Integrated magnetic transformer leakage reactance Metro three-dimensional finite element method

Abstract: The Metro inverter traction system to balance the existence of the reactor to reduce high-power inverter size, lower cost disadvantage. To this end, the use of magnetic integration technology will balance the reactor and transformer combination to construct a new 12-pulse inverter two heavy traction power supply system, to achieve the use of integrated magnetic pieces to replace the balance of the equivalent inductance inductance design. Edge unit based on the steady-state non-linear finite element method, the establishment of Metro three-dimensional finite element model of the transformer, the equivalent of each winding inductance between the analyzed and calculated. Simulation results and prototype field test data are very close to verify that the proposed finite element method is correct and feasible.
        Keywords:: inverter traction system; magnetic integration; inductance; balance reactor; steady-state non-linear; finite element method; Metro
        Shenzhen Metro Line Inverter system uses the multi-inverter circuits, the combination of several rectangular wave, so that the output waveform as close as possible sine-shaped waves. Multi-inverter by a number of basic three-phase inverter bridge formed in parallel, while the inverter bridge there is a balance between the need to take the reactor in order to balance the inverter bridge output voltage and improve the utilization of the bridge inverter to reduce the inverse Variable bridge capacity. Pairs of high-power inverter, the balance of the existence of the reactor to reduce inverter size, lower cost disadvantage. To this end, the paper introduces the integrated magnetic technology, will balance the reactor and transformer integrated in one [1,2], based on steady-state non-linear finite element method, the traction transformer leakage reactance of all-white three-dimensional finite element analysis and calculation, and with on-site after each phase to be short-circuit test of transformer equivalent leakage reactance values were analyzed.
A System Analysis
1.1 Circuit Structure
            High-pressure, high-power multi-voltage source inverter using gate turn-off thyristor for power components, the output voltage is mostly square. Square-wave voltage and current contain more low-order harmonics, seriously affecting the output characteristics, such as for AC motor power supply, make additional loss increases motor efficiency, lower operating power factor deterioration, resulting in harmonic torque, caused by noise and vibration, etc. [3].
            In this paper, the two heavy three-phase voltage source inverter circuit shown in Figure 1.

        Diagram for the DC voltage Ud; Ⅰ and Ⅱ , respectively, from top to bottom two inverter bridge; T for the integration of magnetic pieces; LP for the two inverter bridge the balance between the inductance; LS magnetic pieces for the integrated equivalent inductance, vice party; A , B, C and A1, B1, C1 respectively, two high-voltage transformer winding; a, b, c for the Vice-side transformer winding; N the number of units.
            Choose this circuit configuration is two square wave inverter output will be staggered in the phase angle on the overlay, so get as close as possible sine wave-shaped waveform.
1.2 Structure of magnetic parts
            Magnetic Parts ArkadiyKats the proposed model using E-type core portfolio of methods, as shown in Figure 2 [4]. Through the integration of transformers and inductors to achieve the control of leakage inductance. Transformer winding connection way Ddyny5, transformer primary side winding axial pairs of split forms, and triangles are connected, each run independently, that is, when a high-pressure side of a temporary failure when the other party can continue to work to run. Secondary side winding connected to the star. Figure 2 in the core Ac, Bc was used in combination, the transformer primary winding in the Ac and Bc2 Vice-core, the secondary winding only in the core Ac, so that the transformer leakage inductance concentrated in one side, by adjusting the core Bc The gap can be precisely controlled the size of the leakage inductance, transformer primary side to act as simultaneous multi-inverter system, a balance between the inverter bridge inductive role of LP in order to eliminate inter-individual inverter bridge voltage clamp, so that each inverter bridge at the same time work to reduce the average current through the thyristors to increase their utilization, reduce the phase current of the power components for the impact of the damage, and play a role in the waveform synthesis, thereby reducing the size of inverter and reduce cost; transformer, Deputy Fang equivalent inductance LS constitutes a low-pass filter with sinusoidal resonant circuit in order to improve the output voltage waveform, increase the output dynamic performance.

