energy value of all patterns, and with this, pattern is screened, it is believed that the pattern with of a relatively high energy value is dominant pattern, think that the relatively low pattern of energy value is then ordinary pattern.Factor according to the above-mentioned dominant pattern analyzing influence power system dynamic stability filtered out, the accuracy of the PRONY model estimation analyzed can be improved, PRONY can be reduced and analyze False Rate in Power System Analysis, improve analysis efficiency and accuracy rate, it is thus possible to the redundancy of effort reduced in analysis process, provide guarantee for low-frequency oscillation of electric power system accurate analysis.Make to screen further to previous the selection result by the relevant parameter (including amplitude, phase place, frequency and damped coefficient) of discrete mode, postsearch screening can obtain dominant pattern more accurately such that it is able to improves the accuracy of low-frequency oscillation analysis further.

Accompanying drawing explanation

In order to be illustrated more clearly that the embodiment of the present invention or technical scheme of the prior art, the accompanying drawing used required in embodiment or description of the prior art will be briefly described below, apparently, accompanying drawing in the following describes is only some embodiments of the present invention, for those of ordinary skill in the art, under the premise not paying creative work, it is also possible to obtain other accompanying drawing according to these accompanying drawings.In the accompanying drawings:

Fig. 1 is the schematic flow sheet of the PRONY analysis method of the low-frequency oscillation of electric power system of one embodiment of the invention；

Fig. 2 is the schematic flow sheet setting up Discrete Linear forecast model method in one embodiment of the invention；

Fig. 3 is the schematic flow sheet calculating energy value method in one embodiment of the invention；

Fig. 4 is the schematic flow sheet of the PRONY analysis method of the low-frequency oscillation of electric power system of another embodiment of the present invention；

Fig. 5 is the schematic flow sheet of the method calculating discrete mode relevant parameter in one embodiment of the invention；

Fig. 6 is the structural representation of the PRONY analytical equipment of one embodiment of the invention；

Fig. 7 is the method flow schematic diagram that in one embodiment of the invention, linear prediction model sets up unit；

Fig. 8 is the structural representation that in one embodiment of the invention, energy value generates unit；

Fig. 9 is the structural representation of the PRONY analytical equipment of the low-frequency oscillation of electric power system of another embodiment of the present invention；

Figure 10 is the structural representation of discrete mode parameter generating unit in one embodiment of the invention.

Detailed description of the invention

For making the purpose of the embodiment of the present invention, technical scheme and advantage clearly understand, below in conjunction with accompanying drawing, the embodiment of the present invention is described in further details.At this, the schematic description and description of the present invention is used for explaining the present invention, but not as a limitation of the invention.

In order to solve tradition PRONY method exist when estimating dominant pattern erroneous judgement and and then the problem of the mistake that can cause predicting the outcome, inventor finds, through creative work, the method that Effective selection goes out dominant pattern from multiple patterns, with this, tradition PRONY is analyzed method to be improved, it is possible to increase the accuracy of low-frequency oscillation analysis.

Fig. 1 is the schematic flow sheet of the PRONY analysis method of the low-frequency oscillation of electric power system of one embodiment of the invention.As it is shown in figure 1, the PRONY of this low-frequency oscillation of electric power system analyzes method, it may include step:

S110: the discrete signal of electrically-based system sets up Discrete Linear forecast model；

S120: calculate multiple discrete modes according to the proper polynomial of above-mentioned Discrete Linear forecast model；

S130: calculate the energy value corresponding to each above-mentioned discrete mode；

S140: filter out multiple pattern from above-mentioned multiple discrete modes as the first control oscillation modes by relatively each above-mentioned energy value, and according to above-mentioned first control oscillation modes, the low-frequency oscillation characteristic of power system is analyzed.

In above-mentioned steps S110, this discrete signal can refer to the various signal that can reflect Operation of Electric Systems characteristic, for instance the voltage signal of electrical network.Discrete Linear forecast model can be set up by multiple method, for instance the mode in tradition PRONY method sets up Discrete Linear forecast model, and this Discrete Linear forecast model may refer to the linear combination of several function.The more many foundation that can more be conducive to Discrete Linear forecast model of the number of discrete signal.

In above-mentioned steps S120, Discrete Linear forecast model can be various different exponent numbers, can the linear combination equation of corresponding multiple setting functions, multiple equations are expressed as the form of matrix equation, can obtain stating the proper polynomial of Discrete Linear forecast model by solution matrix equation, solve this proper polynomial further and can obtain multiple characteristic root, can corresponding multiple discrete modes.

In above-mentioned steps S130, the energy value corresponding to discrete mode can pass through the calculating of multiple distinct methods and obtain, for instance obtain based on signal energy Theoretical Calculation.

In above-mentioned steps S140, this first control oscillation modes can be the pattern that the energy value filtered out from above-mentioned multiple patterns is of a relatively high, such as, the energy value corresponding to a pattern be positioned in the energy value corresponding to all patterns before 20% level it is believed that energy value is of a relatively high.It addition, the pattern corresponding to lower energy value may be considered ordinary pattern.Inventor contemplates that for different Discrete Linear forecast models, the size of the energy value corresponding to pattern is likely to difference, absolute size according only to energy value judges that control oscillation modes is not accurate enough, so expecting that the relative size of energy value can more effectively filter out Critical inertial modes corresponding to pattern.

