## 1 Introduction  
With the increasing number of solar and wind power plants in the electrical grid, the installation ratio of traditional synchronous generators to the total production capacity is significantly decreasing, which is leading to weak transmission grids [1]. Worldwide, the transmission system operators are in the process of updating their grid connection requirements for generation units to ensure that transmission networks can continue to be operated in a secure manner when renewable energy resources replace traditional thermal generation units. It is important to have simulation models, which can reliably predict the stability margins under contemporary operational conditions. The grid-stability of such systems can be improved in multiple ways through combinations of properties of the generation units and an additional balance of plant equipment such as STATCOMS, battery storage, etc. In the literature, time-domain analysis [2; 3] and frequency-domain analysis [4; 5] have been used to model and analyse different power electronics-based power systems. Linearised frequency-domain analysis is accurate around an operating point for an intended frequency range. It requires much less computational power than non-linear time-domain simulations [6]. State-space modelling and impedance-based modelling are two popular approaches in the frequency-domain [7; 8]. In these approaches, the stability can be analysed based on poles, eigenvalues, Nyquist plots or Bode plots. So far, state-space and impedance-based modelling have been used in different power electronics-based power systems like microgrids, wind power plants, solar plants, parallel current source converters and voltage source inverters. In the following section, papers, which are based on the state-space and impedance-based methods, are reviewed. In general, there are three methods for state-space modelling: state-space averaging method, harmonic state-space (HSS) method and component connection method (CCM). State-space averaging modelling is a basic method to model and analyse a dynamic system. In this method, a linearised system is presented by the state variable matrix, input matrix and output matrix. In the literature, various power electronic systems like wind power plants and microgrids have been modelled based on this approach [9; 10]. However, as this method is not modular, it can be complex for large-scale power electronic systems [11]. In the linear time-periodic (LTP) systems, where there are couplings between different frequencies, a powerful analysis tool is the harmonic state-space (HSS) method [12; 13]. The harmonic state-space model of an LTP system can generally be written based on the Fourier coefficients of the state matrices [13]. Compared to the state-space averaging method, the harmonic state-space method is more accurate but also more complex, as this approach models the frequency-couplings in the system. In the component connection method (CCM), first a dynamic system is divided into some smaller subsystems and each subsystem is modelled based on the state-space method. Then, all individual matrices will be placed in new diagonal matrices. For large-scale dynamic systems, CCM is much more systematic and modular compared to the state-space averaging method [14; 15; 16]. In addition to state-space modelling, impedance-based modelling is another useful tool for frequency-domain analysis [17]. In this method, the grid output impedance (Zs) and the converter input impedance (Zl) are required for stability analysis [5; 18]. The impedance/admittance matrices can be calculated in the dq domain or in the sequence domain. In the sequence domain, by perturbing a three-phase power converter at a frequency fp + f1 in the positive sequence and a frequency fp - f1 in the negative sequence, the small-signal relationship between the output current and voltages can be written by a \(2\times 2\) impedance/admittance matrix [19].