METHOD AND DEVICE FOR LOAD-FREE DETERMINATION OF LOAD-DEPARATE POSITION ASSIGNMENT PARAMETERS OF A SYNCHRONOUS MACHINE WITHOUT A POSITION SENSOR

Description

1 Stand der Technik

[0001] Methods that enable efficient control of a synchronous machine without a position sensor (often referred to as "sensorless" or "sensorless" control) are divided into 2 classes: 1. Fundamental wave methods [1] [2] [3] evaluate the voltage induced by motion, provide very good signal characteristics at medium and high speeds, but fail at lower speeds, especially when stationary. For operation under load (saturation), fundamental wave methods require current-dependent parameterization of the inductance [4] [5]. 2. Anisotropy-based methods [6] [7] [8] evaluate the position dependence of the machine's inductance, for which no speed is necessary, but exhibit several problems and hurdles that explain why many applications still require a position sensor (with its disadvantages). For operation under load (saturation), anisotropy-based methods require current-dependent parameterization of the anisotropy shift [9]

[10]

[11]

[12] .

[0002] Sensorless control of synchronous machines across the entire speed range is implemented by a combination of methods from both classes [8]

[13] .

[0003] To determine the current-dependent behavior of inductance and anisotropy shift, magnetic simulation data can be used

[14]

[15] , which show deviations from reality and require access to the machine design. Alternatively, these behaviors can be measured on a test bench setup with a load machine and position sensor

[16]

[17] , but this can be too complex or even impossible in practice if an unknown synchronous machine is to be connected in the field.

[0004] For connecting an unknown synchronous machine, there are approaches for initial parameter identification that neglect current dependence

[18]

[19] , which become inaccurate / unstable during operation under increased load. Other approaches additionally identify the load dependence by means of short-term macroscopic excitation

[20]

[21]

[22] , but this inevitably involves torque peaks that are not acceptable in every application and, moreover, distort the identification results when the rotor is not blocked.

[0005] The change in inductance (when current changes) can alternatively be tracked using online identification methods

[23]

[24]

[25]

[26] , which, however, have a time delay due to their nature (a factor of 10-1000 slower than the actual change) and are therefore only accurate / stable in the steady state.

[0006] For the anisotropy shift, there are also approaches for identification

[27]

[28] in operation, which, however, require a correctly (nonlinearly) parameterized fundamental wave model and only provide good results if operating points in a certain speed range with as many different torque values ​​as possible have been traversed over a sufficient period of time, which cannot be assumed in all applications.

[0007] The publication "Impact of bridge-saturation on anisotropy-based initial rotor polarity detection of interior permanent-magnet synchronous machines" by Chen Lei et al., 2016 19th International Conference on Electrical Machines and Systems (ICEMS), The Institute of Electrical Engineers of Japan, November 13, 2016, pages 1-6, XP033054070, presents a method for anisotropy-based determination of rotor polarity in permanent magnet synchronous machines. Since anisotropy-based methods are electrically periodic over 180° and thus ambiguous within a full electrical revolution, they require a one-time additional polarity check during each start-up process. This publication shows that, for certain machine types, the larger current response does not occur in the positive d-direction, as previously assumed, but actually in the negative d-direction.This polarity check therefore yields a binary value, "positive or negative," which relates to the sign of the d-axis. This binary value is not usable in subsequent sensorless operation and provides no information regarding the saturation-related relationship between flux and rotor position or between anisotropy and rotor position. 2 Basic Elements

[0008] The invention is defined in method claim 1 and apparatus claim 20. Preferred embodiments are defined in the dependent claims.

[0009] The following is a general explanation, also concerning optional embodiments of the invention. The following will be shown: Fig. 1 Rotor cross-sections with surface-mounted (left) and buried (right) permanent magnets, soft magnetic material hatched, permanent flux direction indicated by triangle. Fig. 2 Qualitative representation of the current-flux relationship in the d-direction with differential inductances. Fig. 3 Qualitative representation of the current-flux relationship in the q-direction with differential and absolute inductances. Fig. 4 Current vector summation in rotor coordinates and anisotropy shift for geometrically isotropic machines. Fig. 5 Qualitative curve of the anisotropy magnitude versus the magnitude of the saturation current. Fig. 6 Current vector summation in stator coordinates and resulting dependence of the magnitude and angle of the saturation current on the rotor position. Fig. 7a-f Curves calculated from measurement data for 3 geometrically isotropic (SPM) and 3 geometrically anisotropic (IPM) machines. PM synchronous machines, each plotted against the normalized load iq / the prosecutors, each above: the curve of the absolute inductance L q ( iq ) / L qq 0 measured (solid line) and according to saturation assumption (dashed line), each vertically centered: the course of the resulting fundamental wave angular error. θ̂ r - θ r in [° el] without (dotted) and with (dashed) saturation assumption, and below each: the course of the anisotropy-based estimation error θ̂ r - θ r In electrical degrees without (dotted) and with (dashed) saturation assumptions. The vertical dotted line marks the rated current according to the nameplate. Fig. 8a-c Experimental results of the closed sensorless control loop with SPM3, plotted against time in seconds; the estimated rotor position is shown at the top. θ r in [rad], each vertically centered q-current in estimated rotor coordinates i q̂ / the prosecutors and below each is the anisotropy-based estimation error. θ̂ r - θ rin [° el]; Fig. 8a shows operation without saturation assumptions, Fig. 8b with assumptions about anisotropy shift and Fig. 8c with assumptions for unambiguous rotor position assignment (RPA).

