CN111490543A - Fibonacci method-based virtual harmonic resistance type active filter control method - Google Patents

Fibonacci method-based virtual harmonic resistance type active filter control method Download PDF

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Publication number
CN111490543A
CN111490543A CN202010175487.2A CN202010175487A CN111490543A CN 111490543 A CN111490543 A CN 111490543A CN 202010175487 A CN202010175487 A CN 202010175487A CN 111490543 A CN111490543 A CN 111490543A
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harmonic
resistance
apf
power
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王胜
赵峰
周宇
戴云峰
周昕
陈庆海
冯兴明
李正佳
孙大军
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Huatian Power Technology Co ltd
Yancheng Power Supply Co of State Grid Jiangsu Electric Power Co Ltd
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Yancheng Power Supply Co of State Grid Jiangsu Electric Power Co Ltd
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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
    • 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
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • 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

The invention provides a method for controlling a virtual harmonic resistance type active filter based on a Fibonacci method, which specifically comprises the following steps: step (1), carrying out mathematical modeling on an APF (active power filter); step (2), calculating to obtain an h-order harmonic voltage function of the grid-connected point; step (3), calculating to obtain an optimal resistance function of the h-th harmonic power and the h-th harmonic resistance; solving and searching the optimal resistance value of each virtual harmonic resistor by using a Fibonacci method; extracting each harmonic voltage of the grid-connected point, and generating a reference current by using the searched virtual harmonic resistance; step (6), generating a reference current by the direct-current voltage control outer ring, and overlapping the reference current generated in the step (5); and (7) carrying out current inner loop control by using the obtained total reference current to generate a driving signal of the three-phase inverter.

