WO2015117637A1

WO2015117637A1 - System and method for controlling an ac/dc converter

Info

Publication number: WO2015117637A1
Application number: PCT/EP2014/052092
Authority: WO
Inventors: Luis GALVAN GARCIA-PEREZ; Francisco Javier CODESEDA MUÑOZ; Juan Manuel Carrasco Solis; Eduardo GALVAZ DIEZ
Original assignee: Green Power Technologies, S.L.
Priority date: 2014-02-04
Filing date: 2014-02-04
Publication date: 2015-08-13
Also published as: GB2537301A; CN105960755A; GB201612699D0; GB2537301B; BR112016017946A2

Abstract

The invention relates to a control of a power converter (1) with an MMC topology. The inputs to the converter are the branch voltages U₁...U₆. These voltages are obtained by a linear combination (12) of the four types of main voltages: DC main voltages U_DC1, AC main voltages U_AC1 and U_AC2, internal main voltages U_M/1 and U_M/2 and relative main voltages U_MR1. AC and DC main voltages are respectively used to control the power exchanged with AC and DC circuits or grids connected to the converter and to keep the control the total energy stored in the converter. Relative main voltages are used to control the relative voltage between independent circuits. Internal main voltages are used to control completely the balance of the energy stored in the converter branches. This is accomplished by selecting values for the AC and DC components of each main voltage.

Description

System and method for controlling an AC/DC converter

Field of Invention The present invention belongs to the field of electricity. More specifically, it relates to an MMC (Modular Multilevel Converter) which allows exchanging active and reactive power between AC and DC lines at high voltage. In particular, the invention relates to a method and a system to control such converter.

State of the Art

The topology of the modular multilevel converter as well as the most basic scheme of its control has already been disclosed by Anton Lesnicar and Ranier Marquardt in various articles such as "An Innovative Modular Multilevel Converter Topology Suitable for a Wide Power Range" and "A new modular voltage source inverter topology" (both dating from 2003). These two articles are very similar to each other. They present the MMC topology and show how the converter can be controlled to provide any voltage combination to an AC circuit and a DC circuit. In these articles, the DC circuit is a 2- node DC grid and the AC circuit is a 3-phase AC grid. According to the articles, 4 dimensions of the output voltage State Space are used to control the converter: 1 for the DC voltage, 2 for the AC grid voltages and 1 for the common-mode voltage between the AC and DC circuits. However, since the converter comprises six branches, the total number of dimensions for the State Space Modulation is 6. The unused ones correspond to the internal loops in the converter, which are not considered in the articles.

Although the articles mention the concept of accumulator energy balancing, it only states a way to maintain the balance on the branches separately. The energy in the capacitors of a branch could become too high while the energy in those of other branches becomes too low. A branch balance control becomes necessary. The capacitor balance method described for separated branches can also be enhanced to reduce the amount of times each module commutates.

The patent application WO2008/067784 attempts to solve this problem by using more voltage intermediate values in addition to the DC voltage, the AC grid voltages and the unbalanced voltage (or common-mode voltage). These new intermediate values consist of nm branch voltages, and nm balancing voltages. Each of the 5 types of voltages intermediate values serves a purpose. The AC grid voltages control the current exchanged with the AC grid. The DC voltage controls the total energy in the converter. In theory it would also control the current exchanged with the DC grid, but it is impossible to control at once AC current, DC current and total energy due to the principle of conservation of energy. The branch voltages are used to control the currents that go through the branches. Once again, this may conflict with the AC and DC current. The unbalanced voltage is used to control the relative voltage between the DC and AC circuits, that is, the AC common-mode voltage minus the DC common- mode voltage. Finally, the balancing voltages are used to control the balance of the modules accumulators. According to the patent application, these last voltages can be omitted since the branch voltages can already control the current that balances the accumulators.

It can be noted that there are certain conflicts between these effects. If, for example, the branch voltage values are chosen to control the current through each branch, then the AC and DC currents will also be affected by these branch voltage values. This occurs mainly because the number of intermediate voltages is greater than the total number of freedom degrees. A further issue that arises due to the excess of intermediate values is the effect of interferences between the different regulators. Since the number of regulators independent outputs is greater than the number of freedom degrees, negative effects can be expected such as fast saturations of PI regulators, contradictive regulator output values or unnecessarily high intermediate branch voltages.

Another conflict appears when two converters of this type are used for high voltage direct current transmission (HVDC transmission), since the total energy on each one is regulated by the same voltage that regulates the power they exchange. In this case, it would be desirable to regulate this energy by exchanging power through the AC connection.

Finally, no explanation is given about how the branch energies are balanced with one another. Although there is the option of adding a balance current reference or calculating intermediate balance voltages, there is no information about how to choose these currents or voltages. The typical linear regulators do not guarantee the energy balance would be achieved and using them would produce undesired effects to the AC and DC output currents due to the currents synergy. A general method to balance these branch energies is still needed. Brief description of the invention

It would be desirable to control the power that the converter exchanges with the DC and AC circuits and balance the energy in its branches without the exposed inconveniences. The present invention solves these problems using a better decoupling of the branch voltages and energies.

The proposed method and system is designed to control a modular multilevel converter (MMC). Such apparatus comprises m DC nodes and n AC nodes with m≥2 and n≥2, where a branch is formed between each combination of a DC node and an AC node. Each branch comprises an inductance and two or more modules (also called cells) connected in series. Each module comprises an energy accumulator such as a capacitor or a battery, as well as one or more controllable semiconductors capable of connecting and disconnecting the energy accumulator in series with the branch.

Some or all of these m DC nodes and n AC nodes are connected to external DC and/or AC circuits or grids through terminals. There may be any number of unconnected nodes. In addition, the terminals can be connected to different AC or DC circuits which do not share any node with one another. Although there are MMCs where the external AC and DC circuits share the ground node, the invention is preferably intended to be used on MMCs where the DC circuits do not share any node with the AC circuit outside the converter. This way the converter may work when there is galvanic isolation between the AC circuits and the DC circuits.

