Loss evaluation method for loop-flow-free air-core reactor

Abstract

The application discloses a loss evaluation method for a no-loop-flow air-core reactor, and belongs to the technical field of reactor design. The no-loop-flow air-core reactor comprises a reactor coil which is wound by N aluminum flat wires. The aluminum flat wires are independently wound on each star frame arm. Each aluminum flat wire is wound by only N / 1 circle to enter the next circle. The N aluminum flat wires are wound according to the number of the amplitude aluminum flat wires which are wound by each package in a single-layer structure, and then the N aluminum flat wires continue to wind the next layer structure along the reverse direction after the single-layer structure is completed, until the whole reactor coil is wound. Since the equal wire length principle is adopted when the reactor is wound, there is no loop-flow loss in the reactor. The total loss of the reactor is the sum of the resistance loss and the eddy current loss. When the loss calibration of the reactor is performed, the accurate theoretical calculation of the internal magnetic field loss of the new series no-loop-flow reactor is realized, and the influence of the actual loss detection of the reactor caused by the additional loss of the external environment during the actual test is corrected.

Description

Technical Field

[0001] This invention belongs to the field of reactor design technology, and in particular relates to a method for evaluating the loss of a non-circulating air-core reactor. Background Technology

[0002] High-voltage dry-type air-core reactors, characterized by being oil-free, coreless, and explosion-proof, have been widely used in power grids at all levels, playing a crucial role in filtering harmonics, limiting overcurrent, balancing reactive power, and limiting overvoltage. However, after prolonged operation, due to deficiencies in structure, insulation, and manufacturing processes, dry-type air-core reactors are prone to problems such as encapsulation cracking, overheating, and moisture absorption when exposed to various environmental factors such as ultraviolet radiation, moisture, and alternating hot and cold temperatures. Some reactors have been forced to shut down, and some have gradually escalated into accidents or even equipment burnout.

[0003] Existing technologies employ multi-encapsulation, multi-layer branch parallel structures to meet various capacity and voltage level reactance parameter requirements, and have been widely used in medium, high, and ultra-high voltage power grids. However, years of operation and fault analysis have revealed that this traditional air-core reactor structure has also exposed increasing deficiencies and fatal flaws in winding structure, conductor insulation, encapsulation insulation, and manufacturing processes. Furthermore, using general reactor structural designs for reactors with large inductance and small current, as well as those with small inductance and large current, leads to problems such as small capacity and large volume, extremely low design temperature rise, and large fractional-turn errors. These long-standing design, process, and material issues make high-voltage dry-type air-core reactors prone to excessive losses and encapsulation cracking after local circulating current heating in open operating environments, potentially leading to major accidents such as reactor fires.

[0004] In traditional reactors, the coils within each enclosure are connected in parallel, inevitably resulting in unequal conductor lengths within the inner and outer enclosures. This causes circulating currents within the enclosure, leading to severe overheating of the enclosure insulation. Traditional reactors are typically calculated at the factory based on DC resistance losses, with an additional loss factor of 1.15~1.2 to calculate the total reactor loss, including resistance loss, eddy current loss, and circulating current loss. However, experiments have shown that this calculation method yields significant deviations, with inaccurate calculations of circulating and eddy current losses, primarily due to the non-symmetrical structure of traditional reactors. During field loss testing, the dispersed magnetic field of traditional air-core reactors means that environmental losses, such as heating from the ferromagnetic structure, are entirely equivalent to the reactor's own losses, resulting in substantial deviations in the test results.

[0005] Therefore, there is an urgent need for a new technical solution to address this problem. Summary of the Invention

[0006] To overcome the shortcomings of existing technologies, this invention provides a loss assessment method for non-circulating air-core reactors, which addresses the technical problem of large loss deviations in existing technology calculations.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is: a method for evaluating the loss of a non-circulating air-core reactor, comprising the following steps, which are performed sequentially.

[0008] Step 1: Based on the reactor voltage rating, reactance rate, and rated current, calculate the theoretical inductance value of the reactor to be designed, the cross-sectional dimensions of the aluminum flat wire used during winding, the current density value inside the conductor, and the width of the air passage between the encapsulations, and determine the range of values ​​for the reactor's inner diameter, height, and number of encapsulations.

[0009] Step 2: Select any value from the range of reactor inner diameter, height and number of encapsulations determined in Step 1, and treat each encapsulation in the reactor as a single-turn coil. Establish a series model of each encapsulation coil, obtain the series equivalent coil coupling equation set 1, and further obtain the theoretical calculation expression 2 of the reactor equivalent mutual inductance coefficient and equivalent number of turns, and determine the equivalent number of turns of the reactor as a single encapsulation form;

[0010] (1)

[0011] (2)

[0012] in, oh Angular frequency, unit: radians per second; M ij The mutual inductance and self-inductance values ​​between each package. i =1,2…m, j =1,2…m, when i = j The time is the self-sensitivity value. i ≠ j The value is the mutual inductance, in millihenries; I n Rated current value, unit: amperes; U i The voltage values ​​shared by each package, i =1,2…m, unit: volt; f ij The mutual inductance and self-inductance coefficients between each package are given. The mutual inductance and self-inductance values ​​between each package can be determined based on the mutual inductance and self-inductance coefficients and the equivalent number of turns in each package. f e The self-inductance coefficient after converting a multi-encapsulated reactor into a single-encapsulated reactor; L n This is the theoretical inductance value of the reactor, in millihenries; m Number of packages, unit: pieces;n e The equivalent number of turns for a multi-encapsulated reactor to be equivalent to a single-encapsulated reactor, in turns;

[0013] Step 3: Set the initial encapsulation thickness. Determine the axial number of turns using the cross-sectional dimensions of the aluminum flat wire and the reactor encapsulation design height obtained in Step 1. Determine the radial number of turns of the reactor using the equivalent number of turns and axial turns obtained in Step 2.

