Modelagem de unidades de bombeamento de irrigação irrigation pumping units modeling

Abstract

The rotational speed and efficiency of an asynchronous electric motor are both dependent on its shaft load ratio, which represents the ratio between the mechanical power available on its shaft and its rated mechanical power. The rotational speed of an asynchronous motor decreases when its shaft power is increased, and its efficiency tends to decline under reduced shaft power values. However, in the case of pumping units composed of a centrifugal pump driven by an asynchronous electric motor, the theoretical analysis of its performance often considers that: (i) the centrifugal pump operates with a rotational speed that is constant and equal to the rated value of the pump rotational speed, and (ii) that the electric motor operates with an efficiency value that is always very close to its rated efficiency. In this sense, this study aimed to model the real operating conditions of a pumping unit, considering both the specific parameters of the centrifugal pump and the specific parameters of the asynchronous motor used to drive the centrifugal pump. The first part of this study was aimed to analyzing deviations obtained with different mathematical models, which were adjusted to the same set of pairs of flow values and total dynamic head specified in the manufacturer's catalogs of three different models of centrifugal pumps (KSB ETA 50-20, 65-20, and 80-20). The second part of this study was aimed to comparing the real operational conditions of four different pump units, each one with the same pump model (Thebe®, R20, 3500 rpm) being driven a 2-pole electric motor of a different rated power (7.5; 9.2; 11.0, and 15.0 kW). For the rated discharge of the pump´s best efficiency point (28.7 m3 h-1), deviations among modeled values of specific consumption (kWh m-3) and values that were calculated based on the pump rated rotational speed and on the rated electric motor efficiency presented deviations that were lower than 6% of the modeled specific consumption values. However, values of reactive electrical power (kVar) computed based on rated pump speed and rated values of motor efficiency and motor power factor may under-estimate modeled values by up to 30%. The third part of this study aimed at collecting data regarding the operation of a pump (KSB, ETA 80-20) driven by a 4-pole asynchronous motor with a nominal power of 5.52 kW. The values of the parameters of mathematical equations used to represent the curves of electric motor efficiency and electric power factor were adjusted with the application of the inverse method to observed values of rotation speed, active electric power, power factor, current and voltage. Subsequently, the adjusted motor efficiency curve, together with observed values of active electric power and hydraulic power, allowed the parameterization of the pump efficiency curve. The set of models, methods and results presented in this work proved to be useful both for the process of selecting the motor to be used to drive a centrifugal pump and for analyzing the performance of a pumping unit already in operation.