Classical Control of a Neutral Leg - Control of Power Inverters in Renewable Energy and Smart Grid Integration - page 191

11.3 Performance Evaluation
Substitute (11.7) into (11.6), the maximum value of the magnitude frequency response from
the neutral current i N to the shift ε is

1
ω i C N ,

20 lg | T ( j ω ) | max = 20 lg

which is illustrated as g in Figure 11.7. It is independent of the inductor L N . This equation
means that for any neutral current i N containing any single frequency component (assume its
peak value is I N ), the maximal shift

I N

ε m is not larger than

ω i C N , i.e.

I N
ω i C N .

ε m ≤

This is equivalent to the voltage resulted by a sinusoidal current source I N with a frequency
equal to the inner loop frequency ω i flowing through the DC link capacitor. In order to obtain

a small shift , a small neutral current I N and/or a large capacitance C N and/or a high inner

loop frequency

ε

ω i are needed. For a sinusoidal neutral current i N with a specific frequency
component f j and a peak value of I j , the magnitude frequency response (dB), according to
(11.6), is

20 lg f j )

1
ω i C N −

20 lg | T ( j ω ) | = 20 lg ω o − lg(2 π

f j
ω i ω o C N .

2 π

= 20 lg

Thus, the corresponding shift ε j is

f j I j
ω i ω o C N .

2 π

ε j = (11.9)

Moreover, when ω o = ω i ,

2 π f j I j

ε j =

i C N .

(11.10)

2

ω

As is well known, any periodic neutral current i N can be decomposed as a series

i N = +∞

j = 0 I j sin(2

π jft + φ j ) , (11.11)

where f is the fundamental frequency. In practice, only a few components, e.g. up to the
first 31 harmonics, need to be considered, bearing in mind that the DC component does