CN112487693B - Curve magnetic valve type controllable reactor harmonic wave optimization method, system and application - Google Patents

Curve magnetic valve type controllable reactor harmonic wave optimization method, system and application Download PDF

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CN112487693B
CN112487693B CN202011321870.0A CN202011321870A CN112487693B CN 112487693 B CN112487693 B CN 112487693B CN 202011321870 A CN202011321870 A CN 202011321870A CN 112487693 B CN112487693 B CN 112487693B
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陈锴
杨帆
钱少锋
陈炜
张智光
史宇超
陈柏超
田翠华
杨明臻
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Wuhan Haio Electric Co ltd
Hangzhou Power Supply Co of State Grid Zhejiang Electric Power Co Ltd
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Abstract

The invention belongs to the technical field of reactive power compensation of an electric power system and discloses a harmonic optimization method, a harmonic optimization system and application of a curve magnetic valve type controllable reactoriObtaining the optimal Gaussian point by adopting a particle swarm optimization algorithm, and performing inverse transformation by a Gaussian point x' formula to obtain the original integral space [0, l]The optimal gaussian point in (c) and then by fitting to get the solenoid valve curve f (x). The two ends of the curve magnetic valve structure magnetic valve are respectively symmetrically distributed with windings, the upper and lower windings are connected with taps through silicon controlled rectifier K1,K2And the upper and lower windings of the two working column cores are connected in parallel to a power grid after being connected in a cross way, and a freewheeling diode D spans across the cross end point. Compared with the traditional magnetic valve type controllable reactor, the invention can meet the national standard and reduce the cost.

Description

Curve magnetic valve type controllable reactor harmonic wave optimization method, system and application
Technical Field
The invention belongs to the technical field of reactive power compensation of power systems, and particularly relates to a harmonic optimization method, a harmonic optimization system and application of a curve magnetic valve type controllable reactor.
Background
At present, a magnetic valve controlled reactor (MCR) is an important reactive compensation device, the reactive power of which is continuously adjustable, and is more convenient to use in an extra-high voltage environment than a Thyristor Controlled Reactor (TCR), and is currently widely used in an electric power system.
However, because the operating principle of the MCR is based on the magnetic saturation of the magnetic valve, each harmonic is inevitably generated in the saturation process, and as the operating voltage and the capacity of the MCR increase, the injected harmonic also increases, and if no limiting measures are taken, the harmonic injection into the power grid will affect the system safety. And the operation cannot be stabilized.
The harmonic suppression method is generally classified into an external circuit suppression method or an internal magnetic circuit suppression method. The circuit suppression method achieves the purpose of suppressing harmonic waves by externally changing the connection mode of the magnetically controlled reactor or adding an additional filtering device or other equipment, but the application of the additional equipment can cause cost increase, and the cost is higher because the additional equipment is not suitable to be added under certain environments. The internal magnetic circuit inhibition method can fundamentally reduce the harmonic output of the magnetic valve type controllable reactor by improving the internal magnetic valve structure of the magnetic valve type controllable reactor, and the key point is the optimization of the magnetic valve structure.
The research of the prior paper proposes a method for reducing total harmonic by adopting a multi-stage magnetic valve structure.
Through the above analysis, the problems and defects of the prior art are as follows:
the prior art has poor optimization effect on the ratio of the maximum sectional area to the minimum sectional area of the magnetic valve and the curve shape of the magnetic valve, so that the material utilization rate is low, and harmonic waves can not be reduced.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a curve magnetic valve type controllable reactor harmonic wave optimization method, a system, a reactor and application. The purpose is to improve the material utilization rate of the magnetically controlled reactor and reduce output harmonic waves to the maximum extent.
The invention is realized in this way, a harmonic optimization method for a curve magnetic valve type controllable reactor, comprising the following steps:
the harmonic optimization of the harmonic mathematical model of the curved magnetic valve is converted into the harmonic optimization of the Gaussian point xiObtaining the optimal Gaussian point by adopting a particle swarm optimization algorithm, and performing inverse transformation by a Gaussian point x' formula to obtain the original integral space [0, l]The optimal gaussian point in (c) and then by fitting to get the solenoid valve curve f (x).
