METHOD FOR DETERMINING THE MAGNETIC FLUX OF AN ELECTRIC MACHINE

Description

[0001] The present invention relates to the field of control of electrical machines, in particular the control of synchronous electrical machines with salient poles. These electrical machines find application in particular in the field of motor vehicles.

[0002] Typically, an electrical machine consists of a rotor (moving part) and a stator (fixed part). The rotor is usually housed inside the stator. Typically, the stator is annular and is housed inside a tubular support for attachment.

[0003] The stator comprises magnetic flux generators, generally electrical windings. These windings are powered by a plurality (typically three) electrical phases, in order to generate a rotating magnetic field. In addition, depending on the type of electrical machine, particularly for synchronous electrical machines with salient poles, the rotor may comprise permanent magnets.

[0004] When such an electric machine is operating, an electric current flows through the windings to generate the magnetic field needed to drive the rotor into rotation.

[0005] There are several types of control for such electrical machines, as disclosed in documents US 2016 / 254771 A1, EP 2 582 036 A2 or EP 1 885 054 A1. It is known in particular that the direct torque control method is one of the most efficient control strategies, which allows torque control in both steady state and transient conditions, in particular for synchronous electrical machines with salient poles. In addition, this control method is easier to implement than an oriented field control method. Furthermore, this method requires less information relating to the electrical machine, and no current control loop is necessary, which in particular makes it possible to solve the delay problem linked to this current control loop.

[0006] However, the disadvantage of this control method is that it is based on the magnetic flux signal of the electric machine, while this quantity is not directly measurable when the electric machine is in operation. The magnetic flux must then be estimated, for example by means of an observer who uses the other measurable quantities. The paper: Mohamad Koteich. 'Flux estimation algorithms for electric drives: a comparative study'. In: Renewable Energies for Developing Countries (REDEC), 2016 3rd International Conference on. IEEE. 2016, pp. 1-6 (cit. on p. 5) reviews a number of methods for determining the magnetic flux.

[0007] Most prior art methods require knowledge of the resistance, rotor magnetic flux, and inductance. However, while the resistance can be considered known, the exact value of the rotor magnetic flux remains unknown, especially since it depends on the rotor temperature, which cannot be measured directly. Furthermore, in the presence of magnetic saturation, the inductance is a non-linear function of the current. Therefore, the problem of estimating the magnetic flux of the electric machine is non-trivial, leading to complexity and / or inaccuracy in the estimation.

[0008] Patent application FR 3035755 describes a method for controlling an electrical machine based on an estimation of the magnetic flux obtained by an observer and by a discrete extended Kalman algorithm. The modeling used in this method is not very robust to parametric variations, in particular because the magnetic flux is estimated indirectly, since it requires the calculation of currents. In addition, the model described in this patent application does not take into account the non-linearity of the inductances (magnetic saturation). In addition, the discrete extended Kalman algorithm does not allow for variability in the system over time. Indeed, the extended Kalman filter only takes into account the non-linearity linked to the presence of speed in the equations.

[0009] In order to overcome these drawbacks, the present invention relates to a method for determining the magnetic flux of an electrical machine, based on measurements of currents and voltages in the phases of the electrical machine, on a dynamic model of the magnetic flux, and on an adaptive Kalman filter. The dynamic model of the magnetic flux makes it possible to obtain an accurate (taking into account the variability in time of the system) and robust model of the magnetic flux. Thus, the magnetic flux is determined directly. The adaptive Kalman filter allows an adaptation of the noise covariance matrix as a function of the rotational speed of the electrical machine. Thus, the filter is efficient over a wide operating range of the electrical machine. In addition, the adaptive Kalman filter is robust with respect to variations in the magnetic flux of the rotor and the inductance.

