阅读说明：本技术 基于脉宽调制开关模式的转换器的模型预测控制 (Model predictive control of a pulse width modulation switching mode based converter ) 是由 T·格耶 V·施普迪克 C·古特舍尔 A·吕奇 于 2019-01-08 设计创作，主要内容包括：一种用于控制电转换器(12)的方法,所述电转换器(12)适于将DC电压(v<Sub>dc</Sub>)转换为具有至少两个电压电平的多相电压,所述方法包括：从定子通量参考向量(ψ<Sup>*</Sup><Sub>s,αβ</Sub>)来确定调制信号向量(u<Sup>*</Sup><Sub>abc</Sub>)；经由脉宽调制从调制信号向量(u<Sup>*</Sup><Sub>abc</Sub>)来确定开关模式(54),所述开关模式(54)包括开关转变序列,其中开关转变定义开关位置和转变时刻,在所述开关位置处将所述转换器的相从一个电压电平切换到另一个电压电平,以及在所述转变时刻,切换转换器的所述相；通过从估计的定子通量向量(ψ<Sub>s,αβ</Sub>)中减去定子通量参考向量(ψ<Sup>*</Sup><Sub>s,αβ</Sub>)来确定定子通量误差(ψ<Sup>*</Sup><Sub>s,err,αβ</Sub>),所述估计的定子通量向量(ψ<Sub>s,αβ</Sub>)从所述电转换器(12)中的测量来估计；通过移动所述开关模式(54)的开关转变的转变时刻来修改所述开关模式(54),使得所述定子通量误差(ψ<Sup>*</Sup><Sub>s,err,αβ</Sub>)被最小化；以及将修改的开关模式的至少一部分应用于所述电转换器(12)。(A method for controlling an electrical converter (12), the electrical converter (12) being adapted to convert a DC voltage (v) dc ) To a multi-phase voltage having at least two voltage levels, the method comprising: from stator flux reference directionQuantity (psi) * s，αβ ) To determine a modulation signal vector (u) * abc ) (ii) a Modulating a signal vector (u) from a pulse width modulation * abc ) To determine a switching pattern (54), the switching pattern (54) comprising a sequence of switching transitions, wherein a switching transition defines a switching position at which a phase of the converter is switched from one voltage level to another voltage level and a transition time at which the phase of the converter is switched; by deriving the stator flux vector (psi) s，αβ ) Subtracting the stator flux reference vector (psi) * s，αβ ) To determine the stator flux error (psi) * s，err，αβ ) Said estimated stator flux vector (ψ) s，αβ ) Estimated from measurements in the electrical converter (12); modifying the switching pattern (54) by shifting transition moments of switching transitions of the switching pattern (54) such that the stator flux error (ψ) * s，err，αβ ) Is minimized; and applying at least a part of the modified switching pattern to the electrical converter (12).)

1. A method for controlling an electrical converter (12), the electrical converter (12) being adapted to convert a DC voltage (v)_dc) Converting to a multi-phase voltage having at least two voltage levels;

the method comprises the following steps:

from stator flux reference vectorTo determine a modulation signal vector

Via pulse width modulation fromThe modulation signal vectorTo determine a switching pattern (54), the switching pattern (54) comprising a sequence of switching transitions, wherein a switching transition defines a switching position at which a phase of the converter is switched from one voltage level to another voltage level and a transition time at which the phase of the converter is switched; wherein the switching pattern (54) is determined periodically at each sampling instant in a prediction time domain;

by deriving the stator flux vector (psi)_s，αβ) Subtracting the stator flux reference vectorTo determine the stator flux error (psi)_{s，err，αβ}) Said estimated stator flux vector (ψ)_s，αβ) Estimated from measurements in the electrical converter (12);

modifying the switching pattern (54) by shifting transition moments of switching transitions of the switching pattern (54) such that the stator flux error (ψ)_{s，err，αβ}) Is minimized;

applying a portion of the modified switching pattern to the electrical converter (12).

2. The method of claim 1, wherein the first and second light sources are selected from the group consisting of a red light source, a green light source, and a blue light source,

wherein the stator flux correction is defined by the sum of the products of voltage level differences and time differences, said voltage level differences of a switching transition being the difference of said voltage levels before and after said switching transition, and said time differences being the difference between shifted and unmodified transition moments;

wherein the stator flux correction is optimized by shifting the transition instants such that the stator flux correction equals the stator flux error (ψ)_{s，err，αβ})。

3. The method as set forth in claim 1 and 2,

wherein only said part of said modified switching pattern equal to the difference between consecutive sampling instants is applied to said electrical converter (12).

4. The method of any one of the preceding claims,

wherein the switching transition of the switching pattern (54) is determined in a prediction time domain by:

by aligning αβ 0 the modulation signal vector in the coordinate system at the actual angular frequencyDetermining the modulation signal vector in the prediction domain rotated to a time instant of a future sampleThe respective future samples of;

generating a switching transition when the carrier signal crosses the value of the future sample during the time interval of the future sample.

5. The method of any one of the preceding claims,

wherein the stator flux reference vectorIs a three-component vector in the αβ 0 coordinate system, and the stator flux reference vectorThe 0 component of (a) is used for control of the neutral point potential.

6. The method of any one of the preceding claims,

wherein the common mode componentIs added to the modulated signal vector

7. The method of claim 6, wherein the first and second light sources are selected from the group consisting of a red light source, a green light source, and a blue light source,

wherein when a reference vector is derived from the stator fluxAmplitude ofThe common-mode component is determined when the modulation index (m) is less than a threshold valueAt least the modulation index plus a minimum pulse width divided by a carrier spacing length of a carrier signal such that a pulse length of a pulse generated by pulse width modulation with the carrier signal is longer than the minimum pulse width.

8. The method of claim 6, wherein the first and second light sources are selected from the group consisting of a red light source, a green light source, and a blue light source,

wherein the common mode component is controlled using a hysteretic controllerThe hysteretic controller is at a neutral point potential (upsilon)_n) When the common mode component is larger than the maximum valueSet to a first value while in said common mode componentLess than a minimum value of the common mode componentIs set to a second value of opposite sign relative to the first value.

9. The method of any one of the preceding claims,

wherein from a reference angle (theta)^*) And a reference amplitudeTo determine the stator flux reference vector

10. The method of any one of the preceding claims,

wherein the number of pulses (d) for the switching pattern (54) is determined from the fundamental frequency and the maximum allowed switching frequency; and/or

Wherein the switching pattern (54) is determined using pulse width modulation when the number of pulses (d) exceeds a threshold value, and the switching pattern (54) is otherwise determined from a table of optimized pulse patterns (48).

11. The method of claim 10, wherein the first and second light sources are selected from the group consisting of a red light source, a green light source, and a blue light source,

wherein in case when an optimized pulse pattern (48) is used for determining a switching pattern (54), the stator flux reference vector is determined from the optimized pulse pattern (48)

12. A computer program adapted to perform the steps of the method of any one of the preceding claims when executed on a processor.

13. A computer-readable medium on which a computer program according to claim 12 is stored.

14. A controller (24) for controlling an electrical converter (12), the controller (24) being adapted to perform the steps of the method of any of claims 1 to 11.

15. An electrical converter (12) comprising:

a converter circuit (20), the converter circuit (20) being adapted to convert a DC voltage into a multi-phase voltage having at least two voltage levels;

the controller (24) of claim 14, the controller (24) being adapted to control a semiconductor switch (22) of the electrical converter (20).

