Motor control system and method with flux linkage estimation error compensation
09979332 ยท 2018-05-22
Assignee
Inventors
Cpc classification
H02P23/14
ELECTRICITY
H02P1/52
ELECTRICITY
International classification
H02P23/12
ELECTRICITY
H02P21/14
ELECTRICITY
H02P1/52
ELECTRICITY
H02P23/14
ELECTRICITY
Abstract
A chiller system includes a compressor configured to circulate a refrigerant between an evaporator and a condenser in a closed refrigerant loop and a synchronous motor configured to drive the compressor. The motor includes a stator winding and a rotor. The chiller system includes a controller configured to estimate a flux linkage of the rotor and generate a control signal for the motor based on the estimated flux linkage. Estimating the flux linkage includes applying a voltage of the stator winding to a transfer function having an error correction variable, using a first value of the error correction variable in the transfer function to obtain convergence of the flux linkage over an initial motor starting interval, and using a second value of the error correction variable after the initial motor starting interval to reduce an error in estimating the flux linkage.
Claims
1. A chiller system comprising: a compressor configured to circulate a refrigerant between an evaporator and a condenser in a closed refrigerant loop; a synchronous motor configured to drive the compressor, the motor comprising a stator winding and a rotor; and a controller configured to estimate a flux linkage of the rotor by: generating an initial estimate of the flux linkage by applying a voltage of the stator winding to a low pass filter comprising a filter variable; adjusting a magnitude of the initial estimate to compensate for a flux linkage magnitude error resulting from the filter variable; adjusting a phase angle of the initial estimate to compensate for a flux linkage phase angle error resulting from the filter variable; and estimating a phase angle of the rotor by evaluating /, where is an adjusted alpha component of the flux linkage and is an adjusted beta component of the flux linkage; wherein the controller is configured to provide a control signal to the motor based on the estimated flux linkage.
2. The chiller system of claim 1, wherein the controller is configured to adjust the magnitude of the initial estimate by calculating an adjusted magnitude of the flux linkage using a speed of the rotor and the filter variable.
3. The chiller system of claim 2, wherein the controller is configured to calculate the adjusted magnitude of the flux linkage by evaluating
4. The chiller system of claim 1, wherein the controller is configured to adjust the phase angle of the initial estimate by: identifying an alpha component of the initial estimate and a beta component of the initial estimate; calculating the adjusted alpha component of the flux linkage using a speed of the rotor and the filter variable; and calculating the adjusted beta component of the flux linkage using the speed of the rotor and the filter variable.
5. The chiller system of claim 4, wherein the controller is configured to calculate the adjusted alpha component of the flux linkage by evaluating
6. The chiller system of claim 4, wherein the controller is configured to calculate the adjusted beta component of the flux linkage by evaluating
7. The chiller system of claim 1, wherein the controller is configured to adjust the magnitude of the initial estimate and the phase angle of the initial estimate by calculating the adjusted alpha and beta components of the flux linkage using a combined magnitude and phase angle adjustment technique.
8. The chiller system of claim 7, wherein the controller is configured to calculate the adjusted alpha component of the flux linkage by evaluating
9. The chiller system of claim 7, wherein the controller is configured to calculate the adjusted beta component of the flux linkage by evaluating
10. The chiller system of claim 1, wherein the controller is configured to: determine a position of the rotor based on the estimated flux linkage; and generate the control signal for the motor based on the position of the rotor.
11. A method for controlling a synchronous motor having a stator winding and a rotor, the method comprising: generating an initial estimate of a flux linkage of the rotor by applying a voltage of the stator winding to a low pass filter comprising a filter variable; adjusting a magnitude of the initial estimate to compensate for a flux linkage magnitude error resulting from the filter variable; adjusting a phase angle of the initial estimate to compensate for a flux linkage phase angle error resulting from the filter variable; using the adjusted magnitude and the adjusted phase angle to estimate the flux linkage; estimating a phase angle of the rotor by evaluating /, where is an adjusted alpha component of the flux linkage and is an adjusted beta component of the flux linkage; providing a control signal to the motor based on the estimated flux linkage; and using the control signal to operate the motor by adjusting a speed or position of the motor based on the control signal.
12. The method of claim 11, wherein adjusting the magnitude of the initial estimate comprises calculating an adjusted magnitude of the flux linkage using a speed of the rotor and the filter variable.