[0010] The invention also relates to a method and a system for controlling an electrical machine implementing the method for determining the magnetic flux. The method according to the invention

[0011] The invention relates to a method for determining the magnetic flux of an electrical machine, said electrical machine comprising a rotor, a stator, said stator comprising windings connected to a plurality of electrical phases. For this method, the following steps are implemented: a) A current and a voltage are measured in said phases of said electrical machine; b) The electrical rotation speed of said rotor is determined, in particular as a function of the mechanical rotation speed of said rotor; c) A dynamic model of said magnetic flux of said electrical machine is constructed, said dynamic model of said magnetic flux linking said magnetic flux to the current and voltage of the phases of the electrical machine, and to said electrical rotation speed of said rotor; and d) Said magnetic flux φ is determined by applying an adaptive Kalman filter to said dynamic magnetic flux model, said dynamic magnetic flux model being applied to said current and voltage measurements and to said determined electrical rotation speed.

[0012] According to one embodiment, said electrical rotation speed is determined. ω e of said rotor by a formula of the type ω e = pωwith p the number of pairs of poles of the electric machine and ω the mechanical rotation speed of said rotor.

[0013] Advantageously, said mechanical rotation speed is determined by a PLL phase-locked loop method.

[0014] According to one implementation, said magnetic flux dynamic model (MFD) is written as φ d t = L d i d t + 3 2 Φ , φ q t = L qs i q t − b qs , if i q t ≤ − i qm , L q i q t , if − i qm ≤ i q t ≤ i qm , L qs i q t + b qs if i qm ≤ i q t with φ the magnetic flux of the electric machine, i the current, Φ the rotor flux, L the inductances of said electric machine, L qs ,b qs coefficients which take into account the saturation effect, d and q the axes in the Park frame, and i qm the quadrature current value for which the magnetic flux is a linear function of the quadrature current.

[0015] The said adaptive Kalman filter is applied by implementing the following steps: i) said dynamic magnetic flux model is modified by integrating uncertainties in said model and measurement noise; ii) said modified dynamic magnetic flux model is discretized; and iii) an adaptive Kalman filter algorithm is applied to said modified and discretized model.

[0016] The said adaptive Kalman filter algorithm is applied by implementing the following steps: (1) We initialize k = 0, the state vector x̂(0) and the state of the covariance matrix, P(0|0) = P 0 (2) We apply the time update and measurement update equations to obtain x̂ ( k | k ) and P ( k | k ) : x ^ k k − 1 = A d x ^ k − 1 k − 1 + B d u k − 1 , P k k − 1 = A d P k − 1 k − 1 A d T + B d Q ϵ B d T K k = P k k − 1 P k k − 1 + R − 1 x ^ k k = x ^ k k − 1 + K k x k − x ^ k k − 1 , P k k = I − K k P k k − 1 (3) We determine the said magnetic flux φ estimated at time k by the formulas φ ^ d k = x ^ 1 k k , φ ^ q k = x ^ 2 k k With k the discretized time, A_d,B_d, state realization matrices, P the covariance matrix of the state vector, R a calibration matrix, K the gain of the Kalman filter, Q_ε an adjustment parameter.

[0017] Advantageously, said electric machine is a salient pole synchronous electric machine.

[0018] Furthermore, the invention relates to a method for controlling an electrical machine, implementing the following steps: a) A magnetic flux φ of said electrical machine is determined by means of the method for determining said magnetic flux according to one of the preceding characteristics; and b) said electrical machine is controlled (CON) by means of said determined magnetic flux.

[0019] Advantageously, said electric machine (CON) is controlled according to a method of direct control of the torque of the electric machine implemented from said magnetic flux.

[0020] Furthermore, the invention relates to a system for controlling an electrical machine comprising control means for implementing the control method according to one of the preceding characteristics. Brief presentation of the figures

[0021] Other characteristics and advantages of the method according to the invention will appear on reading the following description of non-limiting examples of embodiments, with reference to the figures appended and described below. There figure 1 illustrates the steps of the method according to one embodiment of the invention. The figures 2 And 3 represent the values, in the Park frame, of the magnetic flux of the electric machine as a function of the current. Detailed description of the invention

[0022] The present invention relates to a method for determining, in real time, the magnetic flux of an electrical machine. The electrical machine comprises a rotor and a stator, the latter being equipped with windings connected to several electrical phases, for example to three electrical phases to generate a magnetic field allowing the rotation of the rotor.

