## 1 Introduction  
Emulating the behaviours of a synchronous generator (SG) in the structure of novel control techniques for power electronics converters has been increased in recent years in order to guarantee the stability of the power grid under high penetration of renewable energy sources [1; 2; 3; 4; 5; 6; 7]. Several studies have been reported in the literature of the modelling behaviour of SG in power electronics-based generators [8; 9; 10; 11; 12; 13; 14; 15; 16; 17]. Reference [8] utilizes the concept of power hardware-in-the-loop for emulating a synchronous generator in aircraft power systems applications. A virtual synchronous generator-based control technique is presented in [12], in which the differences between inverters and real synchronous generators are considered by emulating and analysing swing and power equations [12]. Reference [13] presents a control strategy for the emulation behaviour of SG in VSC-HVDC, in which this control strategy consists of the inner and outer control loops. In addition, an inertia element is used to achieve the value of reference frequency, and a secondary frequency regulation is obtained by modulating the scheduled power in the proposed control strategy. The samples of recent research, which concentrated on modelling of power electronics-based SG emulated inertia to compensate for the lack, or low-effect, of inertia generated through conventional power plant [14]; emulated the synchronous machines for the power grid stability issues [15]; proposed an active power controller with a virtual synchronous generator that can modify inertia online [16]; and designed a virtual synchronous machine control for emulating a virtual inertia with the aim of power injection from/to the energy storage system [17]. To provide a conventional droop-based synchronous control for power electronic converters in stand-alone and grid-connected operating modes, a virtual synchronous machine-based control technique was considered in [18], by assessing the small signal responses, due to the inertia emulation characteristics. The general features of the virtual synchronous machine (VSM) are considered in [19] for smart grid applications, in which a specific VSM implementation, together with its mathematical model are discussed in the frame of numerical simulations. In order to regulate the voltage and frequency of a microgrid, a fuzzy secondary controller, based on a virtual synchronous generator is proposed for an interfaced converter in [20]. By emulating synchronous machines for the power grid stability issues, the control of HVDC transmission in [21; 22; 23; 24] were discussed so that the used rectifier emulates the features of a synchronous motor (SM), and the applied converter mimics an SG in its control structure. In this paper, a synchronous power controller is proposed to guarantee the desired frequency and voltage magnitude for the power grid under high penetration of renewable energy sources (RESs). After achieving an active and reactive power-based dynamic model, the virtual inertia and mechanical power parameters are incorporated in the proposed dynamic model through the PMSG swing equation, which is the main contribution of this paper. Compared to previous works, VMP variable and its error as the main effective parameters, in the proposed control technique is introduced in this paper for the first time. In addition, providing such a power-based dynamic model, along with embedding the PMSG features in this model, leads to more effective interfaced converter analogous to PMSG for providing the needed inertia that cannot found in existing methods. Then, two first and second order differential equations for the grid angular frequency are obtained that enable an accurate assessment associated with the effects of virtual mechanical power (VMP) on the active and reactive power, as well as the virtual inertia variation impacts on the grid angular frequency. To this end, the effect of active power error on the reactive power is studied.