As with the previous state of the art, the invention selects a reference voltage for each branch Ui to U_mn and connects the necessary accumulators to the branch so that the total output voltage of each branch modules reaches said branch reference voltage. However, the way it is proposed to select the branch reference voltages is different from the state of the art.

According to the present invention, the branch reference voltages Ui to U_mn are obtained as a linear transformation of their main components U_Mi to U_Mmrv These main components of the branch reference voltages (called main voltages hereinafter) are the representation of these branch reference voltages on a different base. Thus, they encompass the necessary and sufficient information to univocally obtain the branch reference voltages. The base the main voltages are expressed on is defined by the aforesaid linear transformation. In this base each type of main voltage affects either only one type of current or no current at all. Up to four types of main voltages are used: internal main voltages, DC main voltages, AC main voltages and relative main voltages.

The internal main voltages are defined so that they depend on the internal main energy values. These internal main energy values are independent linear combinations of the branch energy values and none of them is proportional to the sum of all the branch energy values. Thus, they describe the differences between the branch energy values (the branches energy unbalance).

The others main voltages to be defined may depend on the sum of energies of branch, but not on their difference.

It is also disclosed an advantageous calculation of the branch reference voltage based on a plurality of internal main active power values transferred between branches.

As a result of this approach, the invention is able to balance the energies of branches without affecting the grid or the circuit to which the converter is connected to.

A centralized control structure is preferably used. All the modules of each branch preferably communicate with a branch control device. The same branch control device may be associated with more than one branch, but it is preferred to communicate with all the modules in the branch it is associated to. All branch control devices communicate with a central control unit. For converters with a number of modules low enough, the branch control devices and the central control unit can be all implemented on the same physical device (such as a DSP or an FPGA). However, this device alone will behave as the combination of the central control unit and the branch control devices, executing independently the duties of each one.

Brief description of the figures

The following is a basic description of the figures. Their complete description is provided in the detailed description of the invention.

Figure 1 shows the classic form of the converter with m=2 and n=3. All the nodes are connected to the external circuits through terminals C1 , C2, A1 , A2 and A3.

Figure 2 shows an already known topology for the modules.

Figure 3 shows a scheme of the modules a branch communicating with a branch control device. Figure 4 shows a scheme of the branch control devices communicating with the modules and with the central control unit. In this case, each branch control device is being used to control two branches instead of just one.

Figure 5 shows a simplified scheme of the main processes occurring in the central control unit. Note that each block represents a process or an operation instead of a device.

Figure 6 shows a more detailed scheme of the processes occurring in the central control unit.

Figures 7 and 8 show two possible control schemes that can be applied when selecting the internal main voltages.

Figures 9 to 1 1 show three different ways to estimate the internal main power values.

Figure 12 shows the proposed control scheme to regulate the DC power using the DC main voltages.

Figure 13 shows the proposed control scheme to regulate the AC power using the AC main voltages.

Figure 14 shows how the references for the power exchanged with the DC and AC circuits are chosen depending on the total stored energy and on the transmitted power reference.

Figure 15 shows a possible closed-loop control structure to regulate the voltage between the AC and DC circuits using the relative main voltages.

Detailed description of the invention

In connection with the figures, several examples of embodiments of the invention are further detailed. The examples are shown simply by a way of illustration and will be regarded not as restrictive of the invention scope.

Firstly, a general picture of how the embodiments work is presented. A branch control device 4 receives, at least, a measure of the corresponding branch modules accumulators 3 voltage. For each module 2 of the corresponding branch, the branch control device 4 may receive or calculate the energy of the accumulator 3. Using this information, for each associated branch the branch control device 4 calculates a branch energy value to E_mn which depends on the energy stored on at least one module of the branch. The branch energy value may depend on the energy stored on more than one module, but it does not necessarily depend on the energy of all modules of the branch. This constitutes an advantage over previous methods which calculate the branch energy value as the sum of all the voltages or energies of the modules since the calculus is faster.

A central control unit 5 receives the branch energy values to E_mn corresponding to all branches and determines a branch reference voltage Ui to U_mn for each branch. Afterwards, the central control unit 5 sends each branch reference voltage to the corresponding branch control unit 4. Finally the branch control units choose for each branch a distribution of voltages for the branch modules 2 to modulate. This distribution (which is later described) can be done in such a way that the modules energy balance and the semiconductors number of commutations are optimized.

According to the embodiments, the central control unit 5 obtains the branch reference voltages Ui to U_mn as a linear transformation of the aforementioned main voltages U_Mi to U_Mmrv Advantageously, the number of main voltages is the same as the number of branches, which ensures that all the freedom degrees can be used. Advantageously, the aforesaid linear transformation may be an orthogonal transformation (i.e. either a proper or an improper rotation), which assures there is no synergy between main voltages.

Four types of main voltages are used, each type producing a different effect on the converter after applying the linear orthogonal transformation. Each type of main voltage is selected according to a different purpose so that there is no conflict between the various control objectives. The four types of main voltages are:

• Internal main voltages: U_Mn , U_Mi2 -■■ These voltages have an effect on the current that circulates through the internal loops of the converter (the internal currents) but they do not influence any current or power exchanged with the external circuits. Their values are selected to control the power that flows between branches so that the branch energy values become balanced.

• DC main voltages: U_MDI , U_MD2- - - These are the only ones which affect the power which the converter exchanges with the external DC circuits. Their values are selected to control such power.

