The present invention relates to a simulation method and virtual monitoring of an electric machine, in particular a synchronous motor.

By "electric machine" in the present invention it is meant both a rotary machine and an electronic power converter (or switch) or a power transformer.

State of the art

Recent developments in the fields of engineering, cybernetics, and artificial intelligence have allowed the progressive passage from the study of physical objects in the real world to their study through their representation in the virtual world. In this context, the so-called “digital twin” was born.

The digital twin is a virtual model or digital model designed to accurately reproduce the characteristics of a physical object to monitor its behavior. The studied object, for example a turbine, an electric motor or a transformer, is covered by sensors that measure essential data and transmit them to the virtual model. This, in its turn, can use the data to implement simulations, make real-time forecasts and study performance problems, and propose possible technical solutions. The digital twin is therefore considered a virtual sensor given its ability to obtain information with considerable precision and detail, avoiding the use of other types of more invasive, expensive, and less reliable physical sensors.

The process of designing a digital twin requires a combination of software technologies, numerical models, and artificial intelligence algorithms, and can be schematized in the following steps:

- Modeling: the studied object is schematized through a physical- mathematical model and the equations that govern behavior are solved through a numerical method. One of the most reliable and commonly used methods is, for example, the Finite Element Method (FEM);

- Simplification: the model used is simplified through Model Order Reduction (MOR) techniques, reducing the computational complexity and allowing virtual monitoring of the physical object in real-time;

- Training: the model is trained using data measured directly on the object under examination by physical sensors in order to calibrate the virtual resource with respect to the physical one. This task is performed by specific artificial intelligence algorithms, which allow to reduce of the uncertainty of the model parameters and to optimize of the predictive capabilities of the model itself.

- "Connection" or "installation": once trained, the model can be considered the virtual counterpart of the physical object. The digital twin and the physical object are connected and exchange data and information during the entire life cycle of the system.

This implementation approach is completely general, but it is not unique. In fact, there are various embodiments, which depend on the field of use and on the specific task to be performed. The digital twin, in fact, can be used in various fields ranging from the energy industry to manufacturing, up to the aerospace sector. A rapidly growing market that can benefit most from the development of this technology is that of electric motors in the automotive industry. The application of the digital twin to electric motors makes it possible to solve some fundamental problems such as the estimation of the driving torque, and the analysis of the internal temperature of the rotor. An example of a virtual simulation and monitoring method of an electric motor, specifically induction, according to the prior art (F. Toso et al., Digital Twins as Electric Motor Soft-Sensors in the Automotive Industry, 2021 ), is shown in Fig. 1.

The virtual monitoring and simulation method 100 comprises several steps which are implemented in sequence.

Initially, in step 1 10 the virtual/digital prototype (geometry, for example via CAD) of an electric induction motor is acquired, going on to specify the physical- mathematical properties and the different materials which characterize the object under examination.

In step 120 a finite element analysis (FEA, Finite Element Analysis) is carried out in which the physical models describing the electric motor are studied. In this case, the FEA analysis is applied to analyze a multi-physics problem 130, which consists in solving the equations describing the electromagnetic behavior coupled to the equations describing the thermal behavior of the system (Fig. 3).

The equations under consideration describe respectively an electromagnetic (EM) model 131 and a thermal model 132. Starting from these two coupled models, and assuming that the initial temperature of the electric machine is known, it is possible to solve the electromagnetic problem and calculate the different heat sources due to the electric currents in the electric machine. Consequently, knowing the heat sources it is possible to calculate the new temperature distributions and solve the thermal problem.

From the temperature distributions, the electrical conductivity is calculated, thus obtaining a closed-loop procedure that is updated iteratively. In practice, by solving the coupled models, it is possible to use the rotor temperature to calculate its electrical resistance, and thus obtain an estimate of the rotor flux and of the transmitted drive torque, parameters which would otherwise be difficult to measure experimentally.

More specifically, step 140 consists in applying Model Order Reduction (MOR) techniques to the EM and thermal models in order to reduce the computational complexity of the models themselves. Specifically, these systems are reduced to a space of smaller size than the original space (Fig. 4), making an approximation to which a given error will be associated. The reduced models (EM 141 and thermal 142) can thus be solved in real-time, monitoring the behavior of the electric machine instant by instant. The accuracy of the virtual model is determined by the error that is deemed acceptable, therefore it is necessary to find a compromise between the accuracy of the digital twin and the computational complexity.

