WO2022123060A1

WO2022123060A1 - Method for driving bidirectional ac/dc converters for synchronizing ac electrical systems connected to one another by a dc link

Info

Publication number: WO2022123060A1
Application number: PCT/EP2021/085313
Authority: WO
Inventors: Fabien BENAVENT
Original assignee: Electricite De France
Priority date: 2020-12-11
Filing date: 2021-12-10
Publication date: 2022-06-16
Also published as: FR3117707A1

Abstract

A method for driving bidirectional AC/DC converters (2a, 2b) of substations linking a first AC system, provided with at least one first AC generator (10a) and/or at least one first load (11a), to at least one second AC system, comprising at least one second AC generator (10b) and/or at least one second load (11b), through a DC line (1), characterized in that each of said converters (2a, 2b) is controlled in voltage source (or grid forming) mode, with a vector control algorithm for controlling the amplitude and the angle of the AC voltage of the converter, on the AC system side; and comprises a function F for driving said converters, of the type balancing the load in terms of active power between each substation of the DC line and its AC system, said function providing a frequency of said AC voltage that is used by said vector control of each of said converters to calculate said angle of said AC voltage.

Description

Title: METHOD FOR CONTROLLING BIDIRECTIONAL ALTERNATING CURRENT / DIRECT CURRENT CONVERTERS FOR THE SYNCHRONIZATION OF ALTERNATING CURRENT ELECTRICAL SYSTEMS CONNECTED TOGETHER BY A DIRECT CURRENT LINK

Technical area

The present invention relates to the field of electrical systems and the stabilization and frequency behavior of alternating current (AC) electrical systems interconnected by direct current lines. These systems comprise, for their connection with the direct current lines, bidirectional alternating current/direct current (AC/DC) conversion stations of the voltage source converter (VSC) type on the alternating current system side.

In the context of electrical networks, direct current lines are mainly high voltage direct current lines (HVDC for high voltage direct current in English).

The invention relates more particularly to alternating current electrical systems (AC for "alternating current" in English) interconnected by links of the high voltage direct current type (HVDC for "high voltage direct current" in English) and comprising alternative/direct AC/DC conversion stations of the voltage source converter type (VSC Voltage Source Converter in English).

Prior technique

[0004] HVDC VSC links are lines with a voltage greater than 1500 volts direct current. Such lines are historically controlled in "grid feeding / grid following" current source mode, i.e. the converter stations are controlled on the alternating current side with an internal current regulation loop and external active and reactive power regulation as well as a phase lock loop (PLL). These converter stations require the presence of production groups regulating the amplitude and frequency of the voltage in each alternating current system so that they can synchronize with it.

If we take the example of a simple HVDC link according to Figure 1 which comprises a continuous line 1 between a first converter station provided with a converter 2a and a second converter station provided with a second converter 2b, one of the two converter stations controls the flow of active power in the link while the second converter station balances its HVDC voltage in order to stabilize the flow of active power in the link as described in Cuiqing Du, Ambra Sannino and Math HJ Bollen, “Analysis of the Control Algorithms of Voltage-Source Converter HVDC”, IEEE, 2005 DOI: 10.1109/PTC.2005.4524566.

[0006] HVDC links in grid feeding/grid following mode can offer system services (contracted functions such as frequency adjustment and voltage adjustment of alternating current systems) similar to energy storage battery systems ( BESS (Battery Energy Storage System) driven in current source mode such as fast frequency adjustment through the modulation of their active power injection or voltage adjustment through the modulation of their reactive power injection.

[0007] Nevertheless, as described in the document Jenny Z. Zhou, Hui Ding, Shengtao Fan, Yi Zhang and Aniruddha M. Gole, “Impact of Short-Circuit Ratio and Phase-Locked-Loop Parameters on the Small-Signal Behavior of a VSC-HVDC Converter”, IEEE Transactions on Power Delivery, vol. 29, No. 5, 2014, HDVC links require a minimum short-circuit ratio (SCR) (this ratio corresponds to a quantification of the proximity of the connected generators and the difficulty of synchronization) in each system in alternating current to operate stably. Similarly, the system services related to frequency adjustment that such a link can convey do not offer the same level of performance and therefore the same operating reliability as an alternating current interconnection directly connecting two alternating current electrical systems (systems AC). It is for example not possible to benefit from an inertial response (or inertia), which is instantaneous, or from a direct release of the reserve of the system located on a first side of the HVDC link for the primary adjustment of frequency of the AC system on the second side of the HVDC link.

