This work focuses on the modeling and simulation of constant pressure systems based on variable speed pumps, with the aim of studying and evaluating their performance from a multidisciplinary approach. Using the physical models of the Simscape library, from MATLAB/Simulink R2019b, two study cases are assembled consisting of: piping system, a hydropneumatic tank, centrifugal pumps with an induction motor, variable speed drives, and a control system. Case one is comprised of one pump at a fixed speed and another at variable speed, and case two with both pumps at variable speed. For the parameterization of the models, data from manufacturers and process requirements are used. The different stages of the control system are integrated and configured; these are constant V/f control, slip compensation, space vector modulation (SVM,) and pressure controller. The dynamic response of the system, power saving, transient current at startup, and harmonic distortion are evaluated. The results showed that both cases kept the pressure constant in the face of variable flow demand and smoothed out the current during startup. Case two saved more energy (between 28 and 49%) but generated more harmonic distortion. In addition, both cases have better performance compared with traditional fixed-speed technologies.