The water-cooled centralized air-conditioning system is a multi-variable coupled nonlinear system with a high degree of sparsity in operational data, leading to poor generalization ability of data-driven machine learning models. A comprehensive physical model reflecting the hydraulic and heat transfer mechanisms has become a key focus of current research. However, there are some technical challenges that urgently need to be addressed, such as the complexity of variable coupling in the system, nested iterations leading to significant computational costs, and that changes in hydraulic structure due to equipment start-stop cycles necessitate frequent model reconstructions. By using continualization of discrete variables and pattern search methods to correlate resistance coefficients with branch openings, and equipment start-stop events with pump operating frequencies, it is possible to integrate discrete variables into continuous ones, reduce nested iterations, and achieve dynamic flow distribution and global hydraulic-thermal coupling calculations. This study established a multi-variable coupled physical model of a water-cooled centralized air-conditioning cold source system with external constraints such as cooling load, chilled water flow rate, chilled water supply temperature, chilled water supply-return pressure difference, and ambient temperature and humidity, enabling asynchronous adjustments of multiple independent variables including the number of chiller units, the number of chilled water pump units and frequencies, the number of cooling water pump units and frequencies, and the number of cooling tower units and frequencies. The reliability of the model was validated through a comprehensive experimental platform to explore the operational characteristics and group control strategies of chiller units, cooling towers, chilled water pumps, and cooling water pumps under different operating conditions. The research findings indicate that the simulation results of the cold source system physical model have an average relative error of less than 10%, with a few cases within 15%. The computational time for a single iteration is approximately 0.32 s. The adjustment of multiple variables can comprehensively balance the energy efficiency of each subsystem. Global optimization of the system can maximize energy-saving opportunities, addressing the shortcomings of traditional subjective empirical control in maintaining stable energy-saving effects and providing a theoretical basis for intelligent diagnostics.