Method for optimizing the efficiency of a rotating electric machine

Abstract

A method for optimizing the efficiency of a rotating electrical machine, implementable on a personal computer or other electronic device, the method having the following steps: - acquiring a data set of hysteresis and eddy current losses in a core of the rotating electrical machine, - initializing a calculation procedure for hysteresis and eddy current loss coefficient functions, - calculating the loss coefficient functions, - calculating the hysteresis and eddy current losses using the equation Formula (I), - optimizing the design of the electric machine to maximize the efficiency of the machine itself.

Description

[0001] METHOD FOR OPTIMIZING THE EFFICIENCY

[0002] OF A ROTATING ELECTRIC MACHINE

[0003] D E S C R I PTI O N

[0004] Technical Field of the Invention

[0005] The present invention relates to a method for optimizing the efficiency of a rotating electrical machine, in particular of a switched reluctance electrical machine, by designing it in such a way as to reduce its losses.

[0006] Background art

[0007] As is well known, a switched reluctance electric machine is a rotating electric machine essentially equipped with a multiphase stator and a rotor with pronounced poles. The stator consists of multiple protruding (salient) ferromagnetic poles alternating with stator slots. The rotor is made of a ferromagnetic material (with narrow hysteresis and high magnetic permeability, such as silicon steel), laminated to limit induced current losses, and has projections that act as salient magnetic poles to maximize magnetic reluctance, magnetic poles alternating with corresponding rotor slots.

[0008] Efficiency is one of the key performance objectives in switched reluctance machines and, more generally, in rotating electric machines. The two main factors that contribute to losses in rotating electric machines are Joule losses and "iron" losses, i.e., losses in the stator and rotor core.

[0009] Calculating Joule losses is simple, as they essentially depend on the current waveform and phase resistance.

[0010] Calculating core losses, on the other hand, is a much more challenging task, as it requires precise knowledge of the flux density waveforms within various "zones" of the stator and rotor cores. Indeed, a "soft" magnetic material, such as the steel used in the cores of electrical machines, is subject to core losses if a magnetic flux density varies over time.

[0011] A first type of core loss is hysteresis losses, which are proportional to the area of the material's hysteresis loop, the frequency of the flux, and its magnitude.

[0012] A second type of core loss is Eddy current losses, which are proportional to the square of the frequency, the magnitude of the flux density, and the thickness of the lamination.

[0013] For grid-powered rotating electrical machines (operating at 50 or 60 Hz with sinusoidal waveforms), calculating core losses is straightforward, as it is generally sufficient to obtain single-value specific core loss data (e.g., in kW / kg) from steel manufacturers.

[0014] On the other hand, modern rotating electrical machines are electrically powered via variable-frequency power electronic converters to enable efficient operation. This implies that the magnetic flux density waveforms within the machine's core have a variable frequency that depends on the machine's operating conditions. For these machines, calculating core losses becomes much more complex, especially considering that magnetic flux density waveforms are not necessarily sinusoidal. Scientific literature has shown that calculating core losses using formulas with fixed coefficients leads to inaccurate results in converter- powered machines.

[0015] These difficulties do not allow to easily design a rotating electrical machine optimizing its efficiency.

[0016] Summary of the Invention

[0017] To solve the technical problems highlighted above, an object of the present invention is to define a methodology that allows to calculate the losses in a rotating electrical machine and to optimize the design of the electrical machine itself in order to reduce its losses and, consequently, improve its efficiency.

[0018] Therefore, according to the present invention, a method is provided to optimize the efficiency of a rotating electrical machine having the features set forth in the independent claim, appended to this specification.

[0019] Further preferred and / or particularly advantageous embodiments of the invention are described according to the features set forth in the appended dependent claims.

[0020] Brief Description of the Drawings

[0021] The invention will now be described with reference to the accompanying drawings, which illustrate some non-limiting examples of its implementation, in which:

[0022] - Figure 1 is a flowchart of the method for optimizing the efficiency of a rotating electrical machine, according to the present invention,

[0023] - Figures 2 through 4 illustrate a graphical flowchart of the method of Figure 1,

[0024] - Figure 5 illustrates an example of validation of the method of Figure 1 on the core of a rotating electrical machine, and

[0025] - Figure 6 illustrates an example of application of the method of Figure 1 to a rotating electrical machine.

