Method for the elimination of excitation field harmonics in turbogenerators

Abstract

The present invention relates to a rotor slot distribution with variable slot dimensions for eliminating harmonics in the excitation field of turbogenerators, and to an excitation winding arrangement with variable number of turns per slot, each of which is calculated by an optimisation method, and to design and manufacturing methods for obtaining this arrangement. With the invention, a method has been developed which enables a rotor with a variable number of turns per slot with slots of variable width and spacing to be obtained in turbogenerators. Thanks to the rotor obtained according to the invention, the excitation field can be eliminated from odd-numbered harmonics depending on the number of slots per rotor pole pair, the quality of energy supplied to the grid is improved, the efficiency of turbogenerators is increased and contributions to energy saving is achieved.

Description

[0001] METHOD FOR THE ELIMINATION OF EXCITATION FIELD HARMONICS IN TURBOGENERATORS

[0002] Technical Field

[0003] The present invention relates to the design and manufacturing methods of a rotor slot arrangement and winding structure for eliminating excitation field harmonics generated in turbogenerators.

[0004] Prior Art

[0005] Turbogenerators are widely used together with high speed gas turbines in electrical power generation. In turbogenerators, which are generally manufactured with 2 or 4 poles, the energy quality depends on the excitation field harmonics in the air gap. These harmonics depend on the rotor slot distribution and the number of turns in the slots. Even numbered harmonics are zero and therefore ineffective due to the symmetry created in the excitation field, but odd numbered harmonics other than the fundamental component have detrimental effects on energy quality.

[0006] Major disturbance effects are mainly caused by harmonics of lower order, except for the fundamental component. According to the solution developed to eliminate the 3rd harmonic and described in the document numbered US4363986A, there are slots symmetrically spread over 2 / 3 of the rotor surface and windings are positioned in these slots, while the remaining 1 / 3 of the rotor surface has no slots and windings. A rotor with 2 poles and 24 slots suitable for this application is shown in Figure 1 and the harmonic spectrum generated by the use of this rotor is shown in Figure 2. As can be seen, only 3rdharmonic and multiples can be eliminated with this structure.

[0007] Although low-order harmonics cause the most disturbing effects and therefore the elimination of the 3rd harmonic makes an important contribution, high-order harmonics may cause negative consequences especially for industrial consumers and may cause losses and additional disturbing effects in transmission and distribution lines. In order to eliminate them, complex and expensive harmonic filtering systems are required. In the document numbered US4700098A, DC motors with poles with variable parameters on the stator are described. The poles are arranged with two different angular spacing or poles with two different tooth angles are used.

[0008] In the document titled “Novel winding and core design for maximum reduction of harmonic magnetomotive force in AC motors” (Kocabas, D. A. (2009). IEEE Transactions on Magnetics, 45(2), 735-746.), the optimisation of different tooth sizes and number of turns per slot on the stator of an induction motor with a three-phase distributed single layer alternating current winding is described.

[0009] In the document numbered US2009015080A1, a synchronous motor comprising a permanent magnet rotor is explained which enables the cancellation of multiple harmonics. By arranging the windings on the stator, a certain selected harmonic can be cancelled. Stated windings are arranged according to the winding factor in the form e1<p.

[0010] In the document numbered CN112564333 A, a motor with a sinusoidal arrangement of the number of turns on the rotor is explained.

[0011] Objects and Brief Description of the Invention

[0012] The aim of this invention is to develop a computer-implemented method for obtaining a rotor core structure and excitation winding distribution that eliminates harmonics in the excitation field of turbogenerators in a manner different from other methods in the literature and that eliminates more harmonics. Another aim of the exhibited invention is to develop a method which enables the design of a rotor that provides the coil pitch of the excitation windings carrying direct current to be reduced and the winding lengths to be shortened. Thus, by reducing harmonic distortion in high-speed machines such as turbogenerators, it will be possible to improve the quality of the energy produced, increase the turbogenerator efficiency and reduce the dependence on harmonic filtering devices.

