[Objective] A day-ahead， real-time optimal scheduling approach for customer directrix load （CDL）-based demand response is proposed to address the problem of the strong uncertainty of the battery swapping demand and inability to define the baseline load of heavy-duty truck battery swapping stations （HTBSSs）， which makes it difficult to characterize their regulation contribution quantitatively and hinders flexibility. [Methods] First， an operation model is constructed based on the classification of the state of charge and considering the number of trucks waiting for switching， which solves the problems of an excessively large strategy space and the difficulty in describing the uncertainty faced by directly controlling the power of each battery. Second， a day-ahead optimization model is proposed for the participation of HTBSSs in CDL-based demand response based on the constructed model， and a real-time rolling optimization method is presented to deal with the uncertainty of the swapping demand. [Results] Examples show that the proposed model is applicable to different swapping demand scenarios， and that the day-ahead and real-time optimization approach can effectively track the CDL and reduce the number of swapping waits. After participating in the CDL-based demand response， the HTBSS and grid operator can reduce the cost by 47.66% and 65.52%， respectively， and the regional renewable energy power abandonment can be reduced by 90.93%. [Conclusions] The proposed method can effectively guide HTBSSs to participate in CDL-based demand response and alleviate the impact of uncertainty of the battery swapping demand in the operation process. The participation of HTBSSs in CDL-based demand response can not only promote the consumption of distributed renewable energy， but also reduce their own operating costs， resulting in a win-win situation for the grid and load.