A method for determining a torque of one or more electric motors of an electric powertrain of a motor vehicle with exploitation of an electric power reserve of a power battery of the powertrain

Abstract

There is described a method for determining a torque of one or more electric motors of an electric powertrain of a motor vehicle with exploitation of an electric power reserve of a power battery of the powertrain. The method enables controlling manoeuvres of short duration, such as e.g. the intervention of an anti-jerk system.

Description

[0001] "A method for determining a torque of one or more electric motors of an electric powertrain of a motor vehicle with exploitation of an electric power reserve of a power battery of the powertrain"

[0002] TEXT OF THE DESCRIPTION

[0003] Field of the Invention

[0004] The present invention relates to vehicles with an electric powertrain of the type including one or more traction motors distributed between a front axle and a rear axle.

[0005] Known Art

[0006] In the vehicles with an electric powertrain it is of paramount importance to control the power delivery from the battery or the batteries to the electric motor (s) (and vice versa, in the regeneration phase) so as to meet the constraints of torque delivery and distribution envisaged for the vehicle dynamics targets, and in order to avoid load profiles (for the motors and for the batteries) which may damage the motors and / or the batteries.

[0007] However, in the known art the delivery of electric power to the motors, as well as the power supply to the batteries in the regeneration phase, are only controlled based on the torque targets envisaged by the vehicle dynamics control. In other words, operating conditions are accepted which - albeit temporarily - exceed power delivery or supply thresholds having a critical nature. Moreover, exceeding said thresholds often takes place without being noticed by the control strategy of the powertrain, precisely because it is only based on torque targets for each motor, and therefore it is inherently ineffective as regards the implementation of a corrective action of any kind for controlling (and moderating) and electric power flow. As a solution of this problem, the Applicant has proposed an open-loop control method of the torque delivered by one or more electric motors of a powertrain, in the Italian Industrial Invention Patent Application n. 10202300002351, which takes into account both the needs regarding the vehicle dynamics and the needs regarding a limitation of the electric power flow.

[0008] Certain situations may arise, particularly during manoeuvres of short or very short duration - for example during the intervention of an anti-jerk system - wherein a control based on operational limits regarding the electric power flow may limit the efficacy of such manoeuvres. On the other hand, if a solution of such further technical problem were to be found in the known art, while removing the constraint on the operational limits in terms of electric power flow, it would become apparent that the problem anyway arises of exceeding the power delivery or supply thresholds having a critical nature.

[0009] Object of the Invention

[0010] The invention aims at solving the technical problem outlined in the foregoing. Specifically, the object of the invention is that of providing a method for controlling the torque of one or more electric motors of the electric powertrain of a vehicle, thereby enabling performing manoeuvres of short duration while exceeding the operational limits of the electric power flow but without exceeding power delivery or supply thresholds having a critical nature, while moreover complying with the torque distribution targets within the powertrain.

[0011] Summary of the Invention

[0012] The object of the invention is achieved by means of a method having the features set forth in the claims that follow, which form an integral part of the technical disclosure provided herein in relation to the invention. Brief Description of the Figures

[0013] The invention will now be described with reference to the annexed Figures, which are provided by way of non-limiting example only and wherein:

[0014] Figures 1, 2 schematically show a first configuration of a vehicle on which a first embodiment of the method according to the invention is implemented,

[0015] - Figures 3, 4 schematically show a second and a third configuration of vehicles on which a second and a third embodiment of the method according to the invention are implemented, whereas Figure 5 is a graphical representation of the same implementation,

[0016] - Figures 6, 7 schematically show a fourth and a fifth configuration of vehicles on which a fourth and a fifth embodiment of the method according to the invention are implemented, whereas Figure 8 is a graphical representation of the same implementation,

[0017] - Figures 9, 10 are representative of a sixth and a seventh configuration of vehicles on which a sixth and a seventh embodiment of the invention are implemented, whereas Figure 11 is a graphical representation of the same implementation, and

[0018] - Figure 12 represents an eighth configuration of a vehicle on which an eighth embodiment of the invention is implemented, whereas Figure 13 is an analytical representation of the same implementation.

[0019] Detailed Description

[0020] In various embodiments, referring to Figures 1, 3, 4, 6, 7, 9, 10, 12, the present invention comprises a method for determining a torque of one or more electric motors of an electric powertrain of a motor vehicle V, with exploitation of an electric power reserve of a power battery of the powertrain.

[0021] The one or more electric motors are operatively associated with a front axle and / or a rear axle of the vehicle, or with respective individual wheels of one and the same axle. In this way, a power flow is exchanged between each motor and (at least) one axle or (at least) one wheel of the vehicle, for the traction of the same vehicle.

[0022] The wording "power flow" indicates both a power flow into the electric motor (from a battery BT), i.e. a flow which originates a driving action of the motor, and a power flow out of the electric motor (and into the battery BT), i.e. a flow which originates when the electric motor is subjected to a resistant load (braking or slowing down due to the vehicle inertia) and operates as an electric generator. The reference Pn in the Figures (with n = 1, 2, 3, 4 in the presently considered embodiments) represents the general power flow associated with the n-th motor. For the sake of simplicity, the vehicle configurations schematically shown in the Figures envisage the presence of a single battery for powering each electric motor, but the method may be applied irrespective of the number or the configuration of the batteries, or of the association thereof with the one or more electric motors of the powertrain .

[0023] In various embodiments, referring to the Figures, the present invention comprises a method for controlling a torque of one or more electric motors M1; M2; M3; M4 of an electric powertrain of a vehicle V. Figures 1, 2 represent the implementation of the method with reference to a very general configuration of the powertrain, comprising a first electric motor M1 associated with a left wheel RL of a rear axle RA, a second electric motor M2 associated with a right wheel RR of the rear axle RA, a third electric motor M3 associated with a left wheel FL of a front axle FA, and a fourth electric motor M4 associated with a right wheel FR of the front axle FA, but it is generally applicable to a plurality of configurations having a smaller number of motors and a different arrangement and association thereof, such as the ones depicted in the following Figures, which are described in the respective following paragraphs of the description.

[0024] According to the invention, and with reference to the Figures 1, 2, the method comprises:

[0025] - defining, for each n-th electric motor M1, M2, M3, M4, a limit value of an n-th electric power flow Piim,n as a polynomial with expression anTn2+bnTn+cn, where an, bn, cnare coefficients dependent on a rotational speed of the corresponding n-th electric motor, and Tnis a torque of the corresponding n-th electric motor,

[0026] - defining an overall limit value Plim, TOTof an electric power flow of the powertrain, comprising a sum of each n-th limit power flow Plim,n,

[0027] - defining, for each n-th electric motor M1, M2, M3, M4, an extended value of an n-th electric power flow Plim,ext,nas a polynomial with expression aext,nTn2+bext , nTn+Cext,nWhere aext,n, bext,n, Cext,nare coefficients dependent on a rotational speed of the corresponding n-th electric motor, and Tnis a torque of the corresponding n-th electric motor,

[0028] - defining an overall extended value Plim,ext,TOTof an electric power flow of the powertrain, comprising a sum of each n-th extended power flow Plim,ext,n,

[0029] - defining a maximum value TnMAXfor the torque Tnof each n-th electric motor by intersection between a geometric locus corresponding to said overall limit value of an electric power flow of the powertrain Plim, TOTand one or more geometric loci each representative of a boundary condition formulated as a function of the torque Tnof one or more of the electric motors,

[0030] - defining an extended value TnEXTfor the torque Tn of each n-th electric motor by intersection between a geometric locus corresponding to a line with origin in a geometric locus having coordinates defined by each maximum value TnMAX, and direction determined by a vector vextwith n components sn, one for each n-th electric motor, and the geometric locus corresponding to said overall extended value of an electric power flow of the powertrain Plim,ext,TOT•

[0031] Generally speaking, examples of boundary conditions - the application whereof will be better understood with reference to the specific embodiments shown in the Figures - may comprise at least one among:

[0032] - a ratio m of a torque delivered to a front axle FA to a torque delivered to a rear axle RA of the motor vehicle V,

[0033] - a relationship between a torque delivered to a right wheel and a left wheel of an axle FA or RA of the motor vehicle.

