Method for determining the electric potentials of the phases of a polyphase motor
Patent Information
- Application Number
- EP2023809697
- Authority / Receiving Office
- EP · EP
- Patent Type
- Applications
- Current Assignee / Owner
- Priority Date
- 2022-10-14
- Filing Date
- 2023-10-13
- Publication Date
- 2025-08-20
AI Technical Summary
Existing methods for determining electrical potentials in polyphase motors are limited, restricting the operating zone and generating harmonics that disturb mechanical torque, necessitating a method to increase electrical potentials while maintaining sinusoidal voltage within safe limits.
A method that calculates reference electrical potentials and adjusts them by adding homopolar and secondary potentials, expressed through specific mathematical functions, to increase the amplitude of sinusoidal voltage across motor windings without exceeding the limiting voltage, thus expanding the operating zone without introducing harmonics.
This approach allows for increased sinusoidal voltage amplitude across motor windings while keeping potentials within safe limits, effectively enlarging the motor's operating zone without disturbing mechanical torque.
Smart Images
Figure 1.1
Abstract
Description
[0001] Description
[0002] Title of the invention: Method for determining the electrical potentials of the phases of a polyphase motor
[0003] Technical Field
[0004] The present invention relates to a method for determining the electrical potentials applied to the phases of a motor comprising several phases so as not to generate disturbances on the mechanical torque supplied by the motor.
[0005] Prior art
[0006] Electric motors are power converters between the electrical and mechanical domains. Mechanical operating points, such as speed and mechanical torque, correspond to electrical operating points, such as voltage, current, or the phase shift between current and voltage. Stresses on the electrical system will be transferred to the mechanical domain by delimiting an accessible operating point zone.
[0007] A polyphase electric machine with N symmetrical sinusoidal phases, N being an integer greater than or equal to 4, has the property of being modelable by three subsystems:
[0008] - a main system u commande of dimension 2 which is the system to be controlled to produce the electromagnetic torque;
[0009] - a secondary system u sesecondary of dimension N-3 which is a passive system not producing torque, but which can provide additional current; and
[0010] - a homopolar system or component Uhomopoiaire of dimension 1 which does not interact functionally with the main system.
[0011] This type of machine is powered by N electrical potentials. It is possible to define a transformation matrix T to link these N potentials to the three subsystems. This matrix T is defined by the following properties:
[0012] - the odd columns from 1 to 2 [(N- 1) / 2 J noted 2k-l (k varying from 1 to [(N- 1) / 2 J), correspond to the vector having as i-th component (with i varying from 1 to N): c(i, 2k-l) = cos (2nk(il) / N);
[0013] - the even columns from 1 to 2[(Nl) / 2 J noted 2k (k varying from 1 to [(N- 1) / 2 J) correspond to the vector having as i-th component (with i varying from 1 to N): c(i, 2k) = sin (2nk(il) / N);
[0014] - in the case where N is odd, column N is defined by a constant vector with the value 1 / √2;
[0015] - in the case where N is even, the column Nl is defined by a vector of alternating constants of value 1 / √2 and value - 1 / √2 and the column N is defined by a constant vector with the value 1 / √2.
[0016] Thus, the N potentials of the polyphase electric machine, and therefore of the N-phase electric motor, are linked to the three vectors by the relation: with V1, ..., V N the N potentials of the motor.
[0017] If the components not producing torque are removed, the N potentials of the motor can be written: with Q a matrix comprising the first two columns of the matrix T.
[0018] The motor is controlled by an electrical controller that calculates control voltages in response to a speed or torque request. These are then transformed into reference potentials by considering the direct approach and the transformation by the Q matrix. The electrical controller produces electrical potentials at each phase of the motor via a power converter, so that it can provide mechanical torque at a given electrical speed. The voltages at the terminals of the motor windings, which result from the potential differences between the phases, must be sinusoidal and of the greatest possible amplitude to reach a maximum of operating points while having zero or the lowest possible harmonic content so as not to generate disturbances on the mechanical torque in a useful frequency range.
[0019] The potentials realized by the controller are limited to values between - V DC / 2 and + V DC / 2, with V DC the voltage of the motor's power supply, the motor being powered by said power supply via a power converter. In order not to cause harmonics to appear, it is common to produce sinusoidal potentials which, by construction, are constrained to be less than V DC / 2. The sinusoidal voltage across the motor windings (resulting from the potential differences between the motor phases) is thus limited to being less than or equal to V DC / 2.
[0020] However, for certain angle values, it would be interesting to be able to increase the electrical potentials applied to the motor phases in order to increase the sinusoidal voltage at the terminals of the motor windings to widen the operating zone while maintaining potentials to be achieved for each phase between -V DC / 2 and +V DC / 2.
[0021] It is therefore desirable to have a new method for determining the electrical potentials supplied to the phases of a motor, so as to widen the operating zone without generating harmonics and disturbances to the mechanical torque supplied by the motor.
[0022] Statement of the invention
[0023] The present invention relates to a method for determining the electrical potentials to be produced at the terminals of the phases of a motor comprising N phases, N being an integer greater than or equal to 4, the method comprising the following steps: - defining a control voltage of amplitude V MAG and phase 0 which is lower than a limiting voltage;
[0024] - determine reference electrical potentials at the terminals of the N phases of the motor for this control voltage with where i is between 1 and N, V REF__i is the reference electrical potential at the terminals of the i-th phase and 0 is the phase of the control voltage between 0 and 2n;
[0025] - compare the reference electrical potentials to a first threshold;
[0026] - if the reference electrical potentials are all less than or equal to the first threshold, then the electrical potentials to be produced at the terminals of the N phases of the motor are equal to the reference electrical potentials, or if at least one of the reference electrical potentials is greater than the first threshold, compare these reference electrical potentials to a second threshold, the second threshold being greater than the first threshold;
[0027] - if these reference electrical potentials are all less than or equal to the second threshold, then the electrical potentials to be achieved at the terminals of the N phases of the motor are equal to Vi = V REF__i + V H , with or if at least one of the reference potentials is greater than the second threshold, then the potentials to be achieved at the terminals of the N phases of the motor are equal to Vi = V REF__i + V S_i + V HN , with V HNa homopolar potential depending on the number of phases and the reference electrical potentials and V S_i a secondary potential depending on the number of phases and the reference electrical potentials.
