Classical Control of a Neutral Leg - Control of Power Inverters in Renewable Energy and Smart Grid Integration - page 188

i N

i L 1

ε u v u N 1 i c

0

K v

sC N

- sL N -

+

+

K i

Figure 11.4 Voltage-current control scheme for the neutral leg

both the voltage loop and the current loop, the two loop controllers can simply be designed as
proportional controllers K v and K i , respectively.

11.2.1 Design of the Current Controller K i
The objective of the current loop is to attenuate the effect of neutral current i N on i c as much
as possible, at least for those frequency components under consideration. For systems with
a fundamental frequency of 50 Hz, the highest frequency components under consideration
can be up to the 31st harmonics, i.e., 1550 Hz. Approximately, the corresponding angular
frequency is 10000 rad/s. As can be seen later, this is a crucial parameter for the performance
of the neutral point (the level of the shift ).

The transfer function from i N to i c in Figure 11.5(a) is

ε

sL N
sL N +

K i , of which the Bode plot
is shown in Figure 11.5(b). The corner angular frequency, called the inner loop (angular)
frequency, is

K i

ω i =

L N . As discussed in Section 11.1, the smaller the current i c , the smaller the

shift ω i should be high

enough while considering the physical limit. 2 Hence, the current-loop control parameter is

ε . In order to make i c as small as possible, the inner loop frequency

K i = ω i L N . (11.4)

Here, ω i is chosen as 10000 rad/s. Accordingly, the switching frequency f s is chosen as 10

kHz, which is larger than 3 ∼ 4 times of 1550 Hz.

11.2.2 Design of the Voltage Controller K v
After the current loop is designed, the system shown in Figure 11.4 is equivalent to the one
shown in Figure 11.6, based on which the voltage controller K v can be designed.
The transfer function from i N to

ε is

sL N
s 2 L N C N +

T ( s ) =

K v .

(11.5)

sK i C N +

2 As can be seen later in Figure 11.8, the larger the ω i , the higher the high frequency gain from i N to u N is required.
But this is usually limited by the low-pass filtering effect of the system.