[0014] Step 4: Combining the equivalent number of turns of the reactor obtained in Step 2, obtain the equivalent loss of the reactor according to the following formula;

[0015] (3)

[0016] in, P e The equivalent loss of the reactor, in watts; k p The additional loss factor for encapsulation is 1.2; r The resistivity of aluminum at 100℃ is 3.9 × 10⁻⁶. -8 O.M.; D e The equivalent diameter of the reactor is given by , and the arithmetic mean of the reactor's inner and outer diameters is given by , in meters. n e The equivalent number of turns of the reactor, in turns; I n Rated current, unit: ampere; J Current density in a conductor, unit: Amperes per square meter;

[0017] Step 5: Based on the rated current, the cross-sectional dimensions of the aluminum flat wire, and the winding coefficient within the aluminum flat wire, round down to calculate the required number of aluminum flat wires in a single turn, and use this to determine the number of star frame arms of the reactor. Each aluminum flat wire is wound independently on each star frame arm.

[0018] Step 6: Based on the radial turns of the reactor obtained in Step 3 and the number of aluminum flat wires required in a single turn obtained in Step 5, obtain the total number of aluminum flat wires wound in the single-layer structure of the reactor.

[0019] Step 7: Based on the principle that the heat load of each encapsulation is equal during isothermal rise, we can conclude that:

[0020] (4)

[0021] (5)

[0022] (6)

[0023] (7)

[0024] in, k p The additional loss factor for encapsulation is 1.2; r The resistivity of aluminum at 100℃ is 3.9 × 10⁻⁶. -8 O.M.; D i , D j The first i , j The equivalent diameter of the package, in meters; H i , H j The first i , j The height of each package, in meters; a i1 , a i2 and a j1 , a j2 The first i , j The heat dissipation coefficient of the inner and outer surfaces of the encapsulation is 1 because the innermost and outermost surfaces are unobstructed. The heat dissipation coefficient of the middle surfaces is related to the width of the air passage and the height of the encapsulation. k i1 , k i2 and k j1 , k j2 The first i , j The occlusion coefficient of each encapsulation support strip is 1 because the innermost and outermost surfaces are unobstructed, and the occlusion coefficient of the middle encapsulation support strip is 0.9. n i , n j The first i , j Equivalent number of turns per package, unit: turns; A i , A j The first i , j Total axial metal width within the package, unit: meters;

[0025] The number of aluminum flat wires in each encapsulation should satisfy the same proportional relationship as in Formula 7, thereby obtaining the number of radial aluminum flat wires wound in each encapsulation in a single-layer structure.

[0026] Step 8: Based on the number of radial aluminum flat wires wound in each encapsulation of the single-layer structure obtained in Step 7, recalculate the encapsulation thickness, and repeat Step 3 to Step 8 with the new encapsulation thickness until the relative error value of the equivalent loss of the reactor calculated by Formula 3 twice is less than 1%, then end the cycle to obtain the thickness and number of turns of each encapsulation.

[0027] Step 9: Based on the equivalent loss value of the reactor obtained in Step 4, calculate the equivalent temperature rise of the reactor using the following formula. I,

[0028] (8)

[0029] in, P e The equivalent loss of the reactor, in watts; m Number of packages, unit: pieces; D i For the first i The equivalent diameter of the package, in meters; H i For the first i The height of each package, in meters; a i1 , a i2 and respectively the first i The heat dissipation coefficient of the inner and outer surfaces of the encapsulation is 1 because the innermost and outermost surfaces are unobstructed. The heat dissipation coefficient of the middle surfaces is related to the width of the air passage and the height of the encapsulation. k i1 , k i2 The first i The shading coefficient of each encapsulation support strip is 1 because the innermost and outermost surfaces are unobstructed, and the shading coefficient of the middle encapsulation support strip is 0.9; 1.35 is a revision coefficient after considering all harmonic losses.

[0030] Judging temperature rise i Is the temperature rise greater than 75K? i When the temperature exceeds 75K, change the reactor's inner diameter, height, and number of encapsulations, and repeat steps two through eight until the temperature rises. i Less than 75K, thus obtaining the structural dimensions of the reactor;

[0031] Step 10: Based on the structural dimensions of the reactor determined in Step 9 and Formula 2, calculate the actual inductance value of the reactor. If the relative error between the actual inductance value and the theoretical inductance value is less than 3%, obtain the design parameters of the reactor. Otherwise, repeat Steps 2 to 9 to adjust the inner diameter, height, and number of encapsulations of the reactor. The structural dimensions of the reactor include the inner diameter, height, number of encapsulations, encapsulation thickness, number of encapsulation turns, and air passage width.

