The active power filter is generally designed as a voltage source type PWM inverter. By controlling the full-control switching device (such as IGBT) of each bridge arm, the output of the filter can track the detected harmonic current well, and realize the grid. Filtering. The main circuit structure is as shown in the figure. The operation of the active filter is actually realized by LC charging and discharging, so the selection of the LC parameters has an important influence on the performance of the filter. The determination of LC parameters, often through experience, undoubtedly makes the results blind. There is also a computer-aided calculation method, but it is necessary to simulate the working process of the filter, so it is more complicated. This paper adopts reasonable assumptions and establishes an analytical method for parameter determination. This method is simple and practical.
2 Mathematical model of active filter In the active filter, each half-bridge arm is composed of a fully-controlled switching device and a diode connected in anti-parallel. It is obvious that the forward conduction is controllable, and the reverse conduction is not possible. Controlled, an ideal switch can be used instead of the switch tube and diode of each half-bridge arm to obtain an equivalent circuit as shown, from which a mathematical model of the active filter can be established.
Conducted, thus obtaining 8 working modes: S, S2S., S2S3S4, S3S4S5, S4S5S6, S5S6S丨, S6S丨S2, S丨S3S5, S4S6S2. The last two working modes, the three-phase output current of the filter are 0, through the analysis of the harmonic source, it is found that the three-phase harmonic does not exist at the same time of zero crossing, so only the first six working modes are analyzed, and the active filter is actually determined by the on-off combination of six sets of switching devices.
The differential equations describing the operation of the filter are as follows: L-hair angle a, commutation overlap angle y, DC current measurement to assume DC-side inductance infinity, ignoring current pulsation), phase A current of phase A, as in 2): The rate of change is large, and the rate of change is small during the conduction of the thyristor.
For the selection of the incoming inductance, the filter must be able to track the compensation current, so i should not be too large, but when i is small, the output current of the filter will be over-adjusted relative to the compensation current, especially The di//d* is small during the thyristor conduction, so the filter output current has a large glitch. In summary, the choice of L should be based on the current tracking capability during commutation and the current overshoot during thyristor conduction.
In order to meet the current tracking capability, the output current rate of change of the filter should be greater than the maximum rate of change of i/ during the commutation period, ie: from equation (1): in order to simplify the calculation, the dia is not directly determined by equation (9). /df, from which the average of d/dr is obtained. If the working time of the active filter is long enough, the average effect of a+77/6) in equation (9) will be zero. At the same time, the probability of taking 2/3 is 1/3, and the probability of taking 1/3 is 2/3, the average value of I is 4/9, then: the working of the active filter is the charging and discharging process of the capacitor. In order to ensure the performance of the filter, the voltage on the DC side must be kept substantially unchanged. The choice of capacitance affects the fluctuation of the DC side voltage. The larger the capacitance, the smaller the voltage fluctuation, but the increase in investment. Therefore, the choice of capacitance is an important part of the filter design.
The voltage fluctuation of the capacitor is consistent with the fluctuation of the charge stored on the plate, and the capacitance can be determined by the fluctuation of the charge. The charge fluctuation condition can be expressed by the charge and discharge current of the capacitor. The amount of charge that a capacitor charges or discharges during a week should be the minimum amount of charge that the capacitor must hold.
It is assumed that the maximum charge amount of the charge and discharge process of the capacitor is 0, and the voltage fluctuation is required to be less than (Aw/u)%, and the maximum charge change amount of the charge stored on the electrode plate can be obtained by integrating the charge and discharge current with time. The current flowing through the capacitor is determined by the output current of the filter by the equation (12) (16) to determine the capacitance.
It should be pointed out that when a is small, the compensation current waveform is different. At this time, the number of zero-crossing points of the compensation current increases in the half cycle, and the charging and discharging frequency of the capacitor increases, and the corresponding maximum electric charge is different from the formula (14). It will be reduced, but the design can still refer to equation (14), except that the DC side voltage fluctuation amplitude is reduced at this time. At the same time, the output current of the filter is sawtooth oscillation around a given compensation current, and its integral effect is very close to the integration effect for a given compensation current, so this assumption is true.
The simulation result must ensure that the compensation current overshoot should not be too large for the selection of an active L for a six-pulse thyristor phase-controlled converter.
The overshoot during the commutation corresponds to the minimum value, set to 5, derived: in the thyristor conduction section: combined, it can be known that 丨d/chl is the 2/3 segment of the cosine curve, the minimum value may be zero, or 丨d" /dtl,=r, or 丨diydfUT. When Idi, /chi takes the minimum value, the maximum overshoot occurs. Take the extreme overshoot, take the maximum allowable overshoot current /, and the switching frequency of the active filter is / It is available: the value of B that satisfies both the current tracking capability and the overshoot limit: the determination of the capacitance, it is known from 4+ that at any time, one phase current is opposite to the other two phase currents, and this The one-phase current happens to be the charging and discharging current of the capacitor.
In order to simplify the calculation, the following assumption is made: the commutation process is ignored, and the DC side current is considered to be pulsating.
The output of the filter completely tracks the given current and uses the given current as the output of the filter.
According to the assumption, a three-phase given compensation current is obtained, as simulated by the filter (EMTP). The middle dashed line is the current of the converter before the compensation, U=140A, a=30., 7=6.4.). Let Au/ u=5%, /,. =250V, the maximum overshoot is controlled at 10%, and the switching frequency of the active filter is 5kHz. According to the calculation of this method, the solid line in i=66.0|jlF. is the compensated current of the grid. The current spectrum of the grid side after compensation is given. It can be seen that the higher harmonics are greatly weakened. At the same time, the power factor is improved and the active filter is better compensated, thus verifying the method of this paper.
5 Conclusions In this paper, a six-pulse thyristor phase-controlled converter is used as the compensation object. The analytical method of the input inductance and DC-side capacitance parameters of the active filter is studied. The inductance is determined by the trade-off between the tracking performance of the compensation current and the overshoot of the output current of the filter; the capacitance is determined by satisfying a certain voltage change rate and the minimum stored charge of the DC-side capacitor, in order to obtain an analytical expression The text uses some reasonable simplifications. The simulation results verify the correctness of the method.
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