Technical Field

The invention relates to a method, a computer program, a computer readable medium and a controller for controlling an electrical converter. Furthermore, the invention relates to an electrical converter.

Background

For electrical converters, model predictive control is used to determine the switching state of the converter circuit via determining the future state of the electrical converter based on a model of the converter and the connected components (e.g., electric motor, generator, power grid, etc.).

In WO 2015078656 a1, the pre-calculated optimized pulse pattern is further optimized with model predictive control by manipulating its switching instants. In this way, the harmonic content of the generated current can be reduced.

The harmonic benefits of optimizing the pulse pattern relative to other modulation methods are particularly high at low pulse counts (i.e., the ratio between the switching frequency and the fundamental frequency). But at very high pulse counts and low fundamental frequencies, the optimal pulse pattern may be difficult to calculate and may use many controller memories. Control methods based on optimized pulse patterns typically solve this problem by switching to other control methods.

In EP 2469692 a1, the power system is controlled in such a way that in a second step the switching sequence with switching moments for the converter, which has been determined for some first optimization goal, is modified. The resulting flux error is determined. The switching moments are modified to reduce flux errors.

In JAMES SCOLTOCK et al: in "A Complex of Model Predictive control schemes for MV indication Motor drivers" (IEEE TRANSACTION ON INDUSTRIALINFORMATICS, IEEE SERVICE CENTER, NEW YORK, NY, US, vol.9, No.2, 2012, 10 months and 10 days (2012-10-10), p. 909,919), several Model Predictive control schemes are compared with pulse width modulation and optimized pulse patterns. It is mentioned that the common mode component can be added to the reference voltage.

In NIKOLAOS OIKONOMOU et al: "Model Predictive Pulse pattern control for the Five-Level Active Neutral-Point-Clamped Inverter" (ieee transport ON input adaptive inverters., vol.49, No.6, 5/15/2013 (2013-05-15), page 2583-.

Disclosure of Invention

It is an object of the present invention to provide an electrical converter adapted to generate an output current with low harmonic distortion at a low fundamental frequency. It is a further object of the invention to provide a simple and computationally inexpensive model predictive control scheme which can also be used at high pulse numbers.

These objects are achieved by the subject matter of the independent claims. Further exemplary embodiments are apparent from the dependent claims and the following description.

A first aspect of the invention relates to a method for controlling an electrical converter. The electrical converter is adapted to convert the DC voltage into a multi-phase voltage having at least two voltage levels. The electrical converter may comprise a converter circuit with semiconductor switches, which may be arranged in at least two (e.g. three) phase branches. The phase branches may be connected in parallel to the DC link and/or may be adapted to convert a DC link voltage or more generally a DC voltage into an AC phase voltage. Each phase branch may be adapted to generate at least two voltage levels.

For example, a phase leg may be adapted to generate three voltage levels, such as a positive DC link voltage, a negative DC link voltage, and a neutral point voltage. The neutral point voltage may be provided by splitting the DC link. The electrical converter may be a neutral point clamped converter. In general, however, the method may also be performed with other types of converters.

The electrical converter may be connected with its AC side to an electrical machine (e.g. a generator or a motor) and/or may supply this electrical machine with electrical power. The stator and/or rotor flux mentioned below may represent the magnetic flux in the stator and/or rotor of this machine. It may also be the case that the electrical converter is connected with its AC side to the power grid. In this case, virtual stator and/or virtual rotor fluxes may also be defined for the power grid.

The electrical converter may be a power converter. The semiconductor switch thereof may be adapted to switch currents exceeding 10A and/or voltages exceeding 1000V.

The electrical converter may comprise a controller, the controller performing the method. For example, the method may be performed at each sampling instant.

According to an embodiment of the invention, the method comprises: a modulation signal vector is determined from the stator flux reference vector. The stator flux reference vector may be provided by an outer control loop that determines the stator flux reference vector based on the measurements and based on a reference speed and/or a reference frequency.

The modulation signal vector is a signal indicative of the output voltage to be generated by the converter. For example, the modulation signal vector may be a normalized voltage vector determined by differentiating the stator flux reference vector.

The invention is also applicable to a grid-side converter, i.e. the stator flux vector may be a virtual stator flux vector. Also, the rotor flux vector may be a virtual rotor flux vector. For example, in case the converter supplies a power grid, the stator flux vector may be a virtual converter flux vector and the rotor flux vector may be a power grid flux vector, which may be defined at a Point of Common Coupling (PCC).

It has to be noted that here and in the following a vector may be a quantity with two or three components.

According to an embodiment of the invention, the method further comprises: determining a switching pattern from the modulated signal vector via pulse width modulation, the switching pattern comprising a sequence of switching transitions, wherein a switching transition defines a switching position at which a phase of the converter is switched from one voltage level to another voltage level and a transition instant at which said phase of the converter is switched.

The modulation signal vector may indicate the actual output voltage to be generated. Along with the actual frequency and/or the actual velocity, the movement of the modulation signal vector may be extrapolated into the future and a sequence of future switching sequences may be determined therefrom. For example, the trajectory of the components of the extrapolated modulated signal vector may be compared to one or more carrier signals (which may be triangular signals having a carrier frequency). The switching transitions may be determined from the trace and carrier signal(s) using pulse width modulation. For example, the intersection of the trace with the carrier signal may determine the switching instant, and/or the direction of the intersection may determine whether to raise or lower the voltage level at the switching instant.

It must be noted that these calculations may all be performed online during a sampling interval (i.e., the time between two sampling instants), and/or may be performed digitally.

According to an embodiment of the invention, the method further comprises: the stator flux error is determined by subtracting an estimated stator flux vector (which is estimated from measurements in the electrical converter) from the stator flux reference vector. The estimated stator flux vector may be provided by an outer control loop. The difference of the stator flux reference vector and the estimated stator flux vector or the magnitude of the difference may be considered as an error, which may be minimized by the following steps of the method and/or by using model predictive control.

According to an embodiment of the invention, the method further comprises: the switching pattern is modified by shifting the transition moments of the switching transitions of the switching pattern such that the stator flux error is minimized. The transition moments can be shifted forward and backward in time, so that the switching pattern, which is generated by pulse width modulation, is modified. The transition moments can be moved such that the modified switching pattern produces a stator flux that is closer to the stator flux reference. In this way, the modified switching pattern may result in a lower amplitude for higher order harmonics than an unmodified switching pattern.

It may be the case that there is a constraint on the movement of the switching moments. For example, the order of switching transitions in one or all of the phases may not be changed.

Furthermore, it may be the case that additional switching instants are included in the unmodified switching pattern (which would, for example, generate a pulse of zero length). After optimization, these pulses may have a non-zero length and may contribute to the compensation of stator flux errors.

Optimization of the switching pattern may be performed online by solving quadratic programming, by minimizing an objective function subject to constraints, and so on.

According to an embodiment of the invention, the method further comprises: at least a portion of the modified switching pattern is applied to the electrical converter. The switching transitions may be translated into switching times and switching states of semiconductor switches of the electrical converter. A corresponding gating signal for the semiconductor switch may be generated.

It may be the case that the switching pattern and/or the modified switching pattern is longer than the sampling time interval. In this case, only a part of the switching pattern can be converted into switching time and switching state.

