The increasing penetration of renewable energy resources via power-electronic converters is turning the modern power grid into a multiple-converter system (MCS). In a MCS, the dynamics of converter-based resources (CBRs) are different from those of traditional synchronous machines, which poses great challenges to the grid planning and operation. One of the major challenges is the emerging small-signal stability problems resulting from the interaction between CBRs and the power network. These small-signal stability problems endanger the reliable and stable grid operation. To maintain grid stability, the capacity of CBR generation in the grid may be limited, which impedes the progress towards a sustainable future. To enhance the grid-accommodable capacity (GAC) of renewable generation while maintaining grid stability, this paper presents a semi-definite programming (SDP)-based method to assess GAC with small-signal stability constraints (GAC-SSSC) in a MCS. In the proposed method, the small-signal stability constraints are formulated by the smallest eigenvalue of a pertinent weighted Laplacian matrix of power network, so that the assessment complexity of GAC-SSSC is significantly reduced for a MCS with large-scale CBRs. It is theoretically proved that the derived SDP can find the optimal solution. The efficacy of the proposed method is demonstrated on a 39-bus test system.

As synchronous generators (SGs) are extensively replaced by converter-based generators (CBGs), modern power systems are facing complicated frequency stability problems. Conventionally, the frequency nadir and the rate of change of frequency (RoCoF) are the two main factors concerned by power system operators. However, these two factors heavily rely on simulations or experiments, especially in a power system with high-penetration CBGs, which offer limited theoretical insight into how the frequency response characteristics are affected by the devices. This paper aims at filling this gap. Firstly, we derive a formulation of the global frequency for a CBG-integrated power system, referred to as common-mode frequency (CMF). The derived CMF is demonstrated to be more accurate than existing frequency definitions, e.g., the average system frequency (ASF). Then, a unified transfer function structure (UTFS) is proposed to approximate the frequency responses of different types of devices by focusing on three key parameters, which dramatically reduces the complexity of frequency analysis. On this basis, we introduce two evaluation indices, i.e., frequency drop depth coefficient (FDDC) and frequency drop slope coefficient (FDSC), to theoretically quantify the frequency nadir and the average RoCoF, respectively. Instead of relying on simulations or experiments, our method rigorously links the system’s frequency characteristics to the characteristics of heterogeneous devices, which enables an in-depth understanding regarding how devices affect the system frequency. Finally, the proposed indices are verified through simulations on a modified IEEE 39-bus test system.