[0032] Step 11: Based on the structural dimensions of the reactor, the number of reactor star frame arms, and the number of radial aluminum flat wires wound in each encapsulation of the single-layer structure determined in Step 10, begin winding the reactor coil. Each aluminum flat wire starts winding independently on each star frame arm. Let the number of reactor star frame arms be N. Each aluminum flat wire is wound only one-Nth of a turn before moving to the next turn. After the N aluminum flat wires have completed the single-layer structure according to the number of radial aluminum flat wires wound in each encapsulation of the single-layer structure, continue winding the next layer of structure in the opposite direction until the entire reactor coil is wound.

[0033] Step 12: Calculate the length of the aluminum flat wire inside the reactor and its equivalent DC resistance R.

[0034] (9)

[0035] in, r The resistivity of aluminum is expressed in ohms-meters. n i Calculate the equivalent number of turns for each package, in turns; m To determine the number of encapsulations for the design reactor; D i The equivalent diameter of each package, in meters; N c The number of aluminum flat wires connected in parallel within a single turn; A Width of aluminum flat wire, unit: meter; B The height of the aluminum flat wire, in meters; k c The winding factor within the aluminum flat wire is 0.83;

[0036] Step 13: Based on the calculated resistance value, calculate its equivalent DC resistance loss at 1.35 times the rated current value. P r :

[0037] (10)

[0038] in, I n Rated current, unit: ampere;

[0039] Step Fourteen: Calculate the magnetic field strength at any location on the reactor, taking its center as the origin of the cylindrical coordinate system. P ( R 2, Z The radial and axial magnetic field components at point 2) are respectively:

[0040] (11)

[0041] (12)

[0042] in, I Flow rate in 1 package, unit: amperes; H 1 represents the height of a single-turn coil, in meters; n 1 represents the total number of turns in a single-turn coil, in turns. R 1 represents the radius of a single-turn coil, in meters; m 0 represents the free permeability, with a value of 4π × 10⁻⁶. -7 ; θ The angle between the lines connecting two points on the circumference of the coil at different positions to the origin of the cylindrical coordinate system, in degrees;

[0043] Step 15: The magnetic induction intensity of the reactor satisfies the principle of vector superposition, and the total radial and axial magnetic fields at all points of a single coil at the same height are the same. Based on the basic reactor structure designed in Step 10, the total radial and axial magnetic fields in each winding layer within each enclosure of the reactor are as follows:

[0044] (13)

[0045] in, m Number of packages; w This refers to the number of winding layers of the reactor. R The radius of a single coil in cylindrical coordinates, in meters; Z The height of a single coil in cylindrical coordinates, in meters;

[0046] Step 16: Based on the reactor structure, calculate the eddy current losses in the axial and radial magnetic field directions of a single aluminum flat wire under an alternating magnetic field. These losses can be expressed as follows:

[0047] (14)

[0048] in, m Number of packages; w This refers to the number of winding layers of the reactor. R The radius of a single coil in cylindrical coordinates, in meters; Z The height of a single coil in cylindrical coordinates, in meters; r The resistivity of aluminum is expressed in ohms-meters. f Power supply frequency, unit: Hertz; A Width of aluminum flat wire, unit: meter; B The height of the aluminum flat wire, in meters; D The diameter of a single coil, in meters; k m The loss correction factor due to winding within the aluminum flat wire is 0.83;

[0049] Step 17: Since the individual windings in each package and each layer of wire are connected in series, the eddy current losses of the individual windings in each package and each layer of wire calculated in Step 16 can be calculated by linear superposition.

[0050] Step 18: Since the reactor is wound with equal wire length, there is no circulating current loss in the reactor. The total loss of the reactor is the sum of the resistance loss and the eddy current loss. If the total loss is less than 3% of the rated capacity after considering harmonics, stop the calculation. Otherwise, change the inner diameter, height and number of enclosures of the reactor design, and repeat steps one to eighteen until the total loss meets the requirements.

[0051] Through the above design scheme, the present invention can bring the following beneficial effects:

[0052] 1. Compared with the traditional air-core reactor design, it realizes the use of only a single aluminum wire specification in the reactor design, reducing the manufacturing difficulty and cost.

[0053] 2. During the factory loss calibration of the reactor, the accurate theoretical calculation of the internal magnetic field loss of this new type of series non-circulating current reactor was realized, and the influence of external environmental additional losses on the actual loss detection of the reactor during actual testing was corrected. Attached Figure Description

[0054] Figure 1 This is a flowchart of a loss assessment method for a non-circulating air-core reactor according to the present invention.

[0055] Figure 2 This is a diagram showing the relationship between the inner diameter of the reactor and the total loss of the reactor in a specific embodiment of the loss assessment method for a non-circulating hollow reactor according to the present invention.

[0056] Figure 3 This is a wiring diagram of the single-layer winding structure of the reactor used in the loss assessment method for a non-circulating hollow reactor according to the present invention.

