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Rural settlements are developing in the direction of functional diversification, driven by rapid urbanization, but also leading to a decline in their vitality as a result of the rapid concentration of rural population in cities. Therefore, this study proposed a theoretical framework to refine the optimization approach for rural settlements from the perspective of "production–living–ecological" functions (PLEF) and vitality. Taking a town in the farming–pastoral ecotone in northern China as a case, we evaluated the level of the PLEF of rural settlements. After exploring the functional requirements of villagers, we revealed the vitality of rural settlements based on social network analysis. The Tapio decoupling model was used to identify the optimization type of rural settlements considering the PLEF and vitality. The results showed that the PLEF of rural settlements was higher in areas with flat terrain, convenient transportation, and rich economies. Rural settlements closer to the central town were stronger in vitality. The PLEF of rural settlements was generally correlated with vitality, which means that rural settlements with a higher level of PLEF also had a stronger vitality. Rural settlements were classified into five types: suburban integration, characteristics protection, agglomeration and upgrading, general survival, relocation, and merger, according to the characteristics of a combination of PLEF and vitality. This study contributes to a deeper comprehension of the functional and structural characteristics of rural settlements and will be beneficial in guiding rural spatial reconstruction. [ABSTRACT FROM AUTHOR]

With the rapid growth of the power grid load and the continuous access of impact load, the range of power system frequency fluctuation has increased sharply, rendering it difficult to meet the demand for power system frequency recovery through primary frequency modulation alone. Given this headache, an optimal control strategy for battery energy storage participating in secondary frequency regulation of the power grid is proposed in this paper based on a double-layer structure. Besides, a coordinated control framework is constructed for energy storage battery joint units engaged in automatic generation control (AGC). At the dispatching level, the power allocation principle is set to coordinate the fast and slow resources of energy storage and conventional thermal power units, and the power decoupling of the two types of frequency modulation (FM) resources is completed. At the system level, a power allocation model representing the real-time frequency modulation capability of energy storage is established to realize the division of frequency modulation responsibilities of each unit and state of charge (SOC) consistency management, and the proposed control strategy is simulated and verified to provide a reference for the energy storage battery to participate in the secondary frequency modulation design of the power grid. [ABSTRACT FROM AUTHOR]