The PRONY of the low-frequency oscillation of electric power system of the embodiment of the present invention analyzes method, analyze on method basis at tradition PRONY, consider that different patterns has different energy values, calculate the energy value of all patterns, and with this, pattern is screened, it is believed that the pattern with of a relatively high energy value is dominant pattern, think that the relatively low pattern of energy value is then ordinary pattern.Factor according to the above-mentioned dominant pattern analyzing influence power system dynamic stability filtered out, it is possible to improve the accuracy of the PRONY model estimation analyzed, it is possible to reduce PRONY analyzes False Rate in Power System Analysis, improves analysis efficiency and accuracy rate.

Fig. 2 is the schematic flow sheet setting up Discrete Linear forecast model method in one embodiment of the invention.As in figure 2 it is shown, in above-mentioned steps S110, the discrete signal of electrically-based system sets up the method for Discrete Linear forecast model, it may include step:

S111: the signal data point in above-mentioned discrete signal is fitted, obtains multiple signal estimation value；

S112: set up above-mentioned Discrete Linear forecast model according to above-mentioned multiple signal estimation values, wherein, the number of above-mentioned multiple signal estimation value is identical with the exponent number of above-mentioned Discrete Linear forecast model, and the number of equation corresponding to above-mentioned Discrete Linear forecast model is the number difference with above-mentioned exponent number of above-mentioned signal data point.

In above-mentioned steps S111, by being fitted obtaining a fitting function to the signal data point in above-mentioned discrete signal, above-mentioned multiple signal estimation values can be the value in this fitting function.Such as, an electrical network being carried out Low Frequency Oscillation Analysis, can first pass through emulation platform and obtain occurring the simulation curve data of low-frequency oscillation, simulation curve is analyzed by the method again through the present invention, to analyze the operation characteristic of this electrical network.

In above-mentioned steps S112, Discrete Linear forecast model can be set up by matching or emulation according to above-mentioned multiple signal estimation values.This Discrete Linear forecast model can be the linear combination setting type of functions.The exponent number of Discrete Linear forecast model can be determined according to the number of above-mentioned multiple signal estimation values.This Discrete Linear forecast model can be made up of equation group.

In one embodiment, by matching, the predictive value of discrete signal is expressed as the linear function of n given data.The general type that exponent number is the Discrete Linear forecast model of n can be:

Y (k)=a₁y(k-1)+a₂y(k-2)+…+a_nY (k-n), (1)

Wherein, y is the title (such as exponential function) of function used, a in matching₁,…,a_i,…,a_nRepresenting the amplitude (being such as the coefficient of linear combination of exponential functions) in fitting result, n is the exponent number of Discrete Linear forecast model.

For obtaining the n rank Discrete Linear forecast model of matrix form, can k=n, n+1 ..., N-1 substitute into formula (1), wherein N is the number of above-mentioned discrete signal, obtains:

$\left[\begin{array}{c}y\left(n\right)\\ y(n+1)\\ y(n+2)\\ .\\ .\\ .\\ y(N-1)\end{array}\right]=\left[\begin{array}{cccc}y(n-1)& y(n-2)& \mathrm{...}& y\left(0\right)\\ y\left(n\right)& y(n-1)& \mathrm{...}& y\left(1\right)\\ y(n+1)& y\left(n\right)& \mathrm{...}& y\left(2\right)\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ y(N-2)& y(N-3)& \mathrm{...}& y(N-n-1)\end{array}\right]\left[\begin{array}{c}{a}_1\\ a_2\\ a_3\\ .\\ .\\ .\\ a_n\end{array}\right],---\left(2\right)$

Wherein, a_iFor the coefficient of characteristic equation and formula (2), 1≤i≤n, i and n is integer, and n is the exponent number of Discrete Linear forecast model.

In one embodiment, it is possible to adopt least-squares estimation (LSE) method to try to achieve coefficient a_i.It is preferred that the exponent number n > p of Discrete Linear forecast model, wherein,Consequently, it is possible to noise and the signal biasing impact on the Low Frequency Oscillation Analysis result of power system can be reduced.It is preferred that the number N-n > 2n of equation in formula (2), consequently, it is possible to may filter that noise.

In one embodiment, at above-mentioned steps S120, the proper polynomial of this Discrete Linear forecast model can be:

zⁿ+a₁z^n-1+…a_n-1z+a_n=0, (3)

Wherein, z is the variable in this proper polynomial, and solution formula (3) can obtain multiple characteristic root z₁,…,z_j,…,z_n, corresponding with discrete mode, wherein, 1≤j≤n, j is integer.

Fig. 3 is the schematic flow sheet calculating energy value method in one embodiment of the invention.As it is shown on figure 3, in above-mentioned steps S130, the method calculating energy value corresponding to each above-mentioned discrete mode, it may include step:

S131: utilize the characteristic root corresponding to above-mentioned discrete signal and above-mentioned discrete mode to calculate the residual obtained corresponding to above-mentioned discrete mode；

S132: above-mentioned discrete mode is classified by Real Number Roots pattern and conjugate complex number root mode；

S133: according to type belonging to above-mentioned discrete mode, utilizes the characteristic root corresponding to above-mentioned discrete mode and corresponding above-mentioned residual to calculate the energy value obtained corresponding to above-mentioned discrete mode.