[0008] The document J. Rocabert, A. Luna, F. Blaabjerg and P. Rodriguez, “Control of power converters in AC microgrids”, IEEE Transactions on Power Electronics, vol. 27, No. 11, 2012 describes for its part an operation of the static converters of which the HVDC converter stations controlled in “grid forming” voltage source mode form part. The main advantages of grid forming mode for an HVDC converter station are to eliminate the SCR limit present in grid feeding mode as well as to allow instantaneous injection or absorption of active power as battery storage systems do in English. Battery Energy Storage System” (BESS) in grid forming mode. [0009] Different algorithm strategies for sharing the load of HVDC converter stations are proposed in the documents Ebrahim Rokrok, Taoufik Qoria, Antoine Bruyere, Bruno Francois, Xavier Guillaud, “Classification and Dynamic Assessment of Droop-Based Grid-Forming Control Schemes: Application in HVDC Systems”, 21st Power Systems Computation Conference, 2020 and Bin Peng, Xin Yin, John Shen, Jun Wang, “Application of Virtual Synchronization Control Strategy in MMC based VSC-HVDC System”, IEEE Transactions on Power Delivery , flight. 29, n° 5, 2014 without however taking into account the complete operation of the HVDC links.

[0010] The document Muhammad Raza, Monica Aragüés Penalba, Oriol Gomis-Bellmunt, “Short circuit analysis of an offshore AC network having multiple grid”, Elsevier, Electrical Power and Energy Systems 102, 2018 considers the HVDC connections in as a whole but only provides for the control in grid forming mode of the converter station of one of the AC systems that they interconnect while the converter station of the second interconnected AC system or the converter stations of the other interconnected AC systems are controlled in grid-feeding mode.

[0011] These documents are based on a conventional operation of an HVDC link in which one of the two converter stations controls the flow of active power in the link while the second converter station balances the HVDC voltage in order to stabilize the flow. of active power in the link.

[0012] The document US2020/335975 A1 relates to a device for adjusting the voltage level of a modular multi-level converter (MMC) to reduce the frequency fluctuation in a power network for which the output level of the MMC converter is adjusted in response to a frequency change in the power network. This device does not seek to pass on variations of the direct current voltage of a converter, line side to direct current, on the frequency of the alternating voltage at the output of this converter on the system side to alternating current.

[0013] In conclusion, current systems with an HDVC VSC link are not intended to make the systems they interconnect synchronous, which does not allow each alternating current network to benefit from the inertia and frequency regulation capacities of the other or other alternating current networks. There is therefore no provision for synchronizing two alternating current systems by a function F for controlling converters arranged in substations on either side of a direct current line.

Summary In view of the foregoing, the present invention relates in particular to a method for decentralized control of converter stations making it possible to make the various alternating current electrical systems interconnected by direct current links such as HVDC VSC links synchronous in order to to improve the stability and frequency behavior of said alternating current electrical systems.

In the context of the present invention, the notion of synchronism between alternating current systems is defined by the capacity of each alternating current system to:

- Participate in the correction of production/consumption imbalances of other alternating current systems without delay linked to the response times of the regulation loops and the acquisition times of the various measurements.

- Stabilize its own production/consumption imbalances and therefore its electrical frequency by indiscriminately using its own primary reserve to adjust its frequency as well as the primary reserves of other alternating current electrical systems.

The present invention thus relates more particularly to a method for controlling bidirectional alternating current/direct current converters, substations connecting a first alternating current system provided with at least one first alternating current generator and/or at least a first load, to at least one second alternating current system, comprising at least one second alternating current generator and/or at least one second load, through a direct current line, for which the control of each of said converters is carried out in voltage source mode (in English grid forming), with an algorithm for vector control of the amplitude and the angle of the alternating voltage of each converter, on the alternating current system side, and comprises a control function F of said converters, or control rule, of the active power load sharing type between each substation of the direct current line and its system e to alternating current, said function providing a frequency of said alternating voltage used by said vector control of said converters for calculating said angle of said alternating voltage.

The control function allows, unlike the systems of the prior art, voltage and frequency regulation of the systems connected by the direct current line through this direct current line.

Preferably, said control function F is such that the electrical frequency f _vsc . of said alternating voltage at the output of a said converter /, on the alternating current system side, is a function of the direct voltage U _DCvsc at the output of said converter /, on the side direct current line, so that variations in the direct current voltage at the output of said converter /, on the direct current line side, are reflected in the frequency of the alternating voltage at the output of this converter, on the alternating current system side.

[0019] The vector control algorithm may comprise an alternating voltage regulation with alternating current loop provided with a function of limiting the alternating current to a limit value. This allows the converter to operate as a voltage source while protecting it in the event of excessive current inrush.

