Photovoltaic (PV) systems are gradually replacing conventional synchronous generators. However, reduced system inertia and lack of dynamic grid support from PV are the main issues that could have a detrimental impact on the transient response in power systems when critical contingencies arise. In this study, the authors modelled and analysed transient and small‐signal stability for a representative transmission system with realistic loading scenarios and high PV penetration levels. First, system eigenvalues were calculated to identify critical modes. Thereafter, the results of the small‐signal analysis were further expanded by performing transient simulations after critical contingencies. Such contingencies detrimentally excited the critical modes of the system. To carry out this analysis, they implemented a positive‐sequence dynamic model of a utility‐scale PV unit (USPVU) in the open programming environment MATLAB/Simulink. This dynamic model is based on a Western Electricity Coordinating Council (WECC) generic model (full converter model), which is suitable for electromechanical transient studies. Also included was the model of the PV array, dc–dc converter, and associated control systems. The most critical factors pertaining to the detrimental or beneficial impact of USPVUs on stability were the unit commitment and dispatch strategy and the protection/control strategy during voltage swell and dip events for equivalent PV penetration and loading scenarios.

In this study, analytical techniques and the Monte Carlo method were both applied to solve a probabilistic load flow in radial distribution networks with photovoltaic-distributed generation, but considering the technical constraints that apply to the networks (e.g. voltage regulation). The analytical technique used in this study combined the method of cumulants with the Gram-Charlier expansion to resolve probabilistic load flow. This was performed by modelling the loads and the photovoltaic (PV) distributed generation as random variables. For this purpose, the authors developed a new probabilistic model that took into account the random nature of solar irradiance and load. The results obtained demonstrate that this new analytical technique can be applied to keep voltages within standard limits at all load nodes of radial distribution networks with photovoltaic-distributed generation. A computational cost reduction has demonstrated that the analytical technique used in this study performed better than the Monte Carlo method. Acceptable solutions were reached with a smaller number of iterations. Convergence was thus rapidly attained with a lower computational cost than that needed with the Monte Carlo method.