Once scaled down, the model is optimized in its parameters. This procedure is implemented, firstly, by carrying out internal and/or external temperature measurements of the rotating machine and subsequently by optimizing the virtual model (EM and thermal) to reproduce the measurements obtained through an evolutionary algorithm (DE, Differential Evolution algorithm) or another optimization algorithm that calibrates the parameters of the differential equations. In this way, it is possible to improve the precision of the digital twin by reducing the error due to the uncertainty of the parameters that the model had during step 140.

In the present exemplifying case of the prior art, the temperature measurements are obtained by means of wireless thermocouple sensors inserted in the crankshaft, and the error of the above method is of the same order as the sensitivity of the sensor used, i.e. ±1.5 °C.

The digital twin, having been calibrated with its physical counterpart, is ready for usage and can be run in real-time.

This and other modern methods that allow the realization of a digital twin, however, still remain computationally complex and need, to be implemented in realtime, to be implemented in hardware platforms with high computational power and therefore with a high cost. This problem prevents the implementation of the digital twin on integrated platforms where computing power and memory are limited; therefore, the use of integrated technology in industrial series productions is limited.

Furthermore, it is currently not possible to calculate in advance the hardware resources precisely needed to be able to perform real-time digital twins deriving from the methods of the prior art.

Scope and object of the invention

Scope of the present invention is to provide a method implemented on a computer, a program for a computer, a programmed computer, and a related system, which, in whole or in part, solve the above-mentioned problems, overcoming the drawbacks of the prior art.

The object of the present invention is a method implemented on a computer, a computer program, a programmed computer, and a related system for the simulation and improved virtual monitoring of electric machines, for example, rotary electric machines, switches, and electronic power converters, according to the attached claims.

Detailed description of examples of embodiments of the invention

List of the figures

The invention will now be described by way of illustration but not in limitation, with particular reference to the drawings of the attached figures, wherein:

- Fig. 1 shows an exemplary block diagram of a method simulation and virtual monitoring of an asynchronous motor, according to the prior art;

- Fig. 2 shows an exemplary block diagram of an improved virtual monitoring and simulation method of rotating electric machines and electronic power converters, according to an embodiment of the invention;

- Fig. 3 shows a system of equations, which describe an electromagnetic and thermal multi-physics model, according to the prior art: the upper block shows the equation that describes the electromagnetic behavior, the lower block shows the equation that describes the thermal behavior; - Fig. 4 shows an exemplary scheme of an approximation method of the equation that describes the electromagnetic behavior of Fig. 3 applied to a synchronous motor, according to the prior art;

- Fig. 5 shows an exemplary graphical representation of the Model Order Reduction (MOR) technique according to the prior art;

- Fig. 6 shows an optimization method of a virtual model through an evolutionary algorithm in different iterations, according to the invention on the basis of the measurements of Fig. 7;

- Fig. 7 shows a graph of the measured stator current intensity and estimated on the rotor of an electric induction motor as a function of time according to experimental tests of the invention; and

- Fig. 8 shows a graph of the current intensity as a function of time, in which the trend of the experimental measurements of current and temperature on an electric motor are compared, the trend of the same quantities calculated with a complete virtual model, and the trend calculated with a reduced virtual model, according to an aspect of the invention;

- Fig. 9 shows perspective views of an electric motor comprising a stator and a rotor and related graphs of the temperature measured by the physical sensor and estimated by the virtual sensor as a function of time according to an application example of the invention;

- Fig. 10 shows a perspective view of a three-step inverter and a graph of the temperature estimated by the virtual sensor as a function of time according to an application example of the invention;

- Fig. 1 1 shows microscopic-level images of contact/junction points of an electronic component of an electric machine.

It is specified here that elements of different embodiments can be combined together to provide further embodiments without limits respecting the technical concept of the invention, as the average person skilled in the art understands without problems from what has been described.

The present description also refers to the prior art for its implementation, with regard to the detailed features not described, such as for example minor elements usually used in the prior art in solutions of the same type.