Description

Fibonacci method-based virtual harmonic resistance type active filter control method
Technical Field
The invention belongs to the field of control of active filters, and particularly relates to a control method of a virtual harmonic resistance type active filter based on a Fibonacci method. The 'virtual harmonic resistance' of the active filter is equivalent to a virtual harmonic resistance by controlling harmonic current output by the inverter so as to absorb harmonic power from the power grid, and the Fibonacci method is used for searching an optimal 'virtual harmonic resistance' value to enable the optimal 'virtual harmonic resistance' value to be equal to a modulus value of equivalent impedance of the power grid, so that the inverter can absorb the harmonic power from the power grid to the maximum extent.
Background
The traditional Active Power Filter (APF) has the defects that the APF needs to be installed near a load, a compensation object is fixed and single, and the like, so that the invention provides a virtual harmonic resistance control strategy of the APF, and the aim of absorbing harmonic Power from a Power grid can be achieved by detecting each harmonic voltage of a grid-connected point and controlling each output current of an inverter. When the 'virtual harmonic resistance' value is determined, if a smaller value is adopted, the distortion rate of the grid-connected point voltage can be reduced to a greater extent, when the 'virtual harmonic resistance' value is zero, the distortion rate of the grid-connected point voltage is reduced to zero, but the harmonic power absorbed from the power grid is zero at the moment, and considering the problems of limited capacity of an inverter and stability of a system, the 'virtual harmonic resistance' value is simply reduced, which is not an optimal strategy. Therefore, the invention provides a new active power filter harmonic wave treatment strategy, namely a virtual harmonic wave resistance algorithm, based on a Fibonacci method, the strategy calculates the power of each harmonic wave absorbed by an APF according to the voltage of each harmonic wave of a grid-connected point and the current of each harmonic wave output by the APF, and adjusts the resistance of each harmonic wave on line in real time by adopting the Fibonacci method, so that the power of each harmonic wave absorbed by the APF is maximized, and the corresponding resistance value of each harmonic wave is called as the optimal resistance value.
The APF controlled by the virtual harmonic resistance needs to sample the voltage and the output current of the grid-connected point at the same time, extract each subharmonic of the voltage and the current by using an FFT algorithm, then calculate each subharmonic power absorbed by each phase respectively, and average the three-phase same subharmonic power to be used as the h subharmonic power P absorbed by the APFhBased on the Fibonacci method, according to PhFor each conductance value KhAdjustments are made in real time. The APF controlled by the virtual harmonic resistance does not require the quick response to the load current like the traditional APF in the operation process, and the power system does not need to respond to each K timehThe change of Kh requires a certain response time, so that each harmonic power calculation link and each admittance regulation link can be performed according to a set time interval, and the original value of Kh is kept unchanged before each harmonic power is updated.
Disclosure of Invention
The invention provides a control method of a virtual harmonic resistance type active filter based on a Fibonacci method. Based on the Fibonacci method, the virtual resistance value of each harmonic is adjusted on line in real time to reach the optimal resistance value of each harmonic, so that the harmonic power is absorbed from the power grid to the maximum extent.
The invention specifically relates to a Fibonacci method-based virtual harmonic resistance type active filter control method, which specifically comprises the following steps:
step (1), carrying out mathematical modeling on an APF (active power filter);
step (2), calculating to obtain an h-order harmonic voltage function of the grid-connected point;
step (3), calculating to obtain an optimal resistance function of the h-th harmonic power and the h-th harmonic resistance;
solving and searching the optimal resistance value of each virtual harmonic resistor by using a Fibonacci method;
extracting each harmonic voltage of the grid-connected point, and generating a reference current by using the searched virtual harmonic resistance;
step (6), generating a reference current by the direct-current voltage control outer ring, and overlapping the reference current generated in the step (5);
and (7) carrying out current inner loop control by using the obtained total reference current to generate a driving signal of the three-phase inverter.
Further, the mathematical modeling of the power active filter APF in the step (1) is specifically as follows:
establishing a mathematical model of APF under an abc three-phase static coordinate system as follows:
Figure BDA0002410678100000021
