Modular multilevel converter, method and control module for controlling the same

Abstract

The invention relates to a modular multilevel converter (2) having a control module (4) and a computer (10) for computing a setpoint for the internal energy of the converter stored in the capacitors of the submodules of the arms. The control module is configured to deduce, from the setpoint for the internal energy of the converter, a setpoint for the voltage across the terminals of each modeled capacitor, which setpoint is used for regulating the voltage across the points of common coupling between the converter and the DC power supply network and the voltage across the terminals of each modeled capacitor.

Claims

1. A multilevel modular voltage converter for converting AC voltage into DC voltage and DC voltage into AC voltage, the converter comprising: a DC portion configured to be connected to a DC power supply network; and an AC portion configured to be connected to an AC power supply network; a plurality of legs, each of said legs comprising an upper arm and a lower arm, each of said upper arms and lower arms comprising a plurality of submodules that are individually controllable by a control member specific to each of said submodules, wherein, in each of said upper arms and lower arms, each of said submodule comprises a capacitor that is connected in series in the respective arm when the control member of the submodule is in an ON state, each of said upper arms and lower arms being configured to model as a modeled voltage source associated with a duty ratio depending on a number of capacitors connected in series in the respective arm, each modeled voltage source being in parallel with a modeled capacitor corresponding to a total capacitance of the respective arm, wherein the converter further comprises a converter control module configured to regulate a voltage across terminals of each modeled capacitor of each leg and to regulate a voltage at connecting points between the converter and the DC power supply network by controlling said control members of the submodules of the converter, wherein the control module of the converter comprises a computer that computes a setpoint for an internal energy of the converter stored in the capacitors of the submodules of each of said upper arms and lower arms by applying a function having an adjustable input parameter, the control module being configured to deduce, from said setpoint for the internal energy, a setpoint for a voltage across the terminals of each modeled capacitor used for regulating the voltage at the connecting points between the converter and the DC power supply network and the voltage across the terminals of each modeled capacitor.

2. The converter according to claim 1, wherein the adjustable input parameter is an adjustable virtual inertia coefficient k.sub.VI.

3. The converter according to claim 2, wherein the computer is configured to compute the internal energy setpoint W*.sub.for the converter using a function: $W_{.Math.}^{*}=\frac{1}{2}6C_{\mathrm{tot}}{k}_{VI}\left(v_{dc}^2-v_{dc0}^2\right)+W_{.Math.0}^{*}$ where C.sub.tot is a total capacitance of a modeled capacitor in one of said upper arms or lower arms, v.sub.dc is a measured voltage of the DC power supply network, v.sub.dc0 is a nominal value of the voltage at the connecting points between the converter and the DC power supply network, and W*.sub.0is a nominal setpoint for a value of an energy stored in the capacitors of the submodules of each of said upper arms and lower arms of the converter.

4. The converter according to claim 1, wherein the control module includes a regulator for regulating an internal energy of the converter, the regulator having as input a squared result of a comparison between said setpoint for the voltage across the terminals of each modeled capacitor and an average of squares of the voltages across the terminals of the modeled capacitors, and delivering a power setpoint for the capacitors of said converter.

5. The converter according to claim 1, wherein the control module is configured to perform a change of variable in order to control intermediate current and voltage variables i.sub.diff, i.sub.gd and v.sub.diff, v.sub.gd, where i.sub.diffand v.sub.diff are associated with the DC power supply network and i.sub.gd and v.sub.dg are associated with the AC power supply network.

6. The converter according to claim 5, wherein the control module includes a regulator for regulating a current i.sub.gd and having as input a setpoint i*.sub.gd corresponding to the current i.sub.gd.

7. The converter according to claim 5, wherein the control module includes a regulator for regulating a current i .sub.diff and having as input a setpoint i*.sub.diff corresponding to the current i.sub.diff.