According to an embodiment of the invention, the stator flux correction is defined as the sum of the products of a voltage level difference and a time difference, the voltage level difference of the switching transition being the difference of the voltage levels before and after the switching transition, and the time difference being the difference between the shifted and unmodified transition instants. This stator flux correction can be determined per phase or for all phases. The switching pattern may be optimized such that the stator flux correction at least partially compensates for the stator flux error. The stator flux correction can be optimized by shifting the transition moments so that the stator flux correction equals the stator flux error.

According to an embodiment of the present invention, the switching pattern is periodically determined at each sampling instant within a prediction horizon (prediction horizon). The prediction time domain may be longer than the difference between consecutive sampling instants. For example, only a part of the modified switching pattern that is shorter than the prediction time domain (e.g. the difference between consecutive sampling instants) may be applied to the electrical converter. In other words, the method may predict the future behavior of the electrical converter and/or the powered motor in a prediction time domain that may be longer than the sampling time interval. At each sampling instant, the future behavior over more than a sampling time interval may be determined.

According to an embodiment of the invention, the switching transition of the switching pattern is determined in the prediction horizon by: determining respective future samples of the modulation signal vector in the prediction time domain by rotating the modulation signal vector in the α β 0 coordinate system to the time instant of the future sample at the actual angular frequency; and generating a switching transition when the carrier signal crosses the value of the future sample during the time interval of the future sample. The future samples may determine the trajectory and/or function of the modulated signal over time. The future samples may be determined by extrapolating components of the modulation signal vector into the future. This can be done by transforming the modulation signal vector into the α β 0 coordinate system, for example, using a clarke transform. Thereafter, the modulation signal vector may be rotated to the time instant of the future sample at the actual angular frequency (which may be determined from the actual velocity and/or the actual frequency). This rotation may rotate the α β component by the actual angular frequency times the time instances of future samples. It can therefore be assumed that the modulation signal vector is rotating at a constant angular frequency. After that rotation, the rotated modulated signal vector may be transformed back into the system in which it is provided (e.g., the abc system). This return transform may be performed using an inverse clarke transform.

The carrier signal may be represented as a triangular signal and the intersection of the trajectory of the extrapolated component of the modulation signal vector with the carrier signal may be determined. For example, the trajectory may be a stepped (or piecewise constant) trajectory over time, the value of which is determined from the value of the future sample at the time of the future sample. Each crossing may determine a switching instant for a switching transition. Depending on the direction of the intersection, it may be determined whether the voltage level increases or decreases at the intersection.

According to an embodiment of the invention, the stator flux reference vector is a three-component vector in an α β 0 coordinate system. The 0 component of the stator flux reference vector may be used to control the neutral point potential. Also, the stator flux error may be a three-component vector in the α β 0 coordinate system.

According to an embodiment of the invention, the common mode component is added to the modulation signal vector. The common mode component may be the sum of the phase components of the modulation signal vector. With this common mode component, the output voltage of the electrical converter can be influenced without changing the output current, assuming that the star point of the load is floating. This may be beneficial for influencing further optimization goals of the electrical converter and/or for complying with physical limitations of the electrical converter.

According to an embodiment of the invention, the common mode component is at least the modulation index plus the minimum pulse width divided by the carrier interval length of the carrier signal when the modulation index determined from the amplitude of the stator flux reference vector is less than the threshold value, such that the pulse length of the pulses generated by pulse width modulation with the carrier signal is longer than the minimum pulse width.

The modulation index may indicate a ratio of the magnitude of the actual output voltage relative to the maximum possible output voltage (e.g., (half) the DC voltage provided by the DC link). When the modulation index is relatively small, it may be necessary to ensure that the pulse length (i.e. the interval of the switching pattern with a non-zero output voltage level) is longer than the minimum pulse length. This minimum pulse length may correspond to a minimum time during which the semiconductor switches have to remain in the on-state before they can be switched off.

According to an embodiment of the invention, the common mode component is controlled by a hysteretic controller which sets the common mode component to a first value when the neutral point potential is greater than a maximum value and to a second value when the common mode component is less than a minimum value. The second value may have an opposite sign with respect to the first value, e.g. a negative first value. The first value may be in the direction of power flow, which may be positive in motoring operation and negative in generating mode.

For example, in the case when the modulation index is above a threshold, the common mode component may be used to control the neutral potential of the split DC link. Since the common mode component can increase and/or decrease the neutral point potential, the neutral point potential can be controlled to remain within the limit by reversing the neutral point potential each time the limit is exceeded.

According to an embodiment of the invention, the flux reference vector is determined from the reference angle and the reference amplitude. The reference angle and the reference amplitude may be provided by an outer control loop which determines them from a reference speed and/or a reference frequency and an optional measurement of the current and/or voltage in the motor supplied by the electrical converter.

According to an embodiment of the invention, the number of pulses of the switching pattern is determined from the fundamental frequency and the maximum allowed switching frequency. The number of pulses may be the ratio of the maximum allowable switching frequency and the fundamental frequency rounded to the nearest whole number. The fundamental frequency may be based on a reference speed and/or a reference frequency for the electrical converter. The number of pulses may determine the number of pulses for the optimized pulse pattern that may be used when the number of pulses is less than or equal to the threshold.

According to an embodiment of the invention, the switching pattern is determined using pulse width modulation (e.g. carrier based) when the number of pulses exceeds a threshold value, and otherwise from a table of optimized pulse patterns.

In general, for low pulse numbers (i.e., less than or equal to the threshold), an optimized pulse mode may be used as the switching mode, while for high pulse numbers, a pulse width modulated (e.g., carrier based) switching mode may be used, as described above and below. Thus, the same outer control loop and/or the same switch mode optimizer can be used in both cases.

The optimized pulse pattern may have been optimized offline and may have the following advantages: they may cause lower total harmonic distortion than (e.g., carrier-based) pulse width modulated switching patterns. However, for high pulse counts, it may be difficult to store large optimal pulse patterns and/or determine them offline.

The pulse width modulation switching pattern can be used to extend the control method based on the optimized pulse pattern to high pulse numbers. The pulse width modulated switching patterns may be generated online and may be fed as optimized pulse patterns to the same switching pattern optimizer. In a variable speed drive, for example, this extension may enable switch mode optimization (which moves the switching times) to be applicable to all operating points ranging from dwell operation to field weakening at high speeds.

According to an embodiment of the invention, the optimized pulse pattern is indexed in the table according to the number of pulses and the modulation index. In contrast to the pulse width modulated switching pattern, the optimum pulse pattern is determined from these two quantities and not from the stator flux reference and/or modulation signal vector. The number of pulses and modulation index may be provided by an outer control loop.

According to an embodiment of the invention, the stator flux reference vector is determined from the optimized pulse pattern in case when the optimized pulse pattern is used as a switching pattern. The stator flux reference may be determined by integrating the voltage waveform that optimizes the switching pattern. To perform the integration, a flux reference angle and a reference amplitude value that may be provided by the outer control loop may be required.

Further aspects of the invention relate to a computer program which, when being executed on a processor, is adapted to carry out the steps of the method as described above and below. For example, a controller of an electrical converter may provide such a processor, and the method is performed by software running in the controller. It may also be possible that the method is implemented at least partly in the form of software. For example, at least part of the method may be performed by an FPGA and/or a DSP.

A further aspect of the invention relates to a computer-readable medium on which such a computer program is stored. The computer readable medium may be a floppy disk, a hard disk, a USB (universal serial bus) memory device, a RAM (random access memory), a ROM (read only memory), an EPROM (electrically erasable programmable read only memory) or a FLASH memory. The computer-readable medium may also be a data communication network, such as the internet, allowing downloading of the program code. Generally, computer-readable media may be non-transitory or transitory media.