[0010] It should be noted that the figures only show exemplary arrangements of machines or progressions of physical quantities, and that the method described here or its embodiments are not limited to the representations in the figures.

[0011] The term "machine" is used here to mean an "electric machine," i.e., an electric motor or an electric generator. Fundamental wave methods utilize the general voltage equation of the machine. u s s = R s i s s + dψ s s dt ψ s s = T θ r ψ s r i s r 2 = cos θ r − sin θ r sin θ r cos θ r L d i d i q i d + ψ pm L q i d i q i q 3 from which, knowing the parameters resistance R s and absolute q-inductance L q The rotor position can be determined from the time profiles of current and voltage at medium and high rotational speeds. θ rcan be calculated, e.g. using the following calculation rule θ r = ∠ ∫ u s s − R s i s s dt − L q i s s .

[0012] These are the so-called absolute inductances. L d and L q defined as the quotient of flux linkage (flux for short) and current, and characterized by the fact that they only carry one axis reference (e.g. q) in the subscript. L d = ψ d − ψ pm i d L q = ψ q i q .

[0013] Anisotropy-based methods utilize the high-frequency relationship u hf s = T θ r L dd L dq L dq L qq T − θ r Δi hf s Δt 7 = T θ a L Σ − L Δ 0 0 L Σ + L Δ T − θ a Δi hf s Δt 8 which, for example, according to

[29] ,

[30] or

[31] , yields the anisotropy angle without knowledge of the parameters. θ a can be calculated. Knowing the load-dependent anisotropy shift. θ ar i s r The measured angle of anisotropy can be determined during operation. θ̃ a a rotor position estimate θ̂ assign r θ ^ r = θ ˜ a − θ ar i s r .

[0014] These are the so-called differential inductances. L dd , L dq and L qq defined as the derivative of the flux according to the stream and carry two axis references in the subscript L dd = dψ d di d L qq = dψ q di q L dq = dψ d di q .

[0015] The flow is usually non-linear across the current, which is why the values L dd , L dq and L qq are current-dependent. The specific value of a current-dependent quantity at zero current (so-called value in the unenergized state) is indicated by the additional variable index 0 – in the case of differential inductances, for example. L dd 0 and L qq 0 .

[0016] However, anisotropy methods often use voltage injection and evaluate the current response, which is why the inverse differential inductance is relevant, often simplified as admittance Y. Δi hf s Δt = T θ r Y dd Y dq Y dq Y qq T − θ r u hf s 13 = T θ a Y Σ − Y Δ 0 0 Y Σ + Y Δ T − θ a u hf s 14 Y dd = di d dψ d Y qq = di q dψ q Y dq = di d dψ q .

[0017] This includes the so-called anisotropy amount. Y Δ half the difference between the direction-dependent largest and smallest admittance Y Δ = Y dd − Y qq 2 2 + Y dq 2 and indicates how strong the directional dependence of the RF current response is.

[0018] Directional dependence (Greek: anisotropy) always means: dependence on the direction in which the current-voltage relationship is considered (not the rotor position) over which different differential inductance values ​​are effective (acting in the d-direction). L dd or Y dd , in the q direction L qq or Y qq etc).

[0019] In the unenergized state, the coupling component Y dq approximately zero, which simplifies (18) to Y Δ 0 = Y dd 0 − Y qq 0 2 .

[0020] The anisotropy angle θ aThe direction of the smallest differential inductance, and consequently the largest admittance, is given by the angle 0°. Shifted by ±90° (electrically), the direction of the largest differential inductance, and consequently the smallest admittance, is found. The anisotropy angle can therefore be calculated equivalently from both quantities, for example, as follows. θ a = 1 2 atan 2 Y αβ + Y βα , Y αα − Y ββ 20 = 1 2 atan 2 L αβ + L βα , L ββ − L αα . 21

[0021] Furthermore, within the framework of the embodiments described here, two classes are distinguished with regard to the rotor topology of synchronous machines: 1. geometrically isotropic Synchronous machines have a rotor cross-section in which the quantity and shape of the soft magnetic material do not differ between the various magnetic paths of the phase windings, so their magnetic anisotropy is solely due to the fact that the exciting element (e.g., permanent magnet or field winding) saturates the soft magnetic material locally (i.e., directionally). The magnetic anisotropy of these machines in the unenergized state is usually smaller, namely L dd 0 − L qq 0 L dd 0 + L qq 0 < 20 % 2. geometric anisotropic Synchronous machines exhibit a rotor cross-section in which the quantity and / or shape of the soft magnetic material differs between the various magnetic paths of the phase windings, creating an additional anisotropic component. The magnetic anisotropy of these machines in the unenergized state is therefore usually greater, namely L dd 0 − L qq 0 L dd 0 + L qq 0 > 20 % .

[0022] Fig. 1The left side shows a typical example of a geometrically isotropic machine, and the right side a typical example of a geometrically anisotropic machine. Only the hatched areas have high magnetic conductivity, and due to the geometry of the right-hand cross-section, this results in a significantly increased inductance in the q-direction.

