EP3161842A1

EP3161842A1 - Multi layered air core reactor design method

Info

Publication number: EP3161842A1
Application number: EP14841391.7A
Authority: EP
Inventors: Ugur Arifoglu
Original assignee: Individual
Current assignee: Individual
Priority date: 2014-06-30
Filing date: 2014-12-30
Publication date: 2017-05-03
Also published as: WO2016003376A1

Abstract

The present invention is a reactor design method which is realized by using a computer (80) in order to determine the parameters which are required for forming an air core reactor (70) comprising coils (72) which are disposed telescopically and which are connected in a parallel manner with respect to each other and accordingly where data is entered through a user interface (81), and where predetermined calculations are made by a processor (83) by means of software, provided in the memory of the processor (83), by taking the entered data as a base, and where the results are transferred to the user through the user interface (81).

Description

SPECIFICATION

MULTI LAYERED AIR CORE REACTOR DESIGN METHOD TECHNICAL FIELD

The present invention relates to a system and method related to the design of air core reactors. PRIOR ART

Air core reactors are used for current delimiting, voltage regulation and reactive power compensation in power systems. Air core reactors are devices operating under high current and/or voltage and which can be grouped under names of serial reactor, shunt reactor, rectifying reactor, line reactor, filter reactor, neutral grounding reactor, current delimiting reactor, arc suppressing reactor.

In the reactor production market, software, which can function in very short durations like minutes by using wires with different cross section for each coil, and which has very small number of design input and great number of design output, can be purchased by paying great amount of money. In the air core reactor design which is tried to be made by using Maxwell magnetic program, the duration of producing design results by the software takes long hours. Moreover, when this program is used, the following information shall be entered' as input before the program- begins functioning: the number of turns of each coil, the coil height, coil inner diameter. It is not possible to operate the Maxwell program before these inputs are entered into the program.

For some of the persons who will use the reactor, the reactor heating value is important, and for some persons, reactor cost is more important, and accordingly, the persons decide which reactor type to be used. Besides, there are persons who demand to use optimum sized reactor by taking into consideration both the reactor heating value and the cost. Since the reactor designs have a single type, the person has to use a single type of reactor.

The optimum design study realized for the dry type air core reactor, by Yanzhen Zhao and et al, has been explained in the article published on 23.11.20110 and named "International Journal of Applied Electromagnetics and Mechanics". In the flow schema formed for dry type air core reactor which is designed based on the additional delimiting balance and hybrid genetic algorithm, the inner diameter of the reactor, number of coils, number of layers and average wire diameter are entered as data, and the design steps are realized.

BRIEF DESCRIPTION OF THE INVENTION

The present invention relates to multi layered air core reactor design method, for eliminating the abovementioned disadvantages and for bringing new advantages to the related technical field. The main object of the present invention is to provide a reactor design method and a reactor design system where said method is applied, in order to design a reactor such that the preference between heating efficiency and cost is left to the customer.

Another object of the present invention is to shorten the duration of the optimum reactor design process.

Another object of the present invention is to decrease the number of design inputs and to increase the number of design outputs. In order to realize the abovementioned objects and the objects which are to be deducted from the detailed description below, the present invention is a reactor design method which is realized by using a computer in order to determine the parameters which are required for forming an air core reactor comprising coils which are disposed telescopically and which are connected in a parallel manner with respect to each other, and accordingly where data is entered through a user interface, and where predetermined calculations are made by a processor by means of software, provided in the memory of the processor, by taking the entered data as a base, and where the results are transferred to the user through the user interface. As an improvement, in order to calculate the reactor weight corresponding to each inner diameter for at least two inner diameter values, and in order to calculate the heat losses of the air core reactor for each inner diameter value; the present method is characterized by comprising the steps of: in the first step, entering the operation frequency (Hz), reactor current value (A) and reactor self (mH) value, in the second step, entering the data regarding the coil wire type, in the third step, entering the .current density of the conductor (A/mm^A2), in the fourth step, entering the first and final inner diameter value (cm) of the air core reactor, in the fifth step, checking whether the reactor inner diameter is greater than the final inner diameter, if not, passing to the sixth step, and in the sixth step, entering the number of layers of the air core reactor, in the seventh and eighth step, entering respectively the number of coils connected in a parallel manner inside a layer of the air core reactor and entering the paper thickness between the parallel coils in millimeters, in the ninth step, entering the isolated and non-isolated diameter (mm) of the coil conductors regarding each layer respectively from outside towards inside, in the tenth step, checking ^'whether the number and thickness of the selected coils are resistant to the reactor current, if the number and thickness of the selected coils are resistant to the reactor current, passing to the twelfth step, and in the twelfth step, checking whether the reactor short circuit current has priority or not, in the twelfth step, if the reactor short circuit current does not have priority, passing to the twenty second step, and in the twenty second step, separately calculating the current carrying (A) capacity of each coil having the determined cross sections, in the twenty third step, calculating the impedance (ohm) of the reactor ordered by the person who will use the air core reactor, in the twenty fourth step, by accepting that the first coil self-value (mH) of the air core reactor is a value which is 1.1.-1.5 times the reactor self-value, and in the twenty fifth step, calculating the number of windings of the outermost coil of the air core reactor, in the twenty sixth step, estimating the number of other parallel coils of the air core reactor such that it is 10-30 % less than the number of winding of the first coil provided above, in the twenty seventh step, calculating the voltage of the air core reactor by using the current and the impedance of the air core reactor, in the twenty eighth step, calculating the estimated height (cm) of the air core reactor, in the twenty ninth step, entering the "dog bone" thickness (cm) between the layers of the air core reactor as data, in the thirtieth step, calculating the diameter (cm) of each coil, in the thirty first step, calculating the L self (mH) value of each coil, coil average radius (cm), number of windings, and the coil height (cm), in the thirty second step, calculating the mutual inductance values between all coils of the air core reactor with the help of the average coil diameter, coil height and number of coil windings, in the thirty third and thirty fourth step, calculating the impedance matrix of the air core reactor and the dc resistance (ohm) of the reactor coils for a temperature value between 55- 85 degrees and a temperature value between 10-30 degrees respectively, in the thirty fifth step, calculating the current values (A) of all parallel connected coils by using the voltage applied to the air core reactor and by using the impedance matrix information of the air core reactor, in the thirty sixth step, calculating the reactor current (A) by adding all parallel connected coil current values, in the thirty seventh step, obtaining the reactor self (mH) value by using reactor current, voltage and frequency values, in the thirty eighth step, entering the allowed iteration number, in the thirty ninth step, entering the allowed lower and upper limits for the reactor current, in the fortieth step, checking whether the reactor current and each coil current are within the limit values and checking whether the iteration number is under the acceptable upper value, in the fortieth step, if the reactor current is within the limit values, if each coil current is within the limit values, and if the iteration number is under the acceptable upper value, passing to the fifty ninth step, and calculating the reactor current (A), the reactor current angle, dc resistance (ohm) for a temperature value between 10-30 degrees and a temperature value between 55-85 degrees for the air core reactor, and reactor reactive power (kVA), reactor Q quality factor, dc loss power (kW) at a temperature value between 55-85 degrees, total wire length (m) for the air core reactor, reactor ac loss power, reactor weight (kg), reactor height, conductor weight of the reactor, total weight of the peripheral units and of the reactor, the self-value (mH) of the air core reactor, in the sixtieth step, increasing the inner diameter value by a predetermined value and returning to the fifth step.

