The Water Cherenkov Detector Array (WCDA) is one of the major components of the Large High Altitude Air Shower Observatory (LHAASO). The installation of the first pool of WCDA is already finished and normally operated. Except for the initially designed 8-inch PMTs (big PMTs) of WCDA installed, each of the 900 cells of the first pool was installed another 1.5-inch PMT (small PMTs) to extend the dynamic range, which is called the WCDA dynamic range extension system (WCDA++). The 900 1.5-inch small PMTs work together with WCDA big PMTs and WFCTA and KM2A to measure the energy spectra of cosmic rays with energy from TeVs to 10 PeV. This paper presents the data analysis and simulation of the system, such as the single rate study, the match of single-channel triggered hits of big and small PMTs, the match of cosmic ray events, the core reconstruction, and full Geant4 simulation and fast simulation based on Geant4.