R Ramachandran
email: ragavendran.ramachandran@supergrid-institute.com

S Poullain
email: serge.poullain@supergrid-institute.com

A Benchaib

Seddik Bacha
email: seddik.bacha@g2elab.grenoble-inp.fr

Bruno François

Bruno Francois
email: bruno.francois@centralelille.fr

AC Grid Forming by Coordinated Control of Offshore Wind Farm connected to Diode Rectifier based HVDC Link-Review and Assessment of Solutions

Keywords: Wind energy, Wind generator systems, Generation of electrical energy, Power management, HVDC

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

With the current pace of Offshore Wind Farm (OWF) development, cumulative installed capacity in Europe could be more than 49 GW by 2030 and considering certain positive scenarios [START_REF]Wind-energy-in-Europe-Scenarios-for-2030[END_REF], it might even become 98 GW by 2030. Wind farms over long distances are generally connected through HVDC transmission to the AC grid. The VSC (Voltage Source Converter) is the preferred converter technology over LCC (Line Commuted Converter) for HVDC offshore transmission applications due to various advantages [START_REF] Cigre | TB 619 2015 HVDC Connection of Offshore Wind Farms -Cigre[END_REF] like avoidance of harmonic filters and reactive power sources, black start capability, ability to use XPLE cables etc.

The VSC technology used extensively today for grid integration of distant OWFs is the MMC (Modular Multilevel Converter) HVDC. The relevant wind generator types today for HVDC based OWFs are Type 3 or DFIG (Doubly Fed Induction Generator) and Type 4 or FSC (Full Scale Converter) coupled generators [START_REF] Siemens | 2nd Generation DC grid Access for Large Scale Offshore Wind Farms[END_REF]. The latter technology is prominent in the case of larger wind turbines (capacity greater than 5 MW). The offshore AC grid voltage and frequency is controlled by the offshore VSC converter in this architecture. This VSC operates in grid forming mode, while the wind generators inject power into the established AC grid, in turn operating in grid following mode. The capital cost, foot print and control complexities of the MMC based HVDC transmission technology have always been matters of great concern in driving the offshore projects forward.

The introduction of Diode Rectifier (DR) as the offshore converter for HVDC transmission or the DR-HVDC is advantageous in terms of reduction of costs, foot print and losses [START_REF] Kouassi | AC Offshore Grid Forming of a Collection Network for Wind Park by Considering Storage and Hybrid Power Electronic Systems[END_REF]. But, newer challenges arise, for instance, the control of the offshore AC grid voltage and frequency, synchronization of WEGs etc., among others. In case of DR-HVDC based OWF, the HVDC voltage is controlled by the onshore VSC and thus the DR output DC voltage must surpass this aforementioned voltage to allow conduction and transfer of power to the onshore station. This functionality can be enabled either by changes in the architecture to have a start-up power supply with external synchronization mechanism, or by using offshore storage system for energization [START_REF] Kouassi | AC Offshore Grid Forming of a Collection Network for Wind Park by Considering Storage and Hybrid Power Electronic Systems[END_REF] and / or by modifying the control algorithms of the wind electric generators (WEGs) to tap their inherent grid forming capabilities. Another interesting approach is to employ an offshore VSC in series (on the DC side) with the DR, to exploit the grid forming capability of this VSC [START_REF] Nguyen | A Series-Connected Topology of a Diode Rectifier and a Voltage-Source Converter for an HVDC Transmission System[END_REF] thus permitting the WEGs to retain their grid following control scheme (or current control scheme). Additionally, the offshore VSC can act as an active filter, targeting the characteristic harmonics pertaining to the DR.

The Fig. 1 shows the electrical architecture of the DR-HVDC based OWF. Multiple WEGs are connected in strings to form clusters. Multiple clusters are integrated at the Point of common coupling (PCC) with reactive power compensation (capacitance bank Cg) and harmonic filters (denoted as Zg). The collection network until PCC is generally at Medium Voltage level (66 kV). Then the DR transformer steps up the voltage to the desired value and this transformer can be of different configurations (two winding or three winding with zig zag connections for necessary phase shifts in the secondary windings) depending on the HVDC system voltage design and the use of 12 or 24 pulse DRUs (Diode Rectifier Units). Additional equipment for start-up could be included as part of the network, for instance additional energy storage near DRU stations or at WEGs, AC umbilical cables (indicated in the figure) etc. This paper reviews in general, some of major solutions ([6]- [START_REF] Yu | Distributed PLL-based Control of Offshore Wind Turbine Connected with Diode-Rectifier based HVDC Systems[END_REF]) tackling the control related challenges of the DR-HVDC OWF and then compares the architectural changes and converter control strategies implemented to achieve grid integration of offshore wind energy. A comprehensive comparison is made among these three solutions, in order to present clearly, the differences in their approaches. Then two of the solutions ([6], [START_REF] Prignitz | FixReF: A control strategy for offshore wind farms with different wind turbine types and diode rectifier HVDC transmission[END_REF]) are implemented in a selected study case electrical architecture and the results show how these solutions achieve the control and power management goals. By using simulation results, further analyses and comparison are presented. The major challenges that have been solved and that continue to persist are highlighted.

Control Solutions for AC Grid Forming in the DR-HVDC based OWF Solution 1 -Distributed Voltage and Frequency Control

The solution 1 ([6], [START_REF] Prignitz | FixReF: A control strategy for offshore wind farms with different wind turbine types and diode rectifier HVDC transmission[END_REF]) was initially proposed with an LCC based HVDC converter onshore, while a later work showed successful implementation using a VSC HVDC converter model onshore [START_REF] Bernal-Perez | Off-shore wind farm grid connection using a novel diode-rectifier and VSC-inverter based HVDC transmission link[END_REF]. This solution proposes changes in the control of the WEG converters (considering only type 4 generators) in order to provide grid forming capability to the GSCs (Grid Side Converters). The onshore VSC converter control functions are not especially modified, meaning its primary function is the control of the HVDC

FIXREF

Signal System link voltage. The voltage control at the offshore PCC is achieved by setting appropriate d-axis current reference of the GSC, taking advantage of the dynamic coupling between voltage and active power. The frequency control is achieved using appropriate setting of the q-axis current of the GSC, thanks to the dynamic coupling between frequency and reactive power. This type of control scheme has been well demonstrated in works like [START_REF] Gierschner | Fixed-reference-frame-control: A novel robust control concept for grid side inverters in HVDC connected weak offshore grids[END_REF], related to converter interfaced micro grids with a prominent capacitance in the network PCC.