[0028] According to a particular characteristic of the invention, the secondary potentials V S_i and homopolar V HN are expressed by the following functions: with
[0029] - if N is odd, with p = (N-1) / 2: with k ranging from 1 to N-3, and
[0030] U a vector with N lines defined by U = T -1 u and u an N-row vector defined by a value 1 for its indices iP, a value 0 for its index iM and a value -1 for its indices iN;
[0031] V a vector with N lines defined by V = T -1v and v an N-row vector defined by a value 0 for its indices iP and iN and a value 1 for its index iM; iP the p indices of the p largest values of the reference electric potentials; iN the p indices of the p smallest values of the reference electric potentials; iM the index of the median value of the reference electric potentials; i varying from 1 to N, and
[0032] T a transformation matrix defined by: o the odd columns from 1 to 2 [(N- 1) / 2 J denoted 2k-l (k varying from 1 to [(Nl) / 2 J), correspond to the vector having as i-th component (with i varying from 1 to N): c(i, 2k-l) = cos (2nk(il) / N); o the even columns from 1 to 2[(Nl) / 2 J denoted 2k (k varying from 1 to [(N- l) / 2 J) correspond to the vector having as i-th component (with i varying from 1 to N): c(i, 2k) = sin (2nk(il) / N); o in the case where N is odd, the column N is defined by a constant vector with the value 1 / √2; o in the case where N is even, the column Nl is defined by a vector of alternating constants of value 1 / √2 and value -1 / √2 and the column N is defined by a constant vector with value 1 / √2,
[0033] - If N is even, with p = N / 2: V H = 0 and V SAB_i (k) is defined by: o If k varies from 1 to p-2: o For the other k between 1 and N-3: V SAB_i (k) = 0 ; with
[0034] PM = qQ -1 ; iP the p-1 indices of the p-1 largest values of the reference electric potentials for i varying from 1 to N; q the row vector formed from the elements of the row of the transformation matrix T corresponding to the last index of iP corresponding to the indexed columns where k varies from 1 to p-2; and Q the matrix formed from the elements of the transformation matrix T at the intersection of the rows corresponding to the first p-2 indices of the iP and the indexed columns where k varies from 1 to p-2.
[0035] Adding the V component H or V HN , called homopolar potential, and / or the V component S_i , called secondary potential, to the reference electrical potentials V REF__i at the terminals of the motor phases thus makes it possible to increase the limit of the control voltage on each phase of the polyphase electric motor, while maintaining potentials to be achieved at the terminals of each phase between - V DC / 2 and +V DC / 2. We thus obtain the capacity of a sinusoidal voltage amplitude at the terminals of the motor windings greater than V DC / 2 and lower than the limiting voltage V LIM - This allows the operating area of the motor to be enlarged without generating harmonics and therefore limiting disturbances to the mechanical torque supplied by the motor.
[0036] According to another particular characteristic of the invention, the limiting voltage and the second threshold are functions dependent on the number of phases of the motor and the electrical potential V DC of a power supply to the motor.
[0037] This allows the second threshold and the limiting voltage to be defined directly as a function of the number of motor phases and the power supply potential. It is therefore possible to determine from which threshold a secondary potential must be added to the reference electrical potentials determined in the process in order to reach the limiting voltage without generating harmonics.
[0038] According to another particular characteristic of the invention, the first threshold is a function dependent on the electrical potential of the electrical supply of the motor.
[0039] This makes it possible to define the first threshold directly as a function of the electrical potential of the motor's power supply. According to another particular characteristic of the invention, the second threshold is expressed by the following function:
[0040] According to another particular characteristic of the invention, the limiting voltage is expressed by the following function: with a = n / (2N) if N is odd or a = 0 if N is even and a multiple of 4 or a = n / N if N is even and not a multiple of 4.
[0041] This function allows you to determine the value of the limiting voltage V LIM maximum possible for a given number of phases N, therefore the maximum amplitude of the sinusoidal voltage across the motor windings. Thus, if the motor has 3 phases, the maximum limiting voltage will be 115% of V DC / 2, or if the motor has 4 phases, it will be 100% of V DC / 2. This therefore makes it possible to know what the maximum amplitude of the sinusoidal voltage at the motor terminals could be, while maintaining for each phase potentials to be achieved between -V DC / 2 and +V DC / 2.
[0042] According to another particular characteristic of the invention, the first threshold is equal to V DC / 2.
[0043] According to another particular characteristic of the invention, the motor is a five-phase motor, N is equal to 5, the first threshold is equal to V DC / 2, the second threshold is equal to 1.05 x V DC / 2 and the limiting voltage V LIM is equal to 1.23 x V DC / 2, with V DC the electrical potential of the power converter's power supply, and if at least one of the reference electrical potentials is greater than the second threshold, then the electrical potentials to be achieved at the terminals of the 5 phases of the motor are equal to V i(i = p) = V M for p, such that the reference electric potentials VREF_ P are the two highest reference electrical potentials; V i(i = i) = -V M for I, such that the reference electric potentials V REF_iare the two smallest reference electric potentials; or V i(i =j) = V c for j, such that the reference electric potential V REF__j is the median reference electric potential, with with p, j and I chosen from {1; 2; 3; 4; 5} and
[0044] Another object of the invention is an electrical controller intended to be connected to an N-phase motor and to an electrical power source, with N an integer greater than or equal to 4, the controller being configured to:
[0045] - define an amplitude control voltage V MAG and phase 0 which is lower than a limiting voltage;
[0046] - determine reference electrical potentials at the terminals of the N phases of the motor for the control voltage with where i is between 1 and N, V REF__iis the reference electrical potential across the i-th phase and 0 is the phase of the control voltage between 0 and 2n;
[0047] - compare the reference electrical potentials to a first threshold;
[0048] - if the reference electrical potentials are all less than or equal to the first threshold, then the electrical potentials to be produced at the terminals of the N phases of the motor are equal to the reference electrical potentials, or if at least one of the reference electrical potentials is greater than the first threshold, compare these reference electrical potentials to a second threshold, the second threshold being greater than the first threshold;
[0049] - if these reference electrical potentials are all less than or equal to the second threshold, then the electrical potentials to be achieved at the terminals of the N phases of the motor are equal to Vi = V REF__i + V H , with or if at least one of the reference potentials is greater than the second threshold, then the potentials to be achieved at the terminals of the N phases of the motor are equal to Vi = V REF__i + V S_i + V HN , with V HN a homopolar potential depending on the number of phases and the reference electrical potentials and V S_i a secondary potential depending on the number of phases and the reference electrical potentials.