[0034] Referring to the Figures 1 and 2, in a first embodiment of the invention the method is applied to a vehicle V with a powertrain comprising an electric motor for each of the wheels FL, FR, RL, RR.

[0035] Referring to Figure 1, the powertrain of the vehicle V in question comprises a first electric motor M1 operatively associated with a rear left wheel RL of the vehicle, a second electric motor M2 operatively associated with a rear right wheel RR of the vehicle, a third electric motor M3 operatively associated with a front left wheel of the vehicle, and a fourth electric motor M4 operatively associated with a front right wheel of the vehicle V.

[0036] This means that each electric motor M1-M4 delivers a torque to the wheel operatively associated therewith.

[0037] The electric motors M1, M2, M3, M4 are powered by a single battery (or battery pack) BT. In the schematical representation of Figure 1, the solid-line arrows indicate a power flow into the motors M1, M2, M3, M4 from the battery BT (power absorbed by the motors), while the dotted-line arrows indicate a power flow out of the motors M1, M2, M3, M4 towards the battery BT (power generated by the motors).

[0038] With this configuration, as taught in the Italian Industrial Invention Patent Application no. 10202300002351, it is possible to express a limit value Piim,n of an n-th electric power flow for each of the motors M1 (index n = 1, torque = T1), M2 (index n = 2, torque = T2), M3 (index n = 3, torque = T3), M4 (index n = 4, torque = T4) - or, during the operation as a generator, the resistant torque applied by each motor M1, M2, M3, M4 - as a second-degree polynomial with the following expressions:

[0039] - Motor M1: Plim,1= a1T12+b1T1+c1

[0040] - Motor M2: Plim,2= a2T22+b2T2+c2- Motor M3: Plim,3=a3T32+b3T3+c3

[0041] - Motor M4: Plim,4= a4T42+b4T4+c4

[0042] The coefficients a1, b2, c1, a2, b2, c2, a3, b3, c3, a4, b4, c4are mapped as a function of the rotational speed of each of the electric motors M1, M2, M3, M4, and therefore the expression of the n-th electric power flow varies as a function of the rotational speed of the n-th electric motor.

[0043] It is therefore simple to determine the expression of the overall limit value Plim, TOTas a sum of the n-th power flows Plim,1, Plim,2, Plim,3, Plim,4

[0044] (1A) Plim, TOT=a1T12+b1T1+c1+ a2T22+b2T2+c2+ a3T32+b3T3+c3+ a4T42+b4T4+c4 The equation which describes the electric power flow Plim, TOT(absorbed by the motors or generated by the motors) is an equation with four variables T4, T2, T3, T4which may be solved if combined into a system with three further equations, corresponding to the boundary conditions mentioned in the foregoing. In the case of the embodiment of the Figures 1, 2, said equations comprise :

[0045] - a first difference 2ΔTVR(2A) between the second torque T2delivered (or absorbed) by the second motor M2 to (or from) the rear right wheel RR and the first torque T1delivered (or absorbed) by the first motor M1 to (or from) the rear left wheel RL;

[0046] - a second difference 2ΔTVF(2A') between the fourth torque T4delivered (or absorbed) by the fourth motor M4 to (or from) the front right wheel FR and the third torque T3delivered (or absorbed) by the third motor M3 to (or from) the front left wheel FL.

[0047] In other words, these two relationships represent a condition of active asymmetrical torque distribution between the wheels of the rear axle RA and of the front axle FA (torque vectoring - the coefficient 2 is a mere convention, due to the fact that the quantity ΔTVR, ΔTVFrepresents the torque which is subtracted from one wheel and transferred to the other, and therefore the overall difference amounts to 2ΔTV)

[0048] (2A) T2- T1= 2ΔTVR

[0049] (2A') T4- T3= 2ΔTVF

[0050] - a ratio m of a sum of the fourth torque T4and of the third torque T3delivered (or absorbed) by the motors M4, M3 to (or from) the respective wheels of the front axle FA to a sum of the torque T2and of the torque T4delivered (or absorbed) by the motors M2, M1 to (or from) the respective wheels of the rear axle RA, and therefore

[0051] (3A) m = (T4+T3) / (T2+T1) m therefore expresses a torque distribution ratio between the front axle and the rear axle.

[0052] This leads to obtaining the system of equations:

[0053] (1A) Plim, TOT— a1T12+b1T1+c1+ a2T22+b2T2+c2+ a3T32+b3T3+c3+ a4T42+b4T4+c4

[0054] (2A) T2- T1= 2ΔTVR(2A') T4- T3= 2ΔTVF(3A) m = (T4+T3) / (T2+T1)

[0055] The equation (1A), i.e. the amount Plim, TOT, describes a four-dimensional geometric locus (dimensions T1, T2, T3,T4) which cannot be represented graphically, but which is completely defined in itself. In the same way, the equations (2A), (2A'), (3A) describe geometric loci in the same four-dimensional space, the common intersection whereof with the geometric locus Plim, TOTyields a locus PW having coordinates (T1,MAX, T2,MAX, T3,MAX, T4,MAX) corresponding to the maximum torques deliverable (or absorbable) by the electric motors M1, M2, M3, M4 at the rotational speeds at a given instant, and as a function of the power limit envisaged for the instantaneous operating condition. In other words, the geometric locus Plim, TOTis a (maximum) isopower locus where the locus PW must be located in order to simultaneously meet the conditions of torque distribution within the powertrain and the limit value condition of the overall power flow in the powertrain.

[0056] As set forth at the beginning of the present description, operating with reference to the power limit Plim, TOTmay jeopardize the execution of short-duration manoeuvres , such aass the intervention of an anti- j erk system. According to the invention, considering the short duration of the manoeuvres which the method is destined to support, it is possible to refer to a second power limit value, or extended power value - both for each motor ( Pext, n) and globally (Pext,TOT) - which again may be expressed as a second-degree polynomial. The extended power value is greater than the limit value

[0057] (both for each motor and globally) and the surplus in comparison with the value Plim, TOTis drawn from a power reserve of the battery of the powertrain which it powers.