• AC main voltages: U_MAI , U_MA2- - - These are the only ones which affect the power which the converter exchanges with the external AC circuits. Their values are selected to control such power. • Relative main voltages: U_MRI , U_MR2 - - - These voltages do not affect any current. Instead they control the relative voltages between nodes belonging to different isolated circuits. To this respect, any unconnected node is considered to be an external circuit on its own which is isolated from all the other circuits. If a certain common mode voltage is necessary on an external circuit relative to another external circuit, these relative main voltages can be used to provide it.

Not all the main voltages need to be used. Some of them may simply be chosen to be null and omitted. Once a value has been selected for each main voltage, the branch reference voltages Ui to U_mn are obtained with the corresponding linear transformation.

First type: Internal main voltages

This type is key. The internal main voltages are the only ones which are calculated in dependence on the branch energy values unbalance. The internal main voltages U_Mn , U_Mi2 -■■ are used to control the power that flows between branches and, ultimately, to balance the energy of the branches. The proposed steps to select these internal main voltages comprise:

1 . Obtaining mn-1 internal main energy values E_Mn , E i2-■■ as independent lineal combinations of the branch energy values Ei to E_mn not proportional to the sum of all the branch energy values

2. Measuring the mn-1 internal main active power values P_Mn , PMI2 - - - , which are a representation of the net active power that is being transferred between branches

3. Using regulators to choose the references for the derivative values of the internal main active power values P'_Mn _ref, P ret- - - in dependence on the internal main energy values E_MM , E_M,₂...

4. Selecting the main internal voltages U_Mn , U_Mi2 - -■ for the internal main active power values P_Mn , PMI2 - - - to evolve according to the reference for their derivative values P'_Mn , P -

When obtaining the internal main energy values E_MM , E_M,₂... for the first step, either these or the branch energy values to E_mn may be filtered. In particular it is proposed to eliminate, or at least mitigate, any oscillation these values have at the frequency of the external AC circuits. The internal main energy values are a representation of the main energy values unbalance. When measuring the internal main active power values P_Mn , PMI2- - - for the second step, it is also possible to measure any internal main reactive power values Q_Mi , QM2- - - These values represent the amount of energy that periodically circulates through the converter branches but, on average, is not transferred from a branch to another. Three ways are proposed to measure the internal main power values.

The simplest proposed way comprises calculating the internal main active power values as the derivative values of the internal main energy values. A filter should be used in this case to attenuate the components corresponding to the frequency of the AC circuits. This way, by itself, does not obtain the internal main reactive power values since these values do not produce any net flow of energy through the branches.

The second proposed way comprises the following steps:

• Measuring the internal main currents l_Mi , IM2- - -

• Filtering the internal currents to obtain its DC and AC components and

• Applying a linear transformation which relates the internal currents DC and AC components with the internal main power values they produce.

The aforesaid linear transformation can be deducted analytically by obtaining the average power flow each component of the internal currents produce between branches. This can be achieved by integrating the products of the corresponding branch currents and voltages during a period. For this purpose the inductance voltages can be neglected. This way obtains both the internal main active power values P_Mn , P_Mi2-■■ and the internal main reactive power values Q_Mi , QM2- - - However, the use of filters still reduces the speed the controller can react to deviations.

The third proposed way comprises the following steps:

• Estimating the new internal main power values P_Mn , PMI2- - - , QMI , QM2- - - using the last known values of such power values and the last calculated reference for their derivative value P'_{MM REF}, P Q'MI ret, Q ref ■■■

• Measuring the internal main currents l_Mi , IM2- - - and

• Correcting these estimations by adding to each estimated internal main power value a term which depends on the difference between at least one measured internal current and the value that would correspond to the same current according to the estimations.

This way obtains all the internal main power values P_Mn , PMI2- - - , QMI , QM2- - - using information that filters would ignore, thus allowing the regulators to react faster than with the previous one. However, it requires solving a more complex mathematical problem on every control cycle. Consequently, this method is appropriate for fast microprocessors.

Both the second and third proposed ways require measuring the converter internal main currents l_Mi , IM2 - - - These currents can be obtained by measuring the branch currents to l_mn and applying a linear transformation. Such linear transformation is the same one that relates the internal main voltages with the branch voltages.

When choosing the references for main internal active power derivative values P'_Mn , P'MI2 - - - , for the third step of the internal main voltages selection, two possible control structures are proposed. The first one comprises a cascade control scheme. On a first loop, each main internal energy E_MM , E_M2... is provided as input to an independent regulator (such as a P or PI regulator) whose output is used as a reference for the corresponding internal main active power value P_Mi _ref, PM2 ret- - - Then, on a second loop, each of the internal main active power values P_Mi , PM2- - - and its references are provided to an independent regulator (such as another P or PI regulator) whose output is the reference for said internal main active power derivative value P'_Mn ref, P ref- - - Alternatively the control scheme can be direct, with only one control loop per internal main power. In this case, each main internal energy E_Mn , E_M2 - - - is provided as input to an independent regulator (such as a P, PI or P I D regulator) whose output is directly the reference for the internal main (active) power derivative value P'_Mn ref, P ref- - -

Either way, if the internal main reactive power values Q_Mi , QM2- - - are intended to be controlled, each of them is supplied to a regulator along with a reference for it. The regulator output is the reference for the corresponding internal main reactive power derivative value Q'_Mi ref, Q'we ref- - - If these values are not intended to be controlled, they can be omitted and let any parasite resistance of the converter dissipate their effect.

Finally the proposed way of selecting the internal main voltages U_Mn , U i2 - - - to control the internal main power values evolution, the fourth step, comprises forming each the internal main voltages with at least one DC component and two AC components, one of them shifted 90^Q relative to the other. The AC components frequency is the same as the AC external circuits frequency.

UMI i = ^an cos(wt) + b_n sin(wt) + c_n

The DC components c_M , C|₂.. . and the amplitudes of the AC components a_M , b_M , ai₂, bi2- . . are all determined as linear functions of the actual internal main power values PMM , PMI2- - - and of the reference for internal main power derivative values P'_Mn ref, P _ref- - - These functions are such that, when applied, the internal main power values evolve according to the references for their derivative values.