[0013] The invention presents, a method that has been developed to enable the design of a rotor with variable width and spacing of slots and variable number of turns in the excitation winding in the slots for turbogenerators. The rotor obtained according to the method developed with the invention provides, the excitation field to be eliminated from odd- numbered harmonics depending on the number of rotor slots. With the method of the invention, a computer-implemented method has been developed for designing a rotor having a cylindrical shape and circular cross-section positioned inside a stator, having a certain and even number of slots per pole on its surface, teeth located between the slots and realising the magnetic flux connection with the stator, windings with a certain total number of turns forming the excitation field located inside the slots and providing voltage induction in the stator. The method developed by the invention essentially comprises the steps expressing the rotor excitation field, which is expressed as a function of the angular position of the slot on the rotor and the magnetomotive force in the form of the product of the current and the turns on the respective winding for each slot angular position, as the sum of functions in the form of the sine and cosine of the slot angular positions and harmonic degrees using the discrete Fourier transform, compiling the equations showing the coefficients of the cosine terms corresponding to the harmonics targeted to be eliminated, whose harmonic degrees are odd numbers, in such a way that these coefficients are zero, determining the number of turns for the angular positions of the slot (3) and the winding (4) at each slot (3) angular position by solving the obtained system of equations for the total number of turns.

[0014] For the method to be applicable, the number of slots per pole in the rotor must be an even number. Accordingly, the invention is particularly capable of eliminating an odd number of harmonics as one less than the number of slots per pole. For example, in a rotor with 2 poles and 24 slots, the number of slots per pole is 12, and the developed method enables the elimination of 11 odd harmonics (3, 5, 7, 9, 11, 13, 15, 17, 19, 21 and 23). An exemplary embodiment of the invention is illustrated in the accompanying figures. The method can be applied to all turbogenerators under the specified conditions.

[0015] Detailed Description of the Invention

[0016] A rotor realized in order the achieve the objects of this invention is shown in the attached figures.

[0017] Figure-1 The schematic view of a rotor according to the prior art.

[0018] Figure-2 The graph showing the observed harmonics with the rotor according to the prior art. Figure-3 The schematic view of a rotor according to the invention.

[0019] Figure-4 The graph showing the observed harmonics with the rotor according to the invention.

[0020] The parts in the figures are numbered individually, and the corresponding descriptions are given below.

[0021] 1. Rotor

[0022] 2. Tooth

[0023] 3. Slot

[0024] 4. Winding

[0025] A cylindrical rotor (1) designed according to the method of the invention for use in a turbogenerator operating at high speeds, which is positioned so as to remain within the stator, essentially comprises slots (3) having an even number per pole in the rotor located on the surface with a circular cross-section (3),

[0026] - teeth (2) positioned between the slots (3) and forming the magnetic flux connection with the stator, direct current windings (4), located inside the slots (3) and forming the excitation field that induces voltage in the stator.

[0027] In the rotor (1), the angular positions of the slots (3) calculated for each slots (3) depending on the number of slots (3) and the number of turns of the winding (4) in each slot (3) and a winding (4) distribution depending on the angular position are calculated by optimisation. The width of the slot (3) is selected depending on the number of turns of the winding (4) in the slot (3) and the depths of the slots (3) are selected to be equal, and the slots (3) are positioned by spreading along the circular cross-section of the respective rotor (1) surface.

[0028] According to the invention, a number of harmonics related to the number of slots (3) on the rotor (1) can be eliminated from the excitation field formed by the excitation winding (4), which is a direct current winding. According to the invention, a rotor (1) contains an even number of slots (3) for each pole, and an odd number of harmonics one less than the number of slots (3) per pole are eliminated. In the example embodiment of the invention shown in Figure 3, with a rotor (1) containing 24 slots (3) for 2 poles, 11 harmonics (harmonics 3, 5, 7, 9, 11, 13, 15, 17, 19, 21 and 23) are eliminated since there are 12 slots per pole.

[0029] In an exemplary embodiment of the invention, a fast Fourier transform is applied to monitor the harmonics contained in the excitation field distribution. Thus, the harmonic coefficients ak and bk are calculated. The equations of these coefficients are given below. Here, F is the value of the magnetomotive force in ampere turns at the angular position of the zth slot (3), a is the angular position of the zth slot (3) and k is the Ath harmonic.

