Synchronous generators (SGs) are the main power sources in our traditional power system. Due to the coupling of their mechanical rotating speed and the frequency of the power grid, their huge inertia makes it difficult to have a big rate of change of frequency (RoCoF) when there is a huge power imbalance between generation and load (frequency event). Furthermore, their power input can be regulated automatically to make up the power imbalance, which stabilizes frequency back to a steady state. These two aspects help to maintain the frequency stability of the power system. However, for up-to-date wind turbines (WTs), namely type-3 WTs or type-4 WTs, either with optimal speed control for maximum power point tracking (MPPT) or with converters fully interfaced with the power grid, make their mechanical rotating speed decoupled from the frequency of the grid. As a result, the inertia of their rotating masses will not help to limit the RoCoF, as an SG does, when there is a frequency event. Besides, another significant difference between a WT and an SG is that the power source for a WT is not controllable, which makes it hard for a WT to change its power output as demanded. These two differences bring a big challenge for the frequency stability of our power system with more and more wind power being integrated into our power grid nowadays.

To improve this problem, the idea comes to our mind that why not control a WT to behave in the same or similar way as an SG. This is how the concept of virtual synchronous machine (VSM) control comes from. Specifically, VSM control is one category of control schemes applied to converters, which enables WTs to perform similar frequency control capability as SGs, by adding SGs' model in the control schemes.

Considering the big differences between a converter and an SG in structures and characteristics, it is feasible only to emulate the desirable properties of an SG rather than also include the undesirable ones, like electromagnetic dynamics and voltage regulation. In this way, the control scheme will also be simpler, which helps to keep the advantages of converter control, like fast response and flexibility. Therefore, the goal of our work is to get a minimized emulation of the SG model for the VSM control scheme, to simplify the control scheme as much as possible while keeping qualified frequency control capability from the WT.

According to our motivation, a VSM control scheme is proposed. There are three loops in the control scheme: outer power control loop, middle voltage control loop and inner current control loop. For the power loop, it mainly mimics the swing equation and governor control of an SG. The swing equation realizes the inertial response while the droop control in the governor realizes primary frequency regulation. The governor branch also contains a first-order delay block, which is specially designed for WTs. This delay represents the response time of changing power output of a WT. The power loop generates a reference voltage vector, consisting of a reference power angle and a reference magnitude. Proportional-resonant controllers are adopted for the voltage loop and current loop.

Based on the proposed VSM control scheme, the small-signal model of an inverter connected to an infinite bus for power angle stability analysis is presented. The state-space representation and block diagram of the system are derived. Parameter design of the control scheme is achieved based on eigenvalue sensitivity analysis and participation factor calculation.

This work is validated by simulations in MATLAB Simulink.