Method and a System for Operating a Variable Speed Motor

Abstract

The present invention relates to a method of operating a variable speed motor (1) drivingly connected to a multiphase pump (3) via a shaft (4). A power transmission device (20) for transmission of power to the variable speed motor (1) from a power source (2) is provided. A first controller (30) is provided between the power source (2) and the power transmission device (20) for controlling the variable speed motor (1). A speed parameter (n) representative of a motor speed (n.sub.mot) is calculated in the first controller (30). A torque reference (Tref) is received in the first controller (30). A second controller (40) is provided in communication with the first controller (30) for compensation of the effect of the power transmission device (20). The second controller (40) comprises a representation of a compensation torque (T.sub.map) as a function of a mapped torque parameter (T.sub.map) and a mapped speed parameter (n.sub.map). The second controller (40) is arranged to receive the torque reference (T.sub.ref) and the speed parameter (n) from the first controller (30). The compensation torque (T.sub.map) for the speed parameter (n) and torque reference (T.sub.ref) is calculated in the second controller (40) based on the said representation. Then, the first controller (30) is arranged to receive the compensation torque (T.sub.map) from the second controller (40) and the first controller is controlling the variable speed motor (1) based on the received compensation torque (T.sub.map), to keep the difference between the torque reference (Tref) and the shaft torque (T.sub.mot) as small as possible.

Claims

1: A method of operating a variable speed motor which is drivingly connected to a multiphase pump via a shaft, the method comprising: providing a power transmission device for transmission of power to the variable speed motor from a power source; providing a first controller between the power source and the power transmission device for controlling the variable speed motor; calculating, in the first controller, a speed parameter (n) which is representative of a motor speed (n.sub.mot); receiving, in the first controller, a torque reference (Tref); providing a second controller in communication with the first controller, wherein the second controller comprises a representation of a compensation torque (T.sub.map) as a function of a mapped torque parameter (T.sub.map) and a mapped speed parameter (n.sub.map); arranging the second controller to receive the torque reference (T.sub.ref) and the speed parameter (n) from the first controller; calculating, in the second controller, the compensation torque (T.sub.map) for the speed parameter (n) and torque reference (T.sub.ref) based on the said representation; arranging the first controller to receive the compensation torque (T.sub.map) from the second controller; and controlling, based on the received compensation torque (T.sub.map), the variable speed motor to minimize a difference between the torque reference (Tref) and a shaft torque (Tmot) of the motor.

2: The method according to claim 1, further comprising: calculating, in the first controller, a first current parameter (Iq) representative of a first motor current (Iq, mot); calculating, in the first controller, a second current parameter (Id) representative of a second motor current (Id, mot); arranging the second controller to receive the first and second current parameters (Iq, Id) from the first controller; calculating, in the second controller, a first compensation current (Iq) based on the compensation torque (T.sub.map) divided by a torque constant (K.sub.T); calculating, in the second controller, a second compensation current (Id) based on a representation of the second compensation current (Id) as a function of the speed parameter (n); calculating, in the second controller, an estimated motor current (Iest) based on the first and second current parameters (Iq, Id) and the first and second compensation currents (Iq, Id); and outputting the estimated motor current (Iest) from the second controller.

3: The method according to claim 2, wherein the estimated motor current (Iest) is calculated as:
I.sub.est={square root over ((Id+Id).sup.2+(Iq+Iq).sup.2)}

4: The method according to claim 2 or 3, further comprising: calculating, in the second controller, an estimated motor voltage (Uest) based on the first and second motor current parameters (Iq, Id), the speed parameter (n), and a stator resistance (Rs), a stator d-inductance (Xsd), a stator q-inductance (Xsq) and a flux linkage (m) of the variable speed motor.

5: The method according to claim 4, wherein the estimated motor voltage (Uest) is calculated as: $U_{\mathrm{est}}=\sqrt{\begin{array}{c}{\left(\mathrm{Np}*\frac{\mathrm{pi}}{30}*n*.Math..Math.m+R_s\left(I_q+.Math..Math.I_q\right)+X_{\mathrm{sd}}\left(i_d+.Math..Math.I_d\right)\right)}^2+\\ {\left(-R_s\left(i_d+.Math..Math.I_d\right)+X_{\mathrm{sq}}\left(I_q+.Math..Math.I_q\right)\right)}^2\end{array}}$

6: The method according to claim 1, wherein the representation of the compensation torque (Tmap) is obtained by performing the following steps: providing a measurement set-up of the first controller, the power transmission device and the motor; measuring the reference torque (T.sub.ref) of the first controller, the speed (n.sub.mot) of the motor and a motor torque (Tmot) of the motor at different operating points; calculating the representation of the compensation torque (Tmap) as a function of the reference torque (T.sub.ref), the mapped torque parameter (T.sub.map) and the mapped speed parameter (n.sub.map) based on said measurements; and storing the representation compensation torque (Tmap) in the second controller.