8. The converter according to claim 1, wherein the control module includes a regulator for regulating the voltage at the connecting points between the converter and the DC power supply network, the regulator having as input a squared result of a comparison between a setpoint for the voltage across the points of common coupling between the converter and the DC power supply network and a squared value taken from the DC power supply network, and delivering a setpoint for an operating power of said converter.

9. The converter according to claim 8, wherein the adjustable input parameter is an adjustable virtual inertia coefficient k.sub.VI and wherein the control module includes a member for adjusting a gain of the regulator for regulating the voltage at the connecting points between the converter and the DC power supply network, as a function of a value of the virtual inertia coefficient k.sub.VI.

10. The converter according to claim 1, wherein the control module includes a limiter for limiting an internal energy of the converter, the limiter having as input the internal energy of the converter, a setpoint for a maximum internal energy of the converter, and a setpoint for a minimum internal energy of the converter, and delivering a limit power setpoint.

11. A method of controlling a multilevel modular voltage converter, the converter serving to convert AC voltage into DC voltage and DC voltage into AC voltage, said converter including a DC portion configured to be connected to a DC power supply network and an AC portion configured to be connected to an AC power supply network, the converter having a plurality of legs, each of said legs comprising an upper arm and a lower arm, each of said upper arms and lower arms having a plurality of submodules that are individually controllable by a control member specific to each of said submodules, and in each of said upper arms and lower arms, each of said submodules comprising a capacitor that is connected in series in the respective arm when the control member of the submodule is in an ON state, each of said upper arms and lower arms being configured to model as a modeled voltage source associated with a duty ratio depending on a number of capacitors connected in series in the respective arm, each modeled voltage source being in parallel with a modeled capacitor corresponding to a total capacitance of the respective arm, the method further comprising: controlling of the converter, in which a voltage across terminals of each modeled capacitor of each leg is regulated and a voltage at connecting points between the converter and the DC power supply network is regulated by controlling said control members of the submodules of the converter, calculating a setpoint for an internal energy of the converter stored in the capacitors of the submodules of each of said upper arms and lower arms by using a function having an adjustable input parameter, and calculating a setpoint for the voltage across the terminals of each modeled capacitor from said setpoint for the internal energy of the converter, the setpoint for the voltage across the terminals of each modeled capacitor being used for regulating the voltage at the connecting points between the converter and the DC power supply network and the voltage across the terminals of each modeled capacitor.

12. The method according to claim 11, wherein an adjustable input parameter is an adjustable virtual inertia coefficient k.sub.VI.

13. The method according to claim 12, wherein the setpoint W*.sub.for the internal energy of the converter is calculated from a function: $W_{.Math.}^{*}=\frac{1}{2}6C_{\mathrm{tot}}{k}_{VI}\left(v_{dc}^2-v_{dc0}^2\right)+W_{.Math.0}^{*}$ where C.sub.tot is a total capacitance of the modeled capacitor in one of said upper arms or lower arms, v.sub.dc is a measured voltage of the DC power supply network, v.sub.dc0 is a nominal value of the voltage at the connecting points between the converter and the DC power supply network, and W*.sub.0 is a nominal setpoint for a value of an energy stored in the capacitors of the submodules of each of said upper arms and lower arms of the converter.

14. The method according to claim 11, further comprising regulating the voltage at the connecting points between the converter and the DC power supply network by using as input a squared result of a comparison between a setpoint for the voltage at the connecting points between the converter and the DC power supply network and a squared value taken from the DC power supply network, and delivering a setpoint for an operating power of said converter.

15. The method according to claim 11, further comprising adjusting a gain for regulating the voltage at the connecting points between the converter and the DC power supply network, as a function of the value of the virtual inertia coefficient.