The vector control algorithm can be a virtual synchronous machine type algorithm, said control function F modulating the electrical frequency of the bidirectional converters on the alternating current side. This amounts to having the control function superimposed on the vector control to carry out a transfer of power through the direct current line.

According to a particular embodiment, the control function F, or control rule, is a function linking the frequency of the current alternating current f _vsc . at the current DC voltage U _DCvsc of the form:

[0022] [Math. 1]

With f _vsc . the frequency of the converter /, U _DCvsc the voltage of the converter / at a given instant and f _vsc ni . and U _DCvvr and K _vsc i. respectively the nominal frequency, the nominal DC voltage and the adjustment gain of the algorithm for each converter /.

[0023] The adjustment gain can be directly implemented at the level of local computers controlling said converters.

[0024] Said adjustment gain can also be set at the level of a computer remote from a control center controlling said substations and transmitted to the bidirectional converters of said substations through a computer network connecting said remote computer to local computers controlling said converters according to operating parameters of the systems connected to said substations.

This can be done when setting up the line and/or makes it possible to adapt the gain in the event of a change in the configuration of one or more systems.

[0026] The control of the power transit in said direct current line can be carried out at the level of the means of production and storage of each of the alternating current systems interconnected via their conventional regulations of active power and of frequency so that the implementation of said method does not require modification of the active power regulation and of the primary frequency adjustment regulation of said production and storage means.

The direct current line is advantageously a line of the HDVC (high voltage direct current link) type connecting at least two alternating current electrical systems.

The invention further relates to a computer program comprising instructions for implementing the method of the invention when this program is executed by a processor.

The invention further relates to a non-transitory recording medium readable by a computer on which is recorded a program for the implementation of the method of the invention when this program is executed by a processor.

The invention further relates to a mixed alternating current / direct current electrical network comprising at least one HVDC line (high voltage direct current link) connecting at least two alternating current systems through converter stations provided with bidirectional converters alternating current/direct current, for which the converters of said converter stations are controlled according to the method of the invention.

Brief description of the drawings

[0031] Other characteristics, details and advantages will appear on reading the detailed description below, and on analyzing the appended drawings, in which:

[0032] [Fig. 1] shows a simplified diagram of an HDVC link and its converters according to the prior art.

[0033] [Fig. 2] shows a simplified diagram of an HDVC link and its converters according to the invention.

[0034] [Fig. 3] shows a simplified diagram of a case study for the invention.

[0035] [Fig. 4] shows a model of a network with two alternating current systems connected by a serial link;

[0036] [Fig. 5] shows a DC line voltage curve;

[0037] [Fig. 6] shows an active power sharing curve;

[0038] [Fig. 7] shows a frequency curve of a first system;

[0039] [Fig. 8] shows an active power sharing curve of the first system; [0040] [Fig. 9] shows a DC line voltage curve;

[0041] [Fig. 10] shows a frequency curve of the second system;

[0042] [Fig. 11] shows an active power sharing curve of the first system;

[0043] [Fig. 12] shows a frequency curve of the second system;

[0044] [Fig. 13] shows a frequency curve of the first system;

[0045] [Fig. 14] shows an active power sharing curve of the first system;

[0046] [Fig. 15] shows a DC line voltage curve;

[0047] [Fig. 16] shows a frequency curve of the second system;

[0048] [Fig. 17] shows an active power sharing curve of the second system.

Figure 1 shows a traditional schematic example of an HDVC link 1 and bidirectional converters 2a, 2b of substations at its ends between alternating current systems S1 and S2. The converters comprise an input transformer 3a, 3b receiving an alternating voltage U1, U2, an alternating current filter 5a, 5b and a choke 6a, 6b, as well as a bidirectional conversion module 4a, 4b. Each converter is controlled by a local computer 7a, 7b. The converters include a DC bus with capacitors 61a, 61b, 62a, 62b which regulate the DC line voltage and act as a power buffer.

According to the prior art, the computers control the converters in GFE current source mode ("grid feeding" in English) or control one converter in GFE current source mode and the other in GFO voltage source mode (" grid forming” in English).

FIG. 2 represents a simplified example of an HDVC link and of converters according to the invention where the computers 71a, 71b drive the converters in GFO voltage source mode with a regulation function as will be described below.

In FIG. 3 are represented simplified systems AC1 and AC2 each comprising a generator and a load and connected to the ends of a direct current line HDVC 1 .

A first system AC1 comprises a generator G1 10a of the rotating machine or energy source type with a converter in GFO voltage source mode, for example of the virtual rotating machine type, a load L1 11 has inductive links X _Gi 12a and Xvsci 13a representing connection lines and the VSC1 converter 2a. A second AC2 system comprises a generator unit G2 10a of the rotating machine or energy source type with a converter in GFO voltage source mode, for example of the virtual rotating machine type, a load L2 11a, inductive links X _G 2 12b and Xvsœ 13b and the VSC2 2a converter.