[0058] The value Pext, n, i . e . the extended value of an n-th electric power flow wwhhiicchh is either input oorr output according to the operating mode, either for driving or for regeneration, may be expressed for each of the motors Ml (index n = 1, torque = T1,ext) , M2 (index n = 2, torque = T2,EXT),) M3 (index n = 3, torque = T3,ext) , M4 (index n = 4, torque = T4,ext) as a second-degree polynomial with the following expressions:

[0059] Motor M1 : Pext , 1= aext,1T12+ bext,1T1+ cext,1

[0060] Motor M2 : Pext , 2= aext,2T22+ bext,2T2+ cext,2

[0061] Motor M3 : Pext , 3= aext,3T32+ bext,3T3+ cext,3- Motor M4 : Pext , 4= aext,4T42+ bext,4T4+ cext,4

[0062] The coef f icients are mapped as a function of the rotational speed of each of the electric motors M1, M2, M3, MM44 (in the same way as the coefficients a1, b1, c1, a2, b2, c2, a3, b3, c3, a4, b4, c4) , and therefore the expression of the n-th extended electric power flow varies aass a function of the rotational speed of the n-th motor.

[0063] It is therefore simple to determine the expression of the overall extended valuPeext, ioi as a sum of the n-th extended power flows Pext,1, Pext,2, Pext,3,Pext,4

[0064] The expression of the valuePext, TOTidentifies, in the same way as Plim, TOT, an isopower geometric locus (having a power value higher than Plim, TOT) which, however, does not necessarily need to meet the boundary conditions envisaged by the vehicle dynamic balance, as determined by the dynamics control system of the same vehicle (unlike the case of Plim, TOT)• On the contrary, since the extended power value intervenes for short-duration manoeuvres which - as in the case of an activation of the anti-jerk system - inherently imply an alteration of the vehicle dynamics with respect to what is envisaged, the boundary conditions for solving the equation and for determining a working point with extended power PWexthaving coordinates (T1,extT2,extT3,extT4,ext) put into mutual relationship the torque values - and specifically the (absolute value of) torque increase - in the passage from the isopower locus Plim, TOTto the isopower locus Pext, TOT•

[0065] The increase of the torque absolute value in the passage from the isopower locus Plim, TOTto the isopower locuPext, TOT, i.e. the evolution from each value Tn,MAXto the corresponding value Tn,ext, follows a predetermined relationship. According to the invention, such a relationship is defined by an evolution belonging to a line with origin belonging to the geometric locus Plim, TOT(i.e., a geometric locus having coordinates defined by each maximum value TnMAX, thus T1,MAX; T2,MAX;T3,MAX; T4,MAXin the present case) and direction determined by a vector with as many one or more components sn, one for each n-th electric motor (thus s1, s2, s3, s4; such values represent the angular coefficients in space).

[0066] This enables writing in a parametric form the equation of said line in the four-dimensional hyperspace T1, T2, T3, T4and with respect to the origin having coordinates (T1,MAX; T2, MAX; T3,MAX; T4,MAX) and in a parametric form by means of the expressions (5), (6),

[0067] (7), (8) of Figure 2, i.e.:

[0068] (5) T1,ext= T1, MAX+ s1λ (thus T1,ext= T1, MAX= s1λ)

[0069] (6) T2,ext=T2, MAX+ s2λ (thus T2,ext=T2, MAX= s2λ)

[0070] (7) T3,ext= T3, MAX+ s3λ (thus T3,ext= T3, MAX= s3λ)

[0071] (8) T4,ext= T4, MAX+ s4λ (thus T4,ext= T4, MAX= s4λ)

[0072] More generally, it will be appreciated that the line considered in the method according to the invention has an n-dimensional parametric equation (wherein the dimensions of the vectorial space depend on the number of electric motors) of the type Tn,ext= Tn,MAX+ snλ, where X is the parameter of the equation. snrepresents both one of the components of the vector vextalong which the line is oriented, and - with reference to the orthogonal vector base with respect to which the parametric equation is written at the n-th component of a corresponding vector vnof the orthogonal base, wherein vnhas n i-th components having a value 0 if i ≠ n, and a value snif i = n.

[0073] In the most general present case, the orthogonal base with respect to which the parametric equation of the line is defined comprises the vectors: v1(s1, 0, 0, 0) v2(0, s2, 0, 0) v3(0, 0, s3, 0) v4(0, 0, 0, s4) and globally the vector vexthas the components (s1, s2, s3, s4).

[0074] The working point PWextis therefore the result of the intersection between the line defined by the equations (5) to (8) and the geometric locus corresponding to the overall extended value of the electric power flow of the powertrain Pext,TOT. The equation deriving from the substitution of the expressions (5) to (8) into the equation (4) is an equation with a single variable - the parameter λ - which, once solved, enables determining the torque values T1,extT2,extT3,extT4,extwhile operating with the extended power value, thereby enabling controlling the torque of the electric motors M1-M4 (either delivered or absorbed, according to the circumstances) based on the needs of short-duration manoeuvres, such as those envisaging the intervention of an anti-jerk system.

[0075] In the following, a few further considerations are provided regarding the coefficients an, bn, cnand aext,n, bext,n, cext,n: they depend, as stated in the foregoing, on the rotational speed of the electric motors, but they show a further dependence - albeit in a much smaller amount with respect to the dependence on the rotational speed - on the supply voltage of the electric motors. During a manoeuvre which requires exceeding the power limit Plim, TOTand resorting to the extended power value Pext,TOT, the coefficients aext,n, bext,n, cext,nmay be instantaneously different from the coefficients an, bn, Cn(aext,n≠ an, bext,n≠ bn, cext,n≠ cn); therefore, at the same rotational speed - given the nature of the manoeuvre - the supply voltage to the electric motors may vary instantaneously, with an increase of the absolute value of the voltage itself. This phenomenon is more evident during the first stages of the manoeuvre, and tends to decrease in entity as the manoeuvre progresses. In preferred embodiments, the calculation is implemented by updating the data every 10 ms, and therefore the individual sets of data resulting from every calculation will reflect this evolution dynamics: in the first stages of the manoeuvre, the maximum deviation (or, at any rate, a non-negligible deviation) will be observed between the coefficients an, bn, cnand aext,;n;bext,;n;cext,n, whereas as the manoeuvre progresses the absolute value of the supply voltage will decrease, thereby aligning again with the value before the manoeuvre, and the supply current will simultaneously tend to increase. This means that the coefficients aext,n, bext,n, cext,nwill tend to align - until they coincide - with the coefficients an, bn, cnin the evolution of the same manoeuvre. The coincidence between the coefficients aext,n, bext,n, cext,nand an, bn, cnis achieved the more rapidly, the more rapid is the evolution dynamics of the supply voltage (deviation from the value preceding the manoeuvre and return to the same value). This is true for all the presently described and considered embodiments, irrespective of the number of electric motors involved (and therefore irrespective of the maximum value of the index n).