Further aspects of the invention relate to a controller for controlling an electrical converter, the controller being adapted to perform the steps of the method as described above and below. As already mentioned, such a controller may comprise a processor running software, which performs the method. Further, the controller may comprise an FPGA and/or a DSP that at least partially implements the method.

A further aspect of the invention relates to an electrical converter comprising: a converter circuit adapted to convert the DC voltage to a multi-phase voltage having at least two voltage levels; and such a controller, which is adapted to control the semiconductor switches of the converter circuit.

It has to be understood that features of the method as described above and below may be features of the computer program, the computer readable medium and the electrical converter as described above and below, and vice versa.

These and other aspects of the invention are apparent from and will be elucidated with reference to the embodiments described hereinafter.

Drawings

The subject matter of the invention will be explained in more detail hereinafter with reference to exemplary embodiments illustrated in the drawings.

Fig. 1 schematically shows a converter system with an electrical converter according to an embodiment of the invention.

Fig. 2 shows a diagram illustrating a controller and a control method according to an embodiment of the invention.

Fig. 3 shows a diagram illustrating a portion of the controller and control method of fig. 2.

Fig. 4 shows a diagram illustrating a portion of the controller and control method of fig. 2.

Fig. 5 shows a diagram illustrating a common mode controller used in the control method of fig. 2.

Fig. 6 shows a diagram about an example for a modulation signal vector and a switch position vector.

Fig. 7 shows a diagram about an example of a switching pattern used in the control method of fig. 2.

Fig. 8 shows a diagram indicating how switching transitions may be determined in the control method of fig. 2.

FIG. 9 shows a diagram indicating how additional switching transitions may be determined in the control method of FIG. 2.

Fig. 10 shows a diagram indicating how the switch transitions may be moved in the control method of fig. 2.

Fig. 11 illustrates a diagram showing a rolling horizon (recording horizon) used in the control method of fig. 2.

Fig. 12a to 12d show diagrams regarding modulation signals, voltages, fluxes and currents generated during normal speed operation by the method of fig. 2.

Fig. 13a to 13d show diagrams regarding modulation signals, voltages, fluxes and currents generated during low speed operation by the method of fig. 2.

Fig. 14a and 14b show the flux reference and the generated switching pattern during a change from an optimized pulse pattern to a carrier based pulse width modulated pulse pattern as performed by the method of fig. 2.

In general, in the figures, like parts are provided with like reference signs.

Detailed Description

Three-level converter system

FIG. 1 shows a converter system 10, the converter system 10 including an electrical converter 12, the electrical conversionThe device 12 is supplied with a DC voltage v_dcAnd generates a three-phase output or stator voltage that is supplied to the motor 14. It is possible that the electrical machine 14 is a generator or a motor and the stator current i_s，abcTo and from the motor 14. It is also possible that the electrical converter is connected to the power grid instead of the electrical machine 14.

As shown, electrical converter 12 is a three-phase three-level neutral point clamped voltage source converter. However, other topologies are possible using the control methods described above and below.

The electrical converter comprises a split DC link 16 providing a neutral point N. The converter circuit 20 is composed of phase branches 18, said phase branches 18 being connected in parallel to the DC-link and to the neutral point N. For each phase a, b, c (three phases as shown in fig. 1), there is a phase branch. Each phase leg 18 includes an output connected to the motor 14, an output current i_s，abcThrough which the corresponding component of (b) flows. At its respective output, each phase leg 18 is adapted to provide an output or stator voltage at a different voltage level. These voltage levels can be synthesized by switching the semiconductor switches 22 of the phase branches 18.

Fig. 2 shows a schematic diagram of the components of the controller 24 for the electrical converter 12. In particular, a general control diagram is shown, including an outer control loop, converter 12 and load 14.

Throughout the following, normalized amounts are used. For this purpose, per unit systems can be introduced. Exemplary base values may be a peak value of a rated phase voltage of the electric machine 14 and/or a peak value of a rated machine current and a rated fundamental frequency.

All variables ξ in a three-phase system (abc)_abc＝[ξ_aξ_bξ_c]^TCan be subjected to Clark transformation ξ_αβ0＝Kξ_abcTo transform to ξ in a fixed orthogonal αβ 0 coordinate system_αβ0＝[ξ_αξ_βξ₀]^TThe inverse Clark transformation may be through ξ_abc＝K^-1ξ_αβ0It is given. The transformation matrix of clark and inverse clark may be

ξ_αβ0，ξ_αAnd ξ_βThe first two elements of (a) are so-called differential mode components, and the third element ξ₀Is the common mode component. When only the differential-mode component is required, the corresponding matrix can be used to define a simplified Clark transformAnd a simplified inverse Clark transformation

It is to be noted that it is preferable that,the first two rows of K are retained, andretention of K^-1The first two columns of (a). K^-1Is thatWherein the 0 component is implicitly assumed to be zero.

In the following, bold variable representation ξ_αβ＝[ξ_αξ_β]^TOr two-dimensional vectors such as ξ_αβ0＝[ξ_αξ_βξ₀]^TAnd ξ_abc＝[ξ_aξ_bξ_c]^TSuch as a three-dimensional vector.

The variable t is used to represent a continuous time axis, whereThe controller 24 may discrete time steps or sampling instants kT at regular intervals_sIs operated in whichIs the controller time step, and T_sIs the controller sampling interval. For example, T may be selected_s＝25μs。

The total (instantaneous) DC link voltage may be upsilon_dc＝υ_dc，up+υ_dc，loWherein upsilon is_dc，upAnd upsilon_dc，loRepresenting the voltage over the upper and lower DC link capacitors, respectively. Potential of neutral point N between two DC link capacitorsCan float.

The electrical converter 12 may generate three voltage levels at its output with respect to the neutral point N. The voltage level can be passedIt is given. These voltages can be varied by an integer variable u_x∈ { -1, 0, 1}, where x ∈ { a, b, c } represents one of three phases the three-phase switch position is defined as u_abc＝[u_au_bu_c]^T. In general, the switch position u_abcMay also be considered as a normalized voltage level.

The phase voltage with respect to the neutral point N is given by

Three-phase voltage equal to upsilon_abc＝[υ_aυ_bυ_c]^T。

When the neutral point potential is near zero, or equivalently, when the voltages over the upper and lower DC link capacitors in FIG. 1 are approximately equal, the three-phase voltages can be written as

In the case of an electric machine connected to the converter phase terminals, the stator voltage of the machine in fixed orthogonal coordinates is

The machine conveniently passes its stator and rotor flux linkage vectors in fixed orthogonal coordinates (i.e. through psi)_s，αβ＝[ψ_sαψ_sβ]^TAnd psi_r，αβ＝[ψ_rαψ_rβ]^T) To describe. Ψ_s＝||ψ_s，αβAnd | is the magnitude of the stator flux vector. Defining the rotor flux vector Ψ accordingly_rThe amplitude of (c). Through omega_sTo represent the angular frequency of the stator. Note that the stator and rotor flux vectors rotate at this angular frequency. The electrical angular velocity of the rotor is ω_r＝pω_mWhere p is the number of pole pairs, and ω_mIs the mechanical angular velocity of the rotor. Omega_sAnd omega_rThe difference between is the slip frequency.