A single aggregated grid forming WEG connected to the Point of Common Coupling (PCC) is shown in the Fig. 2 (a). The DC bus voltage (V dc ) of the back to back converter interface is controlled by the MSC, while the GSCs are involved in controlling the voltage and frequency at the offshore capacitance bus, which is the PCC. Once the AC grid is formed and DR starts conducting, the voltage control loop becomes saturated and in-turn irrelevant. Then, the GSC begins to perform the maximum power point tracking (MPPT) by dynamically setting the limit of the d-axis current, according to the necessary power set point. This along with the pitch control of the wind turbine, ensures optimal power extraction for all wind speeds below rated speed and rated power production above the rated wind speed.

(a) (b) In case of multiple WEGs, their GSCs divide the grid forming responsibility using participation coefficients. These participation coefficients are calculated according to the equation ( 1) for each wind generator in a wind farm with a total of J wind turbines. The integrator part of PI controller for AC voltage control is centralized while the proportional parts of the controllers are distributed across the GSCs as shown in Fig. 2 (b). Thus all GSCs are operating in grid forming mode.

= ℎ ! " ′$′ % & ' '( ) ℎ *+, ℎ - = 1 / 01 (1)
This solution doesn't provide details of how exactly the synchronization is achieved among the WEGs. Also there is a requirement of measuring and communicating the AC voltage at PCC to all the WEGs.

Solution 2 -Grid Forming by Fixed Reference frame and AC Umbilical Cable

This solution has been proposed for both type 3 and type 4 generators [START_REF] Prignitz | FixReF: A control strategy for offshore wind farms with different wind turbine types and diode rectifier HVDC transmission[END_REF]. This solution provides the WEGs with grid forming capability while enabling the GSCs to retain the conventional current control scheme (DC bus voltage control). This is done by providing a fixed reference frame in dq (and thus the name FIXREF) for all GSCs, using GPS / radio signal, to have high accuracy. The conventional closed loop current control is modified into an open loop system with the removal of the PLL and use of the external angle by all the GSCs. Theoretically, instability problems cannot occur in this open loop scheme for synchronization [START_REF] Gierschner | Fixed-reference-frame-control: A novel robust control concept for grid side inverters in HVDC connected weak offshore grids[END_REF]. The control scheme for a single WEG is shown in Fig. 3.

Grid Forming Control 690 V / 66 kV Y V CD * V CD F AC Voltage Control w C * w C F Frequency Control PolarRec i PQ * 1 i PDQ * R CST U /i PDQ F Current Control V VWX * V, f Control GSC C C d dt V DQ * PCC R \ / ] ]_ ] RS DC Voltage Control MSC K Xc i PD * abc αβ w C F g C F g C F _ h _ i j ω l ] _SUmn opp% R _ P q * abc dq K Xc I sD F V CD * V CD F K tD s K cD V CD * V CD F I PDv * w(x (yz p ( " & h { " &(| ]" ! & h I PQv * w C F w C
The start-up / black start of the network is provided by additional equipment in the offshore grid architecture. A Medium voltage AC (MVAC) cable with an AC/AC converter from onshore grid is connected to the offshore PCC, as indicated in Fig. 1. This allows provision of auxiliary power supply for energizing the transformers, charging cables, powering up DFIGs (if part of the OWF) and supporting losses during the OWF start-up [START_REF] Prignitz | FixReF: A control strategy for offshore wind farms with different wind turbine types and diode rectifier HVDC transmission[END_REF]. This converter also uses the same FIXREF signal for start-up. A droop factor (k q ) is introduced in the control scheme for reactive power sharing among the GSCs as shown in Fig. 3. For a particular WEG, this droop factor can be set such that the WEG with lower active power production participates more in reactive power contribution than the one with higher active power production.

This solution relies on the availability of a robust communication network (GPS / radio based) in order to transmit the FIXREF angle in real time to all the GSCs, to ensure synchronization and seamless extraction of wind power.

Solution 3 -Distributed PLL based Control

The solution described in [START_REF] Yu | Distributed PLL-based Control of Offshore Wind Turbine Connected with Diode-Rectifier based HVDC Systems[END_REF] uses the PLL already available as part of the Type 4 WEGs in order to enable synchronization. The startup of the offshore network is achieved using these WEGs with additional storage and then the rest of the WEGs connect and synchronize with the network using the proposed control scheme shown in Fig. 4.

Fig.4: Control Scheme for Solution 3

Grid Following Control 690 V / 66 kV

' DX * U DX F DC Voltage Control V "T * = 0 V "Q F i PQ * 1 i PDQ * R "ST U /i PDQ F Current Control V VWX * U dc Control Q Sharing GSC C C V DQ * PCC R -/ ] _ ] _ -˜ MPPT MSC š T i PD * abc dq g C * FIXREF Frame g C * SVPWM _ h _ oe•ž OE… Ÿ' ¡OE ž¡ ‰'Ž αβ dq 690 V / 66 kV i PDQ * Current Control V, f Control GSC C C PCC R \ ] _ ] ¢ R S _ h _ C _ Y R _ PI abc dq V PD F V PT F PI w \ C _ V PQ F I •D F I •D F w \ C _ V PS F V DQ * V PD * PI R _£ p \ F ¤ \£ V PT * abc dq PI abc dq \£ 1 x V PT F g \ g \ g \ PLL ] p \ * ¤ \ U \ * \ F \£ abc dq k q k f MSC DC voltage Control
The voltage references (R _S * ,R _T * ) are derived by control loops for active and reactive power respectively.

A PI controller is used to set the power reference (p \ * set according to the outputs from optimal power tracking algorithm) for the WEG eventually providing the reference value of R _S * . The reactive power sharing is achieved by a droop scheme as shown in the Fig. 4. An additional reactive power loop is used along with the droop for setting the frequency reference. Similar to solution 1, this work exploits the dynamic relationship between frequency and reactive power. The reference for frequency is derived using the following equation [START_REF] Cigre | TB 619 2015 HVDC Connection of Offshore Wind Farms -Cigre[END_REF].

§ \ * = š T ¨¤\ U € ¤ \£ © ƒ § \£ (2)
The problem of synchronization is solved by setting the R _T * according to the frequency setting of the AC network. Thus the q-axis voltage reference is set accordingly when the measured frequency deviates from its reference. This kind of control can be implemented across all the GSCs to synchronize them. The additional frequency droop controller added is expressed as follows in equation ( 3)

R _T * = š _ ( § \ * € § \ U ) (3)
In this solution, there is no need of any remote measurements to enable grid forming and the WEGs can function independently and auto synchronize using appropriate q-axis current injection.