Further, the harmonic optimization method of the curve magnetic valve type controllable reactor further comprises the following steps:
1) the obtained harmonic mathematical model of the curve magnetic valve is as follows:
Figure BDA0002793124010000021
wherein, betaxIs the magnetic saturation, beta, of the infinitesimal magnetic valve at a distance x from the smallest cross-section0The minimum section magnetic saturation is 0 in the initial state without DC excitation, and the maximum value is beta0max＝(kl-1)π，i1First name value for fundamental current, Bt0Is the magnetic induction at the critical saturation of the minimum cross section, i(2m+1)Is the famous value of the 2m +1 th harmonic current, N is the number of turns of the working coil, mu0Is a vacuum magnetic conductivity;
2) the output harmonic of the magnetically controlled reactor is only equal to the shape f (x) of the magnetic valve and the ratio K of the maximum to the minimum sectional arealTwo parameters are related; establishing a harmonic optimization model as formula (2), and optimizing the shape of a magnetic valve to minimize the maximum harmonic content in the whole work domain of the magnetically controlled reactor:
Figure BDA0002793124010000022
wherein iTHDMax (i) is the total harmonic distortion rate1) For maximum fundamental current value, curve f (x) e C2[0,xl]A second order continuously conducting; the analysis of the condition for obtaining an extreme value of the harmonic of (2) by the variational method must satisfy the following condition:
on the premise that the iron core is not saturated, the 2m +1 th harmonic is optimized by changing the shape of the magnetic valve, and at least the ratio of the sectional area of the iron core to the minimum sectional area of the magnetic valve must be ensured:
Figure BDA0002793124010000031
for 3 rd harmonic optimization, m is 1, there are
Figure BDA0002793124010000032
For 5 th harmonic optimization, m is 2, there are
Figure BDA0002793124010000033
And so on;
3) the invention determines the curve of the magnetic valve by a numerical method, and the Baokuo:
firstly, converting a curve integral form of harmonic waves into a polynomial form by adopting a precise Gauss-Legendre Gaussian integral method, wherein the integral formula is as follows:
Figure BDA0002793124010000034
where ρ (x) is the integrand, wiAs weighting coefficient, xiIs Gaussian point, q is the number of Gaussian points, ρ (x)i) Is an integrand function at xiFunction of (1)A value;
simultaneously reacting i in formula (1) with the following formula (5)2m+1Original integration space [0, l]Medium Gaussian point x to [ -1,1]Gaussian point x' in (1);
Figure BDA0002793124010000035
4) and (3) performing inverse transformation by using a formula (5) to obtain an optimal Gaussian point in the original integral space [0, l ], and then fitting to obtain a magnetic valve curve f (x).
Further, the harmonic optimization method of the curve magnetic valve type controllable reactor further comprises the following steps:
selecting a proper iron core sectional area based on a ratio formula (3) of the iron core sectional area and the minimum magnetic valve sectional area and practical application requirements;
setting parameters of a particle swarm algorithm and randomly setting initial values of Gaussian points of each swarm;
calculating the total harmonic distortion rate of various groups of Gaussian points based on the formulas (1), (2) and (4) to adjust the global optimum and the individual optimum;
step four, if the iteration times are not larger than a set value, updating the positions of the Gaussian points by adopting a particle swarm optimization algorithm, and returning to the step three of calculating the total harmonic distortion rate of the Gaussian points of various groups based on the formulas (1), (2) and (4) to adjust the global optimum and the individual optimum;
if the iteration times are larger than a set value, obtaining an optimal Gaussian point and carrying out inverse transformation based on the formula (5);
and step four, fitting the Gaussian points to obtain an optimal magnetic valve curve.
The invention can be fitted through a matlab fitting tool kit, for example, 4-order Fourier approximation in the matlab fitting tool kit is adopted in the embodiment of the invention, Gaussian points at the head and the tail are connected by line segments, and other similar fitting methods can be adopted in the practical application process to ensure that the harmonic output of the simulation result is the lowest.
Another object of the present invention is to provide a harmonic optimization system for a curved magnetic valve type controllable reactor, comprising:
the iron core sectional area acquisition module is used for selecting a proper iron core sectional area based on the ratio of the iron core sectional area to the minimum magnetic valve sectional area and the practical application requirement;
the initial value setting module of the Gaussian points of various groups is used for setting the initial value of the Gaussian points of various groups based on parameters and randomly setting the particle swarm algorithm;
the global optimum and individual optimum adjusting module is used for calculating the total harmonic distortion rate of various groups of Gaussian points to adjust the global optimum and the individual optimum;
the iteration number is in the set value decision module, is used for if the iteration number is not greater than the set value, adopt the optimization algorithm of the particle swarm to upgrade the position of Gaussian point, return to and calculate the Gaussian point total harmonic distortion rate of various groups and adjust the overall situation best and the individual best; if the iteration times are larger than a set value, obtaining an optimal Gaussian point and performing inverse transformation;
and the magnetic valve curve acquisition module is used for fitting the Gaussian points to obtain an optimal magnetic valve curve.