Alternatively, the stator and rotor flux linkage vectors are replaced by virtual flux vectors when the converter is connected to the power grid. In particular, the stator flux vector is replaced by a virtual converter flux vector, while the rotor flux vector is replaced by a grid flux vector, typically defined at the Point of Common Coupling (PCC).

Outer control ring

Returning to FIG. 2, the inner control loop 26 (the inner control loop 26 generates the switch position signal u)_abc) Supplied by the outer control loop 28 with modulation index m, number of pulses d, stator flux reference amplitudeStator flux reference angle theta^*And estimated stator flux vector psi_s，αβ. Further, a neutral point potential v_nAnd carrier spacing T_c＝1/f_c(wherein f_cIs the carrier frequency) is provided to the inner control loop.

The inner control loop may be based on an optimized pulse pattern or on a pulse width modulation (carrier based) depending on the number of pulses d, as described belowSwitching mode to determine a switch position signal u_abc。

The outer control loop 28 operates as follows:

based on the measured stator current vector i_s，αβAnd stator voltage v_s，αβThe flux observer 30 estimates the estimated stator flux vector ψ_s，αβEstimated rotor flux vector psi_r，αβAnd the estimated electromagnetic torque Te. From the estimated rotor flux vector ψ_r，αβThe amplitude Ψ of the block 32, 34 is determined_rAnd its angular position ∠ psi_r，αβ。

The speed controller 36 operates the electromagnetic torqueAlong its referenceTo adjust the (electrical) angular velocity omega of the rotor_r. Angular velocity omega_rMay be determined by an encoder 38, the encoder 38 measuring the speed of the rotor of the motor 14.

Torque controller 40 manipulates the desired load angle γ^*I.e. the expected angle between the stator flux vector and the rotor flux vector. The torque controller 40 requires a reference for the stator flux magnitudeAnd the actual magnitude Ψ of the rotor flux vector_r。

The flux controller 42 maintains the magnitude of the stator flux vector close to its reference by manipulating the modulation index mIn its simplest form, the feedforward term

Can be used for this purpose. In (6), v_dcIs the (instantaneous) total DC link voltage, and ω_sRepresenting the angular stator frequency. Angular stator frequency omega_sDetermined in block 44 and is the angular velocity at which the flux vector is rotated.

Optimizing pulse patterns

The inner control loop 26 uses an optimized pulse pattern or a pulse width modulated switching pattern for determining the switching position signal u_abc. Depending on the number of pulses d. For a number of pulses d smaller than the threshold an optimized pulse pattern is used, whereas for a number of pulses d larger than the threshold a pulse width modulated switching pattern is used.

Optimizing the use of pulse patterns in the case of high pulse counts (e.g., exceeding d-20) may face the following practical limitations: (i) such off-line computation of optimized pulse patterns can be demanding and time consuming, (ii) these optimized pulse patterns can require a large amount of storage capacity in the controller memory, and (iii) there is less incentive to use optimized pulse patterns because the harmonic benefits of optimized pulse patterns over a given modulation method are significantly reduced at high pulse numbers. Therefore, it may be beneficial to determine the pulse width modulation switching pattern online.

The need to operate at high pulse numbers occurs naturally when operating at low fundamental frequencies. In driving applications, a low fundamental frequency corresponds to low speed operation. In power converters, the semiconductor losses and the employed cooling techniques generally impose an upper limit f on the switching frequency_sw，max. When fundamental frequency f₁When changing, the pulse number needs to be adjusted according to the following formula

Therefore, when the fundamental frequency decreases with decreasing drive speed, the required number of pulses d increases, theoretically toward infinity at zero fundamental frequency.

The switching angles and switching positions for the optimal pulse pattern can be calculated for one phase within a quarter of the fundamental period, assuming 120 ° phase shift between the three phases and quarter and half wave symmetry. The number of (main) switching angles in a quarter period is the so-called number of pulses d, which is a natural number. For a three-level optimized pulse mode and neutral point clamped converter 12, the switching frequency of the semiconductor device may be given by

f_sw＝df₁， (8)

Wherein f is₁Representing the frequency of the fundamental component.

Fig. 3 shows a portion of the inner control loop 26 for optimizing storage, retrieval and modification of pulse patterns.

The pattern loader 46 provides an operating point-specific optimized pulse pattern 48, which operating point-specific optimized pulse pattern 48 is determined by the modulation index m and the number of pulses d. To ensure that the switching frequency does not exceed its maximum value f_sw，maxThe number of pulses d may be selected through (7) to not exceed f_sw，max/f₁Is the largest integer of (a).

The pattern loader 46 provides a vector a of d main switching angles [ α ═ d₁α₂...α_d]^TAnd the corresponding vector U ═ U of the single-phase switch position₁u₂...u_d]^T. The latter is usually referred to as a (single-phase) switching sequence. The three-phase optimized pulse pattern 48 over a complete cycle may be constructed based on vectors a and U using quarter-wave and half-wave symmetry.

The flux reference generator 50 may derive the modulation index m, the stator flux reference amplitude, from the vectors a and U and provided by the outer control loop 28And a stator flux reference angle to determine a stator flux referenceHaving an amplitudeAnd corner (among them, notation (note) ∠ξ_αβIs used to represent the vector ζ_αβAngular position of

θ^*＝∠ψ_r，αβ+γ^*(9)

Stator flux reference ofCan be derived by integrating the voltage waveform of the optimized pulse pattern 48 over time. Alternatively, stator flux referenceCan be derived from the corner points of the stator flux reference trajectories, which can be calculated off-line and stored in a look-up table.

In addition, a common mode flux reference componentCan be added to the stator flux referenceIn order to control the neutral point potential upsilon_n. This common mode flux reference componentCan be determined by the neutral point controller 56, which neutral point controller 56 can monitor the deviation of the neutral point potential through a virtual common mode flux error. By correcting it, a common-mode voltage is actually injected, which will place the neutral potential v_nDriven to its reference.

Instantaneous stator flux error

Is determined as a stator flux referenceAnd estimate psi thereof_s，αβ0The αβ component is provided by the outer control loop 28.

With the switching pattern generator 52, a switching pattern 54 is formed, which switching pattern 54 holds the upcoming switching transitions in each phase. More particularly, having n_xVector of single phase switch positions of individual entries

Is constructed for phase x, where x ∈ { a, b, c }. The reference θ relative to the angle^*By dividing it by the angular stator frequency omega_sTo translate into a nominal switching instant or transition instant (relative to the current instant). This results in a corresponding vector for the nominal transition instant

The pair of U_xAndforming a switching pattern 54 for phase x. Moment of transitionAnd its corresponding switch position u_xiCan be viewed as a switching transition. The pair of U_xAndcan be viewed as a sequence of switching transitions.

The mode controller 58 receives the switching modes 54 and manipulates the transition timesTo reduce stator flux error psi_{s，err，αβ0}. In doing so, the stator flux vector is controlled along its reference trajectory, and the stator flux error ψ is achieved_{s，err，αβ0}Closed loop control of (2). The optimization of the switching pattern 54 will be described in more detail with respect to fig. 4. The result is a modified switching pattern.

In the present example of the three-phase converter 12, the modified switching pattern (and the switching pattern 54) can be understood as a three-phase switching position u_abc＝[u_au_bu_c]^TThe sequence of (a). (integer) three-phase switch position 55 from modified on in first sample time intervalThe off mode is calculated and applied to the converter 12. At the next sampling instant, the modified switching pattern is recalculated according to a rolling time domain strategy.