[0057] Figure 4 This is a schematic diagram of the cross-section of the aluminum flat wire of the reactor used in the loss assessment method for a non-circulating hollow reactor according to the present invention.

[0058] 101 in the figure - aluminum flat wire. Detailed Implementation

[0059] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0060] To more clearly illustrate the present invention, the following description, in conjunction with preferred embodiments, further clarifies the invention. Those skilled in the art should understand that the specific description below is illustrative rather than restrictive, and users may make various changes to the following parameters without departing from the inventive mechanism and scope set forth in the claims. To avoid obscuring the essence of the invention, well-known methods and processes are not described in detail.

[0061] From the appendix Figure 1~4 The following is a method for evaluating the losses of a non-circulating air-core reactor, comprising the following steps, which are performed sequentially.

[0062] Step 1: Based on the reactor voltage level, reactance rate, and rated current, calculate the theoretical inductance value of the reactor to be designed, the cross-sectional dimensions of the aluminum flat wire 101 used during winding, the current density value inside the conductor, and the width of the air passage between the encapsulations, and determine the range of values ​​for the reactor's inner diameter, height, and number of encapsulations.

[0063] Step 2: Select any value from the range of reactor inner diameter, height and number of encapsulations determined in Step 1, and treat each encapsulation in the reactor as a single-turn coil. Establish a series model of each encapsulation coil, obtain the series equivalent coil coupling equation set 1, and further obtain the theoretical calculation expression 2 of the reactor equivalent mutual inductance coefficient and equivalent number of turns, and determine the equivalent number of turns of the reactor as a single encapsulation form;

[0064] (1)

[0065] (2)

[0066] in, oh Angular frequency, unit: radians per second; M ij The mutual inductance and self-inductance values ​​between each package. i =1,2…m, j =1,2…m, when i = j The time is the self-sensitivity value. i ≠ j The value is the mutual inductance, in millihenries; I n Rated current value, unit: amperes; U i The voltage values ​​shared by each package, i =1,2…m, unit: volt; f ij The mutual inductance and self-inductance coefficients between each package are given. The mutual inductance and self-inductance values ​​between each package can be determined based on the mutual inductance and self-inductance coefficients and the equivalent number of turns in each package. f eThe self-inductance coefficient after converting a multi-encapsulated reactor into a single-encapsulated reactor; L n This is the theoretical inductance value of the reactor, in millihenries; m Number of packages, unit: pieces; n e The equivalent number of turns for a multi-encapsulated reactor to be equivalent to a single-encapsulated reactor, in turns;

[0067] Step 3: Set the initial encapsulation thickness. Based on the cross-sectional dimensions of the aluminum flat wire 101 obtained in Step 1 and the design height of the reactor encapsulation, determine the axial number of turns. Based on the equivalent number of turns and axial turns obtained in Step 2, determine the radial number of turns of the reactor.

[0068] Step 4: Combining the equivalent number of turns of the reactor obtained in Step 2, obtain the equivalent loss of the reactor according to the following formula;

[0069] (3)

[0070] in, P e The equivalent loss of the reactor, in watts; k p The additional loss factor for encapsulation is 1.2; r The resistivity of aluminum at 100℃ is 3.9 × 10⁻⁶. -8 O.M.; D e The equivalent diameter of the reactor is given by , and the arithmetic mean of the reactor's inner and outer diameters is given by , in meters. n e The equivalent number of turns of the reactor, in turns; I n Rated current, unit: ampere; J Current density in a conductor, unit: Amperes per square meter;

[0071] Step 5: Based on the rated current, the cross-sectional dimensions of the aluminum flat wire 101, and the winding coefficient within the aluminum flat wire 101, round down to calculate the required number of aluminum flat wires 101 in a single turn, and use this to determine the number of reactor star frame arms. Each aluminum flat wire 101 is wound independently on each star frame arm.

[0072] Step 6: Based on the radial turns of the reactor obtained in Step 3 and the number of aluminum flat wires 101 required in a single turn obtained in Step 5, obtain the total number of aluminum flat wires 101 wound in the single-layer structure of the reactor.

[0073] Step 7: Based on the principle that the heat load of each encapsulation is equal during isothermal rise, we can conclude that:

[0074] (4)

[0075] (5)

[0076] (6)

[0077] (7)

[0078] in, k p The additional loss factor for encapsulation is 1.2; r The resistivity of aluminum at 100℃ is 3.9 × 10⁻⁶. -8 O.M.; D i , D j The first i , j The equivalent diameter of the package, in meters; H i , H j The first i , j The height of each package, in meters; a i1 , a i2 and a j1 , a j2 The first i , j The heat dissipation coefficient of the inner and outer surfaces of the encapsulation is 1 because the innermost and outermost surfaces are unobstructed. The heat dissipation coefficient of the middle surfaces is related to the width of the air passage and the height of the encapsulation. k i1 , k i2 and k j1 , k j2 The first i , j The occlusion coefficient of each encapsulation support strip is 1 because the innermost and outermost surfaces are unobstructed, and the occlusion coefficient of the middle encapsulation support strip is 0.9. n i , n j The first i , j Equivalent number of turns per package, unit: turns; A i , A j The first i , j Total axial metal width within the package, unit: meters;

[0079] The number of aluminum flat wires 101 in each encapsulation should satisfy the same proportional relationship as in Formula 7, thereby obtaining the number of radial aluminum flat wires 101 wound in each encapsulation in the single-layer structure.

