EP3491731A1

EP3491731A1 - Method for controlling a multi-level modular converter

Info

Publication number: EP3491731A1
Application number: EP17758233.5A
Authority: EP
Inventors: Ahmed ZAMA; Abdelkrim Benchaib; Seddik Bacha; Sébastien Silvant; David Frey
Original assignee: Universite Grenoble Alpes; SuperGrid Institute SAS
Current assignee: Universite Grenoble Alpes; SuperGrid Institute SAS
Priority date: 2016-08-01
Filing date: 2017-07-31
Publication date: 2019-06-05
Also published as: FR3054754A1; CN109565247A; FR3054754B1; JP2019523627A; WO2018024977A1

Abstract

The invention relates to a method for controlling a multi-level modular converter (10), the method comprising an internal adjustment that can be modelled by a continuous time model which can be represented in the form of an equation system, the internal adjustment being implemented based on a discrete time model, and the discrete time model being obtained via a step of transforming the equation system to represent it in matrix form, and a step of discretizing the equation system represented in said matrix form.

Description

METHOD FOR CONTROLLING A MULTI-MODULAR CONVERTER

LEVELS

Background of the invention

The present invention relates to the technical field of modular multi-level converters (MMC) ensuring the conversion of an alternating current into a direct current and vice versa.

MMC converters are traditionally used in high voltage direct current (HVDC) transmission networks using DC power for the transmission of electrical energy. They comprise in known manner a so-called continuous portion intended to be connected to a continuous power supply network and an so-called alternative portion intended to be connected to an AC power supply network. These converters comprise, in the traditional way, a plurality of controllable sub-modules, in particular so as to adapt the power exchanges between the DC and AC power supply networks and the converter. Control of the MMC and its submodules is an important aspect of HVDC network management.

The invention relates more precisely to a method of controlling such a multi-level modular converter (MMC), the method comprising an internal regulation step, described as fast regulation.

In industry, it is known to model the behavior of systems using models, in order to predict and analyze the behavior of these systems so as to deduce control laws for controlling said systems.

In particular, it is known to model the internal regulation of the MMC converters by means of so-called continuous time models, the internal regulation being able to be implemented by means of an internal regulation stage or module. By continuous time model, one understands a modelization in which the time can take an infinity of real values, as opposed to a model with discrete time, for which the time is represented by a discrete variable, that is to say sampled . These continuous time models implement, for example, correctors of the integral proportional type.

The control laws enabling the internal regulation of said MMC converters, synthesized from said continuous time models, to be carried out continuous time control laws that it is necessary to discretize, especially for the need of the various digital computers. However, it is known that the discretization of a control law in continuous time causes a loss of information that threatens the fidelity of the control law with respect to the real system. This compromises the accuracy of the results when applying said control law, for example to control an internal control stage.

Also known are discrete time models of the Euler model type, obtained from continuous time models and which make it possible to directly synthesize discrete time control laws. However, the control laws synthesized from these Euler-type models do not offer internal regulation and more specifically control of the sufficiently precise internal regulation stage, which reflects an under-utilization of the potential of the converter. These models are also imprecise and do not offer satisfactory simulation results and control performance, sufficiently close to the actual behavior of the converter, especially with large sampling steps.

Object and summary of the invention

An object of the present invention is to provide a method of controlling a multi-level modular converter remedying the aforementioned problems.

To do this, the invention relates to a method for controlling a multi-level modular voltage converter for converting an alternating voltage into a DC voltage and vice versa, the converter comprising a so-called continuous portion intended to be connected to a network. DC power supply and an so-called alternative portion intended to be connected to an AC power supply network, the method comprising an internal regulation that can be modeled by a continuous time model that can be represented in the form of a system of equations linking variables and parameters associated with the operation of the converter.

According to a general characteristic of the control method, the internal regulation is implemented from a discrete time model, and obtaining the discrete time model comprises:

A step of transforming the system of equations to place said system of equations in a matrix representation in which the variables of the system of equations are represented in the form of vectors and the parameters of said system of equations are represented in the form of matrices; and

A step of discretizing the system of equations placed in said matrix representation.

Modular converter means a converter comprising a plurality of controllable submodules.

Preferably, but not limited to, the multi-level modular converter (MMC) comprises a plurality of arms, each arm having an upper half-arm and a lower half-arm. Each half-arm connects a positive or negative terminal of the DC power supply network to a terminal of the AC power supply. Each half-arm further comprises a plurality of submodules individually controllable by a control member specific to each submodule. Each submodule comprises a capacitor connectable in series in the half-arm when the submodule control member is activated.

Without departing from the scope of the invention, the control method according to the invention can be applied indifferently to modular multi-level converters of different types, and in particular to a half-bridge MMC converter, called Half-Bridge (HB) , a full-bridge converter (FB) or a converter with a structure in Alternate Arm Converter (AAC). These structures are well known to those skilled in the art.

The internal regulation makes it possible for example to control the current of the AC power supply network as well as the differential current generated by the converter.

Preferably, the converter may comprise a control module of said converter and said control module may comprise an internal regulation stage implementing said internal regulation. It is understood that said models with discrete time and continuous time make it possible to model the behavior of said internal regulation stage.

In a nonlimiting manner, the control module may furthermore comprise an external regulation stage, also called a slow regulation stage. This external regulation stage makes it possible in particular to control quantities of alternating powers and of DC voltages of the converter. The floor of External regulation and the internal regulation stage form a so-called "high level" control system. The control module may also include a voltage balancing stage of the submodules of the converter. This balancing stage forms a so-called "low level" control assembly.

