Pulse width modulation generation strategy

Abstract

Title: Pulse Width Modulation Generation Strategy The present invention relates to a method for generating pulse width modulation (PWM) for a converter of an electric machine of an electric or hybrid vehicle, the converter operating with phase shifts with a duty cycle associated with a phase shift, the converter supplying a voltage (20) to a transformer of the electric machine (1), the method for generating pulse width modulation comprising operating the converter with duty cycle change requests, a subdivision period (22) being defined between two duty cycle change requests, the method for generating pulse width modulation being characterized in that half of the duty cycle is applied at the beginning of said subdivision period (22) and half of the duty cycle is applied at the end of said subdivision period (22).Abstract figure: Figure 4.

Description

Title of the invention: Pulse width modulation generation strategy

[0001] The present invention relates to the fields of electronics and electrical engineering, and more particularly the field of electrical machines.

[0002] Electrical machines can be used in electric and hybrid vehicles to provide torque to the vehicle's wheels. The motor may, for example, be an electrically excited synchronous machine or EESM. The EESM is an alternative to permanent magnet synchronous machines because the latter require the use of rare earth materials.

[0003] In an EESM, energy has to be transferred from a non-rotating part, i.e. the stator of the electrical machine, to a rotating part, i.e. the rotor. Such power transfer can be conductive or inductive, but nowadays an inductive power transmission seems preferable because it does not cause any mechanical losses and does not require any maintenance.

[0004] In an electrically excited inductive synchronous machine or iEESM, the stator and rotor are associated with a converter, a transformer and a rectifier. The converter provides a voltage to the transformer and the rectifier is connected between the transformer and the rotor to provide a desired positive voltage to the rotor windings.

[0005] For dynamic and efficient torque control of the iEESM, it is necessary to change the rotor current depending on the requested torque and other boundary conditions (e.g. DC voltage, current limits, motor speed). The torque demand usually follows the driver's demand on the car's accelerator pedal / or brake pedal. The torque demand thus changes over time, and therefore it is necessary to quickly change the torque of the electric machine. Therefore, the voltage supplied to the rotor windings of the iEESM must also change quickly, which is why it is important to operate the converter correctly.

[0006] Various strategies for generating pulse width modulation (PWM) to operate the converter exist in the prior art. For example, it is known to generate voltage pulses so that they are centered on a PWM half-period. This, however, creates DC offsets under dynamic operating conditions, i.e., when the converter duty cycle changes, and therefore causes saturation of the transformer under dynamic conditions. This saturation is caused by the fact that the currents of the transformer do not remain within certain limits, for example due to flux imbalance, and leads to less energy being transferred from a primary side of the transformer to a secondary side.

[0007] Other PWM generation strategies can correct saturation problems but lead to duty cycle errors under dynamic conditions. Such duty cycle errors would result in unexpected limitations of the transformer output voltage. This would result in reduced dynamic response in the current control loop, which must be avoided due to the stringent requirements for transient torque response characteristics.

[0008] The present invention falls within this context by providing a PWM generation strategy in which saturation problems are corrected and duty cycle errors are avoided by aligning half of a given converter duty cycle with the start of a given time period and the other half of the duty cycle with the end of said time period.

[0009] In this context, the present invention relates to a method for generating pulse width modulation (PWM) for a converter of an electric machine of an electric or hybrid vehicle, the converter operating with phase shifts with a duty cycle associated with a phase shift, the converter supplying a voltage to a transformer of the electric machine, the method for generating pulse width modulation comprising operating the converter with duty cycle change requests, a subdivision period being defined between two duty cycle change requests, the method for generating pulse width modulation being characterized in that half of the duty cycle is applied at the beginning of said subdivision period and half of the duty cycle is applied at the end of said subdivision period.

[0010] The pulse width modulation or PWM generation strategy according to the invention is used to operate a DC / AC converter, which is here integrated into an electrical machine. Such an electrical machine is more precisely an electrically excited inductive synchronous machine or iEESM. It comprises, in addition to the converter, various other components including a transformer and a rectifier.

[0011] The converter is a phase-shift full-bridge converter or PSEBC, which operates via the PWM generation method with phase shifts to which a duty cycle is associated. The converter provides bipolar rectangular voltages which are applied to the transformer, more precisely to a primary side of this transformer. A secondary side of the transformer includes a rectifier, which is necessary to provide a desired positive voltage to the rotor windings. The primary side of the transformer is located on a non-rotating part of the electric machine, while the secondary side of the transformer is located on the rotating part of the electric machine.

