76
Figure 3.1: Feeding scheme for an AC motor, from the AC electric grid supply.175
The electrical grid supplies a nominally 230 V, 50 Hz AC voltage: in order to connect the inverter to a DC bus voltage, the AC/DC converter is inserted inside the chain. If a DC power supply is directly available, this conversion is no more necessary. A diodes rectifier (such as a Graetz bridge of figure 3.2) is adopted to rectify the sinusoidal wave, combined with a large-value capacitor – for voltage source inverters – that filters and eliminates the ripple. Obviously, some little oscillations remain in the output voltage, due to the discharging of the capacitor: the low pass filter behaviour of the driven motor will overcome this problem, reducing also the distortion caused by the high-frequency harmonics – this aspect is essential for modulation strategies. For hybrid-electric and electric automotive applications, the energy source – typically a battery in recent vehicles – acts as power supply for the system, providing the necessary DC voltage to the inverter. During the recharging phase, the battery pack is connected to the external electric grid through a charger system in case of plug-in cars: the charger acts as an AC/DC converter for using the AC external electric grid in order to feed the batteries. Alternatively, the regenerative braking is exploited for refilling the onboard energy source.
175 Mohan, N., Undeland, T., & Robbins, W. (2003), op. cit., p. 224.
Figure 3.2: Graetz bridge configuration for rectifying the AC supply voltage.
For induction and synchronous machines control applications, a three-phase system is required for providing the desired three sinusoidal voltages 𝑣𝑎, 𝑣𝑏 and 𝑣𝑐. Each waveform has a phase difference equal to 120 degrees with respect to the others. The three-phase inverters are composed of three legs – or branches – with two switches in each one; the upper and lower switches are turned on and off properly for modulating the output phase and concatenated voltages.176 The need of an inverter for control applications is related to the motor velocity: for controlling the rotational speed of a three-phase AC machine, the following relation expresses the proportionality between frequency and motor speed and inverse proportionality between the latter and the number of pole pairs:177
𝑛 =60 ∙ 𝑓 𝑝𝑝
▪ 𝑛 is the number of revolutions per minute (RPM), that represents the motor rotational velocity;
▪ 𝑓 is the frequency of the voltage waveforms 𝑣𝑎, 𝑣𝑏 and 𝑣𝑐;
▪ 𝑝𝑝 is the number of pole pairs of the motor.
176 Mohan, N., Undeland, T., & Robbins, W. (2003), op. cit., p. 253.
177 Toshiba Electronic Devices & Storage Corporation (2018), Retrieved from DC-AC Inverter Circuit:
https://toshiba.semicon-storage.com/info/docget.jsp?did=61546&prodName=GT30J341, p. 4.
C Vin
Rectified waveform
Vout V
t Vout
Fig.3.2: Graetz bridge and capacitive filter scheme
Due to a little discharging the output voltage of the capacitor contains a little ripple, but it will be eliminated by the low pass filter behaviour of the machine.
The three-phase inverter scheme is shown in figure 3.3:
Fig.3.3: Three phase inverter scheme
The sinusoidal wave can be obtained with different kind of modulations. The simplest is the square wave modulation where every phase is set high for 180°.
Being A,B and C out of phase of 120° the sinusoidal waves are obtained by considering the concatenated voltages as in figure 3.4:
35
78
Figure 3.3: Three-phase inverter.178
3.1.1 Voltage source and current source inverters
Voltage source inverters (VSIs) – or, alternatively, voltage fed inverters – control the output voltage and require a constant DC bus voltage. A large-value capacitor is placed in parallel on the input DC line of the inverter. In case of low impedance load, series reactors are needed for each phase; for AC machine applications the leakage reactance of the motor acts as reactor. As switches, reverse-conducting semiconductor are used;179 in this configuration, the diodes are connected in parallel to the switches.
In current source inverters (CSIs) – called also current fed inverters – a large-value inductor is placed in the input DC line of the inverter in series and the input current is kept constant. In this configuration, the inverter works as a current source and the output current is independent of load – while the output voltage depends on it. Moreover, the commutation circuit is simple because it contains only capacitors, useful for reducing the motor ripple current;180 CSI doesn’t require any feedback diode. On the other hand, BJT, MOSFET and IGBT can be used only for voltage source inverters, because these devices don’t require any reverse-blocking diodes. Reverse-blocking devices such as thyristors are required as
178 Mohan, N., Undeland, T., & Robbins, W. (2003), op. cit., p. 254.
179 Toshiba Electronic Devices & Storage Corporation (2018), op. cit., p. 6.
180 Ibidem.
switching devices for CSI, because they must withstand large reverse voltages; in case of IGBTs and so on, series diodes are needed in each branch of current fed inverters.
Figure 3.4: Voltage source inverter on the left, current source configuration on the right.181
Voltage fed type are the most adopted solution for all home appliance and industrial power applications, thanks to their reduced voltage drop, faster response to system dynamics and easier controllability. In fact, it is easier to obtain a regulated voltage than a regulated current. Generally, a CSI is preferred only where there is a changing input DC voltage source; in some applications like high-voltage direct current transmission – where a DC current travels a long distance – the current fed type inverter is still used. Furthermore, VSI structure is more compact because the reactor is not needed on the DC side. Concerning the modulation strategies, the pulse-width modulation is more efficient and easier to be applied to a VSI. For this reason, in next paragraphs the methods for controlling only voltage source inverters are described.