Electrical submersible pump control

A method for controlling an electrical submersible pump (ESP), comprising:

• providing an electrical drive signal to power the ESP;
• calculating a speed of a shaft of an electric motor of the ESP based on a frequency induced by rotation of the electric motor detected in a current of the electrical drive signal;
• calculating a density of a fluid in the ESP based on the speed;
• determining a torque in the ESP based on the current of the electrical drive signal, a voltage of the electrical drive signal, a resistance of a conductor that electrically couples the ESP to drive circuitry, and a resistance of a stator of the ESP;
• and
• adjusting the speed of the electric motor based on at least one of the speed of the shaft, the density of the fluid, the torque in the ESP, or a flow rate of the fluid in the ESP.

A non-transitory computer-readable medium encoded with instructions that, when executed by a processor, cause operations comprising:

• receiving a measurement of a current of an electrical drive signal powering an electrical submersible pump (ESP);
• receiving a measurement of a voltage of the electrical drive signal;
• calculating a speed of a shaft of an electric motor of the ESP based on a frequency detected in the current, wherein the frequency is induced in the current by rotation of the electric motor;
• calculating:
• a density of a fluid in the ESP based on the speed of the shaft,
• a flow rate of the fluid in the ESP based on the speed of the shaft, and
• a torque in the ESP based on the current, the voltage, a resistance of a conductor of the ESP, and a resistance of a stator of the ESP;
• and
• adjusting the speed of the ESP based on at least one of the speed of the shaft, the density of the fluid, the torque in the ESP, or the flow rate of the fluid in the ESP.