Comparison of the Grid Forming Solutions

With the brief description of each solution, a table is presented (table I) showing the major differences among the solutions. The biggest motivation of adding an Umbilical AC cable and an external signal source for synchronization of GSCs in Solution 2, is to keep the conventional MSC and GSC control functions unchanged. It is seen that solution 1 and 3 are almost similar, except for the aspects of startup, synchronization and requirement of remote measurements for control.

Table I: Comparison between Grid Forming Solutions for DR-HVDC OWF

Simulation and Analysis of the Grid Forming Solutions

In order to provide further analysis of the reviewed solutions, the electrical architecture shown in Fig. 5 is modelled with appropriate control implementations. Each of the three clusters were aggregated (along with their inter array and cluster cable parameters) to represent three WEGs.

The parameters for the offshore network like the DR transformer and AC cables, were obtained from [START_REF]Deliverable 3.2 : Specifications of the control strategies and the simulation test cases[END_REF] and are depicted in the Fig. 5 directly. Other simplifications were made in the dynamic models involved assuming a constant DC voltage for the inner DC bus of the GSC in case of the solution of solution 1 [START_REF] D'derlée | Control strategies for offshore wind farms based on PMSG wind turbines and HVdc connection with uncontrolled rectifier[END_REF] and assuming good HVDC voltage control performed by Onshore VSC. These assumptions were done in order to focus on the analysis of the offshore AC collector network control and operation.

The GSCs were modelled using average value model of the two level VSC and the DR was modelled using switched models. Simulations were conducted in MATLAB Simulink environment. The different simulation cases considered for the implementations of solutions 1 and 2 are indicated in table II. The implementation and analyses of the solution 3 is not done in this paper.

Table II: Simulation Cases Selected for the two Solutions

Results and Analysis of Solution 1

The results for implementation of the solution 1 proposed in [START_REF] D'derlée | Control strategies for offshore wind farms based on PMSG wind turbines and HVdc connection with uncontrolled rectifier[END_REF] with above assumptions taken into account are presented below. In the case 1 simulation of solution 1, no AC marine cables are included between the WEGs and the PCC. The distributed voltage and frequency control illustrated in Fig. 2 (b) has been implemented for all the aggregated WEG models. The WEGs are assumed to produce 50% their rated capacities when the diode starts conducting at t=1s and then higher power is set at t=2 s for II) was performed with inclusion of inter-array cables (in aggregated form) and also cluster cables. The results are shown in Fig. 7 (a) and Fig. 7 (b) for measured quantities at PCC and at each WEG terminal. It is seen that the RMS AC voltage at PCC reaches 1 pu ( Fig. 7 (b)) before the voltage reference (V-ref) reaches 1 pu. Although the tuning of the controllers could be done to achieve a better control performance, the tuning of each WEG controller to achieve the goal is rather a complicated approach.

The capacitive impedance included in the network because of the AC marine cables cannot be taken into account in the control for each WEG and thus the remote PCC voltage control may not be successfully achieved in all cases. This effect of cables could be crucial because the coordinated and precise control of the wind generators is necessary to ensure stable AC grid operation. Thus control of a remote bus (PCC) voltage is rather not the best approach in dealing with OWF control, especially also because the OWF collection network dominantly capacitive.

Results and Analysis of Solution 2

The solution 2 [START_REF] Gierschner | Fixed-reference-frame-control: A novel robust control concept for grid side inverters in HVDC connected weak offshore grids[END_REF] is simulated with the same electrical architecture in Fig. 5, considering the aggregated AC marine cables. It is assumed that the MSC of each WEG performs satisfactory power control along with the pitch control of the wind turbine (MPPT). This allows to simplify DC bus of each WEG using a current source with a capacitance in parallel. The start-up for this solution requires an Umbilical AC cable from onshore as shown in Fig. 1.

The function of this umbilical is mocked by a GSC connected directly to AC offshore PCC to control the voltage and frequency. The Pseudo Umbilical acts as the slack bus to the entire network during the start-up (shown in Fig. 5). The active power of this pseudo umbilical is limited to 5% of the total capacity of the wind farm (in Fig. 8 active, reactive powers of pseudo-umbilical are shown as 'P-M', 'Q-M' respectively). Also in Fig. 8 the reactive power at PCC terminal due to the offshore transformer and DR operation is shown as 'Q-PCC'. Using the pseudo Umbilical the voltage and frequency of offshore AC grid is controlled leading to DR conduction eventually at t=1s shown by the PCC RMS voltage at 1 pu in Fig. 8 (bottom). 8 (top), it is seen that after grid forming at t=1s, until t= 3s, the pseudo-umbilical GSC is compensating for all the cluster / inter array cables' capacitive impedances (close to 0.18 pu). Then at t=3 when the WEGs start injecting active and reactive power (seen in Fig 10), reactive participation by the pseudo umbilical drops close to 0.08 pu. An analysis of the effect of reactive power droop implementation has been made. Two different simulation cases as indicated in the table I are considered.

The results for simulation of case 1 (without reactive power sharing) is shown in Fig. 9 with different power steps for all the WEGs. At t=10s all WEGs are producing at 80% their rated capacities (Fig. 9 top). A few seconds after time t=3s when the WEGs start injecting power, the pseudo-umbilical GSC is switched off at t=7s (as shown with P-M and Q-M tending to zero in Fig. 8). The reactive power contributions by the WEGs correspond to their power rating and they increase uniformly due to increase in power production of the entire wind farm. For instance, from t=3s until t=10s, WEG 3 (with the highest power rating) contributes higher reactive power than that of the rest of the WEGs in this time interval. The major disadvantage in this kind of reactive power sharing is that, the GSC with the highest active power injection has the highest reactive power load; this leads to possible overloading one or few of the GSC, when they are injecting rated active power. The other WEGs with lower power production could compensate for this additional reactive power requirement. The second simulation case has been then implemented with the reactive power droop parameters set for each WEG (as in Table I). These droop parameters are not modified throughout the simulation, but they could be dynamically set if necessary, according to real time active power production of the WEGs. The active and reactive power at various terminals are shown Fig. 10. Again the same power generation scenario is considered for all the WEGs as in simulation case 1 explained previously, for easy comparison. The reactive power participation of WEG1 is higher from t = 7s until t = 15 s as seen in Fig. 10 (bottom). The contribution of WEG1 is deemed advantageous between t = 7s and t = 8 s, when WEG 3 injects the maximum active power. Again the WEG 1 contributes more than other WEGs during time interval between t = 11 s and t=13 s, when WEG 2 injects maximum active power. Thus, particularly in these two time intervals (7-8 s; 11-13 s) an optimal reactive power contribution is achieved among the WEGs, and the participation of WEG 1 due to higher droop factor ( ¶ •¸) is evident (comparing reactive power contributions in Fig. 9). This could be the major advantage achieved in design of WEG reactive power droop compared to the Solution 1 and this permits to avoid GSC overloading in case of full capacity power production in some of the WEGs.