In a preferred embodiment .of the present invention, in the fifth step, the processes are stopped in case the reactor inner diameter is greater than the final inner diameter. In a preferred embodiment of the present invention, if the number and thickness of the coils selected in the tenth step cannot resist the reactor current, in the eleventh step, the new conductor diameters (mm) are entered and said eleventh step is repeated until the number and thickness of the selected^' coils become resistant to the reactor current. In a preferred embodiment of the present invention, the following steps are applied: if the reactor short circuit current has priority in the twelfth step, entering the short circuit current value (A) of the air core reactor in the thirteenth step, in the fourteenth step, checking whether the coil wire is made of copper or not, if the coil wire is made of copper, in the fifteenth and sixteenth step, entering the initial and final temperature of the wire as degrees and entering the short circuit duration of the air core reactor as seconds respectively, in the seventeenth step, calculating the short circuit current density of the air core reactor, after the required calculation is made for the copper wire, checking whether the cross sections of the conductor selected in twenty first step can handle the short circuit current or not, if the cross sections of the selected conductors handle the short circuit current, in the twenty second step, calculating the current carrying (A) capacity separately for each coil in the determined cross sections.

In a preferred embodiment of the present invention, in case wire is not made of copper during the check of the coil wire type in the fourteenth step, the initial and final temperature of the aluminum wire and the short circuit duration of the air core reactor are entered in the eighteenth and nineteenth steps, and in the twentieth step, the short circuit current density of the air core reactor is calculated, and the twenty first step is applied. In a preferred embodiment of the present invention, in case the conductor cross sections, selected in the twenty first step, cannot handle the short circuit current, return to the eleventh step is realized, and the new conductor diameters (mm) are entered as data, and the tenth step is applied. In a preferred embodiment of the present invention, the following steps are applied: if the answer is no in the fortieth step, checking whether all coil currents are within the own current limits in the forty first step, if all coil currents are not within their own current limits, in the forty second step, detecting the coils whose coil currents exceed the limit values, in the forty third step, checking whether the coil current is below the determined limit value or not, if the coil current is not below the determined limit value, in the forty fourth step, increasing the winding number of the coil, whose current value increases above the determined current value, with the help of a changing coefficient depending on the number of iterations, in the forty sixth step, checking whether the reactor current is within its own current limits or not, in case the reactor current is not within its own current limits, in the forty seventh step, checking whether the reactor current is below the lower current limits or not, if the reactor current is not below the lower current limit, in the forty eighth step, reducing the reactor upper limit with the. help of a coefficient changing depending on the number of iterations, in the fiftieth step, calculating the height (cm) of the air core reactor by using the winding number which has been recently calculated, in the fifty first step, calculating the self (mH) values of all coils of the air core reactor by using the coil heights, coil diameters, winding numbers which have been recently calculated, in the fifty second step, calculating the self (mH) values between the parallel connected coils by using self (mH) values of the coils, the calculated coil heights, coil diameters and the winding numbers, in the fifty third step, calculating the dc resistance values (ohm) of all parallel connected coils, in the fifty fourth step, forming the impedance matrix (ohm) for the air core reactor formed by the coils connected in a parallel manner, in the fifty fifth step, calculating the current values of all parallel connected coils by using the impedance matrix data of the air core reactor and the voltage applied to the air core reactor, in the fifty sixth step, calculating the reactor current (A) by adding all current values of the coils connected in a parallel manner, in the fifty seventh step, reaching the reactor self (mH) value by using the reactor current, reactor voltage and frequency values, in the fifty eighth step, increasing the iteration number by one, and returning to the fortieth step. In a. preferred embodiment of the present invention, in case all coil currents are within their own current limits in the forty first step, the forty sixth step is applied where it is checked whether the reactor current is within its own current limits. In a preferred embodiment of the present invention, if the coil current, which is outside of the limit values, is lower than the determined limit value in the forty third step, the number of coil windings which are lower than the current limit determined in forty fifth step is reduced by a coefficient which changes depending on the iteration number, and the forty sixth step is applied.

In a preferred embodiment of the present invention, if the reactor current is within its own current limits during the check of the forty sixth step, directly the fiftieth step is applied.

In a preferred embodiment of the present invention, if the reactor current is below the lower current limit in the forty seventh step, the reactor lower limit is increased with the help of a coefficient which changes depending on the iteration number in the forty ninth step, and the fiftieth step is applied.

In a preferred embodiment of the present invention, in the fifth step, if the reactor inner diameter is greater than the final inner diameter, the processes are stopped.

