## 1. Introduction

A paradigm shift in energy generation has rapidly taken place around the world. The traditional energy industry was aimed at providing energy at a low price. However, the focus is changing to provide safer, cleaner, and more sustainable energy in certain countries. In particular, China has been reinforcing the competitiveness of its sustainable energy industry by supporting a strong policy and developing its technologies. In keeping with this trend, the Republic of Korea has also tried to meet this paradigm shift by establishing an energy policy, which was launched by the government in 2017. As one aspect of this policy, the government announced its Renewable Energy 2030 implementation plan, in which the share of renewable energy sources in the energy mix will increase from its current level of 7% to 20% by 2030. Korea’s major energy administration and industry are making an effort to achieve this goal [

1,

2]. However, such a sudden shift in the energy mix can worsen the conditions of the power system, because renewable energy sources are quite volatile [

3,

4]. Therefore, some countermeasures are required, including strengthening the grid through investments in the facilities and preparing strategies for the effective operation of renewable energies [

5,

6,

7,

8].

To achieve stable operation, the power system under high renewable penetration should respond to the variation and uncertainty of renewable energy sources to secure sufficient flexibility. If a power system achieves sufficient flexibility, it can respond rapidly to events such as a sudden decrease in energy output, and ensure stability and superior quality. Owing to its increased importance, studies related to flexibility have been conducted [

9,

10,

11,

12,

13,

14]. Electric Power Research Institute (EPRI) conducted a study looking at the impact of transmission on system flexibility [

9] and developed a multilevel flexibility assessment tool [

10]. In [

11], the authors clarified flexibility by summarizing the analytic frameworks that recently emerged to measure operational flexibility. The Danish Energy Agency carried out an assessment of flexibility in Denmark and China [

12]. Poncela et al. [

13] proposed a stepwise methodology based on a set of indicators for future power system flexibility applied to a European case. In [

14], flexibility metrics were compared between insufficient ramp resources and the number of periods of flexibility deficit. In particular, the California Independent System Operator carries out annual technical studies to determine the required capacity [

15] and has developed a flexible ramping product to handle increasing amounts of variable renewable generation [

16].

Representative flexible resources include ramp rates, energy storage systems (ESS), and demand response (DR). Among such flexible resources, an ESS can play an important role in supplying balance to the grid by providing a backup to intermittent renewable energy sources and generating a low-carbon power system [

17]. In addition, a decrease in renewable energy curtailment can occur [

18]. Therefore, owing to these merits, an ESS was chosen to meet supply and demand against the variations in renewable energy and to ensure nonnegative flexibility under high-level penetration of sustainable energy.

Traditional optimization methodology is aimed at finding a deterministic result by assuming a parameter and variable in a specific state without considering the uncertainty. However, in this case, it is difficult to guarantee a reliable solution unless the data uncertainty is dealt with. For example, if a parameter with uncertainty is estimated to have a certain value, it can be unclear whether the value is correct. In addition, this can make the solution infeasible owing to the possibility of an error. Therefore, many studies on optimization techniques that can apply uncertainty have been carried out. In particular, in the power system industry, studies related to planning and operation have been considered based on an increase in uncertain resources such as renewable energy sources [

19,

20,

21,

22,

23,

24,

25,

26,

27,

28,

29,

30].

Optimization methods that are able to handle uncertainties have been developed, such as stochastic programming (SP) and robust optimization (RO). Optimization techniques have long been used to deal with uncertainty. Several studies related to SP in power systems have been conducted [

19,

20,

21,

22]. Jirutitijaroen et al. [

19] proposed a mixed-integer stochastic programming approach to find a solution to the generation and transmission line expansion planning problem, including consideration of the system reliability. In [

20], SP based on a Monte Carlo approach was introduced to cope with uncertainties, and a new approach to modeling the operational constraints of an ESS was applied to the capacity expansion planning of a wind–diesel isolated grid. In addition, in [

21], the authors proposed a multistage decision-dependent stochastic optimization model for long-term and large-scale generation expansion planning. The authors in [

22] proposed a novel stochastic planning framework to determine the optimal battery energy storage system (BESS) capacity and the year of installation in an isolated microgrid using a new representation of the BESS energy diagram.