[0030] Due to the quarter-wave symmetry in the excitation field distribution, the ak coefficients and even-order bk coefficients are equal to zero. Therefore, only odd order bk coefficients (Z>z, Z>J, Z>5, ...) are present in the harmonic spectrum. Here bi is the fundamental component and the others are harmonics. The object of the invention is to eliminate the excitation field from these harmonics, starting with the harmonics of the smallest order that cause the greatest distortion.

[0031] For this purpose, the equations of the harmonics to be eliminated are written using equation 2. As can be seen in the equation, the angular positions of the slot (3) and the ampere turn values in the slots (3) are the variables of the equation. Since there is a quarter wave symmetry in the excitation field distribution, the harmonic equation can be written as half of the number of slots (3) per pole and the (3) ampere turn values in these slots. However, in order to make the results applicable and adaptable, the solution is found by keeping the total number of turns constant. In order to design rotors (1) with different total number of turns, the method of the invention is applied to different values of the total number of turns. Therefore, since the ampere turn value in the last slot (3) is equal to the total ampere turn value, this value ceases to be a variable. Since the number of slots (3) per pole is q, there are q-1 variables in the quarter wave as there are half the number of slots (3) (< / / 2) position and one minus half the number of slots (3) (t / / 2- l ) ampere turn value. For this reason, a number of equations one less than the number of slots (3) per pole (< / -l) can be obtained and this number of harmonics can be eliminated.

[0032] After obtaining the number of equations determined according to the number of slots (3) as explained above, the resulting system of equations is solved by Newton-Raphson or a similar iterative method or a nature-inspired solution method such as a genetic algorithm to determine the angular positions of the slots (3) and the number of turns in the slots (3).

[0033] According to the prior art, if the rotor (1) slots (3) are evenly spaced to spread 120° at each pole, the smallest winding (4) pitch is 60°. In this case, only harmonics with degree 3 and multiples of 3 are eliminated. However, the rotor (1) designed according to the inventive method, since it allows the excitation windings (4) to have winding (4) steps smaller than 60° and to eliminate odd-numbered harmonics by one less than the number of slots (3) per pole, it reduces the use of winding (4) copper by shortening the winding step while eliminating more harmonics, and since the wound length of the winding (4) is shortened, the winding (4) resistance and therefore the related excitation winding (4) copper loss is reduced, and the turbogenerator efficiency is increased. The invention also limits the penetration of harmonics into the stator by the application to the rotor (1) by eliminating the harmonics in the excitation field more effectively and more than the precedent methods, and contributes to the turbogenerator efficiency by reducing the stator iron losses. In addition, the stator power factor increases and the stator current decreases, and indirectly the stator copper losses are reduced.

[0034] Thanks to the invention, high-speed turbogenerators driven by gas and steam turbines with lower total harmonic distortion, higher energy quality and higher efficiency can be produced compared to those with rotors produced according to the prior art. Rotors (1) with different numbers of poles and slots (3) can be designed within the scope of the invention.

Claims

CLAIMS1. A computer-implemented method for designing a rotor (1) having a cylindrical shape and circular cross-section positioned inside a stator, having a certain and even number of slots (3) per pole on its surface, teeth (2) located between the slots (3) and realising the magnetic flux connection with the stator, windings (2) with a certain total number of turns forming the excitation field located inside the slots (3) and providing voltage induction in the stator, characterized by comprising the steps expressing the rotor (1) excitation field, which is expressed as a function of the angular position of the slot (3) on the rotor (1) and the magnetomotive force in the form of the product of the current and the turns on the respective winding (4) for each slot (3) angular position, as the sum of functions in the form of the sine and cosine of the slot (3) angular positions and harmonic degrees using the discrete Fourier transform, compiling the equations showing the coefficients of the cosine terms corresponding to the harmonics targeted to be eliminated, whose harmonic degrees are odd numbers, in such a way that these coefficients are zero, determining the number of turns for the angular positions of the slot (3) and the winding (4) at each slot (3) angular position by solving the obtained system of equations for the total number of turns.

2. A method according to claim 1, characterised by the harmonics targeted to be eliminated being the lowest order harmonics up to one less than the number of slots (3) per pole.

3. A method according to claim 1, characterised by the widths of the slots (3) being determined to depend on the number of turns of the winding (4) in the respective slot (3) and the depths of the slots (3) being equal to each other.

4. A method according to claim 1, characterised by determining the winding (4) steps to be smaller than 60°.

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