IT201900015617A1 - METHOD FOR SENSORLESS ESTIMATING THE POSITION OF THE ROTOR AND THE ANGULAR SPEED OF THE ROTOR OF A RELUCTANCE SYNCHRONOUS MACHINE - Google Patents

Description

METHOD FOR SENSORLESS ESTIMATING THE POSITION OF THE

ROTOR AND THE ANGULAR SPEED OF THE ROTOR OF A MACHINE

SYNCHRONOUS RELUCTANCE

Technical field

The present invention generally relates to the sensorless control of a synchronous reluctance machine. In particular, the present invention relates to a method for estimating the position of the rotor and the angular velocity of the rotor of a synchronous reluctance machine.

State of the art

As known, sensorless control consists of a closed loop that controls a synchronous reluctance machine without using a rotor position encoder to synchronize the control reference system with the rotor phase angle or to evaluate the angular velocity of the rotor. same.

The angular position of the rotor and the angular velocity of the rotor are estimated by the digital controller by manipulating electrical quantities and machine parameters via software in real time. Said real-time software is usually called "observer" and includes a flow observer and an angular position observer.

As known, the methods for estimating the flux and angular position of a rotor depend on the stator resistance. The direct measurement of the stator resistance is possible when the machine is not in operation (cold machine); however, the value of the stator resistance when the machine is in use ("warmed-up machine") differs considerably from the result obtained on a cold machine.

In particular, the stator resistance varies with the temperature of the machine during operation, which causes an inaccurate estimate of the internal voltage of the machine and, essentially, errors in the estimates of flux and angular position.

In a sensorless machine control system, the angular position observer is strongly coupled with the flow observer. In particular, the susceptibility of the flow observer to internal voltage estimation errors leads the angular position observer to instability.

To stem this problem, several methods have been evaluated:

● a stator resistance observer for salient synchronous machines is proposed in M. Hinkkanen, T. Tuovinen, L. Harnefors, and J. Luomi, "A Combined Position and Stator-Resistance Observer for Salient PMSM Drives: Design and Stability Analysis" , IEEE Transactions on Power Electronics, vol. 27, no.2, pp. 601–609, 2012;

● a sliding mode observer is developed in D. Liang, J. Li, and R. Qu, "Sensorless Control of Permanent Magnet Synchronous Machine Based on Second-Order Sliding-Mode Observer With Online Resistance Estimation", IEEE Transactions on Industry Applications , vol. 53, no. 4, pp. 3672–3682, 2017 .; And

● a recursive least squares approach is employed to identify resistance online in Y. Inoue, Y. Kawaguchi, S. Morimoto, and M. Sanada, "Performance Improvement of Sensorless IPMSM Drives in a Low-Speed Region Using Online Parameter Identification" , IEEE Transactions on Industry Applications, vol. 47, no.2, pp. 798–804, 2011.

Summary of the invention

The Applicant has perceived that the sensorless control systems of the machines are subject to variations in the stator resistance or require a further online adaptation of the resistance.

In particular, the Applicant has perceived that the known flux and angular position observers have some drawbacks due to errors in estimating the internal voltage due to the variation of the stator resistance or to a non-ideal compensation of the inverter voltage error. . As stated above, several online fitting techniques have been proposed, in addition to the flow and angular position estimation scheme, which require extra processing and calibration effort.

In the light of the above, the Applicant has faced the problem of providing a method for estimating the position of the rotor and / or the angular speed of the rotor of a synchronous reluctance machine which overcomes the above drawbacks.

According to a first aspect, the present invention relates to a method for the sensorless estimation of a position error signal for a synchronous reluctance machine, said synchronous reluctance machine comprising a stator and a rotor, said method comprising:

- receiving an observed chained flux of said stator;

- receiving an estimate based on the current model of the linked flux of said stator;

- selecting a first projection vector in which a position error calculated by means of said first projection vector is within a band of one electrical degree under conditions of maximum torque per ampere; - calculating said position error signal as a function of this observed linked flux, of this estimate based on the current model of the linked flux and of this first projection vector.

According to a second aspect, the present invention relates to a method for the sensorless estimation of at least one of the angular position of the rotor and the angular speed of the rotor of a synchronous reluctance machine comprising:

- calculating said position error signal according to embodiments of the present invention;

- calculating at least one of the observed angular position of the rotor and the observed angular velocity of the rotor as a function of said position error signal.