Another object of the present invention is to provide a curved magnetic valve type controllable reactor, comprising: the magnetic valve comprises I, II two symmetrical working column iron cores, wherein a small section with the length of l is arranged in the middle of each working column iron core, and the small section is a curved magnetic valve structure;
the two ends of the curve magnetic valve structure magnetic valve are respectively symmetrically distributed with windings, the upper and lower windings are connected with taps through silicon controlled rectifier K1,K2And the upper and lower windings of the two working column cores are connected in parallel to a power grid after being connected in a cross way, and a freewheeling diode D spans across the cross end point.
Further, after the maximum and minimum sectional area ratio is determined, the curve magnetic valve structure fits a magnetic valve curve according to Gaussian integration and particle swarm optimization algorithm to obtain a magnetic valve shape with the lowest harmonic.
Further, different maximum to minimum cross-sectional area ratios KlGreater than 1 and less than 3;
the ratio of the maximum cross-sectional area to the minimum cross-sectional area KlThe calculation method which is more than 1 comprises the following steps:
for (2m +1) subharmonic (3, 5)7 … th harmonic) is optimized to have a cross-sectional area ratio at least greater than
Figure BDA0002793124010000051
And the larger the sectional area ratio is, the larger the optimization margin is, and different curve shapes are designed under the condition of different sizes of the sectional area ratios.
Further, the curve magnetic valve structure is a multi-stage magnetic valve structure with infinite series.
Further, a rectangular coordinate system is established along the axial direction and the radial direction by taking the outer edge of the minimum cross section as an origin, A0Is the smallest magnetic valve cross-sectional area, AlIs the sectional area of the iron core, and l is the length of the magnetic valve; the cross-sectional area of a certain part in the magnetic valve is AxThe right subscript x represents the distance of the section from the smallest section, the largest core section outer edge according to KlChanging and changing, the other end point of the curve-determining magnetic valve designs the shape of the magnetic valve into a function f (x) curve structure with the characteristic of continuous monotone increasing.
The invention also aims to provide application of the harmonic optimization method of the curve magnetic valve type controllable reactor in harmonic adjustment of a power system.
By combining all the technical schemes, the invention has the advantages and positive effects that:
on the basis of the structure of the traditional magnetically controlled reactor, the shape of a single machine or multiple stages of the traditional magnetic valve is changed, and a curve structure is adopted.
The maximum and minimum sectional area ratio of the magnetically controlled reactor is reasonably designed according to actual conditions, namely the sectional area ratio is at least larger than that of the magnetically controlled reactor when (2m +1) subharmonic (3, 5 and 7 … subharmonic) is considered to be optimized
Figure BDA0002793124010000061
And the larger the sectional area ratio is, the larger the optimization margin is, and different curve shapes are designed under the condition of different sizes of the sectional area ratios.
After the maximum-minimum sectional area ratio is determined, a magnetic valve curve is fitted according to Gaussian integration and a particle swarm optimization algorithm, and the shape of the magnetic valve with the lowest harmonic is obtained.
The curve magnetic valve structure provided by the invention can further fully reduce harmonic waves, and only the condition that the ratio of the cross-sectional area of the maximum magnetic valve to the cross-sectional area of the minimum magnetic valve is 1:3 is analyzed in the prior art, if the ratio can be reduced, the material utilization rate is improved, and the cost is reduced.
The invention can reduce the harmonic output as much as possible and reduce the influence of the output harmonic of the magnetically controlled reactor on the power system.
The invention considers the maximum and minimum magnetic valve section area ratio, and can improve the material utilization rate although the harmonic optimization is more severe when selecting a smaller proportion in the design.
After the method is optimized, the maximum value of the total harmonic distortion rate is about 0.84%, and the lower harmonic content can be kept in the whole range. Theoretical analysis can be further verified through Simulink simulation, and the simulation enables the magnetic valve to gradually reach half-limit saturation through gradually increasing direct current excitation so as to demonstrate the harmonic content condition in the whole working range: as shown in the simulation results of Simulink of fig. 6.
The invention carries out optimization design aiming at the ratio of the maximum sectional area to the minimum sectional area of the magnetic valve and the curve shape of the magnetic valve, constructs a complete optimization design method of the curve magnetic valve, thereby improving the utilization rate of materials and simultaneously reducing harmonic waves as far as possible.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings needed to be used in the embodiments of the present application will be briefly described below, and it is obvious that the drawings described below are only some embodiments of the present application, and it is obvious for those skilled in the art that other drawings can be obtained from the drawings without creative efforts.