The continuous time model illustrates the operation of internal regulation using the system of equations. Without departing from the scope of the invention, this model can be applied in the context of internal control simulations applied to the converter. It can in particular be used to model the behavior of an internal control stage of the converter.

The various equations included in said system of equations are state equations reflecting the internal regulation process. In a nonlimiting manner, these equations may be linear equations, for example associated with each of the three phases to which the converter is connected.

Without departing from the scope of the invention, said variables and said parameters may be variables and parameters associated with the converter, the DC power supply network or the AC power supply network. Preferably, but in a nonlimiting manner, these variables are alternating current and voltage variables, such as the current and the voltage of the AC power supply network and the AC voltage generated by the converter. These variables can also be continuous current and voltage variables, such as the current and the voltage of the DC power supply network and the DC voltage generated by the converter.

The discrete time model used in the context of the control method according to the invention can also be used in the context of simulations in which it makes it possible to reproduce and analyze the behavior of said MMC converter, in order to achieve internal regulation. of the MMC converter. In a nonlimiting manner, this discrete time model can notably make it possible to model the behavior of an internal regulation stage of the converter. The simulation can be implemented by means of a computer tool or on PLCs intended for simulation. Thanks to the invention, during the intermediate transformation step, the system of equations modeling the internal regulation is placed in a matrix representation facilitating its discretization. In this representation, the number of calculations necessary for the determination of the discrete time model is reduced, so that the calculation times, for example in the context of simulations, are even lower. In a nonlimiting manner, this matrix representation makes it possible, for example, to reduce the number of equations included in said system of equations.

Preferably, the system of equations representing the continuous time model in said matrix representation is expressed as the following differential equation:

dx (t)

A x (t) + B y (t)

dx

t denotes time, where x (t) and (t) are vectors of time variables x (t) and y (t), where - ^ - is a vector of time derivatives of time variable x (t, and where A and B are parameter matrices An interest is to reduce the system of equations to a single equation, in order to further facilitate the discretization of the model in continuous time.

Advantageously, said step of discretizing the system of equations is performed by means of a calculation using exponentials of matrices. It is understood in particular that the discretization step is performed by applying the exponential function to said parameter matrices, obtained following the transformation step of said system of equations.

An interest is that, unlike Euler discrete time models for example, no approximation or simplification is performed during the discretization of the continuous time model allowing to reach the discrete time model used by the method according to the invention. invention. Indeed, the traditional method of discretization to determine the model of Euler requires to make approximations, especially with significant sampling steps. Calculating the discrete time model using matrix exponentials makes it possible to avoid simplifications and approximations.

The discrete time model used by the method according to the invention is therefore closer to the real system and models more accurately the internal regulation. The discrete time model, determined by means of a calculation using exponentials of matrices, is therefore a substantially exact model. The internal modeling implemented by this substantially exact model is therefore all the more precise.

In one implementation mode, the discrete time model is an exact model, for example obtained without approximation or simplification (in particular without approximation of Euler).

In one embodiment, for example if the discrete time model is an exact model (obtained without approximation or simplification), the calculation of an exponential of a matrix is implemented by determining a passing matrix. and a diagonalized matrix of said matrix.

It has been determined by the inventors that it is a calculation of this type which makes it possible to obtain an exact discrete time model. In fact, since the matrix is diagonalized, we obtain its exponential by calculating the exponential of each term on the diagonal. The calculation of a matrix exponential then returns to a plurality of scalar exponential computations.

Advantageously, the internal regulation is modeled as a three-phase system and it implements a Park or Alpha-Beta transformation. These transformations are well known to those skilled in the art who will know how to choose the appropriate transformation according to the application. It is understood that modeling as a three-phase system is particularly suitable for modular multi-level converter which is intended to be connected to the AC power supply network. Indeed, the half arms of the converter connect the terminals of the DC power supply network to the three phases of the AC power supply network. In this three-phase modeling, the system of equations can be expressed to include a phase equation.

However, to facilitate the modeling of the internal regulation and the determination of said discrete time model, a reference change is made by means of a Park transformation or an Alpha-Beta transformation. This Alpha-Beta transformation is also called Clarke transformation when it preserves the Concordia modules or transformation when it allows to conserve power. These transformations make it possible to obtain a two-phase modeling of the internal regulation. In a non In a preliminary stage, these transformations can be applied to the system of equations representing the continuous time model modeling the internal regulation. This facilitates the determination of the discrete time model and therefore its implementation for the internal regulation. Park's transformation places the system of equations in a coordinate system whose axes are named d and q. The transformation of Alpha-Beta, whether it is a transformation of Clarke or Concordia, places the system of equations in a coordinate system whose axes are named a and / ?.

Preferably, said discrete time model has a variable T sampling period. An advantage is to have an additional degree of freedom to adapt the model and its response, for example according to the needs of the simulation.

Preferably, the discrete time model is expressed in the form:

x (k + 1) = F (T) x Î i + G (T) y (fc)

where k denotes the sampling instant, where x {k and y (fc) are vectors of variables x {k) and y (fc), and where F (T) and G (T) are function matrices of the sampling period. This discrete time model makes it possible to model the internal regulation in a precise way. This model can be implemented using a computer tool to perform simulations to predict the behavior of the internal regulation stage.

According to a particularly advantageous aspect of the invention, the control method comprises a step of synthesizing a discrete control law, from said discrete time model, to carry out said internal regulation. An interest is that the synthesized control law is directly sampled and that it is not necessary to proceed to a discretization step of said control law. Indeed, it is known that the discretization of a continuous-time control law implies a loss of detrimental information, inducing the need to use correctors to compensate for this loss of information, during the implementation of said discrete time control law.