Second type: DC main voltages

The DC main voltages U_MDI , U_MD₂- - - are used to control the power exchanged with the external DC circuits. The proposed way to select the DC main voltages comprises the following steps:

1 . Measuring the power exchanged with each independent DC mesh P_D1 , P_D2- - -

2. Supplying these measures and their references to independent regulators whose outputs are the references for the corresponding DC power derivative val Ue P D_{1 re}f, P D₂ ref-■■

3. Selecting the DC main voltages for the DC power values P_m , P_D2- - - to evolve according to the references for their derivative values.

For the third step, it is proposed that each DC main voltage is formed by at least a DC component c_m , c_D2... which is a linear function of the references for the DC meshes power derivative values. These linear functions may include feed forward values which depend on the DC terminal voltages. The resulting DC main voltages are such that, when applied, the DC meshes power values evolve according to the references for their derivative values.

Third type: AC main voltages

The AC main voltages U_MAI , U_MA₂- - - are used to control the active and reactive power exchanged with the external AC circuits P_A, QA- The proposed way to select the AC main voltages comprises the following steps:

1 . Measuring the active and reactive power exchanged with each independent AC mesh P_A1 , Q_A1 , P_A2, Q_A2...

2. Supplying these measures and their references to independent regulators whose outputs are the references for the corresponding AC active and reactive power derivative value P'_Ai , Q'AI , P'A2, Q'A2- - - 3. Selecting the AC main voltages for the AC active and reactive power values P_Ai , QAI , PA₂, QA₂- - - to evolve according to the references for their derivative values. For the third step, it is proposed that each AC main voltage is formed by at least two AC components; one of them shifted 90^Q relative to the other. Their frequency is the same as the external AC circuit frequency.

UMA i = ^aAi cos(cot) + b_Ai sin(cot)

The amplitude of each component a_Ai , b_Ai , a_A2, b_A2... is a linear function of the actual active and reactive power values and of the reference for their derivative values. These linear functions may include feed forward values which depend on the AC terminal voltages. The resulting AC main voltages are such that, when applied, the AC meshes power evolves according to the references of their derivative values.

According to an advantageous further development, the references for the DC and AC active power P_{D ref}, P_{D2 r}ef - - - PAI ret, PA2 ref - - - are selected so that the total energy in the converter is maintained. The proposal to choose them comprises the following steps:

• Obtaining a total energy value E_TOTAL which is proportional to the sum of all the branch energy values to E_MN

• Providing this total energy value E_TOTAL to a regulator (such as a P or a PI regulator) along with a reference for it

• Obtaining a reference for the converter absorbed power P_abs as the output of the regulator

• Selecting at least one of the references for the DC or AC active power P_{D1 ref}, D2 ref - - - AI ref, ΡΑ2 _ΓΘΤ- - - in dependence on the absorbed power reference

In particular, if the converter is connected to two or more external circuits, it is proposed that the DC and AC active power references are obtained as linear combinations of the absorbed power reference P_abs and of the power which the converter is intended to transmit between circuits P_ref1 , P_ref₂- - - It is possible to choose how the absorbed power reference will be distributed through the external DC and AC circuits by adjusting certain coefficients of the linear relationship k_Pm , k_PD2... and k_PAi , kp_A2... This allows controlling the total stored energy with the power absorbed from only certain circuits. The possibility to control such distribution may have an advantage depending on the application. For instance, when the converter is used for high voltage direct current transmission (HVDC transmission) it is possible to regulate the total energy accumulated in the converter with the power exchanged with AC circuits so that the power exchanged with the DC circuits is not perturbed. Fourth type: Relative main voltages

The relative main voltages are used to control the voltage between circuits which are unconnected from each other. This way it is possible to maintain a line-to-ground voltage in circuits which are not connected to ground. Another application is the addition of common-mode voltage with triple harmonics to increase the voltage the converter can modulate in 3-phase AC grids. In order to control these voltages, the provided references for the common-mode voltages are expressed in the same base as the main voltages. Then each relative main voltage is chosen as the same value of its corresponding reference. If this open-loop control scheme proves insufficient, a set of regulators (such as proportional controllers with feed forward) can be used. The regulators receive the actual common-mode voltages and their references expressed in the same base as the main voltages. The output of these regulators is used as the relative main voltages. Note that even with a regulator the most important term will be the feed forward value.

After the central control unit 5 has selected the desired values for the four types of main voltages (internal main voltages, DC main voltages, AC main voltages and relative main voltages), it calculates the branch reference voltages Ui to U_mn as the aforesaid orthogonal transformation. Then these voltage references are transmitted from the central control units 5 to their respective branch control devices 4.

To maintain the energy balance in a branch, each branch control device 4 periodically sorts the modules 2 of the associated branch (or branches). This sorting is done in dependence on the value of a sorting function F, which depends on the branch current, on the module stored energy and, optionally, on the amount of time the module accumulator has been connected to the branch from the last switching period or from the last time the modules were sorted. The branch control device 4 sends the necessary signals to the corresponding branch modules 2 to connect the accumulators 3 of some modules to the branch. The accumulators chosen to be connected are those with the highest values of the function F. The number of accumulators 3 chosen to be connected to a branch is such that their combined voltage is as close as possible to the corresponding branch reference voltage Ui to U_mn. Pulse width modulation (PWM) may be employed on some of the chosen modules to obtain a closer voltage to the branch reference voltage.

Advantageously, letting the sorting function F depend on whether the modules accumulators were connected to the branch (and the time they have been connected) helps reducing the amount of times the modules 2 commutate. Since the current is also taken into account, the energy balancing can be considered more important when the current is high while the reduction of the commutations are more important when the current is low.