16. A control module for controlling a multilevel modular voltage converter, the converter being configured for converting AC voltage into DC voltage and DC voltage into AC voltage, the converter comprising a DC portion configured to be connected to a DC power supply network and an AC portion configured to be connected to an AC power supply network, the converter comprising a plurality of legs, each of said legs comprising an upper arm and a lower arm, each of said upper arms and lower arms comprising a plurality of submodules that are individually controllable by a control member specific to each of said submodules, and in each of said upper arms and lower arms, each of said submodules comprising a capacitor that is connected in series in the respective arm when the control member of the submodule is in an ON state, each of said upper arms and lower arms being configured to model as a modeled voltage source associated with a duty ratio depending on a number of capacitors connected in series in the respective arm, each modeled voltage source being in parallel with a modeled capacitor corresponding to a total capacitance of the respective arm, wherein said control module is included in said converter, and said control module is configured to regulate a voltage across terminals of each modeled capacitor of each leg and to regulate a voltage at connecting points between the converter and the DC power supply network by controlling said control members of the submodules of the converter, wherein said control module comprises a computer that computes a setpoint for an internal energy of the converter stored in the capacitors of the submodules of each of said upper arms and lower arms by applying a function having an adjustable input parameter, and wherein said control module is configured to deduce, from said setpoint for the internal energy, a setpoint for a voltage across the terminals of each modeled capacitor used for regulating the voltage at the connecting points between the converter and the DC power supply network and the voltage across the terminals of each modeled capacitor.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The disclosure can be better understood on reading the following description of an embodiment of the disclosure given by way of non-limiting example, and with reference to the accompanying drawings, in which:

(2) FIG. 1, described above, shows a prior art three-phase modular multilevel converter;

(3) FIG. 2, described above, shows a submodule of a prior art modular multilevel converter;

(4) FIG. 3, described above, shows an equivalent circuit for an arm of a prior art MMC;

(5) FIG. 4, described above, shows a configuration that is equivalent to a prior art modular multilevel converter;

(6) FIG. 5 is a diagrammatic representation equivalent to a modular multilevel converter of the disclosure;

(7) FIG. 6 shows a modular multilevel converter provided with a control module of the disclosure;

(8) FIG. 7 shows an example implementation for adjusting the regulator for regulating the voltage across the points of common coupling between the converter and the DC power supply network;

(9) FIG. 8 shows a simplified loop for adjusting the regulator for regulating the voltage across the points of common coupling between the converter and the DC power supply network;

(10) FIG. 9A shows a power step imposed on an AC network for simulating the operation of the converter of the disclosure;

(11) FIG. 9B shows the voltage response of a DC network to a power step on the AC network as a function of time for different values of k.sub.VI;

(12) FIG. 9C shows the variation in the total energy of a converter in response to a power step on the AC network, as a function of time and for different values of k.sub.VI;

(13) FIG. 9D shows the power response of a DC network to a power step on an AC network as a function of time for different values of k.sub.VI;

(14) FIG. 10A shows the voltage response of a DC network for a first simulation system consisting in an MMC of the disclosure having a virtual capacitance and for a second simulation system consisting in a prior art converter having a real capacitor in parallel with the DC network;

(15) FIG. 10B shows the variations in the total energy of the converter for the two simulation systems;

(16) FIG. 10C shows the power response on the AC network for the two simulation systems;

(17) FIG. 10D shows the power response on the DC network for the two simulation systems; and

(18) FIG. 11 shows an MMC of the disclosure in which the control module is provided with a limiter for limiting the internal energy of the converter.

