## 1 Introduction  
Due to wind power's inherent properties of intermittent and volatility etc., [1], a high level of wind power penetration increases load peak-valley variations and further aggravates the existent peak shaving pressure [2]. It has been the main cause of wind curtailments, hindering further development of wind power in China [3]. In 2015, the average hour of wind power generation is 1728 h with a year-on-year decrement of 172 h, resulting in a significantly reduced wind utilization rate according to the statistics data of The National Energy Administration of PRC. In the case of increasing wind curtailment, the deep peak shaving demand of thermal power units mainly coal-fired units has grown in power engineering [4; 5]. What is worth noting is that deep peak shaving of coal-fired units is actually a process of energy transformation like energy storage, which transfers the reduced output of coal-fired units to renewable energy generation; on the other hand, energy storage can be effectively used to consume wind power and plays a key role in deep peak shaving. Lots of research has been done on the ability of energy storage to peak shaving and benefit power systems [6; 7; 8]. However, energy storage has not been widely used due to its high capital investment costs, and there are only some small-scale demonstrated examples combining coal-fired units with storage devices for peak shaving [9]. In China, especially in regions with abundant wind resources such as the Northeast, the North, and the Northwest areas, since there are an excessive proportion of coal-fired units, irrational power supply structure, and insufficient flexible peak shaving resources, the aggravated peak shaving burden caused by large-scale wind power integration is mainly undertaken by the coal-fired units [10]. In regular peak shaving (RPS), these units normally are unable to turn down at the level to completely accommodate the integrated wind power, and thus a large amount of wind curtailment occurs due to its anti-peak characteristics. Currently, some coal-fired units are operated at the deep peak shaving states (usually 45% to 50% of rated power) to consume much more wind power. When the power output of a coal-fired unit is further reduced to 30% to 45% of its rated value, oil injection is usually adopted to ensure steady combustion of the boiler, but this strategy increases oil cost and results in high pollutant emissions. Simultaneously, since coal-fired units operated at the deep peak shaving states are very likely at low efficiency due to the expensive oil cost and the wear-and-tear cost etc., the enthusiasm of thermal power plants to participate in deep peak shaving is commonly low. On the other hand, though wind power saves fossil fuels and is environmentally friendly, deep peak shaving will markedly increase energy consumption and pollutant emissions of coal-fired units. In order to fulfill the low carbon commitments in the Paris Agreement and to improve the operating cost efficiency of coal-fired units in peak shaving, China's government encourages coal-fired units to carry out the flexibility retrofits strategy under the low-load operation conditions such as the plasma ignition technology and tiny-oil ignition technology. At present, there are few studies on the deep peak-shaving costs of coal-fired units with flexibility retrofit strategy. The authors of [11] studied the losses of coal-fired power plants induced by wind power intermittency while mainly focusing on the increased start/stop cost. In [12; 13; 14], the peak-shaving costs were only indicated by the coal consumption characteristic at the RPS period, and the oil saving benefits of deep peak shaving without combustion supporting (DPSW) was quantitative analyzed, but the unit wear-and-tear cost was not taken into account. In [15], the unit commitment problem was studied for the coal-fired units in deep peak shaving without flexibility retrofits.