7: The method according to claim 2 or 6, wherein the representation of the second compensation current (Id) as a function of the speed parameter (n) is obtained by performing the following steps: using the measurement set-up of the first controller, the power transmission device and the motor; calculating the second compensation current (Id) as the difference between the second motor current (Id,mot) and the second current parameter (Id) as a function of the speed (n.sub.mot) of the motor at different operating points; calculating the representation of the second compensation current (Id) as a function of the speed parameter (n) based on said measurements; and storing the representation of the second compensation current (Id) in the second controller.

8: The method according to claim 1, wherein the torque reference (Tref) is received from a memory in the first controller or from a process controller provided in communication with the first controller.

9: A system for operating a variable speed motor which is drivingly connected to a multiphase pump via a shaft, the system comprising: a power transmission device for transmission of power to the variable speed motor from a power source; a first controller for controlling the variable speed motor, wherein the first controller is provided between the power source and the power transmission device; wherein the first controller is configured to calculate a speed parameter (n) representative of a motor speed (n.sub.mot); wherein the first controller is configured to receive a torque reference (Tref); wherein the system further comprises a second controller in communication with the first controller, the second controller comprising a representation of a compensation torque (T.sub.map) as a function of a mapped torque parameter (T.sub.map) and a mapped speed parameter (n.sub.map); wherein the second controller is arranged to receive the torque reference (Tref) and the speed parameter (n) from the first controller; wherein the second controller is configured to calculate the compensation torque (T.sub.map) for the speed parameter (n) and torque reference (T.sub.ref) based on said representation; wherein the first controller is configured to receive the compensation torque (T.sub.map) from the second controller; and wherein the first controller, based on the received compensation torque (T.sub.map), is configured to control the variable speed motor to minimize a difference between the torque reference (Tref) and the shaft torque (Tmot).

10: The system according to claim 9, wherein: the first controller is configured to calculate a first current parameter (Iq); the first controller is configured to calculate a second current parameter (Id); the second controller is arranged to receive the first and second current parameters (Iq, Id) from the first controller; the second controller is configured to calculate a first compensation current (Iq) based on the compensation torque (T.sub.map) divided by a torque constant (K.sub.T); the second controller is configured to calculate a second compensation current (Id) based on a representation of the second compensation current (Id) as a function of the speed parameter (n); the second controller is configured to calculate an estimated motor current (Iest) based on the first and second current parameters (Iq, Id) and the first and second compensation currents (Iq, Id); and the second controller is configured to output the estimated motor current (Iest).

11: The system according to claim 10, wherein second controller is configured to calculate the estimated motor current (Iest) as:
I.sub.est={square root over ((Id+Id).sup.2+(Iq+Iq).sup.2)}

12: The system according to claim 10 or 11, wherein the second controller is configured to calculate an estimated motor voltage (Uest) based on the first and second motor current parameters (Iq, Id), the speed parameter (n), and a stator resistance (Rs), a stator d-inductance (Xsd), a stator q-inductance (Xsq) and a flux linkage (m) of the variable speed motor, wherein the second controller is configured to calculate the estimated motor voltage (Uest) as: $U_{\mathrm{est}}=\sqrt{\begin{array}{c}{\left(\mathrm{Np}*\frac{\mathrm{pi}}{30}*n*.Math..Math.m+R_s\left(I_q+.Math..Math.I_q\right)+X_{\mathrm{sd}}\left(i_d+.Math..Math.I_d\right)\right)}^2+\\ {\left(-R_s\left(i_d+.Math..Math.I_d\right)+X_{\mathrm{sq}}\left(I_q+.Math..Math.I_q\right)\right)}^2\end{array}}$

Description

DETAILED DESCRIPTION

[0064] Embodiments of the invention will be described in detail with reference to the enclosed drawings, where:

[0065] FIG. 1 illustrates a prior art system for operating a variable speed motor via a power transmission device;

[0066] FIG. 2 illustrates a first embodiment of the system according to the invention;

