Due to the increasing penetration of variable renewable energies, the primary frequency response (PFR) capability of thermal power units is becoming more and more significant for power systems to tackle abrupt active power disturbances. Moreover, the actual thermal states of boilers that are usually assumed to keep rated and constant may degrade PFR capability, and incur unexpected severer frequency deviations and even instability. This study proposes an extended system frequency response

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... model incorporating the influence of thermal states on PFR. The ESFR model is developed by extending the system frequency response (SFR) model with a boiler thermodynamic sub-model, of which a low-order and linear time-domain expression is derived. Then, a quantitative assessment framework is established to assess the influence of thermal states on PFR capability, in which the instantaneous and accumulative quantities are calculated via the expressions of the ESFR and SFR models. Furthermore, based on the developed ESFR model, an improved estimation approach of dynamic frequency response considering thermal states is provided for the preliminary application. Case studies are conducted to validate the proposed model and approach.