In a nonlimiting manner, the synthesized discrete control law can be applied in a real system to control, for example, an internal control stage of a control module of an MMC converter. This control law can also be used in the context of simulations, for example to validate the performance of a given model of behavior of an internal regulation stage or to validate the performance of the control law itself.

It has been stated previously that, in the nonlimiting embodiment for which the step of discretizing the system of equations of the continuous time model is carried out by means of a calculation implementing exponentials of matrices, said calculation is an exact calculation that does not involve approximation or simplification. The discrete time model obtained is therefore a substantially exact model. In this embodiment, the discrete control law synthesized from the substantially accurate discrete time model is therefore also more precise and makes it possible to perform a more efficient internal regulation than a control law synthesized from a model of Euler for example.

Preferably, said discrete control law is a function of said sampling period. An interest is to have an additional input and therefore an additional degree of freedom when applying the control law. Also, without limitation, when the control law is used to control an internal control stage, for example a real converter system, control of the sampling period provides better control of said internal control stage. It is possible to adapt the sampling period to respect the operating limits of said internal control stage or to reduce the response times of said controlled internal control stage. By controlling said sampling period T, it is possible to adjust the performance of the control law. For example, the response of the internal regulation stage controlled by this control law can be converged more or less rapidly.

Still preferably, said discrete control law is expressed in the form:

k) = G -F JWk) + K _gain (x (k + lj - ¾)) + x (k + lj) where G (r) ^_1 is the inverse matrix of the matrix G (T) and K _gain is the vector of gains . Adjusting K _gain adjusts the speed of the command. Advantageously, said internal regulation stage comprises a regulator of a continuous differential current generated by the converter whose behavior is modeled by a first continuous time sub-model, represented in the form of a first subsystem of equations connecting variables and parameters used by said differential current regulator. It is understood that said first continuous time submodel inherits the general characteristics of said continuous time model, so that said first continuous time submodel behaves similarly to said continuous time model. Likewise, said first subsystem of equations has a shape similar to said system of equations. In this way, the method according to the invention, applied to said controller of a continuous differential current, comprises the regulation of the continuous differential current, implemented from the first sub-model with discrete time, and the obtaining of the first sub-model. -detective time model includes a step of transforming the first subsystem of equations to place said first subsystem of equations in a matrix representation in which the variables of the first subsystem of equations are represented in the form of vectors and the parameters of said first subsystem of equations are represented as matrices. Obtaining said first discrete-time sub-model also comprises a step of discretizing the first subsystem of equations placed in said matrix representation.

Advantageously, said regulation stage comprises an AC current regulator of the AC power supply network, the behavior of which is modeled by a second continuous time sub-model, represented in the form of a second subsystem of equations. connecting variables and parameters used by said AC regulator. It is understood that said second continuous time submodel inherits the general characteristics of said continuous time model, so that said second continuous time submodel behaves similarly to said continuous time model. Likewise, said second subsystem of equations has a shape similar to said system of equations.

In this way, the method according to the invention, applied to said alternating current regulator of the AC power supply network, comprises regulating the alternating current of the AC power supply network, implemented from the second sub-model to discrete time, and obtaining the second discrete-time sub-model comprises a step of transforming the second subsystem of equations for placing said second subsystem of equations in a matrix representation in which the variables of the second subsystem of equations are represented as vectors and the parameters of said second subsystem of equations are represented in the form of matrices. Obtaining said second discrete-time sub-model also comprises a step of discretizing the second subsystem of equations placed in said matrix representation.

The method as defined above can be implemented by a computer system.

The invention also relates to a multi-level modular converter for converting an alternating voltage to a DC voltage and vice versa, the converter comprising a so-called continuous portion intended to be connected to a DC power supply network and a so-called alternative portion intended to be connected to an AC power supply network, the converter further comprising a converter control module, the control module comprising an internal regulation stage implementing said internal regulation, said converter implementing a modelizable internal regulation by a continuous time model which can be represented as a system of equations connecting variables and parameters associated with the operation of the converter, characterized in that the internal regulation stage is configured for the implementation of a discrete time model, and obtaining the Delays in discrete time includes:

A step of transforming the system of equations to place said system of equations in a matrix representation in which the variables of the system of equations are represented in the form of vectors and the parameters of said system of equations are represented in the form of dies; and

Without limitation, this converter can implement all modes of implementation of the control method described above.

Moreover, it can be noted that the converter obtained implements a discrete time model which makes it possible to obtain a more precise internal regulation than the models conventionally used in the industry, for example the Euler model. Indeed, the discrete time model implemented by the converter is obtained without approximation and more accurately reflects the behavior of the control stage.

The invention also proposes a computer program comprising instructions for performing the steps of a method as defined above when said program is executed by a processor.

The invention also proposes a recording medium readable by a processor on which is recorded a computer program comprising instructions for performing the steps of a method as defined above.

It may be noted that the computer programs mentioned in this presentation can use any programming language, and be in the form of source code, object code, or intermediate code between source code and object code, such as in a partially compiled form, or in any other desirable form.

In addition, the recording (or information) media mentioned in this disclosure may be any entity or device capable of storing the program. For example, the medium may comprise storage means, such as a ROM, for example a CD ROM or a microelectronic circuit ROM, or a magnetic recording medium, for example a floppy disk or a disk. hard.

On the other hand, the recording media may correspond to a transmissible medium such as an electrical or optical signal, which may be conveyed via an electrical or optical cable, by radio or by other means. The program according to the invention can be downloaded in particular on an Internet type network.

Alternatively, the recording media may correspond to an integrated circuit in which the program is incorporated, the circuit being adapted to execute or to be used in the execution of the method in question.

