# Model Predictive Control of Grid Forming Converters with Enhanced Power Quality
## 1 Introduction  
The concept of microgrids (MGs) has received considerable attention owing to its potential to serve as an alternative power source utilizing unconventional sources interfaced by the power converters, or supplying power to the critical loads in the main grid in case of networks failure [1]. Furthermore, MGs are an agglomeration of distributed energy systems, working in low-voltage, and provide heat or power or combined heat and power (CHP) to a particular area. MGs provide a platform to maximize reliability, availability, efficiency, security, and economic performance and can operate independently to isolate themselves from the main grid in case of faults. Based on the power converters operation, which are vital parts of MGs, they are classified into grid-following,grid-forming, and grid-supporting power converters [2; 3]. The concept of a grid-forming power converter, as the main focus of this paper, is fundamental to the operation of a low-inertia power system dominated by non-rotational generation [4]. In such scenarios, grid-forming converters provide the frequency and voltage references for regulation purposes. Hence, they form the references for the other distributed generations (DGs) [5]. Moreover, grid-forming converters can be used in different cases such as parallel operation, grid-connected, and islanded modes, where grid-forming converters are supplied by stable power sources such as batteries, fuel cell modules, and turbines, as shown in Figure 1[6]. Bearing in mind that connecting a large number of DGs to the grid will result in some difficulties in controlling the MGs system and therefore may cause severe problems in power quality, stability, reliability, and also security [7; 8; 9]. The negative impact generated by the agglomeration of the DGs in the MG entity can be resolved throughout applying some aspects such as optimized cooperation, advanced control strategies, and proper coordination [10]. In fact, providing a high power quality by using the grid forming converters is a very challenging process. Therefore, advanced control techniques have to be adopted in order to diminish the adverse effects caused by poor quality originators. The conventional way of realizing voltage source converter (VSC) control structure in the MGs is through hierarchical and organized linear control loops utilizing a pulse width modulator (PWM). Cascaded linear structure inherently introduces a low-pass filtering behaviour of the overall control system where the dominant time constant tends to rise by an order of magnitude with every loop. Moreover, as the converters usually have an LC filter installed at the output, there exists a dynamic coupling between the inductor current and capacitor voltage, which is cumbersome when cancelling it out due to the presence of computational and PWM delays. In this paper, finite control set model predictive control (FCS-MPC) is used to control a stand-alone voltage source converter in order to form a voltage reference and regulate the frequency for the future use in MGs as a grid-forming type. FCS-MPC has been discussed intensively in [11; 12; 13; 14; 15; 16] for grid-connected applications and [17; 18; 19] provide detailed discussions on the performance of different FCS-MPC algorithms. To sum up the detailed discussion in the references mentioned above, FCS-MPC enabled simplicity and ease of including the constraints and non-linearities, and it has been proposed to be applied in many applications such as electrical drives and grid-connected power electronic systems [20; 21]. Mainly, these promising results were achieved because of the general concept of FCS-MPC, which is based on the principle of using a discrete model of the power converter with an associated filter to predict its future behaviour for all possible control inputs and, consequently, apply the one that minimizes a programmed cost function (CF) at every sampling time [17] (see Figure 2).