DETAILED DESCRIPTION OF THE DISCLOSURE

(19) The disclosure relates to a modular multilevel converter having a control module, with a circuit of equivalent behavior being shown in FIG. 5. In non-limiting manner, this figure shows an MMC 2 for converting DC energy into AC energy. In this example, it should be observed that the converter 2 has an AC portion 2A connected to the AC power supply network 110 on the left-hand side of the diagram. On the right-hand side of the diagram, it can be seen that the converter 2 has a DC portion 2C connected to the DC power supply network 120. It can be seen that a virtual capacitor C.sub.VI of adjustable capacitance C.sub.VI (by abuse of language and for reasons of simplicity, the same notation is used to designate both the capacitor and its capacitance) is associated in parallel with the DC power supply network 2C. The term virtual is used to mean that this capacitor is not physically present in the converter. In contrast, the control module of the disclosure makes it possible to obtain operation of the converter that is analogous to the operation that would be obtained by a converter having the virtual capacitor: the virtual capacitor C.sub.VI represents the behavior of the converter 2 and of its control module 4 of the disclosure. Specifically, by regulating a virtual inertia coefficient k.sub.VI, the stability of the DC power supply network 120 is improved and the behavior of the converter is analogous to the behavior of a converter in which a virtual capacitor C.sub.VI of adjustable capacitance C.sub.VI is connected in parallel with the DC power supply network 120.

(20) The diagram of FIG. 5 also shows transfers of power between the converter 2 and the DC and AC power supply networks 120 and 110. Thus, P.sub.l is the power coming from other stations of the DC power supply network and symbolizes a sudden power disturbance on the DC network, P.sub.dc is the power extracted from the DC power supply network 120, P.sub.ac is the power transmitted to the AC power supply network 110, P.sub.c is the power absorbed by the capacitance C.sub.dc of the DC power supply network 120, P.sub.m is the operating power of the converter 2, and P.sub.w may be considered as being the power absorbed by the virtual capacitor C.sub.VI of adjustable capacitance C.sub.VI. In addition, v.sub.dc is the voltage across the points of common coupling between the converter and the DC power supply network.

(21) In the MMC 2 of the disclosure, and unlike the prior art MMC, surplus power from the DC power supply network 120, written P.sub.w, is absorbed by the virtual converter C.sub.VI and enables the converter to store the internal energy W.sub..

(22) The example of FIG. 6 shows a modular multilevel converter 2 having a control module 4 of the disclosure. The MMC is configured to use closed-loop servo-control to regulate the voltage v.sub.dc across the points of common coupling between the converter and the DC power supply network 120 and the voltage v.sub.c across the terminals of each modeled capacitor.

(23) The control module 4 includes a computer 10 that calculates an internal energy setpoint W*.sub. for the converter 2 that is stored in the capacitors of the submodules of the arms on the basis of an adjustable virtual inertia coefficient k.sub.VI, of a nominal setpoint W*.sub.0 for the value of the energy stored in the capacitors of the converter, of a measured voltage v.sub.dc of the DC power supply network, and of a nominal value v.sub.dc0 for the voltage across the points of common coupling between the converter and the DC power supply network.

(24) From the diagram of FIG. 5, it can be seen that:

(25) $P_l-P_{dc}=P_c=\frac{{\mathrm{dW}}_{dc}}{\mathrm{dt}}=\frac{1}{2}{C}_{dc}\frac{{\mathrm{dv}}_{dc}^2}{\mathrm{dt}}$
where W.sub.dc is the energy of the DC power supply network.

(26) Still with reference to FIG. 5, assuming that P.sub.m is equal to P.sub.ac, it can also be seen that:

(27) $P_{dc}-P_{ac}=P_W=P_{dc}-P_m=\frac{{\mathrm{dW}}_{}}{\mathrm{dt}}=\frac{1}{2}6C_{\mathrm{tot}}\frac{{\mathrm{dv}}_c^2}{\mathrm{dt}}$
where C.sub.tot is the capacitance of the modeled capacitor in an arm.

(28) By combining the above two equations, the following expression can be obtained:

(29) $P_l-P_m=P_c+P_W=\frac{1}{2}{C}_{dc}\frac{{\mathrm{dv}}_{dc}^2}{\mathrm{dt}}+\frac{{\mathrm{dW}}_{}}{\mathrm{dt}}$

(30) This expression shows in particular that by controlling the internal energy W.sub. of the MMC, it is possible to distribute the power P.sub.1-P.sub.m between the capacitance C.sub.dc of the DC power supply network and the capacitors of the submodules of the arms.

