# Analyzing the Impact of Variability and Uncertainty on Power System Flexibility
## 1 Introduction  
In South Korea, wind and photovoltaic (PV) power systems of approximately 41.6 GW installed capacity are planned for construction by 2030, based on the 3020 penetration plan for renewable energy resources. The term \"3020\" indicates that the ratio of electricity generation by renewable energy resources to total electricity generation should reach a target of 20% by 2030 [1]. Under this plan, the installed capacity of renewable energy resources in Korea in 2030 would be about five times higher than in 2018, and a large proportion of the newly installed renewable energy resources would be wind and PV power systems. Setting aside the practicality of the plan, large-scale integration of renewable energy resources into power systems may cause flexibility problems [2; 3], where flexibility is defined as the ability to respond to changes in net load, i.e., the load subtracted from the power outputs of renewable energy resources. The National Renewable Energy Laboratory (NREL) and the North American ElectricReliability Corporation (NERC) have investigated the flexibility problem in light of the expectation that the penetration of renewable energy resources is likely to increase significantly [4; 5]. System operators and planners have begun to encounter this problem, and maintenance of flexibility requires urgent attention. The flexibility problem has arisen because the outputs of the renewable energy resources, such as wind and PV power systems, are variable and unpredictable [6; 7; 8]. High penetration of wind and PV power systems increases the variability and uncertainty of the net load, and exacerbates the flexibility problem in power systems. Variability does not involve uncertainty, i.e., no risk is included in calculations of variability [9; 10]. If the generation capacity is sufficient to satisfy the forecast net load, the variability of this load can be covered by the scheduled outputs of generating units. However, uncertainties such as the unexpected failure of a generating unit or load forecast errors are inevitable, and these can lead to unsatisfied variability. Reserve capacity is thus usually required for uncertainty-contained situations, and system operators address this possibility by securing an adequate level of reserve capacity [11; 12; 13; 14]. To sum up, the scheduled output and reserve capacity are used as countermeasures for variability and uncertainty, respectively [15]. Tailored responses to variability and uncertainty may be possible by separating the variability and uncertainty [16]. Existing studies on the flexibility problem can be categorized into two types: those that discuss the application of flexible resources, such as energy storage systems, and demand-side resources (DSRs) to mitigate the variability and uncertainty [3; 17; 18; 19; 20]; and those that investigate operational methods such as the unit commitment (UC) and power flow to effectively respond to increased variability and uncertainty [21; 22; 23; 24; 25; 26; 27; 28]. In the latter category, the effects of variability and uncertainty are restricted using ramp-up/down constraints (collectively known as ramp constraints) in stochastic and deterministic UC formulations [21; 22; 23; 24; 25; 26]. However, ramp constraints merely guarantee a feasible solution; adequate or optimal flexibility and the trade-off between the available amount of flexible resources and the operating cost are not taken into account. More importantly, the extent to which the variability and uncertainty affect the flexibility has not been explicitly distinguished in those frameworks; existing research [26] has only attempted to quantify the individual effect of variability and uncertainty on flexibility using a proposed index called AACEE, which estimates the power imbalance caused by the variability and uncertainty. However, generator failure was not considered, although this is a major source of uncertainty.