Switch-Mode DC-AC Inverters Applications: ac motor drives Uninterruptible ac power supplies Where a sinusoidal ac output is required whose magnitude and frequency both have to be controlled Terminal voltage is adjustable in its magnitude and frequency

Switch-Mode DC-AC Inverter: Bi-directional power flow

Switch-Mode DC-AC Inverter: Basic concepts Inverters with single- and three-phase ac outputs will be discussed Input is dc voltage source Such inverters are called voltage-source inverters (VSI) The other type of inverter is a current-source inverter (CSI) where the input is a dc current source Discussion will be limited to VSI Four-quadrant operation Rectifier mode: quadrants 2 and 4 Inverter mode: quadrants 1 and 3

Switch-Mode DC-AC Inverter: Basic concepts (cont’d) vo can be assumed to be sinusoidal io will lag vo since the inverter will drive an inductive load such as a motor In interval 1, both vo and io are positive and interval 3, both vo and io are negative Therefore during intervals, 1 and 3, po=voio will be positive, and power will flow from the dc to ac side which is the inverter mode of operation During the intervals 2 and 4, vo and io will be opposite signs, and power will flow from the ac side to the dc side which is the rectifier mode of operation Thus, switch-mode inverters are capable of operating in all four quadrants

Frequency modulation ratio, mf=fs/f1 Synthesis of a Sinusoidal Output by PWM One-leg inverter Inverter output to be sinusoidal with voltage and frequency controllable Inverter switching frequency is determined by - Sinusoidal control signal – which is used to modulate the switch duty ratio and has a frequency f1. - Triangular waveform Output voltage magnitude fluctuates between Vd /2 and –Vd /2 Output voltage frequency is determined by the control signal frequency Vd/2 -Vd/2 Frequency modulation ratio, mf=fs/f1

Single Phase Half-Bridge Inverter Two equal capacitors are connected in series across the dc input Vd /2 is the voltage across each capacitor Items of importance: - peak amplitude of the fundamental frequency component Vo1 is ma (=Vcontrol /Vtri) times Vd /2 - harmonics in the inverter output voltage waveforms

Single Phase Half-Bridge Inverter (cont’d) The switches T+ and T- are controlled based on the comparison of vcontrol and vtri When vcontrol > vtri , T+ is on and vAo=Vd /2 When vcontrol < vtri , T- is on and vAo=-Vd /2 Since the two switches are never off simultaneously, the output voltage vAo fluctuates between Vd /2 and -Vd /2.

Harmonic Spectrum of VAo The normalized harmonic voltages with significant amplitudes are plotted This plot shows three items of importance: The peak value of the fundamental frequency component is ma times Vd/2. Harmonics appear as side bands, cantered around the switching frequency The harmonic mf should be an odd integer.

Fundamental Frequency Component of VAo The peak amplitude of the fundamental-frequency component (VAo)1 is ma times Vd/2. This can be explained by first considering a constant vcontrol as shown in the following figure. The average output voltage (or more specifically, the output voltage averaged over one switching time period Ts = 1/fs) VAo depends on the ratio of Vcontrol to Vtri for a given Vd

Fundamental Frequency Component of VAo (Cont’d) Let us assume that Vcontrol varies very little during a switching time period, that is, mf is large. Therefore, assuming Vcontrol to be constant over a switching time period, following figure indicates how the "instantaneous average" value of vAo (averaged over one switching time period Ts) varies from one switching time period to the next. This "instantaneous average" is the same as the fundamental-frequency component of vAo.

Fundamental Frequency Component of VAo (Cont’d) The average output voltage (or more specifically, the output voltage averaged over one switching time period Ts = 1/fs) VAo depends on the ratio of Vcontrol to Vtri for a given Vd which shows that in a sinusoidal PWM, the amplitude of the fundamental-frequency component of the output voltage varies linearly with ma. Therefore, the range of ma from 0 to 1 is the linear range.

Harmonics in the Inverter Output Voltage VAo The harmonics in the inverter output voltage waveform appear as sidebands, centered around the switching frequency and its multiples, that is, around harmonics mf, 2mf, 3mf, and so on. This general pattern holds true for all values of ma in the range 0-1. the harmonic amplitudes are almost independent of mf, though mf defines the frequencies at which they occur. Theoretically, the frequencies at which voltage harmonics occur can be indicated as fh = (jmf ± k)f1 that is, the harmonic order h corresponds to the kth sideband of j times the frequecy modulation ratio mf. h = j(mf) ± k where the fundamental frequency corresponds to h = 1. For odd values of j, the harmonics exist only for even values of k. For even values of j, the harmonics exist only for odd values of k.

Harmonics in the Inverter Output Voltage VAo

Single-Phase Full-Bridge Inverter Consists of two one-leg inverters Preferred over other arrangements in higher power ratings With the same dc input voltage, output voltage is twice that of the half-bridge inverter

PWM to Synthesize Sinusoidal Output When TA+ is ON, vAo=Vd/2 When TB- is ON, vBo= - Vd/2 vBo(t)= - vAo(t) vo(t)= vAo(t) - vBo(t) = 2 vAo(t) Peak of the fundamental frequency component: where the amplitude modulation ratio Output voltage switches between Vd and - Vd

Example 1: Switch-mode inverter (one phase-leg, half bridge) A general analysis of the switch-mode inverter (shown in the figure below) is to be done. The switching frequency fs, which is also the frequency of the triangular signal is 1450 Hz. The DC voltage, Vd, is 600 V. Output voltage is sinusoidal voltage with a frequency equal to 50 Hz. The load is connected between the inverter leg A and the dc voltage midpoint o. Vd Vd / 2 TA+ TA- DA+ DA- io A N + - vAN o Find the frequency modulation ratio, mf. Calculate the output voltage (rms value of 1. harmonic), when the amplitude modulation ratio, ma, is equal to 0.8? Prove that (Vo1)peak = ma (Vd / 2 ). Compute the rms value of the 5 most dominant harmonics of vAo (at ma=0,8), by using Table 8-1, page 207. Also indicate the frequencies at which these harmonics appear.

Example 2: Bipolar single phase half bridge inverter

Single-Phase Push-Pull Inverters requires a transformer with a center-tapped primary T1 is ON (and T2 is OFF): vo=Vd/n, where n is the transformer turns ratio. T2 is ON (and T1 is OFF): vo= - Vd/n The peak value of the fundamental component of the output voltage: Vo1= ma (Vd/n)

No more than one switch in series conducts at any instant of time Less switching voltage drops Thus, this results in a significant improvement in energy efficiency

Three-Phase Inverter Used to supply three-phase loads Three single-phase inverters could be used, however, 12 switches are necessary, as a result, less efficient Consists of three legs, one for each phase One of the two switches in a leg is always ON at any instant Output of each leg depends on Vd and the switching status

Summary dc-to-ac converters are known as inverters The function of an inverter is to change the dc input voltage to an ac output voltage of desired magnitude and frequency The output voltage waveforms of ideal inverters should be sinusoidal However, the output of practical inverters contains harmonics For high power applications, low distorted sinusoidal waveforms are required Harmonic contents could be minimized by the use of high-speed semiconductor switching techniques Inverters are widely used in industrial applications - motor drives, UPS, induction heating, standby power supplies, etc. - input may be a battery, fuel cell, solar cell, or there dc source dc-to-ac inverters can make smooth transition into the rectification mode, where the flow of power reverses from the ac side to the dc side Two types of inverters: single-phase inverters and three-phase inverters