[0023] There figure 1 describes, schematically and in a non-limiting manner, the steps of the method according to one embodiment of the invention. The method for determining the magnetic flux comprises the following steps: 1) Current and voltage measurements (MES) 2) Determination of the electrical rotation speed (VIT) 3) Construction of the dynamic magnetic flux model (MOD) 4) Application of the adaptive Kalman filter (KAL)

[0024] Steps 1) to 3) are independent, and can be performed in this order, in a different order or simultaneously.

[0025] Step 4) allows the magnetic flux φ of the electric machine to be determined.

[0026] Furthermore, the invention relates to a method for controlling an electrical machine. Such a control method comprises steps 1 to 4) described above and a step 5) of controlling the electrical machine (CTRL).

[0027] This control step 5) is an optional step. Indeed, the magnetic flux can be used in different ways, in particular for diagnosing electrical machine failure.

[0028] Steps 1) to 5) will be detailed in the rest of the description. Ratings:

[0029] During the description, the following notations will be used: v : voltages at the terminals of the phases of the electrical machine. i : currents flowing in the phases of the electrical machine. i qm: quadrature current value for which the magnetic flux is a linear function of the quadrature current ω : mechanical rotation speed of the rotor, corresponding to the rotation speed of the rotor of the electrical machine relative to the stator. ω e : electrical rotation speed of the rotor. Φ: intensity of the magnetic flux of the rotor magnet, considered for the method according to the invention, in a nominal case, for a temperature of 20°C. R(t): resistance of the coils of the electrical machine, this is a known parameter that can be obtained experimentally. L d: direct inductance of said electrical machine; this is a parameter of the electrical machine which is known (manufacturer data or obtained experimentally). L q:quadrature inductance of said electrical machine; this is a parameter of the electrical machine which is known (manufacturer data or obtained experimentally). L qs: inductance which takes into account the saturation phenomenon (manufacturer data or obtained experimentally). p : number of pairs of poles of the electric machine. φ : magnetic flux of the electric machine. A : matrix of the state representation A = 0 ω e t − ω e t 0 . B: identity matrix B = 1 0 0 1 . f: function of the state representation. b qs: scalar coefficient, which takes into account the saturation phenomenon, this value can be obtained experimentally. u: vector of the data of the state representation. x = φ d φ q state vector of the state representation, corresponding to the non-measurable state. ε: the unmodeled dynamics. η: measurement noise. Ts: sampling period. k: discretized time. A d : matrix of the discretized state representation. B d: matrix of the discretized state representation. J: cost function minimized by the Kalman filter. P: covariance matrix of the state vector. P 0 , Q, R: calibration matrices. Q ε : adjustment parameter. K: gain of the Kalman filter.

[0030] Estimated values are indicated by a circumflex. Mean values are indicated by a bar above the variable. Derivatives with respect to time are indicated by a period. Notations indexed by the mention -d (direct) or -q (quadrature) means that the quantities are expressed in the Park frame. In addition, the initial state values are indicated with a 0 (t or k = 0). 1) Measurement of currents and voltages

[0031] During this step, the currents and voltages in the phases of the electrical machine are measured.

[0032] These measurements can be made by voltage and current sensors. 2) Determination of the electrical rotation speed of the rotor

[0033] This involves determining the electrical rotation speed of the rotor.

[0034] According to one embodiment of the invention, the electrical rotation speed of the rotor can be determined from the mechanical rotation speed of the rotor, using the formula: ω e = pω.

[0035] According to an implementation of this embodiment, the mechanical rotation speed of the rotor can be estimated by any method known to those skilled in the art. For example, the mechanical rotation speed can be estimated using a phase-locked loop (PLL) type method. Alternatively, the method for estimating the mechanical rotation speed can be in accordance with that described in patent application FR 2 984 637.

[0036] Alternatively, the mechanical rotational speed of the rotor can be measured by means of a speed sensor placed on the electrical machine.

[0037] Alternatively, the electrical rotational speed can be determined directly. 3) Construction of the dynamic model of magnetic flux

[0038] In this step, a dynamic model of the magnetic flux is constructed. The dynamic model of the magnetic flux relates the magnetic flux to the current, the voltage in the electrical phases of the electrical machine, and the electrical rotational speed of the rotor. The model is called dynamic because it is a function of the rotational speed.

