CN113394782B - Industrial park harmonic monitoring method based on APF direct-current voltage information inversion - Google Patents
Industrial park harmonic monitoring method based on APF direct-current voltage information inversion Download PDFInfo
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/01—Arrangements for reducing harmonics or ripples
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
- H02J2203/10—Power transmission or distribution systems management focussing at grid-level, e.g. load flow analysis, node profile computation, meshed network optimisation, active network management or spinning reserve management
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- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
- Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
- Y02E40/20—Active power filtering [APF]
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Abstract
An industrial park harmonic monitoring method based on APF direct current voltage information inversion belongs to the technical field of harmonic compensation of power systems. The invention aims to provide an industrial park harmonic monitoring method based on APF direct-current voltage information inversion for monitoring industrial park harmonic according to the internal relation between ripple frequency in APF direct-current side capacitor voltage and harmonic frequency of output compensation current. The method comprises the following steps: designing a corresponding relation between the ripple frequency of the direct current side capacitor voltage and the compensation current frequency to obtain a singular eigenmode function of the direct current side capacitor voltage signal, applying Hilbert transform to the optimized IMF, and determining the number of harmonic waves in the distribution network by a table look-up method. According to the invention, the frequency and the relative amplitude of the APF harmonic compensation current are inversely obtained by mining the secondary data of the two-level APF direct-current side capacitor voltage signal, and then the degree of harmonic pollution of the industrial park power distribution network is mastered in real time, so that the capital investment of industrial park enterprises in harmonic monitoring equipment is reduced.
Description
Technical Field
The invention belongs to the technical field of harmonic compensation of power systems.
Background
The industrial park loads are mainly asynchronous motors, frequency converters, precision instruments, building control equipment and other nonlinear equipment containing power electronics, and harmonic currents generated by the equipment in the operation process not only can influence the electric energy quality of the industrial park, but also can threaten the safe and stable operation of the system. An Active Power Filter (APF) has become one of the main devices for solving the problem of harmonic pollution in an industrial park due to the characteristics of high real-time compensation speed, high reliability, simple control and the like. If the APF direct current side capacitor voltage information can be acquired by using the APF self-contained direct current voltage detection module, the condition of APF harmonic compensation is inverted through a data mining algorithm, the harmonic pollution degree of the power distribution network of the industrial park can be mastered in real time under the condition that other electric energy quality monitoring equipment is not added, and the capital investment of enterprises on harmonic monitoring is greatly saved.
Disclosure of Invention
The invention aims to provide an industrial park harmonic monitoring method based on APF direct-current voltage information inversion for monitoring industrial park harmonic according to the internal relation between ripple frequency in APF direct-current side capacitor voltage and harmonic frequency of output compensation current.
The method comprises the following steps:
s1, a star connection mode is adopted among three phases, wherein u s For three-phase mains voltage, i s Is the net side current, i L Is the load current i c Output of a compensating current, u, for the APF dc Is the DC side capacitor voltage i dc For the current flowing through the capacitor, L C Connecting reactance; the three-phase instantaneous active power output to the power grid by the APF system is obtained according to the basic principle of the power system as follows:
wherein U is s Is an effective value of ABC three-phase voltage, I (n) And
for effective values and phases corresponding to n times of output current, n = ± (6 k ± 1) and n = -1 correspond to alternating current parts of three-phase instantaneous power, wherein k =1,2,3 … and n =1 corresponds to direct current parts of three-phase instantaneous power;
when the APF operates in a steady state, the direct current side capacitor voltage consists of a direct current constant component and an alternating current component, namely:
according to the principle that instantaneous power on two sides of APF alternating current and direct current are equal:
let m = n-1, a specific expression of the ac ripple component with an angular frequency of m ω in the dc-side capacitor voltage is further derived from equation (3):
through the above theoretical analysis on the dc side capacitor voltage ripple, the following conclusions can be drawn:
(1) When the APF compensates the m +1 positive sequence (m +1 is more than 0) or the | m +1| negative sequence (-m +1 is less than 0) harmonic current, the capacitor voltage at the direct current side will generate m frequency multiplication fluctuation, and the corresponding relation between the ripple frequency of the capacitor voltage at the direct current side and the frequency of the compensation current
(2) Under the premise that the phase sequence and frequency of the APF output compensation current are not changed, the APF outputs the amplitude (I) of the compensation current (m+1) Or I (-m+1) ) The larger the ripple amplitude of the voltage of the corresponding direct-current side capacitor is, the larger the ripple amplitude is;
s2, obtaining a singular eigenmode function of the direct-current side capacitance voltage signal
(1) Decomposing the DC side capacitance voltage signal by CEEMD to obtain n eigenmode functions, and calculating IMF of each IMF according to the formula (5) and the formula (6)
Wherein: t is the period of the Fourier spectrum, S lnT,i Is the fourier spectrum of the ith IMF with ln T as argument,
for the average period calculated from the frequency spectrum of the ith IMF, E i The energy density of the ith IMF is N, and the data length of the ith IMF is represented by N;
(2) Judging a trip point
Let the first IMF satisfying the condition shown in equation (7) be the trip point p, and calculate all IMFs before the trip point according to equation (8)
Average value of (2)
Wherein, the first and the second end of the pipe are connected with each other,
energy from the ith IMF, i =1,2, …, n-1;
wherein the content of the first and second substances,
the average energy of all IMFs before the trip point p;
(3) Determining singular eigenmode functions and performing threshold optimization
The eigenmode function satisfying the condition shown in the formula (9) is made to be a singular eigenmode function, and after the singular eigenmode function is determined, threshold optimization is performed on the singular eigenmode function according to the formula (10)
Wherein i = p +1, p +2, …, n-1,p are stroke points;
wherein: IMF' i (t) is the singular eigen-mode function, τ, after threshold optimization i Is a threshold value, σ i Is the standard deviation;
s3, applying Hilbert transform to the optimized IMF
The dc side capacitor voltage signal after CEEMD processing is expressed as:
wherein r is n Taking the residual error as m is the number of singular eigenmode functions;
the hilbert transform of the IMFs at different frequencies can result in:
constructing an analytic signal:
obtaining IMF 'from formula (14) or (15)' i Instantaneous amplitude, instantaneous phase and instantaneous frequency:
s4, determining the harmonic frequency in the distribution network through a table look-up method
And (3) obtaining the frequency and the amplitude of the direct current side capacitor voltage ripple according to the formula (16), comparing and comparing the frequency and the amplitude with the corresponding relation between the direct current side capacitor voltage ripple frequency and the compensating current frequency in the step (S1), inverting the frequency of the harmonic wave in the distribution network according to the direct current side capacitor voltage ripple frequency, inverting the change condition of the internal harmonic wave load according to the amplitude of each frequency ripple of the direct current side capacitor voltage, and then grasping the pollution degree of the system caused by the harmonic wave.
According to the invention, the frequency and the relative amplitude of the APF harmonic compensation current are inversely obtained by mining the secondary data of the two-level APF direct-current side capacitor voltage signal, and then the degree of harmonic pollution of the industrial park power distribution network is mastered in real time, so that the capital investment of industrial park enterprises in harmonic monitoring equipment is reduced. And (3) combining complete set empirical mode decomposition (CEEMD) with threshold optimization to complete frequency feature extraction of the APF direct-current side capacitor voltage information, and monitoring typical industrial park harmonic waves according to the internal relation between the ripple frequency and the output compensation current harmonic frequency in the APF direct-current side capacitor voltage.
Drawings
FIG. 1 is a schematic diagram of a two-level APF main circuit;
FIG. 2a shows compensation-5 times (I) -5 = 20A) harmonic content diagram of the dc side capacitor voltage at harmonic current;
FIG. 2b is compensated +13 times (I) +13 = 20A) harmonic content diagram of the dc side capacitor voltage at harmonic current;
FIG. 2c shows compensation 5 times (I) -5 = 25A) harmonic content diagram of the dc side capacitor voltage at harmonic current;
FIG. 2d shows compensation +13 times (I) +13 = 30A) harmonic content diagram of the dc side capacitor voltage at harmonic current;
FIG. 3a is an IMF graph obtained after decomposition of the DC side capacitor voltage signal when compensating an uncontrolled rectifier load;
FIG. 3b is a graph of the instantaneous frequency of the primary IMF obtained by decomposing the DC-side capacitor voltage signal while compensating for an uncontrollable rectified load;
fig. 3c is a graph of the instantaneous magnitude of the principal IMF obtained by decomposing the dc-side capacitor voltage signal while compensating for an uncontrollable rectified load.