[0012] The PWM generation method involves operating the converter with duty cycle change requests. A duty cycle change is an update of the duty cycle. Duty cycle requests that evolve over time. Two consecutive duty cycle change requests define a subdivision period. In this subdivision period, half of the duty cycle is applied at the beginning and the other half is applied at the end. As a result, the duty cycles are aligned with the beginning and end of a given subdivision period.

[0013] With such a PWM generation method, flux balancing is achieved both in steady state and in dynamic operating conditions, thus avoiding transformer saturation.

[0014] Additionally, no duty cycle error is created since the duty cycles start at the same time as a subdivision period; in other words, the duty cycles and subdivision periods are coordinated, with the requested duty cycle matching the actual duty cycle under dynamic operating conditions, without any need for special correction or processing of the PWM generation.

[0015] According to an optional characteristic of the invention, the subdivision period corresponds to a multiple of a PWM half-period.

[0016] For example, the subdivision period may be equal to a half PWM period. In other words, a half PWM period corresponds to the interval between a first duty cycle change request and a second duty cycle change request. Of course, other integer multiples of a half PWM period may alternatively be used to define the subdivision period.

[0017] According to an optional characteristic of the invention, the converter generates at least one positive voltage pulse and at least one negative voltage pulse over a given subdivision period.

[0018] This allows a distribution of a magnetic flux of the converter over a given subdivision period.

[0019] According to an optional characteristic of the invention, a magnetic flux of positive voltage pulses is equal to a magnetic flux of negative voltage pulses over a PWM half-period.

[0020] For example, there are as many positive voltage pulses as negative voltage pulses in a given PWM half-period. Over a PWM period, the added value of the positive voltage pulses and the added value of the negative voltage pulses negative voltages cancel each other out. The magnetic flux of the converter is thus balanced.

[0021] According to an optional characteristic of the invention, when the subdivision period corresponds to a PWM half-period, over a given PWM half-period a positive pulse corresponding to half the duty cycle is generated at the start of the PWM half-period, and a negative pulse corresponding to half the duty cycle is generated at the end of the PWM half-period.

[0022] In this case, the positive pulse corresponds to a left-aligned pulse in the given PWM half-period and the negative pulse to a right-aligned pulse.

[0023] According to an optional characteristic of the invention, when the subdivision period corresponds to a PWM half-period, over a given PWM half-period a negative pulse corresponding to half the duty cycle is generated at the start of the PWM half-period, and a positive pulse corresponding to half the duty cycle is generated at the end of the PWM half-period.

[0024] In this case, the negative pulse corresponds to a left-aligned pulse in the given PWM half-period and the positive pulse to a right-aligned pulse.

[0025] According to an optional characteristic of the invention, when the subdivision period corresponds to a PWM period, over a given PWM period a first negative pulse corresponding to half the duty cycle is generated at the start of the PWM period, a positive pulse corresponding to the duty cycle is generated in the middle of the PWM period, and a second negative pulse corresponding to half the duty cycle is generated at the end of the PWM period.

[0026] The first negative pulse thus corresponds to the left-aligned pulse in the given PWM period while the second negative pulse corresponds to the right-aligned pulse. When added together, the duty cycles corresponding to the first negative pulse and the second negative pulse are equal to the duty cycle corresponding to the positive pulse.

[0027] According to an optional characteristic of the invention, when the subdivision period corresponds to a PWM period, over a given PWM period a first positive pulse corresponding to half the duty cycle is generated at the start of the PWM period, a negative pulse corresponding to the duty cycle is generated in the middle of the PWM period, and a second positive pulse corresponding to half the duty cycle is generated at the end of the PWM period.

[0028] In this alternative, the first positive pulse and the second positive pulse correspond respectively to the left-aligned pulse and the right-aligned pulse in the given PWM period. The combination of the duty cycle corresponding to the first positive pulse and the duty cycle corresponding to the second positive pulse is equal to the duty cycle corresponding to the negative pulse.

[0029] According to an optional feature of the invention, the voltage pulses start when a primary current of the transformer is equal to zero.

[0030] This is the result of balancing the transformer flux, which itself is the result of balancing the positive and negative voltage pulses.