[0026] Detailed Description

[0027] A titolo puramente esemplificativo e non limitative, la presente invenzione verra ora descritta facendo riferimento alle suddette figure.

[0028] According to the invention, core losses in converter-powered rotating electrical machines are calculated by substituting constant-value coefficients into the core loss equation using suitable functions. The proposed method, which can be implemented on a personal computer or other electronic device, including mobile devices, allows these functions to be derived from a limited set of core loss measurements.

[0029] Core losses per unit mass can be calculated using the following expression: where:

[0030] - Pfe are the losses in the "iron" or core,

[0031] - m is the mass of the core,

[0032] - Ph are the hysteresis losses,

[0033] - Pe are the Eddy current losses,

[0034] - B is the magnetic flux density in Tesla,

[0035] - f is the frequency in Hertz.

[0036] The proposed method allows us to obtain the functions kh(B), ke(B), and o(f), which are the hysteresis loss coefficient, the Eddy current loss coefficient, and the magnetic flux density exponent in the hysteresis loss equation, respectively. To do this, only a limited set of core loss measurements per unit mass is needed, typically obtained from the datasheets provided by ferromagnetic lamination manufacturers.

[0037] The proposed method therefore comprises the following steps:

[0038] - acquiring a core loss dataset for an electrical machine,

[0039] - initializing a loss coefficient function calculation procedure,

[0040] - calculating the loss coefficient functions,

[0041] - calculating the hysteresis and Eddy current losses using equation (1),

[0042] - optimizing the electrical machine design to maximize its efficiency.

[0043] In greater detail and with reference to Figure 1, the dataset acquisition phase for losses (due to hysteresis and eddy currents) in the core of the electric machine includes the following step:

[0044] - defining S100 a matrix, for example a 3x3 matrix, of core losses per unit mass from the material manufacturer's data sheet (e.g., mild steel for electric machines) or from tests performed and define it as the dataset matrix. Also with reference to Figure 2, the readings must be at three levels of magnetic flux density B (Bl, B2, B3) and three levels of frequency f (fl, f2, f3). The nine data points 100 in the matrix are the specific losses (in kW / kg) in the core corresponding to a given magnetic flux density B value and a given frequency f value.

[0045] Evidently, the dataset matrix can be larger, for example 4x4 or 5x5, thus achieving greater accuracy in the subsequent calculation phase, but at the expense of considerable computational complexity. The Applicant has verified that the accuracy obtained using a 3x3 matrix is already very good, as will be demonstrated below.

[0046] The initialization phase of the calculation procedure includes the following steps:

[0047] - defining S200 a vector of acquired or measured magnetic flux densities B_vec and a vector of acquired or measured frequencies f_vec. The length of these vectors must be three, depending on the chosen example;

[0048] - setting S300 a parameter k_a and an arbitrary value greater than 0. For example, k_a=40;

[0049] - defining S400 a vector ke_vec in a suitably wide range, for example, from 0.2e-5to 20e-5. This interval can be varied if the next calculation step requires it, as explained below. The length of this vector can be arbitrarily set to a value >100;

[0050] - setting S500 a counter k=l and defining an outer loop, whose index j varies from 1 to the length of the magnetic flux density vector B_vec, for example, 3;

[0051] - defining S600 an inner loop, whose index j varies from 1 to the length of the frequency vector f_vec, for example 3.

[0052] The next phase of calculating the loss coefficient functions includes the following steps:

[0053] - calculating S700 a matrix defined as follows:

[0054] We then proceed by incrementing the counter k by 1, respecting the outer and inner cycles referred to in steps S500 and S600, until their completion. The incrementing of the counter k will end at the end of both the outer and inner cycles. In the example case, with a 3x3 matrix, the final value of k will be 3x3, or 9. The kh_matr matrix will have a number of rows equal to the product of the length of the magnetic flux density vector (B_vec) x the length of the frequency vector (f_vec), and a number of columns equal to the length of the vector (ke_vec). Each row, therefore, will represent a vector of the hysteresis loss coefficient kh as a function of the Eddy current loss coefficient ke;