Fig. 1 is a schematic diagram of a magnetic valve type controllable reactor structure provided by an embodiment of the invention.
FIG. 2 is a schematic diagram of a curved magnetic valve structure provided by an embodiment of the present invention.
Fig. 3 is a flow chart of harmonic optimization design of a curve magnetic valve type controllable reactor provided by the embodiment of the invention.
FIG. 4 is a diagram of an optimized shape of a curved solenoid valve with an area ratio of 2 according to an embodiment of the present invention.
Fig. 5 is a graph of harmonic content of a result of the optimization by the curvilinear magnetic valve according to an embodiment of the present invention.
Fig. 6 is a diagram of Simulink simulation results provided by an embodiment of the present invention.
FIG. 7 is a schematic diagram of a test curve magnetic valve provided in an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The invention provides a harmonic optimization method for a curve magnetic valve type controllable reactor, which comprises the following steps:
the harmonic optimization of the harmonic mathematical model of the curved magnetic valve is converted into the harmonic optimization of the Gaussian point xiObtaining the optimal Gaussian point by adopting a particle swarm optimization algorithm, and performing inverse transformation by a Gaussian point x' formula to obtain the original integral space [0, l]The optimal gaussian point in (c) and then by fitting to get the solenoid valve curve f (x).
The harmonic optimization method of the curve magnetic valve type controllable reactor further comprises the following steps:
1) the obtained harmonic mathematical model of the curve magnetic valve is as follows:
Figure BDA0002793124010000071
wherein, betaxIs the magnetic saturation, beta, of the infinitesimal magnetic valve at a distance x from the smallest cross-section0The minimum section magnetic saturation is 0 in the initial state without DC excitation, and the maximum value is beta0max＝(kl-1)π，i1First name value for fundamental current, Bt0Is the magnetic induction at the critical saturation of the minimum cross section, i(2m+1)Is the nominal value of the 2m +1 th harmonic current, N is workNumber of coil turns, mu0Is a vacuum magnetic conductivity;
2) the output harmonic of the magnetically controlled reactor is only equal to the shape f (x) of the magnetic valve and the ratio K of the maximum to the minimum sectional arealTwo parameters are related; establishing a harmonic optimization model as formula (2), and optimizing the shape of a magnetic valve to minimize the maximum harmonic content in the whole work domain of the magnetically controlled reactor:
Figure BDA0002793124010000081
wherein iTHDMax (i) is the total harmonic distortion rate1) For maximum fundamental current value, curve f (x) e C2[0,xl]A second order continuously conducting; the analysis of the condition for obtaining an extreme value of the harmonic of (2) by the variational method must satisfy the following condition:
on the premise that the iron core is not saturated, the 2m +1 th harmonic is optimized by changing the shape of the magnetic valve, and at least the ratio of the sectional area of the iron core to the minimum sectional area of the magnetic valve must be ensured:
Figure BDA0002793124010000082
for 3 rd harmonic optimization, m is 1, there are
Figure BDA0002793124010000083
For 5 th harmonic optimization, m is 2, there are
Figure BDA0002793124010000084
And so on;
3) the invention determines the curve of the magnetic valve by a numerical method, and the Baokuo:
firstly, converting a curve integral form of harmonic waves into a polynomial form by adopting a precise Gauss-Legendre Gaussian integral method, wherein the integral formula is as follows:
Figure BDA0002793124010000091
whereinρ (x) is the integrand, wiAs weighting coefficient, xiIs Gaussian point, q is the number of Gaussian points, ρ (x)i) Is an integrand function at xiThe function value of (c);
simultaneously reacting i in formula (1) with the following formula (5)2m+1Original integration space [0, l]Medium Gaussian point x to [ -1,1]Gaussian point x' in (1);
Figure BDA0002793124010000092
4) and (3) performing inverse transformation by using a formula (5) to obtain an optimal Gaussian point in the original integral space [0, l ], and then fitting to obtain a magnetic valve curve f (x).
The harmonic optimization method of the curve magnetic valve type controllable reactor further comprises the following steps:
selecting a proper iron core sectional area based on a ratio formula (3) of the iron core sectional area and the minimum magnetic valve sectional area and practical application requirements;
setting parameters of a particle swarm algorithm and randomly setting initial values of Gaussian points of each swarm;
calculating the total harmonic distortion rate of various groups of Gaussian points based on the formulas (1), (2) and (4) to adjust the global optimum and the individual optimum;
step four, if the iteration times are not larger than a set value, updating the positions of the Gaussian points by adopting a particle swarm optimization algorithm, and returning to the step three of calculating the total harmonic distortion rate of the Gaussian points of various groups based on the formulas (1), (2) and (4) to adjust the global optimum and the individual optimum;
if the iteration times are larger than a set value, obtaining an optimal Gaussian point and carrying out inverse transformation based on the formula (5);
and step four, fitting the Gaussian points to obtain an optimal magnetic valve curve.
