CN-115964595-B - Loss evaluation method for no-current air-core reactor

Abstract

The invention discloses a loop-free air-core reactor loss evaluation method, which belongs to the technical field of reactor design and comprises a loop-free air-core reactor, wherein a reactor coil is formed by winding N aluminum flat wires, the aluminum flat wires are independently wound on each star frame arm, each aluminum flat wire is wound for one-half turn to enter the next turn, the N aluminum flat wires are continuously wound in the reverse direction after completing a single-layer structure according to the number of the aluminum flat wires wound in each wrapping manner in the single-layer structure, until the whole reactor coil is wound, the loop loss does not exist in the reactor due to the adoption of an equal wire length principle when the reactor is wound, the total loss of the reactor is the sum of resistance loss and eddy current loss, and the accurate theoretical calculation of the internal magnetic field loss of the novel series loop-free reactor is realized when the factory loss calibration of the reactor is carried out, so that the influence of the external environment additional loss on the actual loss detection of the reactor is corrected during actual test.

Inventors

• SHEN YUBO
• GUO YUN
• LI ZHIBIN
• ZHOU MENG
• HAN SIWEI
• Yuan Meishi
• KONG FANRONG
• LIU HEQIAN
• YUE CHUNFENG
• LIANG JIANQUAN
• WU MINGJUN
• ZHANG JIAN
• SHENG JIE
• YANG HONGDA
• ZHANG MINGZE
• ZHANG HANG
• ZHANG DEWEN
• SUN WEI
• ZHAO CHUNMING
• YU HUA
• LIU JI
• ZHOU HONGYI

Assignees

• 国网黑龙江省电力有限公司电力科学研究院
• 哈尔滨理工大学
• 国网吉林省电力有限公司电力科学研究院
• 国网山西省电力公司电力科学研究院
• 国家电网有限公司

Dates

Publication Date

20260512

Application Date

20221008

Claims (3)

