# Study of a Synchronization System for Distributed Inverters Conceived for FPGA Devices
## 1 Introduction  
In recent years, smart grids have become a very important topic and are extensively debated in the literature [1]. A smart grid is a network that can efficaciously monitor and manage the transport of electricity produced by generators to meet the varying electricity demands of end-users [2, 3]. To add intelligence to a smart grid, the network must integrate signal processing blocks and communication logic. Conventionally, methods such as the use of parallel capacitors, tap-changing transformers and SVC (Static Var Compensator) are adopted [4]. These power controls generally lack precision and do not work in real time; to overcome these limitations, different solutions relying on FPGA (Field Programmable Gate Array)-implemented algorithms can be exploited [5]. In the last few years, the application of FPGA devices has increased exponentially in a wide variety of fields, such as: digital signal processing [6, 7, 8, 9, 10], data processing [11, 12], bioinformatics [13, 14] and power electronics [15, 16, 17]. Among the applications based on FPGAs that recently have been applied to the smart grid field, MPC (Model Predictive Control) has particular importance [18, 19, 20]. An MPC is a control strategy that allows predicting the output of a discrete-time model, combining the input data and the current state of the model to choose the optimal control action. Implementing the complicated and challenging algorithms on FPGA devices can help to minimize the real-time response. Moreover, exploiting FPGAs in this context can lead to a strong advantage in terms of flexibility, reliability and costs [1, 20]. In [20], an example of FPGA application is presented and, specifically, the strategy of voltage control in a smart grid is proposed. The FPGAs are also used in converters and, in particular, in inverter-based applications, such as switching control, voltage balance and fault detection [16]. An inverter isa DC/AC converter that transforms a DC input voltage into a symmetrical AC output voltage. The field of inverter applications has been widely investigated: solutions where inverters are connected in parallel to form a microgrid (a kind of small-scale grid that contains distributed generators of various natures) have been proposed in the literature [21; 22; 23]. The parallel connection of inverters improves redundancy and then reliability, but it is very sensitive and complicated because each module must have the same output voltage as the others. Not respecting this requirement leads to crosscurrent or circulating current between the inverters with the effect of reducing power efficiency and system reliability. The circulating current behavior in multiparallel connected inverters has been widely discussed in [24; 25; 26; 27]. In [24], the authors studied the effect of this current in a system with two inverters and in a more general case of N inverters. In both cases, they reported that the phenomenon exists if there is a difference in the output voltage phase or frequency. The authors also concluded that the circulating current is independent of the load, that is, a current superimposed on the normal current and, finally, that can cause power exchange among the inverters connected (in the case of a no load or low-load condition). In [25], an active rejection control based on a Reduced-order Extended State Observer (RESO) is reported. The scheme proposed reduces the mutual currents with a less model-dependent control design. In [28], the authors studied the circulating current phenomenon, mentioning control methods such as droop control, master-slave control, instantaneous current sharing control and parallelism control. The droop-control method allows one to regulate the frequency and the amplitude of the inverter output voltage by adjusting the active and reactive-power flow through a linear dependence. In particular, the frequency can be used to control the active-power flow, while the amplitude of the output voltage to control the reactive-power flow [21].