Studies on power system operation and planning using RO have been carried out to consider uncertainties such as renewable energy sources [

23,

24,

25,

26,

27,

28,

29,

30]. Ruiz and Conejo [

23] presented a transmission expansion planning (TNEP) method by constructing the load and RES output into uncertainty sets. In [

24], transmission and ESS expansion planning was carried out by characterizing the uncertainty sources pertaining to load demand and wind power production through uncertainty sets. In addition, in [

25], energy generation and ESS expansion planning was implemented by handling the net load as an uncertainty set. The authors in [

26] used variation in the net load as an uncertainty set, and proposed an economic dispatch to cope with variation in the use of ramp rates. In [

27], the authors examined the effectiveness of RO in maximizing the economic benefit for owners of home battery storage systems in the presence of uncertainty in dynamic electricity prices. In [

28], the authors proposed an adaptive robust optimization model for multiperiod economic dispatch, and introduced the concept of dynamic uncertainty sets and the methods to construct such sets for modeling the temporal and spatial correlations of uncertainty. Yi et al. [

29] presented ESS scheduling by constructing the RES output, load, and real-time thermal rating (RTTR) of transmission lines into an uncertainty set. In [

30], algorithms to minimize total cost under Korea’s commercial and industrial tariff system based on robust optimization were proposed.

Stochastic Programming assumes that uncertain data have a probability distribution function (PDF), although this method has difficulty in accurately constructing a PDF for the uncertainty. This is based on the generation of scenarios that describe uncertain parameters, the size of which grows with the number of scenarios, which may result in intractability. However, the RO represents an uncertainty parameter set, which can contain any number of scenarios without specific knowledge of the PDF. As its methodology, it also minimizes the objective value under the worst-case scenario. Scenarios do not need to be generated, which makes the RO computationally tractable. Therefore, owing to such advantages, the RO is more appropriate than the SP for solving the optimization problem with uncertainties [

31,

32,

33,

34,

35,

36,

37]. In this paper, the reasons for using the RO are that it allows for treating uncertainties in the optimization problem and can lead to a robust solution, which is immunized against uncertainty.

Many studies on power system operation and planning with renewable energy have mostly considered its outputs as uncertainties. However, many factors affect the output of renewable energy, including the weather and installation locations, which make it hard to forecast. Thus, this paper proposes using the capacity factor as the output of the RES. Applying the capacity factor can make it simpler to consider the output of renewable energy by using the ratio of the rated capacity to the real outputs of renewable energy without taking the factors into account.

The nameplate capacity of renewable energy is known from the installation planning, while the capacity factor is unknown due to its characteristics, including variable and unpredictable outputs. So, the capacity factor of renewable energy has uncertainty and affects planning because it has difficulty making decisions on how the system will be reinforced. In addition, it needs many scenarios about renewable energy sources. This paper calculates the required capacity of flexible resources like ESS to secure sufficient flexibility without generating scenarios regarding renewable energy resources by constructing its uncertainty set based on the RO.

This paper presents a countermeasure to ensure nonnegative flexibility using flexible resources including the ramp rate and ESS by considering the capacity factor of renewable energy as an uncertainty set. It can be divided into three steps: (i) The range of the capacity factor of renewable energy is predicted in the construction of the uncertainty set. (ii) The initial point where the flexibility deficit occurs within an uncertainty set is detected using the RO. (iii) The capacity of the ESS is estimated to prevent negative flexibility from a variation in renewable energy with the RO. The effectiveness of the proposed method is demonstrated using the Korean Power System for the year 2030.

## 4. Conclusions

A deterministic optimization cannot consider uncertainty, which can undermine the reliability of the solution owing to an inability to reflect the uncertainty. In previous studies using deterministic optimization and stochastic programming, in order to consider uncertainty such as that found with renewable energy, it was necessary to make scenarios. For example, all capacity factors of renewable energy constructed by a planner are reviewed to decide how the system will be reinforced for stable operation despite variation and uncertainty, which may require much effort to do. However, robust optimization does not require creating scenarios or using much effort because it needs the uncertainty set. Therefore, it is proper to use robust optimization to include uncertainty. In actuality, in power system planning and operation, because it is extremely difficult to take into account all possible scenarios, it is reasonable to prepare a countermeasure for the worst case. Therefore, robust optimization is a suitable model in power system planning and operation.

This paper presents a robust optimization model to secure flexible resources and prevent the occurrence of a flexibility deficit from the variability and uncertainty of renewable energy. This model considers the capacity factor of renewable energy as the uncertainty set and is divided into two steps: (i) searching for the initial point of the flexibility deficit and (ii) determining the capacity of the ESS to ensure nonnegative flexibility. In the first step, it is determined whether a flexibility deficit point occurs within the interval of the capacity factor when only considering ramp rates as flexible resources. This step takes place before determining whether to invest in flexible resources. In the next step, the necessary capacity of the ESS is calculated, which can ensure nonnegative flexibility within the uncertainty set. Through this study, the results of the worst case using a deterministic approach and robust optimization are similar. Indeed, searching the worst case using a deterministic approach may require many things, from making to studying scenarios, but robust optimization may be able to reduce the effort of considering the worst case without creating scenarios.

Future work will include more detailed modeling, including power flow limits of transmission lines and unit commitment to improve the quality of the solution. It will also be necessary to contain realistic conditions to guarantee a solution.