In above-mentioned steps S131, utilize the characteristic root corresponding to above-mentioned discrete signal and above-mentioned discrete mode, the residual corresponding to above-mentioned discrete mode can be calculated by means commonly known in the art.

In one embodiment, can pass through to solve equation below and calculate residual:

$\left[\begin{array}{cccc}1& 1& \mathrm{...}& 1\\ z_1& z_2& \mathrm{...}& z_n\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ z_1^{N-1}& z_2^{N-1}& \mathrm{...}& z_n^{N-1}\end{array}\right]\left[\begin{array}{c}{c}_1\\ c_2\\ .\\ .\\ .\\ c_n\end{array}\right]=\left[\begin{array}{c}Y\left(1\right)\\ Y\left(2\right)\\ .\\ .\\ .\\ Y\left(N\right)\end{array}\right],---\left(4\right)$

Wherein, z₁,…,z_j,…,z_nRepresenting characteristic root, 1≤j≤n, j is integer；c₁,…,c_k,…,c_nRepresenting residual, 1≤k≤n, k is integer；Y (1) ..., Y (l) ..., Y (n) represents above-mentioned discrete signal (primary signal, non-pre-measured value), and 1≤l≤n, l is integer.

In above-mentioned steps S132 and S133, Real Number Roots pattern and conjugate complex number root mode can adopt different computational methods to calculate the energy value corresponding to discrete mode, thus improving the accuracy in computation of energy value.

In the present embodiment, energy value is asked in the classification of above-mentioned discrete mode, it is possible to improve the accuracy of energy value.The characteristic root corresponding to above-mentioned discrete mode and corresponding above-mentioned residual is utilized to calculate the energy value obtained corresponding to above-mentioned discrete mode, based on the energy value corresponding to energy signal Theoretical Calculation discrete mode, method for solving is simple, efficient, it is possible to increase the acquisition speed of energy value.

In one embodiment, affiliated type is the energy value corresponding to the discrete mode of Real Number Roots pattern is:

$E_i=\underset{k=1}{\overset{N}{\Σ}}\[{\left(real\right(c_i{z}_i^k)\]}^2,---\left(5\right)$

Wherein, E_iFor the energy value corresponding to i-th discrete mode, N is the data point number of above-mentioned discrete signal, and real () represents treating excess syndrome portion, c_iFor the residual corresponding to discrete mode i, z_iFor the characteristic root corresponding to discrete mode i, k≤N, i, k and N are positive integer.

In one embodiment, affiliated type is the energy value corresponding to the discrete mode of conjugate complex number root mode is:

$E_i=\underset{k=1}{\overset{N}{\Σ}}{\[2real\left(c_i{z}_i^k\right)\]}^2,---\left(6\right)$

Wherein, E_iFor the energy value corresponding to i-th discrete mode, N is the data point number of above-mentioned discrete signal, and real () represents treating excess syndrome portion, c_iFor the residual corresponding to discrete mode i, z_iFor the characteristic root corresponding to discrete mode i, k≤N, k and N is positive integer.

In the present embodiment, it is only necessary to residual and two parameters of characteristic root can try to achieve residual, energy value obtains convenient.

Fig. 4 is the schematic flow sheet of the PRONY analysis method of the low-frequency oscillation of electric power system of another embodiment of the present invention.As shown in Figure 4, the PRONY of the low-frequency oscillation of electric power system shown in Fig. 1 analyzes method, may further comprise the step of:

S150: calculate the amplitude corresponding to above-mentioned discrete mode, phase place, frequency and damped coefficient；

S160: according to above-mentioned amplitude, phase place, frequency and damped coefficient, above-mentioned first control oscillation modes is done screening further, obtain the second control oscillation modes, and according to above-mentioned second control oscillation modes, the low-frequency oscillation characteristic of power system is analyzed.

In above-mentioned steps S150, it is possible to calculate the relevant parameter of discrete mode according to multiple method, including amplitude, phase place, frequency and damped coefficient, for instance calculate according to method well known in the art.

In above-mentioned steps S160, the multiple patterns filtered out according to energy value can be done further screening, wherein it is possible to whether amplitude corresponding to discrete mode, phase place, frequency and damped coefficient filter out above-mentioned second Critical inertial modes in the set point of response from above-mentioned first Critical inertial modes.

The PRONY of the low-frequency oscillation of electric power system of the embodiment of the present invention analyzes method, dominant pattern is screened by the energy value corresponding to discrete mode, and make to screen further to previous the selection result by the relevant parameter (including amplitude, phase place, frequency and damped coefficient) of discrete mode, postsearch screening can obtain dominant pattern more accurately such that it is able to improves the accuracy of low-frequency oscillation analysis further.