Conclusion

Though DR-HVDC is economically quite interesting, many challenges arise if the control capabilities of the offshore VSC station is lost. The objective of this paper has been to shed light on the different possible approaches (in this case three solutions have been selected) to solve the various challenges of the DR-HVDC OWF. Two of these solutions have been implemented in a study case architecture with simulation results and analyses. Regarding the solution 1, although the modification of the control scheme in order to enable grid forming by the GSC and also perform MPPT at the GSC terminals are quite advantageous, the practical questions of clear solutions for start-up and synchronization remain to be solved. The approach to control the remote PCC AC offshore voltage could become quite complicated, especially when AC marine cables are involved and this has been demonstrated in this paper. Considering solution 2, the need for an Umbilical AC cable and a sophisticated communication network to enable grid forming (FIXREF) are highlighted while the functioning of the network in case of failure of the communication network is not dealt. However the reactive power sharing using droop implementation is found to be useful, especially to avoid GSC overloading when different some of the WEGs inject full power. This advantage has also been explained in the paper through simulations. Although the solution 3 has not been implemented, it seems to address most of the challenges -control without remote measurement, local voltage control and synchronization. The start-up is said to be achieved using additional storage devices but the design aspects behind this have not been clearly dealt. From all these solutions, it is clear that enough progress has been made with research on DR-HVDC OWF and it is important that further development of any solution have to account for the all engineering aspects of all the challenges-start-up, synchronization, communication-less control.

Fig. 1 :

 1 Fig.1: Overview of DR-HVDC based OWF Architecture

Fig. 2 :

 2 Fig.2: (a) Grid Forming Solution Proposed for Multiple Wind Generators [6] (b) Distributed and Centralized Parts of the Controllers

Fig. 3 :

 3 Fig.3: Control Scheme for Solution 2

1 ;Fig. 5 :

 15 Fig.5: Study Case Electrical Architecture with relevant network parameters

  to 90% capacity) and finally at t = 4 s for WEGs 1 and 3 (to 90 % of their own capacities); the active and reactive powers at PCC and at various WEG terminals are shown in Fig.6 (a). There is a small increase in RMS voltage seen at PCC in Fig.6(b) due to the effect of overlapping angle during diode commutation. Though it looks to have changed due to power injection events, the RMS rated voltage is below 1.1 pu upper limit for normal operation for voltage. (a) (b) Fig.6: Solution 1-Without AC Marine Cables (a) Active and Reactive Power at various terminals in the OWF (b). PU voltage at PCC and RMS currents at various terminals The next simulation (Solution 1 case 2 in table

Fig. 7 :

 7 Solution 1 -With AC Marine Cables (a) Active and Reactive Power at various terminals in the OWF (b). PU voltage at PCC and RMS currents at various terminals

Fig. 8 :

 8 Fig.8: (Top) P, Q injection by the Pseudo Umbilical and Q at PCC; (bottom) RMS AC voltage at various terminals

Fig. 9 :

 9 Fig.9: Solution 2, Case 1: Without Q droop implementation -P and Q at various terminals

Fig. 10 :

 10 Fig.10: Solution 2, Case 2 -With Q droop implementation -P and Q at various terminals

OWF Clusters HVDC Cable Offshore On Shore

		AC Grid
	DRU	LCC/VSC

MVAC Umbilical Cable with Q compensation Additional Equipment for Solution 2 PCC


Heythem Hamlaoui
email: heythem.hamlaoui@etudiant.univ-lille1.fr

B Francois
email: bruno.francois@centralelille.fr

Interest of storage based STATCOM systems to the power quality enhancement of thyristors based LCC HVDC links for offshore wind farm

Keywords: Power Quality, Offshore wind farm, HVDC, Line commutated converters (LCC), STATCOM. I

This paper defines a three level 48 pulse STATCOM based on GTO-VSC which is used to support the integration of remote large offshore wind farms into the main onshore grid using line-commutated high-voltage dc connection (LCC-HVDC). This mature transmission technology requires a large quantity of reactive power. In order to enhance the dynamic performance of the LCC-HVDC connected to a weak system, this work presents STATCOM applications to improve the power quality and to avoid commutation failures. Simulation results show that HVDC LCC technology connected to a weak system needs extra reactive power compensation. It confirms the STATCOM performance and its dynamic and fast reactive power compensation during voltage fault conditions. Finally, the sizing of the STATCOM dc capacitor is studied.

INTRODUCTION

Facing the CO2 emission and global warming problems, the European Union (EU) encourages the integration of renewable energy in the power system. By 2020, up to 12% of the world's electricity are predicted to be provided by wind power [START_REF] Bozhko | Control of offshore DFIG-based wind farm grid with line-commutated HVDC connection[END_REF]. Offshore wind farms have attracted attention since the wind power is abundant and installations have less visual impact.

For high sized wind farms and for long-distance connection between the offshore and onshore stations, HVDC transmission is more efficient than high-voltag1e ac (HVAC) connections [START_REF] Roses | Practical determination of HVAC-HVDC Hybridization ratio for Offshore Transmission network Architectures through technico-economic considerations[END_REF], [START_REF] Li | Comparison of HVAC and HVDC based grid integration on wind farm[END_REF]. Compared with the VSC-HVDC [START_REF] Shinoda | Modelling of a VSC-Based Multi-Terminal HVDC Network for Dynamic Stability Analysis[END_REF], the LCC-HVDC is the most used one in industrial projects due to its high capacity, low cost and low power losses [START_REF] Oni | A review of lcc-hvdc and vsc-hvdc technologies and applications[END_REF].

The main drawbacks of LCC-HVDC system are the high reactive power consumption, the bad power quality in both sides of the converter, the generation of low order harmonic and its sensibility to weak AC power systems. As the thyristor commutations depend on the zero-crossing of the alternating line voltage, any disturbance in the AC voltage will lead to a commutation failure. For that reason capacitor banks and filters are used for reactive power compensation and for harmonic mitigation to smooth the waveforms. However, the reactive power supply with only passive compensation (fixed capacitors) can be critical for weak systems and they will not supply sufficient reactive power during fault at the point of common connection (PCC). In order to improve the performance of LCC HVDC when it is connected to a weak AC system, a STATCOM is used to enhance the power quality of voltages by generating or absorbing reactive power needed during steady-state and dynamic operation, providing the necessary sine voltage for the LCC operation.