Finally, there is provided a computer system comprising a processor and a memory comprising the computer program as defined above for executing the steps of said method on the processor of the computer system.

Brief description of the drawings

The invention will be better understood on reading the following description of an embodiment of the invention given by way of non-limiting example, with reference to the appended drawings, in which: FIG. 1 illustrates a multi-level three-phase modular converter implemented by the control method according to the invention;

FIG. 2 illustrates a submodule of the multilevel modular converter of FIG. 1;

FIG. 3 illustrates a control module of the MMC converter of FIG. 1;

FIG. 4 illustrates a first simulation assembly aimed at comparing three models of behavior of the AC regulator of the control module of FIG. 3;

FIG. 5 shows the response of the alternating current of the AC power supply network to an input voltage setpoint change of the three models of FIG. 4;

FIG. 6 illustrates a second simulation circuit designed to compare three models of behavior of the DC differential current regulator generated by the converter of FIG. 3;

FIG. 7 shows the response of the DC differential current generated by the converter to an input voltage step of the three models of FIG. 6;

FIG. 8 illustrates a first validation assembly of a control law of the AC current regulator determined by the method according to the invention;

FIG. 9 shows the response of the alternating current in response to a step of the AC current setpoint at the input of the circuit of FIG. 8;

FIG. 10 illustrates a second circuit enabling validation of a control law of the DC differential current regulator determined by the method according to the invention; and

FIG. 11 shows the response of the continuous differential current in response to a step of the continuous differential current reference at the input of the circuit of FIG. 10.

Detailed description of the invention

The invention relates to a method for controlling the behavior of a multi-level modular voltage converter, for converting an alternating voltage into a DC voltage and vice versa. One embodiment of such a converter, used by the control method according to the invention, is represented in FIG. 1. In this example, the multi-level modular converter 10 comprises, for a three-phase input / output current ( comprising three phases φ _αι <p _b and <p _c ), three conversion arms which are referenced by the indices a, b and c on the different components of FIG. 1. Each conversion arm comprises an upper half-arm and a lower half-arm (indicated by the indices "u" for upper and "I" for lower), each of which connects a DC + or DC- terminal of the DC power supply (DC) to a terminal of the power supply network alternative (AC). In particular, each of the arms is connected to one of the three phase lines ψ _αι <p _b and <p _c of the AC power supply network. It should be noted that the terms "arms" and "half-arms" are translated into English respectively by "leg" and "arm". FIG. 1 shows a sub-module assembly 6, in which each half-arm is traversed by a current i _xi with (x indicating whether the half-arm is greater or less and the index i indicating the arm). Further, each half-arm comprises a plurality of sub-modules SM _xij which can be controlled in a desired sequence (with x indicating whether the half-arm is upper or lower, i indicating the phase line to which the half-arm is associated, and; being the sub-module number among the submodules in series in the half-arm). Here, only three sub-modules have been represented by half-arms. In practice, each lower or upper half-arm may comprise a number N of submodules, ranging from a few tens to a few hundred. Each submodule SM _xij comprises a system for storing energy such as at least one capacitor and a controller for selectively connecting this capacitor in series between the terminals of the submodule or to bypass it. The submodules are controlled in a sequence chosen to gradually vary the number of energy storage elements that are connected in series in a half arm of the converter 10 so as to provide several voltage levels. In addition, in FIG. 1, V _dc denotes the voltage at the connection points of the converter to the continuous power supply network, these points being covered by the English expression "PCC: Point of Common Coupling", which is well known in the art. the skilled person. i _dc denotes the current of the continuous power supply network, while currents i _gar i _gb and i _gc pass through the three phase lines φ _αι <p _b and <p _c . In addition, each half-arm has a inductance L _arm and each phase line comprises an inductance L _f and a resistor R _f .

FIG. 2 illustrates a submodule SM _xij belonging to the converter 10 of FIG. 1. This submodule SM _{xij has} a voltage v _{SM at} its terminals. In this submodule, each control member comprises a first electronic switching element T1 such as an insulated gate bipolar transistor ("IGBT: Insulated Gate Bipolar Transistor") connected in series with a storage element of an electrical energy, here a capacitor C _SM . This first switching element T1 and this capacitor C _5M are connected in parallel with a second electronic switching element T2, also a bipolar insulated gate transistor (IGBT). This second electronic switching element T2 is coupled between the input and output terminals of the submodule SM _xij . The first and second switching elements T1 and T2 are both associated with an antiparallel diode shown in FIG.

In operation, the submodule can be controlled in two control states.

In a first state called "on" or controlled state, the first switching element T1 and the second switching element T2 are configured to connect the energy storage element C _SM in series with the other submodules. In a second state called "off" or non-controlled state, the first switching element T1 and the second switching element T2 are configured so as to bypass the energy storage element C _SM .

The converter used in this example is a half-bridge converter. Without departing from the scope of the invention, the control method according to the invention can also be applied to multi-level modular converters of different types, and in particular to a full-bridge MMC converter (FB) or yet to a converter with a structure in Alternate Arm Converter (AAC).

FIG. 3 illustrates a multi-level modular converter 10 according to the invention, comprising a conversion unit 12 and a control module 14 of the converter 10. It can be seen that the control module 14 has a cascade structure. In this example, the control module 14 comprises an external regulation stage 16, an internal regulation stage 18 and a voltage balancing stage 20. The external regulation stage 16 comprises a first set of regulators 22 configured to regulate quantities such as the voltage of the DC and AC power supply networks and the active and reactive AC power of the converter. The external regulation stage 16 further comprises a second set of regulators 24, configured to regulate the different energies of the converter, and in particular the internal energy of the converter, stored in the capacitors of the submodules. The external regulation stage 16 is also called a slow regulation stage.