[0039] The dynamic model of magnetic flux is a state representation of the electrical machine. It is recalled that in systems theory (and in automation), a state representation allows a dynamic system to be modeled in a matrix form, using state variables. This representation can be linear or not, continuous or discrete. The representation allows the internal state and outputs of the system to be determined at any future time if the state at the initial time and the behavior of the input variables that influence the system are known.

[0040] In the Park frame (d, q), the dynamic model of the magnetic flux can be expressed by the following differential equations: φ ˙ d t = − R t i d t + ω e t φ q t + v d t , φ ˙ q t = − R t i q t − ω e t φ d t + v q t

[0041] By writing these differential equations in vector form, we obtain: φ ˙ d t φ ˙ q t = 0 ω e t − ω e t 0 φ d t φ q t + v d t − R t i d t v q t − R t i q t

[0042] Or equivalently: x ˙ t = A t x t + Bu t with x t = φ d t φ q t the unmeasurable state, and u t = υ d t − R t i d t υ q t − R t i q t the model input.

[0043] From this equation, it is clear that the equation of state of the magnetic flux of the electric machine can be described by a linear model in time. However, the equation of state of the magnetic flux of the electric machine is a highly nonlinear function of the currents id And iq and the rotor magnetic flux Φ. We can then write: φ d t = f d i q t , i q t + 3 2 Φ t φ q t = f q i q t , i q t

[0044] THE figures 2 And 3 represent examples of functions fd and fq depending on the currents id And iq for a given application. It can be observed that, while the function fd is a relatively linear function with respect to id , this is not the case for the function fq . Thus, the problem of estimating the magnetic flux of the electric machine becomes more complex, especially since the functions fd And fqare also a function of the mechanical angle of the rotor.

[0045] A solution to this complex problem could be to carry out mappings of magnetic flux quantities φ d And φ q . This solution requires a large memory and a large number of experimental measurements. In addition, the rotor's magnetic flux varies with temperature. This is why the model described above is complex to implement.

[0046] According to one embodiment of the invention, it is possible to construct a dynamic model of the magnetic flux which is simple to implement while retaining its precision, the simplified model being able to be defined by the following equations: φ d t = L d i d t + 3 2 Φ , φ q t = L qs i q t − b qs if i q t ≤ − i qm , L q i q t , if − i qm ≤ i q t ≤ i qm , L qs i q t + b qs if i qm ≤ i q t

[0047] This model has the advantage of being precise and inexpensive in terms of memory and computing time, which facilitates its implementation in an adaptive Kalman filter, and, where appropriate, within an electrical machine control process.

[0048] According to an implementation of this embodiment, the rotor magnetic flux Φ can be considered in a nominal case, for which a temperature of 20°C is considered.

[0049] For this embodiment, the equation of state can be written as follows: x ˙ t = A t x t + Bu t x t = L d i d t + 3 2 Φ f i d t with f i d t = L qs i q t − b qs , if i q t ≤ − i qm , L q i q t , if − i qm ≤ i q t ≤ i qm , L qs i q t + b qs if i qm ≤ i q t 4) Application of the adaptive Kalman filter

[0050] In this step, the magnetic flux of the electric machine is determined. To do this, an adaptive Kalman filter is applied to the dynamic model constructed in step 3), applied to the voltage and current measurements obtained in step 1), and to the electrical rotation speed of the rotor obtained in step 2). The application of the Kalman filter makes it possible to obtain a state observer. The adaptive Kalman filter allows an adaptation of the noise covariance matrix as a function of the rotation speed of the electric machine. Thus, the filter is efficient over a wide operating range of the electric machine. In addition, the adaptive Kalman filter is robust to variations in the rotor magnetic flux and inductance.

[0051] It is recalled that a state observer, or a state estimator, is, in automatic control and systems theory, an extension of a model represented in the form of a state representation. When the state of the system is not measurable, an observer is constructed which allows the state to be reconstructed from a model.