Detailed Description
The specific technical scheme of the invention is as follows:
s1, a two-level APF main circuit topology is shown in figure 1, three phases are connected in a star-shaped mode, and u is s For three-phase mains voltage, i s Is the net side current, i L Is the load current i c Output of a compensating current, u, for the APF dc Is the DC side capacitor voltage i dc For the current flowing through the capacitor, L C Is to connect a reactance.
Experiments show that when the two-level APF compensates the harmonic current, the ripple frequency in the capacitor voltage at the direct current side of the APF and the harmonic frequency of the output compensation current have an internal relation, and the corresponding relation between the ripple frequency and the harmonic frequency of the output compensation current is determined from a theoretical level through mathematical modeling: according to the basic principle of the power system, the three-phase instantaneous active power output to the power grid by the APF system can be obtained as follows:
wherein U is s Is an effective value of ABC three-phase voltage, I (n) And
for the effective value and phase corresponding to the output current n times, n = ± (6 k ± 1) and n = -1 correspond to the alternating current part of the three-phase instantaneous power, where k =1,2,3 … and n =1 corresponds to the direct current part of the three-phase instantaneous power.
When the APF operates in a steady state, the voltage of the capacitor at the direct current side consists of a direct current constant component and an alternating current component, namely:
according to the principle that instantaneous power on both sides of APF alternating current and direct current is equal, the method comprises the following steps:
the dc component of the APF instantaneous active power corresponds to the constant dc component of the dc-side capacitor voltage, while the ac component of the instantaneous active power corresponds to the ripple component of the dc-side capacitor voltage. Let m = n-1, a specific expression of the ac ripple component with an angular frequency of m ω in the dc-side capacitor voltage can be further derived from equation (3):
through the above theoretical analysis of the dc-side capacitor voltage ripple, the following conclusions can be drawn:
(1) When APF compensates for m +1 positive sequence (m +1 > 0) or | -m + 1| negative sequence (-m + 1 < 0)
When current flows, the voltage of the capacitor on the direct current side will generate m-frequency-doubled fluctuation. The specific fluctuation pattern is shown in table 1.
TABLE 1 correspondence between APF DC side capacitor voltage ripple frequency and compensating current frequency
(2) Under the premise that the phase sequence and frequency of the APF output compensation current are not changed, the APF outputs the amplitude (I) of the compensation current (m+1) Or I (-m+1) ) The larger the ripple amplitude of the voltage of the direct current side capacitor is, the larger the ripple amplitude of the direct current side capacitor voltage is.
The method is based on a two-level APF direct-current side capacitor voltage ripple generation mechanism, completely-integrated empirical mode decomposition (CEEMD) is combined with threshold optimization, noise is removed while direct-current side voltage signals are decomposed to obtain singular eigenmode functions of different frequencies, then Hilbert transformation is carried out on the obtained singular eigenmode functions to obtain frequency characteristics of APF direct-current side capacitor voltage information, and finally the frequency of APF compensation output current and the change condition of harmonic load are inversely shown through the frequency and the amplitude of direct-current side capacitor voltage ripples.
S2, (1) obtaining singular eigenmode function of direct current side capacitance voltage signal
1. Decomposing the DC side capacitance voltage signal by CEEMD to obtain n eigenmode functions (IMF), and calculating the IMF of each IMF according to the formula (5) and the formula (6)
Wherein: t is the period of the Fourier spectrum, S lnT,i Is the fourier spectrum of the ith IMF with ln T as argument,
for the average period calculated from the frequency spectrum of the ith IMF, E i For the energy density of the ith IMF, N represents the data length of the ith IMF.
2. Judging a trip point
Let the first IMF satisfying the condition shown in equation (7) be the trip point p, and calculate all IMFs before the trip point according to equation (8)
Average value of (a).
Wherein the content of the first and second substances,
from the energy of the i-th IMF, i = (1,2, …, n-1).
Wherein the content of the first and second substances,
is the average energy of all IMFs before the trip point p
3. Determine singular eigen-mode functions and proceedThreshold optimization
And (3) enabling the eigenmode function meeting the condition shown in the formula (9) to be a singular eigenmode function, and performing threshold optimization on the singular eigenmode function according to the formula (10) after the singular eigenmode function is determined so as to improve the denoising effect of the CEEMD.
