CHAPTER 5

DC to Single-Phase AC Conversion

DC to single-phase AC conversion has been widely used for battery-powered power supplies. The device to perform DC/AC conversion is often called an inverter. The examples include the uninterrupted power supplies (UPS) for critical loads and inverters powered by car batteries. Such systems generally work on low power capacity to supply single-phase AC directly to loads. Figure 5.1 illustrates two types of UPS: offline and online.

FIGURE 5.1 Block diagram of uninterrupted power supplies: (a) standby; (b) online.

In the offline system or so-called standby UPS, the single-pole-double-throw (SPDT) relay connects the critical load with the grid supply, as shown in Fig. 5.1a. The battery bank remains charged through a charger, which performs AC/DC conversion when the grid supply is available. When a power outage happens, the DC to single-phase AC is activated to convert DC power from the battery and supply critical AC loads. The DC/AC inverter is mostly standby without any power conversion. The drawback of standby UPS lies in the transition time of the SPDT and the start-up of the inverter. A short-time delay is always present during the transition from the grid to the inverter output. The delay is short enough to keep desktop computers working without any interruption. Solid-state relays are constructed by power semiconductors that can shorten the transition time to replace the mechanical relay.

The online UPS system can eliminate the transition time and make the DC/AC converter work full-time to support the load, as shown in Fig. 5.1b. The battery bank becomes a DC interlink between the charger and the DC/AC conversion. During a sudden power outage, the charger stops to operate but the DC/AC conversion is not interrupted and shows a seamless transition. However, the stress on both the AC/DC and DC/AC converters is high due to the full-time power process. The solution generally costs higher than the standby counterpart. The DC/AC conversion for UPS belongs to the stand-alone systems that provide power to single-phase AC loads and maintain the output voltage and frequency.

Nowadays, another category of DC to single-phase AC conversion is used for the AC grid interconnection with renewable energy resources. The most common application is the photovoltaic (PV) grid-tied system, which has grown dramatically for home and building installations around the world. Figure 5.2 shows a simplified system diagram, where the PV generator produces DC power. The solar power is converted to single-phase AC and then injected into the public power distribution network.

FIGURE 5.2 Simple version of grid-tied PV power system.

The most common topology is the active four-switch bridge for DC to single-phase AC conversion, which has been introduced in Sec. 2.4 and illustrated in Fig. 2.15b. The bridge topology is typically constructed by either field effect transistors (FETs) or insulated gate bipolar transistors (IGBTs), as shown in Fig. 5.3. The switch selection depends on the power and voltage level, as discussed in Sec. 2.3.5. The four-switch bridge is formed by two legs in parallel, marked as A and B. The AC output is expressed by v_ab = v_ag − v_bg, where v_ag and v_bg show the voltage potential to the common DC ground of Leg A and Leg B, respectively. The voltage potential difference leads to the AC output, v_ab. When one switch is turned on, another in the same leg should be synchronously switched off to avoid any cross conduction or shoot through.

FIGURE 5.3 Bridges for DC to single-phase AC conversion by (a) FETs; (b) IGBTs.

5.1  Square Wave AC

The on/off switching is feasible to produce square waveforms. The diagonal switching patterns of the four-switch bridge can produce either the positive or negative output at the AC terminal, as illustrated in Fig. 5.4. For the positive cycle, the output is v_ab = V_in − 0 = V_in formed by the conduction of the diagonal pair of S_AH and S_BL. The onstate of S_BH and S_AL leads to the negative cycle, where v_ab = 0 − V_in = −V_in. The output voltage, v_ab, becomes an AC waveform when the two cycles are equally split, as shown in Fig. 5.5. The simple switching mechanism starts the DC to single-phase AC conversion.

FIGURE 5.4 Diagonal conduction of four-switch bridges for DC/AC conversion: (a) [+] state; (b) [−] state.

FIGURE 5.5 Square AC waveform produced by active four-switch bridge.

The switching operation is simple to produce square AC waveforms through the four-switch bridge and follow a specified frequency, e.g., 50 or 60 Hz. Nevertheless, the modulation is incapable of regulating the output AC voltage, v_ab. The amplitude and RMS values of v_ab are fixed to the DC level of V_in.

5.1.1  Chopping

Based on the four-switch bridge in Fig. 5.3, another two switching states can be achieved to produce cycles with zero output voltage. Figure 5.6 illustrates the two states, which are also called the flat switching pattern. Either the high-side or low-side switches are on-state at the same time, which leads to v_ab = v_ag − v_bg = 0. The zero states are defined as [H0] and [L0] to distinguish the on-states of both high-side switches and low-side switches, respectively. When the two zero states are introduced in between the state [+] and state [−], the chopped square waveform can be produced for v_ab, as shown in Fig. 5.7. The marks of T₊, T₋, and T₀ represent the periods of the positive, negative, and zero state, respectively. The RMS value of v_ab becomes controllable by adjusting the state periods.

FIGURE 5.6 Flat conduction states of the four-switch bridge for DC/AC conversion: (a) [H0] state; (b) [L0] state.

FIGURE 5.7 Chopped square AC waveform produced by four-switch bridge.