[0052] According to one embodiment of the invention, the adaptive Kalman filter can be applied by implementing the following steps: We modify the dynamic magnetic flux model by integrating unmodeled dynamics and measurement noise, We discretize the modified dynamic magnetic flux model, and We apply an adaptive Kalman filter algorithm to the modified and discretized dynamic model.

[0053] According to an example of this embodiment, the different steps described below can be implemented.

[0054] The dynamic model of the magnetic flux is modified to take into account the uncertainties of the ε(t) model and the measurement noises η ( t ) . The modified model can be written: x ˙ t = A t x t + Bu t + ϵ t x t = L d i d t + 3 2 Φ f i d t + η t

[0055] Thus, it is possible to obtain a more realistic model of the magnetic flux.

[0056] Then, we discretize this model for the application of the Kalman filter. For this, we consider a sampling period T s . We can then write the following equations: x k = A d k − 1 x k − 1 + B d k − 1 u k − 1 + B d k − 1 ϵ k − 1 x k = L d i d k + 3 2 Φ f i d k + η k with A d k − 1 = e T s A t , B d k − 1 = ∫ 0 T s e τ A τ Bdτ

[0057] Since the matrix A is a function of speed, which is itself a function of time, it is not possible to analytically determine the matrices A d and B d .

[0058] According to one aspect of this embodiment, the matrices A d and B d can be obtained by a Taylor series expansion. Preferably, in order to be efficient, the matrices A d and B d can be determined by a Taylor series expansion of order 3. In this case, the matrices A d and B d can be written: A d = 1 0 0 1 + T s 0 ω e − ω e 0 + T s 2 2 0 ω e − ω e 0 2 + T s 3 6 0 ω e − ω e 0 3 , B d = T s 1 0 0 1 + T s 2 2 0 ω e − ω e 0 + T s 3 6 0 ω e − ω e 0 2 + T s 4 24 0 ω e − ω e 0 3

[0059] Finally, an adaptive Kalman filter algorithm is applied.

[0060] Subsequently, we pose: ζ k = B d ϵ k .

[0061] One possibility to determine the unknown state vector x is to take into account the information ζ ( k ) And η ( k ) in the adaptive Kalman filter. Practically, this adaptive Kalman filter provides a solution to the minimization problem described below: min x k J k with J k = x 0 − x ¯ 0 T P 0 − 1 x 0 − x ¯ 0 + ∑ j = 1 k ζ j − 1 T Q − 1 ζ k − 1 + η j T R − 1 η j ζ k − 1 = x k − A d k − 1 x k − 1 − B d u k − 1 η k = x k − L d i d k + 3 2 Φ f i d k

[0062] The cost function J provides a guide for the choice of matrices P 0 , R and Q, with the following conditions: 1. if the initial state x(k) at time k=0 is well known, that is to say x (0) ≈ x(0), then the values of the matrix P 0 are relatively low. Otherwise the values of the matrix P 0 are relatively high. 2. if there is a lot of measurement noise, then the values of the matrix R are relatively low. Otherwise the values of the matrix R are relatively high.

[0063] Furthermore, Q can be chosen as: Q = B d Q ϵ B d T with Q ε an adjustment parameter. This relationship implies that the matrix Q is a function of the rotor rotation speed.

[0064] In order to solve the minimization problem, using the adaptive Kalman filter, we can adopt the following assumptions. These assumptions mainly concern a mathematical interpretation of the matrices P 0 , R and Q. the initial state x(0) is a random vector which is not correlated with the noises ζ ( k ) And η ( k ) the initial state x(0) has a known mean x (0) and a covariance defined by P 0 = E x 0 − x ¯ 0 x 0 − x ¯ 0 T where E denotes the expectation. ζ ( k ) And η ( k ) are uncorrelated, and are zero-mean white noise with covariance matrices Q and R, respectively, in other words: E ζ k ζ j T = Q , if k = j , 0 , if k ≠ j E η k η j T = R , if k = j , 0 , if k ≠ j E ζ k η j T = 0 , for all k , j

[0065] It may be noted that this assumption also implies that Q and R are symmetric positive semi-definite matrices.