[0067] FIG. 3 illustrates a second embodiment of the system according to the invention;

[0068] FIG. 4 illustrates schematically the parameters transferred between the first and second controller during the torque compensation;

[0069] FIG. 5 illustrates the representation of the compensation torque as a function of the motor shaft torque and the motor speed;

[0070] FIG. 6 illustrates a comparison of the reference torque, the compensated motor torque and the non-compensated motor torque as a function of the motor speed;

[0071] FIG. 7 illustrates schematically the parameters transferred between the first and second controller during the motor voltage and current estimation;

[0072] FIG. 8 illustrates a representation of the second compensation current as a function of the motor speed;

[0073] FIG. 9 illustrates a representation of the second compensation current by using a curve-fitting tool and shows the calculation formula for the second compensation current;

[0074] FIG. 10 illustrates the computation of the estimated motor voltage based on the estimated motor current;

[0075] FIG. 11 illustrates a comparison of the estimated motor current and the actual motor current;

[0076] FIG. 12 illustrates a comparison of the estimated motor voltage and the actual motor voltage.

[0077] In order to simplify the understanding of the description below, a list of references used in the description and drawing are given below:

LIST OF REFERENCES USED IN THE DESCRIPTION AND CLAIMS

[0078] Parameters Available (i.e. Measured or Computed) in VSD: [0079] speed parameter n [0080] torque reference Tref [0081] first current parameter Iq [0082] second current parameter Id [0083] output voltage Udri to motor [0084] output current Idri to motor [0085] E= m, where =Np*pi/30*n, where Np is the number of pole pairs of the motor

[0086] Physical Parameters of Motor: [0087] motor voltage Umot [0088] first motor current Iq,mot [0089] second motor current Id,mot [0090] motor current Imot=sqrt(Iq,mot.sup.2+Id,mot.sup.2) [0091] motor speed n.sub.mot [0092] shaft torque T.sub.mot [0093] stator resistance Rs [0094] stator d-inductance Xsd [0095] stator q-inductance Xsq [0096] flux linkage m [0097] number of pole pairs Np of the motor

[0098] Parameters in Representation Map: [0099] compensation torque T.sub.map [0100] mapped torque parameter T.sub.map [0101] mapped speed parameter n.sub.map [0102] mapped reference torque T.sub.ref,map

[0103] Parameters Calculated by Second Controller (in Addition to Those in Map) [0104] first compensation current Iq [0105] second compensation current Id [0106] estimated motor current Iest [0107] estimated motor voltage Uest

[0108] It is now referred to FIG. 1. Here, it is shown a prior art system 10 for operating a variable speed motor 1. The motor 1 drivingly connected to a multiphase pump 3 via a shaft 4. The motor 1 is powered by a power source 2, and is controlled by a first controller 30 connected between the motor 1 and the power source 2.

[0109] In addition, a power transmission device 20 is connected between the first controller 30 and the motor 1, for transmission of power from the power source 2 via the first controller 30 to the motor 1. The power transmission device 20 may comprise a step-up transformer 21, a cable 22 and a step-down transformer 23. In alternative embodiments, the power transmission device 20 may comprise only the cable 22.

[0110] The motor 1 is in the present embodiment a variable speed motor 1, as mentioned in the introduction. The first controller 30 is a variable speed drive, for example Siemens Perfect Harmony GH180. This type of controller may control a wide range of different types of motors. The first controller 30 comprises a communication interface (Profibus, Modbus etc) which can communicate the status of the controller itself, the status of the motor, for monitoring industrial processes. The communication interface also offers a possibility to manipulate variables, for example for connection of sensors to the first controller 30 etc. It should be noted that the first controller 30 is considered to be prior art, which will not be described here in detail.

[0111] As indicated in FIG. 1, the power supply 2 supplies an input voltage and current Uin, Iin to the system 10. The first controller 30 outputs a drive current and voltage Udri, Idri for driving the motor 1, while the motor 1 is receiving the motor voltage Umot and motor current Imot. Due to the power transmission device 20, the motor voltage Umot is not equal to the drive voltage Udri and the motor current Imot is not equal to the drive current Idri.

[0112] It is now referred to FIG. 2.

[0113] In this embodiment, the only connection between the first controller 30 and the motor 1 is the power transmission device 20. The only real-time data about the motor 1 being available to the first controller 30 is its output voltage Udri and its output current Idri. Consequently, there are no speed sensors for sensing the speed of the motor, there are no voltage/current sensors for sensing the motor voltage/current Umot/Imot and there are no torque sensor for measuring the motor torque T.sub.mot.