Each bidirectional converter is controlled by a vector control of the alternating voltage of these converters but, in the context of the invention, the converter is controlled in GFO voltage source mode and a function F, for controlling the converter linking the electrical frequency fvsa of the alternating current of said alternating current system side converter at a voltage Uocvs (here fvsci function of UDCI and fvs > function of UDCS) of said HDVC line side converter is implemented as an overlay of said vector control. Therefore, the electrical frequency of said alternating current on the alternating current system side is related to the variations of the direct current voltage at the level of the direct current side output of the corresponding converter.

The function F or control rule reads:

[Math. 2]

and corresponds to a family of load sharing algorithms with fvsa the electrical frequency of each converter station on the AC side, Uocvsa the voltage of each converter station on the DC side and F the function linking fvsa to Uocvsa-

An example of a particular control rule in the form of a simple function F applicable to the invention is then:

[Math. 3]

With fvscm, Uocvscm and Kvsa respectively the nominal frequency, the nominal DC voltage and the algorithm adjustment gain for each converter station.

Contrary to the embodiments of the prior art, in the present invention none of the converter stations explicitly regulates the transit of power in the HVDC link. This regulation is implicitly entrusted to the energy sources, production groups and storage systems of each of the interconnected AC systems, by means of their conventional active power and frequency regulations. Also the present invention does not require modifying the active power regulation and the primary frequency adjustment of the existing production and storage means. The effects of the invention are illustrated below by the behavior of the systems schematized according to FIG. 2 during various events.

The events illustrating the operation of the systems according to the precedent of the invention are:

[0061] A - Event no. 1: modification of the power setpoints of G1 and G2.

For example, the active power setpoint of the generator group G1 is increased by a value P _cons and the active power of the generator group G2 is reduced by this same value.

The setpoint increase of G1 induces an increase in its real or virtual mechanical power via the process of controlling the primary source of the generator set G1 while the setpoint decrease in G2 induces a decrease in its real or virtual mechanical power. virtual through the process of controlling the primary source of the group G2

This results in an imbalance of the equations of the rotating masses of the two groups which results in a progressive increase in the frequency of the group G1 as well as a progressive decrease in the frequency of the group G2 from the equation of the rotating masses :

[0065] [Math. 4]

a) _m (rad.s ^-1 ): the mechanical rotation speed

J (kg.m ² ): the moment of inertia

P _m ( ) ^: the mechanical power

P _e (V/): the electrical power of the linearized rotating masses:

And the inertia constant of a production group:

[Math. 6] ^{H =} -

With :

H (s), f (Hz): the electrical frequency, a) _n (rad. s ^-1 ): the nominal mechanical rotation speed, S _n (V4): the nominal apparent power, f _n (Hz): the rated electrical frequency.

There is then a variation in the frequencies of the generators in response to the change in setpoint.

[0068] Secondly, there is a modification of the active power sharing in each alternating current system.

We will call the voltage angle the phase angle of the voltages.

The progressive variations of the frequencies f _G1 and f _G2 respectively induce an increase in the angle 0 _Gi of the voltage UGI and a decrease in the angle 0G2 of the voltage UG2 according to the equation:

[Math. 7]

whereas the Qvsci and Ôysc2 angles at the converter stations have not yet changed at this stage.

This results in a new sharing of the active power between the generators and the converter stations according to the equations:

[Math. 8]

which governs the supply of active power by the production group G1 and;

[Math. 9]

which governs the supply of active power by the converter station VSC1 (importing agreement), with:

[0072] P _G1 (W), P _VSC1 (IV), U _G1 (V), U _VSC1 (V), I _L1 (A): the rms voltages between phases of the group G1 and of the converter station VSC1 as well as the rms value of the current of the load L1 and 9 _G1 (rad), 9 _vscl (rad') and y _L1 (rad): the angles of the voltages of the group G1 and of the converter station VSC1 as well as the angle of the current read of the load L1 .

These equations are also valid for the second alternating current system by replacing the indices 1 by indices 2.

In this case we have increasing P _G1 , decreasing Pvsci (importer convention), decreasing PG2 and increasing Pvsc2 The increase in P _G1 is in fact instantly reflected by an equivalent decrease in Pvsci and therefore in the import (or a increase in export depending on the initial operating point) while the drop in P _G2 instantly translates into an equivalent increase in Pvsc2 and therefore in import (or a drop in export depending on the initial operating point ).

