Combined electrical and mechanical model of electric submersible pumps

The electric submersible pump unit consists of a pump powered by a medium-voltage three-phase induction motor. The power transmission system is integrated with the riser pipes. Starting the pump causes heavy dynamic stresses on the motor shaft and the mechanical connection between pump (impellers) and shaft. The motor and its load will generate transient torque pulsations that may be damaging to shaft and coupling, particularly to the key grooves. System models are developed to predict the electrical and mechanical conditions on starting. Different torsional models with certain types of nonlinearities, combined with different motor models have been examined to find combinations that give the best results. The motor models applied include saturation in the main flux path and the leakage flux paths, as well as rotor deep bar effect. It has been shown how the pump parameters, material coefficients, design dimensions, and number of impellers affect the dynamic stresses. The aim has been to optimize the design with respect to the transient stresses. The simulations reveal that the resulting shaft torque, caused by excitation from resonant frequencies during the acceleration period, amount to high values that may result in excessive overloading of shafts, couplings, and key grooves. Maximum torque is, as expected, strongly dependent on the shaft dimensions. Certain shaft diameters may cause resonance and, thereby, heavy torsional amplitudes. It has been shown how the model can be a tool in the struggle to find the optimum shaft diameter.