In the example of FIG. 3, the internal regulation stage 18 comprises a regulator 26 of the alternating current i _g of the alternating electric supply network and a regulator 28 of a continuous differential current i _diff generated by the converter. The internal regulation stage 18 is also called a fast regulation stage.

The external and internal regulation stages 18 provide a high level control of the MMC converter.

The voltage balancing stage 20 ensures a low level control of the converter. It comprises a balancing module 30 for balancing the distribution of voltages between the sub-modules of the half-arms of the converter.

In the prior art, it is known to control the external and internal control stages 16 by means of discrete time control laws synthesized from discrete time Euler models. The results obtained by the application of such control laws, for example in the context of simulations, are however not satisfactory. Indeed, the determination of an Euler model with relatively large sampling steps implies approximations and simplifications which have repercussions on the performance of the resulting control law. Consequently, the results of the simulations, implementing a discrete time control law synthesized from a discrete time Euler model, have a significant error rate compared to real systems, notably due to overtaking. In addition, the control laws synthesized from these Euler-type models do not provide a sufficiently fast control of the internal regulation stage 18, and therefore of the external regulation stage 16. The control of the converter 10 so is too slow. An example of a method of controlling a multilevel modular converter 10 according to the invention, and more specifically the behavior of the internal regulation stage 18 of the control module 14 of the converter 10 is given below, as a non-limiting example.

We will first describe obtaining a discrete time model of the behavior of the regulator 26 of the alternating current i _g of the AC power supply network and a regulator 28 of a continuous differential current i _diff generated by the converter. .

The continuous-time analytical model of the behavior of the AC current regulator 26 of the AC power supply of an MMC converter, such as that presented in FIG. 3, is given, for a phase, by the following equation:

where v _v is a variable designating the AC voltage generated by the MMC converter, v _g is a variable designating the voltage of the AC electrical supply network, i _g is a variable designating the alternating current flowing through the AC power supply network, The _arm and R _arm respectively denote the inductance and the resistance in a half-arm, L _f and R _f respectively denote the inductance and the resistance in a phase line. Then we will denote L = L _f + - and R = R _f + ^ ½. L and R are parameters of the system of equations. Subsequently we will note model AC in continuous time this analytical model in continuous time.

It is understood that the expression of this continuous-time AC model for the three phases of the converter gives a system of three equations, each equation corresponding to one phase. This continuous-time AC model must be discretized in order to be exploited.

According to the invention, obtaining said discrete time model then comprises a step of transforming the system of three equations to place said system of three equations in a matrix representation. In this matrix representation, the variables of the system of three equations are represented in the form of vectors and the parameters of the system of equations are represented in the form of matrices. In this non-limiting example, to facilitate calculations, a Park transformation is used to place itself in a dq, so that the system of equations in said matrix representation, in the dq, is the following one.

^L 9d

^0u = denotes the AC current vector of the AC power supply in the dq, _a \ - k -¾J ^{designate the} input ^vector of the continuous-time AC model and the discrete time model in the

9d

reference dq, v ^ T = V, denotes the vector of the ac voltage of the network

9q

Vd

alternating power supply in the dq, v 9 _t dq is the vector of the AC voltage generated by the converter in the dq. In addition, here we have A = °] and B = [| _j °], A and B being two matrices. Moreover, w represents the pulsation.

This matrix representation facilitates the notation and makes it possible to write the system of equations in the form of a single equation. From this matrix representation, it is possible to discretize the continuous-time model AC by means of calculations implementing exponentials of matrices A and B.

So, by posing: F (T)

and: GT) = i4 ^_1 (e ⁱ⁴ * ^r - l) B, where I is the identity matrix, it is possible to proceed to the step of discretizing the AC model with continuous time.

A non-limiting example of a discrete-time model of the behavior of the alternating current regulator of the AC power supply network, determined from the continuous-time AC model previously described, is then expressed:

TR TR TR TR

wL sin (Tw) e L -R cos (Tw) e L + R wL cos (Tw) e L + R sin (Tw) e L -WL

L ² w ² + R ² L ² w ² + R ²

with: G T) TR TR TR TR

wL cos (Tw) e L + R sin (Tw) e L -WL wLsin (Tw) e L -R cos (Tw) e L + R

L ² w ² + R ² L ² w ² + R ²

An interest of this discretization of the continuous-time AC model, by means of computations implementing exponentials of matrices, is that, contrary to the traditional methods of determining discrete time models of Euler, no approximation or simplification is carried out .

Subsequently, we will note model AC time discrete this example of discrete time model of the behavior of the regulator 26 of the alternating current of the AC power supply network.

FIG. 4 illustrates a first simulation assembly implemented to validate the previously determined discrete time AC model. This simulation aims to compare the AC response i _9d and i _{g of} said discrete-time AC model, of the continuous-time AC model from which said discrete-time AC model has been calculated, and of an Euler AC model. in discrete time. In FIG. 4, the continuous-time AC model is implemented by a first modeling means 32, the previously determined discrete-time AC model is implemented by a second modeling means 34 and the AC model from Euler to discrete time is implemented by a third modeling means 36. Each of the three modeling means receives as input voltage instructions v ^* _ld and v _r ^* _l . The continuous time AC model, implemented by the first modeling means 32, is considered as the reference model.

In this example, the discrete time Euler AC model, commonly used in industry, is a discrete time model also determined from the continuous time AC model. This model also reflects the behavior of the regulator 26 of the alternating current of the AC power supply network. The determination of this Euler AC model implements approximations and simplifications in the calculations.