[0055] - plotting S800 graphs plotting the hysteresis loss coefficient vector kh versus the eddy current loss coefficient kefor each acquired or measured flux density level (Fig. 3a, Fig. 3b, and Fig. 3c, respectively). Each figure will contain a line (kh vs. ke) for each acquired or measured frequency value, so each graph will contain, in the example given, three lines in total;

[0056] - in each graph (Fig. 3a, Fig. 3b, and Fig. 3c), identifying S900 as the intersection point (or the center of gravity of the intersection triangle) of the three curves. The coordinates of the intersection point provide the values of keand kh for three specific magnetic flux density levels B (acquired or measured). If no intersection between the curves is visible, the ke_vec interval defined in step S400 must be varied. Specifically, if in at least one of the three graphs in Figures 3a, 3b, and 3c the three curves converge, but do not intersect, toward values greater than ke, then the upper limit of the ke_vec vector must be increased. Conversely, if the curves converge, but do not intersect, toward values less than ke, then the lower limit of the ke_vec vector must be reduced; - using S1000 linear or polynomial interpolation to identify a function of the hysteresis loss coefficient kh and the Eddy current loss coefficient kewith respect to the magnetic flux density B (Fig. 3d and Fig. 3e, respectively). If the interpolation is not satisfactory, the k_a parameter defined in step S300 must be modified. This parameter can be varied by trial and error or by defining an external iterative loop starting from step S300. For each iteration, the k_a parameter is progressively increased (or decreased) and the quality of the interpolation is evaluated and stored. At the end of the iterative cycle, the value of the k_a parameter that guarantees the best interpolation is selected.

[0057] The calculation phase for hysteresis and Eddy current losses, using equation (1), can therefore be performed using the functions obtained in the previous steps. In particular, the following functions are used: wherein a, b, c, d are interpolation constants if linear interpolation was selected in step S1000. If polynomial interpolation, for example of order n, was selected in step S1000, then the following functions will be used:

[0058] Figure 4 shows the three-dimensional graph of iron losses as a function of magnetic flux density B and frequency f, evaluated using equation (1) and with loss coefficients according to functions (2) or (3).

[0059] Finally, the optimization phase of the rotating electrical machine design to maximize the efficiency of the machine itself is performed by implementing the functions previously described in the design workflow for any variable-speed electrical machine, so as to allow accurate efficiency estimates. This includes, for example, analytical or finite element software for the analysis of rotating electrical machines, in other words, any tool specifically for the design of rotating electrical machines.

[0060] An example of validation of the methodology presented is shown below. The core used as an example is a commercial lamination core (M270- 35A), widely used in rotating electrical machines. From the manufacturer's data sheet, the following core loss [W / kg] table can be found:

[0061] Tabella 1 1.5 2.5 46.24 224.82

[0062] Using the proposed method, the following results are obtained via the linear interpolation approach: ke(B)=1.5579e-05+4.7898e-05*B kh(B) = O.02034-0.0020279*B o(f) = l + 38 / f

[0063] To compare the accuracy of the proposed methodology, additional core loss data are extracted from the supplier's datasheet and compared with the calculated core losses, as shown in Figure 5, which shows the nearperfect fit between the experimental data (indicated by circles) and the numerical data (indicated by asterisks).

[0064] An example of the optimization of a switched reluctance electric machine is illustrated in Figure 6. The switched reluctance electric machine 10 is a substantially axisymmetric structure and comprises at least:

[0065] - a stator 20 equipped with a plurality of salient stator poles 22, arranged circumferentially and projecting radially inward. Each pole has an axial dimension equal to the axial dimension of the stator 20.

[0066] - a rotor 30 contained within the stator 20 and also equipped with a plurality of salient rotor poles 32, arranged circumferentially. The rotor poles 32 project radially outward and have an axial dimension equal to the axial dimension of the rotor 30.