The objective of this work is to consider a STATCOM application in order to ensure dynamic fast reactive power compensation at the PCC under transient conditions. The first part deals with the LCC-HVDC connection to a weak AC system and the different difficulties that will hinder the appropriate operation of this system. The next point will discusses the mathematical modeling of the STATCOM, its principle of working and the proposed control. After that, the system architecture will be presented and followed by the simulation results and discussion of both cases: with and without using a STATCOM. Finally, the paper discuss the impact of the STATCOM and its sizing to tackle the power quality issues in order to mitigate the harmonics and improve the dynamic performance.

II. LCC-HVDC CONVERTERS CONNECTED TO A WEAK AC

SYSTEM

The operation of LCC-HVDC in a power system depends on the strength of the AC system [START_REF] Oni | A review of lcc-hvdc and vsc-hvdc technologies and applications[END_REF]. A small disturbance in a weak system can affect the AC voltage waveform and causes commutation failure of the thyristor valves. This strength is characterized in term of the Short-Circuit Ratio (SCR) [START_REF] Fischer De Toledo | Modelling and control of a line-commutated HVDC transmission system interacting with a VSC STATCOM[END_REF] between the short circuit capacity in MVA of the AC system , compared to the converter rated DC power P :

= (1) With = ;
is the rated AC line voltage (fig. 1), Z is the Thevenin impedance. For a strong system SCR is inferior to 3, weak systems have a SCR between 3 and 2, whereas very weak systems have SCR<2 [START_REF] Jovcic | High-Voltage Direct Current Transmission: Converters Systems and DC Grids[END_REF]. If a weak offshore wind farm AC system is connected to the LCC converter, operating problems may appear such as [START_REF] Jovcic | High-Voltage Direct Current Transmission: Converters Systems and DC Grids[END_REF] As shown in fig. 2.b, the phasor diagram represents the case when the phase difference α between and is negative. The line current will take direction in such way that an active power flows toward the converter and charges the dc capacitor. As conclusion, the rms value of the modulated output voltage V is generated indirectly by charging or discharging a DC capacitor to a different voltage level. Therefore, increasing or decreasing the magnitude of the converter voltage causes the reactive power delivered to the AC bus to rise or fall.

According to hypothesis in [START_REF] Bouhali | Contribution des convertisseurs multi-niveauxau raccordement de la production d'origine éolienne sur un réseau électrique[END_REF], the three inductors are identical, the system is balanced, the resistance of each coil is negligible, compared to its inductance impedance. From the phasor diagram (figure 2.b), we obtain:

= -.jωL (2)
The projections on axis lead to:

!"# $ = + &ωL !"#( ( ) -*)= -ωL &sin * (3) sin $ = &ωL sin( ( ) -*) =ωL &cos * (4)
The active power is given by:

P=3 & cos * =3 12 3 45 (5)
In a same way the reactive power (exchanged with the grid) is given by:

Q=3 & sin * =3 ( 6 78
3) 45 [START_REF] Jovcic | High-Voltage Direct Current Transmission: Converters Systems and DC Grids[END_REF] Hence, the STATCOM may generate or consume reactive power according to . By forcing the output voltage V to lag the voltage of the AC system ( V 8 ) by a small angle, the converter absorbs a small amount of active power from the grid to recover the losses of power electronics devices and the transformer inductance.

B. Mathematical modeling of the STATCOM

As the voltage level is high, topologies of STATCOMs are based on series connection of single elements (semiconductors, bridges, …) and so many multilevel topologies may be considered [START_REF] Francois | Design of a fault tolerant control system for a NPC multilevel inverter[END_REF]. The equivalent circuit of a STATCOM consists of a DC link capacitor (working as an energy storage device), a voltage source converter (VSC) and the coupling transformer between the VSC bridge circuits and AC system (fig. 3). represents the inverter and transformer conduction losses. C is the DC equivalent capacitor. The grid voltages are assumed to be balanced and sinusoidal, no losses and no harmonics are assumed in the AC and DC power circuits. The relationship between the PCC voltages, the inverter output voltages and currents are obtained by writing the Kirchhoff equations for the figure 3 [8]:

= >1 ? >@ + A : (B) = 9 : (B) -9 : (B) (7)
= >1 C >@ + A ; (B) = 9 ; (B) -9 ; (B) (8)
= >1 >@ + A (B) = 9 (B) -9 (B) (9)
Equations ( 7) to ( 9) can be written in a matrix form as:

> >@ D A : A ; A E = F G G G H - I 5 0 0 0 - I 5 0 0 0 - I 5 K L L L M N A : (B) A ; (B) A (B) O + 5 N 9 : (B) -9 : (B) 9 ; (B) -9 ; (B) 9 (B) -9 (B) O (10)
The Park's transformation is used to transform equation from the abc frame to a synchronous dq0 reference frame:

> >@ P A > A Q R = N - I 5 S -S - I 5 O P A > (B) A Q (B) R + 5 P 9 > (B) -9 > (B) 9 Q (B) + 9 Q (B) R (11)
S = 2πV is the system angular frequency of ac voltages. We can write a pair of equations for v (t) and 9 Q (B):

9 Q (B) = Y(B). 9 > (t). sin ($) 9 > (B) = Y(B). 9 > (t). cos ($) (12)
m is the modulation index of the inverter. $ is the angle between the grid voltages and inverter output voltages, and it is the control input. According to the power balance theory, the instantaneous power at the AC terminals of the inverter is equal to the instantaneous power at the DC terminals of the inverter:

9 > (B)A > (B) = [ ) (9 > (B)A > (B) + 9 Q (B)A Q (B)) (13)
By combining previous equations, the current in the DC side of the STATCOM is expressed as:

i (t) = [ ) m(t)]i (t) cos α + i ^(t) sin α_ = C a bc (14)
If the synchronous rotating frame is oriented such that 9 Q =0, then we get:

> >@ D A > A Q 9 > E = d N A > (B) A Q (B) 9 > (B) O -5 D 9 > (B) 0 0 E ( 15
)
Where A is given by:

A= F G G G H - I 5 S - e(@) 5 !"# ($) -S - I 5 e(@) 5 #Af ($) g- [ ) h g e(@) i h !"# ($) -g [ ) h g e(@) i h #Af ($) 0 K L L L M
According to [START_REF] Xi | Control Strategies of STATCOM during System Faults[END_REF], in a steady state, it can be noticed that A >j is very small compared to A Qj ,which means there is nearly zero active power generated by the STATCOM. As A Qj varies, the angle α j will change linearly, which means A Qj has an effect on the angle A Qj . The instantaneous active and reactive powers are expressed as:

P= [ ) ]9 > (B)A > (B) + 9 Q (B)A Q (B)_ = [ ) 9 > (B)A > (B) (16) Q= [ ) ]9 Q (B)A > (B) -9 > (B)A Q (B)_ = - [ ) 9 > (B)A Q (B) (17)
By observing the right hand side of previous equations, the grid voltage is controlled by exchanging reactive power between STATCOM and power network. As i is nearly equal to 0, there is no real power exchange.