[0076] Referring to Figure 3, a second embodiment of the method according to the invention is shown with reference to a vehicle V comprising a first electric motor M1 operatively associated with a rear left wheel RL of the vehicle, a second electric motor M2 operatively associated with a rear right wheel RR of the vehicle, and a third electric motor M3 operatively associated with the front axle FA, thereby indicating a condition wherein the electric motor M3 delivers torque to both the right and the left wheel, FR, FL of the front axle FA. The electric motors M1, M2, M3 are powered by a single battery (or battery pack) BT. In the schematic representation of the Figures 1, 2, the solid-line arrows indicate a power flow into the motors M1, M2, M3 from the battery BT, whereas the dotted-line arrows indicate a power flow out of the motors M1, M2, M3 towards the battery BT.

[0077] With this configuration it is possible to express a limit value Plim,nof an n-th electric power flow absorbed or delivered by each of the motors M1 (index n = 1, torque = T1), M2 (index n = 2, torque = T2), M3 (index n = 3, torque = T3) as a second-degree polynomial with the following expressions: Motor M1: Plim,1= a1T12+b1T1+c1Motor M2: Plim,2 = a2T22+b2T2+c2Motor M3: Plim,3= a3T32+b3T3+c3

[0078] The coefficients a1, b1, c1, a2, b2, c,2and a3, b3, c3are mapped as a function of the rotational speed of each of the electric motors M1, M2, M3, and therefore the expression of the n-th electric power flow varies as a function of the rotational speed of the n-th motor.

[0079] It is therefore simple to determine the expression of the overall limit value Plim, TOTas a sum of the n-th power flows Plim,1, Plim,2, Plim,3

[0080] (IB) Plim, TOT= a1T12+b1T1+c1+ a2T22+b3T2+C2 + a3T32+b3T3+c3

[0081] The equation which describes the electric power flow Plim, TOTis an equation with three variables T1, T2, T3, which may be solved if combined into a system with two further equations corresponding to the boundary conditions mentioned in the foregoing. In the case of the embodiment of Figures 3 to 5, such equations comprise :

[0082] - a difference 2ΔTV (2A) between the second torque T2delivered by the second electric motor M2 to the rear right wheel RR and the first torque T2delivered by the first motor M1 to the rear left wheel RL. In other words, this relationship represents a condition of active asymmetrical torque distribution between the wheels of the rear axle RA (torque vectoring - the coefficient 2 is merely conventional, deriving from the fact that the quantity ΔTV represents the torque which is subtracted from a wheel and transferred to the other, and thus the overall difference amounts to a 2ΔTV)

[0083] (2A) T2- T1= 2ΔTV

[0084] - a ratio m of a third torque T3delivered by the third electric motor M3 to the front axle FA to a sum of a first torque T2delivered by the first motor M1 to the rear left wheel RL and a second torque T2delivered by the second motor M2 to the rear right wheel RR, thus

[0085] (3B) m = T3 / (T1+T2)

[0086] Therefore, m expresses a torque distribution ratio between the front axle and the rear axle.

[0087] From this, the following system of equations is derived:

[0088] (IB) Plim, TOT= a1T12+b1T1+c1+ a2T22+b2T2+c2+ a3T32+b3T3+c3(2A) T2- T1= 2ΔTV (3B) m = T3 / (T1+T2)

[0089] The solution of the system of equations is graphically shown in Figure 5.

[0090] The equation (1), therefore the amount Plim, TOT, describes a tridimensional geometric locus (dimensions T1, T2, T3) corresponding to an (isopower) ellipsoidal surface, while the equations 2 and 3 respectively describe a plane PTV, oriented along the axis T3and parallel to a plane BP bisecting the octant T1T2, and a line Rz (in space) belonging to the plane PTV. The intersection of the plane PTV, the line Rz and the surface Plim, TOTcorresponds to a point PW having coordinates (T1, MAX, T2, MAX, T3, MAX), corresponding to the maximum torques which may be delivered (or absorbed) by the electric motors M1, M2, M3 at the rotational speeds at a given instant, and as a function of the power limit envisaged for the instantaneous operating condition. In other words, the geometric locus Plim, TOTdefines a (maximum) isopower surface whereon the point PW must be located in order to simultaneously meet the conditions of torque distribution within the powertrain and the condition of limit value of the overall power flow in the powertrain.

[0091] The same considerations may be made with reference to the third embodiment of Figure 4, which substantially corresponds to a configuration mirroring the configuration of Figure 1, with a first electric motor M1 operatively associated with a front left wheel FL, a second electric motor M2 operatively associated with a front right wheel FR, and a third electric motor M3 operatively associated with a rear axle RA. Also in this case, the following equations may be written

[0092] - Motor M1: Plim,1= a1T12+b1T1+c1

[0093] - Motor M2: Plim,2 = a2T22+b2T2+c2- Motor M3: Plim,3=a3T32+b3T3+c3

[0094] - Plim, TOT=a1T12+b1T1+c1+ a2T22+b2T2+c2+ a3T32+b3T3+c3

[0095] What changes is the operative definition of the boundary conditions, due to the different arrangement of the powertrain of the vehicle V, but the mathematical definition remains the same:

[0096] - a difference 2ΔTV between the second torque T2delivered by the second motor M2 to the front right wheel FR and the first torque T2delivered by the first motor M1 to the front left wheel FL. In other words, this is a relation representing a condition of active asymmetrical torque distribution between the wheels of the front axle FA (torque vectoring - the coefficient 2 is merely conventional, due to the fact that the amount ΔTV represents the torque which is subtracted from a wheel and transferred to the other, and therefore the overall difference amounts to 2ΔTV)

[0097] T2- T1= 2ΔTV

[0098] - a ratio m of a sum of a first torque T1delivered by the first motor M1 to the front left wheel FL and a second torque T2delivered by the second motor M2 to the front right wheel FR to a third torque T3delivered by the third electric motor M3 to the rear axle RA, thus

[0099] (3B') m = (T1+T2) / T3

[0100] Wherefrom, again, the system of equations (1), (2), (3) mentioned in the foregoing, having identical solution (Figure 3).

[0101] In the case of the embodiment of Figures 3 and 4, the valuePext, n may be expressed, for each of the motors M1 (index n = 1, torque = T1,ext)=, M2 (index n = 2, torque = T2,ext), M3 (index n = 3, torque = T3,ext) as a second- degree polynomial with the following expressions:

[0102] Motor M1: Pe xt , 1= aext,1T12+ be x t,1T1+ cext,1

[0103] Motor M2: Pe xt , 2= aext,2T22+ be x t,2T2+ cext,2

[0104] Motor M3: Pe xt , 3= aext,3T32+ be x t,3T3+ cext,3 The coefficients aext,1, bext,1, cext,2, aext,2, bext,2, Cext,2, aext,3, baext,3,caext,3are mapped as a function of the rotational speed of each of the electric motors M1, M2, M3 (in the same way as the coefficients a1, b1, c1, a2, b3, c2, a3, b3, c3), and therefore the expression of the n-th extended electric power flow varies as a function of the rotational speed of the n-th motor.