Aiming at the problems in the prior art, the invention provides a harmonic optimization method for a curve magnetic valve type controllable reactor, and a novel curve magnetic valve structure can be designed by the method. The present invention will be described in detail below with reference to the accompanying drawings.
Fig. 1 is a structure diagram of a magnetic valve type controllable reactor. The magnetic valve type controllable reactor comprises I, II two symmetrical working columns, each of which has a small section with length l in the middle, called magnetic valve.
Windings are symmetrically distributed at two ends of the magnetic valve, the upper and lower windings are connected with taps through a silicon controlled rectifier K1,K2And the upper and lower windings of the two working columns are connected in parallel to a power grid after being connected in a cross way, and a freewheeling diode D spans across the cross end point.
The magnetic valve type controllable reactor adjusts the direct current excitation size by controlling the conduction angle of the silicon controlled rectifier, the principle is similar to full wave rectification, the magnetic saturation of the magnetic valve is further changed, the equivalent magnetic conductivity is changed, and therefore the reactance value and the reactance capacity are smoothly changed.
The invention provides a novel curve magnetic valve structure based on a traditional magnetically controlled reactor, and the magnetic valve part is shown in figure 2 (a schematic diagram of the curve magnetic valve structure).
Similar to a multistage magnetic valve type controllable reactor, the curve magnetic valve type controllable reactor is equivalent to an infinite-stage multistage magnetic valve type controllable reactor, and the fundamental principle can be referred to in the document 'harmonic analysis mathematical model of a multistage saturation magnetic valve type controllable reactor'. The following description is made of different points with reference to fig. 2:
(1) taking into account different maximum to minimum cross-sectional area ratios KlThe default of the traditional literature is 3:1, the magnetically controlled reactor can reach the limit saturation, different area ratios can be considered in the process of optimization design, the minimum section area is 1 part, and the provisional range of the maximum section area is more than 1 and less than 3.
(2) Establishing a rectangular coordinate system along the axial direction and the radial direction by taking the outer edge of the minimum cross section as an origin as a graph A0Is the smallest magnetic valve cross-sectional area, AlIs the core cross-sectional area and l is the magnetic valve length. The cross-sectional area (infinitesimal) of a certain position in the magnetic valve is AxThe right subscript x represents the distance of the section from the smallest section, the largest core section outer edge according to KlThe change is changed, which determines that the other end point of the curve magnetic valve designs the magnetic valve shape as a shape function f (x) which has the characteristic of continuous monotone increasing.
After the above different points, a harmonic mathematical model of the curved magnetic valve can be obtained (a detailed derivation process is similar to a multi-stage magnetic valve type magnetically controlled reactor document):
Figure BDA0002793124010000111
wherein, betaxIs the magnetic saturation, beta, of the infinitesimal magnetic valve at a distance x from the smallest cross-section0The minimum section magnetic saturation is 0 in the initial state without DC excitation, and the maximum value is beta0max＝(kl-1)π，i1First name value for fundamental current, Bt0Is the magnetic induction at the critical saturation of the minimum cross section, i(2m+1)Is the famous value of the 2m +1 th harmonic current, N is the number of turns of the working coil, mu0Is a vacuum magnetic permeability.
According to a harmonic model, the output harmonic of the magnetically controlled reactor is only equal to the shape f (x) of the magnetic valve and the ratio K of the maximum to the minimum sectional arealTwo parameters are related. Establishing a harmonic optimization model as follows, wherein the optimization model aims to minimize the maximum harmonic content in the whole magnetically controlled reactor working domain by optimizing the shape of a magnetic valve:
Figure BDA0002793124010000112
wherein iTHDMax (i) is the total harmonic distortion rate1) For maximum fundamental current value, and for the convenience of subsequent variational analysis, consider curve f (x) epsilon C2[0,xl]The second order is continuously conductive. The analysis of the condition for obtaining an extreme value of the harmonic of (2) by the variational method must satisfy the following condition:
on the premise that the iron core is not saturated, the 2m +1 th harmonic is optimized by changing the shape of the magnetic valve, and at least the ratio of the sectional area of the iron core to the minimum sectional area of the magnetic valve must be ensured:
Figure BDA0002793124010000113
e.g. optimized for 3 rd harmonic, m 1, there are
Figure BDA0002793124010000114
For 5 th harmonic optimization, m is 2, there are
Figure BDA0002793124010000115
And so on.
