## 1 Introduction  
To alleviate the problem of fossil energy shortages, excessive carbon emissions, and ecological damages, power generation based on large-scale renewables like wind and solar photovoltaic has been developed at a rapid rate. However, uncertainties related to renewable energies bring negative effects to the operation and to the dispatch of the entire power system, such as real-time power balance, load flow of transmission lines and the optimal placement of reserve capacity. In order to address the issue of uncertainties in renewable energy outputs, robust optimization methods have been explored widely. Major strong points of those robust optimization methods include:  
1. An accurate probability distribution function of the uncertain parameters such as the wind power output, which is usually difficult to obtain and may lead to model insolubility [1], is not required;
2. Solutions are feasible even when the worst cases occur in practice [2];
3. With proper mathematical treatments of the robust model, the computational tractability can be realized [3]. Generally, robust optimization methods can be adopted in wind power system analysis for various objectives. One is to determine the base point of the generation output while satisfying the power balance for all possible wind power outputs, followed by the computation of participation factors, which is an effective solution for the penetration of wind power into the power system [4]. In addition, a robust co-optimization to energy and ancillary service joint dispatch considering wind power uncertainties in real-time electricity markets was proposed in [5]. Both models in [4; 5] are based on Direct Current (DC) power flow. Therefore, the participation factors employed in those papers to produce adjustable generation outputs immune to uncertain wind power generation and the robust optimization model can be equivalently transformed into a linear programming model. There are also other discussions on robust optimization models in [6; 7; 8]. For example, the robust scheduling of traditional thermal power plant outputs with wind power generation to match the uncertain load demand can be formulated as a robust shortest path problem (RSSP) [6]. Moreover, to address the problem of security constrained unit commitment (SCUC) in the presence of uncertain active power injection of wind power generation, a two-stage adaptive robust unit commitment model was built up in [7]. Furthermore, a practical solution method based on Benders decomposition type algorithm was also provided in [7]. An optimal power flow (OPF) model using the [PERSON]'s orthogonal array testing and probabilistic power flow calculation to achieve a minimized generation cost robust to uncertainties was introduced in [8]. Beyond merely coping with the operation, planning and scheduling problems linked to uncertainties in the power system, robust optimization can also be used in the electricity market. To address a small size electric energy system equipped with smart grid technology as a virtual power plant that can strategically buy and sell energy, a two-stage procedure based on robust optimization was proposed in [9]. Moreover, when a price-taker participates in the pool market, robust optimization can also provide a bidding strategy along with a technique to build hourly offering curves [10]. In addition to the single-period problem, a robust optimization model for wind power look-ahead dispatch, which aims to manage operational uncertainties over the next several hours, has been discussed in [11]. In terms of equipment controlling, robust optimization can also play a vital role. Furthermore, a fractional order automatic generation control (AGC) adjustment based robust optimization techniques is proposed to address the distributed uncertain renewable energies [12]. To control the conservatism of the robust optimization model, [13] focused on accommodating uncertain wind power while avoiding over-protection by the use of risk measure.