This paper presents a development of a model of a set of multistage centrifugal electro pumps including two 4 stage stainless steel centrifugal pumps, each coupled to a 4 kW three-phase induction motor, connected to a hydraulic application running under two control strategies including constant speed and variable speed methods. Each pump provides 16 m3/hr flow rate and 58mwaterhead at BEP (Best Efficiency Point). Dynamicity of the model causes variations in all operational parameters of pumping system in any variation on consuming flow rate. Each electro pump has been driven with a variable frequency drive utilizing frequency control method for adjusting the rotational speed under a PID control regarding to match of pumping system operational point with the consumption point to save the energy. 83% energy saving is achieved by model in variable speed control strategy comparing to constant speed control strategy. MATLAB/SIMULINK software using ode45 solver and variable step size simulates this model.