2 transformer leakage reactance of the three-dimensional finite element method
2.1 Steady-state non-linear method
            Finite element method in steady-state non-linear method [5] can well solve the transformer leakage magnetic field. Its main features are: ① could be more truly reflect the core material of non-linear change in magnetization curves using the function iterative solution, which can be more accurately reflect core test cases in the distribution of magnetic flux density; ② be able to leakage magnetic field energy calculated by the various windings transformer equivalent inductance between the calculated and experimental values obtained are very close to the equivalent inductance value; ③ calculation time is short, iterative convergence of high accuracy, facilitate a number of simulation tasks.
            Therefore, this steady-state non-linear finite element analysis, magnetic flux leakage power transformer in the finite element expression for

            Where: ω e a unit corresponding to the sub-region; μ is the material permeability, non-linear magnetization curve can be expressed; B for the magnetic flux density; A for the magnetic vector potential.
2.2 Finite Element Modeling
            Metro Multi-inverter traction transformer FEA model shown in Figure 3, due to symmetrical three-phase transformer, so you can build single-phase model (the graph includes only single-phase core and coil), cut into 8-node six-sided unit, the corresponding FEM mesh of unit number 67994, side number 121,926, effective edge number 98942.

2.3 Result Analysis
            Through each phase short-circuit test finite element simulation, using the energy method can be easily obtained with high-pressure high-voltage transformer, two high pressure and low pressure as well as a single high pressure and low pressure equivalent inductance between the specific values shown in Table 1. The short-circuit cases, core of the magnetic flux density distribution as shown in Figure 4, the main core of the magnetic flux density of Ac tends to zero; core Bc the highest magnetic flux density in the central pillar of its EE-type core, its size is about for the 0.5 ~ 0.7T, in a non-saturated. Reposted elsewhere in the paper for free download
        The numerical simulation and field tests carried out in transformer short-circuit between the measured equivalent inductance of each phase is very close to the specific values shown in Table 2, in which high-pressure equivalent to the low inductance value between the test allowable error is 30% ~ 0%, showed that steady-state non-linear three-dimensional finite element method can quickly and accurately calculate the equivalent inductance between the windings and thus the type of magnetic parameters of the transformer design of an integrated metro to provide technical support.

3 multi-inverter system, the design of a balanced inductor LP
        Balance the voltage across inductor LP exchanges UP contain only ingredients, but is mainly six sub-harmonics [6], in its amplitude for ω t = π / 2 Shi, UP The maximum value for

            Where: UA is a group of high-voltage transformer winding three-phase AC voltage.
            Because the greatest circulation of Id / 2, and the circulation is actually a balance of excitation inductor current. Therefore, the balance of the inductor reactance value of XP can be downloaded from the specified minimum load current Idmin estimates derived (only consider the six harmonics), which

        With Integrated Magnetics traction transformer primary side inductance can be completely replaced by the equivalent balance of inductance, the elimination of all clamping voltage between the inverter bridge, so that the inverter bridge simultaneously. Thereby reducing the volume of high-power inverter and cost [7].
4 Conclusion
            (1) the kinds of MTR traction transformer winding through the use of high-pressure axial pairs of magnetic separation, and integration technology to achieve a single 12 pulse transformer used in the double PWM inverter circuit.
            (2) The simulation calculated the two high-voltage transformer winding inductance value between 5.56mH and on-site 5.166mH basically consistent with experimental values, the equivalent inductance value is much greater than the balance of the required systems theory inductor design values 2.11mH, thereby significantly reducing the the inverter size and cost.
            (3) The integrated technology enables magnetic phase current inverter circuit for reduced to zero current, can reduce the transformer noise and vibration, and can improve the output dynamic performance, and has broad application prospects.
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