Pulse width modulation switching pattern

Fig. 4 shows a portion of the inner control loop 26 that is used when the number of pulses d is above the threshold. In this case, the switching pattern 54 determined from the offline calculated optimized pulse pattern 48 is replaced with an online generated switching pattern 54 (the switching pattern 54 is based on pulse width modulation).

However, the same mode controller 58 is used again. And, by shifting the transition momentThe pulse width modulation switching pattern 54 is modified to control the stator flux of the machine 12. Avoiding a handover to another control loop. Only the switching pattern 54 is changed, which can be compared with switching between two optimized pulse patterns 48 having different numbers of pulses.

In the case of fig. 4, the flux reference generator 59 directly derives the stator flux reference amplitude provided by the outer control loop 24And stator flux reference angle theta^*To determine a stator flux reference vectorCommon mode flux reference componentCan be added to the stator flux referenceAs described with respect to fig. 3. The stator flux error ψ may be determined as described for fig. 3_{s，err，αβ0}。

In summary, the modulation signal generator 60 derives a stator flux reference vector fromTo determine a modulation signal vectorThe modulated signal vectorCan be used as differential mode modulation signal vectorTo generate. Common mode generator 62 may generate a common mode componentAnd adds it to the modulated signal vectorPattern generator 64 then modulates the signal vector from the modulation based on pulse width modulation (e.g., carrier based)The on-line generates a switching pattern 54.

The controller blocks 59, 60, 62, 64 and 58 will be described in more detail below.

Differential mode modulation signal generation

When the number of pulses d is high, the ratio between the switching frequency and the fundamental frequency is high. Thus, the stator flux trajectory may be approximated by a circle, thus simplifying the implementation of the flux reference generator 59.

According to its angle theta^*(see (9)) and amplitudeFixing stator flux reference vectors in orthogonal coordinates given a stator flux referenceDirect adherence to

During steady state operation, the reference angle passes through θ^*＝ω_st is given, where ω is_sIs the angular stator frequency. Thus, the stator flux vector is in ω_sAnd (4) rotating. Calculating a stator flux reference vector by the flux reference generator 59 based on (13)

Neglecting the stator resistance, the stator voltage is the derivative of the stator flux:

inserting (13) into (14) causes

Wherein the reference angle theta is used^*The time derivative of (a) is the angular stator frequency ω_s. Thus, the stator voltage reference is equal to the stator flux reference rotated 90 degrees forward and scaled by the angular stator frequency.

To obtain three-phase (differential mode) modulation signal vectorsThe converter voltage is used to be equal to the stator voltage, see (5). Assuming a neutral point potential v_nIs zero, and according to (4), a three-phase modulation signal vectorScaled total DC link voltage v_dcHalf of that. This causes

Modulation signal generator 60 is based on (15) and (16) from stator flux reference vectorsTo determine a modulation signal vector

Common mode voltage injection

Common mode generator 62 may generate a common mode componentAnd adds it to the modulated signal vectorIn general, the common mode componentCan be passed throughOr to the modulated signal vector via the following equation

Operation at very low speeds can be distinguished from operation in the remaining (normal) operating range. At very low speeds, the goal may be twofold: (1) avoidance of excessively narrow switching pulses that violate minimum on-time and must typically be discarded; and (2) avoidance of uneven distribution of semiconductor losses between the upper and lower halves of the converter 12. In normal speed operation, current distortion can be reduced by injecting an appropriate common mode voltage.

Low speed common mode voltage injection

When at very low speeds and correspondingly very low modulation indexes (e.g. m ∈ [0, 0.02)]) In operation, signal vectors are modulatedMay have a small amplitude. Thus, the switch position or voltage level is in the modulated signal vectorIs mostly zero in the case of short positive (negative) pulses. These pulses may have to meet a certain minimum width in time (so-called on-time). In high power converters, the minimum on-time can be as long as t_min50 mus. 0 and t_minThe width of the pulse between can be extended to t_minOr removed by a post-processing unit. Thus, when operating at very low modulation index m, switching can be avoided altogether, which jeopardizes the closed-loop control of the machine current and flux vectors.

To avoid discarding of pulses, appropriate common mode components may be injectedFor example, when operating with a small (non-negative) modulation index m < 1, a positive common mode signal

Can modulate signal vectorShift to the positive half and ensure t is met_minThe minimum pulse width of. Note that the offset t in (17)_min/T_cIt can be generated directly from the rules applied to the carrier spacing and the proportion of the modulated signal.

The second problem (i.e., uneven distribution of semiconductor losses) can be caused by the low fundamental frequency. For pulse width modulation based on a sinusoidal carrier, only the switches in the upper (or lower) converter half can be used during half of the fundamental period. To alleviate this problem, injection of a sufficiently large common mode signal as in (17) can be used to periodically shift the semiconductor losses between the two converter halves. This way the losses can be more evenly distributed, avoiding the need to de-rate the converter or to reduce the switching frequency.

As a side effect, an offset in the modulated signal adds a bias to the neutral point current, thereby increasing or decreasing the neutral point potential v_n. More particularly, in the motoring mode, positiveCausing positive drift d v_n(t)/dt > 0, while in the generation mode, a negative drift occurs. By inverting the sign of the common-mode term, the neutral potential upsilon can be reversed_nThe sign of the derivative of (c).And d upsilon_nThis relationship between (t)/dt > 0 can be used to construct a hysteretic controller which drives the neutral point potential v_nIs kept at a predefined interval [ v_n，min，υ_n，max]Within. The limit of symmetry, i.e. v, can be chosen_n，max＝υ_n，min。

Examples of such hysteretic controllers are:

in discrete time stepsIs operated in, where σ_p(k) ∈ { -1, 1} is the sign of the electrical power flow by definition, the power flow is positive in motoring operation and negative in generating mode₀(k) ∈ {1, 1 }. the common mode component to be injected is

Wherein the non-negative scalar quantityIs a design parameter. For modulation index considered at low speed operationIs selectable to

The choice of (c) is a compromise between two considerations. On the one hand, forPotential v at neutral point_nIs characterized by a particularly strong ripple of the third harmonic component. On the other hand, non-zero DC offsetTo this ripple is added the neutral point potential v over time_nIncrease or decrease linearly. For largeThis linear trend dominates over the ripple, thus facilitating the use of hysteretic controllers (18) and (19). However, too largeRequiring a symbol σ₀And increases current distortion.

Therefore, the temperature of the molten metal is controlled,is determined by the magnitude of the neutral point potential ripple and the degradation of the harmonic performance.

Determining the sign σ of the power flow due to errors in the current and voltage measurements_pIt may be erroneous at low electrical power. Alternative hysteretic controllers avoid pairing σ by only reversing sign whenever a limit is exceeded_pThe correlation of (c). This simplifies (18) to

Operate at low speedNeutral point potential v is balanced under the action of_nThis control scheme, while ensuring minimum width switching pulses, can be implemented by common mode generator 62 using either (18) or (20) as per (19).

Normal speed common mode voltage injection

At higher modulation indices (e.g., m > 0.02), the problem of too short switching pulses does not exist. Conversely, it may be advantageous to inject an appropriate common mode component into the modulation signal to reduce current distortion.

