Applications in Single-phase to Three-phase Conversion - Control of Power Inverters in Renewable Energy and Smart Grid Integration - page 231

and the phase legs. If the switches are controlled so that i L ≈ 0, then almost no

current flows through the split DC-link capacitors. As a result, the voltage V ave is stable and
close to 0. According to (14.2), the current i r is i s −

i r and i C ≈

i c . If this is applied as the reference
current for the inductor L r , then the current i C can be controlled to be nearly 0 by operating the
switches Q 3 and Q 4 . Hence, the control of the neutral leg is also a current-tracking problem
and many control strategies can be applied. Here, the inductor current i L is measured for
feedback and a hysteresis controller is applied so that it is able to track the reference inductor
current i s −

i b −

i b − i c , as shown in Figure 14.6(c).

14.4.4 Control of the Phase Legs
Since a neutral point that is close to the mid-point of the DC link is available, each phase leg
could take the form of a half bridge connected with an LC filter, as shown in Figure 14.4. This
topology has been widely studied, e.g. in (Liang et al . 2009; Srikanthan and Mishra 2010).
One important aspect in this application is that the phase of the voltage generated should be
synchronised with the supply voltage with Phase b lagging the supply voltage by 2 3 rad and
Phase c leading the supply voltage by 2 3 rad. This requires the phase shift at the fundamental
frequency caused by the LC filter to be small. The second important aspect is that the output
voltage should contain low voltage harmonics even when the load is non-linear. There are many
control strategies available for this; see e.g. (Weiss et al . 2004) for repetitive control-based
strategy. The third important aspect is that the RMS value of the generated voltage should be
the same as that of the single-phase supply voltage.

14.4.4.1 Generation of a Clean Voltage with the Right Phase

In order to address the first and second aspects, the simple and effective strategy in (Zhong
et al . 2011) that bypasses the harmonic currents can be adopted; see Chapter 8. As shown
in Figure 14.6(d) or Figure 14.6(e), it consists of a current feedback loop to force the output
impedance of the phase to be resistive and a voltage loop to track the reference phase voltage
v rb or v rc , respectively. The voltage loop is able to reduce the output impedance at harmonic

frequencies, which is able to reduce the harmonic components of the output voltage.
Take Phase b as an example. The following equations hold for the voltage loop and the
current loop:

u b = v rb − K i i b + K R ( s )( v rb − v b )

and

u fb = sLi b + v b .

Since the switches are operated so that the average of u fb during a switching period is the
same as u b , there is

v rb − K i i b + K R ( s )( v rb − v b ) = sLi b + v b .

That is,

v b = v rb − Z o ( s ) i b ,