Then, the complete system stabilizes at the new operating point:

[0076] Variations in the AC active powers of the converter stations are instantly reflected on the DC side and result in an energy charge of the DC bus capacitors of the station in zone 1 and therefore a gradual increase in UDCI and vice versa for the station. of area 2:

[Math. 10]

This gradually results in an increase in the PDC active power transmitted by the HVDC line from zone 1 to zone 2:

[Math. 13]

With P _DC12 (V ), t/ _DC1 (7) and U _DC2 (y) the output voltages of converter stations 1 and 2 on the DC side, R _DC (H): the equivalent resistance of the DC line. The load sharing algorithm for each station according to the equation of the present invention will pass on these changes to their electrical frequency:

[Math. 14]

[Math. 15] dfvsc2 _< Q dt which will gradually reduce then stabilize the phase angle difference between the groups and the converter stations so that PGi=PGiref, PG2=PG2ref-

The primary adjustment term contained in P _G iref and PG2ref:

[Math. 16]

Pref = P ₀ ~ Kàf then allows the global system to stabilize.

[0079] B - Event no. 2: loss of production group G1:

The event is for example a decoupling of G1 in the event of export from system n°1 to system n°2.

The first step is a modification of the active power sharing in the first system. As the G1 group is no longer connected to the network and the L1 load remains generally constant, all of this load is instantly taken over by the VSC1 station. The expression for the active power of the station VSC1 on the alternating current side can be reduced by the equation Math. 9 above to the simplified expression below:

[Math. 17]

The second step is a modification of the power transit on the HVDC link. The power variation of the VSC1 station is supplied in the first moments by its reserve of electrostatic energy, the capacitors 61 a, 52a of figure 1 which causes a rapid drop in the voltage UDCI:

[Math. 18]

2HS _n dU _DC

77~' HVDC AC Equation of a capacitor on a DC bus (in power) linearized.

In this case we have:

[Math. 19]

voltage UDC2 has not yet changed, a gradual drop in the flow of active power PDCI2 takes place until system no. 1 is imported from system no. 2: PDCI2<0.

The third step is stabilization of the complete system at the new operating point.

In system no. 2, it is first of all the capacitors 61b, 62b of station 2 which will gradually discharge to participate in supplying the new power flow PDCI2. In doing so, the UDC2 voltage will also drop according to the power equation of a capacitor on a linearized DC bus:

[Math. 20]

which will contribute to supplying the load of system n°1.

The VSC2 station load sharing algorithm corresponding to the present invention will then pass on this drop to its electrical frequency:

[Math. 21] dfvscz _< Q dt

This change in frequency will cause a gradual drop in the voltage angle of the station VSC2 according to the equation

[Math. 21]

vis-à-vis that of the group G2 leading to a recovery of the active power of VSC2 by G2 according to the equations:

[Math. 22]

and

[Math. 23]

until you find a balance point thanks to G2's frequency tuning algorithm

[Math. 24]

Pref = P ₀ ~ Kaf.

The operation of the invention is illustrated by digital simulation. Three case studies were modeled and simulated with the “Powerfactory” software from Digsilent GmbH version 2020 SP2A:

[0090] Case study no. 1: conventional AC systems - each system is supplied by a conventional production group.

[0091] Case study no. 2: 100% power electronic AC systems: each system is powered by a BESS-type source.

[0092] Case study no. 3: 100% power electronic AC systems operating with two different nominal frequencies: each system is powered by a BESS-type source, system no. 1 has a nominal frequency of 50 Hz while system n°2 has a nominal frequency of 60 Hz.

The results presented below come from dynamic RMS simulations, consequently the phenomena observed correspond to the equations developed above.

[0094] Case study n°1: conventional AC systems - each system is supplied by a conventional production group

The global view of the “Powerfactory” model of case study number 1 is given in figure 4.

The alternating current systems AC1 and AC2 each comprise a generator 211, 212, a first medium voltage alternating current line 221, 222 a medium voltage to high voltage transformer 231, 232, a high voltage line 241, 242 supplying a load 251, 252, a high voltage transformer 261, 262 a high voltage line 271, 272 connecting with a bidirectional AC/DC converter of a converter station 281, 282 and are connected together by the HDVC line 30 between the converter stations.

[0097] Capacitors 291, 292 are connected to both ends of the HDVC line.

[0098] The data of lines, transformers and DC filter capacitors of the simulation test are as follows.

The AC lines 221 and 222 are 33 kV lines with a resistance of 0.047 Ohm for 1 km, an inductance of 0.34 mH for 1 km and a capacitance of 0.3 pF for 1 km.