(31) The computer makes it possible to calculate the appropriate internal energy setpoint W*.sub. using the function:
W*.sub.=6C.sub.totk.sub.VI(v.sub.dc.sup.2v.sub.dc0.sup.2)+W*.sub.0

(32) Said internal energy setpoint W*.sub. of the converter makes it possible to supply a setpoint v*.sub.c for the voltage across the terminals of each modeled capacitor. This setpoint v*.sub.c for the voltage across the terminals of each modeled capacitor, when squared, is itself compared with an average of the squares of the voltages across the terminals of the modeled capacitors.

(33) Without going beyond the ambit of the disclosure, the average may be calculated in any manner. In the non-limiting example shown in FIG. 6, the average is calculated as being the sum of the squares of the voltages of the modeled capacitors in each arm, divided by six (since the converter has six arms). The comparison is supplied to an internal energy regulator 20 of the converter, which delivers a power setpoint P*.sub.w for the capacitors of said converter 2.

(34) In addition, assuming that the energy regulation is sufficiently fast, the following is obtained:

(35) $P_l-P_m=P_c+P_W=\frac{1}{2}{C}_{dc}\frac{{\mathrm{dv}}_{dc}^2}{\mathrm{dt}}+\frac{1}{2}6C_{\mathrm{tot}}{k}_{\mathrm{VI}}\frac{{\mathrm{dv}}_{dc}^2}{\mathrm{dt}}$
or indeed:

(36) 0$P_l-P_m=\frac{1}{2}\left(C_{dc}+C_{\mathrm{VI}}\right)\frac{{\mathrm{dv}}_{dc}^2}{\mathrm{dt}}$

(37) It is thus possible to express the virtual inertia coefficient k.sub.VI in the following form:
C.sub.VI=6C.sub.totk.sub.VI

(38) This expression shows that by regulating the virtual energy coefficient k.sub.VI, it is possible to modify the value of the virtual capacitance C.sub.VI.

(39) In FIG. 6, it can also be seen that the control module 4 includes a regulator 30 for regulating the voltage across the points of common coupling between the converter and the DC power supply network 120, having as input the result of a comparison between the setpoint for voltage v*.sub.dc across the points of common coupling between the converter and the DC power supply network, when squared, and a value v.sub.dc taken from the DC power supply network and that is also squared. The regulator 30 for regulating the voltage across the points of common coupling between the converter and the DC power supply network 120 delivers an operating power setpoint P*.sub.m for said converter 2.

(40) In addition, the control module 4 has a regulator 40 for regulating AC current i.sub.gd having as input a setpoint i*.sub.gd, and a regulator 50 for regulating the current i.sub.diff having as input a setpoint i*.sub.diff.

(41) From FIG. 3, it is known that it is possible to model the submodules of an arm by respective modeled voltage sources, each associated in parallel with a modeled capacitor, such that the modeled voltage sources have a voltage v.sub.mxi across their terminals (where x indicates whether the arm is an upper or lower arm and where i indicates the leg). The current regulators 40 and 50 deliver voltage setpoints v*.sub.diff and v*.sub.v that are used, following a change of variable, by a modulator member 60 and two balancing members 70a and 70b making use of a balancing control algorithm (BCA) in order to deliver the voltages v.sub.mxi across the terminals of the modeled voltage sources. This makes it possible to switch the submodules of the arms ON or OFF. This controls the voltage v.sub.cxi across the terminals of the modeled capacitors and also the voltage v.sub.dc across the points of common coupling between the converter and the DC power supply network.

(42) By varying the virtual inertia coefficient k.sub.VI input to the computer, it is thus possible to influence directly the voltage v.sub.dc of the DC power supply network and the inertia of that DC network.

(43) In this non-limiting example, the control module 4 also has a member 100 for adjusting the gain of the regulator for regulating the voltage across the points of common coupling between the converter and the DC power supply network 120 as a function of the value k.sub.VI of the virtual inertia coefficient. For reasons of simplicity, this member is shown as being outside the control module 4, even though it is included in the control module 4.