FIG. 5 illustrates the simulation results of the first assembly presented in FIG. 4 and in particular the AC response i _9d of each of the three models of FIG. 4 when a setpoint change is applied. voltage on v ^* _ld at time t ₀ , at the input of the modeling means 32, 34 and 36. The simulation is performed with a large sampling period T of ΙΟΟμε. In this figure, the curve a represents the AC response i _9d for the continuous-time DC model serving as a reference, at the output of the first modeling means 32. The curve b here represents the AC response i _9d for the a discrete time AC model previously determined and used by the method according to the invention, at the output of the second modeling means 34, and the curve c illustrates the alternating current response i _9d for the Euler AC model, at the output of the third modeling medium 36.

It can be seen that the curves a and b coincide so that the response of the discrete-time AC model is substantially identical to that of the reference model. This reflects a significant degree of accuracy of said discrete-time AC model, which faithfully models the behavior of the AC current regulator 26, even for a large sampling period T. On the other hand, it is found that the Euler's AC model response is far from that of the reference model. The answer of this model is not sufficiently precise.

This simulation makes it possible to validate the discrete-time AC model previously determined. This discrete time AC model is considered to be substantially accurate. Although not shown here, substantially identical results are observed for the AC current response i _g .

A similar path can be applied to obtain a discrete time model of the behavior of the regulator 28 of a continuous differential current i _d iff generated by the converter, such as that presented in FIG. 3. Such a model will be noted later by the DC model. in discrete time.

The continuous time analytical model, hereinafter denoted as DC model with continuous time, of the behavior of the regulator 28 is given, for a phase, by the following equation:

2 _ ^«u diff - / arm ^di ^ ^ ^I ^diff + FS i ^L diff where v _diff is a variable designating the DC differential voltage generated by the MMC converter, v _dc is a variable designating the voltage of the DC power supply network, i _diff is a variable designating the DC differential current generated by the converter.

Here again, the expression of this DC model with continuous time for the three phases of the converter gives a system of three equations, each equation corresponding to one of the three phases. This DC model with continuous time must be discretized in order to be exploited. In this non-limiting example, it is placed in an ABC frame, so as to maintain a three-phase modeling.

According to the invention, said system of three equations is then placed in a written matrix representation:

Or i _d if f continuous integer ABC generated by

\ dif

the converter,

vdiff ₁

Vdiff ₂ denotes the input vector of the DC model with continuous time ^v dif

and the DC model with discrete time, v _dc denotes the voltage of the supply network

\ ^v diff A

continuous electric, v _dlff ^v diff ₂ is the differential voltage vector vdiff ₃

continuous generated by the converter. we here C =

and D = me of matrices.

From this matrix representation, one proceeds to the discretization of the model DC in continuous time, by means of computations implementing exponentials of matrices C and D.

So, by posing where:

and KT) = C ^{~ 1} (e ^c l) D =

we can proceed to the discretization step of the DC model in continuous time.

A nonlimiting example of a DC model with discrete time of the behavior of the controller of the continuous differential current generated by the converter, determined from the DC model with continuous time previously described, is then expressed:

i _d if ik + 1) v, arm

i- _d ifh ik + 1) H (T) i-difh ik) + K (T) arm 2 '

i- _d iffs ik + 1) arm ₃ ⁽ .

FIG. 6 illustrates a second simulation assembly implemented to validate the DC model with discrete time determined previously, for the purposes of regulation. This simulation aims to compare the DC differential response _diffl i _diff2 and i _difh of the previously determined discrete-time DC model of the continuous-time DC model from which the discrete-time DC model has been calculated, and a model Euler DC in discrete time. In FIG. 6, the continuous-time DC model is implemented by a fourth modeling means 38, the previously determined discrete-time DC model is implemented by a fifth modeling means 40. The DC model from Euler to discrete time is implemented by a sixth modeling means 42. Each of the three modeling means receives as input voltage instructions v ^* _rmi , v ^* _rni2 and v _a ^* _rm The DC model with continuous time is considered as the model reference. In this example, the discrete time Euler DC model, commonly used in industry, is a discrete time model also determined from the DC model with continuous time. This model also reflects the behavior of the regulator 28 of a DC differential current i _diff generated by the converter. The determination of this DC model of Euler also implements approximations and simplifications in the calculations.

FIG. 7 illustrates the simulation results of the second assembly presented in FIG. 6. In particular, FIG. 7 shows the continuous differential current response for a phase, of each of the three models of FIG. 6, when a step is applied. voltage on v * _rmi at the instant t _lr input of said modeling means 38, 40 and 42. In this figure, the curves d, e and / respectively represent the DC differential response _diffl i for the DC model to continuous time as a reference, for the discrete-time DC model used by the method according to the invention and for the DC model of Euler.

It can be seen that the three curves d, e and / are coincidental so that the response of the DC model with discrete time determined previously, for the implementation of the method according to the invention, is substantially identical to that of the reference model and that of the Euler DC model. This reflects a significant degree of accuracy of said discrete-time DC model, which faithfully models the behavior of the regulator 28 of the DC differential current. This simulation makes it possible to validate the DC model with discrete time determined previously. The discrete-time DC model is considered to be substantially accurate. Although not shown here, substantially identical results are observed for the responses of the continuous differential currents i _dif and i _difh corresponding to the other two phases.

In the following of this example of a control method, according to the invention, of a multi-level modular converter, it is proposed to synthesize control laws of the regulators 26 and 28, from the discrete time AC and DC models. , previously determined. These control laws ensure the internal regulation of the converter.