The AC lines 241 and 242 are 150 kV lines with a resistance of 0.06 Ohm for 1 km, an inductance of 0.44 mH for 1 km and a capacitance of 0.14 pF for 1 km.

The transformers 231 and 232 are 33/150 kV transformers with, at the high voltage level, a resistance of 0.79 Ohm and an inductance of 42.13 mH.

The production groups 211 and 212 are identical and have a nominal apparent power of 100 MVA and an inertia constant of 5s.

The converter stations are modeled using the import convention.

The loads L1 and L2 are modeled in the form of constant powers.

The continuous line is a line of ± 150 kV with a resistance of 0.019 Ohm per km and an inductance of 0.1 pH per km.

[0106] The transformers 261, 262 are 150/110 kV transformers with a high voltage level with a resistance of 0.241 Ohm, an inductance of 76.74 mH.

The capacitors 291, 292 are 400 pF capacitors.

The nominal voltages between phases for the AC part and between poles for the DC part of the overall system are as follows:

[0109] [Table 1]

[0110] The primary adjustment algorithm for the production groups and the active power sharing algorithms for the converter stations have been configured as follows: [0111] [Table 2]

The coefficient K will be calculated according to the acceptable deviation of the voltage of the HVDC line and an acceptable deviation in frequency in the event of a dimensioning incident. The maximum frequency deviation and the maximum voltage deviation depend on the grid policy and the dimensioning incident. For example, 200 mHz/30 kV is chosen here. This coefficient can be adapted as needed.

The simulation performed includes the following events:

A: t=10 s: 50% increase in L1 load;

B: t=30 s: increase in the active power setpoint of G1 in the form of a step;

C: t=50 s: the circuit breaker of G1 n°1 opens.

[0114] A: t=10 s: 50% increase in load L1:

A new sharing of the active power of the load L1 251 in the system AC1 is first observed. This new sharing translates for the VSC1 281 converter station into an instantaneous reduction in its export. Before the import of the VSC2 282 converter station decreases, the decrease in the export of VSC1 is first of all fully compensated by the equivalent capacitor Cdc1 291 then shared between the capacitors Cdc1 291 and Cdc2 292. The discharge in electrostatic energy of the capacitors Cdc1 and Cdc2 leads to a drop in the DC voltages of the converter stations VSC1 and VSC2 as shown in figure 5.

The conversion station load sharing algorithm transfers these DC voltage drops to the frequencies of the converters of the VSC 1281 and VSC 2282 converter stations.

At the level of the AC2 system, the fall in the frequency of the converter of the station VSC2 281 leads to a progressive reduction in the angle of the voltage of the converter of the converter station VSC2 282 compared to the angle of the voltage of the generator G2 212 as well as a progressive increase in the power supplied by generator G2 thanks to the phenomenon of synchronizing power as represented in FIG. 6 representing the powers at the level of VSC2 and of G2. The frequencies of the generators G1 and G2 and of the stations VSC1 and VSC2 are then stabilized by the primary frequency adjustment algorithm of the generators G1 and G2.

[0119] B: t=30 s: increase in the active power setpoint of generator G1 211 in the form of a setpoint step:

It can be seen in Figure 7 that the active power setpoint step of G1 results in a gradual increase in its frequency up to about 32 seconds via the action of its turbine regulation and its equation of the rotating masses. This frequency modification will lead to a gradual increase in the angle of the voltage of G1 211 with respect to the converter station VSC1 281 and thus respectively increase the active power supplied by G1 and exported by the converter station VSC1 as represented in figure 8.

As for the previous event, it is initially the capacitors Cdc1 and Cdc2 which will compensate for the production/consumption imbalance of the AC1 system by charging, which will increase the HVDC voltages of the VSC1 and VSC2 stations as represented in figure 9.

[0122] The increase in the HVDC voltage of the VSC2 station will also increase its electrical frequency thanks to its active power sharing algorithm and thus gradually increase the angle of its voltage compared to the angle of the voltage of the generator G2 and thus increase the import of the VSC 2 station while reducing the active power supplied by G2.

As for the previous event, the primary setting of generators G1 and G2 will stabilize the frequency of the two AC systems as shown in Figure 10 for system G2, VSC2.

[0124] C: t=50 s: the G1 circuit breaker opens:

[0125] The disconnection of G1 leads to a complete and instantaneous resumption of the power supply of the load L1 by the station VSC1 which was initially exporting and therefore becomes importing as represented in figure 11 .

The active power enabling station VSC1 to supply L1 is initially supplied by capacitor Cdc 1 then shared between Cdc 1 and Cdc 2, which causes a drop in the HVDC voltages of stations VSC1 and VSC2.