13. The method of claim 12, wherein calculating the adjusted magnitude of the flux linkage comprises evaluating
14. The method of claim 11, wherein the adjusting the phase angle of the initial estimate comprises: identifying an alpha component of the initial estimate and a beta component of the initial estimate; calculating the adjusted alpha component of the flux linkage using a speed of the rotor and the filter variable; and calculating the adjusted beta component of the flux linkage using the speed of the rotor and the filter variable.
15. The method of claim 14, wherein calculating the adjusted alpha component of the flux linkage comprises evaluating
16. The method of claim 14, wherein calculating the adjusted beta component of the flux linkage comprises evaluating
17. The method of claim 11, wherein adjusting the magnitude of the initial estimate and the phase angle of the initial estimate comprises calculating the adjusted alpha and beta components of the flux linkage using a combined magnitude and phase angle adjustment technique.
18. The method of claim 17, wherein calculating the adjusted alpha component of the flux linkage comprises evaluating
19. The method of claim 17, wherein calculating the adjusted beta component of the flux linkage comprises evaluating
20. The method of claim 11, further comprising: determining a position of the rotor based on the estimated flux linkage; and generating the control signal for the motor based on the position of the rotor.
Description
BRIEF DESCRIPTION OF THE DRAWINGS
(1)
(2)
(3)
(4)
(5)
(6)
(7)
DETAILED DESCRIPTION
(8)
(9)
(10) Motor 50 used with compressor 32 can be powered by a variable speed drive (DC) power source. Motor 50 can include any type of PMSM that can be powered by a VSD or directly from an AC or DC power source.
(11)
(12) In an exemplary embodiment, the rectifier/converter 222 may be a three-phase pulse width modulated boost rectifier having insulated gate bipolar transistors to provide a boosted DC voltage to the DC link 224 to obtain a maximum RMS output voltage from VSD 52 greater than the input voltage to VSD 52. Alternately, the converter 222 may be a passive diode or thyristor rectifier without voltage-boosting capability.
(13) VSD 52 can provide a variable magnitude output voltage and variable frequency to motor 50, to permit effective operation of motor 50 in response to a particular load conditions. Control panel 40 can provide control signals to VSD 52 to operate the VSD 52 and motor 50 at appropriate operational settings for the particular sensor readings received by control panel 40. For example, control panel 40 can provide control signals to VSD 52 to adjust the output voltage and output frequency provided by VSD 52 in response to changing conditions in vapor compression system 14, i.e., control panel 40 can provide instructions to increase or decrease the output voltage and output frequency provided by VSD 52 in response to increasing or decreasing load conditions on compressor 32. The estimated rotor phase angle .sub.r and rotor frequency .sub.r, of motor 50, as described in more detail below, may be input to the control panel for feedback control of the position and rotational frequency of motor 50.
(14) Compressor 32 compresses a refrigerant vapor and delivers the vapor to condenser 34 through a discharge passage. In one exemplary embodiment, compressor 32 can be a centrifugal compressor having one or more compression stages. The refrigerant vapor delivered by compressor 32 to condenser 34 transfers heat to a fluid, for example, water or air. The refrigerant vapor condenses to a refrigerant liquid in condenser 34 as a result of the heat transfer with the fluid. The liquid refrigerant from condenser 34 flows through expansion device 36 to evaporator 38. A hot gas bypass valve (HGBV) 134 may be connected in a separate line extending from compressor discharge to compressor suction. In the exemplary embodiment shown in
(15) The liquid refrigerant delivered to evaporator 38 absorbs heat from another fluid, which may or may not be the same type of fluid used for condenser 34, and undergoes a phase change to a refrigerant vapor. In the exemplary embodiment shown in
(16) The control method described with respect to
(17) Referring to
(18) Permanent magnets 84 may be positioned or arranged to provide multiple pole arrangements or configurations, for example 2-pole or 4-pole (see, e.g.,
(19) Referring next to
(20)
(21) wherein:
(22) s represents an S-domain integration operation of the low-pass filter; and
(23) a=the error correction variable for the low-pass filter.