1. 1. A loss evaluation method of a loop-free air reactor is characterized by comprising the following steps in sequence, Calculating theoretical inductance values of the reactor to be designed, cross section sizes of aluminum flat wires (101) adopted during winding, current density values in wires and inter-encapsulation air passage widths according to the voltage class, reactance rate and rated current of the reactor, and determining the value ranges of the inner diameter, the height and the encapsulation number of the reactor; Step two, selecting any numerical value in the value range of the inner diameter, the height and the number of the envelops of the reactor determined in the step one, and equivalent each envelop in the reactor is equivalent to a single-turn coil, establishing a series model of each envelop coil to obtain a series equivalent coil coupling equation set (1), further obtaining a theoretical calculation expression (2) of the equivalent mutual inductance coefficient and the equivalent turns of the reactor, and determining the equivalent turns of the reactor equivalent to a single envelop form; (1) (2) wherein ω is angular frequency in radian/second, M ij is mutual inductance value and self inductance value between each package, i=1, 2..m, j=1, 2..m, when i=j, the self inductance value is the self inductance value, when i is not equal to j, the mutual inductance value is in millihenry; the current is vector rated current value, and the unit is ampere; The vector voltage value shared by each package is i=1, 2.m, the unit is volt, f ij is the mutual inductance coefficient and the self inductance coefficient between each package, the mutual inductance value and the self inductance value between each package can be determined according to the mutual inductance coefficient, the self inductance coefficient and the equivalent turns in each package, f e is the self inductance coefficient after the multi-package reactor is equivalent to a single-package reactor, L n is the theoretical inductance value of the reactor, the unit is millihenry, m is the number of packages, the unit is n e is the equivalent turns equivalent to the multi-package reactor to a single package form, and the unit is turns; setting the initial thickness of the encapsulation, and determining the axial turns according to the cross section size of the aluminum flat wire (101) obtained in the first step and the encapsulation design height of the reactor; Step four, combining the equivalent turns of the reactor obtained in the step two, and obtaining the equivalent loss of the reactor according to the following formula; (3) Wherein P e is equivalent loss of the reactor in terms of watts, k p is an encapsulated additional loss coefficient of 1.2, aluminum resistivity at 100 ℃ in terms of rho is 3.9X10 -8 ohm-meter, D e is equivalent diameter of the reactor in terms of arithmetic average of inner diameter of the reactor and outer diameter of the reactor in terms of meters, n e is equivalent turns of the reactor in terms of turns, I n is rated current in terms of amperes, and J is current density value in a wire in terms of amperes/square meter; Fifthly, according to rated current, the cross section size of the aluminum flat wire (101) and the winding coefficient in the aluminum flat wire (101), the number of the aluminum flat wires (101) required in a single turn of wire is obtained through rounding calculation, the number of the star frame arms of the reactor is determined according to the number, and each aluminum flat wire (101) is independently wound on each star frame arm; Step six, obtaining the total number of the aluminum flat wires (101) wound in the single-layer structure of the reactor according to the radial turns of the reactor obtained in the step three and the number of the aluminum flat wires (101) required in the single-turn wire obtained in the step five; Step seven, according to the principle that the heat load of each package is equal when the temperature of the package is increased, the method can obtain: (4) (5) (6) (7) Wherein k p is the additional loss coefficient of the encapsulation, which is 1.2, the aluminum resistivity at 100 ℃ is 3.9X10. 10 -8 ohm-meter, D i 、D j is the equivalent diameter of the ith and the jth encapsulation, which are respectively given in meters, H i 、H j is the height of the ith and the jth encapsulation, which are respectively given in meters, a i1 、a i2 and a j1 、a j2 are the heat dissipation coefficients of the inner and outer surfaces of the ith and the jth encapsulation, which are respectively given in meters, the middle heat dissipation coefficient is related to the airway width, the encapsulation height, k i1 、k i2 and k j1 、k j2 are the shielding coefficients of the ith and the jth encapsulation stay, which are respectively given in 0.9, n i 、n j is the equivalent number of turns of the ith and the jth encapsulation, which are respectively given in turns, A i 、A j is the total axial metal width of the ith and the jth encapsulation, which is given in meters; the number of the aluminum flat wires (101) in each package meets the same proportional relation of the formula (7), so that the number of the aluminum flat wires (101) wound by each package in a single-layer structure is obtained; Step eight, recalculating the wrapping thickness according to the number of the aluminum flat wires (101) wrapped and wound by each wrapping in the single-layer structure obtained in the step seven, and repeating the steps three to eight for each new wrapping thickness until the relative error value of the equivalent loss of the reactor calculated according to the formula (3) is less than 1% twice, and ending the cycle to obtain the thickness and the number of turns of each wrapping; step nine, according to the equivalent loss value of the reactor obtained in the step four, obtaining the equivalent Wen Sheng of the reactor according to the following formula, (8) Wherein P e is equivalent loss of the reactor, wherein m is the number of packages, D i is the equivalent diameter of the ith package, H i is the height of the ith package, A i1 、a i2 is related to the heat dissipation coefficients of the inner and outer surfaces of the ith package, the middle heat dissipation coefficient is related to the width of the air passage, k i1 、k i2 is the shielding coefficient of the ith