Fig. 5 is the schematic flow sheet of the method calculating discrete mode relevant parameter in one embodiment of the invention.As it is shown in figure 5, in above-mentioned steps S150, the method calculating the amplitude corresponding to above-mentioned discrete mode, phase place, frequency and damped coefficient, it may include step:

S151 (S131): utilize the characteristic root corresponding to above-mentioned discrete signal and above-mentioned discrete mode to calculate the residual obtained corresponding to above-mentioned discrete mode；

S152: calculate above-mentioned frequency and damped coefficient according to above-mentioned residual, the characteristic root corresponding to above-mentioned discrete mode calculates and obtains above-mentioned amplitude and phase place.

In above-mentioned steps S151, it is possible to use the method identical with step S131 calculates the residual corresponding to above-mentioned discrete mode, or can directly adopt the calculated residual of step S131 to carry out subsequent calculations.

In above-mentioned steps S152, characteristic root corresponding to above-mentioned discrete mode can release above-mentioned amplitude and phase place, real part needed for calculating above-mentioned frequency according to above-mentioned residual and solve damped coefficient, is being obtained damped coefficient according to corresponding computing formula by the calculating of this real part.

In one embodiment, for solving the formula of amplitude corresponding to discrete mode, phase place, frequency and damped coefficient it is:

c_i=A_iexp(jφ_i), (7)

z_i=exp [(σ_i+ j2 π f_i) Δ t], (8)

Wherein, c_iFor the residual corresponding to i-th discrete mode, A_iFor the amplitude corresponding to i-th discrete mode, z_iFor the characteristic root corresponding to i-th discrete mode, σ_iFor the real part corresponding to i-th discrete mode, f_iFor the frequency corresponding to i-th discrete mode, Δ t is the sampling time interval of above-mentioned discrete signal, it is preferred that sample for constant duration.

Can deriving according to above-mentioned formula (7)～(8) and calculate amplitude corresponding to above-mentioned discrete mode, phase place, frequency and damped coefficient, specific formula for calculation is as follows:

A_i=| c_i|, (9)

φ_i=arctan (Im (c_i)/Re(c_i)), (10)

σ_i=ln | z_i|/Δ t, (11)

f_i=arctan (Im (z_i)/Re(z_i))/(2 π Δ t), (12)

${\mathrm{\ζ}}_i=\frac{-{\mathrm{\σ}}_i}{\sqrt{{{\mathrm{\σ}}_i}^2+{{\mathrm{\ω}}_i}^2}},---\left(13\right)$

Wherein, in formula (13), ζ_iRepresent the damped coefficient corresponding to i-th discrete mode, ω_iFor the imaginary part corresponding to i-th discrete mode.What deserves to be explained is, the symbol of i is used in above-mentioned many places, and its concrete meaning determines according to the specified context used.

The PRONY of the low-frequency oscillation of electric power system of the embodiment of the present invention analyzes method, analyze on method basis at tradition PRONY, consider that different patterns has different energy values, calculate the energy value of all patterns, and with this, pattern is screened, it is believed that the pattern with of a relatively high energy value is dominant pattern, think that the relatively low pattern of energy value is then ordinary pattern.Factor according to the above-mentioned dominant pattern analyzing influence power system dynamic stability filtered out, the accuracy of the PRONY model estimation analyzed can be improved, PRONY can be reduced and analyze False Rate in Power System Analysis, improve analysis efficiency and accuracy rate, it is thus possible to the redundancy of effort reduced in analysis process, provide guarantee for low-frequency oscillation of electric power system accurate analysis.Make to screen further to previous the selection result by the relevant parameter (including amplitude, phase place, frequency and damped coefficient) of discrete mode, postsearch screening can obtain dominant pattern more accurately such that it is able to improves the accuracy of low-frequency oscillation analysis further.

Analyzing, based on the PRONY of the low-frequency oscillation of electric power system shown in Fig. 1, the inventive concept that method is identical, the embodiment of the present application additionally provides the PRONY analytical equipment of a kind of low-frequency oscillation of electric power system, as described in example below.Owing to the principle of the PRONY analytical equipment solution problem of this low-frequency oscillation of electric power system is similar to the PRONY of low-frequency oscillation of electric power system analysis method, therefore the enforcement of the PRONY analytical equipment of this low-frequency oscillation of electric power system may refer to the enforcement of the PRONY analysis method of low-frequency oscillation of electric power system, repeats part and repeats no more.

Fig. 6 is the structural representation of the PRONY analytical equipment of one embodiment of the invention.As shown in Figure 6, the PRONY analytical equipment of the embodiment of the present invention, it may include: linear prediction model sets up unit 210, discrete mode generates unit 220, energy value generates unit 230 and the first Low Frequency Oscillation Analysis unit 240, and above-mentioned each unit is linked in sequence.

Linear prediction model is set up unit 210 and is set up Discrete Linear forecast model for the discrete signal of electrically-based system.

Discrete mode generates unit 220 and calculates multiple discrete modes for the proper polynomial according to above-mentioned Discrete Linear forecast model.

Energy value generates unit 230 for calculating the energy value corresponding to each above-mentioned discrete mode.

First Low Frequency Oscillation Analysis unit 240 for filtering out multiple pattern as the first control oscillation modes by relatively each above-mentioned energy value from above-mentioned multiple discrete modes, and according to above-mentioned first control oscillation modes, the low-frequency oscillation characteristic of power system is analyzed.