[0127] The load sharing algorithm of the VSC2 station affects its HVDC voltage drop on its frequency and this frequency drop gradually causes a drop in the angle of the voltage of VSC2 with respect to the angle of the voltage of G2 as well as a gradual recovery of the active power of the station VSC2 by G2.

The primary frequency adjustment algorithm of G2 alone makes it possible to stabilize the frequencies of the AC2 system as represented in FIG. 12 as well as of the AC1 system as represented in FIG. 13. The AC1 system is then regulated in voltage and frequency only by the VSC1 station since G1 is disconnected from the AC1 system which no longer has a local energy source.

[0129] Case study no. 2: 100% electronic power system

In this case study, the groups G1 and G2 are replaced by battery energy storage systems (BESS for BATTERY ENERGY STORAGE SYSTEM in English) in grid forming mode with an active power sharing algorithm of droop control type following:

[0131] [Math. 25]

[0132] f _BE ss ⁼ fn fP [?ref ~ ^fiESs]

[0133] with:

f _B Ess (Hz): the frequency of each battery storage system;

f _n (Hz): the nominal frequency of each battery storage system;

Pref (MW): the active power setpoint of each battery storage system;

P BESS (MW): the active power injected by each battery storage system;

Kf _P (Hz/MW): the adjustment gain of the active power sharing algorithm which has been set at 0.01 Hz/MW.

[0139] The equations:

[0140] [Math. 26]

UGI ⁼ U _Glref ; U _G2 = U _G2ref ; U _VSC1 = U vsci _ref JU _VSC2 = U vsc2 _ref

[0141] [Math. 27]

[0142] Remain valid by replacing the indices G by BESS, likewise it is necessary to replace G1 and G2 by BESS1 and BESS2 in figure 4. The simulation performed includes the following events:

D: t=1 s 50% increase in L1 load;

E: t=2 s the BESS 1 active power setpoint changes from 40 MW to 50 MW in the form of a step;

F: t=5 s the BESS 1 circuit breaker opens.

[0144] D: t=1 s: 50% increase in load L1:

A new sharing of the active power of load L1 in system no. 1 is first observed. This new sharing represented in FIG. 14 results for the station VSC1 in an instantaneous reduction in its export.

The reduction in the export of VSC1 is first of all supplied entirely by the equivalent capacitor Cdc1 then shared between Cdc1 and Cdc2. The electrostatic energy discharge of capacitors Cdc1 and Cdc2 leads to a drop in the associated DC voltages represented in figure 15. The import of the VSC2 station has not yet decreased at this time.

The conversion station load sharing algorithm transfers these DC voltage drops to the frequencies of the VSC 1 and VSC 2 converters.

This drop in the frequency of VSC2 leads to a gradual decrease in the angle of the voltage of VSC2 compared to the angle of the voltage of the BESS2 as well as a gradual increase in the power supplied by the BESS2 thanks to the phenomenon of synchronizing power.

The frequencies of the BESS1 and BESS2 and of the stations VSC1 and VSC2 are stabilized by the active power sharing algorithm of the BESS1 and BESS2 which are equivalent in steady state to the primary frequency setting of the groups G1 and G2.

[0150] E: t=2 s: the active power setpoint of the BESS1 changes from 40 MW to 50 MW in the form of a step

It is observed that the active power setpoint step of the BESS1 is translated simultaneously into a step of its frequency by the action of its active power sharing algorithm. This frequency modification will lead to a gradual increase in the angle of the voltage of the BESS1 with respect to the converter station VSC1 as well as an increase in the active power supplied by the BESS1 and exported by the station VSC1. As for the previous event, it is initially the HVDC capacitors which will compensate for the production-consumption imbalance of the AC1 system by charging, which will increase the HVDC voltages of the VSC1 and VSC2 stations.

The increase in the HVDC voltage of the VSC2 station will also increase its electrical frequency thanks to its active power sharing algorithm and thus gradually increase the angle of its voltage compared to the angle of the voltage of the BESS2 as well as the import of the VSC2 station while reducing the active power supplied by the BESS2.

As for the previous event, the primary setting of BESS1 and BESS2 will stabilize the frequency of the two AC systems.

[0155] F: t=5 s: the BESS1 circuit breaker opens

The disconnection of the BESS 1 leads to a complete and instantaneous resumption of the supply of the load L1 by the station VSC1 which was initially exporting.

The power enabling station VSC1 to supply L1 is initially supplied by capacitor Cdc 1 then shared between Cdc 1 and Cdc 2, which causes a drop in the HVDC voltages of stations VSC1 and VSC2.

