The increasing penetration of PhotoVoltaic (PV) generation has a significant impact on the transient stability of power systems. Power electronics interface, control strategies and lack of inherent rotational element are the main factors that distinguish PV generation from conventional synchronous machine-based generation. In addition, the time constants of the PV control loops and Phase Locked Loop (PLL) are of the same order unlike the synchronous generators. The conventional equal area criterion based stability analysis is not applicable for PV generators with DC-link voltage and reactive power control. The transient stability analysis of power system with PV generation is not well explored in the literature. This paper proposes a criterion to assess the transient stability of a grid connected VSCbased PV generator with DC-link voltage and reactive power control. The PV generator is equipped with Low Voltage Ride Through (LVRT) capability, voltage and frequency support functionalities. The grid is modelled as a Synchronous Machine (SM) with finite inertia. The transient stability is assessed considering the dc link capacitor, outer and inner PV controls, PLL and grid dynamics. The proposed criterion is derived using two nonlinear functions and the Voltage Support (VS) signal of PV generator. The proposed criterion is applicable to all types of short-circuit faults with/without fault resistance. The criterion is validated through time-domain simulations. The Critical Clearing Time (CCT) calculated using the proposed criterion matches with the CCT obtained from time-domain simulations.

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For reliable operation of power system, the system should be stable not only in the fundamental domain but also in harmonic domain. Power electronic converters of renewable generators inject harmonics into the power systems. So, at higher renewable penetration levels, study of power system stability in harmonic domain i.e. harmonic stability is required. The Phase Locked Loop(PLL) is used for grid synchronization of renewable generators. PLL affects the dynamic behavior of power electronic converters in harmonic domain also. This paper analyzes the impact of PLL on the harmonic stability of renewable dominated power systems. A small signal state space model is developed for PLL in harmonic domain to analyze the behavior of PLL. The obtained state space model is a periodic Linear Time Varying (PLTV) system, making the state space model of the whole power systems also a PLTV system. As the obtained state matrix is periodic in nature, the concept of time varying eigen-values is employed to analyze the harmonic stability. The standard IEEE-39 bus system is modified to enable high renewable penetration level and the modified system is used to carryout the harmonic stability analysis. Impact of PLL parameters on harmonic stability is analyzed using the modified IEEE 39 Bus system. The impact of renewable penetration level on harmonic stability for given PLL parameters is also analyzed. It is observed that the PLL parameters and renewable penetration level have impact on the harmonic stability of power system.

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