The PRONY analytical equipment of the embodiment of the present invention, analyze on method basis at tradition PRONY, consider that different patterns has different energy values, calculate the energy value of all patterns, and with this, pattern is screened, it is believed that the pattern with of a relatively high energy value is dominant pattern, think that the relatively low pattern of energy value is then ordinary pattern.Factor according to the above-mentioned dominant pattern analyzing influence power system dynamic stability filtered out, it is possible to improve the accuracy of the PRONY model estimation analyzed, it is possible to reduce PRONY analyzes False Rate in Power System Analysis, improves analysis efficiency and accuracy rate.

Fig. 7 is the method flow schematic diagram that in one embodiment of the invention, linear prediction model sets up unit.As it is shown in fig. 7, linear prediction model sets up unit 210 comprises the steps that signal estimation value generation module 211 and linear prediction model set up module 212, the two is connected with each other.

Signal estimation value generation module 211, for the signal data point in above-mentioned discrete signal is fitted, obtains multiple signal estimation value.

Linear prediction model sets up module 212 for setting up above-mentioned Discrete Linear forecast model according to above-mentioned multiple signal estimation values, wherein, the number of above-mentioned multiple signal estimation value is identical with the exponent number of above-mentioned Discrete Linear forecast model, and the number of equation corresponding to above-mentioned Discrete Linear forecast model is the number difference with above-mentioned exponent number of above-mentioned signal data point.

In one embodiment, by matching, the predictive value of discrete signal is expressed as the linear function of n given data.The general type that exponent number is the Discrete Linear forecast model of n can be:

Y (k)=a₁Y (k-1)+a₂y(k-2)+…+a_nY (k-n), (1)

Wherein, y is the title (such as exponential function) of function used, a in matching₁,…,a_i,…,a_nRepresenting the amplitude (being such as the coefficient of linear combination of exponential functions) in fitting result, n is the exponent number of Discrete Linear forecast model.

For obtaining the n rank Discrete Linear forecast model of matrix form, can k=n, n+1 ..., N-1 substitute into formula (1), wherein N is the number of above-mentioned discrete signal, obtains:

$\left[\begin{array}{c}y\left(n\right)\\ y(n+1)\\ y(n+2)\\ .\\ .\\ .\\ y(N-1)\end{array}\right]=\left[\begin{array}{cccc}y(n-1)& y(n-2)& \mathrm{...}& y\left(0\right)\\ y\left(n\right)& y(n-1)& \mathrm{...}& y\left(1\right)\\ y(n+1)& y\left(n\right)& \mathrm{...}& y\left(2\right)\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ y(N-2)& y(N-3)& \mathrm{...}& y(N-n-1)\end{array}\right]\left[\begin{array}{c}{a}_1\\ a_2\\ a_3\\ .\\ .\\ .\\ a_n\end{array}\right],---\left(2\right)$

Wherein, a_iFor the coefficient of characteristic equation and formula (2), 1≤i≤n, i and n is integer, and n is the exponent number of Discrete Linear forecast model.

In one embodiment, it is possible to adopt least-squares estimation (LSE) method to try to achieve coefficient a_i.It is preferred that the exponent number n > p of Discrete Linear forecast model, wherein,Consequently, it is possible to noise and the signal biasing impact on the Low Frequency Oscillation Analysis result of power system can be reduced.It is preferred that the number N-n > 2n of equation in formula (2), consequently, it is possible to may filter that noise.

In one embodiment, at above-mentioned steps S120, the proper polynomial of this Discrete Linear forecast model can be:

zⁿ+ a₁z^n-1+…a_n-1z+a_n=0, (3)

Wherein, z is the variable in this proper polynomial, and solution formula (3) can obtain multiple characteristic root z₁,…,z_j,…,z_n, corresponding with discrete mode, wherein, 1≤j≤n, j is integer.

Fig. 8 is the structural representation that in one embodiment of the invention, energy value generates unit.As shown in Figure 8, energy value generates unit 230 and comprises the steps that residual generation module 231, discrete mode sort module 232 and energy value generation module 233, and above-mentioned each sequence of modules connects.

Residual generation module 231 calculates, for utilizing the characteristic root corresponding to above-mentioned discrete signal and above-mentioned discrete mode, the residual obtained corresponding to above-mentioned discrete mode.

Discrete mode sort module 232 is for classifying to above-mentioned discrete mode by Real Number Roots pattern and conjugate complex number root mode.

Energy value generation module 233 is for according to type belonging to above-mentioned discrete mode, utilizing the characteristic root corresponding to above-mentioned discrete mode and corresponding above-mentioned residual to calculate the energy value obtained corresponding to above-mentioned discrete mode.

In one embodiment, can pass through to solve equation below and calculate residual:

$\left[\begin{array}{cccc}1& 1& \mathrm{...}& 1\\ z_1& z_2& \mathrm{...}& z_n\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ z_1^{N-1}& z_2^{N-1}& \mathrm{...}& z_n^{N-1}\end{array}\right]\left[\begin{array}{c}{c}_1\\ c_2\\ .\\ .\\ .\\ c_n\end{array}\right]=\left[\begin{array}{c}Y\left(1\right)\\ Y\left(2\right)\\ .\\ .\\ .\\ Y\left(N\right)\end{array}\right],---\left(4\right)$

Wherein, z₁,…,z_j,…,z_nRepresenting characteristic root, 1≤j≤n, j is integer；c₁,…,c_k,…,c_nRepresenting residual, 1≤k≤n, k is integer；Y (1) ..., Y (l) ..., Y (n) represents above-mentioned discrete signal (primary signal, non-pre-measured value), and 1≤l≤n, l is integer.