[0080] Step 8: Based on the number of radial aluminum flat wires 101 obtained in Step 7 for each encapsulation in the single-layer structure, recalculate the encapsulation thickness, and repeat Step 3 to Step 8 with the new encapsulation thickness until the relative error value of the equivalent loss of the reactor calculated by Formula 3 twice is less than 1%, then end the cycle to obtain the thickness and number of turns of each encapsulation.

[0081] Step 9: Based on the equivalent loss value of the reactor obtained in Step 4, calculate the equivalent temperature rise of the reactor using the following formula. I,

[0082] (8)

[0083] in, P e The equivalent loss of the reactor, in watts; m Number of packages, unit: pieces; D i For the first i The equivalent diameter of the package, in meters; H i For the first i The height of each package, in meters; a i1 , a i2 and respectively the first i The heat dissipation coefficient of the inner and outer surfaces of the encapsulation is 1 because the innermost and outermost surfaces are unobstructed. The heat dissipation coefficient of the middle surfaces is related to the width of the air passage and the height of the encapsulation. k i1 , k i2 The first i The shading coefficient of each encapsulation support strip is 1 because the innermost and outermost surfaces are unobstructed, and the shading coefficient of the middle encapsulation support strip is 0.9; 1.35 is a revision coefficient after considering all harmonic losses.

[0084] Judging temperature rise i Is the temperature rise greater than 75K? i When the temperature exceeds 75K, change the reactor's inner diameter, height, and number of encapsulations, and repeat steps two through eight until the temperature rises. i Less than 75K, thus obtaining the structural dimensions of the reactor;

[0085] Step 10: Based on the structural dimensions of the reactor determined in Step 9 and Formula 2, calculate the actual inductance value of the reactor. If the relative error between the actual inductance value and the theoretical inductance value is less than 3%, obtain the design parameters of the reactor. Otherwise, repeat Steps 2 to 9 to adjust the inner diameter, height, and number of encapsulations of the reactor. The structural dimensions of the reactor include the inner diameter, height, number of encapsulations, encapsulation thickness, number of encapsulation turns, and air passage width.

[0086] Step 11: Based on the structural dimensions of the reactor, the number of reactor star frame arms, and the number of radial aluminum flat wires 101 wrapped in each encapsulation in the single-layer structure determined in Step 10, begin winding the reactor coil. Each aluminum flat wire 101 starts winding independently on each star frame arm. Assuming the number of reactor star frame arms is N, each aluminum flat wire 101 only winds one-Nth of a turn before moving to the next turn. After N aluminum flat wires 101 have completed winding the single-layer structure according to the number of radial aluminum flat wires 101 wrapped in each encapsulation in the single-layer structure, continue winding the next layer in the opposite direction until the entire reactor coil is wound.

[0087] Step 12: Calculate the length of the aluminum flat wire 101 inside the reactor, and calculate its equivalent DC resistance value R:

[0088] (9)

[0089] in, r The resistivity of aluminum is expressed in ohms-meters. n i Calculate the equivalent number of turns for each package, in turns; m To determine the number of encapsulations for the design reactor; D i The equivalent diameter of each package, in meters; N c The number of aluminum flat wires 101 connected in parallel within a single turn; A Width of aluminum flat wire 101, unit: meter; B The height of aluminum flat wire 101, in meters; k c The winding coefficient within the aluminum flat wire 101 is 0.83;

[0090] Step 13: Based on the calculated resistance value, calculate its equivalent DC resistance loss at 1.35 times the rated current value. P r :

[0091] (10)

[0092] in, I n Rated current, unit: ampere;

[0093] Step Fourteen: Calculate the magnetic field strength at any location on the reactor, taking its center as the origin of the cylindrical coordinate system. P ( R 2, Z The radial and axial magnetic field components at point 2) are respectively:

[0094] (11)

[0095] (12)

[0096] in, I Flow rate in 1 package, unit: amperes; H 1 represents the height of a single-turn coil, in meters; n 1 represents the total number of turns in a single-turn coil, in turns. R 1 represents the radius of a single-turn coil, in meters; m 0 represents the free permeability, with a value of 4π × 10⁻⁶. -7 ; θ The angle between the lines connecting two points on the circumference of the coil at different positions to the origin of the cylindrical coordinate system, in degrees;

[0097] Step 15: The magnetic induction intensity of the reactor satisfies the principle of vector superposition, and the total radial and axial magnetic fields at all points of a single coil at the same height are the same. Based on the basic reactor structure designed in Step 10, the total radial and axial magnetic fields in each winding layer within each enclosure of the reactor are as follows:

[0098] (13)

[0099] in, m Number of packages; w This refers to the number of winding layers of the reactor. R The radius of a single coil in cylindrical coordinates, in meters; Z The height of a single coil in cylindrical coordinates, in meters;

[0100] Step 16: Based on the reactor structure, the eddy current losses in the axial and radial magnetic field directions of a single aluminum flat wire 101 under alternating magnetic field conditions can be expressed as follows:

[0101] (14)

[0102] in, m Number of packages; w This refers to the number of winding layers of the reactor. R The radius of a single coil in cylindrical coordinates, in meters; Z The height of a single coil in cylindrical coordinates, in meters; r The resistivity of aluminum is expressed in ohms-meters.f Power supply frequency, unit: Hertz; A Width of aluminum flat wire 101, unit: meter; B The height of aluminum flat wire 101, in meters; D The diameter of a single coil, in meters; k m The loss correction factor due to winding within the aluminum flat wire 101 is 0.83;

[0103] Step 17: Since the individual windings in each package and each layer of wire are connected in series, the eddy current losses of the individual windings in each package and each layer of wire calculated in Step 16 can be calculated by linear superposition.

[0104] Step 18: Since the reactor is wound with equal wire length, there is no circulating current loss in the reactor. The total loss of the reactor is the sum of the resistance loss and the eddy current loss. If the total loss is less than 3% of the rated capacity after considering harmonics, stop the calculation. Otherwise, change the inner diameter, height and number of enclosures of the reactor design, and repeat steps one to eighteen until the total loss meets the requirements.

[0105] In the further step fourteen, the solution of the elliptic integral in the magnetic field calculation is performed iteratively using a series expansion method.

[0106] Furthermore, the aluminum flat wire 101 is formed by pressing multiple round aluminum wires together.

[0107] In a specific embodiment, the rated voltage is set to 11000 volts, the reactance is 8%, the rated current is 120A, the current density is 1 amp / mm², the encapsulation duct width is 19 mm, and the cross-sectional dimensions of the aluminum flat wire 101 are 10 mm high and 2 mm wide. The reactor inner diameter is set to a range of 0.5 m to 2 m, the height to a range of 0.2 m to 1.8 m, and the number of encapsulations to a range of 1 to 14. Based on the method of the present invention, and considering losses, temperature rise, and design inductance errors within the boundary conditions defined by the method, the following reactor design parameters are obtained. When the inner diameter is 0.85 m, the height is 0.728 m, and the number of encapsulations is 4, the equivalent diameter of the reactor is calculated using the algorithm of the present invention. D e The length is 0.942m, the equivalent number of turns is 140 turns, the radial number of turns is 2 turns, and the axial number of turns is 70 turns. The thicknesses of the four enclosures from the inside out are 10 mm, 7.5 mm, 7.5 mm, and 10 mm, respectively. The equivalent number of turns of the four enclosures from the inside out are 40 turns, 30 turns, 30 turns, and 40 turns, respectively. There are 7 aluminum flat wires 101 in a single turn. The number of aluminum flat wires in each single-layer structure of each enclosure is as follows: 4 in the first enclosure, 3 in the second enclosure, 3 in the third enclosure, and 4 in the fourth enclosure. The wiring method of the single-layer reactor structure is as follows. Figure 3As shown, the wiring method of each package is as follows: Figure 4 As shown, the aluminum flat wire 101 is formed by winding and pressing multiple round aluminum wires together.

[0108] The target inductance is 13.477 millihenries, the inductance of the new reactor is 13.2697 millihenries, the total resistance of the aluminum wire wound inside the reactor is 0.1394 ohms, the temperature rise of the reactor is 54.8034 Kelvin, the resistance loss is 2332.7 watts, the eddy current loss is 1918.4 watts, therefore the total loss of the reactor is 4251.1 watts.

[0109] This invention calculates the total loss value for reactors with the same height of 0.728 meters, the same number of encapsulations (4), and different inner diameters. The inner diameter ranges from 0.65 to 1.5 meters. The relationship between the reactor inner diameter and the total loss value is as follows: Figure 2 As shown in the diagram. Calculations show that when the inner diameter is between 0.65 and 1.25 meters, the total loss increases linearly with increasing inner diameter. The radial number of turns is 2, the axial number is 70, and the total number of turns is 140. The single-layer wiring method is 4 wires enclosed internally, 3 wires in each of the two middle enclosed sections, and 4 wires in the outer enclosed section. When the inner diameter is 1.3 meters, the total loss decreases, mainly because the radial number of turns decreases to 1 after the radius increases, resulting in a total of 70 turns. The single-layer wiring method is 2 wires enclosed internally, 1 wire in each of the two middle enclosed sections, and 3 wires in the outer enclosed section, thus reducing loss. However, when the inner diameter is less than 0.65 meters, the calculated temperature rise of the designed reactor exceeds 75K due to the height restriction, which does not meet national standards. While simply changing the reactor's inner diameter can reduce the total loss to some extent, the error in the inductance value changes more significantly. Therefore, when designing reactors, it is still necessary to consider whether the actual inductance value and the required design inductance value meet the engineering calculation requirements.

[0110] Therefore, the above-mentioned method for evaluating the loss of non-circulating air-core reactors can be used to accurately calculate the actual loss of non-circulating reactors and reduce the impact of additional losses due to the testing environment on the evaluation of actual loss.