[0031] Other characteristics, details and advantages of the invention will appear more clearly on reading the following description, on the one hand, and several exemplary embodiments given for informational and non-limiting purposes with reference to the appended schematic drawings, on the other hand, in which:

[0032] [Fig. 1] is a schematic representation of an electric machine for an electric or hybrid vehicle, the electric machine comprising a rotor, a stator and a transmitter comprising a rectifier and a transformer;

[0033] [Fig.2] is another schematic representation of a part of the electric machine of [Fig.l], further comprising a converter;

[0034] [Fig.3] is a schematic representation of an output voltage control of the converter;

[0035] [Fig.4] is a schematic representation of a first embodiment of a PWM generation method according to the invention;

[0036] [Fig.5] is a schematic representation of the corresponding waveforms of the first embodiment;

[0037] [Fig.6] is a schematic representation of a second embodiment of the PWM generation method according to the invention.

[0038] The features, variants and different embodiments of the invention may be combined with each other in various combinations, provided that they are not incompatible or mutually exclusive. In particular, variants of the invention comprising only a selection of features described later among the other features described may be imagined, if this selection of features is sufficient to confer a technical advantage and / or differentiate the invention from the prior art.

[0039] Like numbers refer to like elements in the drawings.

[0040] Figures 1 and 2 are schematic representations of an electric machine 1, or a part of said electric machine 1. The electric machine 1 is intended to be mounted in a vehicle such as an electric or hybrid vehicle, where it can be used to provide torque to the wheels of the vehicle. Here, the electric machine 1 is an electrically excited inductive synchronous machine, also known by its acronym iEESM.

[0041] As can be seen in [Fig.l], the electric machine 1 comprises a rotor 2 and a stator 4. In this example, the stator 4 is positioned around the rotor 2, but in other embodiments the rotor 2 could be positioned around the stator 4. In electrically excited inductive synchronous machines such as this electric machine 1, the power is transferred to a winding mounted on the rotor 2 using a transformer 6. The transformer 6 is more precisely a rotating high-frequency transformer. The transformer 6 comprises a primary side 8 and a secondary side 10, these two sides 8, 10 being different in that the primary side 8 is located on a non-rotating part of the electric machine 1, namely the stator, while the secondary side 10 is located on a rotating part of said electric machine 1, namely the rotor. In [Fig.l], a separation between the non-rotating part and the rotating part is illustrated in dotted lines.

[0042] A rectifier 12 is associated with the transformer 6. The rectifier 12 is a rotating rectifier, and as such it is positioned on the secondary side 10 of the transformer 6, i.e. on the rotating part of the electrical machine 1. The role of the rectifier 12 is intended to provide only a positive voltage to the rotor 2. This rectifier 12 is, with the transformer 6, implemented in a transmitter 14, here an inductive transmitter.

[0043] As can be seen in [Fig.2], a converter 16 is connected to the primary side 8 of the transformer 6. The converter 16 is a phase-shift full-bridge converter or PSFBC. It operates at a variable pulse width modulation frequency, or PWM frequency. The PWM frequency of the converter 16 can indeed vary in a wide range, for example from 5 to 100 kHz, depending on the design of the converter 16 and / or the transformer 6 and / or a required current in the rotor 2.

[0044] The converter 16 is driven by an electronic control unit of the electrical machine such as a microcontroller, a field-programmable gate array (FPGA) or a digital signal processor (DSP) to convert direct current from a vehicle battery into alternating current, in order to provide an appropriate voltage to the primary side 8 of the transformer 6. The converter 16 may also include an input capacitor 17. As shown here, the converter 16 includes four transistors 18, with two upper transistors 18A and two lower transistors 18B. Each upper transistor 18A is associated with a lower transistor 18B and they are inversely controlled. In order to avoid short circuits, in particular of the input capacitor 17, an additional latching time is introduced into the electrical machine 1.This additional latching time results in a delayed turn-on command of the upper transistor 18A or the lower transistor 18B by one half-bridge relative to the turn-off command of the upper transistor 18A or the lower transistor 18B by one half-bridge.

[0045] The converter 16 operates according to a PWM generation method or strategy of PWM generation according to the invention in order to implement dynamic and efficient torque control of the electrical machine 1. To this end, the converter 16 operates by phase shifts, each phase being offset between 0 and 180°. In addition, each phase shift of the converter 16 is associated with a duty cycle, this duty cycle being between 0 and 1.