During normal speed operation, one or more of the following may be added as common mode components to the modulation signal vector

The first term (21) is the angular fundamental frequency ω triple having an amplitude m/6₁＝2πf₁And the same phase phi as the modulated signal₁Of the sinusoidal signal. The addition of the second term (22) centers the three phase modulated signal at zero. Thus, at any given moment in time,this is true. The third term (23) is based on a scalar and a three-phase term

Note that the items (24) and (22) are the same. (25) The expression ξ mod1 in (1) is defined as the remainder of a euclidean division of ξ with one. The result is limited to between zero and one.

Any of the three common mode terms increases the linear modulation region from m-1 to m-1.155. They also tend to reduce current distortion.

During normal speed operation, the common mode generator 62 may effect generation as per (21), (22), or (23).

As a further example, the neutral point potential v_nCan be controlled by manipulating a modulation signal vectorOf the common mode componentTo be implemented. Positive common mode componentFor example shifting the phase voltage to the upper converter half. Depending on the sign of the phase current (or the direction of the power flow), this shift adds a positive or negative bias to the average current drawn from the neutral point, which in turn modifies the neutral point potential v_n。

Fig. 5 shows an example of such a controller 62. By means of a filter 66 (with cut-off frequency according to the angular stator frequency omega)_sTo adapt) to the neutral point potential v_nLow pass filtering is performed. Potential v at neutral point_nBy gain k_pIs fed to the proportional controller and is related to the sign sigma of the electric power flow_pMultiplication. Generated common mode voltage referenceScaled DC link voltage v_dcTo obtain the common mode component of the modulated signal.

This type of neutral control may tend to be slow, accounting for the neutral potential upsilon_nRather than its instantaneous value. On the other hand, the common-mode voltage and thus the neutral point potential v_nIs instantaneousControl may be achieved by exploiting redundancy in the voltage vector.

Pulse width modulation

Pulse width modulation will modulate a signal vector(the modulated Signal vectorCan be regarded as a real-valued input signal) into a three-phase switch position vector u_abcSaid three-phase switch position vector u_abcCan be viewed as a discrete value output signal using fixed amplitude but variable width pulses. Output waveform u_abcAbout the magnitude and phase approximation of its fundamental components

With DC link voltage v_dcCan be used as an actuator to move the switch position vector u_abcInto a switched voltage waveform v at the converter terminals_abc. By appropriately scaling the reference voltageThe converter voltage v_abcApproximate reference theretoThis principle applies to (machine side) inverters and (grid side) active rectifiers.

FIG. 6 illustrates a vector for a modulated signalAnd switch position vector u_abcSchematic diagram of an example of (1). In this and all following diagrams, the time axis is given in ms.

The carrier based pulse width modulation for a three-level (or N-level) converter is based on two (or N-1) carrier signals 68. The carrier signal 68 may have a triangular waveform at the carrier frequency fc. In general, a carrier waveThe frequency being (significantly) higher than the fundamental frequency, i.e. f_c＞＞f_I. The peak-to-peak amplitude of each carrier signal 68 is one. For a three-level converter, the carrier signals 68 are arranged such that they cover a range from-1 to 1 without overlap. The phase shift between the two carrier signals is a design parameter. When the in-phase stacking scheme (phase displacement) is selected, the two carrier signals are in phase, whereas in the positive and negative anti-phase stacking scheme (phase displacement), their phases are shifted by 180 ° from each other. The former option is typically used because it causes lower harmonic distortion. Carrier spacing

Is the time interval between the upper peaks of the carrier signal. The three phases a, b, c use the same carrier signal 68.

Using asymmetric regular sampling and carrier spacing T_cIn discrete time steps k_c0.5T_c Every 0.5T_cThe carrier signal 68 is sampled. In general, the subscript c denotes a "carrier".

By modulating signal vectorsEach component ofAndthe carrier based pulse width modulation is achieved in comparison to two (or more) carrier signals 68. In phase a, e.g. based on modulated signalsAnd the following three rules for selecting the switch position u_a：

When in useWhen less than two carrier signals, u is selected_a＝-1。

When in useU is selected when it is smaller than the upper carrier signal but exceeds the lower carrier signal_a＝0。

When in useWhen more than two carrier signals are present, u is selected_a＝1。

In the case of a digital implementation,is a sampled signal, resulting in a regular sampled pulse width modulation. Using symmetric sampling, with a spacing T per carrier_cE.g. once at the upper triangular peak. The modulated signal is kept constant throughout the rest of the carrier interval. With asymmetric sampling, the modulation signal is sampled twice per carrier interval, i.e., at the upper and lower peaks of the carrier. The modulation signal is kept constant for half the carrier spacing.

In fig. 6, the dotted line is a continuous modulation signal, and the solid line shows an asymmetric regularly sampled modulation signal.

Consider the in-phase stacking approach and asymmetric sampling. The sampling instant of the modulated signal may be defined as t_c＝0.5T_ck_cWhereinAre discrete time steps. When sampling the modulated signalWhen intersecting the carrier signal, a handover is performed. This moment (relative to the sampling instant t)_c) Is the instant of switching or the instant of transition. For phase a, for example, variable t_aIs introduced to indicate the switching instant. Instantaneous switching and new switching positionThe position can be derived as a function of the polarity of the modulated signal and the slope of the carrier.

The switching instants or transition instants are shown as vertical dashed lines in fig. 6. The switch position u is shown below_abcThe resulting time evolution of (a).

Online generation of pulse width modulation switching patterns

Pattern generator 64 in FIG. 4 generates switching patterns 54, the switching patterns 54 being formed from vectors of x ∈ { a, b, c } for each phaseAnd U_xIs formed by said pairs of. Vector quantityIncluding the nominal transition time, and vector U_xIncluding the single phase switch position or voltage level of the x-phase. The definitions of these vectors are provided in (11) and (12). In discrete time steps k_cTo update the switching pattern 54 as indicated in fig. 7. Each switching pattern 54 spans from 0.5T_ck_cTo 0.5T_c(k_c+ K-1) of K carrier half-spaced prediction time domains. Step of timeRepresent these half intervals, wherein

To make with a time step k_cTo calculate the switching pattern 54, sample the modulated signalTransformed into αβ 0 coordinate system through clarke transformation matrix K (see (1)), and then rotated forwardSecond, assume a constant angular frequency ω_s. This allows the following formula to be followed in time stepsTo predict future samples of a modulated signal

WhereinAndrecall, K^-1Is a matrix of the inverse clark transform.

Variable of integer(where σ_c∈ { -1, 1}) indicates a time step sizeThe sign of the lower carrier slope. Modulated signalTo obtain a linear mapping with respect to time t_cNominal switching instant. This mapping needs to be done according to the polarity of the modulated signal and the carrier slope. This is half-spaced for the first carrier as shown in fig. 8 (where) Four different situations arise. In x phase ofThe switching transition occurs at a nominal time as follows

Based on the polarity of the modulated signal

And carrier slope σ_cTo identify the new switch position. Therefore, the temperature of the molten metal is controlled,

additional switching transitions may be in time steps when the modulated signal changes its signThis occurs. An example is shown in fig. 9, where the additional switching transition occurs at a time step kc + 1. These additional transitions need to be captured and included when generating the switching pattern 54.

Mode controller

The mode controller 58 operates the switching instants of the switching modes 54 to achieve fast closed loop control of the stator flux. Fig. 10 shows an example of how the switching instant may be moved by the mode controller 58.

As an example, a mode controller based on the deadbeat control is described below.