5.1.2  Phase Shift and Modulation

Modulation can generate the switching sequence described as the following:

1. S_AH switched on ⇒ S_AL off ⇒ v_ag = V_in & v_bg = 0 ⇒ v_ab = V_in ⇒ state [+].

2. S_BH switched on ⇒ S_BL off ⇒ v_ag = V_in & v_bg = V_in ⇒ v_ab = 0 ⇒ state [H0].

3. S_AH switched off ⇒ S_AL on ⇒ v_ag = 0 & v_bg = V_in ⇒ v_ab = −V_in ⇒ state [−].

4. S_BH switched off ⇒ S_BL on ⇒ v_ag = 0 & v_bg = 0 ⇒ v_ab = 0 ⇒ state [L0].

At each switching moment, one switch is turned on, and another on the same leg is automatically turned off. Each switch maintains on-state for half cycle or 50% duty cycle, which results in rectangular waveforms of v_ag and v_bg. A time delay is applied between the switching-on of S_AH and S_BH. The time delay represents the period of the positive state, which is equal to that of the negative state. Figure 5.8 demonstrates the equivalent circuits in response to the switching sequence.

FIGURE 5.8 Switching sequence to produce chopped square waveform.

The above operation can be explained in the phase domain, as shown in Fig. 5.9. Phase shift between two rectangular waves is a common modulation technique that can produce the chopped square waveform for the DC to single-phase AC conversion. The phase value is represented by Φ for analysis, which is indicated in Fig. 5.9. The pulse width of the states [+] and [−] corresponds with Φ in each 2π cycle. The zero states, [H0] and [L0], lead to zero output voltage. The RMS value of the output AC voltage is regulated by the phase-shift angle. Based on one half-cycle in steady state and the waveform shown in Fig. 5.9, the RMS value of v_ab can be derived by

When Φ = 0, the rectangular waveforms of v_ag and v_bg are overlapped and result in zero output of v_ab. When Φ = π, the square waveform appears and represents the highest voltage conversion ratio from DC to single-phase AC. When the RMS value is determined as

FIGURE 5.9 Phase shift to produce single-phase AC waveform.

FIGURE 5.10 Equivalence of sine wave with chopped square waveform.

To match and compare with the sine wave, the pulse of the chopped square waveform is centered in each half-cycle, as shown in Fig. 5.10, when The margin angle, α, is defined to represent half of the zero states (T₀). Both Φ or α can be the modulation index for the output voltage regulation since the relation is defined as 2α + Φ = π. Therefore, the RMS value of the output voltage can also be derived as in (5.2), which is equivalent to (5.1). Thus, the output voltage can be regulated by adjusting either α or Φ.

5.1.3  Total Harmonic Distortion

The phase shift technology can modulate the four-switch bridge to produce single-phase AC output with controllable voltage output. The main concern results from the distortion in comparison with the ideal AC signal in power systems. The total harmonic distortion (THD) has been introduced in Sec. 4.5.2 to quantify the difference. For the chopped square waveform, v_ab, the Fourier transform (FT) series is expressed by

where the fundamental frequency refers to ω₀, and the odd number of harmonics is counted. The amplitudes for the n odd harmonic component of the chopped square waveform is expressed by (5.4). The amplitude and RMS value for the fundamental component, v₁, can be derived as in (5.5) and (5.6).

According to the THD definition for voltage in (4.24), the value for the chopped square waveform can be determined by

where RMS(v_ab) and RMS(v₁) can be determined by (5.2) and (5.6), respectively. Figure 5.11 illustrates the correlation between the THD value and the modulation index, the margin angle of α. The THD value of the pure square waveform when α = 0 has been discussed in Sec. 4.5.2, which is rated as 48.43 percent. The region when shows better representation of the ideal AC signal due to the relatively lower THD.

FIGURE 5.11 Conversion ratio of chopped square waveforms.

The chopped square AC waveform is commonly used as the output of the low-cost and low-capacity AC power supplies because of the simple phase-shift modulation at relatively low frequency. The power supply is usually sourced from rechargeable batteries, e.g., from cars, and provides power to many household AC appliances. The DC to single-phase AC conversion is commonly called the “modified sine wave inverter,” which refers to the output of the chopped square waveform for AC. However, the THD level of the square-like waveforms is always higher than 20%, which cannot be accepted by various industry standards, especially for high-capacity AC power supply or grid interconnection.

5.2  Sine-Triangle Modulation

Industry demands high-quality AC output from the DC/AC conversion. The technique of pulse width modulation at high frequency and low-pass filtering can be utilized to achieve the goal. Industry sometimes calls such DC/AC conversion the “pure sine wave inverter.” The modulation technology is commonly called the sinusoidal pulse width modulation (SPWM).

5.2.1  Bipolar Pulse Width Modulation

The PWM operation has been introduced in Sec. 3.1 and illustrated in Fig. 3.2 for the DC/DC conversion. Regarding DC/AC conversion, the same comparison mechanism can be applied with the variation in the reference and carrier signals. The applied signal for the reference should reflect the nature of AC voltage output, which carries the fundamental frequency. The bipolar pulse width modulation (BPWM) is a straightforward way to manipulate switching pulse for the DC/AC conversion. The carrier signal, v_c, shows bipolar triangle waveform, including the positive and negative half cycle, as illustrated in Fig. 5.12. The reference signal, v_r, is a sine waveform, which reflects the fundamental frequency of the AC output, ω. The frequency of v_c is higher than ω to produce fine PWM pulses. The comparison between v_r and v_c produces the PWM signal, as shown in Fig. 5.12.

FIGURE 5.12 Demonstration of bipolar PWM operation and output waveform.

When v_r > v_c, the PWM outputs ‘1’ and controls the diagonal switch pair of S_AH and S_BL to conduct, as illustrated by the equivalent circuit in Fig. 5.4a