When evaluating the modules accumulators energy, the skilled person can understand that, if the accumulators are capacitors, the square of their voltage is a possible value of its energy, while if they are batteries, the state of charge (SOC) is a better value. When two or more types of accumulators are being combined, a different function may be used for each type. This allows weighing differently the energy deviation of different types of accumulators.

According to an advantageous further development, the deviation of the energy value from a user-defined reference may be considered instead of simply the accumulated energy. This allows the user to choose a different energy level on each accumulator. In this case, the user provides the energy reference for each accumulator and the total energy reference E_TOTALRef is calculated internally as the sum of all these energy values expressed in consistent units. Advantageously this allows the user to choose which batteries charge and discharge each time to preserve the batteries state of health (SOH).

According to an advantageous further development, since the modules are sorted by the value of a function which strongly depends on their energy, the branch energy values Ei to E_mn can be chosen in dependence on the energy values of only some of the modules that occupy a particular position when sorted. It is also possible to select the branch energy value as the energy stored on a module accumulator chosen at random every time the modules are sorted. Once the branch energy values have been chosen, they are transmitted to the central control unit 5 to be used for the next iteration of the method.

Hereinafter, particular mention is made to the accompanying drawings.

Figure 1 shows a possible topology for the converter 1 . In this case, the converter comprises 2 DC nodes and 3 AC nodes. The converter is connected to one DC circuit and to one AC circuit through terminals. Each DC node is connected to the DC circuit through a terminal (C1 , C2), and each AC node is connected to the AC circuit through a terminal (A1 , A2, A3). The AC and DC circuits do not share any node, not even the ground node. If the converter needed to be used with AC and DC circuits which are connected to one another, a transformer could be added between the converter and the AC circuit.

A branch is formed between each DC node and each AC node. Each branch comprises an inductance L and a series of modules 2. Figure 2 shows an already known topology for these modules. Each of these modules comprises an energy accumulator 3. The accumulator of the module shown in Figure 2 is a capacitor, but it is also possible to use batteries. It is further possible to combine modules with different types of accumulators.

Figure 3 shows a simplified scheme of the branch control device 4 communicating with all the modules 2 of a branch. The branch control device receives the voltage of the modules and returns the necessary signals for the modules to modulate the commanded voltage.

As shown in figure 4, a branch control device 4 is being used for each two branches, although it would have been possible to use one branch control device for each branch. For this example, the branch control devices are FPGAs. If one FPGA alone was incapable of managing a whole branch, then several FPGAs connected to one another could constitute the branch control device 4. All branch control devices further communicate with the central control unit 5. In particular, this communication includes the transmission of a branch energy value per branch Ei to E₆ from the branch control devices to the central control unit and the transmission of a branch reference voltage per branch Ui to U₆ from the central control unit to the corresponding branch control devices. For this example, the central control unit 5 is either a microprocessor or a microcontroller.

Each branch control device 4 periodically receives the measures of voltages corresponding to the associated branches modules accumulators 3, as well as a measure of the current circulating through said branches. With this data, the branch control devices calculate the energy stored on the accumulators of the associated branches. Afterwards, each branch control device evaluates a certain sorting function F for each module of the associated branches and sorts the modules of each associated branch according to the obtained results: On each branch the module with the highest result for said function is indexed as first; the module with the second highest result is the second and so on. The sorting function F mainly depends on the energy stored in the module accumulator (E_A) but it may also depend on other variables such as a reference for said energy (E_A R_ef) , the amount of time the accumulator was connected to the branch during a previous time period (TON) or the current which circulates through the branch (I). A possible expression for this function is the following:

where K is a constant parameter.

Once the modules have been sorted, a branch energy value to E₆ is chosen in dependence on the energy stored in the accumulators of the modules that occupy certain positions after being ordered. In particular, for this example, the branch energy value is the sum of energy stored on the accumulators corresponding to the median and the upper and lower quartiles of the distribution. So, for example, if each branch comprises 35 modules, the branch energy value would be the sum of the energy values that correspond to the modules which have been indexed as the 9_th, the 18_th and the 27_th. It would also be possible to use a pseudo random number generator to select any number of branch modules at random and choose the branch energy value as the sum of their stored energy. After obtaining the branch energy values, these are sent to the central control unit 5.

Figure 5 shows a scheme of the main processes that occur on the central control unit 5: The central control unit receives the branch energy values E, along with measures of the branch currents I and the DC and AC circuits' voltages V. Orthogonal linear transformations 12 are applied to obtain the main energy values E_M, the external circuit main voltages V_M and the main currents l_M. These main values are simply linear combinations of the measured values. Then, these values are used to obtain the internal main voltages (U_Mn and U_Mi2) , the DC main voltage (U_MDI), the AC main voltages (U_MAI and U_MA2) and the relative main voltage (U_Mm) through the corresponding processes (6, 7, 8 and 9 respectively). Once all the six main voltages have been obtained, an orthogonal linear transformation 12 is applied to translate these main voltages into the branch reference voltages Ui to U₆.