package stay, the shielding coefficient of the middle package stay is 0.9, and 1.35 is the revision coefficient considering all harmonic loss; judging whether the temperature rise theta is greater than 75K, changing the inner diameter, the height and the encapsulation number of the reactor when Wen Sheng is greater than 75K, and repeating the steps two to eight until the temperature rise theta is less than 75K to obtain the structural size of the reactor; Step ten, according to the structural size of the reactor determined in the step nine and the combination formula (2), calculating to obtain an actual inductance value of the reactor, and when the relative error value between the actual inductance value and the theoretical inductance value is less than 3%, obtaining each design parameter of the reactor, otherwise, repeating the steps two to nine, and adjusting the inner diameter, the height and the number of packages of the reactor, wherein the structural size of the reactor comprises the inner diameter, the height, the number of packages, the thickness of packages, the number of turns of packages and the width of an air channel; Step eleven, according to the structural size of the reactor, the number of the star arms of the reactor and the number of the aluminum flat wires (101) wrapped and wound in each wrapping mode in a single-layer structure which are finally determined in the step ten, starting to wind the reactor coil, wherein each aluminum flat wire (101) is independently wound on each star arm, the number of the star arms of the reactor is N, each aluminum flat wire (101) is wound for one-half turn to enter the next turn, and the N aluminum flat wires (101) are wound in the opposite direction along the next-layer structure after finishing the single-layer structure according to the number of the aluminum flat wires (101) wrapped and wound in each wrapping mode in the single-layer structure until the whole reactor coil is wound; step twelve, calculating the length of the aluminum flat wire (101) in the reactor, and calculating the equivalent direct current resistance value R: (9) Wherein ρ is the resistivity of aluminum material in ohm-meter, N i is the equivalent calculated number of turns of each encapsulation in turn, m is the number of encapsulation of the designed reactor, D i is the equivalent diameter of each encapsulation in meter, N c is the number of aluminum flat wires (101) connected in parallel in a single turn wire, A is the width of the aluminum flat wires (101) in meter, B is the height of the aluminum flat wires (101) in meter, and k c is the winding coefficient in the aluminum flat wires (101) of 0.83; Thirteenth, calculating the equivalent direct current resistance loss P r according to the calculated resistance value at 1.35 times of rated current value: (10) wherein I n is rated current in ampere; fourteen, calculating the magnetic field intensity at any position of the reactor, taking the center of the magnetic field intensity as the origin of the cylindrical coordinates, wherein the radial and axial magnetic field components at any point P (R 2 ,Z 2 ) in the space are respectively as follows: (11) (12) Wherein, the unit of flow in I 1 encapsulation is ampere, H 1 is the height of a single-turn coil, n 1 is the total number of turns of the single-turn coil, R 1 is the radius of the single-turn coil, m, mu 0 is the vacuum magnetic permeability, the value is 4pi× -7 , and theta is the included angle between two points on the circumference of the coil at different positions and the connecting line of the origin of the cylindrical coordinates, and the unit is the degree; fifteen steps, the magnetic induction intensity of the reactor meets the vector superposition principle, and the radial and axial total magnetic fields at each point of a single coil at the same height are the same, and the radial and axial total magnetic fields in each winding layer in each encapsulation of the reactor are respectively obtained according to the reactor structure designed in the tenth step: (13) Wherein m is the encapsulation number, w is the number of layers of the winding of the reactor, R is the radius of the single coil in a cylindrical coordinate system, and Z is the height of the single coil in the cylindrical coordinate system, and the unit is meter; sixthly, according to the reactor structure, calculating eddy current loss in the axial and radial magnetic field directions of a single aluminum flat wire (101) in an alternating magnetic field, wherein the eddy current loss is respectively expressed as: (14) Wherein m is the encapsulation number, w is the number of windings of the reactor, R is the radius of a single coil in a cylindrical coordinate system, Z is the height of the single coil in the cylindrical coordinate system, rho is the resistivity of an aluminum material, rho is ohm-meter, f is the power supply frequency, A is the width of an aluminum flat wire (101), B is the height of the aluminum flat wire (101), D is the diameter of the single coil, k m is the loss correction coefficient generated by winding in the aluminum flat wire (101) and is 0.83; Seventeenth, because the single winding in each wrapping and each layer of wire is in a series structure, the eddy current loss of the single winding in each wrapping and each layer of wire calculated in sixteenth is calculated by linear superposition; Eighteen steps, because the principle of equal line length is adopted when the reactor is wound, no circulation loss exists in the reactor, the total loss of the reactor is the sum of resistance loss and eddy current loss, and when the total loss is less than 3% of rated capacity after harmonic wave consideration, calculation is stopped, otherwise, the inner diameter, the height and the encapsulation number of the designed reactor are changed, and the steps one to eighteen are repeated until the total loss meets the requirement.
2. 2. The method for evaluating loss of the loop-free air-core reactor according to claim 1, wherein the solving of elliptic integral in the magnetic field calculation in the step fourteen is performed by iterative calculation in a series expansion mode.
3. 3. The method for evaluating loss of a loop-free air-core reactor according to claim 1, wherein the aluminum flat wire (101) is formed by compression molding a plurality of round aluminum wires.

