A method for characterizing transient electrical quantities in power systems based on Takenaka-Malmquist system

Abstract

The present invention belongs to the technical field of synchronous measurement of power systems, and specifically discloses a method for characterizing transient electrical quantities of power systems based on a Takenaka‑Malmquist system, comprising the following steps: first, by analogy with the form of traditional synchronous phasors, a TM phasor based on a TM system and a Blaschke dynamic basis is defined; secondly, based on the TM phasor, an inter-window frequency is defined to characterize the phase change between measurement time windows; and then, based on the Blaschke basis, an intra-window frequency is defined to characterize the phase change within the measurement time window; then, the inter-window frequency is extended so that its data length is equal to the intra-window frequency, and the two are combined to obtain the TM frequency; finally, according to an adaptive Fourier transform algorithm, the TM phasor and the TM frequency are calculated from the signal sampling value of a sampling module. The present invention adopts the above-mentioned method for characterizing transient electrical quantities of power systems based on a Takenaka‑Malmquist system, and the fault recording data test shows that the waveform reconstruction error of the proposed method is less than one-tenth of that of the FFT method, and the non-redundant characterization of transient electrical quantities of power systems can be achieved.

Description

Technical Field

[0001] The invention relates to the technical field of synchronous measurement of power systems, and in particular to a method for characterizing transient electrical quantities of power systems based on a Takenaka-Malmquist system. Background Art

[0002] At present, electrical quantities in power systems are mainly represented by two forms: phasor and waveform, which correspond to synchronous phasor measurement and synchronous waveform measurement in the field of synchronous measurement of power systems respectively.

[0003] The definition of phasor comes from Fourier transform, which consists of amplitude and phase, and cooperates with Fourier basis to realize the characterization of electrical quantity. At present, the research on synchronous phasor measurement mainly focuses on improving the dynamic performance of measurement algorithm. In other words, the idea of ​​most research is to make the phasor move, and extract the dynamic time-varying phasor by completely extracting the oscillation component in the frequency domain or fitting it with a dynamic model, which has achieved good results in the tracking and characterization of low-frequency oscillation or sub-supersynchronous oscillation. However, the time scale of low-frequency oscillation or sub-supersynchronous oscillation changes very slowly relative to the time scale of several cycle measurement time windows, which makes the oscillation component relatively stable within the time window. However, the waveform distortion is serious after the power system fault, and mutations and discontinuities are prone to appear in the time window, which is no longer stable and regular. The amplitude and frequency of the Fourier basis are static and unchanged in the measurement time window, and there is only one phasor calculation result in each time window, which makes it difficult for the method based on phasor and Fourier transform to capture the local characteristics of transient signals and is not suitable for transient signals after faults.

[0004] The waveform of electrical quantities is the most primitive form of representation. With the improvement of communication capabilities, synchronous waveform measurement has also been widely studied recently. Related research mainly involves waveform compression methods, communication protocols, and applications in fault type identification and fault location in distribution networks. Although synchronous waveform measurement can provide complete transient process recording results, the data it provides needs to be reprocessed to achieve other application purposes, that is, its intermediate representation quantities do not have physical meaning. In addition, the existing synchronous waveform measurement is separated from the synchronous phasor measurement, and the two measurement systems are incompatible with each other, which leads to increased device development costs and system operation and maintenance costs.

[0005] Therefore, it is urgent to introduce a new dynamic characterization basis and study the electrical quantity characterization method that is applicable to both transient and steady states. Summary of the invention

[0006] The purpose of the present invention is to provide a method for characterizing transient and steady-state electrical quantities of a power system based on a Takenaka-Malmquist system, which can realize the characterization of transient and steady-state signals of the power system.