The area ratio is determined according to the actual situation and the constraint (3), and since the numerical solution of f (x) is difficult to directly solve according to the (2), the magnetic valve curve is determined by a numerical method, which comprises the following steps:
firstly, converting a curve integral form of harmonic waves into a polynomial form by adopting a Gauss-Legendre Gaussian integral method with higher precision, wherein the integral formula is as follows:
Figure BDA0002793124010000121
where ρ (x) is the integrand, wiAs weighting coefficient, xiIs Gaussian point, q is the number of Gaussian points, ρ (x)i) Is an integrand function at xiThe function value of (c).
Simultaneously, the formula (1) is shown in the specification, wherein i is2m+1Original integration space [0, l]Medium Gaussian point x to [ -1,1]The gaussian point x' in (a), the gaussian point position and the weight can be selected and found in many documents.
Figure BDA0002793124010000122
So far, the harmonic optimization of the formula (1) by (f), (x) is converted into the harmonic optimization of a Gaussian point xiThe original integration space [0, l ] can be obtained by inverse transformation of the optimal Gaussian point obtained by adopting the particle swarm optimization algorithm through the formula (5)]The optimal gaussian point in (c) and then by fitting the solenoid valve curve f (x) can be obtained.
In summary, the flow chart of the harmonic wave optimized design of the magnetic valve type controllable reactor of the invention is shown in the flow chart of the harmonic wave optimized design of the line magnetic valve type controllable reactor in fig. 3.
The method specifically comprises the following steps:
selecting a proper iron core sectional area based on a ratio formula (3) of the iron core sectional area and the minimum magnetic valve sectional area and practical application requirements;
setting parameters of a particle swarm algorithm and randomly setting initial values of Gaussian points of each swarm;
calculating the total harmonic distortion rate of various groups of Gaussian points based on the formulas (1), (2) and (4) to adjust the global optimum and the individual optimum;
step four, if the iteration times are not larger than a set value, updating the positions of the Gaussian points by adopting a particle swarm optimization algorithm, and returning to the step three of calculating the total harmonic distortion rate of the Gaussian points of various groups based on the formulas (1), (2) and (4) to adjust the global optimum and the individual optimum;
if the iteration times are larger than a set value, obtaining an optimal Gaussian point and carrying out inverse transformation based on the formula (5);
and step four, fitting the Gaussian points to obtain an optimal magnetic valve curve.
Wherein the particle swarm optimization algorithm step can be referred to in the document "Harmonic optimization for the multi-stage structured magnetic controlled reactor using particle swarm optimization algorithm" (Xuxuan Chen, Jianxun Chen, Baicha Chen).
The following table shows the optimal harmonics under different maximum-to-minimum cross-sectional area ratios obtained after designing an optimal curve according to a flow chart, including three-phase (without considering the third harmonic, the third harmonic is offset by a triangular connection method) and single-phase conditions:
TABLE 1 harmonic distortion ratio after harmonic optimization of curved solenoid valves under different area ratios
Figure BDA0002793124010000131
Figure BDA0002793124010000141
The table exemplifies that the area ratio is within the range of 1.5-3 and every 0.1 is a partition according to the flow chart, more area ratio situations or specific harmonics of a certain order can be refined in practical application, and the optimization of 5 harmonics when the area ratio is too small does not meet the formula (3) and far exceeds the national standard, so that the optimization is not listed.
The method herein is applicable to any number in the range of the maximum to minimum cross-sectional area ratio from 1 to 3, depending on which harmonics are optimized and other practical situations, such as a particular higher harmonic, as a range is an inexhaustible example, but the optimization method is applicable.
Hereinafter, the magnetic valve is exemplified as being capable of reaching a half-limit saturation at maximum when the area ratio is 2.
The optimized shape of the curved magnetic valve is the optimized shape chart of the curved magnetic valve when the area ratio of the curved magnetic valve is 2 in figure 4.
FIG. 5 is a graph of harmonic content of a curve magnetic valve type optimization result.
The invention is further described below in connection with simulation experiments.
After the method is optimized, the maximum value of the total harmonic distortion rate is about 0.84%, and the lower harmonic content can be kept in the whole range. Theoretical analysis can be further verified through Simulink simulation, and the simulation enables the magnetic valve to gradually reach half-limit saturation through gradually increasing direct current excitation so as to demonstrate the harmonic content condition in the whole working range: as shown in the simulation results of Simulink of fig. 6.
