In this paper, the investment-return period is accepted as objective function under the control condition satisfying flow-rate distribution A mathematical model is suggested to do optimal design in various schemes of flow modulation for arbitrary fan-primp system (FPS). This paper analyzes and discusses the numerical methods of energy saving of various modulation schemes including the single and the parallel FPS, the correct application of Affinity Laws to the caculation of energy saving, and the allowed minimum flow-rate. Thus the paper has provided a useful method to do energy saving and optimal modulation for FPS.