[0023] Regardless of the actual geometry, most machines can be assigned to their corresponding class based on their clamping behavior if the initially found anisotropy is compared against the threshold of 20%. 3 Sättigungsannahmen

[0024] The following describes a method for determining load-dependent position assignment parameters of a synchronous machine without a position sensor. The synchronous machine is driven by pulsed terminal voltages, from which the inductance and admittance are calculated in conjunction with the measured current response. Alternatively, the smallest and largest load-free differential inductances can be determined ( L dd 0 and L qq 0) may also be known. From the smallest no-load and largest no-load differential inductance ( L dd 0 and L qq 0 ) and the short-circuit current ( the prosecutors ) the magnetic saturation behavior under load of the absolute inductance and the magnetic anisotropy of the synchronous machine is predicted and compensated in position sensor-less control operation and / or used for position assignment.

[0025] In some embodiments, a load-free differential inductance corresponds to the derivative of the flux linkage with respect to the current (see (10)-(12)) at the operating point with zero current.

[0026] In some embodiments, the smallest and largest differential inductances are the direction-dependent smallest and largest differential inductance values ​​of an operating point, where the direction dependence corresponds to the magnetic anisotropy.

[0027] If the smallest no-load and the largest no-load differential inductance L dd 0 and L qqSince the values ​​are unknown, they can be calculated from the current-voltage relationship by electrically exciting the machines. The excitation can be, for example, test pulses, sinusoidal voltage waveforms, or a discrete-time voltage injection pattern. Various approaches are readily available for the calculation, which typically relate the voltage excitation to the current response (e.g., current amplitude or current difference per time interval). For example, in anisotropy methods with a discrete-time injection pattern

[31]

[32] , the anisotropy magnitude can be calculated. Y Δ and the isotropic component Y Σ may be internal calculation parameters, from whose values ​​and the isotropic component at zero current are derived. Y Δ0 and Y Σ0 the inductances L dd 0 and L qq for example, they can be calculated as follows L dd 0 = 1 Y Σ 0 + Y Δ 0 L qq 0 = 1 Y Σ 0 − Y Δ 0 .

[0028] However, any other rules for calculating differential inductance can also be used to determine the values. L dd 0 and L qq to provide 0 as a basis for the procedure and / or embodiments described in this document.

[0029] Although differential inductances are only directly effective for anisotropy methods, in some embodiments they are also used for parameterizing fundamental wave methods.

[0030] The short-circuit current the prosecutors is generally an equivalent current amount to that produced by the permanent magnet (PM), which, for example, ▪ impressed in the negative d-direction to cancel out the flow chain ψ s s = 0 leads to, or ▪ occurs when the shaft is driven quickly (e.g., rated speed) with a short circuit of the terminals (zero voltage), or ▪ is determined according to a principle physically equivalent to the aforementioned methods, or ▪ is determined using one of the following calculation rules within the framework of the presented saturation assumption.

[0031] However, any other rules for calculating a current equivalent to the excitation by the PM can also be used to determine the value of the short-circuit current. the prosecutors to provide for the method and / or embodiments described in this document.

[0032] The basic idea of ​​the saturation assumption and all its embodiments is that, in the unenergized state, the machine is saturated to a certain degree in the d-direction by the PM and unsaturated in the q-direction, and that the same degree of saturation will be present in the q-direction when the short-circuit current in the q-direction the prosecutors is imprinted. Specifically, some embodiments assume that the q-axis (direction perpendicular to the PM) assumes the same magnetic behavior as the d-axis (direction of the PM) in the unenergized state when the short-circuit current in the q-direction ( iq = the prosecutors ) is imprinted.

[0033] Fig. 2 qualitatively shows an exemplary current-flux relationship in the d-direction, which exhibits a curved shape due to the saturation of the soft magnetic material. Without d-current id At = 0, the flow is equivalent to the PM flow. ψ d = ψ pmand the slope (indicated by the dashed tangent with slope triangle) equals the differential d-inductance in the unenergized state. L dd = L dd 0 . At id = - the prosecutors The river has been extinguished ψ d = 0, the iron is therefore unsaturated and, according to the saturation assumption, the slope of the flux curve is equal to the differential q-inductance in the uncurrent state. L dd = L qq 0 .

[0034] When connecting an unknown synchronous machine, the PM flux can ψ pm Typically calculated from the nameplate data (e.g., 0.471 times the rated torque divided by the rated current and number of pole pairs) or alternatively determined by rotating the shaft (e.g., from the ratio of induced voltage to rotational speed).

[0035] Based on this data ψ pm , L dd 0 and L qqUnder the saturation assumption, the short-circuit current can now be 0. the prosecutors They are calculated as follows. Fig. 2 It is evident that for d-currents between - the prosecutors ≤ id ≤ 0 all slope values L dd between L dd 0 ≤ L dd ≤ L qq 0 lie, where the exact transition from L qq 0 towards L dd This may vary depending on the machine.

[0036] In some embodiments, the short-circuit current ( the prosecutors ) as the quotient of the PM flow chain ( ψ pm ) divided by a combination of the smallest no-load and the largest no-load differential inductance ( L dd 0 and L qq ). This calculation can be performed, for example, as follows. i pm = ψ pm k d L dd 0 + k q L qq 0 , where by means of kd and kq The influence of the respective inductance can be weighted.