C. Proposed control

The goal is to control the AC voltage at the PCC by generating or consuming the appropriate AC current (A Q ) and so managing the required reactive power (eq. 17). The control scheme is illustrated in fig. 4, the main blocks are:

• A Phase Locked Loop (PLL) is used to synchronize GTO pulses so that the AC generated voltages will be in phase with the network voltages. inverter and the voltage system) and in turn generates gating pulse, the value of (& Q ) is compared with (& Q * ) and the error signal is controlled to generate the angle l. • For balancing the two DC capacitor voltages (that are used to create the total capacitor C in fig. 3), the difference between voltages ( > and > ) ) is sensed and processed by a PI controller to introduce a phase shift Δl, which will be added to the main phase conduction angle variation l. The obtained angle (l + Δl) will be used to generate the triggering pulses for GTO-VSC units.

• Firing angle generator creates pulses for the four inverters. Each wind farm consists in 4 MW turbines, which are gathered in clusters by an AC 66kV network. The voltage is rised up to 150kV in order to export the AC offshore power. A 300km (400 kV, 2 kA) LCC HVDC interconnection, with 12 pulse converters on both rectifier and inverter sides, is used to transmit power to the onshore network (345 kV, 50 Hz). The submarine cable is modeled as a π model with parameters coming from ABB datasheets [START_REF] Abb | XLPE submarine cable systems -Attachment to XLPE land cable systems -User ś guide[END_REF] [10] and [START_REF] Roses | Practical determination of HVAC-HVDC Hybridization ratio for Offshore Transmission network Architectures through technico-economic considerations[END_REF]. Filters and capacitive banks are connected on both sides to mitigate the harmonics and to supply reactive power. Also, smoothing reactors are connected in both rectifier and inverter side. The STATCOM based VSC is located at the rectifier side of the HVDC link.

V. SIMULATION AND DISCUSSION OF RESULTS

The modeling of the STATCOM in the studied power system is simulated by using the MATLAB/SIMULINK. In this study, the wind energy profile has arbitrary variable power (fig. 6) that will influence the operation of the network. Therefore the contribution of the STATCOM and the dynamic response will be seen under this scenario: The first 400 MW wind power cluster is disturbed and the other cluster will deliver a constant 400 MW power.

A. System without a statcom

The interaction between HVDC and AC system is investigated, the SCR is varied from a strong system (SCR=4) to a weak one (SCR= 2.5) to see the effect of the weak and strong AC system on the LCC operation. The profile of generated wind power disturbance just in one collection of 400 MW is shown in figure 6.

1) AC Voltage and current at the rectifier side

As it can be seen clearly in fig. 7, the voltage and the current at the rectifier side are not affected much in the case of a strong system (SCR=4). However in the case of the weak side (SCR=2.5). The obtained AC voltage and the current at the rectifier side have been affected by the variation of the generated wind power; At t=1.2, when the generated wind power reaches high values, the transient voltage on the rectifier side exceeds 1.6 pu (60 % higher than the nominal value). This high transient voltage makes failure to the rectifier switching.

3) DC voltage and current at the rectifier side

When an overvoltage occurs at the rectifier side (t =1.2 s), as it is illustrated in fig. 7, the DC current (fig. 9) increases to 2.1 pu and the DC voltage starts to fall to a low value at the rectifier side. This DC voltage drop is sensed by the Voltage Dependent Current Order Limiter (VDCOL). The VDCOL reduces the reference current to 0.35 pu at the rectifier. A DC current still continue to circulate. Then, at t=1.27 s, after detecting a low DC voltage by the DC fault protection, the rectifier now operates in inverter mode. Since the DC line voltage becomes negative during a period following the commutation failures, no active power will be transmitted during this time and the energy stored in the line is returned to the AC system. Via the previous simulation results, some problems and difficulties hinder the good operation of the LCC system at a low SCR, therefore a STATCOM is needed to support the work of the LCC HVDC technology.

B. System with a statcom

To overcome previous problems, a STATCOM is installed in the system to deliver and control the reactive power and therefore reduce voltage fluctuations. It is located at the rectifier side of the HVDC link and has a rating of ±100 MVA. It consists of a three-level 48-pulse inverter and two series-connected 3000 µF capacitors. This work is related to the study of the STATCOM impact at a LCC HVDC rectifier connected to a weak AC offshore network with SCR=2.5.

1) AC voltage and current at rectifier side

Used parameters are @ =0.1 Ω, = @ =1 mH, @ =0.55 μF. First, the effective operation of the model and of its control is tested. Then, different plausible scenarios for the isolated mode are simulated.

The STATCOM has a good impact on the rectifier side (fig. 10). At t= 1.2 s the transient ripple of the AC voltage does not exceed 1.19 pu, whereas without STATCOM, this transient exceeds 1.6 pu. Also, it can be observed that the AC current keeps conducting in normal condition (where the current becomes zero at t=1.25 s in the absence of a STATCOM).

As shown in figure 11 the reference voltage V0 is set to 1.0 pu, the STATCOM does not operate initially (zero current) from t=0.4 s to t=0.8 s and the DC voltage is maintained at 13 kV, which is a consequence of the constant wind power generated. At t=0.8s, the voltage is suddenly decreased by 20% from the nominal voltage (0.8 pu), so Vmeas becomes lower than the reference voltage V0, the voltage regulator will generate high reactive current to supply an extra capacitive reactive power. As it is shown in fig. 12, the STATCOM reacts by generating reactive power (Q= -85Mvar) to keep the voltage at the rectifier side at 0.97 pu (compared to 0.93 pu without STATCOM). At this point, the DC voltage has increased to 15 kV due to the reduction in generated power (fig. 13). Then, at t=1.2 (s) the source voltage is increased to 1.2 pu of its nominal value. The STATCOM reacts by changing its operating point from capacitive to inductive mode to keep the voltage at the rectifier side at 1.02 pu (compared to 1.08 pu without STATCOM). At this point the STATCOM absorbs 65 Mvar and the DC voltage has been decreased to 11.5 kV.

Finally, at t=1.6s, and after some transients, the voltage source is set back to its nominal value, the STATCOM operating point comes back to zero Mvar and the STATCOM dc link voltage returns to its rated value.