By utilizing the optimization method, a 22kVA/380V test prototype is designed, and the physical diagram is shown in figure 7 (the physical diagram of a test curve magnetic valve). The harmonic output conditions under different working current conditions are tested, the result is matched with the simulation result, the national harmonic standard is met, and the effectiveness of the invention is verified.
In the description of the present invention, "a plurality" means two or more unless otherwise specified; the terms "upper", "lower", "left", "right", "inner", "outer", "front", "rear", "head", "tail", and the like, indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings, are only for convenience in describing and simplifying the description, and do not indicate or imply that the device or element referred to must have a particular orientation, be constructed in a particular orientation, and be operated, and thus, should not be construed as limiting the invention. Furthermore, the terms "first," "second," "third," and the like are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.
It should be noted that the embodiments of the present invention can be realized by hardware, software, or a combination of software and hardware. The hardware portion may be implemented using dedicated logic; the software portions may be stored in a memory and executed by a suitable instruction execution system, such as a microprocessor or specially designed hardware. Those skilled in the art will appreciate that the apparatus and methods described above may be implemented using computer executable instructions and/or embodied in processor control code, such code being provided on a carrier medium such as a disk, CD-or DVD-ROM, programmable memory such as read only memory (firmware), or a data carrier such as an optical or electronic signal carrier, for example. The apparatus and its modules of the present invention may be implemented by hardware circuits such as very large scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, or programmable hardware devices such as field programmable gate arrays, programmable logic devices, etc., or by software executed by various types of processors, or by a combination of hardware circuits and software, e.g., firmware.
The above description is only for the purpose of illustrating the present invention and the appended claims are not to be construed as limiting the scope of the invention, which is intended to cover all modifications, equivalents and improvements that are within the spirit and scope of the invention as defined by the appended claims.

Claims (8)

1. A harmonic optimization method for a curve magnetic valve type controllable reactor is characterized by comprising the following steps:
harmonic optimization of a harmonic mathematical model of the curve magnetic valve is converted into harmonic optimization of Gaussian points, the Gaussian points are subjected to particle swarm optimization to obtain optimal Gaussian points, inverse transformation is performed through a Gaussian point formula to obtain the optimal Gaussian points in an original integral space, and then a magnetic valve curve is obtained through fitting;
for Gaussian point xiObtaining the optimal Gaussian point by adopting a particle swarm optimization algorithm, and performing inverse transformation by a Gaussian point x' formula to obtain the original integral space [0, l]The optimal Gaussian point in the curve I represents the length of the magnetic valve, and then a magnetic valve curve f (x) is obtained through fitting;
the harmonic optimization method of the curve magnetic valve type controllable reactor further comprises the following steps:
1) the obtained harmonic mathematical model of the curve magnetic valve is as follows:
Figure FDA0003259703270000011
wherein, betaxIs the magnetic saturation, beta, of the infinitesimal magnetic valve at a distance x from the smallest cross-section0The minimum section magnetic saturation is 0 in the initial state without DC excitation, and the maximum value is beta0max＝(kl-1)π，i1First name value for fundamental current, Bt0Is the magnetic induction at the critical saturation of the minimum cross section, i(2m+1)Is the famous value of the 2m +1 th harmonic current, N is the number of turns of the working coil, mu0Is a vacuum magnetic conductivity;
2) the output harmonic of the magnetically controlled reactor is only equal to the shape f (x) of the magnetic valve and the ratio K of the maximum to the minimum sectional arealTwo parameters are related; establishing a harmonic optimization model as formula (2), and optimizing the shape of a magnetic valve to minimize the maximum harmonic content in the whole work domain of the magnetically controlled reactor:
Figure FDA0003259703270000021
wherein iTHDMax (i) is the total harmonic distortion rate1) For maximum fundamental current value, curve f (x) e C2,x∈[0,l]A second order continuously conducting; the analysis of the condition for obtaining an extremum for the harmonic of expression (2) by the variational method must satisfy the following condition:
on the premise that the iron core is not saturated, the 2m +1 th harmonic is optimized by changing the shape of the magnetic valve, and at least the ratio of the sectional area of the iron core to the minimum sectional area of the magnetic valve must be ensured:
Figure FDA0003259703270000022
for 3 rd harmonic optimization, m is 1, there are
Figure FDA0003259703270000023
For 5 th harmonic optimization, m is 2, there are
Figure FDA0003259703270000024
And so on;
3) determining a magnetic valve curve by a numerical method comprising:
firstly, converting a curve integral form of harmonic waves into a polynomial form by adopting a Gauss-Legendre Gaussian integral method, wherein the integral formula is as follows:
Figure FDA0003259703270000025
Figure FDA0003259703270000026
Figure FDA0003259703270000027
where ρ (x) is the integrand, wiAs weighting coefficient, xiIs Gaussian point, q is the number of Gaussian points, ρ (x)l) Is an integrand function at xiThe function value of (c);
simultaneously reacting i in formula (1) with the following formula (5)2m+1Original integration space [0, l]Medium Gaussian point x to [ -1,1]Gaussian point x' in (1);
Figure FDA0003259703270000031
4) and (3) performing inverse transformation by using a formula (5) to obtain an optimal Gaussian point in the original integral space [0, l ], and then fitting to obtain a magnetic valve curve f (x).