[0066] We also adopt the following notations: x̂ ( k | k - 1) is the estimate of x(k) from measurements to time k - 1, either x(k - 1), x(k - 2), ... and u(k - 1), u(k - 2), ... x̂ ( k | k ) is the estimate of x(k) from measurements to time k, either x(k), x ( k - 1), ... and u ( k ) , u ( k - 1), ... P ( k | k - 1) is the covariance matrix of x(k) given x(k - 1), x(k - 2), ... and u(k - 1), u(k - 2), ... P ( k | k ) is the covariance matrix of x(k) from measurements to time k, either x ( k ) , x ( k - 1), ... and u ( k ) , u ( k - 1), ...

[0067] Then, the adaptive Kalman filter algorithm can be summarized as follows, with a temporal updating equation: x ^ k k − 1 = A d x ^ k − 1 k − 1 + B d u k − 1 , P k k − 1 = A d P k − 1 k − 1 A d T + B d Q ϵ B d T and an equation for updating the measurements: K k = P k k − 1 P k k − 1 + R − 1 x ^ k k = x ^ k k − 1 + K k x k − x ^ k k − 1 P k k = I − K k P k k − 1

[0068] Thus, the magnetic flux of the electric machine can be determined.

[0069] According to one implementation of the invention, the adaptive Kalman filter approach can be summarized as follows: 1. We use the estimated inputs at the previous times listed below, and the parameters Q ε and R (covariance matrices) and determine: x k = L d i d k + 3 2 Φ f i d k u k = υ d t − R t i d t υ q t − R t i q t x ^ k − 1 k − 1 P k − 1 k − 1 2. We determine the output by implementing the following steps (1) We initialize k = 0, the state vector x̂(0) and the state of the covariance matrix, P(0|0) = P 0 (2) We apply the time update and measurement update equations to obtain x̂ ( k | k ) and P ( k | k ) : x ^ k k − 1 = A d x ^ k − 1 k − 1 + B d u k − 1 , P k k − 1 = A d P k − 1 k − 1 A d T + B d Q ϵ B d T K k = P k k − 1 P k k − 1 + R − 1 x ^ k k = x ^ k k − 1 + K k x k − x ^ k k − 1 , P k k = I − K k P k k − 1 (3) We determine the magnetic flux φ estimated at time k by the formulas φ ^ d k = x ^ 1 k k , φ ^ q k = x ^ 2 k k

[0070] In these equations, the subscript 1 denotes the first term of the vector x, and the subscript 2 denotes the second term of the vector x. 5) Electrical machine control

[0071] This step is optional.

[0072] The invention also relates to a method for controlling, in real time, a synchronous electrical machine, for which the following steps are carried out: the magnetic flux of the electric machine is determined using the method (steps 1) to 4)) described above; and the torque of said synchronous machine is controlled as a function of the determined magnetic flux. For this step, any conventional means of controlling the electric machine, which takes into account the magnetic flux, can be used. For example, the control of the electric machine can be based on a high-performance direct torque control method, particularly suitable for synchronous electric machines with salient poles.

[0073] Furthermore, the invention relates to a system for controlling a synchronous electrical machine suitable for applying the method as described above. Such an electrical machine control system may comprise means for controlling the electrical machine comprising means for determining the magnetic flux of the electrical machine and means for controlling the torque of the electrical machine. The means for determining the magnetic flux determine the magnetic flux of the electrical machine from current and voltage measurements. These are the currents and voltages of each of the three phases of the electrical machine. The torque control means apply voltages to the terminals of the electrical machine as a function of the magnetic flux in order to provide a torque setpoint for the electrical machine. Advantageously, the control system may be a controller comprising computer means.

[0074] This method and this control system can be used for an electrical machine on board a vehicle, in particular on board an electric or hybrid motor vehicle. However, the control system described is not limited to this application and is suitable for all applications of electrical machines.

[0075] According to one aspect, the electric machine is a salient pole synchronous electric machine. Indeed, the method is particularly suitable for this type of machine, on the one hand, because the dynamic model of the electric machine is well representative of this type of electric machine, and because the determination of the magnetic flux allows the control of such an electric machine, in particular by direct control of the torque.