In a preferred embodiment of the present invention, in the twenty fourth step, the first coil self-value (mH) of the air core reactor is accepted to be 1.25 times the reactor self-value.

In a preferred embodiment of the present invention, in the twenty sixth step, the other parallel coil numbers of the air core reactor is estimated to be 20 % less than the winding number of first coil located above itself.

In a preferred embodiment of the present invention, the impedance matrix (ohm) of the air core reactor and the dc resistance (ohm) of the reactor coils are calculated for both 25 degrees and 75 degrees respectively in the thirty third step and in the thirty fourth step. In a preferred embodiment of the present invention, in the fortieth step, if the reactor current is within the limit values, if each coil current is within the limit values, and if the iteration number is below the acceptable upper value, the fifty ninth step is applied, and the following are calculated: the reactor current (A), reactor current angle, dc resistance (ohm) of the air core reactor at 25 degrees and 75 degrees, reactor reactive power (kVA), reactor Q quality factor, dc loss power (kW) at 75 degrees, total wire length (m) of the air core reactor, reactor ac loss power, reactor weight (kg), reactor height, conductor weight of the reactor, the total weight of the reactor together with the peripheral units, and the self-value (mH) of the air core reactor.

In a preferred embodiment of the present invention, in the sixtieth step, the inner diameter value is increased by 0.5-1.5 cm.

In a preferred embodiment of the present invention, in the sixtieth step, the inner diameter value is increased by 1 cm. BRIEF DESCRIPTION OF THE FIGURES

In Figure 1 , a representative view of the subject matter reactor design system is given.

In Figure 2a, a longitudinal representative cross sectional view of an air core reactor is given.

In Figure 2b, a view of the electrical circuit schema of all layers of the air core reactor is given. In Figure 2c, a view of the longitudinal cross section of a layer comprising four coils is given. In Figure 3, the steps of the reactor design method are given. REFERENCE NUMBERS

I First step

2 Second step

3 Third step

4 Fourth step

5 Fifth step

6 Sixth step

7 Seventh step

8 Eighth step

9 Ninth step

10 Tenth step

I I Eleventh step

12 Twelfth step

13 Thirteenth step

14 Fourteenth step 15 Fifteenth step

16 Sixteenth step

17 Seventeenth step

18 Eighteenth step 19 Nineteenth step

20 Twentieth step

21 Twenty first step

22 Twenty second step

23 Twenty third step 24 Twenty fourth step

25 Twenty fifth step

26 Twenty sixth step

27 Twenty seventh step

28 Twenty eighth step 29 Twenty ninth step

30 Thirtieth step

31 Thirty first step

32 Thirty second step

33 Thirty third step 34 Thirty fourth step

35 Thirty fifth step

36 Thirty sixth step

37 Thirty seventh step

38 Thirty eighth step 39 Thirty ninth step

40 Fortieth step

41 Forty first step

42 Forty second step

43 Forty third step 44 Forty fourth step

45 Forty fifth step

46 Forty sixth step

47 Forty seventh step

48 Forty eighth step 49 Forty ninth step

50 Fiftieth step

51 Fifty first step 52 Fifty second step

53 Fifty third step

54 Fifty fourth step

55 Fifty fifth step

56 Fifty sixth step

57 Fifty seventh step

58 Fifty eighth step

59 Fifty ninth step

60 Sixtieth step

61 Sixty first step

70 Air core reactor

71 Layer

72 Coil

73 Dog bone

80 Computer

81 User interface

82 Memory unit

83 Processor

THE DETAILED DESCRIPTION OF THE INVENTION

In this detailed description, the subject matter air core reactor (70) design method is explained with references to examples without forming any restrictive effect only in order to make the subject more understandable.

The air core reactor (70) comprises coils (72) which are telescopically disposed and which are connected parallel with respect to each other. In the preferred application, there are layers (71) having four coils (72). In the present invention, air core reactor (70) design is made for the inner diameter value corresponding to each cm increase of the inner diameter range of the coil (72). Thus, the reactor weight corresponding to each inner diameter is determined, and at the same time, the thermal losses of the reactor for each inner diameter value are determined.

There is a computer (80) comprising a user interface (81) where the data is entered, and a processor (83) saving the data in a memory unit (82) and making calculations according to the saved data and formulas, and transferring the results to the user through a user interface (81).

In order for the air core reactor (70) design to be made, software and method are formed, and the algorithm entered through the user interface (81) is saved to the memory unit (82) by the processor (83). An algorithm is formed which makes reactor design for each inner diameter value which is within the reactor inner diameter range which has been initially determined and which changes from the lower value of this range and which is increased by 1 cm each time (this 1 cm distance can be reduced as desired) and which changes up to the upper limit of this range. The. optimum design model, formed on the base of Kirchhoff voltage law equation, is applied for all coils (72). In the algorithm, passage is realized from the low valued inner diameter of the air core reactor (70) to another inner diameter thereof which is at a higher value. The algorithm has mathematical calculations based on magnetic field theory. One of these is to calculate the mutual self-values for the parallel connected coils (72). The other is to calculate the self-values of all coils (72) of all layers (71).

The total number of layers (71) is taken as n; and the total number of coils (72) in a layer (71) is taken as m. The total number of coils (72) in the air core reactor (70) is equal to m^*n. For all the coils (72) of the air core reactor (70), Kirchhoff voltage equation can be written as follows (1a). jwLiI] +jwM₁₂l2 + + jwMijIj +.·· + jwM_]m*_n I_m*_n +1^1] = V_nom

jwM₂iIi +jwL₂I₂ + + jw ₂j[j +... + jwM_2m*_nI_m*_n +R₂I₂ =V_nom jw nl! +jwM_i2I₂ + + jwLjIj + + jwMjjlj +... + jw _im*_nI_m*n +^Ri^ri = ^vnom (^1a)

jwM_m*_n)Ii +jwM_m*_n2I₂ +... + jwL_m*_nI_m*_n +.. + jwM_m*_njIj +.. + jwL_m*_{n m}*_n I_m*_n +R_m*_nIm*_n

The equation (1a) can be written in matrix form as in the equation (1b) given below.