(24) In one embodiment, the low pass filter represented by the transfer function may be implemented in software. Alternately, the low pass filter may be implemented in hardware components, e.g., integrated circuit, ASIC, or R-L-C circuit. By increasing the value of variable in Equation 1 the convergence of the estimated flux can occur in a shorter time interval, but the error in the estimated flux will be greater. By decreasing the value of the variable convergence can occur more slowly, but with a smaller estimation error. For example, when rotor speed is 94.25 rad/s, a different a value yields different angle errors.
(25) a=2 sin =0.9997749 angle error=1.2167
(26) a=4 sin =0.99910058 angle error=2.43025
(27) a=6 sin =0.99797971 angle error=3.64265
(28) a=8 sin =0.99641682 angle error=4.851787
(29) a=10 sin =0.99441813 angle error=6.056610
(30) An open loop estimation method 100 is shown in
(31) An -axis current value i.sub.a, representing the phase a stator, or armature, current, is provided to a current prediction model 104 which predicts the current used in the estimation. The output i.sub.a of current prediction model 104 is multiplied by stator resistance r.sub.s at block 106 to generate an estimated drop-off voltage on stator winding. The output of block 106 is then subtracted from -axis phase a voltage v.sub.a in summation block 102, and the output of block 102 is applied to transfer function block 108, represented by the transfer function of Equation 1. In transfer function block 108, filter variable a is introduced to achieve a minimum error at different speed ranges within a required convergence time. The output of block 108 is then compensated at block 110 to reduce or remove the error introduced by a in block 108. The output of block 110 is combined at summation block 112 with an output of block 114. Block 114 represents the stator mutual inductance L.sub.m, which is the value by which the input predicted current i.sub.a is multiplied to generate the output of block 114. The output of block 114 is subtracted from the error compensated air gap flux linkage, or output of block 110, at block 112. The difference of blocks 110, 114 is the output of block 112, representing the estimated rotor flux linkage in -axis. Then the rotor phase angle .sub.r is estimated by angle calculation block 116 using the estimated rotor flux linkage from both and -axis. The estimated rotor phase angle .sub.r 120 is applied to block 118, and the time domain derivative of the estimated rotor phase angle .sub.r 120 is generated at the output of block 117 as the rotor frequency .sub.r.
(32) More precise flux estimation and control of PMSM 86 may be achieved by adjusting the value of variable a at selected intervals. For example, the value of a may be changed as a function of the rotor speed wherein the value of a is greater initially, i.e., upon starting PMSM 86 to obtain a faster convergence at the beginning of the estimation. After the convergence, a smaller value of a is applied to reduce the error in the flux estimation. In addition, in an exemplary embodiment, the value of a may be transitioned gradually, or ramped down from the higher initial value of a to the lower value of a, to provide improved system stability.
(33) An exemplary embodiment of the method is described as follows:
(34) ramp down a:
(35) If (.sub.r>1200 and .sub.r<1500)
(36) a=5(.sub.r1200)*0.01
(37) If (.sub.r>1500)
(38) a=2
(39) (a=error correction variable)
(40) A compensation method is disclosed to reduce the estimation error due to a. The estimated flux linkage includes two components, a real component alpha () and an imaginary component beta (). Alpha and beta components of the estimated flux linkage may be used to compensate for the magnitude error due to the error correction variable . The expressions of the magnitude compensation are given by the following equations:
(41)
(42) wherein:
(43) a is the error correction variable and
(44) .sub.r is the rotor speed.
(45) The second step is for the phase angle correction, in which the flux linkage complex variable includes two components, a real component alpha and an imaginary component beta, is used. Alpha and beta components of this complex variable may be used to compensate for the phase error due to the error correction variable . The expressions of the complex variable used for phase angle correction is given as:
(46)
(47) If the magnitude compensation and the phase compensation are combined, the expressions of the compensation are given by the following equations:
(48)
(49) wherein:
(50) f.sub. and f.sub. are the alpha and beta components of the flux linkage after compensation;
(51) f.sub. and f.sub. are the alpha components of the flux linkage before compensation; and
(52) .sub.r is the rotor speed.
(53) Since the ratio of the sampling frequency to the fundamental frequency is low, a relatively long delay is unavoidable without increasing the sampling frequency. Increasing the sampling frequency generally increases the cost of a control system. A current prediction method can be employed to predict the current to eliminate the effect of the sampling delay, without the need for increasing the sampling frequency. For high speed and ultra high speed applications, the sampling number per cycle becomes greatly reduced. To reduce the estimation error, the current at the N.sup.th sampling interval may be used to predict the current at the next (N+1).sup.th sampling interval. The predicted current may then be used to reduce the error in the flux linkage estimation. The current prediction is based on the PMSM machine model.