Figure 6 is a more detailed representation of the same scenario. It shows how the necessary data is obtained to calculate each main voltage. An orthogonal linear transformation 12 is applied to the branch energy values Ei to E₆ to obtain the main energy values. One of these main energy values is the total energy value E_Totai, which is proportional to the sum of the branch energy values. The remaining main energy values are the internal main energy values E_Mn to E_Mi5- The same linear transformation 12 is applied to the branch currents h to l₆ to obtain the main currents. Two of these main currents are the internal main currents l_Mn and l_Mi2- A linear transformation 12 is also applied to the AC and DC circuits' voltages in order to obtain the external circuit main voltages. One of them is the DC circuit main voltage V_MDI , which depends only on the DC circuit voltage, two of the others are the AC circuit main voltages V_MAI and V_MA2, which depend only on the AC circuit voltages, and the last one is external relative main voltage V_MRI , which depends on the common mode voltage of the AC and DC circuits. A filtering process 13 is applied to the internal main energy values (E_MM to E_M|₅) to mitigate their AC component. The internal main currents (l_Mn and l_Mi2) and the filtered internal main energy values (E_MM ,_N to E_M|₅ ,_N) are used to calculate the internal main voltages U_Mn and U_Mi2 (in process 6). The total energy value E_TOTAL is used to choose the DC and AC power references P_Di _ref and P_Ai _ref (in process 10), which are later used when calculating the DC and AC main voltages U_MDI , U_MAI and U_MA2 (in processes 7 and 8). Finally, the external circuit main voltages are used as feed forward when calculating the DC, AC and relative main voltages U_MDI , U_MAI , U_MA2 and U_Mm (in processes 7, 8 and 9).

Figures 7 and 8 show how the internal main voltages are used to control the internal main energy values E_MM to E_M|₅. In figure 7, each filtered internal main energy value E_MM fii to E_Mi5 fii is supplied to an independent regulator 17 whose output is the reference for the derivative value of the corresponding internal main active power P'_Mn to P'_Mi5- For this example, the regulators are Pis or PIDs regulators, which select the internal main active power derivative values to maintain the received filtered internal main energy values as close as possible to certain references. In figure 8, these internal main power derivative references are obtained through a cascade control structure: First each filtered internal main energy value E_MM to E_M|_{5 FI}| is supplied to a regulator 17 which selects a reference for the corresponding internal main active power value P_Mn _ref to P_Mi5 ref to maintain the received filtered internal main energy value as close as possible to a reference. Then each of these internal main active power references is provided to another regulator 17 along with a measure of the actual internal main active power value. In this case all the regulators are PI controllers. The output of these regulators is a reference for the derivative value of the corresponding internal main power values P'_Mn to P'_Mi5- Irrespective of whether the control structure is direct (as shown in figure 7) or through a cascade (as in figure 8), the internal main reactive power values are always controlled in the same way: A measure of each internal main reactive power values Q_Mn is provided to a regulator 17 along with a reference for it QMM ref - The output of the regulator is a reference for the derivative value of the same internal main reactive power value Q'_Mn ref - The internal main reactive power values do not need to be regulated, it is optional. After obtaining the internal main power derivative references, the internal main voltages UMH and U_Mi2 are selected for the internal main power values to evolve according to the chosen derivative reference. The internal main voltages are constructed each with a DC component and two AC components one of them shifted 90^Q in phase relative to the other. The DC component c_M and c_l2 and the amplitude of the AC components a_M , b_h , a,₂ and b,₂ are obtained as linear functions 11 of the internal main power values and of their derivative references. These functions may depend on other parameters such as characteristic AC or DC voltages (the line-to-line AC voltage and the nominal DC voltage) the AC circuit frequency or the inductances value. The skilled person will understand that, since the alpha and beta voltage components of the AC circuit are shifted 90^Q in phase from one another and their frequency is the same as the AC circuit frequency, they can replace the sine and cosine functions shown in Figures 7 and 8 when constructing the AC main voltages. The amplitude of the AC components only needs to be multiplied by the alpha and beta voltage components respectively and scaled appropriately.

In order to execute the aforesaid method, the internal main power values P_Mn to P_Mis (and, if desired Q_Mn ) are required to be known. This presents a problem as these power values cannot be measured instantaneously. Figures 9 to 1 1 present three ways to measure these values. The scheme shown in figure 9 is based on the definition of the internal main power values: the net active power that is being transferred between branches. Since the internal main energy values represent differences in the energy stored in the branches, its derivative values represent power being transferred between branches. According to this proposed method, a numerical derivation process 16 is applied to the filtered internal main energy values E_Mn m to E_M5 \n to obtain the internal main active power values P_Mn to P_Mi5- The internal main reactive power values Q_Mn are not obtained this way.

The scheme shown in figure 1 0 is based on the relationship between the internal main power values P_Mn , PMI₂, MI₃, PMI₄, PMI_S and Q_Mn and the internal currents DC and AC components l_ai , l_bi , l_ci , Ib2 and l_c2. The proposed way of obtaining the internal main powers comprises two operations:

• A filtering process 13 is applied to the internal main currents in order to identify their DC and AC components l_ai , l_bi , l_ci , Ib2 and l_c2 and

• The internal main power values P_Mn , PMI2, PMI3, PMW, PMIS and Q_Mn are obtained as linear functions 11 of said current components. The scheme proposed in figure 1 1 is based on the relationship between the internal main power values P_Mn , PMI2, PMI3, PMI₄, PMIS and Q_Mn and the instantaneous values of the internal currents l_Mn and l_Mi2- Since the number of internal currents is lower than the number of internal main power values, only some combinations of these values can be measured at a time. However, since the regulators provide references for the derivative value of all the internal main power values, it is easy to estimate the instantaneous value of each internal main power value. The proposed way to do so comprises two operations:

• Estimations of the internal main power values P_MI1 , P_MI2 , P_Mi3 , PMI4 > PMIS and Q_MI1 are obtained by numerical quadrature 14 of the references for the derivative value of the internal main power values P'_Mn _ref , P ret, P'MI3 ret, P'MI₄ ret, P'Mi5 ref and Q'_Mii ref, for example using Euler method or a Runge-Kutta based method from a previously known set of main power values and

• A correction 15 is applied to the estimations according to the combinations of these values that can be measured using the internal currents l_Mn and l_Mi2-

The correction can comprise solving a least square problem with restrictions, which is possible using mathematical tools such as Lagrange multipliers. A simpler and more stable (but slower) way to correct the estimation comprises the following steps:

• calculating the internal currents that would correspond to the estimation ί_ΜΙ1, IMI2 J