In the present embodiment, energy value is asked in the classification of above-mentioned discrete mode, it is possible to improve the accuracy of energy value.The characteristic root corresponding to above-mentioned discrete mode and corresponding above-mentioned residual is utilized to calculate the energy value obtained corresponding to above-mentioned discrete mode, based on the energy value corresponding to energy signal Theoretical Calculation discrete mode, method for solving is simple, efficient, it is possible to increase the acquisition speed of energy value.

In one embodiment, affiliated type is the energy value corresponding to the discrete mode of Real Number Roots pattern is:

$E_i=\underset{k=1}{\overset{N}{\Σ}}\[{\left(real\right(c_i{z}_i^k)\]}^2,---\left(5\right)$

Wherein, E_iFor the energy value corresponding to i-th discrete mode, N is the data point number of above-mentioned discrete signal, and real () represents treating excess syndrome portion, c_iFor the residual corresponding to discrete mode i, z_iFor the characteristic root corresponding to discrete mode i, k≤N, i, k and N are positive integer.

In one embodiment, affiliated type is the energy value corresponding to the discrete mode of conjugate complex number root mode is:

$E_i=\underset{k=1}{\overset{N}{\Σ}}{\[2real\left(c_i{z}_i^k\right)\]}^2,---\left(6\right)$

Wherein, E_iFor the energy value corresponding to i-th discrete mode, N is the data point number of above-mentioned discrete signal, and real () represents treating excess syndrome portion, c_iFor the residual corresponding to discrete mode i, z_iFor the characteristic root corresponding to discrete mode i, k≤N, k and N is positive integer.

In the present embodiment, it is only necessary to residual and two parameters of characteristic root can try to achieve residual, energy value obtains convenient.

Fig. 9 is the structural representation of the PRONY analytical equipment of the low-frequency oscillation of electric power system of another embodiment of the present invention.As shown in Figure 9, the PRONY analytical equipment of the low-frequency oscillation of electric power system shown in Fig. 6, may also include that discrete mode parameter generating unit 250 and the second Low Frequency Oscillation Analysis unit 260, the two is connected with each other, and discrete mode parameter generating unit 250 is connected with the first Low Frequency Oscillation Analysis unit 240.

Discrete mode parameter generating unit 250 is for calculating amplitude corresponding to above-mentioned discrete mode, phase place, frequency and damped coefficient.

Second Low Frequency Oscillation Analysis unit 260 is for doing screening further according to above-mentioned amplitude, phase place, frequency and damped coefficient to above-mentioned first control oscillation modes, obtain the second control oscillation modes, and according to above-mentioned second control oscillation modes, the low-frequency oscillation characteristic of power system is analyzed.

The PRONY analytical equipment of the low-frequency oscillation of electric power system of the embodiment of the present invention, dominant pattern is screened by the energy value corresponding to discrete mode, and make to screen further to previous the selection result by the relevant parameter (including amplitude, phase place, frequency and damped coefficient) of discrete mode, postsearch screening can obtain dominant pattern more accurately such that it is able to improves the accuracy of low-frequency oscillation analysis further.

Figure 10 is the structural representation of discrete mode parameter generating unit in one embodiment of the invention.As shown in Figure 10, above-mentioned discrete mode parameter generating unit 250 comprises the steps that residual generation module 251 (231) and discrete mode parameter generation module 252, and the two is connected with each other.

Residual generation module 251 (231) calculates, for utilizing the characteristic root corresponding to above-mentioned discrete signal and above-mentioned discrete mode, the residual obtained corresponding to above-mentioned discrete mode.

Discrete mode parameter generation module 252, for calculating above-mentioned frequency and damped coefficient according to above-mentioned residual, the characteristic root corresponding to above-mentioned discrete mode calculates and obtains above-mentioned amplitude and phase place.

In one embodiment, for solving the formula of amplitude corresponding to discrete mode, phase place, frequency and damped coefficient it is:

c_i=A_iexp(jφ_i), (7)

z_i=exp [(σ_i+j2πf_i) Δ t], (8)

Wherein, c_iFor the residual corresponding to i-th discrete mode, A_iFor the amplitude corresponding to i-th discrete mode, z_iFor the characteristic root corresponding to i-th discrete mode, σ_iFor the real part corresponding to i-th discrete mode, f_iFor the frequency corresponding to i-th discrete mode, Δ t is the sampling time interval of above-mentioned discrete signal, it is preferred that sample for constant duration.