[0046] [Fig. 3] illustrates the relationship between the phase shifts, the duty cycles associated with these phase shifts and the voltage pulses that are applied in relation to these duty cycles. To do this, [Fig. 3] illustrates five successive PWM periods, with a phase shift modified at each change of PWM period. During the first PWM period T PWM1, a phase shift of 180° between the first upper transistor 18A and the second upper transistor 18A corresponds to a duty cycle of 1, and the duration of application of the voltage pulses corresponds to the total duration of this duty cycle, first PWM period T PWM1. During the second PWM period T PWM2, a phase shift of 135° between the first upper transistor 18A and the second upper transistor 18A corresponds to a duty cycle of 0.75.During the third PWM period T PWm3, a 90° phase shift between the first upper transistor 18A and the second upper transistor 18A corresponds to a duty cycle of 0.5, and the duration of application of the voltage pulses is half the duration of this third PWM period T PWM 3. PWM period T PWm3. During the fourth PWM period T pwm4, a 45° phase shift between the first upper transistor 18A and the second upper transistor 18A corresponds to a duty cycle of 0.25. During the fifth PWM period T PWm5, a 0° phase shift between the first upper transistor 18A and the second upper transistor 18A corresponds to a duty cycle of 0, and no voltage pulses are applied.

[0047] The converter 16 generates a voltage waveform 20, this waveform 20 being visible in FIGS. 3, 4 and 6. The voltage waveform 20 can be divided into a plurality of PWM periods. Generally, for a duty cycle equal to 1, positive or negative voltages are applied successively throughout the given PWM period, without zero voltage values, each positive or negative voltage being applied for half of the PWM period, whereas for a duty cycle equal to 0.5 for example, positive and negative voltages are applied for a shorter duration during the given PWM period, with zero voltage values ​​provided between them, each positive or negative voltage being applied for half the time of what is done for the duty cycle equal to 1.

[0048] In order for the duty cycles to change, the converter 16 operates with duty cycle change requests. Such duty cycle change requests are indicated by white arrows in Figures 4 and 6, which respectively present a first embodiment and a second embodiment. In these two figures, a requested duty cycle is represented at the top and the voltage pulses implemented according to the PWM generation method according to the invention to obtain said duty cycle are represented at the bottom.

[0049] Two consecutive duty cycle change requests define a subdivision period 22. This subdivision period 22 corresponds to a PWM period in the first embodiment of [Fig.4], while it corresponds to a half-PWM period in the second embodiment of [Fig.6]. In other words, the duty cycle change request occurs at each PWM period in the first embodiment, while it occurs at each half-PWM period in the second embodiment. More generally, the subdivision period 22 may correspond to any integer multiple of a half-PWM period, which means that the duty cycle change request may occur at each multiple of a half-PWM period. Preferably, the subdivision period 22 corresponds to a control period. Such a control period is defined by a period of time during which a particular voltage is obtained.Therefore, the control period can be equal to a PWM period according to the first embodiment or to a half-PWM period according to the second embodiment. The duty cycle change requests thus occur between two successive control periods.

[0050] According to the invention, the PWM generation method is such that half of the duty cycle is applied at the start of a given subdivision period 22 and half of the duty cycle is applied at the end of said subdivision period 22.

[0051] In both embodiments, it should be noted that the converter 16 generates at least one positive voltage pulse 24 and at least one negative voltage pulse 26 for each subdivision period 22. More particularly, in the first embodiment the converter 16 generates, for each subdivision period 22 corresponding to a PWM period, one positive voltage pulse 24 and two negative voltage pulses 26. In the second embodiment, on the other hand, the converter 16 generates exactly one positive voltage pulse 24 and one negative voltage pulse 26 for each subdivision period 22 corresponding to a half-PWM period.

[0052] As mentioned previously, in the first embodiment of [Fig.4], that is to say for a subdivision period 22 equal to a PWM period, the duty cycle change request occurs at each PWM period. For a duty cycle of 0.25 requested at a first time t0.5, half of the duty cycle, i.e. 0.125, is achieved at the start of the PWM period at the first time t0.5, and the other half of the duty cycle, which is also 0.125, is achieved at the end of the PWM period at a second instant tl,5. Similarly, for a duty cycle of 0.5 requested at the second instant tl,5, half of the duty cycle, i.e. 0.25, is achieved at the start of the PWM period at the second instant tl,5, and the other half of the duty cycle is achieved at the start of the PWM period at the second instant tl,5. the duty cycle, which is also 0.25, is achieved at the end of the PWM period at a third instant t2,5.