[0050] According to a particular characteristic of the invention, the secondary potentials V S_i and homopolar V H are expressed by the following functions: with :
[0051] - if N is odd, with p = (Nl) / 2: with k ranging from 1 to N-3, and
[0052] U a vector with N lines defined by U = T -1 u and u an N-row vector defined by a value 1 for its indices iP, a value 0 for its index iM and a value -1 for its indices iN;
[0053] V a vector with N lines defined by V = T -1 v and v an N-row vector defined by a value 0 for its indices iP and iN and a value 1 for its index iM; iP the p indices of the p largest values of the reference electric potentials; iN the p indices of the p smallest values of the reference electric potentials; iM the index of the median value of the reference electric potentials; i varying from 1 to N, and
[0054] T a transformation matrix defined by: o the odd columns from 1 to 2 [(N- 1) / 2 J denoted 2k-l (k varying from 1 to [(Nl) / 2 J), correspond to the vector having as i-th component (with i varying from 1 to N): c(i, 2k-l) = cos (2nk(il) / N); o the even columns from 1 to 2[(Nl) / 2 J denoted 2k (k varying from 1 to [(N- l) / 2 J) correspond to the vector having as i-th component (with i varying from 1 to N): c(i, 2k) = sin (2nk(il) / N); o in the case where N is odd, the column N is defined by a constant vector with the value 1 / √2; o in the case where N is even, the column Nl is defined by a vector of alternating constants of value 1 / √2 and value -1 / √2 and the column N is defined by a constant vector with the value 1 / √2.
[0055] - If N is even, with p = N / 2: V H = 0 and V SAB_i (k) is defined by: o If k varies from 1 to p-2: o For the other k between 1 and N-3: V SAB_i (k) = 0 ; with
[0056] PM = qQ -1 ; iP the p-1 indices of the p-1 largest values of the reference electric potentials for i varying from 1 to N; q the row vector formed from the elements of the row of the transformation matrix T corresponding to the last index of iP corresponding to the indexed columns where k varies from 1 to p-2; and
[0057] Q the matrix formed from the elements of the transformation matrix T at the intersection of the rows corresponding to the first p-2 indices of the iP and the indexed columns where k varies from 1 to p-2.
[0058] The controller of the invention makes it possible to supply the electrical potentials to the terminals of the N phases of the motor to increase the operating area of the motor by modifying the potentials of the phases to obtain a sinusoidal voltage at the terminals of the motor windings of maximum amplitude equal to the limiting voltage, while maintaining potentials to be achieved at the terminals of each phase of the motor between -V DC / 2 and +V DC / 2.
[0059] According to another particular characteristic of the invention, the limiting voltage and the second threshold are functions dependent on the number of phases of the motor and the electrical potential of the electrical supply intended to be connected to the electrical controller.
[0060] According to another particular characteristic of the invention, the second threshold is expressed by the following function: with V DCthe voltage of the power supply intended to be connected to the electrical controller and N the number of phases of the motor intended to be connected to the electrical controller. According to another particular characteristic of the invention, the limiting voltage is expressed by the following function: with a = n / (2N) if N is odd or a = 0 if N is even and a multiple of 4 or a = n / N if N is even and not a multiple of 4, and with V DC the voltage of the power supply intended to be connected to the electrical controller and N the number of phases of the motor intended to be connected to the electrical controller.
[0061] Yet another object of the invention is an electrical device comprising:
[0062] - a power supply source;
[0063] - an electrical controller according to the invention, one input of which is connected to the electrical power source;
[0064] - a power converter, whose inputs are connected to the electrical controller, and
[0065] - an N-phase motor connected to the power converter,
[0066] N being an integer greater than or equal to 4 and the power converter being configured to provide electrical potentials at the input of the N phases of the motor.
[0067] Brief description of the drawings
[0068] Other characteristics and advantages of the present invention will emerge from the description given below, with reference to the appended drawings which illustrate exemplary embodiments thereof which are not limiting in nature.
[0069] [Fig. 1] Figure 1 shows, schematically and partially, a flowchart of the method for determining electrical potentials to be produced at the terminals of the phases of a multi-phase motor according to one embodiment of the invention. [Fig. 2A] Figure 2A shows the reference electrical potential V REF__i at the terminals of the five phases of a five-phase motor before the application of the method of the invention for a control voltage V MAG of amplitude equal to 90% of V DC / 2.
[0070] [Fig. 2B] Figure 2B represents the reference electric potential V REF__i at the terminals of the five phases of a five-phase motor before the application of the method of the invention, and the homopolar potential V H as described in the method of the invention for a control voltage V MAG of amplitude equal to 100% of V DC / 2.
[0071] [Fig. 2C] Figure 2C represents the reference electric potential VREF__i at the terminals of the five phases of a five-phase motor before the application of the method of the invention, and the electrical potential to be achieved V at the terminals of the five phases of the motor after the application of the method of the invention, as well as the values of the homopolar potential V H possible for a control voltage V MAG of amplitude equal to 105% of V DC / 2.
[0072] [Fig. 3A] Figure 3A represents the reference electric potential V REF__i at the terminals of the five phases of a five-phase motor before the application of the method of the invention, and the electrical potential to be achieved V at the terminals of the five phases of the motor after the application of the method of the invention, as well as the values of the homopolar potential V HN and V components SAB_i of the secondary potential V S_i possible for a control voltage V MAG of amplitude equal to 110% of V DC / 2.
[0073] [Fig. 3B] Figure 3B represents the reference electric potential V REF__i at the terminals of the five phases of a five-phase motor before the application of the method of the invention, and the electrical potential to be achieved V at the terminals of the five phases of the motor after the application of the method of the invention, as well as the values of the homopolar potential V HN and V components SAB_i of the secondary potential V S_i possible for a control voltage V MAG of amplitude equal to 123% of V DC / 2, equal to the limiting voltage V LIM -
[0074] [Fig. 4] Figure 4 shows, schematically and partially, an electrical device according to one embodiment of the invention. [Fig. 5A] Figure 5A shows the reference electrical potential V REF__i at the terminals of the six phases of a six-phase motor before the application of the method of the invention for a control voltage V MAGof amplitude equal to 90% of V DC / 2.