(44) FIG. 7 shows an example of adjusting the regulator for regulating the voltage v.sub.dc across the points of common coupling between the converter and the DC power supply network by using a proportional integral (PI) corrector on the servo-control loop for v.sub.dc and W.sub.. In this non-limiting example, the PI corrector is adjusted by a conventional pole placement method.

(45) This circuit includes in particular loops 42 and 52 for regulating the currents i.sub.diff and i.sub.gd towards their respective setpoints i*.sub.diff and i*.sub.gd.

(46) By simplifying, it is possible to obtain an equivalent representation of the loop for regulating the voltage across the points of common coupling between the converter and the DC power supply network 120 with adjustment of the regulator of said voltage across the points of common coupling between the converter and the DC network using a PI corrector. Such a representation is given in FIG. 8.

(47) FIGS. 9A to 9D show the results of a simulation of the behavior of a modular multilevel converter 2 having a control module 4 of the disclosure, and in particular a simulation by controlling power. In this simulation, a test system is created in which the DC portion of the converter is connected to an ideal DC power source, simulating a DC power supply network 120, while the AC portion of the converter is connected to an AC power source, simulating an AC power supply network 110. A power step is then imposed on the simulated AC network, the virtual inertia coefficient k.sub.VI is varied, and the results on other magnitudes of the system are observed.

(48) As can be seen in FIG. 9A, the curve l represents a power step of 0.03 per unit (pu) imposed on the simulated AC network for 0.1 seconds (s) prior to bringing the AC power back to its initial zero value. This behavior simulates a transfer of active power from the MMC 2 to the AC power supply network 110.

(49) The voltage response of the simulated DC network for different values of k.sub.VI is shown in FIG. 9B. Each of these curves corresponds to a value of k.sub.VI such that the curves a, b, c, d, and e correspond to k.sub.VI having respective values equal to 0, 0.5, 1, 2, and 3. It can be observed that for greater values of k.sub.VI, the variations in the simulated DC network are smaller. This agrees with the principle of the disclosure, since by increasing k.sub.VI, the inertia of the converter is increased, thereby enabling the DC network to contain the disturbances better and to stabilize the voltage of the DC network.

(50) FIG. 9C shows the variation in the total energy of the converter for several values of k.sub.VI. The curves g, h, i, j, and k correspond to k.sub.VI having respective values equal to 0, 0.5, 1, 2, and 3. By increasing the virtual inertia coefficient k.sub.VI, the value of the virtual capacitance is increased, thereby implying that the contribution of the converter increases and that more energy is extracted from the virtual capacitor. This increase in the contribution of the energy of the converter thus leads to a drop in the total energy of the converter when increasing the virtual inertia coefficient.

(51) The consequence of this can be seen in FIG. 9D, which shows how power varies on the simulated DC network as a function of values for the virtual inertia coefficient k.sub.VI. In this example, the curves m, n, o, p, and q correspond to k.sub.VI having respective values equal to 0, 0.5, 1, 2, and 3. It can be seen that when the value of the virtual inertia coefficient k.sub.VI increases, the impact on the power of the simulated DC network of the variation of power in the simulated AC network is reduced. In particular, less energy is extracted from the capacitors of the DC power supply network. This is due to the fact that more energy is extracted from the virtual capacitor. The virtual capacitance serves to stabilize and improve the inertia of the DC network.

(52) FIGS. 10A to 10D show a simulation by controlling the voltage across the points of common coupling between the converter and the DC network, in which the behaviors of two systems are compared. The first system consists in a modular multilevel converter of the disclosure, configured as in the above simulation. The virtual inertia coefficient is adjusted and set so that k.sub.VI=1. The second system consists in a prior art MMC in which the DC portion is likewise connected to an ideal DC power source, while the AC portion of the converter is connected to an AC voltage source. In this second system, a real capacitor is connected in parallel with the simulated DC network. The value of the capacitance of this real capacitor is selected to be equal to the capacitance of the virtual capacitor C.sub.VI of the first system. The comparison is thus between the influences of a virtual capacitor C.sub.VI and of a real capacitor associated with an MMC, in parallel with a simulated DC network.