[0053] Furthermore, in this first embodiment, since the subdivision period 22 is one PWM period, there is an additional pulse in the middle of the PWM period in order to provide the appropriate voltage during the PWM period to obtain the required duty cycle. As shown in [Fig.4], for each PWM period there is a first pulse 26A, here a negative pulse 26A, corresponding to half of the duty cycle that is generated at the beginning of the PWM period, then an additional pulse 24 of the opposite direction, sign, here a positive pulse 24, corresponding to the duty cycle that is generated in the middle of the PWM period, and a second pulse 26B, here a second negative pulse 26B, corresponding to half of the duty cycle that is generated at the end of the PWM period.Thus, after the first duty cycle change request of the first embodiment, the first negative pulse 26A corresponding to a duty cycle of 0.125 starts at the first time t0.5, the positive pulse 24 corresponding to a duty cycle of 0.25 is generated so that it is centered around the fourth time t1, and the second negative pulse 26B corresponding to a duty cycle of 0.125 is generated so that it ends at the second time t1.5.

[0054] Considering two successive subdivision periods 22 with a first subdivision period 22 associated with a duty cycle request of 0.25 and a second subdivision period 22 associated with a duty cycle request of 0.5, it results from the strategy of the invention that a first pulse, here a negative pulse 26A, corresponding to a duty cycle of 0.125 is generated at the beginning of the first subdivision period 22, that a second pulse, here a positive pulse 24, corresponding to a duty cycle of 0.25 is then generated in the middle of the first subdivision period 22, and that a third pulse, here another negative pulse 26B, is then generated, said third pulse corresponding to a duty cycle of 0.325, which corresponds to a duty cycle of 0.125 at the end of the first subdivision period 22 and a duty cycle from 0.25 at the start of the second subdivision period 22.

[0055] Although not illustrated here, there could be a variant of the first embodiment of the invention in which it is a first positive pulse 24A corresponding to half the duty cycle which is generated at the beginning of the subdivision period 22, a negative pulse 26 corresponding to the duty cycle which is generated in the middle of subdivision period 22, and a second positive pulse 24B corresponding to half the duty cycle which is generated at the end of subdivision period 22.

[0056] In the second embodiment of [Fig.6], i.e. for a subdivision period 22 which is equal to a half PWM period, the duty cycle change request occurs at each half PWM period; in other words, this occurs twice as much as in the first embodiment. As can be seen in [Fig.6], for a duty cycle of 0.25 requested at the first time t0.5, half of the duty cycle, i.e. 0.125, is achieved at the beginning of the half PWM period at said first time t0.5. , and the other half of the duty cycle, which is also 0.125, is achieved at the end of the half PWM period at a fourth time t1.Similarly, for a following duty cycle of 0.5 requested at the fourth instant tl, half of the duty cycle, i.e. 0.25, is achieved at the beginning of the PWM half-period at the fourth instant tl, and the other half of the duty cycle is achieved. The cycle, which is also 0.25, is achieved at the end of the PWM half-period at the second instant tl.5.

[0057] As shown in [Fig.6], for a subdivision period 22 of a PWM half-period, for each PWM half-period, there is only one negative pulse 26 corresponding to half the duty cycle that is generated at the beginning of said PWM half-period and one positive pulse 24 corresponding to half the duty cycle that is generated at the end of the PWM half-period. Thus, after the first duty cycle change request of the second embodiment, the negative pulse 26 corresponding to a duty cycle of 0.125 starts at the first time t0.5, and the positive pulse 24 corresponding to a duty cycle of 0.125 ends at the fourth time t0.5. In the second embodiment, no voltage pulse occurs in the middle of the PWM half-period.

[0058] In a similar manner to what has been described for the first embodiment, the second embodiment could alternatively consist of a positive pulse 24 corresponding to half the duty cycle being generated at the start of the subdivision period 22 and a negative pulse 26 corresponding to half the duty cycle being generated, generated at the end of said subdivision period 22, without departing from the scope of the invention.

[0059] By virtue of what has been described above, whether for the first embodiment of [Fig.4] or the second embodiment of [Fig.6], for a given subdivision period 22, the positive and negative voltage pulses 24, 26 are balanced. In other words, over a PWM period or a half PWM period for the first embodiment and the second embodiment respectively, a magnetic flux of positive voltage pulses 24 is equal to a magnetic flux 26 negative voltage pulses.

[0060] In [Fig. 5], which relates to the first embodiment in which a subdivision period 22 is equal to a PWM period, different waveforms are illustrated. These waveforms correspond, from top to bottom, to a transformer input voltage waveform 28, a converter input current waveform 30 and a primary transformer current waveform 32. generated in the transformer 6. Here, "corresponding" means that the transformer input voltage waveform 28, the converter input current waveform 30 and the primary transformer current waveform 32 are observed in the same PWM periods.