[0007] To achieve the above object, the present invention provides a method for characterizing transient electrical quantities of a power system based on a Takenaka-Malmquist system, comprising the following steps:

[0008] S1. Analogously to the form of traditional synchronized phasors, define the TM phasors based on the TM system and the Blaschke dynamic basis;

[0009] S2. Based on the TM phasor, define the inter-window frequency to characterize the phase change between the measurement time windows;

[0010] S3, according to the Blaschke basis, define the frequency within the window to characterize the phase change within the measurement time window;

[0011] S4, extending the inter-window frequency so that its data length is equal to the intra-window frequency, and combining the inter-window frequency with the intra-window frequency to obtain the TM frequency;

[0012] S5. According to the adaptive Fourier transform algorithm, the TM phase and the TM frequency are calculated from the signal sampling values ​​of the sampling module.

[0013] Preferably, in S1, the form of the traditional synchronized phasor is as follows:

[0014] The voltage and current time domain signals of the power system are expressed as:

[0015] (1);

[0016] in, X ( t )and φ ( t ) represent the time-varying amplitude and phase angle, Indicates fundamental frequency, which refers to the rated frequency of the power system;

[0017] The traditional Fourier analysis method is used to characterize the voltage and current time domain signals of the power system as a superposition of a series of phasors and Fourier basis products:

[0018] (2);

[0019] in, Represents the Fourier transform The characterization result of the signal at time is given by R The frequency components are superimposed, and each frequency component is composed of the phasor multiplied by the basis; R Represents the total number of frequency components; r In the amount, represents the phasor, represents the Fourier basis, Indicates rThe frequency of the component, is the phase amplitude, is the phasor phase, is the imaginary unit;

[0020] In order to characterize the power system voltage and current time domain signals in the form of equation (2), the signals are subjected to discrete Fourier transform to calculate each characterization quantity:

[0021] (3);

[0022] In the formula, x ( n ) indicates the first n discrete power system voltage and current time domain signal sampling values, N Represents the total number of sampling points in the time window, w ( n ) indicates the n filter coefficients, represents the Fourier operator, Indicates the sampling frequency.

[0023] Preferably, in S1, the TM system is a collection of a series of Blaschke dynamic bases, and the Blaschke dynamic bases are:

[0024] (4);

[0025] (5);

[0026] (6);

[0027] (7);

[0028] in, d Indicates d Second decomposition, D represents the total number of decompositions, B d Representative d The base of the second decomposition, Representative d Free variables in the second decomposition The value of is a complex number with modulus less than 1, C represents a complex set, z represents a variable related to the signal phase, t represents the signal phase, N Indicates the total number of sampling points in the time window.

[0029] Preferably, in S1, the TM phasor is defined as a superposition of a series of phasors and a Blaschke basis product:

[0030] (8);

[0031] in, represents the result obtained based on the TM system and the Blaschke basis t k The characterization result of the signal at time is given by M Each component is also composed of the representation quantity, that is, the TM phase multiplied by the basis. In the amount, represents the phasor, is the new phasor amplitude, is the phase of the TM phasor.

[0032] Preferably, in S2, the method for calculating the inter-window frequency is:

[0033] (9);

[0034] In the formula, express Moment The window frequency of the components, and Respectively The next calculation time and the previous time The phase of the components, Indicates the TM phasor calculation frequency.

[0035] Preferably, in S3, the method for calculating the frequency within the window is:

[0036] (10);

[0037] In the formula, express Moment The frequency within the window of the component, and Respectively represent The Blaschke basis in the subdecomposition is The phase between the next sampling instant and the previous sampling instant.

[0038] Preferably, in S4, the TM frequency calculation method is:

[0039] (11);

[0040] In the formula express Moment The complete TM frequency of the components, and The time granularity of is different, and the number of them is respectively and Decide;

[0041] Specifically, Reflects the change of frequency between windows. There is only one value in each measurement time window. Reflects the frequency change in the time window. In each measurement time window, values, T Indicates that the measurement time window is long, and there is a difference in the total number of the two. Therefore, when calculating the TM frequency in each time window, equation (11) is changed to:

[0042] (12);

[0043] In the formula, t m It represents the time in each calculation time window, that is, the TM phasor calculation time.