2. A curvilinear magnetic valve type controllable reactor harmonic optimization system designed according to the curvilinear magnetic valve type controllable reactor harmonic optimization method of claim 1, wherein the curvilinear magnetic valve type controllable reactor harmonic optimization system comprises:
the iron core sectional area acquisition module is used for selecting a proper iron core sectional area based on the ratio of the iron core sectional area to the minimum magnetic valve sectional area and the practical application requirement;
the initial value setting module of the Gaussian points of various groups is used for setting the initial value of the Gaussian points of various groups based on parameters and randomly setting the particle swarm algorithm;
the global optimum individual optimum adjusting module is used for calculating the total harmonic distortion rate of various groups of Gaussian points to adjust the global optimum and the individual optimum;
the iteration number set value judging module is used for updating the positions of the Gaussian points by adopting a particle swarm optimization algorithm if the iteration number is not more than a set value, and returning to calculate the total harmonic distortion rate of the Gaussian points of various groups to adjust the global optimum and the individual optimum; if the iteration times are larger than a set value, obtaining an optimal Gaussian point and performing inverse transformation;
and the magnetic valve curve acquisition module is used for fitting the Gaussian points to obtain an optimal magnetic valve curve.
3. A curved magnetic valve type controllable reactor designed according to the harmonic wave optimization method of the curved magnetic valve type controllable reactor of claim 1, wherein the curved magnetic valve type controllable reactor comprises: the magnetic valve comprises I, II two symmetrical working column iron cores, wherein a small section with the length of l is arranged in the middle of each working column iron core, and the small section is a curved magnetic valve structure;
the curved magnetic valveWindings are symmetrically distributed at two ends of the structure magnetic valve, the upper and lower windings are connected with taps through silicon controlled rectifiers K1,K2And the upper and lower windings of the two working column cores are connected in parallel to a power grid after being connected in a cross way, and a freewheeling diode D spans across the cross end point.
4. The curvilinear magnetic valve type controllable reactor according to claim 3, wherein the curvilinear magnetic valve structure fits the magnetic valve curve according to Gaussian integration and particle swarm optimization algorithm after determining the maximum and minimum sectional area ratio to obtain the magnetic valve shape which minimizes harmonics.
5. A solenoid valve-type controllable reactor according to claim 4, wherein the ratio K of the area of the different maximum cross-sections to the minimum cross-section is differentlGreater than 1 and less than 3;
the ratio of the maximum cross-sectional area to the minimum cross-sectional area KlThe calculation method which is more than 1 comprises the following steps:
optimizing the (2m +1) subharmonic to satisfy the condition that the cross-sectional area ratio is at least larger than
Figure FDA0003259703270000041
And the larger the sectional area ratio is, the larger the optimization margin is, and different curve shapes are designed under the condition of different sizes of the sectional area ratios.
6. A curvilinear magnetic valve type controllable reactor according to claim 4, characterized in that said curvilinear magnetic valve structure is an infinite series of multi-stage magnetic valve structures.
7. A solenoid valve type controllable reactor according to claim 4, wherein a rectangular coordinate system, A, is established in the axial and radial directions with the minimum cross-sectional outer edge as the origin0Is the smallest magnetic valve cross-sectional area, AlIs the sectional area of the iron core, and l is the length of the magnetic valve; the cross-sectional area of a certain part in the magnetic valve is AxThe right subscript x represents the distance of the section from the smallest section, the largest core section outer edge according to KlThe other end point determining the curve magnetic valve designs the shape of the magnetic valve as oneA function f (x) with the characteristic of continuous monotone increasing.
8. Use of a method for harmonic optimization of a curved-magnetic-valve controllable reactor according to claim 1 in harmonic regulation of an electric power system.
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