2) DC current and voltage at DC rectifier side

The connection of a STATCOM to the power system enhanced the DC voltage and current at the rectifier DC side, as illustrated in fig. 15. The STATCOM kept the DC voltage at almost equals to 1 p.u with small ripples. Furthermore, the overvoltage at t=1.2 (s) did not affect the voltage very much compared to the output without STATCOM and there is no negative DC voltage neither negative active power (fig. 14), so the converter always work as a rectifier. In addition to that, the recovery time is very fast. Those results confirm the huge importance and the good performance of a STATCOM during faults conditions.

A. Power quality improvement

AC and DC voltages and currents are affected by the variation of wind power (table 1). However, when the STATCOM is connected to the system; the power quality improvement can be noticed. Moreover, table 3 illustrates the reduction of the capacitor size increases. The figure 18 shows the effect of the capacitor size on the DC link voltage, it can be seen clearly that the high transient voltage, at t=1.2 s in the case of small capacitor, is totally reduced when the capacitor value increases.

VII. CONCLUSION

According to obtained simulation results, a STATCOM is a good solution for enhancing the power quality of the AC voltage and, so, the operation of a LCC connected to a weak AC networks. Finally, a good sizing of the STATCOM DC capacitor is essential to enable the effective decrease of transient overvoltages.

For future research, it is proposed to use a STATCOM Multi-level inverter with Pulse Width Modulation (PWM) technology based on the IGBT to the high-voltage transmission grid. This type has many advantages such as: harmonic reduction, reduce the size of the STATCOM, short response time

Fig. 1 .

 1 Fig. 1. Equivalent single phase circuit

: 1 )Fig. 2 .

 12 Fig. 2. STATCOM operating characteristics

Fig. 3 .

 3 Fig. 3. Equivalent circuit of the studied STATCOM 9 : , 9 ; , 9 are voltages at the PCC. 9 : , 9 ; , 9 are inverter output voltages. = is the transformer leakage inductor.represents the inverter and transformer conduction losses. C is the DC equivalent capacitor. The grid voltages are assumed to be balanced and sinusoidal, no losses and no harmonics are assumed in the AC and DC power circuits. The relationship between the PCC voltages, the inverter output voltages and currents are obtained by writing the Kirchhoff equations for the figure3[8]:

•

  AC Voltage and current regulation: This structure consists of two PI controllers: the outer voltage control loop and the inner current control loop. The outer voltage loop computes the reference reactive current (& Q * ), which will be used by the current regulator block. (& Q * ) is obtained by controlling the error signal between the reference voltage (v*) to the magnitude of the line voltage (V >Q ). The inner control loop determines l (which is the phase shift between the voltage

Fig. 4 .Fig. 5 .

 45 Fig. 4. Control scheme of the 48 pulse STATCOMIV. SYSTEM CONFIGURATION The studied power system consists of two 400 MW offshore wind farms and an islanded platform for the HVDC rectifier station, which comprises auxiliaries, ac filters and a STATCOM (fig.5)[START_REF] Kouassi | AC Offshore Grid Forming of a Collector Network for Wind Park by Considering Storage and Hybrid Power Electronic Systems[END_REF].

Fig. 6 .

 6 Fig. 6. Active power profile of 400 MW collections

Fig. 7 .

 7 Fig. 7. AC current and voltage magnitude at rectifier side 2) Commutation failure As shown in fig. 8, the plot of the rectifier valve thyristor current indicates a number of commutation failures of the valve

Fig. 8 .

 8 Fig. 8. Valve currents during a failed commutation

Fig. 9 .

 9 Fig. 9. DC current and voltage at rectifier side

Fig. 10 .Fig. 11 .

 1011 Fig. 10. AC current and voltage at rectifier side

Fig. 15 .

 15 Fig. 15. DC voltage and current at the rectifier side3) Successful commutation:Contrary from the result obtained without using STATCOM, commutation failures are not observable in fig.16. Again, the positive impact of the STATCOM is evident.

Fig. 16 .

 16 Fig. 16. Valve current during successful commutation VI. POWER QUALITY

F

  (Ca) = a*exp(b*Ca) + c*exp(d*Ca) (18) a = 0.08085; b = -0.01788; c = 1.121; d = -3.292e-06.

Fig. 17 .

 17 Fig. 17. Characteristic of the DC-link capacitance on the rectifier overvoltage with fitted curve

Fig. 18 .

 18 Fig. 18. DC voltage and current at rectifier side

TABLE I .

 I POWER QUALITY INDEXES WITH AND WITHOUT STATCOM

	Max/Min AC voltage	1.67/0.55 (p.u)	1.19/0.931 (p.u)
	Max/Min AC current	7.44/0 (p.u)	5.11/4.20 (p.u)
	Max/Min DC voltage	1.35/-1.77 (p.u)	1.34/0.88 (p.u)
	Max/Min DC current	2.1/0 (p.u)	1.176/0.946 (p.u)
	Transient time (s)	1.55	1.33
	B. Harmonic Compensation
	The STATCOM in harmonic compensation mode acts as an
	Active filter. From table 2, it is clear that the STATCOM
	mitigates the harmonics at the rectifier connection point; this
	will ensure a good power quality of the signals and prevent
	commutation failure.
			Without statcom	With statcom

TABLE II .

 II THD MEASUREMENT IN % AT DIFFERENT TIMES To investigate the influence of the capacitor sizing on the operating of the STATCOM, the transient overvoltage at the rectifier is recorded for different capacitance values. From the obtained characteristic (fig.17), it seems that the overvoltage is decreased exponentially as the size of the DC capacitor (Ca) increases. An exponential function that fits the different points is in the form of:

	Time (s)	1.2	1.3	1.4	1.5	1.6
	With statcom	8.18	1.61	1.33	1.12	6.45
	Without statcom 4.23	28.19	3.51	2.38	8.05
	C. Analysis of the STATCOM sizing

TABLE III .

 III EFFECT OF DC CAPACITANCE ON TRANSIENT DC LINK VOLTAGE

	DC capacitance	Max transient	Min transient
	value in µF	voltage in (kV)	voltage in (kV)
	3000	21.04	9.02
	9000	20.24	9.14
	12000	19.76	9.43
	20000	18.98	9.94
	30000	18.31	10.08
	60000	17.38	10.37
	200000	15.74	10.46


Keriero hoard from Bangor (Morbihan

Process

The chronological period studied is distinguished by a very wide corpus, covering Northwest France. The latest inventories count more than 15,000 metal remains in more than 250 hoards (Milcent 2015, ill. 3.11, and additions). However, despite the extensive literature referring to Late Bronze Age, many hoards are still largely under documented. In fact, many of them formerly discovered are in fact very partially known and published. They cannot, therefore, satisfactorily supply research on metal hoards. For example, only 25% of them are illustrated exhaustively and benefit from precise data (masses, dimensions, states of the metal scraps). Moreover, the development since a few years of illicit excavations, requires a special effort to save the recent data what still can be. Unfortunately, most of newly discovered atlantic hoards do not come from scientific excavations and there are certainly a lot of hoards which are not still known. Thus, in order to go beyond the simple state of the art and to offer new data, we have undertaken a research campaign to checks and to inventory public and private collections known and preserved in Brittany, in Normandy and in the region Pays-de-la-Loire.

