Classical Control of a Neutral Leg - Control of Power Inverters in Renewable Energy and Smart Grid Integration - page 185

11

Classical Control of a Neutral Leg

In this chapter, a controller is developed for the independently-controlled neutral leg by using
classical control techniques to provide a neutral line for a 3-phase 4-wire inverter. The neutral
point can be steadily regulated at the mid-point of the DC link by a simple controller, involved
in voltage and current feedback, even when the three-phase converter system (mostly, the
load) is extremely unbalanced. The achievable performance is analysed quantitatively and the
parameters of the neutral leg are determined accordingly.

11.1 Mathematical Modelling
Here, the linear model of the neutral leg is developed in a slightly different way from that in
(Zhong et al. 2006) in order to gain some insightful understanding about the neutral leg, by
ignoring the resistance of the inductor and assuming that the capacitors are the same.
Assume that the voltages across the capacitors C N with respect to the neutral point N are
V + and V − , respectively. Then the DC link voltage is

V DC = V + − V − ,

and the shift of the neutral point is 1

ε = V + + V − .

According to Kirchhoff's laws, the following equations are satisfied:
⎧
⎨

L N di L u N =

dt ,

i N = i L + i c , (11.1)

⎩

dV +
dt +

dV −
dt

d dt .

i c = C N C N = C N

1 Actually, ε is twice the shift of the neutral point with respect to the mid-point of the DC link. In order to simplify
the exposition, it is called the shift.