[0061] As can be seen in this [Fig.5], there is no deviation in the waveforms; the positive and negative pulses are balanced in the input voltage waveform of transformer 28, in the input current waveform of converter 30 and in the primary transformer current waveform 32. More precisely, the primary transformer current waveform 32 is symmetrical about the current line 0, which is characteristic of a balanced primary transformer current. Such a balanced primary transformer current is desired because it means that saturation and / or flux imbalance of transformer 6 is avoided.

[0062] Furthermore, there is no shift of the duty cycle in the waveforms, in particular there is no error between the requested duty cycle and the realized duty cycle; due to the balancing of the primary transformer current, the voltage pulses start when the primary transformer current of transformer 6 is equal to zero. Therefore, decreases in the dynamic response of the torque control are avoided.

[0063] The present invention thus covers a PWM generation strategy that generates a balanced transformer flux without duty cycle error, by aligning the converter duty cycles with the start and end of a given predefined time period.

[0064] Numerous modifications and other embodiments of the invention presented herein will occur to those skilled in the art to which the invention relates, benefiting from the teachings presented in the foregoing descriptions and the associated drawings. Accordingly, it is to be understood that the invention is not to be limited to the specific embodiments disclosed and that modifications and other embodiments are intended to be included within the scope of the appended claims. Although specific terms are employed herein, they are used in a generic and descriptive sense only and not for purposes of limitation.

Claims

Claims

1. A method of generating pulse width modulation (PWM) for a converter (16) of an electric machine of an electric or hybrid vehicle (1), the converter (16) operating with phase shifts with a duty cycle associated with a phase shift, the converter (16) supplying a voltage (20) to a transformer (6) of the electric machine (1), the method of generating pulse width modulation comprising operating the converter (16) with duty cycle change requests, with a subdivision period (22) being defined between two duty cycle change requests, the method of generating pulse width modulation being characterized in that half of the duty cycle is applied at the beginning of said subdivision period (22) and half of the duty cycle is applied at the end of said subdivision period (22).

2. A method of generating pulse width modulation according to the preceding claim, wherein the subdivision period (22) corresponds to a multiple of a half PWM period.

3. A method of generating pulse width modulation according to any preceding claim, wherein the converter (16) generates at least one positive voltage pulse (24) and at least one negative voltage pulse (26) over a given subdivision period (22).

4. A method of generating pulse width modulation according to any preceding claim, wherein a magnetic flux of positive voltage pulses (24) is equal to a magnetic flux of negative voltage pulses (26) over a PWM half-period.

5. A method of generating pulse width modulation according to any preceding claim in combination with claim 2, wherein when the subdivision period (22) corresponds to a PWM half-period, over a given PWM half-period, a positive pulse (24) corresponding to half the duty cycle is generated at the beginning of the PWM half-period, and a negative pulse (26) corresponding to half the duty cycle is generated at the end of the PWM half-period.

6. A method of generating pulse width modulation according to one of

7.

8.

9. any of claims 1 to 4 in combination with claim 2, wherein when the subdivision period (22) corresponds to a PWM half-period, over a given PWM half-period, a negative pulse (26) corresponding to half the duty cycle is generated at the start of the PWM half-period, and a positive pulse (24) corresponding to half the duty cycle is generated at the end of the PWM half-period. A method of generating pulse width modulation according to any preceding claim in combination with claim 2, wherein when the subdivision period (22) corresponds to a PWM period, over a given PWM period, a first negative pulse (26A) corresponding to half of the PWM period's duty cycle is generated at the beginning of the PWM period, a positive pulse (24) corresponding to the duty cycle is generated in the middle of the PWM period, and a second negative pulse (26B) corresponding to half of the duty cycle is generated at the end of the PWM period. A method of generating pulse width modulation according to any one of claims 1 to 6 in combination with claim 2, wherein when the subdivision period (22) corresponds to a PWM period, over a given PWM period, a first positive pulse (24A) corresponding to half the duty cycle is generated at the beginning of the PWM period, a negative pulse (26) corresponding to the duty cycle is generated in the middle of the PWM period, and a second positive pulse (24B) corresponding to half the duty cycle is generated at the end of the PWM period. A method of generating pulse width modulation according to any one of the preceding claims, wherein the voltage pulses (24, 26) start when a primary transformer current of the transformer (6) is zero.

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