[0037] In some embodiments, the combination corresponds to averaging, for example with the coefficients k d = k q = 1 2 For example, it is assumed that the mean increase equals the mean of the extreme increases. L dd ¯ = L dd 0 + L qq 2 , so that the prosecutors as follows i pm = 2 ψ pm L dd 0 + L qq 0 .

[0038] Alternatively, the short-circuit current can be the prosecutors for example, it can be determined by a short-circuit test. Regardless of its determination, the short-circuit current the prosecutors a key parameter for the following calculations of parameters for fundamental wave methods in section 3.1 and for anisotropy methods in sections 3.2 and 3.3.

[0039] The presented calculation approaches for the parameters of anisotropy methods are preferably applicable to geometrically isotropic machine types. Therefore, in some embodiments, compensation and / or use for position assignment of the anisotropy saturation calculations only takes place if the difference between the largest and smallest load-free differential inductances is less than 20% of their sum. 3.1 Grundwelleninduktivität

[0040] One parameter of fundamental wave methods, which is stored as a current-dependent variable to account for saturation, is, for example, the absolute inductance in the q-direction. L q .

[0041] In some embodiments, the absolute inductance L q as a parameter for evaluating the induced voltage, calculated such that, starting from its value valid at zero current, the largest unloaded differential inductance ( L qq 0 ) ,as the current increases, it decreases so that when the short-circuit current is reached ( the prosecutors ) the mean of the smallest and largest unloaded differential inductances ( L dd 0 and L qq 0 ) is the same.

[0042] Fig. 3 shows an exemplary current-flux relationship in the q-direction, which for a geometrically isotropic machine is the same as that of the d-direction - with the difference that the curves are shifted horizontally relative to each other in such a way that the q-curve is point-symmetric through the origin and the d-curve through - the prosecutors proceeds.

[0043] According to the above saturation assumption, to which the following exemplary implementations are subject, the following is achieved: ψ q = ψ pm , if iq = the prosecutors , where the increase also began L qq = L dd 0 is the absolute inductance. L q However, it carries one of L qqdifferent values, as illustrated by the dotted lines.

[0044] To obtain from the (possibly injection-based measured) differential inductances L dd 0 and L qq 0 on the curve of the absolute inductance L q ( iq To conclude, for example, it is initially assumed that the course of the differential inductance L qq ( iq linear and symmetrical L qq ( iq ) = L qq ( -iq ) is L qq i q = L qq 0 + L dd 0 − L qq 0 i q i pm .

[0045] According to (11) ψ q ( iq ) for example via integration ψ q i q = ∫ 0 i q L qq i q di q 27 = L qq i q + L dd 0 − L qq 0 2 i pm i q i q 28 and according to (6) the course L q ( iq ) for example by division ψ q / iq L q i q = L qq 0 + L dd 0 − L qq 0 2 i pm i q 29 = L qq 0 + m L i q 30 m L = L dd 0 2 − L qq 0 2 4 ψ pm , where m L expressed using (25). For iq = the prosecutors results (29) L q = L dd 0 + L qq 0 2 and is therefore consistent with the calculation of the short-circuit current (25). For iq = 0 results in (29) L q = L qq 0, which corresponds to the fact that for zero current the differential and the absolute inductance are equal.

[0046] For example, with this linear law (29) or (30)-(31) it is possible to determine, based on the initially measurable and / or calculable parameters L dd 0 , L qq 0 and ψ pm the saturation of the central fundamental wave parameter L q can be approximated. This approximation works well for geometrically isotropic machines. For geometrically anisotropic machines, this approximation is subject to errors in the conservative range – i.e., the saturation is undercompensated – because the saturation behavior of the soft magnetic material in the q-direction cannot be derived from the d-direction, but it is still applicable.

[0047] Compensation according to this approximation is better than no compensation at all. Therefore, the law for the current dependence of the fundamental inductance (29) or (30)-(31) can be applied to all PM machines – for geometrically isotropic as well as geometrically anisotropic ones. 3.2 Anisotropieverschiebung

[0048] The anisotropy of geometrically isotropic machines is caused by local saturation of the soft magnetic material, which is maximal in the PM direction when the machine is not energized. In this state, the anisotropy is aligned with the rotor and approximately rotates with it. When a torque-generating current is applied, a relative shift between the rotor and the anisotropy occurs because the current, directed perpendicular to the PM, influences the saturation state.

[0049] In some embodiments, a saturation current vector is calculated by vectorial addition of the phase current vector and the short-circuit current vector, where the short-circuit current vector has the magnitude of the short-circuit current and is directed towards the PM.

[0050] In the following exemplary description of the embodiment, the saturation current vector is defined by i sat s , the phase current vector through i s s and the short-circuit current vector through i pm s represented - each expressed in stator coordinates (superscript) s The same vectors represented in rotor coordinates are i sat r , i s r and i pm r .

[0051] The short-circuit current i pm r and the current in the stator winding i s r They now overlap, for example, linearly, and the sum yields the saturation current. i sat r i sat r = i pm r + i s r 32 = i pm + i d i q , 33 whose direction determines the saturation maximum and thus aligns the anisotropy. This results in the so-called anisotropy shift. θ ar , i.e., the shift of the anisotropy angle relative to the rotor (or the anisotropy angle in rotor coordinates), according to the orientation of the saturation current in rotor coordinates ∠ i sat r θ ar = θ a − θ r 34 = atan 2 i satq , i satd = ∠ i sat r . 35

[0052] In some embodiments, the anisotropy shift is thus θ ar The parameter for evaluating the magnetic anisotropy is calculated in such a way that it increases with increasing phase current, such that the assumed orientation of the anisotropy corresponds to the direction of the saturation current vector.

