Method and Apparatus for Control of a Synchronous Permanent Magnet Motor, Particularly Over a Long Cable in a Well

1 . A method of controlling an electric power supply electrically connected to a synchronous permanent magnet motor having a plurality of windings comprising:

supplying each of the plurality of windings of the synchronous permanent magnet motor with a root mean square supply voltage applied at a supply frequency via an electrical conductor in a wellbore, wherein the root mean square supply voltage is determined from an initial constant voltage, a constant ratio of voltage over frequency, and the supply frequency; and

determining, prior to supplying each of the plurality of windings with the root mean square supply voltage applied at the supply frequency, the initial constant voltage from one or more characteristics of the synchronous permanent magnet motor and one or more characteristics of the electrical conductor,

wherein the initial constant voltage is a predetermined value that supplies a current to generate a torque that turns the motor from a stationary position,

wherein the constant ratio of voltage over frequency is used to operate the synchronous permanent magnet motor for a start-up period and an operation period without regard to a motor load, and

wherein the electric power supply is controlled without feedback from a rotor position signal.

2 . The method of claim 1 , further comprising determining the constant ratio of voltage over frequency by determining a minimum current value for each frequency within a range of supply frequencies that are associated with a range of speeds for the synchronous permanent magnet motor, wherein the minimum current value for each frequency within the range of supply frequencies corresponds to a locus on a current:voltage curve.

3 . The method of claim 1 , further comprising determining, prior to supplying each winding with the root mean square supply voltage applied at the supply frequency, the constant ratio of voltage over frequency from the one or more characteristics of the synchronous permanent magnet motor and the one or more characteristics of the respective conductor that supplies the root mean square supply voltage to the synchronous permanent magnet motor.

4 . The method of claim 1 , wherein the synchronous permanent magnet motor is arranged to drive an electric submersible pump, wherein the one or more characteristics of the respective conductor used to determine the initial constant voltage V 0 comprises an impedance of the respective conductor, and wherein the impedance of the respective conductor is determined from a length of the respective conductor.

5 . The method of claim 1 , wherein the one or more characteristics of the synchronous permanent magnet motor used to determine the initial constant voltage is selected from the group consisting of: a back-emf of the synchronous permanent magnet; an inductance of the synchronous permanent magnet motor; and a resistance of the synchronous permanent magnet motor.

6 . The method of claim 1 , wherein the supply frequency is determined from a speed of the synchronous permanent magnet motor and the motor pole pairs of the synchronous permanent magnet motor.

7 . A method of controlling an electric power supply to a synchronous permanent magnet motor, comprising:

determining a plurality of system parameters;

determining according to the system parameters a root mean square first voltage supplied by the electric power supply that starts the synchronous permanent magnet motor in rotation;

determining based on the system parameters a ratio between the supply voltage and the supply frequency, wherein the ratio defines, for each of a range of supply frequencies corresponding to a range of speed, a root mean square second voltage at which a current flowing through each of a plurality of windings of the synchronous permanent magnet motor increases with an increase in a voltage corresponding to the root mean square second voltage;

supplying power to each of the plurality of windings of the synchronous permanent magnet motor at the root mean square first voltage to start the synchronous permanent magnet motor from rest; and

increasing both the root mean square supply voltage and the supply frequency and maintaining the ratio and delivering the supply voltage at a desired relationship to the root mean square second voltage until the synchronous permanent magnet motor has reached a desired operating speed.

8 . The method of claim 7 , wherein the ratio between the root mean square supply voltage and the supply frequency is determined from the system parameters to provide a desired rate of acceleration.

9 . The method of claim 7 , wherein the root mean square supply voltage is maintained according to the supply frequency at a value, whereby the root mean square supply voltage V 3 is less than 1.3*the root mean square second voltage.

10 . The method of claim 7 , wherein the root mean square supply voltage is maintained according to the supply frequency at a value whereby the root mean square supply voltage is less than 1.2*the root mean square second voltage.

11 . The method of claim 7 , wherein the root mean square supply voltage is maintained according to the supply frequency at a value whereby the root mean square supply voltage is less than 1.1*the root mean square second voltage.

