## 1 Introduction  
Renewable energy can provide an inexhaustible and clean source of energy, with wind-turbine generation (WTG) and photovoltaic generation (PVG) being the two most popular forms for the conversion of clean energy [1]. However, power fluctuations due to renewable energy sources (RES) generally have a detrimental effect on small-signal stability (SSS), and can be conveniently studied using probabilistic methods [2; 3; 4; 5]. Small-signal stability is related to the occurrence of low frequency oscillations (typically from 0.2 to 3 Hz) in the power flow between lines that can limit power-transfer capabilities, and can even lead to blackouts in the power system [6; 7]. In References [2; 3; 4], the authors studied the effect of off- and onshore wind farms on dynamic stability, and proposed an analytical method based on cumulant and Gram-Charlier expansion to assess probabilistic SSS (SPSS). The researchers' result showed that wind fluctuations have a probability of making a system's small signal unstable. However, the authors constructed a probability density function (PDF) of wind-output power using a wind speed vs. power curve, which has discontinuities and is difficult to use in analytical techniques [5]. Thus, there was a need to develop a simple and accurate probabilistic model for wind-output power. The effect of PVG considering fluctuations on SSS was studied in References [8; 9; 10]. Unlike wind, solar energy has less variability but higher uncertainty. Thus, it is also important to analyze its effects on power-system stability. In References [8; 9], the effects of stochastic fluctuations due to PVG on PSSS in a distribution network were studied. The authors found that PVG has the potential to deteriorate small-signal stability. The impact of PVG using real measured data on a large transmission system was studied in Reference [10], where the authors concluded that stochastic fluctuation due to solar irradiance can greatly hamper dynamic stability. Consequently, there is much need to study the combined effect of the two intermittent renewable sources on PSSS. Power-system stabilizers (PSSs) are generally selected as the first option to improve SSS as they can be conveniently located at generating stations. However, other power-system devices, such as flexible AC transmission systems (FACTS), and wind and solar farms incorporating power-oscillation dampers (PODs), can also enhance low-frequency stability [7; 11; 12]. In recent times, as a result of its plummeting cost, research efforts on utilizing battery energy-storage systems (BESSs) to provide different power-system functions, such as frequency regulation, power-quality improvement, and oscillation damping have also gained wide popularity [13]. BESS are usually equipped with POD (termed as BESS controllers in this paper) when they are employed for oscillation damping [14; 15]. They can directly modulate real output power, making them more suitable for oscillation damping compared to PSS and FACTS devices [14]. As the placement of energy-storage devices is very flexible compared with RES, it is easier to install them at locations where the controllability index to damp oscillation is highest, making it a more efficient candidate than RES with POD to improve SSS [16]. There are some recent studies in the literature that analyze the effect of BESS on low-frequency oscillatory stability [17; 18]. The effect of BESS on dynamic stability with high penetration of solar and wind farms was investigated in Reference [17]. The authors observed that the tuning of a BESS controller is extremely crucial, and improper tuning may result in oscillatory instability. In Reference [18], the output power of multiple BESSs was coordinated using particle-swarm optimization (PSO) to enhance dynamic stability. The method proposed by [PERSON] [17; 18] provides extensive information about the enhancement of oscillatory stability using a single or multiple BESS(s).