[0075] [Fig. 5B] Figure 5B represents the reference electric potential V REF_i at the terminals of the six phases of a six-phase motor before the application of the method of the invention, and the electrical potential to be achieved Vi at the terminals of the six phases of the motor after the application of the method of the invention, as well as the values of the component V SAB_i (3) of the secondary potential V S_i possible for a control voltage V MAG of amplitude equal to 105% of V DC / 2.
[0076] [Fig. 5C] Figure 5C represents the reference electric potential V REF_i at the terminals of the six phases of a six-phase motor before the application of the method of the invention, and the electrical potential to be achieved Vi at the terminals of the six phases of the motor after the application of the method of the invention, as well as the values of the component V SAB_i (3) of the secondary potential V S_ipossible for a control voltage V MAG of amplitude equal to 115.7% of V DC / 2.
[0077] Description of the embodiments
[0078] In the remainder of the description, in order to simplify the wording, we speak of "reference electrical potential of a phase" or "electrical potential to be achieved of a phase" to designate the reference electrical potential at the terminals of the phase or the electrical potential to be achieved at the terminals of the phase.
[0079] The term "potential" is also used to refer to "electric potential."
[0080] In the rest of the description, we call V DC the voltage of the motor's power supply, the motor being powered by this power supply via a power converter.
[0081] Figure 1 represents a flowchart of the method 100 for determining the potentials to be achieved V of the phases of an N-phase motor, N being an integer greater than or equal to 4 and k being between 1 and N. The method 100 comprises the definition 101 of a control voltage V MAG which is lower than a limiting voltage V LIM as well as the determination 102 of the reference potentials V REF__i of the N phases of the motor from the control voltage V MAG , i being an integer between 1 and N and V REF__i representing the reference potential of the i-th phase of the motor.
[0082] The reference potentials V REF__i of the N phases are expressed by the following formula: with 0 the phase of the control voltage between 0 and 2n.
[0083] The limiting voltage V LIM represents the maximum amplitude that we want to have for the control voltage V MAGat the terminals of the motor windings, while keeping potentials to be achieved between -V DC / 2 and +V DC / 2 for the N phases.
[0084] It can be defined by a user and vary between 0 and +V DC / 2.
[0085] It can also be a function dependent on the potential V DC of the motor's power supply for example, it can be equal to a fraction of V DC , for example 80 x V DC / 100 or 110 x V DC / 100. It can still be a function dependent on the potential V DC and the number of phases N in the motor.
[0086] Advantageously, the limiting voltage V LIM is expressed by the following function, depending on the number of phases N of the motor and the motor supply potential V DC : with a = n / (2N) if N is odd or a = 0 if N is even and a multiple of 4 or a = n / N if N is even and not a multiple of 4.
[0087] These N-dependent functions make it possible to determine the limiting voltage V LIM , and therefore the maximum amplitude of the control voltage V MAG for a given number of phases N. The method 100 then comprises the comparison 103 of the reference potentials
[0088] V REF__i determined during step 102 at a first threshold.
[0089] The first threshold can be a potential value chosen by the user or a function dependent on the potential of the motor supply V DC - For example, we can choose the first threshold equal to 0.8 x V DC / 2 or to V DC / 2. Preferably, the first threshold is equal to V DC / 2.
[0090] If the reference potentials V REF__i are all less than or equal to the first threshold regardless of i (step 104), then the potentials to be achieved Vi of the N phases of the motor are equal to the reference potentials VREF__i determined in step 102.
[0091] If at least one of the reference potentials V REF__i determined in step 102 is greater than the first threshold, then the method comprises the comparison 105 of the reference potentials V REF__i to a second threshold higher than the first threshold.
[0092] The second threshold can be a potential value chosen by the user or a function dependent on the potential of the motor supply V DC or a function dependent on the number of phases N of the motor and the potential of the motor power supply V DC - For example, we can choose the second threshold equal to 1.1 x V DC / 2.
[0093] Advantageously, the second threshold is expressed by the following function, depending on the number of phases N of the motor and the motor supply potential V DC :
[0094] When the limiting voltage V LIMis chosen by the user between 0 and +V DC / 2, it can more particularly be chosen as being equal to the first threshold or to the second threshold.
[0095] Following this comparison 105, if the reference potentials V REF__i are all less than or equal to the second threshold regardless of i (step 106), then the potentials to be achieved V of the N phases of the motor are equal to V = V REF__i + V H , with V H a homopolar potential expressed by the following formula: where max k=1 denotes the maximum potential among the reference potentials
[0096] V REF__i determined in step 102, and min denotes the minimum potential among the reference potentials V REF__i determined in step 102.
[0097] If at least one of the reference potentials V REF__iis greater than the second threshold, then the potentials to be achieved Vi of the N phases of the motor are equal to V = V REF__i + Vsj + V HN , with V HN a homopolar potential depending on the number of phases N and the reference electrical potentials V REF__i and V S_i a secondary potential depending on the number of phases N and the reference electrical potentials V REF__i .
[0098] In this case, the secondary potentials V S_i and homopolar V HN can be expressed by the following functions: with :
[0099] - if N is odd, with p = (Nl) / 2: with: o U a vector with N lines defined by U = T- 1 u and u an N-row vector defined by a value 1 for its indices iP, a value 0 for its index iM and a value -1 for its indices iN; o V an N-row vector defined by V = T -1v and v an N-line vector defined by a value 0 for its indices iP and iN and a value 1 for its index iM; where iP the p indices of the p largest values of the reference potentials
[0100] V REF__i o iN the p indices of the p smallest values of the reference potentials
[0101] V REF__i o iM the index of the median value of the reference potentials V REF__i ; oi varying from 1 to N, and o T a transformation matrix defined by:
[0102] ■ the odd columns from 1 to 2 [(N- 1) / 2 J noted 2k-l (k varying from 1 to L(Nl) / 2 J), correspond to the vector having as i-th component (with i varying from 1 to N): c(i, 2k- 1) = cos (2nk(il) / N);
[0103] ■ the even columns from 1 to 2[(Nl) / 2 J noted 2k (k varying from 1 to L(Nl) / 2 J) correspond to the vector having as i-th component (with i varying from 1 to N): c(i, 2k) = sin (2nk(i- 1) / N);
[0104] ■ in the case where N is odd, column N is defined by a constant vector with the value 1 / √2;
[0105] ■ in the case where N is even, column Nl is defined by a vector of alternating constants of value 1 / √2 and value - 1 / √2 and column N is defined by a constant vector with value 1 / √2.