The VSC2 station load sharing algorithm affects its HVDC voltage drop on its frequency as shown in Figure 16. This frequency drop gradually causes a drop in the voltage angle of VSC2 with respect to -vis the angle of the voltage of the BESS 2 which leads to a gradual increase in the active power of the BESS 2 as shown in figure 17.

The BESS 2 load sharing algorithm alone makes it possible to stabilize the frequencies of the AC2 system as well as of the AC1 system (defined exclusively by the VSC1 station) which no longer has a local energy source.

[0160] Case study no. 3: 100% electronic power system with Hz and

f>n=60Hz:

The present case study no. 3 is identical in all respects to case study no. 2 except that the nominal frequency of the BESS2 and of the VSC station 2 is 60 Hz. The behavior of the system global is also identical to case study 2 with slight time differences related to the change in the nominal frequency of the AC2 system. There is therefore also synchronization of the systems in terms of power sharing despite the different frequencies. Contrary to the prior art, the present invention makes several AC electrical systems interconnected by HVDC VSC links synchronous.

Claims

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Claims

[Claim 1] Method for controlling bidirectional alternating current/direct current converters (2a, 2b), of substations connecting a first alternating current system comprising at least one first alternating current generator (10a) and/or at least one first load (11a), to at least one second alternating current system, comprising at least one second alternating current generator (10b) and/or at least one second load (11b), through a direct current line ( 1), characterized in that the control of each of said converters (2a, 2b) is carried out in voltage source mode (in English grid forming), with a vector control algorithm of the amplitude and the angle of the voltage converter AC, AC system side; and comprises a function F for controlling said converters or control rule, of the active power load sharing type between each substation of the direct current line and its alternating current system, said function providing a frequency of said alternating voltage exploited by said vector control of each of said converters for calculating said angle of said alternating voltage.

[Claim 2] Method for controlling bidirectional converters according to claim 1, for which said control function F is such that the electrical frequency f _vsc . of said alternating voltage at the output of a said converter /, on the alternating current system side, is a function of the direct current voltage U _DCvsc at the output of said converter /, on the direct current line side, so that variations in the direct current voltage at the output of said converter /, on the direct current line side, are reflected in the frequency of the alternating voltage at the output of this converter, on the alternating current system side.

[Claim 3] Method for controlling bidirectional converters according to claim 1 or 2, for which said vector control algorithm comprises an alternating voltage regulation with an alternating current loop provided with a function of limiting the alternating current to a limit value.

[Claim 4] A method of driving bidirectional converters according to claim 1 or 2, for which said vector control algorithm is a virtual synchronous machine type algorithm, said driving function F modulating the electric frequency of the bidirectional converters on the alternating current side.

[Claim 5] Method for controlling bidirectional converters according to any one of the preceding claims, for which the control function F, or control rule, is a function linking the frequency of the current alternating current f _vsc . of a converter / to the current DC voltage U _DCvsc of this converter / of the form:

[Math. 28]

With f _VSCi the frequency of said converter /, U _DCvsc the voltage of said converter / at a given instant and fvsc _ni and ^U DC _VSC ^{and K} vsc _t respectively the nominal frequency, the nominal DC voltage and the adjustment gain of the algorithm for each converter /.

[Claim 6] Method for controlling bidirectional converters according to Claim 5, for which the said adjustment gain is directly implemented at the level of local computers controlling the said converters.

[Claim 7] Method for driving bidirectional converters according to claim 5, for which said adjustment gain is set at the level of a computer remote from a control center controlling said substations and transmitted to the bidirectional converters of said substations through a computer network connecting said remote computer to local computers controlling said converters according to operating parameters of the systems connected to said substations.

[Claim 8] Method for controlling bidirectional converters according to any one of the preceding claims, for which the control of the power transit in the said direct current line is carried out at the level of the means of production and storage of each of the alternating current systems interconnected via their conventional active power and primary frequency adjustment regulations so that the implementation of said method does not require modification of the active power regulation and the primary frequency adjustment regulation of said production and storage means.

[Claim 9] Method for controlling bidirectional converters according to any one of the preceding claims, for which the direct current line is a line of the HDVC type (high voltage direct current link) connecting at least two alternating current electrical systems.

[Claim 10] Computer program comprising instructions for implementing the method according to one of Claims 1 to 9 when this program is executed by a processor. [Claim 11] Non-transitory recording medium readable by a computer on which is recorded a program for implementing the method according to one of Claims 1 to 9 when this program is executed by a processor.

[Claim 12] Mixed alternating current / direct current electrical network comprising at least one HVDC line (high voltage direct current link) connecting at least two alternating current systems through converter stations equipped with bidirectional alternating current / direct current converters, characterized in that the converters of said conversion stations are controlled according to the method of any one of claims 1 to 9.