According to a third aspect, the present invention relates to a control system for a synchronous reluctance machine, said synchronous reluctance machine comprising a rotor and a stator, said control system comprising:

- a hybrid flow observer configured for:

- calculating an observed chained flux of said stator on the basis of estimated values of electrical quantities associated with said synchronous reluctance machine;

- calculating an estimate based on the current model of the chained flux of said stator on the basis of detected values of electrical quantities; - an error evaluation block configured for:

- receiving from said hybrid flow observer said observed linked flow and said estimate based on the current model of the linked flow;

- selecting a first projection vector in which a position error calculated by means of said first projection vector is within a band of one electrical degree under conditions of maximum torque per ampere;

- calculating a position error signal as a function of said observed linked flux, said estimate based on the current model of the linked flux and said first projection vector;

- a block for estimating position and angular velocity, configured to calculate an observed angular position of the rotor and / or an observed angular velocity of the rotor as a function of said position error signal; wherein said control system is configured to drive said synchronous reluctance machine based on said observed angular position of the rotor and / or said observed angular velocity of the rotor.

Brief description of the figures

The present invention will become clearer thanks to the following detailed description, provided by way of example and not of limitation, to be read with reference to the attached drawings, in which:

Figure 1 shows a block diagram illustrating a control system of a synchronous reluctance machine according to the present invention;

Figure 2 shows a block diagram illustrating a hybrid flow observer;

Figure 3 shows a block diagram of an error evaluation block according to the present invention.

Detailed description of preferred embodiments of the invention In the following, the vectors in a rotating reference system, associated with the rotor, are indicated with the subscript dq. The vectors in a stationary reference system, associated with the stator, are denoted by the subscript αβ. Finally, abc indicates the phase quantities of the machine.

In the following, the expression "estimated quantity" indicates a quantity calculated by means of a numerical model; an estimated quantity is represented by the apex ̂. This also includes the observed chain flow vector, because an observed quantity is also an estimated quantity.

Figure 1 shows a block diagram of a control system 100 controlling a synchronous reluctance machine 5 (also referred to as "SyR machine" below), for example the SyR machine may be a SyR motor. The synchronous reluctance machine 5 comprises a rotor and a stator.

Preferably, the control system 100 is a sensorless control system. Preferably, the control system 100 comprises a proportional integral speed controller 1, a maximum torque per ampere regulator (MTPA controller) 2, a current vector regulator control) 3, a voltage source inverter 4.

As shown in Figure 1, the target angular velocity of the rotor ω <∗> r is set to drive the rotor at an effective angular velocity ω ,.

Preferably, the MTPA 2 regulator, which implements a maximum torque per ampere regulation strategy, selects a target current vector

(in an estimated rotor reference system that satisfies the condition of maximum torque per ampere at the target angular velocity of the rotor ω <∗> r.

Note that the MTPA regulator is known, as described in:

- L. Xu, X. Xu, T. A. Lipo and D. W. Novotny, "Vector control of a synchronous reluctance machine including saturation and iron loss", in IEEE Transactions on Industry Applications, vol. 27, no.5, pp. 977-985 , Sept.-Oct.1991.

- S. Morimoto, M. Sanada and Y. Takeda, "Wide-speed operation of interior permanent magnet synchronous machines with high-performance current regulator", in IEEE Transactions on Industry Applications, vol. 30, no. 4, pp.

The current regulator 3 receives the target current vector from the MTPA regulator 2 and generates a target voltage vector The target voltage vector is converted in the stator reference system in a first conversion and transformation block 3a, which generates an estimated voltage vector (the control voltage is also used as an estimate of the voltage used by the flow observer). Preferably, the first conversion and transformation block 3a is an inverse Park transformation.

The reference voltage vector is sent in input, after a further conversion and transformation block 3b, to the voltage generator inverter 4 which generates a three-phase machine power supply voltage. Preferably, the further conversion and transformation block 3b is a transformation of Reverse Clarke. The transformations of Clark and Park are known and will not be described below. The three-phase machine power supply voltage is supplied in input to the SyR 5 machine to drive it.

During operation, the rotor and / or stator quantities, such as rotor angular position and / or rotor angular velocity, are estimated and used by the control system 100 to drive the SyR 5 machine.

A mathematical model of the SyR 5 machine is provided below.

