FR3117707A1 - METHOD FOR CONTROLLING BIDIRECTIONAL ALTERNATING CURRENT / DIRECT CURRENT CONVERTERS FOR THE SYNCHRONIZATION OF ALTERNATING CURRENT ELECTRICAL SYSTEMS CONNECTED TOGETHER BY A DIRECT CURRENT LINK - Google Patents

Abstract

Method for controlling bidirectional alternating current/direct current converters (2a, 2b), substations connecting a first alternating current system provided with 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 alternating voltage of the converter, AC system side; and comprises a function F for controlling said converters, 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 used by said command vector of each of said converters for the calculation of said angle of said alternating voltage. Abstract Figure: Figure 3

Description

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

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

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 the 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 to stabilize the active power flow 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.

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 for 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.

Nevertheless, as described in 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 operational safety 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.

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 remove 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.

Different HVDC converter station load sharing algorithm strategies are proposed in the papers 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, vol. 29, n° 5, 2014 without however taking into account the complete operation of the HVDC links.

The document Muhammad Raza, Mònica Aragüés Peñalba, Oriol Gomis-Bellmunt, “Short circuit analysis of an offshore AC network having multiple grid”, Elsevier, Electrical Power and Energy Systems 102, 2018 does indeed consider HVDC connections 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 mode feeding.

These documents are based on a classic 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.

In conclusion, it is not planned in current systems with HDVC VSC link 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.

Summary

In view of the foregoing, the present invention relates in particular to a process for decentralized control of converter stations making it possible to make synchronous the various alternating current electrical systems interconnected by direct current links such as HVDC VSC links in order to improve the stability and frequency response 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 to 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 one 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 the said converters is carried out by voltage source mode (grid forming in English), with a vector control algorithm for the amplitude and the angle of the alternating voltage of each converter, on the alternating current system side, and comprises a function F for controlling said converters, of the active power load sharing type between each substation of the direct current line and its alternating current system, said e function providing a frequency of said alternating voltage used by said vector control of said converters for the calculation of 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 of said alternating voltage at the output of a said converter i , on the alternating current system side, is a function of the direct voltage at the output of said converter i , line side to direct current, so that variations in the direct current voltage at the output of said converter i , line side to direct current, are reflected in the frequency of the alternating voltage at the output of this converter, system side alternating current.

The vector control algorithm may include an AC voltage regulation with an AC current loop provided with a function of limiting the AC 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 is a function linking the frequency of the current alternating current at the current DC voltage of shape :

With the frequency of the converter i , the voltage of the converter i at a given instant and And And respectively the nominal frequency, the nominal DC voltage and the adjustment gain of the algorithm for each converter i .

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

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 allows the gain to be adapted in the event of a change in the configuration of one or more systems.

The control of the transit of power 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 frequency so that the implementation of said method does not 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 equipped with bidirectional alternating current/direct current converters. direct current, for which the converters of said converter stations are controlled according to the method of the invention.

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

shows a simplified diagram of an HDVC link and its converters according to the prior art.

shows a simplified diagram of an HDVC link and its converters according to the invention.

shows a simplified diagram of a case study for the invention.

shows a model of a network with two alternating current systems connected by a serial link;

shows a DC line voltage curve;

shows an active power sharing curve;

shows a frequency curve of a first system;

shows an active power sharing curve of the first system;

shows a DC line voltage curve;

shows a frequency curve of the second system;

shows an active power sharing curve of the first system;

shows a frequency curve of the second system;

shows a frequency curve of the first system;

shows an active power sharing curve of the first system;

shows a DC line voltage curve;

shows a frequency curve of the second system;

shows an active power sharing curve of the second system.

There shows a traditional schematic example of an HDVC link 1 and substation bi-directional converters 2a, 2b at its ends between AC 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 serve as a power buffer.

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

There 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 are shown 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 voltage source mode GFO, for example of the virtual rotating machine type, a load L1 11a of the inductive links X _G1 12a and X _VSC1 13a representing connection lines and the VSC1 converter 2a.

A second system AC2 comprises a generator group G2 10a of the rotating machine or energy source type with a converter in voltage source mode GFO, for example of the virtual rotating machine type, a load L2 11a, inductive links X _{G 2} 12b and X _{VSC 2} 13b and the VSC2 2a converter.

Each bidirectional converter is controlled by 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 f _VSCi from the alternating current of said alternating current system-side converter to a voltage U _DCVSCi (here f _{VSC 1} function of U _DC1 and f _{VSC 2} function of U _DC2 ) 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 reads: and corresponds to a family of load sharing algorithms with f _VSCi the electrical frequency of each converter station on the AC side, U _DCVSCi the voltage of each converter station on the DC side and F the function linking f _VSCi to U _DCVSCi .