(53) A power disturbance step is imposed by the DC power source on both systems, as can be seen in dashed-line curve z in FIG. 10D.

(54) In FIG. 10A, curves r and s represent the variation in the voltage of the simulated DC network for the first and second systems respectively. It can be seen that the variation in the voltage of the simulated DC network is the same for both systems.

(55) Since those systems are configured so that the values of the real and virtual capacitances are equal, the power response of the simulated AC network is the same for both systems. In FIG. 10C, this response is represented by the curve v, while the curve w represents the power disturbance step on the simulated DC network.

(56) By means of curve t, FIG. 10B shows an increase in the total energy in the first system having a virtual capacitance, representing the energy stored in the virtual capacitor. In contrast, in the second system, which is represented by the curve u, no variation can be observed in the total energy, given that for this converter there is no internal energy contribution to the simulated DC network.

(57) In FIG. 10D, curves y and x represent the simulated DC network power for the first and second systems respectively, and it can be seen that the presence of a virtual capacitance improves the power response to a power disturbance on the simulated network, as represented by the curve z. The disturbance thus has less impact on the simulated DC network and the power of said DC network is controlled better.

(58) A variant of the converter of the disclosure is shown in FIG. 11, in which the control module includes an energy limiter 80 that receives as input the internal energy W.sub. of the converter, a maximum internal energy setpoint W.sub.lim.sup.+ for the converter, and a minimum internal energy setpoint W.sub.lim.sup. for the converter. The energy limiter 80 delivers a limit power setpoint P*.sub.EL associated with a limit power P.sub.EL. This energy limiter serves to put a bound on the internal energy W.sub. between the maximum and minimum internal energy setpoint values for the converter.

(59) The limit power P.sub.EL appears as a disturbance on the energy control. The nominal setpoint W*.sub.0 of the value for the energy stored in the capacitors of the converter is thus corrected so as to provide the computer 10 for computing the internal energy setpoint with a corrected nominal setpoint W*.sub.0 for the value of the energy stored in the capacitors.

(60) This gives:
P.sub.ac=P.sub.m+P.sub.EL
such that:

(61) $P_l-P_m-P_{\mathrm{EL}}=P_c+P_W=\frac{1}{2}{C}_{dc}\frac{{\mathrm{dv}}_{dc}^2}{\mathrm{dt}}+\frac{{\mathrm{dW}}_{}}{\mathrm{dt}}$

(62) Furthermore, the corrected nominal setpoint W*.sub.0 for the value of the energy stored in the capacitors is expressed as follows:
W*.sub.=6C.sub.totk.sub.VI(v.sub.dc.sup.2v.sub.dc0.sup.2)+W*.sub.0

(63) By substituting in the above equations, the following is obtained:

(64) $P_l-P_m-P_{\mathrm{EL}}=\frac{1}{2}{C}_{dc}\frac{{\mathrm{dv}}_{dc}^2}{\mathrm{dt}}+\frac{1}{2}6C_{\mathrm{tot}}{k}_{\mathrm{VI}}\frac{{\mathrm{dv}}_{dc}^2}{\mathrm{dt}}-P_{\mathrm{EL}}$

(65) I.e.:

(66) $P_l-P_m=\frac{1}{2}\left(C_{dc}+C_{\mathrm{VI}}\right)\frac{{\mathrm{dv}}_{dc}^2}{\mathrm{dt}}$

(67) It can thus be seen that the energy limiter 80 does not modify the behavior of the converter within the maximum and minimum internal energy limits. The behavior of the converter is analogous to the behavior of a converter in which a virtual capacitor C.sub.VI of adjustable capacitance C.sub.VI is connected in parallel with the DC power supply network 120.