The model of the machine is expressed in the reference system integral with the rotor

(i.e. a rotating reference system). In the absence of a

rotor position (sensorless control), the rotation reference system used is the estimated one

For example, the SyR 5 machine voltage equation is defined as follows:

[1]

In which the Lap variable is the existence of the stator at a nominal temperature of the machine, (the apex T indicates a vector or a "transposed" matrix) is the concatenated flux vector of the stator, is the voltage vector of the stator is the stator current vector is the estimated angular velocity <of the rotor and ࡶ is the orthogonal rotation matrix>

The concatenated flux of the stator and its time derivative can be expressed on the basis of an incremental inductance matrix, an apparent inductance matrix ࡸ and a position error in which θ is the actual rotor position (i.e. the correct angular position of the rotor) , is the estimated angular position of the rotor, as shown in [2a] and [2b]:

<[2a]>

[2b]

in which the components of the inductance matrices are:

[3]

where they respectively respect the incremental inductance along the main axis d and the quadrature axis q, while it represents the cross-saturation term.

The electromagnetic torque is given by:

[4]

where N is the number of pole pairs.

Preferably, the SyR 5 machine is driven in a condition of maximum torque per ampere (also referred to as "MTPA condition").

The analytical expression of the MTPA condition can be derived from equation [4], differentiating with respect to a current angle γ in which the angle

current is obtaining the following expression:

<[5]>

By incorporating the inductances defined in [3], a the expression [5] simplifies to:

[6]

Preferably, the control system 100 comprises a second conversion and transformation block 4a. For example, the second conversion and transformation block 4a is a Clarke transformation block configured to convert three-phase current measurements acquired by means of current transducers on the power supply line of the machine, into the stator reference system, obtaining an effective current of stator ࢏஑ஒ in which Preferably, as shown in Figure 1, a third conversion and transformation block 4b converts the measured three-phase current into the estimated reference system of the rotor

to use it as feedback for closed loop current vector control. Preferably, the third conversion and transformation block 4b is a Park transformation.

According to embodiments of the present invention, as shown in Figure 1, the control system 100 comprises an observer block 6.

The observer block 6, preferably, receives as input the angular position <estimated rotor> <the estimated voltage vector> <and the effective stator current>

respectively provided by the first conversion and transformation block 3a e

from the second conversion and transformation block 4a - and calculates an estimate based on the current model of the chained flux of the stator and an observed chained flux of the stator

Preferably, the observer block 6 is a Hybrid Flux Observer (HFO) 6.

In particular, HFO 6 is configured for:

- calculate an observed chained flux of said stator on the basis of estimated values of electrical quantities, for example the estimated voltage vector

associated with said synchronous reluctance machine 5;

- calculate an estimate based on the current model of the chained flux of the stator of said stator based on measured values of said electrical quantities, for example the effective stator current

Preferably, the HFO 6 in the stator reference system is defined by:

<[7]>

In which

[8]

Where is a gain matrix is the observed chained flux of the stator in the stator reference system, is the time derivative of the observed chained flux of the stator in the stator reference system,

is the estimated voltage vector in the stator reference system, is la

effective stator current e is the estimated inductance. Referring to equation [8], ઩ is the lookup table of the flow map of the SyR 5 machine. Preferably, in the estimated reference system of the rotor, HFO 6 is defined by:

Note that, for equivalence holds

As shown in Figure 2, HFO 6 computes - as a function of the actual stator current of the estimated voltage vector and the estimated angular position of the rotor - the model-based estimate of the stator linked flux and the observed stator linked flux for by means of equations [7] [8] [9] [10].

As shown in Figure 3, the current model-based estimation of the stator linked flux and the observed stator linked flux

they are sent as input to an error evaluation block 11.

The error evaluation block 11 calculates a position error signal

Preferably, the position error signal is defined as the projection of the difference between the observed linked stator flux and the current model estimate of the stator linked flux

For example, the position error signal is defined as:

As described in i. and further developed in ii.

the. M. Hinkkanen, S. E. Saarakkala, H. A. A. Awan, E. Molsa, and T. Tuovinen, “Observers for Sensorless Synchronous Machine Drives: Framework for Design and Analysis”, IEEE Transactions on Industry Applications, p. 1, 2018; and

ii. Varatharajan and G. Pellegrino, “Sensorless Control of Synchronous Reluctance Machine Drives: Improved Modeling and Analysis beyond Active Flux”, in Electric Machines and Drives Conference (IEMDC), IEEE International, 2019.

Where is a first projection vector.

According to embodiments of the present invention, the first projection vector is expressed as:

Where is the angular velocity of the rotor, it is an auxiliary chained flux vector.

In the following, the dynamics of the flow error and the dynamics of the position error are expressed with reference to stationary operating conditions. Quantities in stationary operating points are indicated with the subscript 0.

