This paper examines the dynamic aggregation of a group of M same wind turbine generators (WTGs) in parallel connection. The group of WTGs could either be a part of a grid-connected wind farm or constitute the entire wind farm. Analytical derivation in the paper indicates that the group of M same WTGs is equivalent to M dynamically independent subsystems. Each of the subsystems is comprised of a single WTG. Hence, the dynamic aggregation of grid-connected group of same WTGs in parallel connection can be represented by grid-connected single WTG subsystems for studying the oscillation stability. Further analysis in the paper reveals that when the number of WTGs in parallel connection increases, it is possible that oscillation modes of group of WTGs may move into the right half of complex plane. Thus, dynamic coupling of increasing number of WTGs in parallel connection may likely cause growing oscillations in the wind farm. An example grid-connected DFIG wind farm is used to demonstrate and evaluate the analysis and conclusions made in the paper. Oscillation stability of example wind farm was examined when the dynamic models of a group of DFIGs in parallel connection in the example wind farm were identical and different.

This paper presents a derivation of the small-signal stability limit of a grid-connected wind farm with M permanent magnet synchronous generators (PMSGs) as determined by the dynamics of phased locked loops (PLLs). The stability limit reveals the mechanism whereby the PLLs can destabilize the wind farm in the case of a weak grid connection. Computation of the derived stability limit is simple and obviates the need to establish a parametric model of the wind farm. The stability limit can approximately indicate the potential instability risk collectively posed by the PLLs in the wind farm. Case studies are presented to evaluate the analytical conclusions obtained and the derived small-signal stability limit. Application of the stability limit during the planning and operating stages of a grid-connected wind farm is also demonstrated. Various factors that can affect the stability of the wind farm, and that must be considered during planning and operation, are examined and useful conclusions are obtained. These factors include the length of the transmission line connecting the wind farm to the AC grid, the topology of the wind farm, the wind speed, and its distribution over the wind farm, as well as the parameters of the PLLs.

This paper proposes a method to design power system stabilizers (PSSs) based on single-machine infinite-bus system models to mitigate the risk of low-frequency electro- mechanical power oscillations in an N-machine power system. First, models of N fabricated identical-machine power systems are established for the N-machine power system. Analysis in the paper indicates that the electromechanical oscillation mode of fabricated identical-machine power systems with the least damping is of less damping than the electromechanical oscillation modes of N-machine power system. Second, it is proved that models of fabricated identical-machine power systems are dynamically equivalent to the single-machine infinite-bus system models. Finally, it is suggested that the PSSs are designed using single-machine infinite-bus system models to enhance the least damped electromechanical oscillation mode of fabricated identical-machine power systems. This eventually improves the damping of electromechanical oscillation modes of N-machine power system, thus mitigating the risk of low-frequency electromechanical power oscillations. In the paper, the proposed method is demonstrated and evaluated by using three well-known example multi-machine power systems. Effectiveness of PSSs is confirmed by the results of modal computation and simulation.

Case-by-case study in the literature has found from the results of numerical computation and simulation that a grid-connected virtual synchronous generator (VSG) can maintain the stability under the condition of extremely weak grid connection. This paper presents the theoretical proof to the finding and thus, generally concludes that the grid-connected VSG is immune to the instability risk under the condition of weak grid connection. In addition, the paper extends the theoretical proof to the case of a grid-connected PMSG wind farm with multiple VSGs. An example grid-connected PMSG wind farm with twenty VSGs is presented to demonstrate and evaluate the theoretical analysis and conclusion made in the paper.

For planning the grid connection of a wind farm, small-signal stability needs to be examined to ensure the stability of wind farm as a standalone system. However, for a large-scale wind farm with m wind turbine generators (WTGs), the dimension of state matrix is nm if on average the order of dynamic models of the WTGs is n. Thus, when the number of the WTGs in the wind farm is over several hundred or more, high-dimensional numerical difficulty of modal computation may occur. Therefore, in this paper, we propose a method of reduced-order modal computation for the application in planning the grid connection of the large-scale wind farm. Dimensions of matrices involved in the reduced-order modal computation are m and n such that the numerical difficulty of modal computation is effectively avoided. In the paper, the effectiveness of proposed method of reduced-order modal computation is demonstrated and evaluated by an illustrative simple example wind farm and an example large-scale wind farm with 200 WTGs.

In this paper, an approximate aggregated impedance model (AAIM) of a grid-connected wind farm with multiple wind turbine generators (WTGs) for the small-signal stability study is derived. The derivation is conducted under the condition that the WTGs inside the wind farm are of the same type and from the same manufacturer. The AAIM derived can be seen as the impedance model (IM) of a grid-connected aggregated WTG. The IM of the aggregated WTG is the weighted average of the IMs of the individual WTGs in the wind farm and hence is simple to be built. The reactance of the line connecting the aggregated WTG to the external AC grid is the maximum eigenvalue of the network reactance matrix of the grid-connected wind farm. In addition, the derivation justifies the representation of a wind farm by an aggregated WTG in the IM-based small-signal stability analysis. Finally, two example grid-connected wind farms are used to evaluate and demonstrate the effectiveness of the AAIM proposed in the small-signal stability analysis. It is also shown that the computational burden of the stability analysis of a large-scale wind farm could be effectively reduced when the AAIM is used.