Description

Loss evaluation method for no-current air-core reactor Technical Field The invention belongs to the technical field of reactor design, and particularly relates to a loss evaluation method for an annular flow air-core reactor. Background The high-voltage dry type air-core reactor has the characteristics of oil free, no iron core, explosion prevention and the like, is widely applied to various levels of power grids, and plays an important role in filtering harmonic waves, limiting overcurrent, balancing reactive power of a system, limiting overvoltage of the system and the like. However, the dry air-core reactor is easy to cause problems of package cracking, overheating, wetting and the like under the action of various environmental factors such as ultraviolet, moisture, cold-hot alternation and the like due to the defects of structure, insulation, process and the like after long-time operation, and part of the reactor is forced to be shut down, and the reactor gradually evolves into accidents and even equipment burnout. The prior art adopts a multi-encapsulation and multi-encapsulation branch parallel structure, can meet the reactance parameter requirements of various capacities and voltage grades, and is widely applied to medium-voltage, high-voltage and ultra-high voltage power grids. However, operation and fault analysis for many years show that the traditional air-core reactor structure also exposes more and more defects and fatal defects in winding structures, wire insulation, encapsulation insulation, manufacturing processes and the like, and in addition, the structural design of a large-capacity large-volume, extremely low design temperature rise, large fractional turn error and the like of a general reactor still adopted for a large-inductance, small-current and small-inductance large-current type reactor can also cause the problems of small capacity large volume, extremely low design temperature rise, large fractional turn error and the like, and the long-standing problems in design, process and material can cause excessive loss, encapsulation cracking after local circulation heating and the like of the high-voltage dry-type air-core reactor in an open operation environment, so that serious accidents such as fire burning and the like of the reactor can be finally caused. In the traditional reactor, each turn of coil in each envelope is of a parallel structure, so that wires in the inner envelope and the outer envelope are inevitably unequal in length, circulation is generated in the inner envelope, and serious heat generation is caused by envelope insulation. The loss calculation of the traditional reactor is mostly based on direct current resistance loss when leaving the factory, and the total loss of the reactor is calculated after the additional loss coefficient is 1.15-1.2, wherein the total loss comprises resistance loss, eddy current loss and circulation loss, but the loss deviation calculated by the method is found to be larger according to experiments, and the circulation loss and the eddy current loss are not accurately calculated, mainly because the structure of the traditional reactor is not completely symmetrical. When the reactor field loss test is performed, because the magnetic field of the traditional air core reactor is diffused, the additional loss of the environment such as heating of the ferromagnetic framework in the external environment is all equivalent to the self loss of the reactor, so that the deviation of the test result is extremely large. There is a need in the art for a new solution to this problem. Disclosure of Invention In order to overcome the defects in the prior art, the invention provides a loss evaluation method of an annular flow air-core reactor, which is used for solving the technical problem of larger loss deviation calculated in the prior art. In order to achieve the aim, the invention adopts the technical scheme that the loss evaluation method of the no-loop air-core reactor comprises the following steps which are sequentially carried out, Calculating theoretical inductance values of the reactor to be designed, cross section sizes of aluminum flat wires adopted during winding, current density values in wires and air channel widths among packages according to voltage grades, reactance rates and rated currents of the reactor, and determining the value ranges of the inner diameter, the height and the number of packages of the reactor; Step two, selecting any numerical value in the value range of the inner diameter, the height and the number of the envelops of the reactor determined in the step one, and equivalent each envelop in the reactor is equivalent to a single-turn coil, establishing a series model of each envelop coil to obtain a series equivalent coil coupling equation set 1, further obtaining a theoretical calculation expression 2 of the equivalent mutual inductance coefficient and the equivalent turns of the reactor, and determining the equivalent