• comparing these currents with the actual internal main currents l_Mn and l_Mi2 and calculating the difference and

• subtracting from the estimated internal main power values P_MI1 , P_MI2 , P_MI3 , PMI4 > P_MI5 and Q_MI1 a set of values proportional to the gradient of said difference. This way, the more the error depends on an internal main power value, the more its estimation will be modified. This is similar to the LMS algorithm but it considers the priori information. If the power exchanged with the external circuits is not uniformly distributed among the branches, then it can be considered in the estimation 14 and/or the correction 15. Figure 1 2 shows how the DC main voltage U_MDI is used to control the power the converter exchanges with the DC external circuit P_Di . A regulator 17 (such as a PI controller) is supplied the reference and the actual value of the power exchanged with the DC circuit (P_{D ref} and P_D respectively). The regulator returns a reference for the exchanged power derivative value P'_{m ref}. Then, a DC voltage component c_Di is obtained as a linear function 11 of this reference. The DC circuit main voltage V_MD1 is added as a feed forward term. The result is used as the DC main voltage U_MDI -

Similarly, Figure 1 3 shows how the AC main voltages U_MAI and U_MA2 are used to control the active and reactive power exchanged with the AC circuit. The reference and actual value of the active and reactive power exchanged with the AC circuit (P_Ai _ref , PAL QAI ref and Q_Ai ) are each supplied to two independent regulators 17 such as Pis The regulators return a reference for the exchanged active and reactive power derivative values (P'_Ai _ref and Q'_Ai re - Then, each AC main voltage U_MAI and U_MA2 is constructed with two AC components, one of them shifted 90^Q in phase relative to the other, whose amplitudes a_Ai , b_Ai , a_A2 and b_A2 are obtained as linear functions 11 of the aforesaid references (P'_Ai _ref and Q'_{A ref}) and of the actual active and reactive power exchanged with the AC circuit (P_A and Q_A ). The AC circuit main voltages V_MA1 and V_MA2 are added as feed forward terms. Although it would be possible, in this example no reverse sequence is controlled.

As shown in Figure 6, the references for the power to be exchanged with the AC and DC circuits are chosen to regulate the total energy stored in the converter. This regulation process 10 is detailed in Figure 14. First, the total energy value E_Totai is provided to a regulator 17 (for example a PI controller). Depending on whether the branch energy values Ei to E₆ were calculated with the modules accumulated energy or with the deviation of said energy from their desired value, a reference for the total energy value E_Totai may also be provided to the regulator. The regulator returns the absorbed power reference P_Abs Ref- This absorbed power reference is distributed between the external circuits according to two previously configured coefficients k_Pm and k_PAi . The skilled person understands that only the proportion of these coefficients is responsible of the distribution and, consequently, increasing both of them proportionally is just equivalent to increasing the gain of the regulator 17. Once the distribution has been chosen, a power reference P_ref selected by the user is added to or subtracted from each circuit absorbed power reference. This reference represents how much power is transmitted from the DC circuit to the AC circuit (or vice versa). The resulting references for the external circuit power P_{D1 re}, and P_{A ref} are consistent as they do transfer a certain amount of power from one circuit to the other and absorb the necessary power to maintain the converter stored energy. Moreover, the user can choose one of the distribution coefficients to be null so that the power reference for that circuit coincides with the one provided by the user. For example, if this converter was connected to an HVDC transmission line and to a relatively rigid AC grid, the user could choose k_Pm to be 0 and k_PAi to be 1 , so that the converter maintained its energy by exchanging power only with the grid. This way, the HVDC transmission line voltage would not be perturbed.

The relative main voltage U_MRI is chosen to maintain the external relative main voltage, V_MRI which represents the relative voltage between the circuits. For example, if the common-mode voltages of the AC and DC circuits are intended to be the same, the relative main voltage can be chosen to be null. Otherwise, the desired relative voltage V_{MR1 re}, can simply be applied as the main relative voltage with the appropriate scale. Should this open loop scheme prove insufficient a closed loop control structure can be applied as shown in Figure 1 5. In this case, the external relative main power voltage V_MRI is provided to a regulator 17 (in this case a PI regulator with feed forward) along with the desired reference. The feed forward component of the regulator provides a fast response while the proportional component corrects any possible deviations

Once all the six main voltages U_Mn , U_Mi2, U_MDI , U_MAI U_MA2, and U_MRI have been calculated, the branch reference voltages Ui , to U₆ are obtained as an orthogonal linear transformation 12 of the main voltages. Then, the central control unit 5 transmits each branch reference voltage to the corresponding branch control device 4.

After the branch control devices 4 receive branch reference voltages, they command the associated modules to modulate the received branch voltages. As it was said before, the modules of each branch are periodically sorted in dependence on the value of the sorting function F, which depends on the amount of energy accumulated in the module, on branch current and on the previous duty cycle. If energy unbalance is intended, the sorting function F may depend on the energy deviation instead of on the actual energy stored on the accumulator. The modulation of the total branch reference voltage is distributed among the modules so that the accumulators belonging to the modules whose value of such function F is higher are connected to the branch. If necessary, one module can be chosen to be connected or disconnected during the control cycle.

