Research on high voltage resonant transformer

    Abstract: This article discusses the principle, design method and several issues that should be paid attention to in the development of resonant transformers, and proves the accuracy and practicability of the calculation formula in this article by comparing the calculated values ​​with the measured values.

    Keywords: Resonant transformer, inductor, capacitor, quality factor

1 Introduction

    With the development of power electronics technology, it has become possible to use high-voltage resonance technology to conduct power-frequency withstand voltage tests on large-capacity electrical equipment. It has been widely used in AC tests of power equipment with large capacitance such as cables, capacitors, and generators. The principle is to obtain a continuously changing inductance L by adjusting the air gap length of the core magnetic circuit, so that it resonates with the capacitance C of the test object to ground. This article uses a 150kVA test device as a model to explain the principle of high-voltage resonant transformer and the calculation of relevant parameters.

2 Principle of resonant transformer

    2.1 Structural characteristics

    The core of the resonant transformer can be made into two different structures: shell type and core type. The core-type core transformer is not as good as the shell-type core transformer in a series of main indicators. Its weight and outer size are larger, and the transmission mechanism for adjusting the air gap is more complicated. For this reason, the test device we developed adopts a shell structure, as shown in Figure 1. The resonant transformer windings are housed outside the movable center column.

2.2 Characteristic curve

    The characteristic curve of the resonant transformer is shown in Figure 2. It can be seen from Figure 2 that under different air gap lengths δ, the volt-ampere characteristics of the resonant transformer have a good linear relationship, and its inductance L has nothing to do with the voltage value on the transformer. Therefore, when this kind of resonant transformer is used for AC resonance tests, it can be tuned under low voltage conditions first (changing the air gap length between the moving iron core and the lower yoke core through the transmission mechanism). When it is tuned to resonance, the test can be raised to voltage, system tuning is very convenient.

2.3 Relationship between loop inductance L and core air gap length δ

    The air-gap adjustable resonant transformer, whether it is a series type or a parallel type, changes the loop inductance L by adjusting the length of the air gap in the iron core to cause the resonant transformer to resonate. This is the mechanism of resonating the resonant transformer by changing the length of the core air gap for the device under test with a certain capacitance to ground. However, it should be noted that the air gap length cannot be too large, otherwise the established resonance conditions will be destroyed.

2.4 Tuning Principle

(1) The equivalent circuit of the series tuned

    series resonant transformer is shown in Figure 3. When the power frequency voltage of US=220V, f=50Hz is applied to the resonant transformer, through manual or automatic adjustment, when ωL=1/ωC, that is, XL=X C , the loop will undergo series resonance, where the maximum loop current IS

    = Us /(RL+RC)

    Because RC>>RL, then there is

    Is≈US/Rc (1)

    The voltage UC on the tested product and the voltage UL on the tuning reactor are respectively:

    Uc=(1/ωc)Is=XcIs UL=ωLIs=XLIs

    When tuned to resonance, Uc=UL=ω0LIs=(ω0L/Rc)Us (2)

    The ratio in formula (2) ω0L/Rc=(square root L/C to the power 2)/Rc=Q (3)

    ω0 is the resonant angular frequency Q, which is called the quality factor of the series resonant circuit. Because (square root L/C raised to the power 2)>>RC, Q>>1. Thus, the power capacity

    Ps=UsIs=(Uc/Q)Is=Pc/Q (4)

    It can be seen from equation (4) that when the resonant transformer is tuned to resonance, the power supply voltage and capacity are both 1/Q of the corresponding voltage and capacity of the test product. Therefore, compared with general test transformers, resonant transformers have the advantages of light weight and small size.

    (2) Parallel tuning

    The equivalent circuit of the parallel resonant transformer is shown in Figure 4.

    When RL≤ωL and Rc≤1/ωc, the resonant frequency fo of parallel resonance is:

    The quality factor Q of the parallel circuit is:

    Q=(ω0L)/(RL+Rc)=1(RL+Rc)ω0C (6)

    In the formula, RL, RC——equivalent series resistance of inductor and capacitor (Ω)

    L——Tuning reactor inductance (H)

    C——Capacitance of test sample to ground (F)

    When a 50Hz AC voltage is applied to a parallel resonant transformer, forced oscillation will occur in the loop as the voltage increases. When the oscillation frequency of the loop is equal to the frequency of the external power supply, the impedance of the loop is maximum (and purely resistive), so the loop current is minimum, but the currents IL and IC on L and C are both Q times the loop current I, that is, IL =IC=QI.

