Harmonic Droop Controller to Improve Voltage Quality - Control of Power Inverters in Renewable Energy and Smart Grid Integration - page 338

not depend on the type of the output impedance at the h -th harmonic frequency, which could
be resistive, inductive, capacitive or even complex.
Since the controller (21.6) in the voltage channel is a proportional controller, there is a static
error and V oh is not exactly zero (but close to zero). The V oh can be calculated approximately via

ω ∗ ) ω ∗ ) V oh ≈ E h −| Z o ( jh | I h ≈− n h V oh I h −| Z o ( jh | I h .

That is,

ω ∗ )

V oh ≈− |

Z o ( jh | I h

.

n h I h + 1

ω ∗ )

Its contribution to the voltage THD is approximately |

Z o ( jh | I h

. The smaller the output

( n h I h + 1) E ∗

ω ∗ , the smaller the THD. Hence, strategies like the one
proposed in (Zhong et al . 2011) can be adopted to reduce

impedance at the harmonic frequency h

ω ∗ ) and the voltage THD.

The parameter n h can be chosen to be large to make V oh small as long as the system remains
stable. As a rule of thumb, the tuning can be started with

| Z o ( jh |

ω ∗ )

n h = |

Z o ( jh |

,

γ E ∗

with which the contribution of the h -harmonic component to the THD is about . If this causes

instability, then it can be reduced. The parameter m h can be determined in the same way as m 1
because m h Q h
h

γ

is the frequency drop ratio at the h -th harmonics, which should be the same
as that at the fundamental frequency, i.e., m 1 Q ∗
ω ∗

ω ∗

. Hence,

hQ ∗
Q h .

m h = m 1

As a result, m h is often much larger than m 1 because Q h is often much smaller than hQ ∗ .
In order to reduce multiple harmonics in the output voltage, several harmonic droop con-
trollers corresponding to the harmonic orders can be included in the controller to generate
the required

v r 1 ,
which is generated by the droop controller at the fundamental frequency, e.g. the robust
droop controller presented in Chapter 19. The resulting complete droop controller is shown
in Figure 21.5. It is worth noting that the fundamental droop controller depends on the type
of the output impedance and the fundamental droop controller adopted in Figure 21.5 is for
R-inverters. If the output impedance of the inverter at the fundamental frequency is not pre-
dominantly resistive, then the fundamental droop controller should be changed accordingly. It
is worth stressing that the difficulty in defining the reactive power (Montano 2011; Watanabe
et al . 1993) for the conventional droop controller has been avoided because the reactive power
in the this strategy is defined at the corresponding frequency.

h v rh . The voltage reference v r can then be obtained via adding h v rh to