Single-phase half-bridge VSC

Let us consider first the simplest and basic solid-state DC-AC converter, namely the single-phase half-bridge VSC. Figure 6.23 shows the power circuit. It consists of two switching devices (S₁ and S₂) with two antiparallel diodes (D₁ and D₁) to accommodate the return of the current to the DC bus when required. This happens when the load power factor is other than unity. In order to generate a mid-point (0) to connect the return path of the load, two equal value capacitors (C₁ and C₂) are connected in series across the DC input. The result is that the voltage V_dc is split into two equal sources across each capacitor with voltage of V_dc/2. The assumption here is that the value of the capacitors is sufficiently large to ensure a stiff DC voltage source. This simply means that their voltage potential remains unchanged during the operation of the circuit. This also means that the potential of the mid-point (0) is constant with respect to both positive and negative DC bus rails at all times (V_dc/2) and - V_dc/2 respectively).

Fig. 6.22 Single-phase half-bridge VSC.

Let us now examine the operation of this circuit. It can be explained in combination with Figure 6.24. The two control signals for turning on and off the switches S₁ and S₂ are complementary to avoid destruction of the bridge. This would happen due to the throughput of high current coming from the low impedance DC voltage sources, if both switches were turned on simultaneously. When the switch S₁ is turned on (t₃ < t < t₅), the output voltage v₀ = v_AO is equal to the voltage V_dc/2 of the capacitor C₁. The mode of operation of the switching block (S₁ and D₁) is then controlled by the polarity of the output current i₀. If the output current is positive, with respect to the direction shown in Figure 6.23, then the current is flowing through switch S₁ (t₄ < t < t₅, Figure 6.24). If the output current is negative, the diode D₁ is conducting, although switch S₁ is turned on (t₃ < t < t₄). Similarly, if the switch S₂ is turned on (t₁ < t < t₃), the output voltage is equal to the voltage V_dc/2 of the capacitor C₂ with the polarity appearing negative this time. The output current i₀ once again determines the conduction state of the switch and diode. If the output current is positive, the diode D₂ is conducting (t₁ < t < t₂). If the output current is negative, the current flows through switch S₂ (t₂ < t < t₃). Such states of switches and diodes are clearly marked in the waveforms of Figure 6.24 for the various time intervals. The modes of operation of the half-bridge single-phase VSC are also summarized in Table 6.3.

Figure 6.24(a) shows the output voltage waveform v₀ = v_A0 generated by the converter operation as previously explained. Due to the square-wave generated by the converter, the output voltage waveform is rich in harmonics. Specifically, as shown in Figure 6.24(c) all odd harmonics are present in the spectrum of the output voltage. The fact that the converter cannot control the rms value of the output voltage waveform at fundamental frequency is also a limitation. A separate arrangement must be made to vary the DC bus voltage V_dc in order to vary and control the output voltage v₀.

Fig. 6.24 Key waveforms of the single-phase half-bridge VSC circuit operation. (a) output voltage V₀ = V_A0; (b) output current i₀; and (c) harmonic spectrum of the output voltage V₀ = V_A0.

The amplitude of the fundamental component of the output voltage square-wave v₀ shown in Figure 6.24(a) can be expressed using Fourier series as follows

                 (6.18)

The amplitude of all the other harmonics is given by

           (6.19)

where h is the order of the harmonic.

Fig. 6.25 quadrants of operation of the single-phase half-bridge VSC.

The converter discussed here operates in all four quadrants of output voltage and current as shown in Figure 6.25. There are two distinct modes of operation associated with the transfer of power from the DC to the AC side. When the power flows from the DC bus to the AC side, the converter operates as an inverter. The switches S₁ and S₂ perform this function. In the case that the power is negative, which means power is returned back to the DC bus from the AC side, the converter operates as a rectifier. The diodes D₁ and D₁ perform this function.

The capability of the converter to operate in all four quadrants (Figure 6.25)

means that there is no restriction in the phase relationship between the AC output voltage and the AC output current. The converter can therefore be used to exchange leading or lagging reactive power. If the load is purely resistive and no filter is attached to the output the diodes do not take part in the operation of the converter and only real power is transferred from the DC side to the AC one. Under any other power factor, the converter operates in a sequence of modes between a rectifier and an inverter. The magnitude and angle of the AC output voltage with respect to the AC output current control in an independent manner the real and reactive power exchange between the DC and AC sides.

This converter is also the basic building block of any other switch-mode VSC.

Specifically, the combination of the switching blocks (S₁ and the antiparallel diode D₁) and (S₂ and D₂) can be used as a leg to build three-phase and other types of converters with parallel connected legs and other topologies. These types of converters will be described later.

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