R, + L, M|2 M,3 Ml.m'n ^' Il ^" ¼iom

M21 R₂ +L₂ Μ₂₃· ^M2,m»n %iom

M31 M₃₂ R₃ + L₃ M3,m*n

=

Mm»n,l M_m*n,2 Mm*n,3 V

_'m*n. ^vnom _ By using the current law of Kirchhoff, the equation (2) written for the current of all coils (72) of the air core reactor (70) is as. follows.

In the equations 1 a, 1 b and 2, for the coil (72) with number i; R, is the resistance, L, is the self-value, and lj is the current. MM is the mutual inductance between the coil (72) with number i and the coil (72) with number j. V_n0m and l_n0m are the nominal voltage and nominal current of the air core reactor respectively, w is the angular frequency.

The calculation of the self-values of the air core reactor (70) is as follows. Kirchhoff formula separates a coil (72) in the circular windings and it joins the mutual inductances between the windings calculated by the g(0) elliptical integral. L = ng(0) + 2(n - 1) g(y) + 2(n - 2) g(2_Y) + + 2g((n - 1)γ) ; g(z) = μ₀ - (2 - k )K - 2E (3)

The variables used in Equation 3 are as follows.

k² = -^—; _§(0) = μ_οΓ(1η^ - ¾ ; γ =— ; g(0) = μ₀Γ(2(Κ E) + - ) ; k = - — (4) h 2 _{+ z}2 β 4 n 4 r

2r 7inc

P = Θ = tan p ; k = sin Θ ; k = cos Θ ; z P = 0.5c (5) β is the wire radius. The new equation (6) of the self-value of a coil (72), where the Equation 4 and Equation 5 are disposed in Equation 3, is as follows. μ₀ .

)

4π

Here, K and E are the exact elliptic integral of the first and second types together with coefficient k respectively.

For the equations between 3 and 7, r is the coil (72) radius; h is the coil (72) height, and c is the wire diameter, n is the winding number of the coil (72) and it has to be an integer.

The calculation of the mutual inductances of the air core reactor (70) is as follows. The equation [A] for the mutual inductance between a circular ring and a winding coil is as follows. - E c'²

Μ_θ = ^-0(A + a)ck +— (K -n(k, c) (8)

4π k² c²

A is the radius of the winding coil; and a is the radius of the loop. The definitions regarding the variables used in Equation 8 are as follows.

0 (1 -c sin (p)-^l - k sin φ p is the height of a winding coil divided by 2ττ. Θ is the final angle of the 2ττη solenoid. The equation 10 is the exact elliptical integral of the third type. When Equation 9 and 10 are disposed in Equation 8, the new mutual inductance equation is as follows.

The definitions of the variables existing in Equation 11 are as follows. Another equation for Equation 11 is as follows.

The equations for the variables given in Equation 13 are as follows.

The equation for the mutual inductance between the two winding coils is as follows.

^2πηΐ^η2 |_W(_b2 __bl +h₂) + W(b₂ -b, +h,)-W(b2 -b, +h₂ -h,)- W(b₂ - (15) h1^h2

For Equation 15, ^ is the distance between the base of the first coil (72) and the reference point, and b₂ is the distance between the base of the second coil (72) and the reference point; hi is the height of the first coil (72); h2 is the height of the second coil (72); n1 is the turn number of the first coil (72), and n2 is the turn number of the second coil (72). If the bases of both coils (72) are coincident with the reference point, b1=b2=0. W(x) and w'(x) equations in Equation 15 are as follows. .

8(r_tr₂) 3/2

W(x) = xW -(— -lXK-E) (16)

3k k² r₂ ² KE(k,0)-(( -E)F(k,e)-- (17)

For Equation 16 and 17; r1 is the radius of the first coil (72), r2 is the radius of the second coil (72). The other variables have the following equations.

r,r₂ 4rir₂

c = 2 (20)

(ri+r₂ x²+(r, +r₂)² W (x) =— 2LLi_ ( - (21)

The short circuit test of the air core reactor (70) is made as follows. F1 is the initial temperature (C°) of the air core reactor (70); F2 is the final temperature (C°) of the air core reactor (70); F3 is the short circuit duration (seconds), and the current density of the air core reactor (70) for the short circuit condition is calculated as follows for aluminum. ' The current density of the air core reactor (70) for copper is as follows.

,49804. . ,235 + F₂ . , . . ₂ ,

F₄ = J(— ) log₍^ ₎ ( ) (23)

In case of short circuit, the total coil (72) cross section of the air core reactor (70) shall be greater than the equation given below.

S = ^- ( mm² ) (24) F₄

Here, F5 is the short circuit current (A) for the air core reactor (70).

The winding number (N) of the first coil (72) is calculated by means of the following equation

N = (L₁10°) - A₁ + A₂ (25)

L1 is the self-value of the first coil (72). A1 and A2 are explained by the following equations.

A! = 0.002πϋ₁Ν²(1ο_§(1 + ^^-)) (26)

dN

A, = (27)

2.3 + (3.437dN / D_j ) + 1.7636(dN / D, )² - 0.47((0.755 + (dN/ Dj ))^L

Here, d is the diameter (cm) of the isolated wire; and D1 is the inner diameter (cm) of the reactor. The winding number of the coils (72) versus the number of coils (72) is shown in Graphic 1. Graphic -1

Number of coils

The distribution of the voltage along a coil (72) is very important in order to apply the same voltage value (V_nom) to all coils (72). As can be seen in Graphic 2, if the coil (72) with number m has windings with number N, the voltage value for two adjacent windings is V_max/N for coil (72) with number m. If the coil (72) with number (m-1) has K windings, the voltage value between the two adjacent windings is Vmax/K for the coil (72) with number (m-1). In this case, the voltage between the winding of A and the winding of B is calculated as follows. A-B = (-ⁱ^¹ - ^¹)Vno_m (28)