3 Calculation of main parameters of resonant transformer

3.1 Calculation of inductance L

    (1) Calculation of leakage inductance LS

    Ls=[(4πN 2 Ss×10 -9)/Ls](H) (7)

    Where SS——equivalent cross-sectional area of ​​leakage flux (cm2)

    lS——Equivalent length of magnetic flux leakage (cm)

    N——number of winding turns

    (2) Calculation of main inductance LO

    L0=[(4πN 2 Ss×10 -9)/δ](H) (8)

    where δ——air gap length (cm)

    Sδ——equivalent cross-sectional area of ​​the gap magnetic circuit (cm2)

    (3) Calculation of total inductance L

    =Ls+L0=[[(4πN 2 Ss×10 -9)/Ls](H) Ss×10 -9)/Ls]+[(4πN 2 Ss×10 -9 )/δ]

    =[(4πN 2(Ss/Ls+Sδ/δ)×10 -9 (H) (9)

    3.2 Calculation of core size

    (1) The diameter of the outer circle of the stepped core

    D=K (square root of the fourth power) (cm) (10)

    In the formula, S - core single column capacity (kVA)

    K——Proportional coefficient, 4.5~5.5 (take the smaller value when using cold-rolled silicon steel sheets)

    (2) Core effective cross-sectional area SG

    SG=(πD2/4)KyKd (11)

    In the formula, Ky=0.9——core series utilization coefficient

    Kd=0.93——core lamination coefficient

3.3 Calculation of winding turns (12)

    In the formula, N1——the number of turns of primary coil

    U1——primary coil voltage (power supply voltage), which can be 220V or 380V

    f——power frequency, 50Hz

    B——Core magnetic flux density, (1.5～1.8)×104Gs

    The method for calculating the number of turns N2 of the secondary coil is the same as above. Just replace U1 in the formula with the voltage of the secondary coil.

3.4 Calculation of the minimum air gap δmin and the maximum air gap δmax

    (1) Calculation of δmin

    In the formula, KL——Inductance adjustment coefficient, 6.5~7.0

    (2) Calculation of δmax

    δmax≈KδKLKδmin (14)

    In the formula, K δ=2.2 ~ 2.5

    The calculation of other parameters of the resonant transformer is similar to that of the ordinary reactor.

4 Design of 150kVA resonant test transformer

    Use the above calculation formula to design a resonant transformer with power supply voltage U1 = 0.22kV, output voltage U2 = 15kV, output power P2 = 150kVA, and which can conduct power frequency and high voltage tests on a sample with a maximum calculated capacitance of 2 μF . The moving iron core of the transformer and the primary and secondary windings enclosed outside are shown in Figure 5. The calculation results of the main parameters are as follows:

    D=12cm, the diameter of the external circle of the moving iron core

    D1=13.5cm, inner diameter of primary winding

    D2=18cm, inner diameter of secondary winding

    D3=25.5cm, secondary winding outer diameter

    H=37cm, winding height

    N1=66 turns, the number of primary winding turns

    N2=4464 turns, the number of secondary winding turns

    The calculated and measured values ​​of the tuning inductance parameters of the resonant transformer are shown in Table 1.

Table 1 Calculated and measured values ​​of tuning inductor parameters

5 Conclusion

    (1) It can be seen from Table 1 that the maximum error between the calculated value and the measured value does not exceed 6%, indicating that the above calculation formula has high accuracy and is sufficient to meet the requirements of engineering calculations.

    (2) When the test is close to the calculated maximum capacitance of the test sample, the voltage on the test sample may exceed the value determined by the transformation ratio. In order to reduce the effect of voltage resonance, the leakage reactance of the secondary coil of the transformer should be made as small as possible. , and at the same time, an overvoltage prevention device should be installed in the output circuit.

    (3) Since the voltage has nothing to do with the air gap δ , tuning should be performed at a lower voltage first. When resonance occurs, the output voltage should be increased to the test value of the test product.

    (4) During the air gap adjustment process, the core and mechanical transmission mechanism of the transformer are subject to a large electromagnetic force, causing strong vibration and noise, and in severe cases, the components of the resonant transformer may be damaged. Therefore, the mechanical structure of this device should be specially designed.