Conventional Synchronisation Techniques - Control of Power Inverters in Renewable Energy and Smart Grid Integration - page 347

of the controllers for most of the grid-connected applications nowadays (Barrena et al . 2008;
Freijedo et al . 2009; Kesler and Ozdemir 2011; Santos Filho et al . 2008; Shen et al . 2009;
Singh et al . 2009; Teodorescu and Blaabjerg 2004), e.g. in renewable energy applications (Shen
et al . 2009; Teodorescu and Blaabjerg 2004), FACTS devices (Barrena et al . 2008; Singh et al .
2009), active power filters (Freijedo et al . 2009), UPS applications (Santos Filho et al . 2008)
and power quality control (Kesler and Ozdemir 2011). The robustness and accuracy of the
PLL are essential to the operation of these controllers (Barrena et al . 2008; Rolim et al . 2006).
In recent years, the second-order generalised integrator (SOGI)-based PLL and the sinusoidal
tracking algorithm (STA) (Karimi-Ghartemani and Ziarani 2003; Karimi-Ghartemani and
Iravani 2001, 2002), also called the enhanced PLL (EPLL), have attracted a lot of attention.
One common issue with three-phase systems is the voltage imbalance. The SRF-PLL can
achieve excellent performance for ideal balanced conditions but the performance degrades
dramatically with unbalanced voltages due to the second-order harmonics appearing in the
PLL output (Chung 2000; Rodriguez et al . 2007b). Reducing the PLL bandwidth could mitigate
this problem but at the cost of lowering the dynamic performance (Rodriguez et al . 2007b).
Another simple solution is to filter out the second-order harmonics by using a repetitive
controller (Timbus et al . 2006b). There are also several more sophisticated techniques, e.g.
the decoupled double synchronously rotating reference frame PLL (DDSRF-PLL) (Rodriguez
et al . 2007a, 2007b, 2008), the delayed signal cancellation (Wang and Li 2011a,b), the fixed-
reference-frame PLL (FRF-PLL) (Escobar et al . 2011), and the DSOGI-FLL (Rodriguez et al .
2006).
It is worth mentioning that there are also frequency-domain detection methods, e.g.
Fourier transform methods (Lascu et al . 2009; McGrath et al . 2005) and space-vector dis-
crete Fourier transform method (Neves et al . 2010, 2012). These methods require intensive
data storage and computational resources (Wang and Li 2011b) and, thus, are not suitable for
real-time control applications.
Some of the methods mentioned above are discussed in detail in this chapter. Simulation
and experimental results are provided for SOGI-PLL and STA.

22.2 Zero-crossing Method
Zero-crossing is the simplest way to calculate the frequency and to provide the phase infor-
mation of a sinusoidal signal (Timbus et al . 2005). For AC to DC converters with triacs or
thyristors, zero-crossing is often used to calculate the firing angle for the distributed gating
pulses (Valiviita 1999; Weidenbrug et al . 1993). For DC to AC converters, this can be used
to detect the frequency and phase of the grid voltage so that the generated voltage can be
synchronised with the grid voltage.
The method is depicted in Figure 22.1. A timer is restarted each time when the input signal
crosses zero. The interval between the two crosses is multiplied by two (or added with the
previous stored interval) to get the period T of the signal, from which the frequency of the
signal can be easily derived as f

1

T . An integrator can also be reset when the signal crosses
zero so that the phase of the signal can be obtained.
Although the method is very simple and therefore takes minimum computational resources,
there are several well-known problems. One problem is the slow updating rate because the
frequency information is only available every half cycle. Moreover, the frequency is assumed

=