N

Graphic - 2

If the voltage value given in the equation is higher than the spark-over voltage value, short circuit is formed between wire A and wire B. According to the equations and information given above, the design of the air core reactor (70) is realized step by step as follows. In the first step (1), the operation frequency (Hz), the reactor current value (A), and the reactor self (mH) value are entered. In the second step (2), the coil wire type is entered. Aluminum or copper is used as the coil wire. In the third step (3), the current density (A/mm^A2) is entered into the software. In the fourth step (4), the initial and final inner diameter values (cm) of the air core reactor (70) are entered. The fifth step (5) is the control step. It is checked whether the reactor inner diameter is greater than the final inner diameter. If not, the sixth step (6) is applied. In the sixth step (6), the number of layers of the air core reactor (70) is entered. In the seventh step (7) and in the eighth step (8), the number of parallel connected coils in a layer of the air core reactor (70) and the paper thickness (mm) in the parallel coils (72) are entered as parameters. In the ninth step (9), the isolated and non-isolated diameters (mm) of the coil conductors of each layer (71) respectively from outside towards inside are entered. In the tenth step (10), it is checked whether the number and thickness of the selected coils (72) can resist the reactor current or not. If the number and thickness of the selected coils (72) cannot resist the reactor current, in the eleventh step (11), the new conductor diameters (mm) value is entered, and again the same check is realized. The same data entry is made until the number and thickness of the selected coils (72) resist the reactor current. When the received answer is favorable, in the twelfth step (12), it is checked whether the reactor short circuit current has priority or not.

If the reactor short circuit current has priority, in the thirteenth step (13), the short circuit current value (A) of the air core reactor (70) is entered. After said value is entered, in the fourteenth step (14), the type of the coil type is checked, in other words, it is checked if it is copper or not. If the coil wire is made of copper, in the fifteenth step (15) and in the sixteenth step (16), the initial and final temperature of the wire are entered as degrees and as the short circuit duration (seconds) of the air core reactor (70) respectively. In the seventieth step (17), the short circuit current density (A/mm^A2) of the air core reactor (70) is calculated by means of equation (23). If it is detected that the wire is not made of copper during the check of the coil wire type in the fourteenth step (14), the initial and final temperature of the aluminum wire and the short circuit duration of the air core reactor (70) are entered in the eighteenth step (18) and in the nineteenth step (19). Moreover, in the twentieth step (20), the short circuit current density of the air core reactor (70) is calculated by means of equation (22). After the required calculation is realized by using both of the two wire types, it is checked whether the selected conductor cross sections remove the short circuit current or not in the twenty first step (21). The total coil cross section shall be greater than equation (24). If the selected conductor cross sections do not resist the short circuit current, the eleventh step (11) is re-applied, and the new conductor diameters (mm) are entered as data, and the tenth step (10) is continued. If the answer in the twenty first step (21) is favorable, the current carrying (A) capacity of each coil (72) having the cross sections determined in the twenty second step (22) is calculated separately. In the twelfth step (12), even if the short circuit current has priority, the reactor passes to the twenty second step (22) in the same manner. In the twenty third step (23), the reactor impedance (ohm) which has been ordered by the person who will use the air core reactor (70) is calculated. In the twenty fourth step (24), the initial coil self-value (mH) of the air core reactor (70) is accepted as 1.25 times the self-value of the reactor, and in the twenty fifth step (25), the winding number of the outermost coil (72) of the air core reactor (70) is calculated by means of the equation (25, 26 and 27).

In the twenty sixth step (26), the other parallel coil numbers of the air core reactor (70) is estimated to be 20 % less than the winding number of the first coil (72) provided above itself, and in the twenty seventh step (27), the impedance and current of the air core reactor (70) are used, and the voltage of ^'the air core reactor (70) is calculated by using equation (28). In the twenty eighth step (28), the estimated height (cm) of the air core reactor (70) is calculated. In the twenty ninth step (29), the "dog-bone" (73) thickness (cm) between the layers of the air core reactor (70) is entered as data. In the thirtieth step (30), the diameter (cm) of each coil (72) is calculated. In the thirty first step (31), the L self (mH) value of each coil (72), the coil average radius (cm), the number of windings and the coil height (cm) are calculated.

In the thirty second step (32), the mutual inductance values between all coils (72) of the air core reactor (70) is calculated with the help of the average coil diameter, the coil height and the coil winding numbers. In order to realize the calculations of the thirty first step (31) and of the thirty second step (32), the equations between equation (3) and equation (21) are used. In the thirty third step (33) and in the thirty fourth step (34), the dc resistance (ohm) of the reactor coils for both 25 degrees and 75 degrees, and the impedance matrix (ohm) of the air core reactor (70) are calculated respectively.

In the thirty fifth step (35), the current values (A) of all the parallel connected coils (72) are calculated by using the voltage to be applied to the air core reactor (70) and by using the impedance matrix data of the air core reactor (70). In the thirty sixth step (36), the reactor current (A) is calculated by adding all coil current values connected in a parallel manner and by using equation (2). In the thirty seventh step (37), the reactor self (mH) value is reached by using the reactor current, voltage and frequency values. In the thirty eighth step (38), the permitted iteration number is entered. In the thirty ninth step (39), the permitted lower and upper limits of the reactor current are entered. After this, there is a checking process in the fortieth step (40).