Where i = (p +1, p +2, …, n-1), p is the trip point.
Wherein: IMF' i (t) is the singular eigen-mode function, τ, after threshold optimization i Is a threshold value, σ i Is the standard deviation of the measured data to be measured,
(2) Applying Hilbert transform to optimized IMF
The dc side capacitor voltage signal after CEEMD processing can be expressed as:
wherein r is n M is the number of singular eigenmode functions for the residual.
The hilbert transform of the IMFs at different frequencies can result in:
constructing an analytic signal:
IMF 'can be obtained from the formulae (14) and (15)' i Instantaneous amplitude, instantaneous phase and instantaneous frequency:
(3) Determining harmonic times in industrial park network distribution by table look-up method
The frequency and amplitude of the DC side capacitor voltage ripple can be obtained according to equation (16), and by looking up table 1,
the frequency of harmonic waves in the distribution network of the industrial park can be inverted according to the frequency of the capacitor voltage ripple at the direct current side, the change condition of harmonic load in the industrial park can be inverted according to the amplitude of each frequency ripple of the capacitor voltage at the direct current side, and then the pollution degree of the system by the harmonic waves can be mastered.
Example verification
In order to verify the correctness of the method provided by the patent, a simulation model is built based on MATLAB/Simulink, and simulation parameters are as follows: electric network380V voltage, 50Hz network frequency and L connecting reactance C =1.3mH, dc-side capacitance C =1000 μ F, and dc-side reference voltage is 800V.
1) DC side capacitor voltage when compensating-5 th harmonic and +13 th harmonic
FIGS. 2a and 2b first show that the two-level APF compensates-5 times with an amplitude of 20A (I) -5 ) And +13 times (I) +13 ) When the harmonic current is measured, the corresponding dc-side capacitor voltage THD is multiplied by 6 when the two-level APF compensates-5 harmonic current as can be seen from observing fig. 2a and 2 b; when the two-level APF compensates +13 harmonic current, the corresponding direct-current side capacitor voltage ripple is 12 times frequency, which is consistent with theoretical analysis. Fig. 2c and fig. 2d are graphs of the dc-side capacitor voltage THD corresponding to-5 times of compensation amplitude 25A and +13 times of compensation amplitude 30A, and comparing fig. 2a, fig. 2c, fig. 2b, and fig. 2d, it can be found that as the amplitude of the compensation current at the same frequency increases, the amplitude of the dc-side capacitor voltage ripple of the current corresponding to the frequency also increases, which is consistent with the theoretical analysis, and the correctness of the proposed theory is verified in conclusion.
2) DC side capacitor voltage when load is uncontrolled rectifying load
Fig. 3a, 3b, and 3c are graphs showing the effect of CEEMD decomposition of the dc-side capacitor voltage signal when the two-level APF compensates the uncontrolled rectifying load, where fig. 3a is an IMF graph obtained by decomposing the dc-side capacitor voltage signal, fig. 3b is an instantaneous frequency graph of the main IMF obtained by decomposing the dc-side capacitor voltage signal, and fig. 3c is an instantaneous amplitude graph of the main IMF obtained by decomposing the dc-side capacitor voltage signal. Observing fig. 3a, 3b, and 3c, it can be found that the extraction of the APF dc side capacitance voltage frequency characteristic can be completed while the calculation amount is reduced based on the signal processing method combining the complete set empirical mode decomposition (CEEMD) and the threshold optimization, and the correctness of the proposed signal processing method is verified.
By observing the graph 3a, the frequency of the voltage ripple of the direct-current side capacitor when the two-level APF compensates the harmonic current can be known, and the frequency of each harmonic current in the industrial park distribution network can be inverted according to the information; by observing fig. 3b, the amplitude information of each frequency ripple of the direct current side capacitor voltage can be known when the two-level APF compensates the harmonic current, and the related information of the harmonic load change in the distribution network of the industrial park can be inverted according to the information.
Simulation experiment results show that the processing method based on the combination of complete set empirical mode decomposition (CEEMD) and threshold optimization can complete frequency feature extraction of APF direct current side capacitor voltage information, and can master the degree of harmonic pollution of the power distribution network of the industrial park and the change condition of harmonic load without adding other monitoring equipment.