[0114] The reasons for this are that such subsea sensors are expensive and that one or several signal lines would add to the cost of the power transmission device 20. Another reason is that the control of the motor 1 should not be dependent of such sensorsdependency of sensors increases the risk of a shut down of the subsea pump and hence stopping the production of the subsea facility in which the pump is used.

[0115] The first controller 30 is able to calculate a speed parameter n which is representative of the motor speed n.sub.mot, where the motor speed n.sub.mot is the real motor of the motor.

[0116] The reference torque Tref is representative for a value for the actual motor torque Tmot. The second controller aims to improve the accuracy of this representation.

[0117] The first controller is also receiving a torque reference Tref. The main object of the first controller 30 is to control the motor 1 to keep the difference between the torque reference Tref and the real shaft torque Tmot of the motor as small as possible. As is known, the shaft torque Tmot is approximately proportional to the motor current Imot. Hence, since the driving current Idri is not equal to the motor current Imot, it is not possible for the first controller 30 to calculate the motor torque Tmot accurately.

[0118] The torque reference Tref can be a fixed value stored in a memory provided in the first controller 30. Alternatively, the torque reference Tref can be received by the first controller 30 from a process controller (not shown) provided in communication with the first controller 30, for example the process controller of the pump.

[0119] The system 10 further comprises a second controller 40 in communication with the first controller 30. In FIG. 2, it is shown that the second controller 40 is provided as a separate controller external of the first controller 30. The second controller 40 may here be a programmable logic controller (a PLC) connected to the first controller via a data bus (such as Profibus, Modbus etc). In FIG. 3, it is shown that the second controller 40 is provided inside, i.e. as a part of, the first controller 30. The first controller 30 here allows separate control blocks to be added to itself, where these control blocks may communicate with the other control blocks in the first controller 30.

[0120] It is now referred to FIGS. 4 and 5. The purpose of the second controller 40 is to compensate for the effect of the power transmission device 20. This is achieved by providing a representation or so-called representation map of a compensation torque T.sub.map as a function of a mapped torque parameter T.sub.map, a mapped reference torque T.sub.ref,map, and a mapped speed parameter n.sub.map. The representation map of the compensation torque T.sub.map is stored in, and used by, the second controller 40. This will be explained in detail below.

[0121] During operation, the second controller 40 is arranged to receive the torque reference Tref and the speed parameter n from the first controller 30. The speed parameter n, and possibly also the torque reference Tref may be received continuously or approximately continuously (for example every second, every 1/10 second etc).

[0122] The second controller 40 is configured to calculate the compensation torque T.sub.map for the speed parameter n and torque reference T.sub.ref based on the said representation. It should be noted that even if four variables compensation torque T.sub.map, mapped torque parameter T.sub.map, mapped speed parameter n.sub.map, and mapped reference torque T.sub.ref,map are shown in the representation map, there is a direct relation between the compensation torque T.sub.map, the mapped torque parameter T.sub.map, and the mapped reference torque T.sub.ref,map, indicated in FIG. 5 as

T.sub.map=T.sub.ref,mapT.sub.map(1)

[0123] Hence, by knowing a value for Tref (T.sub.ref,map in the map) and n (nmap in the map), it is possible to use the representation to find a value for Tmap and hence also a value for T.sub.map.

[0124] When the compensation torque T.sub.map has been found in the second controller, the first controller 30 is configured to receive the compensation torque T.sub.map from the second controller 40, as indicated in FIG. 4.

[0125] The compensation torque T.sub.map is then used by the first controller to compensate for the power transmission device 20. As mentioned above, the first controller is configured to control the variable speed motor 1 to keep the difference between the torque reference Tref and the shaft torque Tmot as small as possible.

[0126] Again, the first controller 30 does not know the exact motor torque Tmot.

[0127] Tref is representative of Tmot. When the representation map is used, this representation becomes accurate. The torque reference Tref plus the compensation torque Tmap gives an effective torque which encompasses Tmot and the effect of the transmission system.

[0128] In the following, the representation map shown in FIG. 5 will be described more in detail. Initially, a measurement set-up of the first controller 30, the power transmission device 20 and the motor 1 will be provided. The measurement set-up is provided by a medium voltage measurement setup using the GH180 VSD from Siemens, medium-voltage topside and subsea transformers by Siemens, a medium-voltage umbilical from Nexans and a Mark 1 PM motor-pump from FMC-Sulzer.

