Method for operating a compressor

A rolling piston compressor comprising:

• a casing defining a cylindrical cavity defining a central axis, a suction port, and a discharge port;
• an electric motor comprising a drive shaft, the drive shaft extending along the central axis;
• a rolling piston positioned within the cylindrical cavity, the rolling piston being eccentrically mounted on the drive shaft;
• a sliding vane that extends from the casing toward the rolling piston to maintain contact with the rolling piston as it rotates about the central axis, the sliding vane and the rolling piston dividing the cylindrical cavity into a suction volume in fluid communication with the suction port and a compression volume in fluid communication with the discharge port;
• and
• a controller operably coupled to the electric motor, the controller configured to:
• obtain a mechanical angle of the rolling piston;
• determine an amplitude of a fundamental harmonic of a periodic load torque exerted on the rolling piston as the rolling piston rotates through each revolution based at least in part on the mechanical angle and a harmonic series representation of the periodic load torque;
• obtain an angular speed of the rolling piston;
• obtain a speed error by subtracting the angular speed from a reference angular speed;
• determine a DC component of the periodic load torque based at least in part on the speed error and a closed loop feedback control algorithm;
• calculate an electromagnetic torque using the DC component of the periodic load torque and the amplitude of the fundamental harmonic of the periodic load torque;
• and
• operate the electric motor to generate the calculated electromagnetic torque on the rolling piston,
• wherein calculating the electromagnetic torque using the DC component of the periodic load torque and the fundamental harmonic of the periodic load torque comprises using the following equation:
• Tem={circumflex over (T)}0+{circumflex over (T)}1 cos(θ−{circumflex over (ϕ)}1)
• where:
• Tem=the electromagnetic torque applied by the electric motor;
• {circumflex over (T)}0=the DC component of the periodic load torque;
• {circumflex over (T)}1 the amplitude of the fundamental harmonic of the periodic load torque;
• θ=the mechanical angle of the rolling piston;
• and
• {circumflex over (ϕ)}1=a phase of the periodic load torque.

A method for operating a compressor comprising a rotor driven by an electric motor, the method comprising:

• obtaining a mechanical angle of the rotor;
• determining an amplitude of a fundamental harmonic of a periodic load torque exerted on the rotor as the rotor rotates through each revolution based at least in part on the mechanical angle and a harmonic series representation of the periodic load torque;
• obtaining an angular speed of the rotor;
• obtaining a speed error by subtracting the angular speed from a reference angular speed;
• determining a DC component of the periodic load torque based at least in part on the speed error and a closed loop feedback control algorithm;
• calculating an electromagnetic torque using the DC component of the periodic load torque and the amplitude of the fundamental harmonic of the periodic load torque;
• and
• operating the electric motor to generate the calculated electromagnetic torque on the rotor,
• wherein determining the amplitude of the fundamental harmonic of the periodic load torque comprises using the following equation:
• {circumflex over (T)}1=∫k1{tilde over (ω)}sin(θ−{circumflex over (ϕ)}1)
• where:
• {circumflex over (T)}1=the amplitude of the fundamental harmonic of a periodic load torque;
• k1=a real, positive estimator gain value;
• {tilde over (ω)}=the speed error;
• θ=the mechanical angle of the rotor;
• and
• {circumflex over (ϕ)}1=a phase of the periodic load torque.