In order to ensure the convergence of the state variable towards its reference, the following equation must be respected by the regulator 26 of the alternating current:

where Kgaim is the vector of gains taking values ranging from -1 to 1.

With the aid of a pole placement method, an example of a control law of the regulator 26 of the alternating current is obtained. This control law will be noted later by AC order law and expresses:

vrl _d W = G (ry -F (T)

The control law AC has therefore been synthesized from the discrete time model AC, itself determined from a continuous time model of the behavior of the regulator 26 of the alternating current of the AC power supply network. It can be seen that this control law AC is a discrete control law and that it depends on the sampling period T. The sampling period T represents an additional input variable and therefore constitutes an additional degree of freedom. By controlling said sampling period T it is possible to adjust the performance of the control law. For example, the response of the regulator controlled by this control law may be converged more or less rapidly.

A validation step of this AC control law is then carried out by simulation by means of a first validation circuit shown in FIG. 8. It can be seen in this FIG. 8 that the performance of the AC control law on a continuous-time AC model representing the behavior of the AC current regulator 26 of the AC power supply network, implemented by the first modeling means 32. In this nonlimiting example, the continuous-time AC model is used as a reference for the purpose of validation. The continuous-time AC model is therefore not the subject of this simulation. In particular, the discrete time AC model previously determined could have been used as a reference model.

The control law AC is implemented by a first control means 44. This first control means 44 provides voltage setpoints v ^* _ld and v _r ^* ₁ at the input of the first modeling means 32. The control law enables to determine these voltage setpoints from ac instructions i _g ^* _d and i _g ^* and from the ac values i _9d and i _g, which are determined by the AC model continuous time and delivered by the first modeling means 32.

The results of this simulation are presented in FIG. 9. In particular, FIG. 9 shows the evolution of the alternating current i _Qd determined by the reference model with continuous time, controlled by the control law AC, in response to a step of the setpoint of alternating current i ₃ ^* _d at time t ₃ . In other words, FIG. 9 shows the evolution of the alternating current i _Qd coming out of the first modeling means 32 in response to a current step i ₃ ^* _d at the input of the first control means 44. In this figure, the curves g, h, i and; illustrate the evolution of the alternating current i _9d for a sampling period T respectively equal to ΙΟΟμε, 200με, 500με and 1ms. Curve k represents the reference alternating current corresponding to the set current step i _g ^* _d .

It can be seen in FIG. 9 that the alternating current i _9d at the output of the reference model, driven by the control law AC determined previously, follows the dynamics of the reference alternating current. In particular, even for a large sampling period, corresponding to the curve the overshoot and the tracking error are substantially zero. The control law AC determined previously thus ensures precise control of the model AC continuous time. This control law thus makes it possible to effectively control the regulator 26 of the alternating current of the AC power supply network.

In addition, for sampling periods T of the order of ΙΟΟμε, the response times of the reference model, controlled by the control law AC determined by the method presented above, are of the order of 1ms to 5ms. These response times are shorter than the response times of the AC current regulators used in industrial systems, conventionally controlled by control laws synthesized from Euler AC models. This simulation thus makes it possible to validate the performance of the control law AC determined previously. This AC control law is likely to be applied to a real AC regulator system of the AC supply network of a control module of an MMC converter. A similar method can be implemented to determine and validate a control law of the regulator 28 of the DC differential current.

With the aid of a method of placing poles, a control law of the regulator 28 of the continuous differential current is obtained. This control law will be noted later by DC control law and expresses:

_GAIN2 where K is the vector of gains taking values ranging from -1 to 1. Again, the DC control law was synthesized from the template discrete-time DC, which is determined from an analytical model continuous time of the behavior of the regulator 28 of the continuous differential current generated by the converter 10. It can be seen that this DC control law is a discrete control law and that it depends on the sampling period T.

A validation step of this DC control law is then carried out by simulation by means of a second validation circuit shown in FIG. 10. It can be seen from this FIG. 10 that the performance of the DC control law is tested on a continuous-time DC model, implemented by the fourth modeling means 32. In this non-limiting example, the DC model with continuous time is used as a reference for the purposes of the validation. The DC model with continuous time is therefore not the object of this simulation. In particular, the discrete time DC model previously determined could have been used as a reference model.

The control law DC is implemented by a second control means 46. This second control means 46 provides voltage instructions v ^* _rmi , v ^* _rni2 and v ^* _rni3 input of the fourth modeling means 38. The law The DC control device is used to determine these voltage setpoints from continuous differential current setpoints ¾ _£ / Λ / ¾t ₂ ^and ¾i // ₃ ^and from the values of the continuous differential current tdt ₂ and i _d iff ₃ , these setpoints and DC differential current values being determined by the DC model with continuous time and delivered by the fourth modeling means 38. The results of this simulation are presented in FIG. 11. In particular, FIG. 11 shows the evolution of the differential direct current i _diffl determined by the reference model with continuous time, controlled by the control law DC, in response to a step current i _d ^* _IFFI at time t _4. In other words, Figure 11 shows the evolution of the differential DC current i out _DiffL the fourth modeling means 38 in response to a level of the differential current reference i _d ^* continuous input _IFFI the second control means 46. On this Figure, the curves /, m, n and o illustrate the evolution of the continuous differential current i _d ifh P for ^a sampling period T respectively equal to ΙΟΟμε, 200με, 500με and 1ms. The curve p represents the differential reference DC current corresponding to the current step i _diffl .

It can be seen in FIG. 11 that the continuous differential current i _diffl at the output of the reference model, driven by the control law DC determined previously, follows the dynamic of the reference continuous differential current. In particular, even for a large sampling period, corresponding to the curve o, the overshoot and the tracking error are substantially zero. The control law DC determined previously thus ensures precise control of the DC model with continuous time. This control law thus makes it possible to effectively control the regulator 28 of the continuous differential current generated by the converter.