[0129] Hence, the representation map in FIG. 5 will be achieved by performing measurements on the same equipment or equipment of the same type as the equipment being installed subsea. Now, the reference torque T.sub.ref of the first controller 30, the speed n.sub.mot of the motor 1 and the motor torque Tmot of the motor 1 will be measured at different operating points, i.e. for a variety of relevant values for the reference torque T.sub.ref, the motor speed n.sub.mot and the motor torque Tmot.

[0130] Then, these values are used to calculate the above representation map. In the representation map, the subscript map is used, as some approximations will be performed on the measured values in the representation map. For example, in the present embodiment, a curve fitting algorithm has been used on the measurements in order to compute the three-dimensional function of Tmap (y-axis) as a function of nmap (x-axis) and Tmap/nmap (z-axis), where Tmap=Tref,mapTmap as in equation 1 above.

[0131] In a final step, the representation of the compensation torque Tmap is stored in the second controller (40).

[0132] Accordingly, the measured values for Tref is represented by Tref,map in the representation map, the measured values for Tmot is represented by Tmap in the map and the measured values for n.sub.mot is represented by nmap in the map.

[0133] In an alternative embodiment, the three-dimensional function of Tmap could also have been expressed as a function of nmap and Tmap.

[0134] In yet an alternative embodiment, the representation may be stored as values or coordinates, where approximation calculations are performed in the second controller 40 during operation of the present invention.

[0135] In yet an alternative embodiment, the representation map could be provided as values for n.sub.map along the x-axis, values for Tmap along the z-axis and values for Tref along the y-axis. Here, a value for Tmap can be found directly in a first step during operation based on the received speed parameter n and reference torque Tref received in the second controller 40 from the first controller 30, and in a second step, a value for Tmap can be calculated as the difference between Tref and Tmap.

[0136] In yet an alternative embodiment, the representation can be achieved by using a digital modelling tool (example of such software) instead of using a full measurement set-up. Here a digital model of the power transmission device 20 and the motor 1 is used together with the first controller 30, and the variety of relevant values for the reference torque T.sub.ref, the motor speed n.sub.mot and the motor torque Tmot are achieved by running simulations of this model.

[0137] It is now referred to FIG. 6. Here, curves of the motor torque Tmot without using the present invention (indicated as Tmot (no comp)), the reference torque Tref and the motor torque Tmot with using the present invention have been shown as functions of the motor speeds. Here, it is shown that the curve for the motor torque Tmot with using the present invention is closer to the reference torque Tref than the motor torque Tmot (no comp) achieved when not using the present invention. Consequently, it is shown that a better torque control of the motor is achieved.

[0138] The new torque reference equal to T.sub.ref+T is communicated to the first controller 30. This new torque reference causes a sequence of results: a modified voltageboth magnitude and phaseat the output of the first controller 30, and at the motor terminals and hence modified speed and shaft torque on the motor. The effect is that the pump operates at the desired operating point. Hence, the above described system and method modifies the drive output, so that the effect of the cable and the transformers is compensated for and the desired shaft torque is achieved.

[0139] A second embodiment will now be described. As mentioned in the introduction above, it is also desired to monitor the status of the motor without the use of subsea sensors. Two important parameters of the motor are the motor voltage Umot of the motor terminals and the motor current Imot of the motor terminals. As mentioned above, the output voltage Udri from the first controller to the motor and the output current Idri to the motor are not considered representative for the motor voltage Umot and the motor current Imot due to the effect of the power transmission device 20.

[0140] Below, it is described how an estimated motor current Iest and an estimated motor voltage Uest can be outputted from the second controller 40, where this estimated current/voltage are more accurate than the output current/voltage from the first controller 30.

[0141] As is known for a skilled person, the motor current of such a motor can be represented as vectors in a (d, q) coordinate system with orthogonal components along a d-axis (direct axis) and a q-axis (quadrature axis). The first controller 30 is also using this d-q representation during its operation.

[0142] Hence, the first controller 30 is calculating a first current parameter Iq representative of an actual first motor current Iq,mot. The first motor current Iq,mot is corresponding to the quadrature axis current of the motor.

[0143] The first controller 30 is also calculating a second current parameter Id representative of an actual second motor current (Id,mot). The second motor current Id,mot is corresponding to the direct axis current of the motor.