wherein u isdcIs the DC side capacitor voltage usa、usb、uscThree-phase voltage, i, being PCC of grid-connected pointsca、icb、iccFor APF three-phase output current, da、db、dcRespectively, the three-phase equivalent input duty ratio of the APF, C is a direct-current side capacitor, L is a filter inductor of the APF, and R is a parasitic resistor of the filter inductor;
and transforming the model into a dq rotation coordinate system to obtain a mathematical model in the dq coordinate system as follows:
Figure BDA0002410678100000022
wherein id，iqD-and q-axis components, d, of the APF three-phase output current, respectivelyd，dqThe d-axis component and the q-axis component of the APF three-phase equivalent input duty ratio are respectively.
Further, the h-order harmonic voltage function of the grid-connected point in the step (2) is specifically as follows:
Figure BDA0002410678100000031
wherein, Ysh(s)＝1/(sXsh/hω+Rs)，YLh(s)＝1/(sXLh/hω+RL)，YRh(s)＝1/Rh(ii) a When Y isRhThe larger(s), i.e. RhThe smaller the harmonic resistance RhThe stronger the inhibition capability on h-order harmonic voltage of the PCC points is; when Y isRhWhen(s) is ∞, the h-th harmonic voltage at the PCC point is completely suppressed.
Further, the optimal resistance function of the h-th harmonic power and the h-th harmonic resistance calculated in the step (3) is specifically as follows:
grid connection point h harmonic voltage ushHas effective values of:
Figure BDA0002410678100000032
wherein the content of the first and second substances,
Figure BDA0002410678100000033
harmonic resistance RhThe absorbed h harmonic power is:
Figure BDA0002410678100000034
PRhwith RhPresents a quadratic parabolic mathematical relationship with the opening facing downwards, PRhThere is a maximum value, PRhAnd (3) obtaining a derivative, and calculating to obtain the optimal resistance value of the h-th harmonic resistance as follows:
Figure BDA0002410678100000035
further, the step (4) of finding the optimal resistance value of each virtual harmonic resistor by using a fibonacci method specifically includes:
① selecting an initial interval [ a ]1,b1]And precision, select n>0 such that it satisfies the following formula;
Fn≥(b1-a1)/ Fnas a Fibonacci series
Let k equal to 1 and calculate
Figure BDA0002410678100000041
② judging f (lambda)k)＜f(μk) If so, jumping to step ③, otherwise, jumping to step ④;
③ order
Figure BDA0002410678100000042
If yes, jumping to step ⑥, otherwise, jumping to step ⑤;
④ order
Figure BDA0002410678100000043
If yes, jumping to step ⑥, otherwise, jumping to step ⑤;
⑤ let k be k +1, go to step ②;
⑥ order lambdan＝λn-1,μn＝λn-1+, stop calculating, maximum value included in interval [ an,bn]In which a isn,bnRespectively as follows:
Figure BDA0002410678100000044
searching the maximum harmonic power point by using a Fibonacci method, and dynamically adjusting KhThe value of the harmonic wave conductance value is enabled to reach the optimal resistance value, so that each harmonic wave power absorbed by the APF is enabled to reach the maximum value, the search interval is continuously shortened by comparing the power of two adjacent harmonic waves in the dynamic adjustment process of the h-order virtual harmonic wave conductance value based on the Fibonacci method, and when the search interval is small enough and meets the precision requirement, the middle point value of the search interval is taken as the optimal virtual harmonic wave conductance value KhAt the moment, the h-th harmonic power absorbed by the APF from the power grid reaches the maximumIs large.
Drawings
Fig. 1 is a block diagram of the structure of an active power filter APF;
FIG. 2 is an h-th harmonic equivalent circuit diagram of a power system;
FIG. 3 is PRh、VghWith RhA graph of variation of (d);
FIG. 4 is a diagram of a "virtual harmonic resistance" control implementation;
FIG. 5 is a process for adjusting h-order virtual harmonic conductance values based on the Fibonacci method;
FIG. 6 is an improved search process for h-th order virtual harmonic conductance values based on the Fibonacci method;
fig. 7 is an overall control block diagram of the APF.
Detailed Description
The following describes in detail a specific embodiment of a method for controlling a virtual harmonic resistance type active filter based on a fibonacci method according to the present invention with reference to the accompanying drawings.
The invention provides a technical scheme of a 'virtual harmonic resistance' control strategy of an active filter based on a Fibonacci method, which mainly comprises the following steps of mathematical modeling of an APF, harmonic resistance principle analysis, harmonic power maximization, virtual harmonic resistance control, a virtual harmonic resistance algorithm based on the Fibonacci method and overall control of the APF.
1. Mathematical modeling of APF
According to fig. 1, a mathematical model of APF in abc three-phase stationary coordinate system can be established as follows:
Figure BDA0002410678100000051
wherein u isdcIs the DC side capacitor voltage usa，usb，uscIs a point-of-connection (PCC) three-phase voltage ica，icb，iccFor APF three-phase output current, da，db，dcThe three-phase equivalent input duty ratio of the APF is respectively, C is a direct-current side capacitor, L is a filter inductor of the APF, and R is a parasitic resistor of the filter inductor.
Transforming the data into a dq rotation coordinate system to obtain a mathematical model in the dq coordinate system as follows:
Figure BDA0002410678100000052