[0106] - If N is even, with p = N / 2: V H = 0 and V SAB_i (k) is defined by: o If k varies from 1 to p-2: o For the other k between 1 and N-3: V SAB_i (k) = 0 ; with
[0107] P M = qQ -1 ;
[0108] IP the p-1 indices of the p-1 largest values of the reference potentials V REF__i for i varying from 1 to N; q the row vector formed from the elements of the row of the transformation matrix T corresponding to the last index of iP corresponding to the indexed columns where k varies from 1 to p-2; and
[0109] Q the matrix formed from the elements of the transformation matrix T at the intersection of the rows corresponding to the first p-2 indices of the iP and the indexed columns where k varies from 1 to p-2.
[0110] Thus the electrical potentials to be achieved Vi determined by the method 100 can include a homopolar potential and / or a secondary potential according to the values of the reference potentials V REF__i compared to the first and second thresholds.
[0111] Figures 2A, 2B, 2C, 3A and 3B represent an implementation of the method of the invention for a five-phase motor, therefore for N = 5. Thus, by applying the formulas proposed for the limiting voltage V LIM and for the second threshold, the second threshold is equal to 1.05 x V DC / 2 and the limiting voltage V LiM is equal to 1.23 x V DC / 2. In this example, the first threshold is equal to V DC / 2. The control voltage V MAGmust therefore remain less than or equal to 1.23 x V DC / 2.
[0112] Moreover, if at least one of the reference potentials V REF__i determined in step 102 is greater than the second threshold, then the potentials to be realized Vi become:
[0113] - V i(i = p) = V M for p such that the reference potentials V REF__p determined in step 102 are the two highest potentials;
[0114] - V i(i = i) = -V M for I such that the reference potentials V REF__i determined in step 102 are the two smallest potentials; and
[0115] - V i(i = j) = V c for j such that the reference potential V RE FJ determined in step 102 is the median potential, with and p, I and j chosen from {1; 2; 3; 4; 5}; and V M and V c expressed by the following functions: And
[0116] In fact, for a five-phase motor, the transformation matrix T is expressed as follows:
[0117]
[0118] The homopolar and secondary potentials which are expressed generically in the following manner: with : are simplified by posing:
[0119] The homopolar potential and the secondary components of the secondary potential are then expressed by the following formulas:
[0120] The main system u CO command is then written: The potentials to be realized V1, V2, V3, V4 and V5 are therefore written:
[0121] Either
[0122] Without loss of generality, considering that the phase of the control voltage VMAG varies between 0 and n / 5, then the values of the reference potentials V REF__iare arranged from smallest to largest in the order 4, 3, 5, 2 and 1. The other cases, that is to say for a phase between n / 5 and 2n, are obtained by symmetry and permutation of indices.
[0123] It follows that the vectors u, v, U and V are defined by:
[0124] Noting that: And we obtain the following expressions linking the reference potentials V REF_1 , V REF_2 ,
[0125] V REF__ 3, V REF__ 4 and V REF_ 5 between them:
[0126] We then calculate the vector W which is written in a simplified way: This allows the calculation of the secondary components of the secondary potential and the homopolar potential: and we obtain for the potentials to be realized V k (with k between 1 and 5):
[0127] Either :
[0128] Figures 2A, 2B and 2C represent, more particularly, the implementation of the method for a five-phase motor, in the case where the reference potentials
[0129] V REF__i determined at the start of the process are less than or equal to the second threshold and therefore the potentials to be achieved Vi only include the possible addition of a homopolar potential V H .
[0130] In the case where the control voltage V MAG = 90% V DC / 2, the reference potentials of the five phases (curves 201a, 202a, 203a, 204a and 205a of Figure 2A) are all lower than the first threshold. Thus, it is not necessary to add a zero sequence potential V H , nor secondary potential V S_i in accordance with the method of the invention.
[0131] In the case where the control voltage V MAG = V DC / 2, the reference potentials of the five phases (curves 201b, 202b, 203b, 204b and 205b of Figure 2B) are well below or equal to the first threshold. Thus, it is not necessary to add a zero sequence potential V H nor secondary potential V S_i .
[0132] In fact, the maximum and minimum values of homopolar potential V H represented by curves 211b and 212b show that a homopolar potential equal to 0 allows the potentials of the N phases to be kept between -V DC / 2 and +V DC / 2. The maximum homopolar potential is expressed by V DC / 2 - max(V REF_ j) and the minimum homopolar potential is expressed by -V DC / 2 - min(V REF__i ). Curve 213b represents the homopolar potential V Hproposed in the method of the invention, that is to say in the case where the reference electrical potentials of the five phases would be less than or equal to the second threshold but where at least one of the reference potentials would be greater than the first threshold.
[0133] In the case where the control voltage V MAG = 105% V DC / 2, the reference potentials of the five phases (curves 201c, 202c, 203c, 204c and 205c of Figure 2C) reach the first threshold, but remain lower than or equal to the second threshold. Thus, it is necessary to add a homopolar potential V H so that they are always between -V DC / 2 and +V DC / 2. Curves 211c and 212c represent the maximum and minimum values of the homopolar potential V H possible so that the amplitude of the potentials to be realized in the five phases remains less than or equal to V DC / 2.
[0134] Curve 213c represents the homopolar potential VH proposed in step 106 of the method 100 according to the invention. It can be seen that this curve 213c is well included between the curves 211c and 212c, that is to say between the maximum and minimum values of possible homopolar potential. After application of the method 100 of the invention, it can be seen that the potentials to be achieved of the five phases have been well corrected (curves 221c, 222c, 223c, 224c and 225c which represent the potential Vi = V REF_i + V H ) so as to remain between -V DC / 2 and +V DC / 2 while being increased for certain values of angle 0 so that the amplitude of the voltage across the motor windings can rise to the control voltage V MAG , or 105% V DC / 2.
[0135] Figures 3A and 3B represent, more particularly, the implementation of the method for a five-phase motor, in the case where at least one of the reference potentials V REF__iis greater than the second threshold and therefore the potentials to be achieved Vi include the addition of a homopolar potential V HN depending on the number of phases and a secondary potential V S_i .