In addition, for sampling periods T of the order of ΙΟΟμε, the response times of the reference model, controlled by the control law DC determined by the method presented above, are of the order of 1ms to 5ms. These response times are less than the response times of the DC differential current regulators used in industrial systems, conventionally controlled by control laws synthesized from Euler DC models. This simulation thus makes it possible to validate the performances of the control law DC determined previously. This DC control law is likely to be applied to a real system for regulating the DC differential current of an MMC converter.

It may be noted that in the implementation and implementation modes described above, the discrete time model may be an exact model obtained without approximation or simplification (for example without approximation of Euler). The calculating an exponential of a matrix can then be implemented by determining a passage matrix and a diagonalized matrix of said matrix.

For example, using the formula described above:

x (k + 1) = F (T) x (k) + G (T) y {k)

For example, to determine the exponential form of F we have:

FT) = e ^AT

This expression is the exact expression to be determined. In the prior art, the following formulation is used:

AT (AT) ² (AT) ⁿ

1! 2? not\

AT

With 1 + - the term which corresponds to the approximation of Euler (the remaining terms being neglected).

Here, an exact calculation can be obtained by determining a passage matrix P and a diagonalized matrix D for written F as follows:

F (T) = Pe ^DT P ^{~ 1}

This facilitates the determination of the exponential matrix because for a diagonalized matrix, it is the exponential of each term on the diagonal.

This leads to an exact discrete time model.

Claims

A method for controlling a multi-level modular voltage converter (10), said converter for converting an alternating voltage into a DC voltage and vice versa, the converter comprising a so-called DC portion intended to be connected to a power supply network continuous and an so-called alternative part intended to be connected to an alternating electric supply network, the method comprising an internal regulation that can be modeled by a continuous time model that can be represented in the form of a system of equations connecting variables and parameters associated with the operation of the converter,

characterized in that the internal regulation is implemented from a discrete time model, and obtaining the discrete time model comprises:

A step of discretizing the system of equations placed in said matrix representation, performed by means of a calculation implementing exponentials of matrices.

A control method according to claim 1, wherein the converter comprises a converter control module, the control module comprising an internal regulation stage implementing said internal regulation.

A control method according to any one of claims 1 or 2, wherein said system of equations representing the continuous time model in said matrix representation is expressed as the following differential equation:

dx (t)

= A x (t) + B y (t)

dx

where t denotes time, where x (t) and (t) are vectors of temporal variables x (t) and y (t), where is a vector of time derivatives of the time variable x (t), and where A and B are parameter matrices.

A control method according to any one of claims 1 to 3, wherein the internal regulation is modeled as a three-phase system and in which a Park or Alpha-Beta transformation is implemented.

A control method according to any one of claims 1 to 4, wherein said discrete time model has a variable T sample period.

A control method according to claim 5, wherein said discrete time model is expressed as: x {k + 1) = F (T) xQc) + G (T) y {k) where k is the instant sampling, where x {k and y (k are vectors of variables x {k) and y (/ c), and where F (T) and G (T) are function matrices of the sampling period. 7. Control method according to any one of claims 5 or 6, comprising a step of synthesizing, from said discrete time model, a discrete control law to achieve said internal regulation. 8. Control method according to claim 7, wherein said discrete control law is a function of said sampling period.

9. Control method according to claims 6 to 8, wherein said discrete control law is expressed in the form: y ij = G -F (T) x) + K _gain (x (k + lj-xk)) + xfr + lj) where G (r) ^_1 is the inverse matrix of the matrix G (T) and where K _gain is the vector of earnings. The control method as claimed in any one of claims 2 to 9, wherein said internal regulation stage comprises a regulator of a current continuous differential generated by the converter whose behavior is modeled by a first continuous time sub-model, represented in the form of a first subsystem of equations connecting variables and parameters used by said differential current regulator .

11. Control method according to any one of claims 2 to 9, wherein said internal regulation stage comprises an AC current regulator of the AC power supply network whose behavior is modeled by a second continuous-time sub-model. , represented as a second subsystem of equations connecting variables and parameters used by said AC current regulator.

The method of any one of claims 1 to 11, wherein the discrete time model is an exact model.

13. The method as claimed in claim 1, the calculation of an exponential of a matrix is implemented by determining a matrix of passage and a diagonalized matrix of said matrix.

14. Modular multi-level converter for converting an alternating voltage to a DC voltage and vice versa, the converter comprising a so-called continuous portion intended to be connected to a DC power supply network and an so-called alternative portion intended to be connected to a power supply. alternating power supply network, the converter further comprising a converter control module, the control module comprising an internal regulation stage implementing an internal regulation that can be modeled by a continuous time model that can be represented in the form of a system of equations connecting variables and parameters associated with the operation of the converter, characterized in that the internal regulation stage is configured for the implementation of a discrete time model, and obtaining the model in time discreet includes:

A step of transforming the system of equations to place said system of equations in a matrix representation in which the variables of the system of equations are represented in the form of vectors and the parameters of said system of equations are represented in the form of dies; and A step of discretizing the system of equations placed in said matrix representation.

A computer program comprising instructions for executing the steps of a method according to any one of claims 1 to 13 when said program is executed by a processor.

A processor-readable recording medium on which a computer program is recorded including instructions for performing the steps of a method according to any one of claims 1 to 13.

A computer system comprising a processor and a memory comprising the computer program of claim 15 for performing the steps of said method on the processor of the computer system.