Classical Control of a Neutral Leg - Control of Power Inverters in Renewable Energy and Smart Grid Integration - page 193

in Section 11.1. It means that for a given system the allowable high frequency neutral current
decreases when the frequency increases. The Bode plot with

1

2 ω i , corresponding to the
case when the two poles of the closed-loop system are identical and K v =

ω o =

1 2

i L N C N ,isalso
shown in Figure 11.8. There is no peak anywhere, but as shown in (11.9) the shift will be
doubled and, as can be seen later, the capacitor needed is doubled, too. Hence, it is worth using
ω o = ω i .

4 ω

11.4 Selection of the Components
11.4.1 Capacitor C N
The capacitor C N can be designed, according to (11.9), as

π

fI N
ω i ω o ε m

2

C N ≥

(11.14)

where I N is the maximal peak value of the main component of the neutral current i N , f is the
frequency of the main component of i N ,

ω i is the inner loop frequency, ω o is the outer loop

ε m is the desired maximal ripple voltage.
If the other components in the neutral current form a large portion of i N , a conservative
design is to add all the capacitance for the different components together and then verify if the
achievable shift meets the requirement.

frequency and

Example. Assume the neutral current is I N = 100 A (peak) at f = 50 Hz and ω i = ω o =

10000 rad/s. If the desired maximal shift is 1 V, then C N ≥ 314 μ F.

11.4.2 Inductor L N
Equation (11.9) shows that the inductor does not affect the shift (when the control signal u N
is not limited). However, it does affect the shift when the neutral current is too big and the
neutral leg cannot supply the required voltage.
As discussed in Section 11.1, the current i L needs to be almost equal to the neutral current
i N . Hence, for a sinusoidal neutral current i N with a specific frequency f (of which the peak
value is I N ), the control signal u N is required to be

u N ≈ 2 π fL N I N .

k

This has been verified in (11.13). Assume the possible peak voltage of u N is about

2 V DC

( k is a constant coefficient, which may often be 0 1 depending on the PWM waveform

generating scheme and V DC is the DC link voltage), then

. 8 ∼

k

L N ≤

fI N V DC .

(11.15)

4 π

This formula can also be used to verify if the inductor L N makes the control signal u N
constrained by the DC link voltage. Since a large inductor does not improve the shift, a small