## 1 Introduction  
In the face of escalating concerns over environmental pollution, global warming, and energy security, power systems worldwide are evolving towards a higher penetration of renewable energy sources (RESs) [1]. However, the inherent variability and intermittency of RESs, such as wind turbines (WTs) and photovoltaic (PV) generation, pose significant challenges to their integration [2]. Efficiently accommodating these fluctuations within the existing power grid infrastructure is a critical challenge that needs to be addressed. With the continued growth in the installed capacity of RESs, there is an urgent need for a more flexible power system that would maximize the economic and environmental benefits of clean energy [3]. To achieve effective RES utilization, it is essential to leverage the flexibility support from conventional power sources on the generation side. In areas predominantly reliant on coal, thermal power units (TPUs) act as the main providers of power system flexibility [4]. Enhancing the flexibility of TPUs through technical retrofitting emerges as the most realistic and feasible method to augment the power system's adaptability [5]. By implementing measures like optimizing auxiliary combustion and steam-water processes, TPUs can enhance their ramping efficiency and operate below the minimum output of a regular peak regulation (RPR) state, thereby achieving deep peak regulation (DPR) capabilities [6, 7]. This enables TPUs to provide a greater regulation capacity, fostering better RES utilization and obtaining additional revenues from auxiliary services [8]. To assess RES accommodation capabilities through flexible power sources like TPUs, the authors of [9] evaluated the capabilities of existing coal-fired power plants in Germany to integrate different shares of RESs based on historical operation data. Reference [10] assessed the technical and economic performance of the main flexible resources for RES accommodation based on the Beijing-Tianjin-Hebei region in China. Reference [11] assessed the flexibility requirements, including the maximum ramping rate and minimum output for TPUs, to accommodate future large-scale variable RESs. These studies focused on conducting a macro-level evaluation of the RES accommodation capability of flexible resources across broad regions but failed to precisely explore and utilize the potential flexibility of retrofitted TPUs. The optimization and coordination between TPUs and RESs are important ways to schedule the TPUs at the time-step level to improve the accommodation of RESs. In [12], a stochastic rolling economic dispatch was developed to explore the benefits of retrofitted TPUs in wind-integrated power systems. In [13], an appropriate look-ahead scheduling framework for a wind-thermal power system considering the retrofitted coal-fired TPUs and the flexible load transfer strategy was proposed to smooth power fluctuations with an economic dispatch. In [14], an optimal scheduling model for TPUs and WTs considering the cost of DPR was proposed to minimize the total cost by searching for the optimal wind power curtailment. In [15], a nondominated-sorting grey wolf optimizer algorithm for the multi-objective load dispatch of TPUs and RESs with the consideration of efficient nondominated sorting was proposed. In [16], a dispatching model based on RES forecasting errors was proposed for wind-PV-thermal-coordinated operations. In [17], a multi-technical flexibility retrofit planning model of TPUs was developed to reduce the total cost and increase the accommodation of stochastic wind power within the power grid. The coordination of TPUs and RESs discussed above is primarily based on power systems that may encompass long electrical distances and grid structures between power sources with a potentially complicated power-flow distribution. Such power-flow constraints in the coordinated operation may hinder the full utilization of the flexibility offered by retrofitted TPUs.