[0044] Preferably, in S5, the adaptive Fourier transform algorithm AFD is:

[0045] In each calculation of AFD, the free variables are calculated first. Then calculate the basis B i , and finally calculate the decomposition amount;

[0046] Specifically, the AFD algorithm first generates a dictionary at a certain resolution, including All possible values ​​of ;

[0047] Furthermore, the signal to be decomposed and Energy evaluation operator e i , the calculation formula is:

[0048] (13);

[0049] in Remainder i Indicates The signal to be decomposed in the second decomposition is a set of sampling points, which is the original signal minus the previous The decomposition amount is obtained; Weight Represents the calculation weight array; corresponding to each one in the dictionary , each has one e i Correspondingly, the largest value e i The corresponding Selected:

[0050] (14);

[0051] in, Indicates for finding e i The maximum value corresponds to Function of

[0052] when e i After being determined, Sub-decomposed base B i and TM phasor It is determined, B i Calculated by formula (2), Calculated by the following formula:

[0053] (15).

[0054] Therefore, the present invention adopts the above-mentioned method for characterizing transient electrical quantities of power systems based on the Takenaka-Malmquist system, and the beneficial effects are as follows:

[0055] (1) The present invention replaces the static sine-cosine basis of the traditional synchronous phasor of the power system with a dynamic Blaschke basis, thereby improving the dynamic performance of the basis and supporting the characterization of the local time-frequency characteristics of the power signal within the measurement time window.

[0056] (2) The present invention defines TM phasor as a new type of characterization quantity. While maintaining the representation form of the traditional synchronous phasor multiplied by the Fourier basis, it realizes the non-redundant representation of the transient and steady-state signals of the power system, and improves the characterization efficiency of the transient signal while keeping the representation form of the steady-state signal unchanged.

[0057] (3) The present invention defines the TM frequency and proposes a TM frequency calculation method, which combines the traditional inter-window frequency domain with the intra-window frequency to achieve the characterization of the frequency change of the power signal within the measurement time window.

[0058] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 It is an overall flow chart of an embodiment of a method for characterizing transient and steady-state electrical quantities of a power system based on a Takenaka-Malmquist system of the present invention;

[0060] Figure 2It is the energy distribution of the field fault signal after TM decomposition in an embodiment of the method for characterizing transient-stable electrical quantities of a power system based on the Takenaka-Malmquist system of the present invention;

[0061] Figure 3 It is the second-layer TM phasor amplitude and TM frequency obtained by decomposing the field fault signal of an embodiment of a method for characterizing transient-steady-state electrical quantities of a power system based on a Takenaka-Malmquist system of the present invention, wherein (a) is the phasor amplitude and (b) is the TM frequency;

[0062] Figure 4 It is the third-layer TM phasor amplitude and TM frequency obtained by decomposing the field fault signal of an embodiment of a method for characterizing transient-steady-state electrical quantities of a power system based on a Takenaka-Malmquist system of the present invention, wherein (a) is the phasor amplitude and (b) is the TM frequency;

[0063] Figure 5 It is the waveform reconstruction error of two methods of an embodiment of a method for characterizing transient-steady-state electrical quantities of a power system based on a Takenaka-Malmquist system of the present invention. DETAILED DESCRIPTION

[0064] The technical solution of the present invention is further described below through the accompanying drawings and embodiments.

[0065] Unless otherwise defined, technical or scientific terms used in the present invention shall have the common meanings understood by one having ordinary skills in the field to which the present invention belongs.

[0066] like Figure 1 As shown, a method for characterizing transient electrical quantities of a power system based on a Takenaka-Malmquist system includes the following steps:

[0067] S1. By analogy with the traditional synchronized phasor, the TM phasor based on the TM (Takenaka-Malmquist) system and the Blaschke dynamic basis is defined;

[0068] The traditional synchronized phasor is in the following form:

[0069] The voltage and current time domain signals of the power system can be expressed as:

[0070] (1);

[0071] in, X ( t )and φ ( t ) represent the time-varying amplitude and phase angle, Indicates the fundamental frequency, which refers to the rated frequency of the power system.