Can deriving according to above-mentioned formula (7)～(8) and calculate amplitude corresponding to above-mentioned discrete mode, phase place, frequency and damped coefficient, specific formula for calculation is as follows:

A_i=| c_i|, (9)

φ_i=arctan (Im (c_i)/Re(c_i)), (10)

σ_i=ln | z_i|/Δ t, (11)

f_i=arctan (Im (z_i)/Re(z_i))/(2 π Δ t), (12)

${\mathrm{\ζ}}_i=\frac{-{\mathrm{\σ}}_i}{\sqrt{{{\mathrm{\σ}}_i}^2+{{\mathrm{\ω}}_i}^2}},---\left(13\right)$

Wherein, in formula (13), ζ_iRepresent the damped coefficient corresponding to i-th discrete mode, ω_iFor the imaginary part corresponding to i-th discrete mode.What deserves to be explained is, the symbol of i is used in above-mentioned many places, and its concrete meaning determines according to the specified context used.

The PRONY analytical equipment of the low-frequency oscillation of electric power system of the embodiment of the present invention, on tradition PRONY analysis foundation, consider that different patterns has different energy values, calculate the energy value of all patterns, and with this, pattern is screened, it is believed that the pattern with of a relatively high energy value is dominant pattern, think that the relatively low pattern of energy value is then ordinary pattern.Factor according to the above-mentioned dominant pattern analyzing influence power system dynamic stability filtered out, the accuracy of the PRONY model estimation analyzed can be improved, PRONY can be reduced and analyze False Rate in Power System Analysis, improve analysis efficiency and accuracy rate, it is thus possible to the redundancy of effort reduced in analysis process, provide guarantee for low-frequency oscillation of electric power system accurate analysis.Make to screen further to previous the selection result by the relevant parameter (including amplitude, phase place, frequency and damped coefficient) of discrete mode, postsearch screening can obtain dominant pattern more accurately such that it is able to improves the accuracy of low-frequency oscillation analysis further.

In the description of this specification, specific features, structure, material or feature that the description of reference term " embodiment ", " specific embodiment ", " some embodiments ", " such as ", " example ", " concrete example " or " some examples " etc. means in conjunction with this embodiment or example describe are contained at least one embodiment or the example of the present invention.In this manual, the schematic representation of above-mentioned term is not necessarily referring to identical embodiment or example.And, the specific features of description, structure, material or feature can combine in an appropriate manner in any one or more embodiments or example.

Those skilled in the art are it should be appreciated that embodiments of the invention can be provided as method, system or computer program.Therefore, the present invention can adopt the form of complete hardware embodiment, complete software implementation or the embodiment in conjunction with software and hardware aspect.And, the present invention can adopt the form at one or more upper computer programs implemented of computer-usable storage medium (including but not limited to disk memory, CD-ROM, optical memory etc.) wherein including computer usable program code.

The present invention is that flow chart and/or block diagram with reference to method according to embodiments of the present invention, equipment (system) and computer program describe.It should be understood that can by the combination of the flow process in each flow process in computer program instructions flowchart and/or block diagram and/or square frame and flow chart and/or block diagram and/or square frame.These computer program instructions can be provided to produce a machine to the processor of general purpose computer, special-purpose computer, Embedded Processor or other programmable data processing device so that the instruction performed by the processor of computer or other programmable data processing device is produced for realizing the device of function specified in one flow process of flow chart or multiple flow process and/or one square frame of block diagram or multiple square frame.

These computer program instructions may be alternatively stored in and can guide in the computer-readable memory that computer or other programmable data processing device work in a specific way, the instruction making to be stored in this computer-readable memory produces to include the manufacture of command device, and this command device realizes the function specified in one flow process of flow chart or multiple flow process and/or one square frame of block diagram or multiple square frame.

These computer program instructions also can be loaded in computer or other programmable data processing device, make on computer or other programmable devices, to perform sequence of operations step to produce computer implemented process, thus the instruction performed on computer or other programmable devices provides for realizing the step of function specified in one flow process of flow chart or multiple flow process and/or one square frame of block diagram or multiple square frame.

Particular embodiments described above; the purpose of the present invention, technical scheme and beneficial effect have been further described; it is it should be understood that; the foregoing is only specific embodiments of the invention; the protection domain being not intended to limit the present invention; all within the spirit and principles in the present invention, any amendment of making, equivalent replacement, improvement etc., should be included within protection scope of the present invention.

Claims (12)

1. the PRONY of a low-frequency oscillation of electric power system analyzes method, it is characterised in that including:

The discrete signal of electrically-based system sets up Discrete Linear forecast model；

Proper polynomial according to described Discrete Linear forecast model calculates multiple discrete modes；

Calculate the energy value corresponding to each described discrete mode；

From the plurality of discrete mode, filter out multiple pattern as the first control oscillation modes by relatively each described energy value, and according to described first control oscillation modes, the low-frequency oscillation characteristic of power system is analyzed.

2. the PRONY of low-frequency oscillation of electric power system as claimed in claim 1 analyzes method, it is characterised in that also include:

Calculate the amplitude corresponding to described discrete mode, phase place, frequency and damped coefficient；

According to described amplitude, phase place, frequency and damped coefficient, described first control oscillation modes is done screening further, obtain the second control oscillation modes, and according to described second control oscillation modes, the low-frequency oscillation characteristic of power system is analyzed.