[0067] In the example illustrated, the method according to the present invention was used to select an appropriate value for the thickness of the corona (outer layer) of the stator of the rotating electric machine. Fig. 6a schematically illustrates the original design, while Fig. 6b shows the design optimized using this method. The magnetic field lines are visible in the diagrams, while the colors represent the higher (warm colors) or lower (cool colors) magnetic flux density. Using this method, it was possible to vary the loss distribution in the rotating electrical machine, leading to improved efficiency and simultaneously improving the structural behavior of the stator, thanks to a thicker stator crown.

[0068] Ultimately, the method according to this invention achieves the following main advantages:

[0069] - easy application: the method requires a limited amount of experimental data to provide accurate results; - use of loss coefficient functions, rather than constant values;

[0070] - possibility of implementation in electrical machine design tools to optimize the sizing of the stator and rotor.

[0071] In addition to the embodiment of the invention, as described above, it should be understood that numerous other variations exist. It should also be understood that such embodiments are only exemplary and do not limit either the scope of the invention, nor its applications, nor its possible configurations. On the contrary, although the description above allows the person skilled in the art to implement the present invention at least according to one of its exemplary embodiments, it should be understood that many variations of the described components are possible, without thereby departing from the scope of the invention, as defined in the appended claims, which are interpreted literally and / or according to their legal equivalents.

Claims

CLAIMS1. Method for optimizing the efficiency of a rotating electrical machine, the method being implementable on a personal computer or other electronic device, the method comprising the following steps:- acquiring a data set of hysteresis and eddy current losses in a core of the rotating electrical machine,- initializing a procedure for calculating functions of loss coefficients of the hysteresis and eddy current,- calculating the functions the loss coefficients,- calculating the hysteresis and eddy current losses, using the equation:where:- Pfe are the core losses,- m is the core mass,- Ph are the hysteresis losses,- Peare the eddy current losses,- B is the magnetic flux density- f is the frequency- kh is the hysteresis loss coefficient- keis the eddy current loss coefficient- a is the exponent of the magnetic flux density in the above equation,- optimizing the design of the electric machine to maximize theefficiency of the machine itself, the method being characterized in that the phase of acquiring the data set of losses in the core comprises the step of defining a matrix of losses per unit mass in the core corresponding to a magnetic flux density (B) value and a frequency (f) value.

2. The method according to claim 1, wherein the loss matrix is a matrix of size 3X3.

3. A method according to claim 1 or 2, wherein the initialization phase of the calculation process comprises the following steps:- defining a vector of acquired magnetic flux densities (B_vec) and a vector of acquired frequencies (f_vec),- setting a parameter (k_a) and an arbitrary value thereof greater than 0,- defining a vector (ke_vec) in a suitably large range,- setting a counter and defining an external calculation cycle, whose index i varies from 1 to the length of the magnetic flux density vector (B_vec),- defining an internal calculation cycle, whose index j varies from 1 to the length of the frequency vector (f_vec).

4. The method according to claim 3, wherein the phase of calculating the loss coefficient functions comprises the following steps:- calculating a matrix (kh_matr) with a number of rows equal to the product of the length of the magnetic flux density vector (B_vec) x length of the frequency vector (f_vec) and a number of columns equal to the length of the vector (ke_vec);- plotting graphs in which the hysteresis loss coefficient vector (kh) is reported as a function of the eddy current loss coefficient (ke) for each of the acquired flux density levels;- in each graph, identifying the intersection of the curves, which provide the values of the eddy current loss coefficient (ke) and the hysteresis loss coefficient (kh) for the specific magnetic flux density levels (B);- using linear or polynomial interpolation to identify a function of the hysteresis loss coefficient (kh) and the eddy current loss coefficient (ke) with respect to the magnetic flux density (B).

5. The method according to claim 4, wherein if no intersection between the curves is visible, the interval of the vector (ke_vec) must be varied.

6. The method according to claim 4, wherein if the interpolation is not satisfactory, the value of the parameter (k_a) must be modified.

7. The method according to any of claims 4 to 6, wherein the step of calculating the hysteresis and eddy current losses is performed using the following functions:where a, b, c, d are constants of the linear interpolation.

8. A method according to one of claims 4 to 6, wherein the step of calculating the hysteresis and eddy current losses is performed using the following functions:where a, b are variables of the polynomial interpolation of order n.

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