[0105] Therefore, it is simple to determine the expression of the overall extended valuePext,TOTas a sum of the n-th extended power flows Pext,i, Pext,2, Pext,3

[0106] (4B) Pext, TOTaext,1T12^+bext,1T1+cext , 1+ aext,2T22+bext,2T2+Cext , 2

[0107] + aext,3T3+bext , 3T3+Cext , 3

[0108] As has already been observed, the expression of the value Pext, TOTidentifies, in the same way as Plim, TOTan isopower geometric locus (having a power value higher than Plim, TOT) which, however, does not necessarily need to meet the boundary conditions envisaged by the vehicle dynamic balance, as determined by the dynamics control system of the same vehicle (contrarily to the case of Plim, TOT)• The boundary conditions for solving the equation and for determining an extended-power working point PWexthaving coordinates (T1,ext;=T2,extT3,ext) put into mutual relationship the torque values - and specifically the (absolute value) torque increase - in the passage from the isopower locus Plim, TOTto the isopower locuPsext, TOT.

[0109] The increment of the absolute value of the torque in the passage from the isopower locus Plim, TOTto the isopower locusPext, TOT, i.e. the evolution from each value Tn,MAXto the corresponding value Tn,ext, follows a predetermined relationship. According to the invention, said relationship is defined by an evolution belonging to a line with origin belonging to the geometric locus Plim, TOT(i.e., located in a geometric locus having the coordinates defined by each maximum value TnMAX, thus T1, MAX; T2, MAX; T3,MAXin the present case) and direction determined by a vector with as many one or more components sn, one for each n-th electric motor (thus s1, s2, s3; such values represent the angular coefficients in space and are represented in Figure 5, together with the line).

[0110] This enables writing the equation of said line in a parametric form in the tridimensional space T1, T2, T3and with respect to the origin having coordinates (T1,MAX; T2, MAX; T3,MAX), and in a parametric form by means of the expressions (5), (6), (7) in Figure 5, i.e.:

[0111] (5) T1,ext= T1, MAX+ s1λ (thus T1,ext= T1, MAX= s1λ)

[0112] (6) T2,ext=T2, MAX+ S2.X (thus T2,ext=T2,MAX+ s2λ)

[0113] (7) T3,ext= T3, MAX+ s3λ (thus T3,ext= T3, MAX= s3λ)

[0114] The working point PWextis therefore the result of the intersection between the line defined by the equations (5) to (7) and the (ellipsoidal) geometric locus corresponding to the overall extended value of the electric power flow of the powertrainPext,TOT. The equation resulting from the substitution of the expressions (5) to (7) into the equation (4B) is an equation with a single variable - i.e., the parameter X - which, once solved, enables determining the torque values T1,ext; T2,ext; T3,extin the operation with extended power value, thereby enabling the control of the torque of the electric motors M1-M3 (which is either delivered or absorbed, according to circumstances) based on the needs of short-duration manoeuvres such as an intervention of an anti-jerk system.

[0115] Referring to Figures 6 to 8, in a fourth and in a fifth embodiment, the method according to the invention is applied to a vehicle V with a powertrain including a single electric motor M1, operatively associated to the rear axle only (Figure 6) or to the front axle only (Figure 7).

[0116] In these embodiments, the limit value P1,limof the power flow of the electric motor M1 coincides with the overall value Plim, TOT, and the expression thereof corresponds to a parabola in the plane Plim, TOT_T1

[0117] (1C) P1,limPlim, TOT- a1T12+b1T1+c1where, as described in the foregoing, the coefficients a1, b2, c1, are mapped as a function of the rotational speed of the electric motor M1, and therefore the expression of the electric power flow P1,limvaries as a function of the rotational speed of the motor M1.

[0118] In these embodiments, the boundary condition (2) is substantially devoid of meaning, since the torque delivered to the right and to the left wheels (whatever the axle) is the same, while the equation (3) substantially degenerates into the conditions wherein m = 0 or which correspond to a line parallel to the axis T1or to a line parallel to the axis Plim, TOTin the diagram of Figure 8. This means that the maximum torque deliverable by the motor M1 corresponds to a torque T1,MAXwhich solves the second-degree equation (1C) defined by the expression of Plim, TOT. In practice, the constraint Plim, TOTitself constitutes a boundary condition expressed as a function of the torque T1. In other words, reasoning in terms of a degenerate boundary condition, the intersection between the geometric locus defined by the expression of Plim, TOTand said degenerate boundary condition corresponds to the intersection between the parabola Plim, TOTand the line Plim = Plim, TOTfor the embodiment of Figure 6, and to the intersection between the parabola Plim, TOTand the line TI = T1,MAX. In the embodiments of Figures 6 to 8, the value Pext,nmay be expressed for the motor M1 only (index n = 1, torque = T1,ext) as a second-degree polynomial having the following expression:

[0119] - Motor M1: Pext, 1= aext, 1T12+bext, 1T1+cext, 1which identifies, in the plane P-T in Figure 8, a second parabola Pext, TOT. The coefficients aext, 1, bext, 1, cext, 1are mapped as a function of the rotational speed of the electric motor M1, and therefore the expression of the extended electric power flow varies as a function of the rotational speed of the motor M1.

[0120] It is therefore simple to determine the expression of the overall extended value Pext, TOT, as it is identical to the value Pext, 1.

[0121] (4C) Pext, TOT= Pext, 1= aext, 1T12+bext, 1T1+Cext, 1

[0122] As has already been observed in the foregoing, the expression of the value Pext, TOTidentifies, in the same way as Plim, TOT, an isopower geometric locus (having a power value higher than Plim, TOT) which, however, does not necessarily need to meet the boundary conditions envisaged by the vehicle dynamic balance, as determined by the dynamics control system of the vehicle (contrarily to the case of Plim, TOT)• The boundary conditions for solving the equation and for determining an extended power working point PWextin practice degenerate to the mere belonging of the point PWextto the parabola Pext, TOT.

[0123] The increase of the absolute value of the torque in the passage from the isopower locus Plim, TOTto the isopower locus Pext, TOT, i.e. the evolution from each value Tn, MAXto the corresponding value Tn,ext, follows a predetermined relationship, which is defined by an evolution belonging to a line having origin belonging to the geometric locus Plim, TOT(thus in a one-dimensional geometric locus having coordinate T1MAX, and direction determined by a vector with a component Si.

[0124] This enables writing in a parametric form the equation of the line in the one-dimensional space T1with respect to the origin having coordinates (T1, MAX) and in a parametric form by means of the expression (5) of Figure 8, i.e.:

[0125] (5) T1,ext= T1, MAX+ s1λ (thus T1,ext= T1, MAX= s1λ)

[0126] The working point PWextis shown in Figure 8. The equation resulting from the substitution of the expression (5) into the equation (4C) is an equation with a single variable - the parameter X - which, once solved, enables determining the torque value T1,ext. From a geometric point of view, it corresponds to the intersection between a line oriented in the dimension T1and the point T1,ext(one-dimensional geometric locus). As an alternative, in this specific embodiment it is simply possible to solve the equation which describes the expression Pext, TOT.

[0127] Due to what has been described in the foregoing with reference to the dependence of the coefficients ai, bi, c1and a1,ext, b1,ext, c1,ext, the evolution of the coefficients may be represented graphically with reference to the two parabolas represented in the diagram of Figure 8: the condition shown corresponds to a condition of maximum deviation between the value of the supply voltage of the electric motor in the steady state and the value of the supply voltage of the electric motor during the short-duration manoeuvre, resorting to the extended value Pext, TOTand, during the evolution of the manoeuvre, the result of the calculation update with the indicated frequency (10 ms) produces a realignment of both parabolas towards the parabola having coefficients a1, b1, c1(up to the condition a1, b1, c1= a1,ext, b1,ext, c1,ext, such that also the extended valuePext,TOTbecomes a point belonging to the parabola a1T12+b1T1+c1, thus Pext,TOT= a1T12+b1T1+c1).