3. the PRONY of low-frequency oscillation of electric power system as claimed in claim 2 analyzes method, it is characterised in that calculate the energy value corresponding to each described discrete mode, including:

The characteristic root corresponding to described discrete signal and described discrete mode is utilized to calculate the residual obtained corresponding to described discrete mode；

By Real Number Roots pattern and conjugate complex number root mode, described discrete mode is classified；

According to type belonging to described discrete mode, the characteristic root corresponding to described discrete mode and corresponding described residual is utilized to calculate the energy value obtained corresponding to described discrete mode.

4. the PRONY of low-frequency oscillation of electric power system as claimed in claim 3 analyzes method, it is characterised in that calculate the amplitude corresponding to described discrete mode, phase place, frequency and damped coefficient, including:

Calculate described frequency and damped coefficient according to described residual, the characteristic root corresponding to described discrete mode calculates and obtains described amplitude and phase place.

5. the PRONY of low-frequency oscillation of electric power system as claimed in claim 1 analyzes method, it is characterised in that the discrete signal of electrically-based system sets up Discrete Linear forecast model, including:

Signal data point in described discrete signal is fitted, obtains multiple signal estimation value；

Described Discrete Linear forecast model is set up according to the plurality of signal estimation value, wherein, the number of the plurality of signal estimation value is identical with the exponent number of described Discrete Linear forecast model, and the number of equation corresponding to described Discrete Linear forecast model is the number difference with described exponent number of described signal data point.

6. the PRONY of low-frequency oscillation of electric power system as claimed in claim 3 analyzes method, it is characterised in that affiliated type is the energy value corresponding to the discrete mode of Real Number Roots pattern is:

$E_i=\underset{k=1}{\overset{N}{\Σ}}\[{\left(real\right(c_i{z}_i^k)\]}^2,$

Wherein, E_iFor the energy value corresponding to i-th discrete mode, N is the data point number of described discrete signal, and real () represents treating excess syndrome portion, c_iFor the residual corresponding to discrete mode i, z_iFor the characteristic root corresponding to discrete mode i, k≤N, i, k and N are positive integer.

7. the PRONY of low-frequency oscillation of electric power system as claimed in claim 3 analyzes method, it is characterised in that affiliated type is the energy value corresponding to the discrete mode of conjugate complex number root mode is:

$E_i=\underset{k=1}{\overset{N}{\Σ}}{\[2real\left(c_i{z}_i^k\right)\]}^2,$

Wherein, E_iFor the energy value corresponding to i-th discrete mode, N is the data point number of described discrete signal, and real () represents treating excess syndrome portion, c_iFor the residual corresponding to discrete mode i, z_iFor the characteristic root corresponding to discrete mode i, k≤N, k and N is positive integer.

8. the PRONY analytical equipment of a low-frequency oscillation of electric power system, it is characterised in that including:

Linear prediction model sets up unit, and the discrete signal for electrically-based system sets up Discrete Linear forecast model；

Discrete mode generates unit, calculates multiple discrete modes for the proper polynomial according to described Discrete Linear forecast model；

Energy value generates unit, for calculating the energy value corresponding to each described discrete mode；

First Low Frequency Oscillation Analysis unit, for filtering out multiple pattern from the plurality of discrete mode as the first control oscillation modes by relatively each described energy value, and is analyzed the low-frequency oscillation characteristic of power system according to described first control oscillation modes.

9. the PRONY analytical equipment of low-frequency oscillation of electric power system as claimed in claim 8, it is characterised in that also include:

Discrete mode parameter generating unit, for calculating amplitude corresponding to described discrete mode, phase place, frequency and damped coefficient；

Second Low Frequency Oscillation Analysis unit, for described first control oscillation modes being done screening further according to described amplitude, phase place, frequency and damped coefficient, obtain the second control oscillation modes, and according to described second control oscillation modes, the low-frequency oscillation characteristic of power system is analyzed.

10. the PRONY analytical equipment of low-frequency oscillation of electric power system as claimed in claim 9, it is characterised in that described energy value generates unit and includes:

Residual generation module, for utilizing the characteristic root corresponding to described discrete signal and described discrete mode to calculate the residual obtained corresponding to described discrete mode；

Discrete mode sort module, for classifying to described discrete mode by Real Number Roots pattern and conjugate complex number root mode；

Energy value generation module, for according to type belonging to described discrete mode, utilizing the characteristic root corresponding to described discrete mode and corresponding described residual to calculate the energy value obtained corresponding to described discrete mode.

11. the PRONY analytical equipment of low-frequency oscillation of electric power system as claimed in claim 10, it is characterised in that described discrete mode parameter generating unit includes:

Discrete mode parameter generation module, for calculating described frequency and damped coefficient according to described residual, the characteristic root corresponding to described discrete mode calculates and obtains described amplitude and phase place.

12. the PRONY analytical equipment of low-frequency oscillation of electric power system as claimed in claim 8, it is characterised in that described linear prediction model is set up unit and included:

Signal estimation value generation module, for the signal data point in described discrete signal is fitted, obtains multiple signal estimation value；

Linear prediction model sets up module, for setting up described Discrete Linear forecast model according to the plurality of signal estimation value, wherein, the number of the plurality of signal estimation value is identical with the exponent number of described Discrete Linear forecast model, and the number of equation corresponding to described Discrete Linear forecast model is the number difference with described exponent number of described signal data point.