In said fortieth step (40), it is checked whether the reactor current and each coil current are within the limit values and whether the iteration number is lower than the acceptable upper value. If the answer is no, in the forty first step (41), it is checked whether all coil currents are within their own current limits. If all coil currents are not within their own current limits, the forty second step (42) is applied, and the coils (72) which exceed the limit values are determined from the coil currents. Meanwhile, the winding numbers of the coils (72) remaining within the limits are not changed. In the forty third step (43), a checking process is made where it is checked whether the coil current is below the determined limit value or not. If the coil current does not stay under the determined limit value, the winding number of the coil (72), whose coil current exceeds the current limit determined in the forty fourth step (44), is increased by means of a coefficient which changes depending on the iteration number. If the coil current, which stays outside the limit values, stays under the determined limit value, the winding number of the coil (72), which stays under the current limit determined in the forty fifth step (45), is decreased by means of a coefficient which changes depending on the iteration number. In the forty sixth step (46), it is examined whether the reactor current is within it own current limits or not. In the forty first step (41), in case all coil currents are within their own current limits, the forty sixth step (46) is applied. In case the reactor current is not within its own current limits; in the forty seventh step (47), it is checked whether the reactor current is below the lower current limits or not. If the reactor current does not stay below the lower current limit, in the forty eighth step (48), the reactor upper limit is decreased with the help of a coefficient which changes depending on the iteration number. If the reactor current stays below the lower current limit; in the forty ninth step (49), the reactor lower limit is increased with the help of a coefficient which changes depending on the iteration number. In the fiftieth step (50), the winding numbers, which have been recently calculated, are used and the height (cm) of the air core reactor (70) is calculated. In the check realized in the forty sixth step (46), if the reactor current is within its own current limits, the fiftieth step (50) is applied. By using the winding numbers, coil diameters and coil heights which have been recently calculated in the fifty first step (51), the self (mH) values of all the coils (72) of the air core reactor (70) are calculated. In the fifty second step (52), by using the calculated winding numbers, coil diameters, coil heights and the self (mH) values of the coils, the self-values (mH) between the parallel connected coils (72) are calculated. In the fifty third step (53), the dc resistance values (ohm) of all parallel connected coils (72) are calculated. In the fifty fourth step (54), the impedance matrix (ohm) regarding the air core reactor (70) and parallel connected coils (72) is formed. In the fifty fifth step (55), by using the voltage applied to the air core reactor (70) and the impedance matrix data of the air core reactor (70), the current values (A) of all parallel connected coils (72) are calculated. In the fifty sixth step (56), the current values of all parallel connected coils (72) are added, and the reactor current (A) is calculated by means of equation (2). In the fifty seventh step (57), the reactor current, reactor voltage and frequency values are used, and thereby the reactor self (mH) value is obtained. In the fifty eighth step (58), the iteration number is increased by one, and it is returned to the fortieth step (40) and the steps are repeated. In the fortieth step (40), if the reactor current is between the limit values, if each coil current is between the limit values, and if the iteration number is lower than the acceptable upper value, the fifty ninth step (59) is applied, and the following are calculated: reactor current (A), reactor current angle, dc resistance (ohm) of the air core reactor (70) between 25 and 75 degrees, reactor reactive power (kVA), reactor Q quality factor, dc loss power (kW) at 75 degrees, total wire length (m) of the air core reactor (70), reactor ac loss power, reactor weight (kg), reactor height, reactor conductor weight, the total weight of the reactor together with the peripheral units, the self-value (mH) of the air core reactor (70). The reactor current is calculated by means of equation (2). In the sixtieth step (60), the inner diameter value is increased by 1 cm, and it is returned to the fifth step (5). If the reactor inner diameter_, is greater than the final inner diameter in the fifth step (5), the processes are stopped in the sixty first step (61).

The reactor inner diameter range is determined in the beginning, and said steps are repeated for the reactor inner diameter range at intervals of 1 cm for each different inner diameter (cm) value. The software calculates the height of all coils (72) and the winding numbers, and for each inner diameter value, it^' calculates and saves the weight (kg) of the air core reactor (70) and the heat loss (kW) of the air core reactor (70). Thus, design is made according to the reactor heating value and according to the reactor weight, and it permits the customer to select various alternative reactor designs. The customer selects the most suitable design accordingly. In the exemplary application, said method is used for designing an air core reactor (70) having the properties of 600 A, 50 Hz, 1.27 mH, 6 mm conductor diameter. For the inner diameters between 20 cm and 120 cm, the conductor weight, dc power loss and optimum reactor inner diameter versus the reactor height have been observed. The optimum results are given in Graphic 3. The most important superiority of the used algorithm when compared with the prior art is that the algorithm has the ability to calculate all production parameters of the reactor in terms of the reactor cost and reactor dc power loss for each inner diameter value by increasing the reactor inner diameter value by one each cm (may be decreased by 1 cm if desired) until the reactor inner diameter final value, determined at the beginning, from the reactor inner diameter beginning value, determined at the beginning, for the reactor design parameters instead of making optimum design by using parameters which are very difficult to obtain and very difficult to measure. When the whole algorithm is converged, the user will have information which will be sufficient for drawing 3 different curves. For each three curves, the horizontal axis will be the reactor inner diameter value (cm), in the first curve the vertical axis shows the reactor weight (Graphic 3, A), in the second curve the vertical axis shows the reactor dc loss (kW) (Graphic 3, B), in the third curve, the vertical axis shows the reactor height (cm) (Graphic 3, C). At the minimum point (with respect to the vertical axis) of the first two curves, the required inner diameter values of the reactor for optimum design occur. From the third curve, for the desired (optimum) inner diameter value, (optimum) reactor height (cm) can be observed. The reactor optimum inner diameter value and the optimum reactor height corresponding to this value are written in the known formulas, and all other parameters which are required for the optimum design of the reactor can be easily calculated. According to the results of this design, the user can easily reach reactor design values with minimum cost or with minimum dc loss.

Graphic - 3

Moreover, the reactor designs formed by means of said software can meet the properties expected from the air core reactor (70) by using different cross sectioned copper or aluminum wire if desired, thanks to the background generating pluralities of design outputs in minutes by means of small number of design inputs. The properties expected from the air core reactor (70) can be arranged as follows. The most important property is that the current, passing through each coil (72) connected in a parallel manner, shall not exceed the value allowed by the wire forming said coil (72) in terms of heating, and besides, it shall not be lower than the current value allowed by the wire in order for said wire to be used in an economic manner. The other expected properties are that no circulation current shall be formed or minimum level of circulation current shall be formed between the parallel connected coils (72) and that the self (mH) value of the ordered reactor shall be within the determined tolerance when the reactor design is finished, and that the air core reactor (70) shall resist the determined short circuit current within the allowed duration, and it shall resist the allowed spark-over voltage. If the voltage calculated in Equation 28 is greater than the spark-over voltage, short circuit is formed between wire A and wire B. The subject matter software provides these properties and besides, it can be produced under the condition of using minimum wire cost for the air core reactor (70).