When introducing an element, it is always understood that it can be "at least one or one or more . When a list of elements or features is listed in this description it is meant that the invention according to the invention "comprises" or alternatively" is composed of" such elements.

When listing features within the same sentence or bulleted list, one or more of the individual features may be included in the invention without connection to the other features in the list.

Two or more of the parts (elements, devices, systems) described below can be freely associated and considered as a kit of parts according to the invention.

Embodiments

Referring to Fig. 2, an embodiment of the improved virtual monitoring and simulation method 200 according to the invention of an electric machine (not shown, known per se), may comprise several steps.

The step 210 consists in acquiring a digital model of the electric machine created for example through design and graphic manipulation software, for example, CAD (Computer-Aided Design) software. The digital model characterizes the geometry and materials of which the electric machine is made.

The step 220 consists of a modeling and a discretization of the geometry of the virtual prototype acquired in the previous step: the physical object is divided into essential geometries (triangles, quadrilaterals, tetrahedrons, for example) connected one to the other by nodes. This modeling technique is commonly called "mesh" and can be implemented with various software, such as Gmsh, Opencascade and MeshLab.

In step 230 a finite element FEA analysis is carried out, in which the physical models describing the electric machine are studied. To this end, the physical- mathematical properties are acquired (differential equations, for example for the thermal and electromagnetic behavior of an electric machine, in particular for a synchronous electric motor). The FEA method is applied to study one of the various versions of the equation describing the electromagnetic behavior coupled to various versions of the equations describing the thermal behavior of the system (Fig. 3, equations per se known). The multi-physics system or model of differential equations has dimension n, with n positive integer, i.e. n is the number of variables in the system. Corresponding pre-defined electromagnetic and thermal initial conditions (currents and initial temperatures of the electric machine) are also acquired.

Equation (EM) can be expressed in the following form:

Where is the magnetic vector potential, V a scalar electric potential, μ is the magnetic permeability tensor, σ the electrical conductivity tensor, B _r is the residual magnetization flux density (the field produced by the magnets, if any) and is an excitation current density. By means of 2D finite element analysis, the EM equation is reduced to the following non-linear system of differential equations (electromagnetic model): where x is the unknown relative to the magnetic vector in each point of the space discretized through the mesh, K is the stiffness matrix of the system, which depends on x, and therefore on is the damping matrix of the system, and b is the right-hand side (rhs) of the system (it varies in weather).

While the differential equation associated with the thermal behavior of the systems at issue can be expressed in the following form: where T is the temperature, p is the density, K and c _p are respectively the thermal conductivity and the heat capacity of the machine materials, and q _ioss represents the heat generation inside the machine itself. The equation of Figs. 3 and 4 are given for K, the equation just expressed is more general as K can vary.

In turn, the thermal equation is discretized through the FEA method obtaining a non-linear system of differential equations (thermal model): where θ is the temperature vector, K is the stiffness matrix of the system, which depends on the thermal conductivity, and D the damping matrix of the system, which depends on the specific heat. Obviously K and D are different in the two magnetic and thermal cases (they could also be indicated with The vector q corresponds to the excitation in the thermal model and can be expressed as follows: where q _conv is the convective heat, which depends on the external temperature, while q _in is the heat input calculated with the electromagnetic FEM model and with the currents measured in the system.

The heat exchange component by convection with the external environment can be used to simulate the heat exchange on any edge surface of the system. Newton's law is used to calculate the heat flux on the edge surfaces of the system: where h is the convective heat transfer coefficient, T _c and T _b the ambient temperatures outer and edge surfaces, respectively. The part of H that depends linearly on θ must be integrated into the matrix K. It is not necessary to measure both temperatures, in some cases, one can be derived from the other, and even the ambient temperature can be known a priori.

However, the problem remains non-linear since q _in is a function of the resistivity of the materials, which in turn is a function of θ, therefore there is the new system of differential equations: where K _new e q _new are respectively the new stiffness matrix of the system and the new thermal excitation vector. q _new depends on the resolution of the EM model.

