## 1 Introduction  
With the advancement of renewable energy technologies and the rising enthusiasm for environmental protection, various countries have proposed energy strategies emphasizing the increase of renewable energy power generation to reduce reliance on fossil fuel power generation. According to the latest Renewable 2018 Global Status Report released by the Renewable Energy Policy Network for the 21 st Century, total renewable power capacity reached 2195 GW by the end of 2017, with wind power accounting for the highest proportion (539 GW), followed by solar photovoltaics (PV) at 402 GW [1]. The Taiwanese government has actively promoted the development of renewable energy in recent years, planning to achieve a total of 27 GW renewable power capacity by 2025, which will account for 20% of the total power capacity and will include 4.2 GW of offshore and onshore wind power and 20 GW of solar PV. The government also proposed two-year and four-year implementation projects for solar PV and wind power generation, respectively. The short-term goal comprised a total installed capacity of PV of 1520 MW and cumulative installed capacities of onshore and offshore wind power of 814 and 520 MW, respectively [2]. In the traditional unit commitment (UC) problem, the startup and shutdown times of various units and the power output within a dispatch time period of 1 day to 1 week or even 1 month to 1 season are planned according to the system load to achieve the lowest operating cost. In addition, with the load requirement being satisfied, the traditional unit commitment problem ensures that the criteria for the operation of each unit can be met. These criteria include the upper and lower limits of power output for each unit, the ramp rates of the units, and the balance between the supply of and demand for electricity. However, because of the intermittent characteristic of renewable energy, the power output may substantially decrease or increase within a few minutes due to weather events (such as an eclipse, no wind, or strong wind). Such circumstances are typically managed by using pre-established spinning reserves and storage systems [3]. However, all these methods require additional costs and are unable to effectively use renewable energy. Some studies on the ramp rate of power generating units after the integration of renewable energy into the system are described as follows. [PERSON] et al. used a dynamic ramping model, namely mixed-integer linear programming, which considered the flexibility of ramping limits to reduce the dynamic errors caused during ramping [4]. [PERSON] and [PERSON] used the IEEE 118 bus as an example; the Lagrangian relaxation method was integrated with the diagonal quadratic approximation method to solve the dynamic economic dispatch optimization problem after consideration of the unit ramp rate [5]. [PERSON] et al. controlled the rapidly changing ramp rate caused by the integration of a large-scale photovoltaic system into the electrical grid. The authors integrated an ultracapacitor (Maxwell), two flywheels (Beacon Power), and two batteries (Li-ion and Lead Acid) to effectively control the power output of solar energy to prevent frequency changes from destabilizing the system [6]. [PERSON] et al. considered transmission losses, ramp rate limits, and prohibited operating zones, and used the vortex search algorithm for scheduling the economic load dispatch problem [7]. [PERSON] et al. also applied the mixed-integer linear programming to the unit ramp rate constraint to effectively allocate operating reserves to thermal units, especially gas-fired generators [8]. [PERSON] et al. proposed an optimal dispatching strategy for the dispatch of the power system during peak load periods under high wind power penetration and rapid ramp events. In that study, the prediction of wind power rapid ramp events and spinning reserve procurement were used as the conditions for analysis [9].