A method and apparatus for determining a fluid level and/or output flow during operation of a centrifugal pump, are provided, which may be used for production of gas and/or oil from a well, and include a vector feedback model to derive values of torque and speed from signals indicative of instantaneous current and voltage drawn by the pump motor, a pump model which derives values of the fluid flow rate and the head pressure for the pump from torque and speed inputs, a pumping system model that derives, from the estimated values of the pump operating parameters, an estimated value of fluid level and other pumping system parameters. Controllers responsive to the estimated values of the pumping system parameters control the pump to maintain fluid level at the pump input, near an optimum level, or within a safe operating range and/or output flow from the pump.