Where is the first projection vector in stationary operating conditionar <is the angular velocity of the rotor in such stationary operating condition,>

is an auxiliary linked flow vector in this operating condition

stationary.

<As shown in Figure 1 and Figure 3, an observed angular velocity of the rotor> and / or an observed angular position of the rotor are calculated as a function of the position error signal Preferably, the observed angular velocity of the rotor and the observed angular position of the rotor are calculated from a position and angular velocity estimation block 12.

For example, the observed angular velocity of the rotor and the observed angular position of the rotor are calculated as:

In cu is the observed angular velocity of the rotor, and are the proportional gain and integral gain, respectively, and is the integral output of the proportional-integral regulator of the phase locked loop, and is the speed error angle of the rotor

Considering equation [13] and a stator flux error defined as:

Where is the stator flux error, is the actual stator flux vector is the observed stator flux vector, the flux error dynamics can be represented as:

In which

And considering the invariance of the incremental inductance, the following expression is obtained:

<By means of the above expression, an auxiliary chained stream vector> defined as:

Therefore, the dynamics of the flow error ݏࣅ <෨> ௗ ෢ ௤ simplifies to:

therefore, the position error signal is defined as:

If the system is stable, the condition holds in stationary conditions. By manipulating equations [20] and [21], the position error in stationary conditions due to an error of the stator resistance is expressed as follows:

By substituting the expression of the proposed projection vector [13] in equation [22], the position error under stationary conditions can be expressed as:

Equation [23] and equation [6] show that, as long as the MTPA condition is met, the rotor position error calculated by means of the first projection vector is not substantially affected by the resistance error of the stator

According to the mathematical model, the position error, due to the error of the stator resistance calculated by means of said first projection vector, is substantially zero under MTPA conditions.

In other words, the measured position error calculated by means of said first projection vector is within a band of one electrical degree under MTPA conditions.

In particular, the aforementioned measured position error is due to, for example, white noise and / or inaccuracies in the flow maps.

Note that, said band of an electrical degree under MTPA conditions is proportional to:

- accuracy of the magnetic model of the machine under examination; And

- deviations from the trajectory of MTPA.

Furthermore, advantageously, a fundamental component of the voltage error due to the dead time of the converter is in phase with the effective stator current.

In particular, the voltage error caused by the converter dead time is <reflected in the stator resistance error> <In other words, the position error>

calculated by means of said first projection vector is independent

from the voltage error due to the dead time of the converter.

As shown in Figure 1, the observed angular position of the rotor and / or the observed angular velocity of the rotor is / are used to drive the SyR 5 machine.

For example, a conventional phase-locked loop with proportional integral regulator is used to drive the position error signal to zero. The control of a synchronous reluctance machine by means of observed quantities is well known and will not be discussed below.

Note that the MTPA condition, imposed by the MTPA 2 regulator, deviates from the maximum torque values per ampere for small loads due to the imposition of a fundamental excitation current Another case of deviation from the MTPA condition is the so-called weakening of Flux weakening, but at high speeds, the effects of stator resistance error are negligible. If the SyR 5 machine is not in the MTPA condition, a position error occurs in stationary conditions calculated as described above in [23]. Nonetheless, control remains stable.

Preferably, when the MTPA condition is not met, a stator resistance match is provided.

Preferably, the error evaluation block 11 calculates a resistance error signal

Preferably, the resistance error signal is defined as:

Where is a second projection vector.

Preferably, the control system comprises a resistance calculation block 13. The resistance calculation block 13 calculates an observed stator resistance as a function of said resistance error signal

For example, the estimated stator resistance 'is calculated as:

In which it is a constant.

Preferably, the resistance error signal is used to implement a software matching of the stator resistance of the estimated stator resistance. The software adaptation of the stator resistance compensates for the voltage error caused by the converter dead time even in the absence of compensation for this error. For example, inaccurate dead time compensation causes a constant voltage error, independent of operating point, currents or speed. For example, considering an experiment where a dead time error of 1 μs causes a constant voltage error of about 6 V. if the amplitude of the current operating point is 1 A, the software adaptation of the stator resistance value increases the rated resistance by 6 Ω to compensate for the voltage error of 6V. Conversely, at a higher load, if the operating current is 2 A, the estimated resistance will be 3 Ω higher than the real resistance.

Preferably, the position error signal and the resistance error signal are independently estimated. Preferably, the second projection vector is a vector orthogonal to the first projection vector Even more preferably, the second projection vector is a vector orthogonal to the first projection vector and is scaled in proportion to the working point to have a constant loop gain .