wherein id，iqD-and q-axis components, d, of the APF three-phase output current, respectivelyd，dqThe d-axis component and the q-axis component of the APF three-phase equivalent input duty ratio are respectively.
2. Harmonic resistance principle analysis
According to fig. 2, the h-th harmonic voltage of the grid-connected point can be calculated as:
Figure BDA0002410678100000061
wherein, Ysh(s)＝1/(sXsh/hω+Rs)，YLh(s)＝1/(sXLh/hω+RL)，YRh(s)＝1/Rh。
As can be seen from the above equation, when Y isRhThe larger(s), i.e. RhThe smaller the harmonic resistance RhThe stronger the suppression capability on the h-th harmonic voltage of the PCC point. When Y isRhThe h-th harmonic voltage at the PCC point is completely suppressed when(s) is ∞.
3. Harmonic power maximization
According to FIG. 2, the grid-connected point h subharmonic voltage ushHas effective values of:
Figure BDA0002410678100000062
wherein the content of the first and second substances,
Figure BDA0002410678100000063
harmonic resistance RhThe absorbed h harmonic power is:
Figure BDA0002410678100000064
from FIG. 3, it can be seen that PRhWith RhPresents a quadratic parabolic mathematical relationship with the opening facing downwards, PRhThere is a maximum value, PRhAnd (3) calculating a derivative, wherein the optimal resistance value of the h-th harmonic resistance can be calculated as follows:
Figure BDA0002410678100000065
4. virtual harmonic resistance control
According to the figure 4, the specific control process of the virtual harmonic resistance is that ① detects the three-phase voltage u of the grid-connected pointsabcUsing P LL algorithm to pair usabcPhase locking is carried out, ② an FFT algorithm is adopted to extract usabc③ converts the extracted harmonic voltages into instantaneous values and divides the instantaneous values by the virtual harmonic resistance values, i.e. multiplies the reciprocal value to obtain the reference values of the three-phase current.
5. Fibonacci method-based virtual harmonic resistance algorithm
The fibonacci method is a bidirectional search algorithm, i.e. two end points of a search interval can be changed simultaneously to accelerate convergence speed, and for the maximum value of a function f (x), the general steps of solving are as follows:
⑦ selecting an initial interval [ a ]1,b1]And precision, select n>0 such that it satisfies the following formula;
Fn≥(b1-a1)/Fnas a Fibonacci series
Let k equal to 1 and calculate
Figure BDA0002410678100000071
⑧ judging f (lambda)k) If f (μ k), go to step ③, otherwise go to step ④.
⑨ order
Figure BDA0002410678100000072
If yes, go to step ⑥, otherwise go to step ⑤.
⑩ order
Figure BDA0002410678100000073
If yes, go to step ⑥, otherwise go to step ⑤.
Figure BDA0002410678100000075
Let k be k +1, go to step ②.
Figure BDA0002410678100000076
Let lambdan＝λn-1,μn＝λn-1+, stop calculating, maximum value included in interval [ an,bn]In which a isn,bnRespectively as follows:
Figure BDA0002410678100000074
the invention adopts the Fibonacci method to search the maximum harmonic power point and dynamically adjust KhThe value is enabled to reach the optimal resistance value, so that each harmonic power absorbed by the APF is enabled to reach the maximum, fig. 5 is a dynamic adjusting process of h-order virtual harmonic conductance value based on a Fibonacci method, a search interval is continuously shortened by comparing the power of two adjacent harmonics, and when the search interval is small enough and meets the requirement of precision, the midpoint value of the search interval can be taken as the optimal virtual harmonic conductance value KhAt this time, the h-th harmonic power absorbed by the APF from the grid is maximized.
In the actually-operated power grid, the equivalent impedance is dynamically changed, and the adjustment process according to fig. 5 cannot ensure that the power grid is always operated with the optimal resistance value of each harmonic, so that some improvements need to be made to the adjustment process of fig. 5, and fig. 6 is an h-order virtual Fibonacci method-based improved power gridSearching process of harmonic conductance value, when K is searched according to the adjusting process of FIG. 5hStoring the maximum harmonic power, judging that the system running state has changed when the calculated real-time harmonic power is too different from the maximum harmonic power value, and performing K again according to the steps of FIG. 5hThe optimal search.
6. Overall control of APF
Fig. 7 is an overall control block diagram of the APF, which is divided into 4 parts in total, and first, an optimal resistance value of each sub-virtual harmonic resistor is found by using a fibonacci method; secondly, extracting each harmonic voltage of the grid-connected point, and generating a reference current by using the searched virtual harmonic resistance; thirdly, the direct-current voltage control outer ring generates reference current which is overlapped with the reference current generated by the second part; fourthly, the obtained total reference current is used for carrying out current inner loop control, and driving signals of the three-phase inverter are generated.
Finally, it should be noted that the above embodiments are only used for illustrating the technical solutions of the present invention and not for limiting the same. It will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (5)