[0136] In the case where the control voltage V MAG = 110% V DC / 2, the reference potentials of the five phases (curves 301a, 302a, 303a, 304a and 305a of Figure 3A) are higher than the first threshold and the second threshold. Thus, in accordance with the method of the invention, it is necessary to add a homopolar potential V HN and a secondary potential V S_i The gray areas around curves 311a, 312a and 313a represent respectively the possible values of the homopolar potential V HN and the two components V SAB (1) and V SAB (2) of the secondary potential V S_i . In particular, curve 311a represents the first component V SAB (1) of the secondary potential V S_i, and curve 312a represents the second component V SAB (2) of the secondary potential Vsj according to the formulas of the invention described previously. Curve 313a represents the value of the homopolar potential V HN according to the formula of the invention described above. After application of the method of the invention, and therefore the addition of the secondary and homopolar potentials V S_i (let V SAB (1) and V SAB (2)) and V HN represented by curves 311a, 312a and 313a, the reference potentials of the five phases are corrected and the potentials to be achieved are represented by curves 321a, 322a, 323a, 324a and 325a. We see that the potentials to be achieved are now well between -V DC / 2 and +V DC / 2, and that their amplitude has indeed been modified for certain values of angle 0 to increase the voltage across the motor windings.
[0137] In the case where the control voltage V MAGis equal to the limiting voltage V LIM , or 123% V DC / 2, the reference potentials V REF__i of the five phases (curves 301b, 302b, 303b, 304b and 305b of Figure 3B) are greater than the first threshold and the second threshold. Thus, in accordance with the method of the invention, it is necessary to add a homopolar potential V HN and a secondary potential V S_i The gray areas around curves 311b, 312b and 313b represent respectively the possible values of the homopolar potential V HN and V components SAB (1) and V SAB (2) of the secondary potential V S_i . Unlike the case of Figure 3A, we see that the area around curves 311b, 312b and 313b has shrunk and that there is now almost only one possible value for each component and potential to reach the control voltage V MAG and keep the potentials to be realized from the five phases between -V DC / 2 and +V DC / 2. After application of the method of the invention, and therefore the addition of the secondary components V SAB (1) and V SAB (2) of the secondary potential V S_i and the homopolar potential V HN represented by curves 311b, 312b and 313b, the reference potentials V REF__i of the five phases are corrected and the potentials to be realized V are represented by curves 321b, 322b, 323b, 324b and 325b. We can clearly see that these potentials to be realized V are between -V DC / 2 and +V DC / 2, and that their amplitude has indeed been modified for certain values of angle 0 to increase the voltage across the motor windings.
[0138] Figure 4 represents, schematically and partially, an electrical device 400 according to one embodiment of the invention.
[0139] The electrical device 400 comprises a power supply 401 connected to an input of an electrical controller 402. The electrical controller 402 is connected to a power converter 403 which is itself connected to an electric motor 404 comprising N phases, N being an integer greater than or equal to 4. The electrical controller 402 supplies N electrical potentials to the converter 403 so that the latter converts them and supplies them to the N phases of the electric motor 404. The potentials supplied to the motor 404 correspond to the potentials to be achieved Vi determined by the method of the invention and converted by the power converter 403.
[0140] The electrical controller 402 is notably configured to implement the method of the invention. Thus, the controller 402 is configured to determine the reference potentials and the potentials to be achieved Vi of the N phases of the motor 404 for a control voltage V MAGlower than a limiting voltage V LIM provided by a user, as shown in Figure 4, or defined by the controller 402 according to the following formula: with a = n / (2N) if N is odd or a = 0 if N is even and a multiple of 4 or a = n / N if N is even and not a multiple of 4.
[0141] The electrical potentials to be achieved V are determined according to the values of the reference electrical potentials V REF__i determined by the controller 402, the reference potentials V REF__i being given by the following formula: with i between 1 and N, and V REF__i representing the reference potential of the i-th phase of motor 404.
[0142] Then the controller 402 compares these reference potentials V REF_i at the first and second thresholds, which can be defined as shown with reference to Figure 1.
[0143] If the reference potentials V REF__iare all less than or equal to the first threshold, then the potentials Vi supplied to the power converter 403 then to the motor 404 will be equal to the reference potentials V REF__i previously defined.
[0144] If the reference potentials V REF__i are all less than or equal to the second threshold, but at least one of the reference potentials is greater than the first threshold, then the potentials Vi supplied to the power converter 403 then to the motor 404 will be equal to Vi = V REF__i + V H , with V H the homopolar potential defined by the following formula: where max k=1 ... N V REFk represents the maximum reference potential among the reference potentials V REF__i determined previously and min represents the minimum reference potential among the reference potentials V REF__i previously determined.
[0145] If the reference potentials VREF_i are all greater than the second threshold, then the potentials V supplied to the power converter 403 then to the motor 404 will be equal V = V REF_i + V S_i + V HN , with V HN a homopolar potential depending on the number of phases N and the reference electrical potentials V REF_i and V S_i a secondary potential depending on the number of phases N and the reference electrical potentials V REF__i .
[0146] In this case, the secondary potentials V S_i and homopolar V HN can be expressed by the following functions: with :
[0147] - if N is odd, with p = (Nl) / 2: with: o U a vector with N lines defined by U = T -1 u and u an N-row vector defined by a value 1 for its indices iP, a value 0 for its index iM and a value -1 for its indices iN; o V an N-row vector defined by V = T -1v and v an N-line vector defined by a value 0 for its indices iP and iN and a value 1 for its index iM; where iP the p indices of the p largest values of the reference potentials
[0148] V REF__i ; where iN the p indices of the p smallest values of the reference potentials
[0149] V REF__i o iM the index of the median value of the reference potentials V REF__i ; oi varying from 1 to N, and o T a transformation matrix defined by:
[0150] ■ the odd columns from 1 to 2 [(N- 1) / 2 J noted 2k-l (k varying from 1 to [(Nl) / 2 J), correspond to the vector having as i-th component (with i varying from 1 to N): c(i, 2k- 1) = cos (2nk(il) / N); ■ the even columns from 1 to 2[(Nl) / 2 J noted 2k (k varying from 1 to [(Nl) / 2 J) correspond to the vector having as i-th component (with i varying from 1 to N): c(i, 2k) = sin (2nk(i- 1) / N);
[0151] ■ in the case where N is odd, column N is defined by a constant vector with the value 1 / √2;
[0152] ■ in the case where N is even, column Nl is defined by a vector of alternating constants of value 1 / √2 and value - 1 / √2 and column N is defined by a constant vector with value 1 / √2.