(54) An exemplary embodiment of the method is described.
(55) The prediction method is based on the q-d reference:
(56) Predicted q axis current is given as:
(57)
(58) predicted d-axis current is given as:
(59)
(60) wherein,
(61) V.sub.qs.sup.N and V.sub.ds.sup.N are the q- and d-axis voltages at the Nth sampling interval;
(62) i.sub.qs.sup.N and i.sub.ds.sup.N are the q- and d-axis currents at the Nth sampling interval;
(63) i.sub.qs.sup.N and i.sub.ds.sup.N+1 are the predicted q- and d-axis currents at the (N+1).sup.th sampling interval;
(64) .sub.qs.sup.N and .sub.ds.sup.N are the q- and d-axis flux linkages at the N.sup.th sampling interval;
(65) .sub.r is the rotor speed.
(66) While the foregoing describes a control system and method for controlling a sensorless PMSM, the control system and method for estimating an angle position and speed of a motor may be applied to other types of sensorless, synchronous motors, e.g., induction-type motors, and such synchronous motors are considered to be within the scope of control system herein described and claimed.
(67) It should be understood that the application is not limited to the details or methodology set forth in the following description or illustrated in the figures. It should also be understood that the phraseology and terminology employed herein is for the purpose of description only and should not be regarded as limiting.
(68) While the exemplary embodiments illustrated in the figures and described herein are presently preferred, it should be understood that these embodiments are offered by way of example only. Accordingly, the present application is not limited to a particular embodiment, but extends to various modifications. The order or sequence of any processes or method steps may be varied or re-sequenced according to alternative embodiments.
(69) The present application contemplates methods, systems and program products on any machine-readable media for accomplishing its operations. The embodiments of the present application may be implemented using an existing computer processors, or by a special purpose computer processor for an appropriate system, incorporated for this or another purpose or by a hardwired system.
(70) It is important to note that the construction and arrangement of the flux estimation method for PMSM control as shown in the various exemplary embodiments is illustrative only. Although only a few embodiments have been described in detail in this disclosure, those who review this disclosure will readily appreciate that many modifications are possible (e.g., variations in sizes, dimensions, structures, shapes and proportions of the various elements, values of parameters, mounting arrangements, use of materials, colors, orientations, etc.) without materially departing from the novel teachings and advantages of the subject matter recited in the application. For example, elements shown as integrally formed may be constructed of multiple parts or elements, the position of elements may be reversed or otherwise varied, and the nature or number of discrete elements or positions may be altered or varied. Accordingly, all such modifications are intended to be included within the scope of the present application. The order or sequence of any process or method steps may be varied or re-sequenced according to alternative embodiments. Other substitutions, modifications, changes and omissions may be made in the design, operating conditions and arrangement of the exemplary embodiments without departing from the scope of the present application.
(71) As noted above, embodiments within the scope of the present application include program products comprising machine-readable media for carrying or having machine-executable instructions or data structures stored thereon. Such machine-readable media can be any available media that can be accessed by a general purpose or special purpose computer or other machine with a processor. By way of example, such machine-readable media can comprise RAM, ROM, EPROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium which can be used to carry or store desired program code in the form of machine-executable instructions or data structures and which can be accessed by a general purpose or special purpose computer or other machine with a processor. When information is transferred or provided over a network or another communications connection (either hardwired, wireless, or a combination of hardwired or wireless) to a machine, the machine properly views the connection as a machine-readable medium. Thus, any such connection is properly termed a machine-readable medium. Combinations of the above are also included within the scope of machine-readable media. Machine-executable instructions comprise, for example, instructions and data which cause a general purpose computer, special purpose computer, or special purpose processing machines to perform a certain function or group of functions.
(72) It should be noted that although the figures herein may show a specific order of method steps, it is understood that the order of these steps may differ from what is depicted. Also two or more steps may be performed concurrently or with partial concurrence. Such variation will depend on the software and hardware systems chosen and on designer choice. It is understood that all such variations are within the scope of the application. Likewise, software implementations could be accomplished with standard programming techniques with rule based logic and other logic to accomplish the various connection steps, processing steps, comparison steps and decision steps.