[0111] Obviously, the embodiments described above are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

Claims

1. A method for evaluating the losses of a non-circulating air-core reactor, characterized in that: Includes the following steps, And the following steps are performed in sequence. Step 1: Based on the reactor voltage level, reactance rate and rated current, calculate the theoretical inductance value of the reactor to be designed, the cross-sectional dimensions of the aluminum flat wire (101) used during winding, the current density value in the conductor and the width of the air passage between the encapsulations, and determine the range of values ​​for the reactor's inner diameter, height and number of encapsulations. Step 2: Select any value within the range of reactor inner diameter, height and number of encapsulations determined in Step 1, and treat each encapsulation in the reactor as a single-turn coil. Establish a series model of each encapsulation coil and obtain the series equivalent coil coupling equation set (1). Further obtain the theoretical calculation expression (2) of the reactor equivalent mutual inductance coefficient and equivalent number of turns, and determine the equivalent number of turns of the reactor as a single encapsulation. （1） （2） in, ω Angular frequency, unit: radians per second; M ij The mutual inductance and self-inductance between each package i =1,2…m, j =1,2…m, when i = j The time is the self-sensitivity value. i ≠ j The value is the mutual inductance, in millihenries; This is the vector rated current value, in amperes (A). The vector voltage values ​​shared by each package, i =1,2…m, unit: volt; f ij The mutual inductance and self-inductance between each package are given. The mutual inductance and self-inductance between each package can be determined based on the mutual inductance and self-inductance and the equivalent number of turns in each package. f e The self-inductance coefficient after converting a multi-encapsulated reactor into a single-encapsulated reactor; L n This is the theoretical inductance value of the reactor, in millihenries; m Number of packages, unit: packages; n e The equivalent number of turns for a multi-encapsulated reactor to be equivalent to a single-encapsulated reactor, in turns; Step 3: Set the initial encapsulation thickness. Determine the axial number of turns using the cross-sectional dimensions of the aluminum flat wire (101) obtained in Step 1 and the design height of the reactor encapsulation. Determine the radial number of turns of the reactor using the equivalent number of turns and axial turns obtained in Step 2. Step 4: Combining the equivalent number of turns of the reactor obtained in Step 2, obtain the equivalent loss of the reactor according to the following formula; （3） in, P e The equivalent loss of the reactor, in watts; k p The additional loss factor for encapsulation is 1.2; ρ The resistivity of aluminum at 100℃ is 3.9 × 10⁻⁶. -8 O.M.; D e The equivalent diameter of the reactor is given by , and the arithmetic mean of the reactor's inner and outer diameters is given by , in meters. n e The equivalent number of turns of the reactor, in turns; I n Rated current, unit: ampere; J is Current density in a conductor, unit: Amperes per square meter; Step 5: Based on the rated current, the cross-sectional dimensions of the aluminum flat wire (101), and the winding coefficient within the aluminum flat wire (101), round down to calculate the required number of aluminum flat wires (101) in a single turn, and use this to determine the number of reactor star frame arms. Each aluminum flat wire (101) is wound independently on each star frame arm. Step 6: Based on the radial turns of the reactor obtained in Step 3 and the number of aluminum flat wires (101) required in a single turn obtained in Step 5, obtain the total number of aluminum flat wires (101) wound in the single-layer structure of the reactor; Step 7: Based on the principle that the heat load of each encapsulation is equal during isothermal rise, we can conclude that: （4） （5） （6） （7） in, k p The additional loss factor for encapsulation is 1.2; ρ The resistivity of aluminum at 100℃ is 3.9 × 10⁻⁶. -8 O.M.; D i , D j The first i , j The equivalent diameter of the package, in meters; H i , H j The first i , j The height of each package, in meters; a i1 , a i2 and a j1 , a j2 The first i , j The heat dissipation coefficient of the inner and outer surfaces of the encapsulation, and the heat dissipation coefficient in the middle are related to the width of the air passage and the height of the encapsulation. k i1 , k i2 and k j1 , k j2 The first i , j The occlusion coefficient of each encapsulation support strip is 0.9, with the middle encapsulation support strip having an occlusion coefficient of 0.