The protection scope of the present invention is set forth in the annexed Claims and cannot be restricted to the illustrative disclosures given above, under the detailed description. It is because a person skilled in the relevant art can obviously produce similar embodiments under the light of the foregoing disclosures, without departing from the main principles of the present invention.

Claims

1. A reactor design method which is realized by using a computer (80) in order to determine the parameters which are required for forming an air core reactor (70) comprising coils (72) which are disposed telescopically and which are connected in a parallel manner with respect to each other and accordingly where data is entered through a user interface (81), and where predetermined calculations are made by a processor (83) by means of software, provided in the memory of the processor (83), by taking the entered data as a base, and where the results are transferred to the user through the user interface (81); in order to calculate the reactor weight corresponding to each inner diameter for at least two inner diameter values, and in order to calculate the heat losses of the air core reactor (70) for each inner diameter value; the present method is characterized by comprising the steps of: in the first step (1), entering the operation frequency (Hz), reactor current value (A) and reactor self (mH) value, in the second step (2), entering the data regarding the coil wire type, in the third step (3), entering the current density of the conductor (A/mm^A2), in the fourth step (4), entering the first and final inner diameter value (cm) of the air core reactor (70), in the fifth step (5), checking whether the reactor inner diameter is greater than the final inner diameter, if not, passing to the sixth step (6), and in the sixth step (6), entering the number of layers of the air core reactor (70), in the seventh (7) and eighth step (8), entering respectively the number of coils (72) connected in a parallel manner inside a layer (71) of the air core reactor (70) and entering the paper thickness between the parallel coils (72) in millimeters, in the ninth step (9), entering the isolated and non-isolated diameter (mm) of the coil conductors regarding each layer (71) respectively from outside towards inside, in the tenth step (10), checking whether the number and thickness of the selected coils (72) are resistant to the reactor current, if the number and thickness of the selected coils (72) are resistant to the reactor current, passing to the twelfth step (12), and in the twelfth step (12), checking whether the reactor short circuit current has priority or not, in the twelfth step (12), if the reactor short circuit current does not have priority, passing to the twenty second step (22), and in the twenty second step (22), separately calculating the current carrying (A) capacity of each coil (72) having the determined cross sections, in the twenty third step (23), calculating the impedance (ohm) of the reactor ordered by the person who will use the air core reactor (70), in the twenty fourth step (24), by accepting that the first coil self-value (mH) of the air core reactor (70) is a value which is 1.1.-1.5 times the reactor self-value, and in the twenty fifth step (25), calculating the number of windings of the outermost coil (72) of the air core reactor (70), in the twenty sixth step (26), estimating the number of other parallel coils (72) of the air core reactor (70) such that it is 10-30 % less than the number of winding of the first coil (72) provided above, in the twenty seventh step (27), calculating the voltage of the air core reactor (70) by using the current and the impedance of the air core reactor (70), in the twenty eighth step (28), calculating the estimated height (cm) of the air core reactor (70), in the twenty ninth step (29), entering the "dog bone" (73) thickness (cm) between the layers (71) of the air core reactor (70) as data, in the thirtieth step (30), calculating the diameter (cm) of each coil (72), in the thirty first step (31), calculating the L self (mH) value of each coil (72), coil average radius (cm), number of windings, and the coil height (cm), in the thirty second step (32), calculating the mutual inductance values between all coils (72) of the air core reactor (70) with the help of the average coil diameter, coil height and number of coil windings, in the thirty third (33) and thirty fourth step (34), calculating the impedance matrix (ohm) of the air core reactor (70) and the dc resistance (ohm) of the reactor coils for a temperature value between 55-85 degrees and a temperature value between 10-30 degrees respectively, in the thirty fifth step (35), calculating the current values (A) of all parallel connected coils (72) by using the voltage applied to the air core reactor (70) and by using the impedance matrix information of the air core reactor (70), in the thirty sixth step (36), calculating the reactor current (A) by adding all parallel connected coil current values, in the thirty seventh step (37), obtaining the reactor self (mH) value by using reactor current, voltage and frequency values, in the thirty eighth step (38), entering the allowed iteration number, in the thirty ninth step^' (39), entering the allowed lower and upper limits for the reactor current, in the fortieth step (40), checking whether the reactor current and each coil current are within the limit values and checking whether the iteration number is under the acceptable upper value, in the fortieth step (40), if the reactor current is within the limit values, if each coil current is within the limit values, and if the iteration number is under the acceptable upper value, passing to the fifty ninth step (59), and calculating the reactor current (A), the reactor current angle, dc resistance (ohm) for a temperature value between 10-30 degrees and a temperature value between 55-85 degrees for the air core reactor (70), and reactor reactive power (kVA), reactor Q quality factor, dc loss power (kW) at a temperature value between 55-85 degrees, total wire length (m) for the air core reactor (70), reactor ac loss power, reactor weight (kg), reactor height, conductor weight of the reactor, total weight of the peripheral units and of the reactor, the self- value (mH) of the air core reactor (70), in the sixtieth step (60), increasing the inner diameter value by a predetermined value and returning to the fifth step (5).

A reactor design method according to Claim 1 , characterized in that in the fifth step (5), the processes are stopped in case the reactor inner diameter is greater than the final inner diameter.

A reactor design method according to Claim 1 , characterized in that if the number and thickness of the coils (72) selected in the tenth step (10) cannot resist the reactor current, in the eleventh step (1 1 ), the new conductor diameters (mm) are entered and said eleventh step (11) is repeated until the number and thickness of the selected coils (72) become resistant to the reactor current.