For example, a cumulative error vector is defined as

Where is a projection vector matrix.

As described, the present invention provides important advantages. In particular, the present invention provides the following advantages:

- No need for online adaptation of the resistance in MTPA condition: this simplifies the calibration and execution of the control algorithm;

- The use of the first projection vector in the control system 100 makes the control inherently stable at low speed;

- The position error calculated by means of said first projection vector is independent of the voltage error caused by the dead time of the converter, so that a precise MTPA control of the torque is possible, with consequent maximization of efficiency;

- The second vector of projection compensates for variations in resistance when the machine is deliberately controlled outside the conditions of MTPA; - If the second projection vector is used, the identification of the converter voltage error can be omitted: this simplifies the preliminary phase of commissioning the electric drive.

Claims (12)

CLAIMS 1. A method for sensorless estimation of a position error signal for a reluctance synchronous machine (5), said synchronous reluctance machine (5) comprising a stator and a rotor, said method comprising: - receiving an observed chained flux of said stator; - receiving an estimate based on the current model of the linked flux of said stator; - selecting a first projection vector in which a position error calculated by means of said first projection vector is within a band of one electrical degree in the MTPA condition; - calculating said position error signal (ϵ ஘) as a function of said observed linked flux of said estimate based on the current model of the linked flux and said first projection vector The method according to claim 1 wherein said position error signal is calculated as the projection of a difference between said concatenated flow observed and said estimate based on the current model of the chained flux on said first projection vector The method according to any one of the preceding claims in which the position error calculated by means of the first projection vector n is substantially influenced by a resistance error of the stat in MTPA condition. The method according to any one of the preceding claims wherein said method further comprises: - selecting a second projection vector, said second projection vector, being orthogonal to said first projection vector - calculating a resistance error signal as a function of said linked flux observed said estimate based on the current model of the linked flux and said second projection vector The method according to claim 4 wherein said resistance error signal is calculated as the projection of a difference between said chained flux observed and said estimate based on the current model of the chained flux on said second projection vector 6. A method for sensorless estimation of at least one of the observed angular position of the rotor and the observed angular velocity of the rotor of a synchronous reluctance machine (5) comprising: - calculating said position error signal according to any one of claims 1 to 3; - calculate at least one of the observed angular position of the rotor and the observed angular velocity of the rotor as a function of said position error signal The method according to claim 6 wherein said method further comprises: - calculating said resistance error signal (߳ ୰) according to claim 4 or 5; - calculating an observed resistance of the stator as a function of said resistance error signal 8. A control system (100) for a reluctance synchronous machine (5), said reluctance synchronous machine (5) comprising a rotor and a stator, said control system (100) comprising: - a hybrid flow observer (5) configured for: - calculating an observed chained flux of said stator on the basis of estimated values of electrical quantities associated with said synchronous reluctance machine (5); - calculate an estimate based on the current model of the flux chained on the basis of measured values of electrical quantities; - an error evaluation block (11) configured for: - receiving said observed linked flow and said estimate based on the current model of the linked flow from said hybrid flow observer (5); - selecting a first projection vector in which a position error calculated by means of said first projection vector is within a band of one electrical degree under MTPA conditions; - calculating a position error signal as a function of said linked flux observed said estimate based on the current model of the linked flux and said first projection vector - a position and angular velocity estimation block (12), configured to calculate an observed angular position of the rotor and / or an observed angular velocity of the rotor as a function of said position error signal wherein said control system (100) is configured to drive said synchronous reluctance machine (5) based on said observed angular position of the rotor and / or said observed angular velocity of the rotor The control system (100) according to claim 8 wherein said control system (100) is configured to drive said synchronous reluctance machine (5) in a condition of maximum torque per ampere. The control system (100) according to claim 8 or 9 wherein said error evaluation block (11) is configured for: - selecting a second projection vector, said second projection vector, being orthogonal to said first projection vector - calculate a resistance error signal as a function of said chained flux observing said estimate based on the current model of the chained flux hec second projection vector the control system (100) comprising a resistance calculation block (13) configured to calculate an observed stator resistance as a function of said resistance error signal The control system (100) according to claim 10 wherein said control system (100) comprises a stator resistance matching software block based on said observed stator resistance The control system (100) according to any one of claims 8 to 11 wherein, said error evaluation block (11) is configured to select said first projection vector in which said position error calculated by means of the first vector projection is not substantially affected by a stator resistance error in the MTPA condition.