[0128] Referring to the Figures 9, 10, 11, in a sixth and in a seventh embodiment the method is applied to a vehicle V having a powertrain comprising:

[0129] - a first electric motor M1 operatively associated with a rear left wheel RL of the vehicle, and a second electric motor M2 operatively associated with a rear right wheel RR of the vehicle (Figure 9), or

[0130] - a first electric motor M1 operatively associated with a front left wheel FL of the vehicle, and a second electric motor M2 operatively associated with a front right wheel FR of the vehicle (Figure 10).

[0131] Whatever the embodiment, the electric motors M1, M2 are powered by a single battery (or battery pack) BT and, as shown in the schematic representation of the Figures 9, 10, the solid-line arrows indicate a power flow into the motors M1, M2, M3 from the battery BT, whereas the dotted-line arrows indicate a power flow out of the motors M1, M2, M3 towards the battery BT.

[0132] With this configuration, it is possible to express (for the front axle or for the rear axle) a limit value Plim,nof an n-th electric power flow absorbed or delivered by each of the motors M1 (index n = 1, torque = T1), M2 (index n = 2, torque = T2) as a second-degree polynomial with the following expressions: Motor M1: Plim,1= a1T12+b1T1+c1Motor M2: Plim,2= a2T22+b2T2+c2

[0133] As has already been described in the foregoing, the coefficients a1, b2, c1, and a2, b2, c2are mapped as a function of the rotational speed of each of the electric motors M1, M2, and thus the expression of the n-th electric power flow varies as a function of the rotational speed of the n-th motor.

[0134] The expression of the overall limit value Plim, TOTis equal to a sum of the n-th power flows Plim,1, Plim,2,

[0135] (ID) Plim, TOT- a1T12+b1T1+c1+ a2T22+b2T2+c2

[0136] The equation (ID) which describes the electric power flow Plim, TOTis therefore an equation with two variables T1, T2, which may be solved if combined into a system with a further equation, corresponding to a boundary condition of the type corresponding to equation (2).

[0137] In more detail, in the case of the embodiments of Figures 9 and 10, the equation (2) is written with reference to the torques T1, T2, and it expresses:

[0138] - a difference 2ΔTV between the second torque T2delivered by the second motor M2 to the rear right wheel RR and the first torque T1delivered by the first motor M1 to the rear left wheel RL for Figure 9

[0139] - a difference 2ΔTV between the second torque T2delivered by the second motor M2 to the front right wheel FR and the first torque T1delivered by the first motor M1 to the front left wheel for Figure 10.

[0140] As in the foregoing, this is a relationship representing a condition of active asymmetrical torque distribution between the wheels of the rear or of the front axle RA (torque vectoring - the coefficient 2 is merely conventional, deriving from the fact that the amount ΔTV represents the torque which is subtracted from a wheel and transferred to the other, and thus the overall difference amounts to 2ΔTV)

[0141] (2) T2- T1= 2ΔTV Wherefrom the system of equations:

[0142] (ID) Plim, TOT- a1T12+b1T1+c1+ a2T22+b2T2+c2

[0143] (2) T2- T1= 2ΔTV

[0144] The solution of the system of equations is graphically shown in Figure 11. The equation (IB), thus the amount Plim, TOT, describes a bidimensional geometric locus (dimensions T1, T2) corresponding to an (isopower) ellipse, while the equation 2 describes a line Rz parallel to a bisector BS of the quadrant T1T2. The intersection between the line Rz and the curve Plim, TOTcorresponds to a point PW with coordinates (T1, MAX, T2, MAX), corresponding to the maximum torques deliverable (or absorbable) by the electric motors M1, M2 at the rotational speeds in a given instant, and as a function of the power limit envisaged for the instantaneous operating condition. In other words, the geometric locus Plim, TOTdefines a (maximum) isopower curve on which the point PW must be located in order to simultaneously meet the conditions of torque distribution within the powertrain and the condition of limit value of the overall power flow in the powertrain.

[0145] In the case of the embodiments of Figures 9 and 10, the value Pext,nmay be expressed by each of the motors M1 (index n = 1, torque = T1,ext), M2 (index n = 2, torque = T2,ext) as a second-degree polynomial with the following expressions :

[0146] Motor M1:

[0147] Motor M2:

[0148] The coefficients aext, 1bext, 1cext, 1aext,2, bext,2, cext,2,are mapped as a function of the rotational speed of each of the electric motors M1, M2 (in the same way as the coefficients a1, b1, c1, a2, b2, c2), and thus the expression of the n-th extended electric power flow varies as a function of the rotational speed of the n-th motor.

[0149] It is therefore simple to determine the expression of the overall extended valuePext,TOTas a sum of the n- th extended power flows Pext,1,, Pext,2

[0150] (4D) Pext,TOT= aext, 1T12+bext, 1T1+cext, 1+ aext , 2T22+bext , 2T2+Cext,2

[0151] As has already been observed in the foregoing, the expression of the valuePext,TOTidentifies, in the same way as Plim, TOTan isopower geometric locus (ellipse) (having a power value higher than Plim, TOT) which, however, does not necessarily need to meet the boundary conditions envisaged by the dynamic balance of the vehicle, as determined by the dynamics control system of the same vehicle (contrarily to the case of Plim, TOT)• The boundary conditions for solving the equation and for determining an extended power working point PWexthaving coordinates (T1,ext; T2,ext) put into mutual relationship the torque values - and specifically the (absolute value of) torque increase - in the passage from the isopower locus Plim, TOTto the isopower locusPext, TOT.

[0152] The increase of the absolute value of the torque in the passage from the isopower locus Plim, TOTto the isopower locusPext, TOT, i.e. the evolution from each value Tn,MAXto the corresponding value Tn,extfollows a predetermined relationship. According to the invention, said relationship is defined by an evolution belonging to a line with origin belonging to the geometric locus Plim, TOT(therefore, in a geometric locus with coordinates defined by each maximum value TnMAX, thus T1, MAX; T2, MAXin the present case) and direction determined by a vector with as many one or more components sn, one for each n-th electric motor (thus s1, s2; such values represent the angular coefficients in space and are represented in Figure 11, together with the line).

[0153] This enables writing in a parametric form the equation of said line in the bidimensional space T1, T2and with respect to the origin having coordinates (T1, MAX; T2,MAX) and in a parametric form by means of the expressions (5), (6) of Figure 11, i.e.:

[0154] (5) T1,ext= T1, MAX+ s1λ (thus T1,ext= T1, MAX= s1λ)

[0155] (6) T2,ext=T2, MAX+ S2.X (thus T2,ext=T2,MAX+ s2λ)

[0156] The working point PWextis therefore the result of the intersection between the line defined by the equations (5), (6) and the geometric locus corresponding to the overall extended value of the electric power flow of the powertrain Pext,ioi. The equation resulting from the substitution of the expressions (5), (6) into the equation (4D) is an equation with a single variable - the parameter X - which, once solved, enables determining the torque values T1,ext;= T2,extwhile operating with extended power value, thereby enabling controlling the torque of the electric motors M1, M2 (delivered or absorbed, depending on the circumstances) based on the needs of short-duration manoeuvres such as the intervention of an anti-jerk system.

