The high proportion of renewable energy connected to the grid through power electronic devices leads to a continuous decrease in system inertia. The frequency response capability to large disturbances is also weakened. To ensure system frequency security

it is necessary to enhance coordination between regional frequency regulation resources. Current studies on spot markets considering frequency security constraints mostly focus on clearing from intra-regional perspectives. For high-voltage direct-current (HVDC) interconnected systems

HVDC lines can transmit various frequency responses between areas by applying additional control methods. In this paper

the values of frequency responses mentioned above are considered and incorporated into market clearing to enhance system security and economies. Firstly

different control methods for HVDC in inter-regional frequency mutual sharing processes is analyzed. Based on the characteristics of various frequency regulation resources

including response delay

response type

and frequency fluctuation during response processes

the corresponding frequency security constraints are derived. Secondly

a joint clearing model of electric energy

inertia

and primary frequency response auxiliary services considering asynchronously interregional frequency mutual sharing is proposed to accurately quantify the economic value of frequency response transmitted by HVDC. Finally

the effectiveness of the model is verified based on examples

and the impact of different response methods on the clearing results is discussed.