[0072] The traditional Fourier analysis method is used to characterize the voltage and current time domain signals of the power system as a superposition of a series of phasors and Fourier basis products:

[0073] (2);

[0074] in, Represents the Fourier transform The characterization result of the signal at time is given by R The frequency components are superimposed, each of which is composed of a phasor (characteristic quantity) multiplied by a basis (determined by frequency and time scale); R Represents the total number of frequency components; r In the amount, represents the phasor, represents the Fourier basis, Indicates r The frequency of the component, is the phase amplitude, is the phasor phase, is the imaginary unit.

[0075] In order to characterize the power system voltage and current time domain signals in the form of equation (2), the signals are subjected to discrete Fourier transform to calculate each characterization quantity:

[0076] (3);

[0077] In the formula, x ( n ) indicates the first n discrete power system voltage and current time domain signal sampling values, N Represents the total number of sampling points in the time window, w ( n ) indicates the n filter coefficients, represents the Fourier operator, Indicates the sampling frequency.

[0078] The TM system is a collection of a series of Blaschke dynamic bases, which are:

[0079] (4);

[0080] (5);

[0081] (6);

[0082] (7);

[0083] in, d Indicates d Second decomposition, D represents the total number of decompositions, B d Representative d The base of the second decomposition, Representative d Free variables in the second decomposition The value of is a complex number with modulus less than 1, C represents a complex set, z represents a variable related to the signal phase, t represents the signal phase, N Indicates the total number of sampling points in the time window.

[0084] The TM phasor is defined as the superposition of a series of phasors and the Blaschke basis product:

[0085] (8);

[0086] in, represents the value obtained based on the TM system and the Blaschke basis The characterization result of the signal at time is given by M Each component is also composed of the representation quantity, that is, the TM phase multiplied by the basis. In the amount, represents the phasor, is the new phasor amplitude, is the phase of the TM phasor.

[0087] S2. According to the TM phasor, define the inter-window frequency to characterize the phase change between the measurement time windows. The specific operation is as follows;

[0088] The calculation method of the window frequency is:

[0089] (9);

[0090] In the formula, express Moment The window frequency of the components, and Respectively The next calculation time and the previous time The phase of the components, Indicates the TM phasor calculation frequency.

[0091] S3. According to the Blaschke basis, define the frequency within the window to characterize the phase change within the measurement time window. The specific operation is as follows;

[0092] The frequency calculation method within the window is:

[0093] (10);

[0094] In the formula, express Moment The frequency within the window of the component, and Respectively represent The Blaschke basis in the subdecomposition is The phase between the next sampling instant and the previous sampling instant.

[0095] S4, extend the inter-window frequency so that its data length is equal to the frequency in the window, combine the inter-window frequency with the frequency in the window to obtain the TM frequency, specific operation;

[0096] The TM frequency calculation method is:

[0097] (11);

[0098] In the formula express Moment The complete TM frequency of the components, it is worth noting here, and The time granularity of is different, and the number of them is respectively and Decide.

[0099] Specifically, Reflects the change of frequency between windows. There is only one value in each measurement time window. Reflects the frequency change in the time window. In each measurement time window, values, T It indicates that the measurement time window is long. Obviously, there is a difference in the total number of the two. Therefore, when calculating the TM frequency in each time window, equation (11) needs to be changed to:

[0100] (12);

[0101] In the formula, t m It represents the time in each calculation time window, that is, the TM phasor calculation time.

[0102] S5. According to the adaptive Fourier transform algorithm, the TM phasor and TM frequency are calculated from the signal sampling values ​​of the sampling module. The specific operations are as follows.