12 . The method of claim 7 , wherein determining the plurality of system parameters further comprises determining at least one selected from the group consisting of: a characteristic of the load; an impedance of the synchronous permanent magnet motor; a back-emf of the synchronous permanent magnet motor; and an impedance of each of the respective conductors.

13 . The method of claim 7 , wherein the root mean square first voltage and the ratio are determined without sensing a plurality of synchronous permanent magnet motor parameters during operation.

14 . The method of claim 7 , further comprising increasing an acceleration rate of the synchronous permanent magnet motor by increasing the ratio, and wherein the supply frequency is regulated by a speed of the synchronous permanent magnet motor and the motor pole pairs of the synchronous permanent magnet motor.

15 . A system comprising:

a synchronous permanent magnet motor deployed in a wellbore and configured to drive a load, the synchronous permanent magnet motor comprising a plurality of windings; and

a control apparatus operatively coupled to the synchronous permanent magnet motor via one or more electric cables, wherein the control apparatus is configured to:

supply each of the plurality of windings of the synchronous permanent magnet motor with a root mean square supply voltage V applied at a supply frequency f in determined from an initial constant voltage V 0 , a constant ratio of voltage over frequency vf_Ratio, and the supply frequency f;

determine, prior to supplying each of the plurality of windings with the root mean square supply voltage V applied at the supply frequency f, the initial constant voltage V 0 from one or more characteristics of the synchronous permanent magnet motor and one or more characteristics of the corresponding electric cable; and

select a value for the constant ratio of voltage over frequency vf_Ratio that compensates for an acceleration torque of the synchronous permanent magnet motor,

wherein the initial constant voltage V 0 is selected to generate a torque that turns the synchronous permanent magnet motor at a standstill state, and

wherein the initial constant voltage V 0 and the constant ratio of voltage over frequency vf_Ratio is determined without reliance on sensing a plurality of motor parameters corresponding to the synchronous permanent magnet motor in operation.

16 . The system of claim 15 , wherein the synchronous permanent magnet motor is configured to drive an electric submersible pump.

17 . The system of claim 15 , wherein the control apparatus is further configured to increase an acceleration rate of the synchronous permanent magnet motor by increasing the value of the constant ratio of voltage over frequency vf_Ratio.

18 . The system of claim 15 , wherein the selection of the constant ratio of voltage over frequency vf_Ratio is prior to supplying each winding with the root mean square supply voltage V applied at the supply frequency f, and wherein the constant ratio of voltage over frequency vf_Ratio is determined from the at least the impedance of the synchronous permanent magnet motor and the impedance of the corresponding electric cable.

19 . The system of claim 15 , wherein supplying each winding via the electric cables with a root mean square supply voltage V applied at a supply frequency f in relation to an initial constant voltage V 0 , a constant ratio of voltage over frequency vf_Ratio, and the supply frequency f is based upon the expression V=V 0 +vf_Ratio*f.

20 . The system of claim 15 , wherein the control apparatus is further configured to determine the initial constant voltage V 0 from at least a back-emf of the synchronous permanent magnet motor and an inductance of the synchronous permanent magnet motor.

21 . The system of claim 15 , wherein the supply frequency f is related to the speed of the synchronous permanent magnet motor and the motor pole pairs of the synchronous permanent magnet motor.

22 . A method of controlling a synchronous permanent magnet motor comprising:

determining a plurality of system parameters;

determining based on the plurality of system parameters a ratio between a supply voltage and a supply frequency, wherein the ratio provides a desired rate of acceleration determined by the supply voltage;

supplying power to a plurality of windings at a first voltage to start a rotor from rest; and

increasing the supply voltage and the supply frequency and simultaneously maintaining the supply voltage at a predetermined relationship to a second voltage until the synchronous permanent magnet motor has reached a desired operating speed, wherein the second voltage is greater than the first voltage and generates an increasing current with a decrease in the second voltage,

wherein the first voltage and the ratio are determined without a reliance on a position sensing of the rotor.