Claims

1. Method for determining the magnetic flux of an electric machine, said electric machine comprising a rotor and a stator, said stator comprising windings connected to a plurality of electric phases, characterized in that the following steps are implemented: a) a current and a voltage in said phases of said electric machine are measured (MES); b) the electrical rotation speed (VIT) of said rotor is determined, notably as a function of the mechanical rotation speed of said rotor; c) a dynamic model (MOD) of said magnetic flux of said electric machine is constructed, said dynamic model of said magnetic flux connecting said magnetic flux to the current and to the voltage of the phases of the electric machine and to said electrical rotation speed of said rotor; and d) said magnetic flux φ is determined by applying an adaptive Kalman filter (KAL) to said dynamic magnetic flux model (MOD), said dynamic magnetic flux model (MOD) being applied to said current and voltage measurements (MES) and to said determined electrical rotation speed (VIT), characterized in that said adaptive Kalman filter is applied by implementing the following steps: i) said dynamic magnetic flux model is modified by integrating uncertainties into said model and measurement noise; ii) said modified dynamic magnetic flux model is discretized; and iii) an adaptive Kalman filter algorithm is applied to said modified and discretized model, by implementing the following steps: (1) k = 0, the state vector x̂(0) and the state of the covariance matrix, P(0|0) = P0, are initialized, (2) the time update and measurement update equations are applied in order to obtain x̂(k|k) and P(k|k): x ^ k k − 1 = A d x ^ k − 1 k − 1 + B d u k − 1 , P k k − 1 = A d P k − 1 k − 1 A d T + B d Q ϵ B d T K k = P k k − 1 P k k − 1 + R − 1 x ^ k k = x ^ k k − 1 + K k x k − x ^ k k − 1 P k k = I − K k P k k − 1 , (3) said magnetic flux φ estimated at the time k is determined by the formulae φ ^ d k = x ^ 1 k k , φ ^ q k = x ^ 2 k k with k being the discretized time, A_d, B_d matrices of the state description, P the covariance matrix of the state vector, R a calibration matrix, K the gain of the Kalman filter and Q_ε an adjustment parameter.

2. Method for determining the magnetic flux according to Claim 1, wherein said electrical rotation speed ωe of said rotor is determined by means of a formula of the type ωe = ρω with p being the number of pole pairs of the electric machine and ω the mechanical rotation speed of said rotor.

3. Method for determining the magnetic flux according to Claim 2, wherein said mechanical rotation speed is determined by means of a phase-locked loop, PLL, method.

4. Method for determining the magnetic flux according to one of the preceding claims, wherein said dynamic magnetic flux model (MOD) is written φ d = L d i d t + 3 2 Φ , φ q t = L qs i q t − b qs , if i q t ≤ − i qm , L q i q t , if − i qm ≤ i q t ≤ i qm L qs i q t + b qs if i qm ≤ i q t , with φ being the magnetic flux of the electric machine, i the current, Φ the flux of the rotor, L the inductances of said electric machine, Lqs and bqs coefficients which take into account the saturation effect, d and q the axes in the Park reference system and iqm the quadrature current value for which the magnetic flux is a linear function of the quadrature current.

5. Method for determining the magnetic flux according to one of the preceding claims, wherein said electric machine is a salient pole synchronous electric machine.

6. Method for controlling an electric machine, wherein the following steps are implemented: a) a magnetic flux φ of said electric machine is determined by means of the method for determining said magnetic flux according to one of the preceding claims; and b) said electric machine is controlled (CON) by means of said determined magnetic flux.

7. Control method according to Claim 6, wherein said electric machine is controlled (CON) according to a method for directly controlling the torque of the electric machine implemented on the basis of said magnetic flux.

8. System for controlling an electric machine, said electric machine comprising a rotor and a stator, said stator comprising windings connected to a plurality of electric phases, said control system comprising voltage and current sensors, means for determining the speed of the rotor and control means for implementing the control method according to one of Claims 6 and 7.