Numerical references: 1 Converter

2 Module

3 Accumulator

4 Branch control device

5 Central control unit 6 Branch energy control process, which selects the internal main voltages

7 DC power control process, which selects the DC main voltage

8 AC power control process, which selects the AC main voltages

9 Circuit relative voltage control process, which selects the relative main voltage 10 Total energy regulation process

1 1 Lineal functions

12 Orthogonal lineal transformation

13 Filtering process

14 Estimation process performed by numerical quadrature

15 Correction process

16 Numerical derivation

17 Linear regulator (such as P, PI or PID regulator)

Claims

1. System for controlling an AC/DC converter with a plurality of branches, a branch formed between an AC node and a DC node, the branch comprising an inductance and a plurality of modules connected in series, a module comprising a disconnectable accumulator (3), wherein the system comprises:

- a plurality of branch control devices (4), each branch control device (4) is configured to obtain the energy stored on a plurality of accumulators of at least one branch, the branch control device (4) is further configured to determine a branch energy value (Ei ...E_mn) which depends on the at least one accumulator energy of one module of the branch;

- a central control unit (5) configured to receive the branch energy (Ε^,.Ε™) of a plurality of branches, the central control unit (5) is further configured to provide a branch reference voltage (Ui ...U_mn) for the plurality of control devices (4); characterised in that: the central control unit (5) is configured to calculate the branch reference voltage (Ui ...U_mn) by applying a linear transformation to a plurality of main voltages (UMi ... U_Mmn), wherein at least one of the main voltages is an internal main voltage (UMM , UMI₂) with influence on the current that internally circulates through the converter and without influence on the external power to be exchanged, and the control devices (4) are further configured to select at least one accumulator (3) to be disconnected in order to modify the total output voltage of the branch modules, so that the difference between the branch reference voltages (Ui ...U_mn) and the total output voltage of modules in at least one branch is below a threshold.

2. System according to claim 1 , wherein the linear transformation applied to the plurality of the main voltages (UMi ...U_Mmn) to calculate the branch reference voltages (Ui ...U_mn) is orthogonal.

3. System according to claim 1 or 2, wherein the main voltages also comprises at least one DC main voltage (U_Dci) responsible for exchanging power with a DC external circuit, at least one AC main voltage (U_Aci) responsible for exchanging power with a AC external circuit and/or at least one relative main voltages U_MRI without influence on any current.

4. System according to any of previous claims, wherein calculating the branch reference voltage (Ui ...U_mn) by the central control unit (5) comprises determining a plurality of internal main active power (P_Mn , PMI2) transferred between branches.

5. System according to claim 4, wherein determining a plurality of internal main active power (P_Mn , PMI2) comprises calculating the derivative (E'_Mn , E ) of the internal main energy values (EMU , E_M|₂)-

6. System according to claim 4, wherein determining a plurality of internal main active power (P_MM , P_M|₂) comprises measuring a plurality of internal main currents (l_Mn , IMI2) and obtaining the AC and DC components of said internal main currents (l_Mn , l_Mi2) -

7. System according to claim 4, wherein determining a plurality of internal main active power (P_MM , P_M|₂) comprises considering previous values thereof along with their corresponding previous reference for their derivative values (P'_Mn _ref, P _ret) and measuring a plurality of internal main currents (l_Mn , l_Mi2)-

8. System according to claim 4, wherein it further comprises selecting a plurality of internal main voltages (U_Mii ...U_Mi_mn) for a plurality of internal main active power

(P_MM ...P_Mi_mn) to evolve according to a plurality of references for the derivative values of the internal main power (P'_{MM ref}, P _re -

9. System according to any of previous claims, wherein the control device (4) is configured to connect or disconnect a plurality of accumulators (3) from a plurality of modules according to at least one of the following criteria:

- the branch current,

- the time of the accumulator being connected during a previous switching period,

- the time of the accumulator being disconnected during a previous switching period,

- the energy stored on the accumulator, or - a combination thereof.

10. Method for controlling a converter with a plurality of branches, a branch formed between an AC node and a DC node, the branch comprising an inductance and a plurality of modules connected in series, a module comprising a disconnectable accumulator (3), wherein the system comprises: - measuring the energy stored on a plurality of accumulators of at least one branch, - determining a branch energy value (Ei ... E_mn) which depends on at least one accumulator energy of one module of the branch;

- calculating a branch reference voltage (Ui ... U_mn) based on the branch energy by applying an orthogonal linear transformation to a plurality of main voltages (U_Mi ... U_Mmn) , wherein at least one of the main voltages is an internal main voltage (U_Mn , U_Mi2) with influence on the current that internally circulates through the converter and without influence on the external power to be exchanged, and- selecting at least one accumulator (3) to be disconnected in order to modify the total output voltage branch modules, so that the difference between the branch reference voltage and the output voltage for modules of at least one branch is bellow a threshold.

11. Method according to claim 10, wherein the linear transformation plurality of the main voltages (UMi . . . U_Mmn) is orthogonal.

12. Method according to claim 10 or 1 1 , wherein calculating the branch reference voltage (Ui ...U_mn) comprises determining a plurality of internal main active power (P_MM , PMI2) transferred between branches.

13. Method according to claim 12, wherein determining a plurality of internal main active power (P_MM , P_M|₂) comprises calculating the derivative (E'_MM , E'_M|₂) of the internal main energy (E_MM , E_M,₂).

14. Method according to claim 12, wherein determining a plurality of internal main active power (P_MM , P_M|₂) comprises measuring a plurality of internal main currents (l_Mn ,

IMI2) and obtaining the AC and DC components of said internal main currents (l_Mn , )-

15. Method according to claim 12, wherein determining a plurality of internal main active power (P_Mn , PMI2) comprises considering previous values thereof along with their corresponding previous reference for their derivative values (P'_Mn _ref, P ret,) and measuring a plurality of internal main currents (l_Mn , l_Mi2)-

16. Method according to any of claims 12 to 15, wherein it further comprises selecting a plurality of internal main voltages (υ_Μιι...υ_Μΐηη) for a plurality of internal main active power (P_Mn - - - PMimn) to evolve according to a plurality of references for the derivative values of the internal main power (P'_Mn _ref, P re - 17. Method according to any of claims 10 to 16, wherein it further comprises balancing the energy in at least one branch by sorting the modules (2) in dependence on the value of a sorting function (F), which depends on the branch current, on stored energy of the accumulators (3) and/or on the time of the accumulator (3) being connected to the branch during a previous time interval.