[0157] Figure 12 and Figure 13 represent an eighth embodiment of the invention, wherein the method is applied to a vehicle V with a powertrain comprising a first electric motor M1 operatively associated with the rear axle RA, and a second electric motor M3 associated with the front axle FA.

[0158] With this configuration, it is possible to express a limit value Plim,nof an n-th electric power flow absorbed or delivered by each of the motors M1 (index n = 1, torque = T1), M3 (index n = 3, torque = T3) as a second-degree polynomial with the following expressions:

[0159] - Motor M1: Plim,1= a1T12+b1T1+c1- Motor M3: Plim,3= a3T32+b3T3+c3

[0160] As described in the foregoing, the coefficients ai, b1, c1, and a3, b3, c3are mapped as a function of the rotational speed of each of the electric motors M1, M3, and thus the expression of the n-th electric power flow varies as a function of the rotational speed of the n-th motor.

[0161] The expression of the overall limit value Plim, TOTamounts to a sum of the n-th power flows Plim,1, Plim,3,

[0162] (1E) Plim, TOT= a1T12+b1T1+c1+ a3T32+b3T3+c3

[0163] The equation (1E), which describes the electric power flow Plim, TOT, is therefore an equation with two variables T1, T3which may be solved if combined into a system with a further equation, corresponding to a boundary condition of the type (3).

[0164] In detail, in the embodiment of Figure 12, the equation (3E) is written with reference to the torques T1, T3and it expresses a ratio m of torque distribution between the front axle and the rear axle, thus a ratio of a third torque T3delivered by the second electric motor M3 to the front axle FA to a torque T1delivered by the first motor M1 to the rear axle

[0165] (3E) m = T3 / T1

[0166] The system of equations may therefore be written as

[0167] (1E) Plim, TOT- a1T12+b1T1+c1+ a3T32+b3T3+c3 (3E) m = T3 / T1

[0168] The solution of the system of equations is graphically shown in Figure 13. The equation (IE), thus the amount Plim, TOT, describes a bidimensional geometric locus (dimensions T1, T3) corresponding to an (isopower) ellipse, whereas the equation (3E) describes a line Rz passing through the origin of the quadrant T1T3. The intersection between the line Rz and the curve Plim, TOTcorresponds to a point PW having coordinates (T1,MAX, T3, MAX), corresponding to the maximum torques deliverable (or absorbable) by the electric motors M1, M3 at the rotational speeds at a given instant, and as a function of the power limit envisaged for the instantaneous operating condition. In other words, the geometric locus Plim, TOTdefines a (maximum) isopower curve, whereon the point PW must be located in order to simultaneously satisfy the conditions of torque distribution within the powertrain and the condition of limit value of the overall power flow in the powertrain.

[0169] In the embodiment of Figure 12, the value Pext,nmay be expressed for each of the motors M1 (index n = 1, torque = T1,ext), M3 (index n = 3, torque = T3,ext) as a second-degree polynomial with the following expressions:

[0170] Motor M1: Pext, 1= aext, 1T12+bext, 1T1+cext, 1Motor M3: Pext,3= aext,3T22+bext,3T2+cext,3

[0171] The coefficients aext, 1bext, 1cext, 1aext,3, bext,3, cext,3are mapped as a function of the rotational speed of each of the electric motors M1, M2 (in the same way as the coefficients a1, b1, c1, a3, b3, c3), and thus the expression of the n-th extended electric power flow varies as a function of the rotational speed of the n- th motor. It is therefore simple to determine the expression of the overall extended valuePext,TOTas a sum of the n- th extended power flowsPext, i, Pext,3

[0172] (4E) Pext,TOT= aext, 1T12+bext, 1T1+cext, 1+ aext , 3T22+bext , 3T2+cext,3

[0173] As has already been observed in the foregoing, the expression of the valuePext,TOTidentifies, in the same way as Plim,TOTan isopower geometric locus (ellipse) (having a power value higher than Plim, TOT) which, however, does not necessarily need to meet the boundary conditions envisaged by the vehicle dynamic balance as determined by the dynamics control system of the same vehicle (contrarily to the case of Plim, TOT)• The boundary conditions for solving the equation and for determining an extended power working point PWextwith coordinates (T1,ext; T3,ext) put into mutual relationship the torque values - and specifically the (absolute value of) torque increase - in the passage from the isopower locus Plim, TOTto the isopower locusPext, TOT.

[0174] The increase of the absolute value of the torque in the passage from the isopower locus Plim, TOTto the isopower locusPext, TOT, i.e. the evolution from each value Tn,MAXto the corresponding value Tn,ext, follows a predetermined relationship. According to the invention, said relationship is defined by an evolution belonging to a line with origin belonging to the geometric locus Plim, TOT(thus, in a geometric locus having coordinates defined by each maximum value TnMAX, therefore T1, MAX; T3, MAXin the present case) and direction determined by a vector with as many one or more components sn, one for each n-th electric motor (thus s1, s3; such values represent the angular coefficients in space and are represented in Figure 13, together with the line).

[0175] This enables writing in a parametric form the equation of said line in the bidimensional space T1, T3and with respect to the origin with coordinates (T1, MAX; T3, MAX) and in a parametric form by means of the expressions (5), (7) in Figure 13, i.e.:

[0176] (5) T1,ext= T1, MAX+ s1λ (thus T1,ext= T1, MAX= s1λ)

[0177] (7) T2,ext=T2, MAX+ S2.X (thus T2,ext=T2,MAX+ s2λ)

[0178] The working point PWextis therefore the result of the intersection between the line defined by the equations (5), (6) and the geometric locus corresponding to the overall extended value of electric power flow of the powertrain Pext,TOT. The equation resulting from the substitution of the expressions (5), (7) into the equation (4E) is an equation with a single variable - the parameter λ - which, once it is solved, enables determining the torque values T1,ext;= T3,extin the operation with extended power value, thereby enabling controlling the torque of the electric motors M1, M3 (delivered or absorbed, depending on the circumstances), based on the needs of short-duration manoeuvres, as in the intervention of an anti-jerk system.

[0179] The determination of the coordinates of the point PWext is in any case an operation which may easily be executed in real time by any electronic control unit, and therefore the electric motors M1, M2, M3, M4 (when they are present, respectively) may be controlled on a substantially instantaneous basis, therefore enabling performing in real time short-duration manoeuvres, with a deviation from the conditions of torque distribution determined by meeting the limit value Plim, TOT, but still remaining within a confidence domain represented by Pext,TOT. It will be appreciated, moreover, that the method according to the invention may be applied to any number and configuration of electric motors (thus, to expressions of limit power defined in any n-dimensional space), even if the motors are powered by independent batteries.