[0153] - If N is even, with p = N / 2: V H = 0 and V SAB_i (k) is defined by: o If k varies from 1 to p-2: o For the other k between 1 and N-3: V SAB_i (k) = 0 ; with:
[0154] PM = qQ' 1 ; iP the p-1 indices of the p-1 largest values of the reference potentials V REF__i for i varying from 1 to N; q the row vector formed from the elements of the row of the transformation matrix T corresponding to the last index of iP corresponding to the indexed columns where k varies from 1 to p-2; and
[0155] Q the matrix formed from the elements of the transformation matrix T at the intersection of the rows corresponding to the first p-2 indices of the iP and the indexed columns where k varies from 1 to p-2.
[0156] Figures 5A, 5B and 5C show another example of implementation of the method according to the invention for N = 6, i.e. for a 6-phase motor.
[0157] For a 6-phase motor, the transformation matrix T is expressed as follows:
[0158] As N is even, in accordance with the invention, the reference electrical potentials V REF__i at the terminals of the six phases for a control voltage V MAG are defined by: with i between 1 and 6.
[0159] Then, by applying the formulas of the invention, as N is even, the homopolar potential V HN is zero and the secondary potentials are defined by: with
[0160] The electrical potentials to be achieved Vi at the terminals of the six phases are then equal to:
[0161] Figure 5A represents the reference electric potential V REF__i at the terminals of the six phases of the six-phase motor before the application of the method of the invention for a control voltage V MAG of amplitude equal to 90% of V DC / 2-
[0162] In this case, the reference potentials of the six phases are all lower than V DC / 2, which is the first threshold. It is therefore not necessary to add a secondary potential in accordance with the method of the invention. The potentials to be achieved are therefore equal to the reference electrical potentials V REF__i .
[0163] Figure 5B represents the reference electric potential V REF__i at the terminals of the six phases of the 6-phase motor before the application of the method of the invention (graph (a)), the secondary potential V SAB_i(3) as described previously (graph (b)) as well as the potentials to be achieved Vi (graph (c)) for a control voltage V MAG of amplitude equal to 105% of V DC / 2.
[0164] Figure 5C represents the reference electric potential V REF__i at the terminals of the six phases of the 6-phase motor before the application of the method of the invention (graph (a)), the secondary potential V SAB_i (3) as described previously (graph (b)) as well as the potentials to be achieved V (graph (c)) for a control voltage V MAG of amplitude equal to 115.7% of V DC / 2.
Claims
Claims
1. Method (100), implemented by an electrical controller, for determining electrical potentials (V i ) to be carried out at the terminals of the phases of a motor comprising N phases, N being an integer greater than or equal to 4, the method comprising the following steps: - define (101) an amplitude control voltage V MAG and phase 0 which is lower than a limiting voltage (V LIM ) ; - determine (102) reference electrical potentials (V REF__i ) at the terminals of the N phases of the motor for this control voltage with where i is between 1 and N, V REF__i is the reference electrical potential across the i-th phase and 0 is the phase of the control voltage between 0 and 2n; - compare (103) the reference electrical potentials (V REF__i ) to a first threshold (threshold 1); - if the reference electrical potentials (V REF__i ) are all less than or equal to the first threshold (104), then the electrical potentials to be achieved (V) at the terminals of the N phases of the motor are equal to the reference electrical potentials (V REF__i ), OR if at least one of the reference electrical potentials (V REF__i ) is greater than the first threshold, compare (105) these reference electrical potentials (V REF__i ) to a second threshold (threshold 2), the second threshold being higher than the first threshold; - if these reference electrical potentials (V REF__i ) are all less than or equal to the second threshold (106), then the electrical potentials to be achieved (V) at the terminals of the N phases of the motor are equal to V = V REF__i + V H , with or if at least one of the reference electrical potentials (V REF__i ) is greater than the second threshold (107), then the electrical potentials to be achieved (V) at terminals of the N phases of the motor are equal to Vi = V REF__i + V S_i + V HN , with V HN a homopolar potential depending on the number of phases (N) and the reference electrical potentials (V REF_i ) and V S_i a secondary potential depending on the number of phases (N) and the reference electrical potentials (V REF_ j).
2. A determination method according to claim 1, wherein when at least one of the reference potentials is greater than the second threshold, the secondary potentials (V S_i ) and homopolar (V HN ) are expressed by the following functions: with : - if N is odd, with p = (Nl) / 2: with k ranging from 1 to N-3, and U a vector with N lines defined by U = T -1u and u an N-row vector defined by a value 1 for its indices iP, a value 0 for its index iM and a value -1 for its indices iN; V a vector with N lines defined by V = T -1 v and v an N-line vector defined by a value 0 for its indices iP and iN and a value 1 for its index iM; iP the p indices of the p largest values of the reference electrical potentials (V REF_i ) ; iN the p indices of the p smallest values of the reference electric potentials (V REF__i ); iM the index of the median value of the reference electrical potentials (V REF__i ); i varying from 1 to N, and T a transformation matrix defined by: o the odd columns from 1 to 2 [(N- l) / 2 J denoted 2k-l (k varying from 1 to [(Nl) / 2 J), correspond to the vector having as i-th component (with i varying from 1 to N): c(i, 2k-l) = cos (2nk(il) / N); o the even columns from 1 to 2[(Nl) / 2 J denoted 2k (k varying from 1 to [(N- l) / 2 J) correspond to the vector having as i-th component (with i varying from 1 to N): c(i, 2k) = sin (2nk(il) / N); o in the case where N is odd, the column N is defined by a constant vector with the value 1 / √2; o in the case where N is even, the column Nl is defined by a vector of alternating constants of value 1 / √2 and value -1 / √2 and the column N is defined by a constant vector with the value 1 / √2. If N is even, with p = N / 2: V HN = 0 and V SAB_i (k) is defined by: o If k varies from 1 to p-2: o For the other k between 1 and N-3: V SAB_i (k) = 0 ; with P M = qQ-1 ; iP the p-1 indices of the p-1 largest values of the reference electrical potentials (V REF_i ) for i varying from 1 to N; q the row vector formed from the elements of the row of the transformation matrix T corresponding to the last index of iP corresponding to the indexed columns where k varies from 1 to p-2; and Q the matrix formed from the elements of the transformation matrix T at the intersection of the rows corresponding to the first p-2 indices of the iP and the indexed columns where k varies from 1 to p-2.