Claims (1)
1. An industrial park harmonic monitoring method based on APF direct current voltage information inversion is characterized in that: the method comprises the following steps:
s1, adopting a star connection mode among three phases, wherein u s For three-phase mains voltage, i s Is the network side current, i L As a load current, i c Output of a compensating current, u, for the APF dc Is the DC side capacitor voltage i dc For the current flowing through the capacitor, L C To connect a reactance; the three-phase instantaneous active power output to the power grid by the APF system is obtained according to the basic principle of the power system as follows:
wherein U is s Is an effective value of ABC three-phase voltage, I (n) And
for effective values and phases corresponding to n times of output current, n = + ± (6 k ± 1) and n = -1, wherein k =1,2,3 … and n =1 corresponds to a direct current part of three-phase instantaneous power;
when the APF operates in a steady state, the direct current side capacitor voltage consists of a direct current constant component and an alternating current component, namely:
according to the principle that instantaneous power on two sides of APF alternating current and direct current are equal:
let m = n-1, a specific expression of the ac ripple component with an angular frequency of m ω in the dc-side capacitor voltage is further derived from equation (3):
through the above theoretical analysis on the dc side capacitor voltage ripple, the following conclusions can be drawn:
(1) When the APF compensates the m +1 positive sequence harmonic current, wherein m +1 is more than 0, or the | m +1| negative sequence harmonic current, wherein-m +1 is less than 0, the direct current side capacitor voltage will generate m frequency multiplication fluctuation, and the corresponding relation between the direct current side capacitor voltage ripple frequency and the compensation current frequency
(2) Under the premise that the phase sequence and the frequency of the APF output compensation current are not changed, the APF outputs the amplitude I of the compensation current (m+1) Or I (-m+1) The larger the ripple amplitude of the voltage of the corresponding direct-current side capacitor is, the larger the ripple amplitude is;
s2, obtaining a singular eigenmode function of the direct-current side capacitance voltage signal
(1) Decomposing the DC side capacitance voltage signal by CEEMD to obtain n eigenmode functions, and calculating the IMF of each IMF according to the formula (5) and the formula (6)
Wherein: t is the period of the Fourier spectrum, S lnT,i Is the fourier spectrum of the ith IMF with lnT as the argument,
for the average period calculated from the frequency spectrum of the ith IMF, E i The energy density of the ith IMF is N, and the data length of the ith IMF is represented by N;
(2) Judging a trip point
Let the first IMF satisfying the condition shown in equation (7) be the stroke point p, and calculate all IMFs before the stroke point according to equation (8)
Average value of (2)
Wherein, the first and the second end of the pipe are connected with each other,
is the energy of the ith IMF, i =1,2, …, n-1;
wherein the content of the first and second substances,
the average energy of all IMFs before the trip point p;
(3) Determining singular eigenmode functions and performing threshold optimization
The eigenmode function satisfying the condition shown in the formula (9) is made to be a singular eigenmode function, and after the singular eigenmode function is determined, threshold optimization is performed on the singular eigenmode function according to the formula (10)
Wherein i = p +1, p +2, …, n-1,p are stroke points;
wherein: IMF i ' (t) is the singular eigenmode function after the threshold is optimized, τ i Is a threshold value, σ i Is the standard deviation;
s3, applying Hilbert transform to the optimized IMF
The direct current side capacitor voltage signal is represented as follows after CEEMD processing:
wherein r is n Taking the residual error as m is the number of singular eigenmode functions;
the hilbert transform of the IMFs at different frequencies can result in:
constructing an analytic signal:
obtaining IMF from the formula (14) or (15) i Instantaneous amplitude, instantaneous phase and instantaneous frequency of':
s4, determining the harmonic frequency in the distribution network through a table look-up method
And (3) obtaining the frequency and the amplitude of the direct current side capacitor voltage ripple according to the formula (16), comparing and comparing the frequency and the amplitude with the corresponding relation between the direct current side capacitor voltage ripple frequency and the compensating current frequency in the step (S1), inverting the frequency of the harmonic wave in the distribution network according to the direct current side capacitor voltage ripple frequency, inverting the change condition of the internal harmonic wave load according to the amplitude of each frequency ripple of the direct current side capacitor voltage, and then grasping the pollution degree of the system caused by the harmonic wave.
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