In fact, assuming that the initial temperature distribution of the electric machine is known, it is possible to solve the electromagnetic problem and calculate the different heat sources due to the electric currents. Consequently, knowing the heat sources it is possible to calculate the new temperature distributions and solve the thermal problem. Finally, the new electrical conductivity tensor is obtained from the temperature distributions, thus obtaining a closed-loop procedure, which is updated iteratively. In practice, by solving the coupled models it is possible to obtain the rotor temperature of an electric motor, for example. Knowing the rotor temperature it is possible to calculate the electrical resistance, and obtain a reliable estimate of the flux of the magnets (if present) and of the transmitted drive torque, essential parameters for the control and monitoring of an electric machine.

An example of the iterations between the two thermal and electrical models is given in Fig. 4 for a permanent magnet synchronous motor.

In step 240, the EM and thermal models are parameterized through the application of parametric Parametric Model Order Reduction (PMOR) techniques, in order to reduce the computational complexity of the models themselves. Specifically, the non-linear system of EM and thermal differential equations is converted into a parametric system of differential equations, linear within a given integration interval. The original system is thus described in a space of dimension n with p parameters: where y(t,p) is the solution of the linear system depending on time t and p parameters, with p belonging to a closed set fl, x and u being the state and input of the system. These parametric systems are subsequently projected into a space of dimension r, smaller than /?: where is the solution of the reduced linear system, which approximates y(t, p) up to a specific measured error (Fig. 5, the values vary according to the need to reduce the problem). The models (differential equations) reduced in this way can be solved in real-time, monitoring the behavior of the electric machine instant by instant (for example by estimating one or more temperatures in corresponding one or more pre-determined points of the electric machine of a synchronous electric motor). However, it may be advantageous to calibrate the parameters of the virtual model with the parameters of the real electric machine.

In this sense, in step 250 it is possible to carry out a series of measurements on the physical object over time, including: temperature measurements on parts (known) of the electric machine, temperature measurements of the external environment, and current intensity measurements in the time, with a known time sampling step of the measurements; optionally, a thermal regime analysis of the system can also be carried out, to identify the parameters of convective heat exchange with the external environment (parameters of differential equations of the system used by the invention).

In the training step 260, the virtual model (EM and thermal) is optimized so as to be as faithful as possible to the real system of the electric machine. The parameters obtained in the previous step are entered into an optimization algorithm, for example, an evolutionary algorithm (DE, Differential Evolution algorithm), which optimizes the virtual model to reproduce the measurements obtained in step 250. In other words, the algorithm solves the following optimization problem: with where Y*(p, t) is a vector of temperatures predicted at the instant t of the measurements and where T _measures (t is the vector of the acquired temperature measurements. After performing a minimum number of iterations, the algorithm allows for reaching a good agreement between the model and the experimental data. In this way, it is possible to improve the accuracy of the digital twin by reducing the approximation error made during step 240.

Step 270 consists of a further reduction (with respect to what has already been done with the previously used known MOR techniques 240) of the numerical space in which the virtual model operates. The model, in fact, once calibrated on the physical system is no longer parametric, as all the parameters are known. It is therefore possible to project the space of dimension r obtained in step 240 onto a space s of smaller dimension. This innovative procedure further reduces the computational complexity of the model, which can be run on hardware devices where memory and computational power are limited.

The step 280 consists in installing the virtual model, integrating it on a hardware platform, or in a generic software simulation environment, for example, Matlab Simulink. The step 280 is the use of the reduced equations to simulate and to monitor the electric machine. This makes it possible to calculate in advance, according to the settings chosen by the user, the necessary memory and the operations required for the implementation of the virtual model on hardware and software platforms, thus guaranteeing the feasibility of real-time execution. These hardware and software platforms can be different from those used to obtain the reduced differential equations according to the invention.

Such hardware and software platforms can form a system for simulating and virtual monitoring of an electric machine, comprising:

- one or more current sensors configured to measure one or more respective currents flowing in said electric machine;

- one or more temperature sensors configured to measure one or more respective temperatures at pre-determined points of the electric machine or of an environment where the electric machine is; and

- a computer connected to said one or more current sensors and to said one or more temperature sensors; wherein a program configured to carry out step H of the method according to the invention is installed on said computer.