[0103] The adaptive Fourier transform algorithm AFD is:

[0104] Easy to know B i Only Influence, in each calculation of AFD, the free variables are also calculated first Then calculate the basis B i , and finally calculate the decomposition amount;

[0105] Specifically, because is a complex number with a modulus less than 1, so the AFD algorithm first generates a dictionary with a certain resolution, including All possible values ​​of ;

[0106] Furthermore, the signal to be decomposed and Energy evaluation operator e i , the calculation formula is:

[0107] (13);

[0108] in, Remainder i Indicates The signal to be decomposed in the second decomposition is a set of sampling points, which is the original signal minus the previous The amount of decomposition is obtained. Weight represents the calculation weight array, which is set to 1 in this embodiment. , each has one e i Correspondingly, the largest value e i The corresponding Selected:

[0109] (14);

[0110] in, Indicates for finding e i The maximum value corresponds to function.

[0111] when e i After being determined, Sub-decomposed base and TM phasor It is determined, Calculated by formula (2), Calculated by the following formula:

[0112] (15).

[0113] The present invention is described below by means of specific examples.

[0114] Embodiment 1

[0115] In order to verify the effect of the method proposed in the present invention, a section of ultra-high voltage line voltage fault signal was selected as the analysis object, the signal sampling rate was 9600 Hz, and the fault occurred at 0.1 s.

[0116] The overall energy distribution of the field fault signal after TM decomposition is as follows: Figure 2 As shown by Figure 2 It can be seen that after the fault occurs, the amplitude of the second-layer TM phasor begins to oscillate, and the energy leaks to the higher-layer TM phasor.

[0117] The second and third layer TM phase amplitudes and TM frequencies obtained by decomposing the field fault signal are shown in Figure 3 and Figure 4 As shown in the figure, it can be seen that before the fault, the amplitude of the second-layer TM phasor is stable at the rated value, the TM frequency is around 50 Hz, and the amplitude of the second-layer TM phasor is close to zero; after the fault, the method proposed in the present invention efficiently and dynamically decomposes the signal through different levels of TM characterization quantities, which is manifested in that the second-layer TM phasor amplitude and TM frequency begin to oscillate, and the second-layer TM phasor amplitude at the beginning and end of the time window suddenly increases, and the higher-dimensional TM characterization quantities are similar.

[0118] like Figure 5 As shown, the maximum error of waveform reconstruction of the characterization method of this embodiment is 0.68%, and the maximum error of the comparison method is 9.48%. It can be seen that the reconstructed waveform of the characterization method of this embodiment almost coincides with the original signal, while the reconstructed waveform of the FFT method has a larger offset compared to the original signal. One reason for this phenomenon is the sudden change of the signal, and another reason is the large number of non-integer harmonics in the signal after the fault. Because the FFT of the short window is limited by the frequency resolution, it is difficult to distinguish these interharmonics. If the window length is increased, it will be difficult to track the signal changes within the time window. The traditional method based on the Fourier basis is difficult to take into account both frequency resolution and dynamic performance. The characterization method of this embodiment uses a series of dynamic Blaschke bases, which is no longer limited by concepts such as frequency resolution in the frequency domain, and has good fitting and characterization effects.

[0119] Therefore, the present invention adopts the above-mentioned method for characterizing transient electrical quantities of power systems based on the Takenaka-Malmquist system. The fault recording data test shows that the waveform reconstruction error of the proposed method is less than one tenth of that of the FFT method, and the non-redundant characterization of transient electrical quantities of power systems can be achieved.