1. The method for controlling the virtual harmonic resistance type active filter based on the Fibonacci method is characterized by specifically comprising the following steps of:
step (1), carrying out mathematical modeling on an APF (active power filter);
step (2), calculating to obtain an h-order harmonic voltage function of the grid-connected point;
step (3), calculating to obtain an optimal resistance function of the h-th harmonic power and the h-th harmonic resistance;
solving and searching the optimal resistance value of each virtual harmonic resistor by using a Fibonacci method;
extracting each harmonic voltage of the grid-connected point, and generating a reference current by using the searched virtual harmonic resistance;
step (6), generating a reference current by the direct-current voltage control outer ring, and overlapping the reference current generated in the step (5);
and (7) carrying out current inner loop control by using the obtained total reference current to generate a driving signal of the three-phase inverter.
2. The fibonacci method-based virtual harmonic resistive active filter control method according to claim 1, wherein the mathematical modeling of the power active filter APF in step (1) is specifically:
establishing a mathematical model of APF under an abc three-phase static coordinate system as follows:
Figure FDA0002410678090000011
wherein u isdcIs the DC side capacitor voltage usa、usb、uscThree-phase voltage, i, being PCC of grid-connected pointsca、icb、iccFor APF three-phase output current, da、db、dcRespectively, the three-phase equivalent input duty ratio of the APF, C is a direct-current side capacitor, L is a filter inductor of the APF, and R is a parasitic resistor of the filter inductor;
and transforming the model into a dq rotation coordinate system to obtain a mathematical model in the dq coordinate system as follows:
Figure FDA0002410678090000012
wherein id，iqD-and q-axis components, d, of the APF three-phase output current, respectivelyd，dqThe d-axis component and the q-axis component of the APF three-phase equivalent input duty ratio are respectively.
3. The fibonacci method-based virtual harmonic resistive active filter control method according to claim 2, wherein the h-order harmonic voltage function of the grid-connected point in step (2) is specifically:
Figure FDA0002410678090000021
wherein, Ysh(s)＝1/(sXsh/hω+Rs)，YLh(s)＝1/(sXLh/hω+RL)，YRh(s)＝1/Rh(ii) a When Y isRhThe larger(s), i.e. RhThe smaller the harmonic resistance RhThe stronger the inhibition capability on h-order harmonic voltage of the PCC points is; when Y isRhWhen(s) is ∞, the h-th harmonic voltage at the PCC point is completely suppressed.
4. The fibonacci method-based virtual harmonic resistive active filter control method according to claim 3, wherein the optimal resistance function of the h-th harmonic power and the h-th harmonic resistance calculated in step (3) is specifically:
grid connection point h harmonic voltage ushHas effective values of:
Figure FDA0002410678090000022
wherein the content of the first and second substances,
Figure FDA0002410678090000023
harmonic resistance RhThe absorbed h harmonic power is:
Figure FDA0002410678090000024
PRhwith RhPresents a quadratic parabolic mathematical relationship with the opening facing downwards, PRhThere is a maximum value, PRhAnd (3) obtaining a derivative, and calculating to obtain the optimal resistance value of the h-th harmonic resistance as follows:
Figure FDA0002410678090000025
5. the fibonacci method-based virtual harmonic resistive active filter control method according to claim 1, wherein the step (4) of finding the optimal resistance value of each virtual harmonic resistance by using the fibonacci method is specifically:
① selecting an initial interval [ a ]1,b1]And precision, select n>0 such that it satisfies the following formula;
Fn≥(b1-a1)/Fnas a Fibonacci series
Let k equal to 1 and calculate
Figure FDA0002410678090000031
② judging f (lambda)k)＜f(μk) If so, jumping to step ③, otherwise, jumping to step ④;
③ order
Figure FDA0002410678090000032
If yes, jumping to step ⑥, otherwise, jumping to step ⑤;
④ order
Figure FDA0002410678090000033
If yes, jumping to step ⑥, otherwise, jumping to step ⑤;
⑤ let k be k +1, go to step ②;
⑥ order lambdan＝λn-1,μn＝λn-1+, stop calculating, maximum value included in interval [ an,bn]In which a isn,bnRespectively as follows:
Figure FDA0002410678090000034
searching the maximum harmonic power point by using a Fibonacci method, and dynamically adjusting KhThe value of the harmonic wave conductance value is enabled to reach the optimal resistance value, so that each harmonic wave power absorbed by the APF is enabled to reach the maximum value, the search interval is continuously shortened by comparing the power of two adjacent harmonic waves in the dynamic adjustment process of the h-order virtual harmonic wave conductance value based on the Fibonacci method, and when the search interval is small enough and meets the precision requirement, the middle point value of the search interval is taken as the optimal virtual harmonic wave conductance value KhAt this time, the h-th harmonic power absorbed by the APF from the grid is maximized.
CN202010175487.2A 2020-03-13 2020-03-13 Fibonacci method-based virtual harmonic resistance type active filter control method Withdrawn CN111490543A (en)

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113036764A (en) * 2021-03-08 2021-06-25 山东科汇电力自动化股份有限公司 Synchronous fixed-frequency current control method based on virtual harmonic resistance
CN113422591A (en) * 2021-06-17 2021-09-21 哈尔滨工程大学 Multichannel filter based on quasi-periodic structure

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113036764A (en) * 2021-03-08 2021-06-25 山东科汇电力自动化股份有限公司 Synchronous fixed-frequency current control method based on virtual harmonic resistance
CN113036764B (en) * 2021-03-08 2022-09-09 山东科汇电力自动化股份有限公司 Synchronous constant-frequency current control method based on virtual harmonic resistor
CN113422591A (en) * 2021-06-17 2021-09-21 哈尔滨工程大学 Multichannel filter based on quasi-periodic structure

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Application publication date: 20200804