From what has been described above it is apparent that the improved simulation and monitoring method of an electric machine can be used to achieve specific technical purposes, such as for example (i) the monitoring of a physical parameter, such as for example the temperature, of one or more predetermined points of the electric machine or a component of the electric machine; (ii) the discrepancy between the data produced by the physical sensor and the data produced by the virtual sensor, in order to determine an anomaly in the reading or in the operation of the physical sensor; (iii) checking the operation of the electric machine or its component based on the information obtained by monitoring a physical parameter, in order to improve the performance of the electric machine and/or reduce the probability of its failure.

Application examples of the simulation and monitoring method will be described as follows.

As shown in Fig. 9, in a first exemplary application the presence of at least one physical sensor is exploited to acquire the measurements relating to a measured physical parameter and compare the measurement obtained from the physical sensor with the measurement determined by means of the virtual sensor arranged in the same position as the physical sensor.

For example, by placing a virtual sensor in a position in the digital model corresponding to the same position as the physical sensor, it can be achieved a virtual redundancy of the physical sensor, capable of determining one or more temperatures TDT in corresponding one or more pre-determined points of the model of the electric motor.

Said one or more temperatures of the model constitute an estimate of one or more temperatures, which should be detected by the physical sensors in one or more pre-determined points of the electric machine.

The placement of a virtual sensor can take place during the digital twin construction process.

The method can proceed with an acquisition step of one or more respective temperatures from one or more physical temperature sensors Tmeans configured to measure said one or more respective temperatures in one or more pre-determined points of the electric machine or of an environment where there is an electric machine.

The method further comprises the step of determining one or more temperatures TDT in corresponding one or more pre-determined points of the digital model of the electric machine, wherein said one or more pre-determined points of the digital model correspond to said one or more pre-determined points of the electric machine.

This is followed by a comparison step of one or more temperatures acquired by the virtual sensors TDT with one or more respective temperatures Tmeans acquired by one or more physical temperature sensors.

Based on the comparison made, the method can determine a difference between the data produced by physical sensors and the data produced by virtual sensors. This deviation will be indicative of a potential anomaly associated with said one or more temperature sensors, and/or with the electric machine.

The determination of the temperature values obtained from the virtual sensor can be synchronous with the sampling of the temperature obtained from the physical sensor. This also makes it possible to track the deviation between the data produced by physical sensors and the data produced by virtual sensors over time.

This first application example makes it possible to promptly recognize the occurrence of an anomaly; in fact, in response to a determination that the deviation reaches a threshold value, information indicative of the achievement of the threshold value can be transmitted to a control module of the electric machine. The control module can consequently intervene in the actuation of the machine, in order to reduce the damage or avoid the failure of the entire electric machine, for example by interrupting its operation.

In a second application example, through the use of the simulation and monitoring method, monitoring the average temperature and the thermal oscillation amplitude of an electrical junction/contact of an electronic component of an electric machine without the use of specialized equipment or dedicated physical sensors is possible.

For example, an electric machine can include a three-step inverter shown in Fig. 10, which has the task of transforming electric energy into mechanical energy or vice versa and can be actively controlled by a dedicated control unit (ECU).

In particular, the three-step inverter in Fig. 10 allows an alternating current electric traction motor to be interfaced with an energy accumulation system that is capable of delivering direct current.

The inverter is equipped with electronic components such as, for example, electronic switches which open and close in a certain sequence and allow the energy to be modulated so as to make it compatible with the request from the electric motor. For this reason, an oscillatory thermal phenomenon, also called "swing", can be observed on the electronic switches, through which all the energy directed to the electric motor passes. In fact, when the switch is in conduction (closed switch) its temperature suddenly increases, while when the switch is off (open switch), its temperature decreases because it cools down by exchanging heat with the environment. This continuous electrical opening and closing of the switch cause continuous thermal stress on the component which is heated and cooled at even very high frequencies (of the order of hundreds of Hertz).

This phenomenon is physically related to mechanical fatigue stress of a component which, after a certain number of stress cycles, reaches failure. In the case of the electronic switch, “lifting” and “cracking” mechanisms can be triggered as shown in Fig. 1 1 , in which degradation of the contact/junction points occurs at a microscopic level and the switch fails.

Therefore the simulation and monitoring method described allows monitoring of the average temperature and the oscillation amplitude on an electrical junction/contact.