[0053] Fig. 4 shows, for example, how the short-circuit current i pm r and the stator current i s r in rotor coordinates are added vectorially, from which the saturation current is obtained. i sat r results in the orientation in rotor coordinates of geometrically isotropic machines of the anisotropy shift. θ ar is the same.

[0054] This displacement angle θ ar For example, during operation under load, the measured anisotropy angle θ̃ a (Result of the anisotropy identification, e.g. one of the methods [6] [7] [8]

[31] ) subtracted to obtain the estimated rotor position θ ^ r = θ ˜ a − θ ar .

[0055] Because the so-called maximum torque-per-ampere (MTPA) setpoint current trajectory of geometrically isotropic machines lies almost on the q-axis, these machines are usually operated without a d-setpoint current component in the lower speed range. This simplifies equation (35) to θ ar = atan 2 i q , i pm 37 ≈ 0 , 8 i pm i q . 38

[0056] The latter linear approximation (38) behaves, for example, in the range | iq | < the prosecutorsTends to be conservative (no overcompensation) with approximation errors down to less than 3.7°, being more computationally efficient than (37), especially because the factor k ar = 0.8 / the prosecutors is constant during operation. 3.3 Parameter for eindeutige Anisotropy-Rotorlage-Zuordnung

[0057] Is the anisotropy amount also taken into account? Y Δ = y Δ s depending on the saturation current i sat r Including the values ​​known at the beginning, L dd 0 , L qq 0 and the prosecutors Likewise, a regulation for the unambiguous assignment of rotor position can be derived.

[0058] In some embodiments, the anisotropy amount Y Δ as a parameter for the unique anisotropy-rotor position assignment is calculated such that it starts from its value effective at zero current. Y Δ0 increases progressively above the saturation current magnitude. Y Δ = f Δ i s r f Δ i pm = Y Δ 0 = 1 2 1 L dd 0 − 1 L qq 0 , what in Fig. 5 is presented in a qualitative way.

[0059] In some embodiments, according to (40), the value of the anisotropy magnitude effective at zero current is Y Δ0 from the unloaded differential inductances ( L dd 0 and L qq 0 ) determined.

[0060] A progressive course specifically means that the increase in f Δ ( x ) for positive arguments x is always positive and increases with the strength of the argument. df Δ x dx > 0 , ∀ x > 0 d 2 f Δ x dx 2 > 0 , ∀ x > 0 .

[0061] In some embodiments, the progressive increase of the anisotropy magnitude corresponds to an increase proportional to the cube of the saturation current magnitude. This is represented, for example, by the following formula: Y Δ = Y Δ 0 i pm 3 i sat r 3 = Y Δ 0 i pm 3 i sat s 3 .

[0062] An exemplary anisotropy vector can be constructed from the anisotropy magnitude and the anisotropy orientation. y Δ s = Y Δ cos 2 θ a sin 2 θ a in which all variables Y Δ and θ a from the saturation current vector i sat r depend. In contrast to (37), however, the derivation of the unique rotor position assignment cannot now assume that the d-current component is zero. θ ar = atan 2 i q , i d + i pm = ∠ i sat r and, for example, the anisotropy shift relative to the rotor is not taken into account. θ ar , but the anisotropy angle in stator coordinates θ a used, which is as follows depending on the saturation current in stator coordinates i sat s can be described θ a = atan 2 i q , i d + i pm + θ r 46 = atan 2 i β + i pm sin θ r , i α + i pm cos θ r = ∠ i sat s 47

[0063] Fig. 6 shows by way of example how the short-circuit current in (47) i pm s and the stator current i s s Add the vectorial values ​​in stator coordinates and calculate the saturation current in stator coordinates. i sat s This results from varying the rotor angle. θ r at constant stator current i s s (SFC condition) the short-circuit current moves i pm s on a concentric circular path (dotted line) and the saturation current consequently on a path around i s s displaced circular path (dashed line). Along this displaced circular path, both its magnitude and its magnitude change. i sat s = i sat r as well as its angle ∠ i sat s above the rotor rotation, which explains (43) and (47).

[0064] With (43), (47) and i sat r = i sat s can the anisotropy vector y Δ s now, for example, as a function of the current in stator coordinates i s s and the rotor position θ r to be expressed y Δ s = Y Δ 0 i pm 3 cos 2 atan i β + i pm sin θ r i α + i pm cos θ r sin 2 atan i β + i pm sin θ r i α + i pm cos θ r i α + i pm cos θ r 2 + i β + i pm sin θ r 2 3 = f s θ r i s s , which, according to

[33] , is the basis for calculating a unique rotor position assignment rule.

[0065] In some embodiments, a model anisotropy vector is used. y Δ s constructed, which determines the length of the anisotropy magnitude ( Y Δ ) has and in twice the anisotropy angle (2 θ a ) is aligned, with the anisotropy angle ( θ a ) the sum of rotor position ( θ r ) and anisotropy shift ( θ ar) corresponds, so that the model anisotropy vector is a function of the phase current vector ( i s s ) and rotor position ( θ r ) is described. This model anisotropy vector is then, for example, by y Δ s θ r i s s represented.