4. A reactor design method according to Claim 1 , characterized in that the following steps are applied: if the reactor short circuit current has priority in the twelfth step, entering the short circuit current value (A) of the air core reactor (70) in the thirteenth step (13), in the fourteenth step (14), checking whether the coil wire is made of copper or not, if the coil wire is made of copper, in the fifteenth (15) and sixteenth step (16), entering the initial and final temperature of the wire as degrees and entering the short circuit duration of the air core reactor (70) as seconds respectively, in the seventeenth step (17), calculating the short circuit current density of the air core reactor (70), after the required calculation is made for the copper wire, checking whether the cross sections of the conductor selected in the twenty first step (21) can handle the short circuit current or not, if the cross sections of the selected conductors handle the short circuit current, in the twenty second step (22), calculating the current carrying (A) capacity separately for each coil (72) in the determined cross sections.

A reactor design method according to Claim 4, characterized in that in case wire is not made of copper during the check of the coil wire type in the fourteenth step (14), the initial and final temperature of the aluminum wire and the short circuit duration of the air core reactor (70) are entered in the eighteenth (18) and nineteenth steps (19), and in the twentieth step (20), the short circuit current density of the air core reactor (70) is calculated, and the twenty first step (21) is applied.

6. A reactor design method according to Claim 4 or 5, characterized in that in case the conductor cross sections, selected in the twenty first step (21), cannot handle the short circuit current, return to the eleventh step (11) is realized, and the new conductor diameters (mm) are entered as data, and the tenth step (10) is applied.

7. A reactor design method according to Claim 1 , characterized in that the following steps are applied: if the answer is no in the fortieth step (40), checking whether all coil currents are within the own current limits in the forty first step (41), if all coil currents are not within their own current limits, in the forty second step (42), detecting the coils (72) whose coil currents exceed the limit values, in the forty third step (43), checking whether the coil current is below the determined limit value or not, if the coil current is not below the determined limit value, in the forty fourth step (44), increasing the winding number of the coil (72), whose current value increases above the determined current value, with the help of a changing coefficient depending on the number of iterations, in the forty sixth step (46), checking whether the reactor current is within its own current limits or not, in case the reactor current is not within its own current limits, in the forty seventh step (47), checking whether the reactor current is below the lower current limits or not, if the reactor current is not below the lower current limit, in the forty eighth step (48), reducing the reactor upper limit with the help of a coefficient changing depending on the number of iterations, in the fiftieth step (50), calculating the height (cm) of the air core reactor (70) by using the winding number which has been recently calculated, in the fifty first step (51 ), calculating the self (mH) values of all coils (72) of the air core reactor (70) by using the coil heights, coil diameters, winding numbers which have been recently calculated, in the fifty second step (52), calculating the self (mH) values between the parallel connected coils (72) by using self (mH) values of the coils, the calculated coil heights, coil diameters and the winding numbers, in the fifty third step (53), calculating the dc resistance values (ohm) of all parallel connected coils (72), in the fifty fourth step (54), forming the impedance matrix (ohm) for the air core reactor (70) formed by the coils (72) connected in a parallel manner, in the fifty fifth step (55), calculating the current values (A) of all parallel connected coils (72) by using the impedance matrix data of the air core reactor (70) and the voltage applied to the air core reactor (70), in the fifty sixth step _, (56), calculating the reactor current (A) by adding all current values of the coils (72) connected in a parallel manner, in the fifty seventh step (57), reaching the reactor self (mH) value by using the reactor current, reactor voltage and frequency values, in the fifty eighth step' (58), increasing the iteration number by one, and returning to the fortieth step (40).

8. A reactor design method according to Claim 7, characterized in that in case all coil currents are within their own current limits in the forty first step (41), the forty sixth step (46) is applied where it is checked whether the reactor current is within its own current limits.

9. A reactor design method according to Claim 7, characterized in that if the coil current, which is outside of the limit values, is lower than the determined limit value in the forty third step (43), the number of coil (72) windings which are lower than the current limit determined in forty fifth step (45) is reduced by a coefficient which changes depending on the iteration number, and the forty sixth step (46) is applied.

10. A reactor design method according to Claim 7, characterized in that if the reactor current is within its own current limits during the check of the forty sixth step (46), directly the fiftieth step (50) is applied.

11. A reactor design method according to Claim 7, characterized in that if the reactor current is below the lower current limit in the forty seventh step (47), the reactor lower limit is increased with the help of a coefficient which changes depending on the iteration number in the forty ninth step (49), and the fiftieth step (50) is applied.

12. A reactor design method according to Claim 1 , characterized in that in the fifth step (5), if the reactor inner diameter is greater than the final inner diameter, the processes are stopped.

13. A reactor design method according to Claim 1 , characterized in that in the twenty fourth step (24), the first coil self-value (mH) of the air core reactor (70) is accepted to be 1.25 times the reactor self-value.

14. A reactor design method according to Claim 1 , characterized in that in the twenty sixth step (26), the other parallel coil (72) numbers of the air core reactor (70) is estimated to be 20 % less than the winding number of first coil (72) located above itself.

15. A reactor design method according to Claim 1 , characterized in that the impedance matrix (ohm) of the air core reactor (70) and the dc resistance (ohm) of the reactor coils are calculated for both 25 degrees and 75 degrees respectively in the thirty third step (33) and in the thirty fourth step (34).

16. A reactor design method according to Claim 1 , characterized in that in the fortieth step (40), if the reactor current is within the limit values, if each coil current is within the limit values, and if the iteration number is below the acceptable upper value, the fifty ninth step (59) is applied, and the following are calculated: the reactor current (A), reactor current angle,^' dc resistance (ohm) of the air core reactor (70) at 25 degrees and 75 degrees, reactor reactive power (kVA), reactor Q quality factor, dc loss power (kW) at 75 degrees, total wire length (m) of the air core reactor (70), reactor ac loss power, reactor weight (kg), reactor height, conductor weight of the reactor, the total weight of the reactor together with the peripheral units, and the self-value (mH) of the air core reactor (70).

17. A reactor design method according to Claim 1 , characterized in that in the sixtieth step (60), the inner diameter value is increased by 0.5-1.5 cm.

18. A reactor design method according to Claim 17, characterized in that in the sixtieth step (60), the inner diameter value is increased by 1 cm.