Sinusoid-locked Loops - Control of Power Inverters in Renewable Energy and Smart Grid Integration - page 367

23.3 Tracking of the Frequency and the Phase
For synchronverters, the reference frequency ˙ θ r is provided and the actual frequency ˙ θ is

normally not the same as ˙ θ r because of the frequency droop control. For an SLL, ˙ θ should

, denoted ˙ track the frequency of voltage v θ g , in order to drive T e to 0. Hence, it is expected

that ˙

˙

θ g and a mechanism should be added to achieve this.
After setting the desired real power to zero for a synchronverter, the electromagnetic torque
T e can be driven to zero only when the output of the frequency droop control block D p is
zero, which means ˙

θ r =

should be the same as the reference frequency ˙ θ r . This is actually what

is expected. Hence, on one hand, the output of the frequency droop control block D p needs to
be zero and, on the other hand, a reference frequency ˙

θ

θ r needs to be generated so that ˙

˙

θ r = θ g .

These can be achieved by the integrator K i
s

in Figure 23.2(a). At the steady state, T e is driven

to zero and the real power generated is

˙

P = θ T e = 0 (23.7)

as well. As a result, ˙ is the same as the (angular) frequency ˙ θ θ g of voltage v and the phase θ

is the same as the phase θ g of voltage v as well, i.e.,

˙

˙

θ = θ g ,

θ = θ g .

(23.8)

The SLL tracks the frequency and phase without any error.

23.4 Tracking of the Voltage Amplitude
The voltage droop control in synchronverters is not needed for the SLL because the generated
voltage is expected to be the same as the voltage

. The desired reactive power is set to 0 and
the loop to drive the reactive power Q to zero is kept. At the steady state, Q

v

= 0 in addition

to P = 0. Hence, (23.2) is equivalent to

E = v m . (23.9)

Together with (23.8), the condition (23.3) is satisfied and the SLL is synchronised with the
voltage v.

It is worth noting that one advantage of the SLL is that the frequency, phase, voltage
amplitude and the recovered signal are all directly available internally without any extra
calculation.

23.5 Tuning of the Parameters
The SLL mainly contains an amplitude loop to regulate the reactive power (and the voltage),
a frequency loop to regulate the real power (and the frequency ˙ θ ) and a loop to generate the

reference frequency ˙ θ r for the frequency loop.