The mode controller 58 is at the sampling instant t ═ kT_sIs operated in, wherein T_s＜＜T_c. The input to the mode controller 58 is the flux error psi_{s，err，αβ0}And having vectors as defined in (11) and (12) for each phase xAnd U_xWhere x ∈ { a, b, c }.

Vector quantityCapturing the nominal unmodified switching instant. In the case of fig. 4, in which the pulse width modulated switching pattern 54 is generated, the carrier sampling instant t is referenced_cTo give these switching instants. At the input of the mode controller 58, the nominal switching instant is redefined asThus, by subtracting the time interval t-t_cIs defined relative to the current time tNominal switching instant. In the case of FIG. 3, when the optimized pulse mode is used, there is no requirement forModification of (2).

Vector U_xSingle phase switch positions containing x-phase. To indicate a change in switch position, for the x-phase, from switch position u_x(i-1)To u_xiIntroducing ith switching transition

Δu_xi＝u_xi-u_x(i-1). In general,. DELTA.u_xiIs limited to-1, 1, but-2, -1, 1, 2, etc. are also possible during large transients and disturbances.

The dead beat control algorithm of the mode controller 58 is summarized below.

Step 1. required stator flux correction is converted from α β 0 to abc according to the following equation

Δψ_s，abc＝K^-1ψ_{s，err，αβ0}， (30)

Wherein the inverse Clark transformation K^-1The transformation matrix of (2) is defined in (1).

Step 2 the flux correction is scaled to the inverse of the instantaneous DC link voltage to make it independent thereof. To this end,. DELTA.. psi'_s，abc[Δψ′_saΔψ′_sbΔψ′_sc]^TIs introduced and defined as

For phase a, for example, this implies by basing Δ t_aiModifying n in a phase_aSwitching to achieve the desired volt-second modification in phase a, i.e.

Similar statements hold for b and c.

Step 3. consider x phase and i is set to 1. For a nominal switching instantAnd switching transition Deltau_xiThe ith switching transition in this phase, the following operation is performed (see fig. 10):

1. calculating an expected modification at_xi＝-Δψ_sx/Δu_xi。

2. The switching instant is modified to

3. Constraining switching transients t by applying timing constraints_xi. For i ═ 1, applyAnd for i > 1, apply

4. By usingSubstituted delta psi'_sxTo update the expected volt-second correction in the x-phase.

Although the expected volt-second correction in this phase, Δ ψ_sxIs non-zero and has a stopping criterion for i (e.g. i ═ n)_x) Not yet reached, but i +1 is set and this process is repeated for the next switching transition. Step 3 is performed for each of the three phases.

Since the deadbeat controller is directed to removing stator flux errors as quickly as possible, and since the correction in the switching instant is not penalized, the deadbeat controller tends to be aggressive, and it achieves a fast response during transients and disturbances. The predicted time domain is a time interval that starts at the current time instant, such that a certain number of switching transitions per phase are covered. In the simplest version, the prediction horizon is the shortest time interval until the switching transitions in all three phases are included. In both cases, the length of the prediction time domain is time-varying.

Alternatively, the optimal control problem can be formulated with a quadratic cost function and linear constraints, which leads to a Quadratic Program (QP). The numerical result of QP is the optimal modification at the switching instant Δ t_xi。

FIG. 11 illustrates how the time domain T may be predicted_pInherently at each sampling instant kT_sThe switching pattern 54 is determined periodically. The upper part of the diagram shows the sampling instant kT_sLower prediction time domain T_pAnd the lower part shows the sampling time (k +1) T_sLower prediction time domain T_p. The time domain T may be predicted only for motion_pThe time intervals within to determine the modified pulse pattern 54. Thereafter, an unmodified pulse pattern may exist.

Even at time kT_sIn the prediction time domain T_pInternally planned switch position sequence, also only during the sampling interval T_sThe switching sequence in (c) is applied to the converter 12. Only the portion of the modified switching pattern 54 having a time length equal to the difference between successive sampling instants is applicable to the electrical converter 12.

Using the new measurement at the next sampling instant (k +1) T_sRecalculating the prediction; a shift and/or revised sequence of switch positions may be derived. This is called a rolling time domain strategy. This strategy provides feedback and makes the controller robust to flux observer noise and modeling errors.

Simulation results

Fig. 12a to 12d show the quantities of the converter system 10 during normal speed operation and under the control of the controller 24 as described above. The carrier frequency is selected as f_cThis results in a device switching frequency of approximately 200Hz at 400 Hz. FIG. 12 shows the torque at rated torque and 20% speed (with fundamental frequency f)₁10Hz) of the system 10 operating. The corresponding pulse number d is 20. The modulated signal is shown in fig. 12 a. The common mode component (23) is added to the toneThe signals are modulated to produce a switching pattern 54 corresponding to space vector modulation, the resulting three-phase switching positions are shown in fig. 12b, fig. 12c shows the (piecewise affine) trajectory of the stator flux vector in the fixed orthogonal αβ coordinate system, the stator flux trajectory is almost circular at this high number of pulses, the rotor flux trajectory is the inner circular trajectory, the three-phase stator currents of the machine are shown in fig. 12d, the total demand distortion for current is 7.5%.

Fig. 13a to 13d show the quantities of the converter system 10 during low speed operation and under the control of the controller 24 as described above. At 2% speed (i.e. at f)₁1Hz) and the rated torque to operate the system 10. One quarter of the fundamental period is shown. The carrier frequency is kept at f_c400Hz, resulting in a high pulse count d of 200.Is added to the modulated signal. In particular, selectionThis allows the use of a hysteresis controller (18) to control the neutral point potential upsilon_n. Large common mode offsetThe three-phase switching pattern is shifted completely into the upper or lower half, see fig. 13 b. Whenever the neutral point potential v_nIn upsilon_n，min(. about.0.025) and upsilon_n，maxThe limit is reached at 0.025, the hysteretic controller (18) inverts the sign of the common mode component. This occurs at time t ═ 37.5ms, 113.75ms, and 190 ms. Regardless of the effective common mode component, the stator current is almost sinusoidal, as can be seen in fig. 13 d.

Fig. 14a and 14b show the switching from the optimized pulse mode to the carrier-based pulse width modulated pulse mode at time t-0. Before time t is 0, an optimized pulse pattern with a number d of pulses 11 is used, and after time t is 0, a carrier-to-fundamental frequency ratio f is used_c/f₁The switching pattern is generated online 22.

Fig. 14a shows that the change in the generation of the switching pattern does not cause any transients or disturbances. At time t-0, the shape of the flux reference changes from piecewise affine (for an optimized pulse pattern) to sinusoidal. When using on-line generated switching patterns, the stator flux ripple increases because these switching patterns and their flux trajectories are sub-optimal. The corresponding three-phase switch positions are depicted in fig. 14 b. The shift of the fixed modulation cycle from the optimized pulse mode to the pulse width modulated switching mode is clearly visible at time t-0.

While the invention has been illustrated and described in detail in the drawings and foregoing description, such illustration and description are to be considered illustrative or exemplary and not restrictive; the invention is not limited to the disclosed embodiments. Other variations to the disclosed embodiments can be understood and effected by those skilled in the art and practicing the claimed invention, from a study of the drawings, the disclosure, and the appended claims. In the claims, the word "comprising" does not exclude other elements or steps, and the indefinite article "a" or "an" does not exclude a plurality. A single processor or controller or other unit may fulfill the functions of several items recited in the claims. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage. Any reference signs in the claims shall not be construed as limiting the scope.