[0180] Of course, the implementation details and the embodiments may amply vary with respect to what has been described and illustrated herein without departing from the scope of the present invention, as defined by the annexed claims.

Claims

CLAIMS1. A method for controlling a torque of one or more electric motors (M1; M2; M3; M4) of an electric powertrain of a vehicle (V), the method including:- defining, for each n-th electric motor (M1; M2; M3; M4), a limit value of an n-th electric power flow(Plim,n) as a polynomial with expression anTn2+bnTn+cnwhere an, bn, cnare coefficients dependent on a rotational speed of the corresponding n-th electric motor, and Tnis a torque of the corresponding n-th electric motor,- defining an overall limit value (Plim, TOT) of an electric power flow of the powertrain comprising a sum of each n-th limit power flow (Plim,n),- defining, for each n-th electric motor (M1; M2; M3; M4), an extended value of an n-th electric power flow (Plim,ext,n) as a polynomial with expression Sext,nTn2+bext , nTn+Cext , nWhere aext,n,bext,n, Cext,nare coefficients dependent on a rotational speed of the corresponding n-th electric motor, and Tnis a torque of the corresponding n-th electric motor,- define an overall extended value (Plim,ext,TOT) of an electric power flow of the powertrain comprising a sum of each n-th extended power flow (Plim,ext,n),- defining a maximum value Tn,MAXfor the torque Tnof each n-th electric motor by intersection between a geometric locus corresponding to said overall limit value of an electric power flow of the powertrain (Plim, TOT) and one or more geometric locus each representative of a boundary condition formulated as a function of the torque Tnof one or more of the electric motors,- defining an extended value TnEXTfor the torque Tnof each n-th electric motor by intersection between a geometric locus corresponding to a line with origin(T1,MAX, T2,MAX, T3,MAX, T4,MAX) belonging to said geometric locus corresponding to the overall limit value of an electric power flow of the powertrain (Plim, TOT) and direction determined by a vector with n components sn, one for each n-th electric motor, and the geometric locus corresponding to said overall extended value of the electric power flow of the powertrain (Pext,TOT)•2. The method according to claim 1, wherein said overall extended value (Plim,ext,TOT) of an electric power flow of the powertrain is greater than said overall limit value of an electric power flow of the powertrain.

3. The method according to claim 1 or claim 2, wherein said line has a n-dimensional parametric equation of the type Tn,ext= Tn,MAX+ snλ, wherein λ represents the parameter of said parametric equation.

4. The method according to any one of the preceding claims, wherein said one or more boundary conditions comprise at least one among:- a relationship between a torque delivered, or absorbed, by one or more of said electric motors to, or from, a front axle (FA) and a torque delivered, or absorbed, by one or more of said electric motors to, or from, a rear axle of the vehicle (RA),- a relationship between a torque delivered, or absorbed, by a first electric motor to, or from, a right wheel of a vehicle axle, and a torque delivered, or absorbed, by a second electric motor to, or from, a left wheel of the same vehicle axle.

5. The method according to any one of the preceding claims, wherein the motor vehicle comprises a first electric motor (M1) operatively associated with a left rear wheel (RL), a second electric motor (M2) operatively associated with a right rear wheel (RR), and a third electric motor (M3) operatively associated with a front axle (FA), wherein said one or more boundary conditionsinclude:- a ratio m = T3 / (T1+ T2) between a third torque T3delivered, or absorbed, by the third electric motor (M3) to, or from, the front axle (FA) and a sum of a first torque T1delivered, or absorbed, by the first electric motor (M1) to, or from, the left rear wheel (RR) and a second torque T2delivered, or absorbed, by the second electric motor (M2) to, or from, the right rear wheel (RR), and- a difference 2ΔTV = T2- T1between the second torque T2delivered, or absorbed, by the second electric motor (M2) to, or from, the right rear wheel (RR) and the first torque T1delivered, or absorbed, by the first electric motor (M1) to, or from, the left rear wheel (RL), and where said line has three-dimensional parametric equationT1, ext= T1, MAX+ S1λ T2, ext= T2,MAX+ S2λT3, ext=T3,MAX+ S3λ6. The method according to any one of claims 1 to 4, wherein the vehicle (V) comprises a first electric motor (M1) operatively associated with a left rear wheel (RL), and a second electric motor (M2) operatively associated with a right rear wheel of the vehicle (V), wherein said one or more boundary conditions include a difference 2ΔTV = T2- T1between a second torque T2delivered by the second electric motor (M2) to the right rear wheel (RR) and a first torque T1delivered by the first electric motor (M1) to the left rear wheel (RL), and wherein said line has two-dimensional parametric equationT1, ext= T1, MAX+ m1λ T2, ext= T2,MAX+ m2λ7. The method according to any one of claims 1 to 4, wherein the vehicle (V) comprises a first electric motor (M1) operatively associated with a rear axle (RA) of the vehicle (V), and a second electric motor (M3) operatively associated with a front axle (FA) of the vehicle (V), wherein said one or more boundary conditions include a ratio m = T3 / TI between a second torque T3delivered by the second electric motor (M3) to the front axle (FA) and a first torque T1delivered by the first electric motor (M1) to the rear axle (RA), and wherein said line has two-dimensional parametric equationTl,ext=T1fMAX + S1XT3,ext=T3fMAX + S3X8. The method according to claim 1 or claim 2, wherein the vehicle (V) comprises a first electric motor (M1) operatively associated with a left rear wheel (RL), a second electric motor (M2) operatively associated with a right rear wheel, a third electric motor (M3) operatively associated with a left front wheel (FL), and a fourth electric motor (M4) operatively associated with a right front wheel, wherein said one or more boundary conditions include:- a first difference 2ΔTVR= T3- T1between a second torque T3delivered by the second electric motor (M2) to the right rear wheel (RR) and a first torque T1delivered by the first electric motor (M1) to the left rear wheel (RL),- a second difference 2ΔTVF = T4- T3between a fourth torque T4delivered by the fourth electric motor (M4) to the right front wheel (FR) and a third torque T3delivered by the third electric motor (M3) to the left front wheel (FL),- a ratio m = (T3+ T4) / (T1+ T2) between a sum of the third torque T3and the fourth torque T4and a sum of the first torque T1and the second torque T2, and where said line has a four-dimensional parametric equationT1, ext= T1, MAX+ S1λ T2, ext= T2,MAX+ S2λ T3, ext= T3,MAX+ S3λ T4, ext= T4,MAX+ S4λ9. The method according to any of the preceding claims, wherein the coefficients an, bn, cndepend additionally on a supply voltage of the corresponding n- th electric motor, and wherein the coefficients an,ext, bn,ext, cn,extdepend additionally on a supply voltage of the corresponding n-th electric motor, the coefficients an, bn, cnbeing different from the coefficients an,ext, bn,ext, Cn,ext, respectively.

10. The method according to any one of the preceding claims, wherein the coefficients an, bn, cnadditionally depend on a supply voltage of the corresponding n-th electric motor, and wherein the coefficients an,ext, bn,ext, cn,extadditionally depend on a supply voltage of the corresponding n-th electric motor, the coefficients an, bn, cnbeing equal to the coefficients an,ext, bn,ext, cn,ext, respectively.

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