An example of a simple function F applicable to the invention is then: With f _VSCni , U _{DC VSCni} and K _VSCi respectively the nominal frequency, the nominal DC voltage and the adjustment gain of the algorithm for each converter station.

Unlike 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 the at different events.

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

AT - Event n°1: modification of the power setpoints of G1 and G2 .

For example, the active power setpoint of the generator set G1 is increased by a value and the active power of the generator set G2 is lowered by this same value.

The increase in G1 setpoint 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 decrease in G2 setpoint induces a decrease in its real or virtual mechanical power via the process for controlling the primary source of 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:

With : : mechanical rotational speed : the moment of inertia : mechanical power : electric power

The linearized rotating masses equation: And the inertia constant of a production group: With : , : electrical frequency, : the nominal mechanical rotation speed, : nominal apparent power, : the nominal electrical frequency.

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

Secondly, there is a modification of the active power shares in each alternating current system.

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

The progressive variations of the frequencies And respectively induce an increase in the angle θ _G1 of the voltage U _{G 1} and a decrease in the angle θ _G2 of the voltage U _G2 according to the equation: whereas the angles θ _VSC1 and θ _{VSC 2} 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: which governs the supply of active power by the production group G1 and; which governs the supply of active power by the converter station VSC1 (importing agreement), with:

, : 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 , And : the angles of the voltages of the group G1 and of the converter station VSC1 as well as the angle of the current I _L1 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 P _VSC1 (importer agreement), decreasing P _G2 and increasing P _VSC2 The increase in P _G1 is in fact instantly reflected by an equivalent decrease in P _VSC1 and therefore in the import (or an increase in export as a function of the initial operating point) while the drop in P _{G 2} results instantly in an equivalent increase in P _{VSC 2} 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:

Variations in the AC active powers of the converter stations are instantly reflected on the DC side and result in an energy charge on the DC bus capacitors of the station in zone 1 and therefore a gradual increase in U _DC1 and vice versa for the station in zone 1. area 2:

This gradually results in an increase in the active power P _DC transmitted by the HVDC line from zone 1 to zone 2: With , And the output voltages of converter stations 1 and 2 on the DC side, : the equivalent resistance of the DC line.

The algorithm for sharing the load of each station according to the equation of the present invention will pass on these changes to their electrical frequency: which will gradually reduce and then stabilize the phase angle difference between the groups and the converter stations so that P _G1 =P _G1ref , P _G2 =P _G2ref .
The primary adjustment term contained in P _G1ref and P _G2ref : then allows the overall system to stabilize.

B- Event n°2: loss of production group G1 :

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

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 61a, 52a of the which causes a rapid drop in voltage UDC1: Equation of a capacitor on a DC bus (in power) linearized.

In this case we have:

Since the voltage UDC2 has not yet changed, a gradual drop in the transit of active power P _DC12 takes place until system no. 1 is imported from system no. 2: P _DC12 <0.

The third step is a 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 progressively discharge to participate in supplying the new power transit P _DC12 . In doing so, the voltage U _DC2 will also drop according to the power equation of a capacitor on a linearized DC bus: 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:

This change in frequency will cause a gradual drop in the voltage angle of the station VSC2 according to the equation vis-à-vis that of group G2 leading to a recovery of the active power of VSC2 by G2 according to the equations: And until you find a balance point thanks to the frequency adjustment algorithm of G2 .

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:

Case study 1: conventional AC systems - each system is powered by a conventional generator.

Case study n°2: 100% power electronic AC systems: each system is powered by a BESS-type source.

Case study n°3: 100% power electronic AC systems operating with two different nominal frequencies: each system is powered by a BESS type source, system n°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, therefore the observed phenomena correspond to the equations developed above.

Case study 1: conventional AC systems - each system is powered by a conventional generator

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

The AC1 and AC2 alternating current systems 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 for connection 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.

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

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

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 µF for 1 km.

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 µF for 1 km.

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.

Generating sets 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 in import convention.

Loads L1 and L2 are modeled as constant powers.

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

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.

Capacitors 291, 292 are 400 µF capacitors.

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

HVDC link 300kV AC loads 150kV Production groups 15KV AC side converter stations 110kV

The primary control algorithm of the production groups and the active power sharing algorithms of the converter stations have been configured as follows:

Production groups droop 5% Converter stations: 0.167Hz/kV

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 G1 n°1 circuit breaker opens.

AT : t=10 s: 50% increase in load L1:

We first observe a new sharing of the active power of the load L1 251 in the system AC1. 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 from capacitors Cdc1 and Cdc2 causes the DC voltages of converter stations VSC1 and VSC2 to drop as shown in .

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

At the AC2 system level, the fall in the frequency of the VSC2 station converter 281 leads to a gradual decrease in the angle of the voltage of the converter station VSC2 282 compared to the angle of the voltage of the G2 generator 212 as well as a progressive increase in the power supplied by the generator G2 thanks to the phenomenon of synchronizing power as represented in representing the powers at VSC2 and G2.