3. A determination method according to any one of claims 1 or 2, wherein the limiting voltage (V LIM ) and the second threshold (threshold 2) are functions dependent on the number of phases (N) of the motor and the electrical potential of a motor power supply (V DC )-
4. A determination method according to any one of claims 1 to 3, wherein the first threshold (threshold 1) is a function dependent on the electrical potential of the motor's power supply (V DC )-
5. A determination method according to any one of claims 1 to 4, wherein the second threshold is expressed by the following function:
6. A determination method according to any one of claims 1 to 5, wherein the limiting voltage (V LIM ) is expressed by the next function: with a = n / (2N) if N is odd or a = 0 if N is even and a multiple of 4 or a = n / N if N is even and not a multiple of 4.
7. A determination method according to any one of claims 1 to 6, wherein the first threshold is equal to V DC / 2.
8. A determination method according to any one of claims 1 to 7, wherein the motor is a five-phase motor, N is equal to 5, the first threshold is equal to V DC / 2, the second threshold is equal to 1.05 x V DC / 2 and the limiting voltage (V LIM ) is equal to 1.23 x V DC / 2 with V DC the electrical potential of the motor's power supply, and if at least one of the reference electrical potentials (V REF__i ) is greater than the second threshold, then the electrical potentials to be achieved (V i ) at the terminals of the 5 phases of the motor are equal to V i(i = p) = V M for p, such that the reference electric potentials V REF_p are the two highest reference electrical potentials, V i(i = i) = -V M for I, such that the reference electric potentials V REF__i are the two smallest reference electric potentials or V i(i = n = Vc for j, such that the reference electric potential V REF__i is the median reference electric potential, with: and with p, j and I chosen from
9. An electrical controller for connection to an N-phase motor and an electrical power source, with N an integer greater than or equal to 4, the controller being configured to - define an amplitude control voltage V MAG and phase 0 which is lower than a limiting voltage (V LIM ) ; - determine reference electrical potentials (V REF_i ) at the terminals of the N phases of the motor for the control voltage (V MAG ) with where i is between 1 and N, V REF__i is the reference electrical potential across the i-th phase and 0 is the phase of the control voltage between 0 and 2n; - compare the reference electrical potentials to a first threshold; - if the reference electrical potentials are all less than or equal to the first threshold, then the electrical potentials to be produced at the terminals of the N phases of the motor are equal to the reference electrical potentials, or if at least one of the reference electrical potentials is greater than the first threshold, compare these reference electrical potentials to a second threshold, the second threshold being greater than the first threshold; - if these reference electrical potentials are all less than or equal to the second threshold, then the electrical potentials to be achieved at the terminals of the N phases of the motor are equal to Vi = V REF__i + V H , with or if at least one of the reference potentials is greater than the second threshold, then the potentials to be achieved at the terminals of the N phases of the motor are equal to Vi = V REF_i + V S_i + V HN , with VHN a homopolar potential depending on the number of phases (N) and the reference electrical potentials (V REF_ j) and V S_i a secondary potential depending on the number of phases (N) and the reference electrical potentials (V REF_ j).
10. An electrical controller according to claim 9, wherein when at least one of the reference potentials is greater than the second threshold, the secondary potentials (V S_i ) and homopolar (V HN ) are expressed by the following functions: with : - if N is odd, with p = (Nl) / 2: with k ranging from 1 to N-3, and U a vector with N lines defined by U = T -1 u and u an N-row vector defined by a value 1 for its indices iP, a value 0 for its index iM and a value -1 for its indices iN; V a vector with N lines defined by V = T -1v and v an N-line vector defined by a value 0 for its indices iP and iN and a value 1 for its index iM; iP the p indices of the p largest values of the reference electrical potentials (V REF__i ); iN the p indices of the p smallest values of the reference electric potentials (V REF__i ); iM the index of the median value of the reference electrical potentials (V REF__i ); i varying from 1 to N, and T a transformation matrix defined by: o the odd columns from 1 to 2 [(N- 1) / 2 J noted 2k-l (k varying from 1 to L(Nl) / 2 J), correspond to the vector having as i-th component (with i varying from 1 to N): c(i, 2k-l) = cos (2nk(il) / N); o the even columns from 1 to 2[(Nl) / 2 J noted 2k (k varying from 1 to [(N- l) / 2 J) correspond to the vector having as i-th component (with i varying from 1 to N): c(i, 2k) = sin (2nk(il) / N); o in the case where N is odd, the column N is defined by a constant vector with the value 1 / √2; o in the case where N is even, the column Nl is defined by a vector of alternating constants with the value 1 / √2 and the value -1 / √2 and the column N is defined by a constant vector with the value 1 / √2. - If N is even, with p = N / 2: V H = 0 and V SAB_i (k) is defined by: o If k varies from 1 to p-2: o For the other k between 1 and N-3: V SAB_i (k) = 0 ; PM = qQ -1 ; iP the p-1 indices of the p-1 largest values of the reference electrical potentials (V REF__i) for i varying from 1 to N; q the row vector formed from the elements of the row of the transformation matrix T corresponding to the last index of iP corresponding to the indexed columns where k varies from 1 to p-2; and Q the matrix formed from the elements of the transformation matrix T at the intersection of the rows corresponding to the first p-2 indices of the iP and the indexed columns where k varies from 1 to p-2.
11. An electrical controller according to any one of claims 9 or 10, wherein the limiting voltage (V LIM ) and the second threshold are functions dependent on the number (N) of phases of the motor and the electric potential (V DC ) of the power supply intended to be connected to the electrical controller.
12. An electrical controller according to any one of claims 9 to 11, wherein the second threshold is expressed by the following function: with V DC the voltage of the power supply intended to be connected to the electrical controller and N the number of phases of the motor intended to be connected to the electrical controller.
13. An electrical controller according to any one of claims 9 to 12, wherein the limiting voltage (V LIM ) is expressed by the following function: with a = n / (2N) if N is odd or a = 0 if N is even and a multiple of 4 or a = n / N if N is even and not a multiple of 4, and with V DC the voltage of the power supply intended to be connected to the electrical controller and N the number of phases of the motor intended to be connected to the electrical controller.
14. Electrical device (400) comprising: - an electrical power source (401); - an electrical controller (402) according to any one of claims 9 to 13, one input of which is connected to the electrical power source; - a power converter (403), inputs of which are connected to the electrical controller; - an N-phase motor (404) connected to the power converter, N being an integer greater than or equal to 4, and the power converter being configured to provide electrical potentials (V i ) at the input of the N phases of the motor.