Classical Control of a Neutral Leg - Control of Power Inverters in Renewable Energy and Smart Grid Integration - page 187

i N

1 1

ε

i L

u N

sL N - sC N

Figure 11.3 Simplified model of the neutral leg

Based on these two facts, the problem is equivalently changed from controlling the average p
of the firing pulse as shown in Figure 11.2 to controlling the inductor voltage u N ,asshownin
Figure 11.3. As can be seen later, the proportional gain from the shift to u N is designed to

be much larger than 2 . Hence, when implementing the controller, this block is usually ignored
and only the scaling block

ε

2
V DC

is needed to cascade to the designed controller.

According to (11.1),

t

1
C N ( i N −

ε = i L )dt . (11.3)

0

Since the control objective is to maintain the point N as a neutral point (i.e. the shift ε ≈ 0),

then

t

( i N − i L )dt = C N ε ( t )

0

is expected to be very close to 0 all the time. As a result, i L is expected to be almost equal to
i N . This means the majority of the neutral current should flow through the inductor L N but not
through the capacitors C N . The smaller the i c , the smaller the shift

. Hence, the capacitors
are not necessarily very large like those in the conventional split DC link topology. This is a
very important fact.

ε

11.2 Controller Design
The system shown in Figure 11.3 is a double integrator system. A proportional-integral (PI)
controller or even a proportional (P) controller cannot stabilise it. A possible option is to adopt
a lead compensator

K p bs

+ 1

C ( s ) =

1 , as +

with K p > 0 and b > a > 0, taking the measurement of ε . Three control parameters need to

be determined.
Since the neutral leg is effectively a second-order system, another option is to adopt a
controller that has only two parameters to be determined. The states of the neutral leg can be
chosen as the shift

ε and the current i c based on the fact that the smaller the current i c ,the

smaller the shift . The corresponding control scheme is shown in Fig. 11.4, where an inner

current loop is introduced to attenuate the effect of the neutral current i N on the current i c
and an outer voltage loop is used to regulate the shift

ε

ε . Because there exists an integrator in