[0066] Two embodiments are described below, which (49) are converted into a unique position assignment rule (e.g. θ ^ r = f s ′ y Δ s i s s ) transfer. 3.3.1 Linear Lagezuordnung

[0067] In some embodiments, the positional dependence of the model anisotropy vector for different stator-fixed current values ​​at the target current operating point is linearized, and a linear position assignment rule is used, which corresponds to a projection of the measured anisotropy vector ( y ˜ Δ s ) corresponds to the linearization applicable to the measured current.

[0068] For this purpose, the dependence of function (49) on the rotor position is θ r under the boundary condition of an unchanged current in stator coordinates i s s = const . (the so-called SFC trajectory) linearized at the target current operating point.

[0069] As mentioned previously, for geometrically isotropic machines the target current operating point lies on the q-axis. ∠ i s s = θ r + π 2 .

[0070] This operating point can be adjusted (50) by means of the virtual shift h (small value, e.g. 1°) are linearized y Δ 0 s i s s = f s ∠ i s s − π 2 , i s s m Δ s i s s = f s ∠ i s s − π 2 + h 2 , i s s − f s ∠ i s s − π 2 − h 2 , i s s h , wherein m Δ s the increase and y Δ 0 s the offset of the line which (49) describes in and near the operating point y ΔL s θ r = m Δ s i s s θ r + y Δ 0 s i s s .

[0071] From these linearized parameters m Δ s and y Δ 0 s An exemplary linear position assignment rule can now be derived. θ ^ r = m Δ s T y ˜ Δ s − y Δ 0 s m Δ s T m Δ s , the projection of the measured anisotropy vector y ˜ Δ s = Y ˜ Δα Y ˜ Δβ T onto the straight y ΔL s θ r with the adoption of the corresponding angle value.

[0072] Because no information about anisotropy harmonics is available within the framework of this exemplary saturation assumption, m Δ s and y Δ 0 s already all available information for an electricity amount i s s . For this purpose, an evaluation in double-stream coordinates can be carried out according to

[33] y Δ ii = Y Δx Y Δy 55 = cos 2 θ i sin 2 θ i − sin 2 θ i cos 2 θ i y Δ s 56 θ i = atan 2 i α i β = ∠ i s s

[0073] This can be calculated more easily, for example, within the framework of this saturation assumption, by fs (·) from (49) for current angle θ i = 0, i.e. i β = 0 and θ r ≈ − π 2 is evaluated y Δ 0 ii i q = f s − π 2 , i q 0 m Δ ii i q = f s − π 2 + h 2 , i q 0 − f s − π 2 − h 2 , i q 0 h .

[0074] From (51) and (52) or (58) and (59) an exemplary linear position assignment rule can now be derived. k x = m x m x 2 + m y 2 k x = m y m x 2 + m y 2 k 0 = − m x Y 0 x + m y Y 0 y m x 2 + m y 2 − θ i θ ^ r = k x Y ˜ Δx + k y Y ˜ Δy + k 0 + θ i , where (60)-(62) can be calculated in advance and it is sufficient to only carry out (63) during operation. The coefficients are... kx, ky and k 0 stored model parameters and Ỹ Δx , Ỹ Δy and θ i the current result of the current measurement and anisotropy identification during operation.

[0075] In some embodiments, the position assignment coefficients are kx, ky and k 0 only once after the initial determination of the inductances L dd 0 , L qq 0 and the PM flux value ψ pm (or the short-circuit current) the prosecutors The coefficients for several q-current values ​​are calculated using equations (58)-(62), (48), and (25) and stored as a table above the current. Then, during operation, it is sufficient to select the coefficients corresponding to the current value. k × ( i ∥ ) to select / interpolate and to assign the rotor position using (63). 3.3.2 Suchansatz

[0076] In some embodiments, the anisotropy model (for example) y Δ s θ r i s s ) or y Δ ii θ r i s s ) the measured current and a variable rotor position estimate ( θ̂ r) is supplied, whereby this estimated value is varied so that the model best matches the current anisotropy measurement (for example, y ˜ Δ s or y ˜ Δ ii ) matches.

[0077] For this purpose, the point of the SFC model trajectory can be used, for example, to assign a location within the company. y Δ ii i ∥ to be sought that corresponds to the measured value y ˜ Δ ii This is obvious and the associated location value can be used as an estimate. For example, following (58), the model based on (48) is used. fs (·) now with variable rotor position value θ r considered y ΔM ii θ r = f s θ r − θ i , i ∥ 0 , where θ i and i ∥ measured values ​​during operation are and θ r so that the model is varied in the best possible way with the current measurement value. y ˜ Δ ii agrees. In some embodiments, varying the values ​​to achieve the best possible agreement corresponds to minimizing the difference between the model value and the measured value. min θ ^ r y ˜ Δ ii − y ΔM ii θ ^ r 2 .

[0078] The identified extreme point can then be used as an estimate. θ̂ r to be adopted. For minimization, a gradient descent method can be used, for example. d θ ^ r dt = − k f y ˜ Δ ii − y ΔM ii θ ^ r + h 2 2 − y ˜ Δ ii − y ΔM ii θ ^ r − h 2 2 h , in which the prefactor kf for example, depending on the location ∂ y ΔM ii ∂ θ r , the tracking bandwidth of θ̂ r can scale. 4 Experimentelle Ergebnisse

[0079] Fig. 7a-f This study verifies the saturation assumptions for the fundamental inductance and the anisotropy shift using three geometrically isotropic (SPM) and three geometrically anisotropic (IPM) synchronous machines from six different manufacturers with varying rated power and anisotropy ratio (SR) values. The vertical dotted lines, marking the rated load, define the depicted overload range and the point of short-circuit current ( iq / the prosecutors = 1) in relation.