The frequencies of the generators G1 and G2 and of the stations VSC1 and VSC2 are then stabilized by the primary frequency tuning algorithm of the generators G1 and G2.

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

We observe in that the active power setpoint step of G1 results in a progressive 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 .

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 shown in .

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 with the previous event, the primary setting of generators G1 and G2 will stabilize the frequency of both AC systems as shown in for the G2 system, VSC2.

VS : t=50 s: the G1 circuit breaker opens:

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 .

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 leads to a drop in the HVDC voltages of stations VSC1 and VSC2.

The load sharing algorithm of the VSC2 station reflects its HVDC voltage drop on its frequency and this frequency drop gradually causes the angle of the VSC2 voltage to drop 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.

G2's primary frequency tuning algorithm alone stabilizes the frequencies of the AC2 system as shown in as well as the AC1 system as shown in . 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.

Case study n°2: 100% electronic power system

In this case study, 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 algorithm for sharing active power of the control type by droop control) following:

with :

f _BESS (Hz): the frequency of each battery;

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

P _ref (MW): the active power setpoint of each battery;

P _BESS (MW): the active power injected by each battery;

K _fP (Hz/MW): the tuning gain of the active power sharing algorithm which has been set to 0.01 Hz/MW.

The equations:

Remain valid by replacing the indices G by BESS, in the same way it is necessary to replace G1 and G2 by BESS1 and BESS2 in the .

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.

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

We first observe a new sharing of the active power of the load L1 in the system n°1. This new division represented in results for the VSC1 station 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 discharge of electrostatic energy from capacitors Cdc1 and Cdc2 leads to a drop in the associated DC voltages shown in . The import of the VSC2 station has not yet decreased at this time.

The load sharing algorithm of the converter stations 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 progressive decrease in the angle of the voltage of VSC2 compared to the angle of the voltage of the BESS2 as well as a progressive increase in the power supplied by the BESS2 thanks to the phenomenon of synchronizing power.

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

E : t=2 s: the active power setpoint of the BESS1 changes from 40 MW to 50 MW as a step

It can be seen that the active power setpoint step of the BESS1 is simultaneously translated 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 voltage angle 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.

Raising 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 than importing the VSC2 station while reducing the active power supplied by the BESS2.

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

F: t=5 s: BESS1 circuit breaker opens

The disconnection of the BESS 1 results in a complete and instantaneous resumption of the supply of the load L1 by the VSC1 station 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 leads to a drop in the HVDC voltages of stations VSC1 and VSC2.

The VSC2 station's load sharing algorithm reflects its HVDC voltage drop on its frequency as shown in . This frequency drop gradually causes a drop in the voltage angle of VSC2 with respect to the voltage angle of the BESS 2 which causes a gradual increase in the active power of the BESS 2 as shown in .

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

Case study n°3: 100% electronic power system with f _1n =50Hz and f _2n =60Hz:

This case study n°3 is identical in all respects to case study n°2 except that the nominal frequency of the BESS2 and the VSC station 2 is 60 Hz. The behavior of the overall system is also identical to case study n°2 with slight time differences linked 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 synchronous several AC electrical systems interconnected by HVDC VSC links.

Claims (12)

Method for controlling bidirectional alternating current/direct current converters (2a, 2b), substations connecting a first alternating current system provided with 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 alternating voltage of the converter, system side to alternating current; and comprises a function F for controlling said converters, 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 used by said command vector of each of said converters for calculating said angle of said alternating voltage. Method for controlling bidirectional converters according to claim 1, for which said control function F is such that the electrical frequency of said alternating voltage at the output of a said converter i , on the alternating current system side, is a function of the direct voltage at the output of said converter i , line side to direct current, so that variations in the direct current voltage at the output of said converter i , line side to direct current, are reflected in the frequency of the alternating voltage at the output of this converter, system side alternating current. 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. Method for 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. Method for controlling bidirectional converters according to any one of the preceding claims, for which the control function F is a function linking the frequency of the current alternating current at the current DC voltage of shape :

With the frequency of the converter i , the voltage of the converter i at a given instant and And And respectively the nominal frequency, the nominal DC voltage and the adjustment gain of the algorithm for each converter i . Method for controlling bidirectional converters according to claim 5, for which said adjustment gain is directly implemented at the level of local computers controlling said converters. Method for controlling 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. Method for controlling bidirectional converters according to any one of the preceding claims, for which the control of the transit of power 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 regulations conventional active power and frequency 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. 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. Computer program comprising instructions for implementing the method according to one of Claims 1 to 9 when this program is executed by a processor. 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. 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 converter stations are controlled according to the method of any one of claims 1 to 9.