For example, the method may comprise a step of determining one or more temperature values function in a short time or in real-time from one or more virtual sensors arranged in the position of the junction/electrical contact or in the vicinity of the junction/electrical contact; a step of calculating an oscillation average temperature and thermal oscillation amplitude on the basis of the thermal data obtained; and a step of comparison of said oscillation average temperature of and thermal oscillation amplitude with respective threshold values, in order to determine whether said threshold values have been reached.

Based on the average temperature and thermal oscillation amplitude, it is possible to determine the thermal stress to which the component is subjected and consequently the state of degradation of the component itself.

Furthermore, it is possible to exploit the thermal data obtained to actively manipulate the opening and closing of the electronic switches by means of a control unit of the component and in such a way as to (i) avoid bringing the average temperature of oscillation into the critical zone, and (ii) reduce the amplitude of the oscillation itself.

In a third application example, through the use of the simulation and monitoring method, it is possible to monitor the local internal temperature of the rotor of an electric machine in one or more points exposed to demagnetizing fields, produced by the stator current.

The increase in the local internal temperature of the rotor negatively influences the magnetization characteristic of the permanent magnets present in the rotor, making the demagnetization phenomena more frequent. Therefore the simulation and monitoring method described allows the monitoring of the temperature in one or more selected points in a short time or in real-time.

For example, the method can comprise a step of selecting one or more points exposed to demagnetized magnetic fields, determining at least one temperature value from one or more virtual sensors arranged in one or more selected points or close to them; and a step of comparing at least one temperature value obtained with respective threshold values, in order to determine that said respective threshold values have been reached.

Finally, it is possible to drive the electric machine, in such a way as to reduce the increase in temperatures in said one or more selected points, preventing the occurrence of local demagnetization phenomena, which then risk compromising the electric machine over time.

Example of Prototyping and Testing embodiment

Below is a proof of concept of the Improved Virtual Monitoring and Simulation Method 200 with experimental tests performed in the laboratory.

Initially, a faithful model of an electric motor has been created by following the first three method steps 210, 220, 230, and then using the CAD, mesh and FEM techniques. In this way, a three-dimensional model of the electric motor has been obtained, in which geometry, materials, and physical properties are specified.

Subsequently, the model has been parameterized and reduced through PMOR techniques (240), obtaining thermal parameters to be optimized. To do this, the temperature of at least one point of the electric motor has been measured directly during step 250. In particular, the external temperature of the casing has been measured in an operating cycle of the motor, which explored about 70% of the thermal dynamics of the system. Fig. 7 shows the effective values of the currents, heat sources of the system, recorded in one hour of operation.

At this point, the parameter optimization algorithm 260 has been set up. Fig. 6 shows the results obtained by the algorithm, which solves the optimization problem described above. The number of parameters to be optimized is 13, corresponding to the specific heats and thermal conductivities of all the materials involved in the system, to which is added the convective heat exchange coefficient with the external environment. The model has been further reduced, again using the model order reduction techniques 270 (non-parametric) on the aforementioned system with optimized and fixed parameters.

Finally, the resulting digital twin was integrated into the microcontroller that drives the motor through Matlab Simulink software on a PC (step 280).

Fig. 8 shows the trend of the virtual model with respect to two sets of measurements taken inside and outside the electric motor. This figure shows the predictive capacity of the model that is capable of making predictions on a different spatial point than the one chosen for the training. Furthermore, it can be noted the high degree of correspondence between the complete model performed with a complex FEM simulation and the virtual model (ROM) using a low computational cost. The table below shows the parameters of the two models in comparison.

It is important to underline that the maximum error committed by the digital twin in estimating the temperature is 1 .5 °C, which is equal to the sensitivity of the K-type thermocouple sensor used for the experiment.

Advantages of the invention

From the previous description, it is evident that the improved simulation and monitoring method of an electric machine allows for achieving the intended purposes by reducing the computational complexity of the current methods of the prior art while allowing to implement of a virtual model on integrated platforms where power and memory are limited.

In the foregoing, the preferred embodiments have been described and variants of the present invention have been suggested, but it should be understood that those skilled in the art will be able to make modifications and changes without thereby departing from the relative scope of protection, as defined by the attached claims.