[0080] The estimation errors caused by the fundamental inductance are significantly reduced in all machines using the saturation assumption compared to operation neglecting saturation, i.e., with a constant parameter. L q . For all SPMs, this estimation error does not exceed an electrical error threshold of 5° in practically relevant parameters of four times the overload, while with constant L q Errors of up to 20° can occur. With IPMs, these estimation errors are larger (<10° electrical in the load range shown) than with SPMs, but still significantly lower than with constant operation. L q . Therefore, using the saturation assumption of the fundamental inductance can also be useful for geometrically anisotropic machines.

[0081] The estimation errors caused by the anisotropy shift are significantly reduced for geometrically isotropic machines when using the saturation assumption compared to operation without considering saturation, i.e., with direct use of the anisotropy angle as the rotor position value. For SPMs, this estimation error with the saturation assumption usually remains less than 7° electrical, whereas with θ ar Errors of up to 60° can occur. However, SPM1 also presents a more difficult case where the estimation error increases to up to 15° even with the saturation assumption. In contrast, with IPMs, these anisotropy estimation errors are not only significantly larger than with SPMs, but also often larger in magnitude than when the anisotropy angle is used directly as the rotor position value. Therefore, using the saturation assumption for the anisotropy shift is not advisable for geometrically anisotropic machines.

[0082] Fig. 8a-cThis study compares the experimental results from sensorless operation with the geometrically isotropic machine SPM3 under parameterization without saturation assumptions, with anisotropy-shift assumptions, and with assumptions for unique rotor position assignment according to the embodiment in Section 3.3.1. In all cases, SPM3 was driven slowly by a load machine, and its rotor position was estimated solely based on anisotropy and used for the transformation of the field-oriented current control. The target current (q) was determined from t = 0 slowly increased, so that it reaches the nominal current at approximately 0.6s and the short-circuit current at approximately 3s the prosecutors has been reached. Without assuming saturation ( Fig. 8a The mean (harmonics ignored) estimation error grows rapidly, exceeding 10° even at nominal current, and the control loop becomes unstable before reaching the short-circuit current. With the presented assumption regarding the anisotropy shift ( Fig. 8b) the mean estimation error only exceeds the 10° threshold at approximately three times the rated current and is therefore still usable for efficient current control even at higher torques. However, even in this case, the control loop becomes unstable before reaching the short-circuit current because the relationship between the anisotropy angle and the rotor position becomes ambiguous

[34] . With the presented assumption for the unambiguous assignment of the rotor position ( Fig. 8cThe mean estimation error remains less than 10° across the entire load range and can therefore be used for efficient current control without torque limitations. Furthermore, the control loop does not become unstable even at high loads because the causes described in

[34] do not apply to this type of assignment. However, in all cases, two- and six-periodic harmonics can be seen in the estimated rotor position and especially in the estimation error. These are caused by a stator-fixed and a negative fourth anisotropy harmonic

[32] , which are not taken into account in the presented method. However, the additional consideration of these or further harmonics is not excluded in any of the presented embodiments.

[0083] Other aspects include: (i) A device for controlling and regulating a rotating field machine, comprising a stator and a rotor, with a device for detecting a number of phase currents and with a controller for controlling the PWM converter, which is configured and designed to carry out the method as described above; and (ii) a synchronous machine, comprising a stator and a rotor with or without permanent magnets, with a device for controlling and / or regulating as described in point (i). 5 Zusammenfassung

[0084] Today's established, highly efficient control methods for electric machines require that the rotor angle is known at all times, i.e., usually measured. Without this knowledge, only significantly less efficient control methods can be used. The measurement is performed during operation using a sensor attached to the rotor shaft – the so-called rotor position sensor, or simply sensor.

[0085] Encoders bring with them a number of disadvantages, such as increased system costs, reduced robustness, increased probability of failure and greater installation space requirements, which justify the great industrial interest in obtaining the angle signal without using an encoder and using it for efficient control.

[0086] Methods that enable this are called "sensorless" or "sensorless" control and are divided into 2 classes: 1. Fundamental wave methods evaluate the voltage induced by motion, deliver very good signal characteristics at medium and high speeds, but fail at lower speeds, especially when stationary. 2. Anisotropy-based methods evaluate the position dependence of the machine's inductance, which does not require rotational speed, but have several problems and obstacles that explain why many applications still require a position sensor (with its disadvantages).

[0087] Both methods require specific magnetic parameters of the machine to calculate the rotor position from voltage and current. However, due to magnetic saturation, these parameters depend on the current state. Therefore, the accuracy and stability of the position estimation at high loads depends on the precision of the knowledge regarding the saturation behavior of the parameters.

[0088] The saturation behavior for a given machine type can either be derived with medium accuracy from the data of computer-aided machine design, or determined experimentally with high accuracy on a test bench using a position sensor and a load machine. However, both options are often unavailable, for example, when an unknown synchronous machine is connected to a frequency converter and the goal is to achieve the best possible control results based on short initialization tests. Furthermore, because these tests often need to be torque-free, a direct measurement of the saturation behavior is not always feasible.