[0144] The total actual motor current Imot is given by the formula

I.sub.mot={square root over (I.sub.q,mot.sup.2+I.sub.d,mot.sup.2)}(2)

[0145] It is now referred to FIG. 7. Here it is disclosed that the second controller 40 is arranged to receive the first and second current parameters Iq, Id from the first controller 30, together with the speed parameter n and the torque reference Tref.

[0146] During operation of the motor, the second controller 40 is calculating a first compensation current Iq based on the compensation torque T.sub.map divided by a torque constant K.sub.T. In the present embodiment of the invention, the torque constant K.sub.T was calculated as 1.53 Nm/A.

[0147] During operation of the motor, the second controller 40 is also calculating a second compensation current Id based on a representation of the second compensation current Id as a function of the speed parameter n. It has been found that the second compensation current Id varies with the motor speed, but that it is similar for different loads. Hence, a single-variable representation has been found sufficient.

[0148] The representation of the second compensation current Id will be described further in detail below by referring to FIGS. 8 and 9. Also the measurement set-up of the first controller 30, the power transmission device 20 and the motor 1 is used here.

[0149] The first and second motor current parameters Iq, Id are measured in the first controller 30 while the first and second motor currents Iq,mot, Id,mot are calculated at different operating points.

[0150] The first motor current Iq,mot is calculated as Iq,mot=Iq+Iq=Iq+Tmap/K.sub.T. The second motor current Id,mot is calculated according to the above formula (2) as Id,mot=sqrt(Imot.sup.2Iq,mot.sup.2)

[0151] Then, the second compensation current Id is calculated as the difference between the second motor current Id,mot and the second current parameter Id as a discrete function of the speed n.sub.mot of the motor 1. This discrete function Id(n) is disclosed in FIG. 8. Here it is also shown that the second compensation Id is almost identical for two different loads on the motor 1.

[0152] Also here, a curve fitting algorithm has been used on the discrete measurements to provide a continuous function Id(n), shown with a dashed curve Id(n) in FIG. 9. In the present embodiment, the function Id(n) is given as

Id(n)=5e-8*n.sup.27.46e-4*n+0.75(3)

[0153] Of course, this function will be dependent on the measurement set-up of the first controller 30, the power transmission device 20 and the motor 1, i.e. it must be computed for each application.

[0154] The above function Id(n) is the representation of the second compensation current Id as a function of the speed parameter n. This representation is stored in the second controller 40 and is used by the second controller 40 during the operation of the motor 1.

[0155] Based on the first and second current parameters Iq, Id and the first and second compensation currents Iq, Id, the estimated motor current Iest can be calculated and outputted from the second controller (40) for example for monitoring purposes.

[0156] The estimated motor current Iest is then calculated as:

I.sub.est={square root over ((Id+Id).sup.2+(Iq+Iq).sup.2)}(4)

[0157] It is now referred to FIG. 10, where a known vector diagram of a motor 1 is shown, where the motor voltage Umot can be expressed by first and second motor currents Id, Iq, a voltage E and physical properties such as the stator resistance Rs, the stator d-inductance Xsd, the stator q-inductance Xsq and the flux linkage m of the motor. Here, the voltage E= m, where =Np*pi/30*n, where Np is the number of pole pairs of the motor and n is the motor speed.

[0158] Consequently, by using the first and second compensated currents Iq and Id, the estimated motor voltage Uest may be calculated as:

[00003]$\begin{array}{cc}{U}_{\mathrm{est}}=\sqrt{\begin{array}{c}{\left(\mathrm{Np}*\frac{\mathrm{pi}}{30}*n*.Math..Math.m+R_s\left(I_q+.Math..Math.I_q\right)+X_{\mathrm{sd}}\left(i_d+.Math..Math.I_d\right)\right)}^2+\\ {\left(-R_s\left(i_d+.Math..Math.I_d\right)+X_{\mathrm{sq}}\left(I_q+.Math..Math.I_q\right)\right)}^2\end{array}}& \left(5\right)\end{array}$

[0159] This formula is also stored in the second controller 40 and is used by the second controller 40 during the operation of the motor 1.

[0160] It is now referred to FIGS. 11 and 12. In FIG. 11 it is shown that the curve for the estimated motor current Iest is close to the actual motor current Imot. In FIG. 12, it is shown that the curve for the estimated motor voltage Uest is close to the actual motor voltage Umot.