9. n i , n j The first i , j Equivalent number of turns per package, unit: turns; A i , A j The first i , j Total axial metal width within the package, unit: meters; The number of aluminum flat wires (101) in each encapsulation should satisfy the same proportional relationship as formula (7), thereby obtaining the number of radial aluminum flat wires (101) wound in each encapsulation in the single-layer structure; Step 8: Based on the number of radial aluminum flat wires (101) wound in each encapsulation in the single-layer structure obtained in Step 7, recalculate the encapsulation thickness, and repeat Step 3 to Step 8 with the new encapsulation thickness until the relative error value of the equivalent loss of the reactor calculated by the two formulas (3) is less than 1%, and then end the cycle to obtain the thickness and number of turns of each encapsulation. Step 9: Based on the equivalent loss value of the reactor obtained in Step 4, calculate the equivalent temperature rise of the reactor using the following formula. θ, （8） in, P e The equivalent loss of the reactor, in watts; m Number of packages, unit: packages; D i For the first i The equivalent diameter of the package, in meters; H i For the first i The height of each package, in meters; a i1 , a i2 and respectively the first i The heat dissipation coefficient of the inner and outer surfaces of the encapsulation, and the heat dissipation coefficient in the middle are related to the width of the air passage and the height of the encapsulation. k i1 , k i2 The first i The shading coefficient of each encapsulation support strip is 0.9 for the middle encapsulation support strip; 1.35 is a revised coefficient after considering all harmonic losses. Judging temperature rise θ Is the temperature rise greater than 75K? θ When the temperature exceeds 75K, change the reactor's inner diameter, height, and number of encapsulations, and repeat steps two through eight until the temperature rises. θ Less than 75K, thus obtaining the structural dimensions of the reactor; Step 10: Based on the structural dimensions of the reactor determined in Step 9 and formula (2), calculate the actual inductance value of the reactor. If the relative error between the actual inductance value and the theoretical inductance value is less than 3%, obtain the design parameters of the reactor. Otherwise, repeat Steps 2 to 9 to adjust the inner diameter, height, and number of encapsulations of the reactor. The structural dimensions of the reactor include the inner diameter, height, number of encapsulations, encapsulation thickness, number of encapsulation turns, and air passage width. Step 11: Based on the structural dimensions of the reactor, the number of reactor star arms, and the number of radial aluminum flat wires (101) wrapped in each encapsulation in the single-layer structure determined in Step 10, start winding the reactor coil; each aluminum flat wire (101) starts winding independently on each star arm. Let the number of reactor star arms be N. Each aluminum flat wire (101) is wound only N-th of a turn before entering the next turn. After the N aluminum flat wires (101) have completed the single-layer structure according to the number of radial aluminum flat wires (101) wrapped in each encapsulation in the single-layer structure, continue to wind the next layer structure in the opposite direction until the entire reactor coil is wound. Step 12: Calculate the length of the aluminum flat wire (101) inside the reactor and its equivalent DC resistance value R: （9） in, ρ The resistivity of aluminum is expressed in ohms-meters. n i Calculate the equivalent number of turns for each package, in turns; m To determine the number of encapsulations for the design reactor; D i The equivalent diameter of each package, in meters; N c The number of aluminum flat wires (101) connected in parallel within a single turn; A Width of aluminum flat wire (101), unit: meter; B The height of the aluminum flat wire (101) is in meters. k c The winding coefficient within the aluminum flat wire (101) is 0.83; Step 13: Based on the calculated resistance value, calculate its equivalent DC resistance loss at 1.35 times the rated current value. P r : （10） in, I n Rated current, unit: ampere; Step Fourteen: Calculate the magnetic field strength at any location on the reactor, taking its center as the origin of the cylindrical coordinate system. P ( R 2, Z The radial and axial magnetic field components at point 2) are respectively: （11） （12） in, I Flow rate in 1 package, unit: amperes; H 1 represents the height of a single-turn coil, in meters; n 1 represents the total number of turns in a single-turn coil, in turns. R 1 represents the radius of a single-turn coil, in meters; μ 0 represents the free permeability, with a value of 4π × 10⁻⁶. -7 ; θ is The angle between the lines connecting two points on the circumference of the coil at different positions to the origin of the cylindrical coordinate system, in degrees; Step 15: The magnetic induction intensity of the reactor satisfies the principle of vector superposition, and the total radial and axial magnetic fields at all points of a single coil at the same height are the same; based on the reactor structure designed in Step 10, the total radial and axial magnetic fields in each winding layer within each enclosure of the reactor are as follows: （13） in, m Number of packages; w This refers to the number of winding layers of the reactor. R The radius of a single coil in cylindrical coordinates, in meters; Z The height of a single coil in cylindrical coordinates, in meters; Step 16: Based on the reactor structure, calculate the eddy current losses in the axial and radial magnetic field directions of a single aluminum flat wire (101) under an alternating magnetic field, as follows: （14） in, m Number of packages; w This refers to the number of winding layers of the reactor. R The radius of a single coil in cylindrical coordinates, in meters; Z The height of a single coil in cylindrical coordinates, in meters; ρ The resistivity of aluminum is expressed in ohms-meters. f Power supply frequency, unit: Hertz; A Width of aluminum flat wire (101), unit: meter; B The height of the aluminum flat wire (101) is in meters. D The diameter of a single coil, in meters; k m The loss correction factor due to winding within the aluminum flat wire (101) is 0.83; Step 17: Since the individual windings in each package and each layer of wire are connected in series, the eddy current losses of the individual windings in each package and each layer of wire calculated in Step 16 are calculated by linear superposition. Step 18: Since the reactor is wound with equal wire length, there is no circulating current loss in the reactor. The total loss of the reactor is the sum of the resistance loss and the eddy current loss. Stop the calculation when the total loss is less than 3% of the rated capacity after considering harmonics. Otherwise, change the inner diameter, height and number of enclosures of the reactor design and repeat steps one to eighteen until the total loss meets the requirements.

2. The method for evaluating the loss of a non-circulating air-core reactor according to claim 1, characterized in that: In step fourteen, the elliptic integral in the magnetic field calculation is solved using a series expansion method for iterative calculation.

3. The method for evaluating the loss of a non-circulating air-core reactor according to claim 1, characterized in that: The aluminum flat wire (101) is formed by pressing multiple round aluminum wires together.

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