Resistive load of single-phase half-wave controllable rectifier circuit

Resistive load of single-phase half-wave controllable rectifier circuit

(1) Working principle and waveform

The circuit diagram and waveform diagram of the single-phase half-wave controlled rectifier circuit (Single Phase Half Wave Controlled Rectifier) with resistive load are shown in Figure 1.

Resistive load of single-phase half-wave controllable rectifier circuit
Figure 1 – Circuit diagram and waveform diagram of a single-phase half-wave controlled rectifier circuit with resistive load

Figure 1a is a circuit diagram of a single-phase half-wave controlled rectifier circuit with a resistive load. The waveform diagram of the AC voltage u2 on the secondary side of the transformer, the trigger pulse ug, the rectified output voltage (that is, the load voltage) ud and the voltage uVT across the thyristor is shown in Figure 1b. When measuring the waveform with an oscilloscope, pay attention to: ① The line segment that jumps up or down vertically in the waveform cannot be displayed; ②To measure the waveform with DC component, it must be input from the DC measurement terminal (DC) of the oscilloscope and the position of the reference horizontal line must be determined in advance. Since it is a resistive load, the waveform of the load DC current id is the same as the phase of the waveform of the rectified output voltage ud, and because the thyristor is connected in series with the load, the current iVT flowing through the thyristor is the load DC current id.

It can be seen from Figure 1 that during the period of 0~ωt1, although the AC voltage u2 is in the positive half cycle, the thyristor is subjected to the forward voltage, but because the gate does not trigger the pulse ug, the thyristor is in the forward blocking state, and the load voltage ud=0. At the moment of ωt1, a trigger pulse is applied to the gate, the thyristor is triggered and turned on, and the voltage of u2 is output to the load Rd. If the forward voltage drop of the thyristor is omitted, the rectified output voltage (load voltage) ud=u2.

When ωt=π, the AC voltage u2 drops to zero, the anode current of the thyristor is less than the holding current, and the thyristor is turned off. In the negative half cycle of the AC voltage u2, the thyristor continues to maintain the reverse blocking state due to the reverse voltage, and the voltage and current on the load are always zero. Until ωt2 of the next cycle, the gate is added with a trigger pulse, and the thyristor is turned on again. In this way, the voltage waveform shown in Figure 1b is obtained on the load Rd.

In the single-phase half-wave controllable rectifier circuit, it is obvious that the conduction angle Θ=π-α, the smaller the trigger delay angle α, the larger the conduction angle and the larger the average value Ud(that is, the average value of the shaded part of the ud waveform in one cycle) of the rectified output voltage. It can be seen that as long as the size of the trigger delay angle α is changed, the size of the average value Ud of the rectified output voltage can be changed.

The voltage waveform uVT across the thyristor is shown in Figure 1b. When the thyristor is in a conducting state, if the voltage across the thyristor is ignored, the voltage across the thyristor is zero. When the thyristor is in the forward and reverse blocking states, the voltage across the thyristor is equal to the AC voltage u2.

(2) Calculation of the average value Ud of the rectified output voltage

Ud is the average value of the area of the ud waveform in one cycle, which is measured by the DC voltmeter. Ud can be obtained by integrating the following formula

Resistive load of single-phase half-wave controllable rectifier circuit
(1-1)

When α=0°, the average value of the rectified output voltage Ud is the largest, that is, U=0.45U2, which is the same as the average value of the rectified output voltage of the diode half-wave rectifier circuit. With the increase of α, the average value of rectified output voltage Ud decreases gradually, when α=180°, the output voltage Ud=0. Therefore, with resistive load, the phase shift range of single-phase half-wave controlled rectifier circuit is 0°~180°.

At the load, the average value of the DC output current is

Resistive load of single-phase half-wave controllable rectifier circuit
(1-2)

(3) Calculation of thyristor current and voltage

Because the thyristor is in series with the load, the current flowing through the thyristor is obviously the load current.

The average value of thyristor current IdVT=Id. Thyristor current effective value IVT=KfIdVT=KfId. Among them, Kf is the current form factor. When the single-phase half-wave controllable rectifier circuit has a resistive load, the DC load current waveform is the waveform of the rectified output voltage (load voltage), which is a sine half-wave waveform with missing corners. The current form factor is related to the current waveform and the trigger delay angle α. The calculation is relatively complicated. Generally, it can be obtained by checking the curve or table. The form factor of the single-phase half-wave controllable rectifier circuit is shown in Table 1.

Resistive load of single-phase half-wave controllable rectifier circuit
Table 1 – Form factor of single-phase half-wave controllable rectifier circuit

It can be known from Table 1 that when α=0°, the current waveform coefficient Kf=157.

It can be seen from the uVT waveform diagram in Figure 1b that the maximum forward and reverse voltage UTM that may appear at both ends of the thyristor is the peak voltage of the AC power supply voltage u2, namely: UTM=√2U2.