[0120] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A method for characterizing transient electrical quantities of a power system based on the Takenaka-Malmquist system, characterized in that: The following steps are involved: S1. Analogously to the form of traditional synchronized phasors, define the TM phasors based on the TM system and the Blaschke dynamic basis; S2. Based on the TM phasor, define the inter-window frequency to characterize the phase change between the measurement time windows; S3, according to the Blaschke basis, define the frequency within the window to characterize the phase change within the measurement time window; S4, extending the inter-window frequency so that its data length is equal to the intra-window frequency, and combining the inter-window frequency with the intra-window frequency to obtain the TM frequency; S5, calculating the TM phase and TM frequency from the signal sampling values ​​of the sampling module according to the adaptive Fourier transform algorithm; In S1, the TM system is a collection of Blaschke dynamic bases, which are: （1）； （2）； （3）； （4）； in, Indicates Second decomposition, D represents the total number of decompositions, Representative The base of the second decomposition, Representative Free variables in the second decomposition The value of c is a complex number with modulus less than 1, C represents a complex set, z represents a variable related to the signal phase, t represents the signal phase, N Indicates the total number of sampling points in the time window; In S1, the TM phasor is defined as the superposition of a series of phasors and the Blaschke basis product: （5）； in, represents the result obtained based on the TM system and the Blaschke basis The characterization result of the signal at time is given by M Each component is also composed of the representation quantity, that is, the TM phase multiplied by the basis. In the amount, represents the phasor, is the amplitude of the TM phasor, is the phase of the TM phasor, represents the Blaschke base; In S2, the frequency between windows is calculated as: （6）； In the formula, express Moment The window frequency of the components, and Respectively The next calculation time and the previous time The phase of the components, Indicates the TM phasor calculation frequency; In S3, the frequency calculation method within the window is: （7）； In the formula, express Moment The frequency within the window of the component, and Respectively represent The Blaschke basis in the subdecomposition is The phase between the next sampling moment and the previous sampling moment, Indicates the sampling frequency.

2. The method for characterizing transient electrical quantities of a power system based on the Takenaka-Malmquist system according to claim 1, characterized in that: In S1, the traditional synchronized phasor is in the following form: The voltage and current time domain signals of the power system are expressed as: （8）； in, and denote the time-varying amplitude and phase angle, respectively. Indicates fundamental frequency, which refers to the rated frequency of the power system; The traditional Fourier analysis method is used to characterize the voltage and current time domain signals of the power system as a superposition of a series of phasors and Fourier basis products: （9）； in, Represents the Fourier transform The characterization result of the signal at time is given by R The frequency components are superimposed, and each frequency component is composed of the phasor multiplied by the basis; R Represents the total number of frequency components; In the amount, represents the phasor, represents the Fourier basis, Indicates The frequency of the component, is the phase amplitude, is the phasor phase, is the imaginary unit; In order to characterize the power system voltage and current time domain signals in the form of equation (9), the signals are subjected to discrete Fourier transform to calculate each characterization quantity: （10）； In the formula, Indicates the first discrete power system voltage and current time domain signal sampling values, N Represents the total number of sampling points in the time window, Indicates filter coefficients, represents the Fourier operator, Indicates the sampling frequency.

3. The method for characterizing transient electrical quantities of a power system based on the Takenaka-Malmquist system according to claim 2 is characterized in that: In S4, the TM frequency calculation method is: （11）； In the formula express Moment The complete TM frequency of the components, and The time granularity of is different, and the number of them is respectively and Decide; Specifically, Reflects the change of frequency between windows. There is only one value in each measurement time window. Reflects the frequency change in the time window. In each measurement time window, values, T Indicates that the measurement time window is long, and there is a difference in the total number of the two. Therefore, when calculating the TM frequency in each time window, formula (11) is changed to: （12）； In the formula, It represents the time in each calculation time window, that is, the TM phasor calculation time.

4. The method for characterizing transient electrical quantities of a power system based on the Takenaka-Malmquist system according to claim 3 is characterized in that: In S5, the adaptive Fourier transform algorithm AFD is: In each calculation of AFD, the free variables are calculated first. Then calculate the basis , and finally calculate the decomposition amount; Specifically, the AFD algorithm first generates a dictionary at a certain resolution, including All possible values ​​of ; Furthermore, the signal to be decomposed and Energy evaluation operator , the calculation formula is: （13）； in Indicates The signal to be decomposed in the second decomposition is a set of sampling points, which is the original signal minus the previous The decomposition amount is obtained; Weight Represents the calculation weight array; corresponding to each one in the dictionary , each has one Correspondingly, the largest value The corresponding Selected: （14）； in, Indicates for finding The maximum value corresponds to Function of when After being determined, Sub-decomposed base and TM phasor It is determined, Calculated by formula (9), Calculated by the following formula: （15）。

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