[0089] The embodiments described here relate certain physical properties of a synchronous machine in such a way that rules can be derived to infer the saturation behavior under load, up to multiple overloads, from measured values ​​obtained in the torque-free state. This now makes it possible to control even unknown synchronous machines stably and efficiently across the entire speed and load range, up to multiple overloads, without a test bench (typical field conditions), after a short, torque-free initialization measurement and without a position sensor. 6 Bibliography

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Claims

1. Method for the no-load determination of load-dependent position assignment parameters of a synchronous machine with a permanent magnet and without a position sensor, which is controlled via clocked terminal voltages, from which the inductance is calculated in conjunction with the measured current response, characterized in that from the smallest no-load inductance and the largest no-load inductance (Ldd0, Lqq0) and a short-circuit current (ipm) which is an equivalent current amount for excitation by the permanent magnet, the curve(s) of the absolute inductance (Lq) and / or the magnetic anisotropy of the synchronous machine under load as a function of the current in the magnetic saturation range and is / are used as position assignment parameters for position assignment in position sensor-less control operation.

2. Method according to claim 1, wherein the course of the absolute inductance and / or the magnetic anisotropy of the synchronous machine under load is predicted as a function of the current in the magnetic saturation range and compensated for in position sensor-free control operation.

3. Method according to one of the preceding claims, wherein a no-load inductance of the derivation of the flux linkage corresponds to zero current at the operating point.

4. Method according to one of the preceding claims, wherein the smallest and largest inductance values are the direction-dependent smallest and largest inductance values of an operating point, wherein the direction dependence corresponds to the magnetic anisotropy.

5. Method according to one of the preceding claims, wherein the value of the short-circuit current corresponds to the amount of the stator current that is set at zero voltage at rated speed.

6. Method according to one of the preceding claims, wherein the short-circuit current is calculated as the quotient of the permanent magnet flux linkage divided by a combination of the smallest no-load inductance and the largest no-load inductance.

7. Method according to claim 6, wherein the combination corresponds to averaging.

8. Method according to one of the preceding claims, wherein the method is subject to the assumption that the q-axis, i.e., the direction transverse to the permanent magnet, assumes the same magnetic behavior as the d-axis, i.e., the direction of the permanent magnet, in the de-energized state when the short-circuit current is applied in the q-direction.

9. Method according to one of the preceding claims, wherein the absolute inductance (Lq) is calculated as a parameter for evaluating the induced voltage in such a way that, starting from its value at zero current, the maximum no-load inductance , it decreases with increasing current so that, when the short-circuit current is reached, it equals the mean value of the minimum no-load inductance and the maximum no-load inductance.

10. Method according to one of claims 1 to 8, wherein a saturation current vector is calculated by vectorial addition of a phase current vector and a short-circuit current vector, wherein the short-circuit current vector has the magnitude of the short-circuit current and is aligned in the direction of the permanent magnet.

11. Method according to claim 10, wherein the anisotropy shift (θar) is calculated as a parameter for evaluating the magnetic anisotropy in such a way that it increases with increasing phase current so that the assumed alignment of the anisotropy corresponds to the direction of the saturation current vector.

12. Method according to one of claims 10 or 11, wherein the anisotropy amount (YΔ) is calculated as a parameter for unambiguous anisotropy-rotor position assignment in such a way that it increases progressively from its effective value YΔ0 at zero current above the saturation current amount.

13. Method according to claim 12, wherein the effective value of the anisotropy amount (YΔ0) at zero current is determined from the smallest no-load inductance and the largest no-load inductance.

14. Method according to claim 12 or 13, wherein the progressive increase corresponds to an increase proportional to the cube of the saturation current amount.

15. Method according to one of claims 11 to 14, wherein a model anisotropy vector is constructed which has the length of the anisotropy magnitude and is oriented at twice the anisotropy angle, wherein the anisotropy angle corresponds to the sum of the rotor position and the anisotropy shift, so that the model anisotropy vector is described as a function of the phase current vector and the rotor position.

16. Method according to claim 15, wherein the positional dependence of the model anisotropy vector is linearized for different stator-fixed current values at the target current operating point, and a linear position assignment rule is used which corresponds to a projection of the measured anisotropy vector onto the linearization applicable to the measured current.

17. Method according to claim 15, wherein the measured current and a variable rotor position estimate are fed into the anisotropy model, wherein this estimate is varied such that the model corresponds as closely as possible to a current anisotropy measurement value.

18. Method according to claim 17, wherein the variation corresponds to the best possible match of a minimization of the difference between the model value and the measured value.

19. Method according to one of claims 10 to 18, wherein compensation and / or utilization for position assignment of the anisotropy saturation calculations only takes place if the difference between the no-load maximum and no-load minimum inductance is less than 20% of their sum.

20. Device for controlling and regulating a rotating field machine, comprising a stator and a rotor, with a controllable PWM converter for outputting clocked terminal voltages, with a device for detecting a number of phase currents, and with a controller for controlling the PWM converter, which is set up and designed to carry out the method according to one of the preceding claims.

21. Synchronous machine comprising a stator and a rotor with or without permanent magnets, with a device for control and / or regulation according to claim 20.