First Observations

This approach allowed us to document several important hoards which are partially unpublished (fig. 1, 2, 5 and 7). In addition to recording the data required for our investigations, we were able to rectify inventories mistakes and to find some objects considered to be lost (fig. 7, n° 4). At the same time, datag mining on archives preserved in the CReAAH-Archéosciences laboratory in Rennes offer us to complement missing data with unpublished iconographic documentation (fig. 6). After all, few close collaborations have fully contributed to the development of the corpus, especially concerning recent discoveries (fig. 6).

Thus, more than 3000 new metal remains have integrated our database. In the light of this initial phase, some facts can already be asked. First of all, all these hoards have a relatively homogeneous structure composed mainly of traditional cultural traits for the BFa 3. We can off course systematically observe a strong fragmentation, peculiar phenomena of handling (fig. 5, n ° 35 and 46) and recurrent choices in the deposited parts (fig. 5, 14 and 7, n ° 1). However, in detail, some differences are observed, highlighting geographical divisions that will require special attention. It is clear, for example, that the South-Brittany coast shows more marked affinities with hoards from the Centre-West of France than with the rest of Brittany.

By enriching the available corpus, we will be able to sharpen the maps of distribution of many types of objects and thus better understand the exogenous flows. This is especially true for certain types of bracelets (types of Réallon-Saint-Genouph, Vaudrevanges, Homburg) as well as for harness and chariot elements (fig. 2 and5, n° 1 and 19) or cauldrons (Bordas, 2016). Distribution maps had hitherto shown a rather tenuous presence of these remains in the Armorican Massif. It will also be possible to supplement the research focusing on the atlantic swords (Brandherm, Burgess, 2008)

Prospects

By investing a significant part of our doctoral research in the updating of data concerning carp's tongue french hoards, we now benefit from a partially renewed corpus. It will allow us to enrich the knowledge of material culture and to better understand the rate of constitutions of hoards. However, much remains to be done to fully exploit the new data from these hoards. In particular, it will be necessary to expand our investigations to the north and east of the French Atlantic Complex. In addition, a campaign of radiocarbon dating of organic remains will also enrich this study to try to deliver some new key to the chronology. Similarly, ceramic containers will be the subject of a comprehensive approach (fig. 4). Ultimately, once this survey is completed, we will have reliable and exhaustive documentation for the BFa 3, allowing us to base our thoughts on the difficult question of hoards interpretation as well as their socio-economic and cultural meanings. The Keriero hoard was discovered in several times between the years 1995 and 1999. Several discoverers still retain few remains but the main part of the hoard is preserved in the Museum of Prehistory of Carnac. With more than 1,200 copper alloy objects and fragments, the Keriero hoard is the most important dated from the BFa 3 in Northwest France. The metal mass weighs 27.16 kg. Fragmented objects represent 97% of total (Bordas, forthcoming).

The types of objects present are quite characteristic of the Armorican Massif but also include unique objects and someone which are relatively rare for Brittany. This hoard thus seems to confirm the fact that hoards which have a significant number of objects, show a higher level of exogenous remains than the norm.

Contact :

Francis Bordas 06 61 22 67 08 francis.bordas@hotmail.fr Francis Bordas Université de Toulouse-Jean Jaurès Laboratoire TRACES-Umr 5608

  by recognition of rare or unusual types for carp's tongue hoards (fig. 7). The sword fragment attributed to Monté-Sa-Idda type from the Kergal hoard in Guidel (Morbihan) is one of the best examples (fig. 7, n° 3).

  1, Gouesnac'h (Finistère) 10 -Kergaradec 2, Gousnac'h (Finistère) 11 -Kergaradec 3, Gouesnac'h (Finistère) 12 -Le Pont Pierre, Bréhand (Côtes-d'Armor) 13 -Kerch'Leus, St Pabu (Finistère) 14 -Le Vern, Moëlan-sur-Mer (Morbihan) 15 -La Motte, Lannilis (Finistère) 16 -La Chapelle des Roche, Le Châtellier (Orne) 17 -Soullans (Vendée) 18 -La Chaire au Diable, La Haie-Traversaine (Mayenne) 19 -Bernay, Saint-Germain-le-Gaillard (Manche) 20 -Chemin des deux jumeaux, Longueville (Calvados) 21 -Le Castel, Port-en-Bessin (Calvados) 22 -Saint-Ouen, Jersey (R.-U.) 23 -Clisson (Loire-Atlantique) Carp's tongue sword hoards News data from northwest France

Figure 5 :

 5 Figure 5 : Examples of metallic production from unpublished or little known carp's tongue french hoards : 1 à 6 : Bordustart, Le Palais (Morbihan) ; 7 à 11 : Kergal, Guidel (Morbihan) ; 12-13 : Le Parc aux Boeufs, Questembert (Morbihan) ; 14-21 : Kerhar, Guidel (Morbihan) ; 22-27 : Pont er vil, Locmariaquer (Morbihan) ; 28-33 : Kerlouan (Finistère) ; 34 : Plouenan (Finistère) ; 35 : Kerch'Leus, Saint Pabu (Finistère) ; 36-39 : Le Vern, Moëlan-sur-Mer (Morbihan) ; 40-45 : La Chapelle des Roches, Le Châtellier (Orne) ; 46-48 : Port-en-Bessin (Calvados) ; 49 : Pseudo «Ecobuts», (Nantes, Loire-Atlantique) : 50 : Clisson, Loire-Atlantique. DAO et Photographs : F. Bordas

Figure 7 :

 7 Figure 7: a few unpublished sword's hilts. Drawings and DAO: F. Bordas 1 -Kerlouan (Finistère): Carp's tongue sword with archaic features ; 2 -Pont-er-Vil, Locmariaquer (Morbihan): Hybrid sword with peculiar features ; 3 -Kergal, Guidel (Morbihan): Monte Sa Idda sword (close to variant Boom) ; 4 -Prairie de Mauves, Nantes (Loire-Atlantique): Semi-solid hilted sword ; 5 -Parc aux Boeufs, Questembert (Morbihan): Sword close to type Huelva (transitional hilt) ; 6 -Keriero, Bangor (Morbihan): Classic carp's tongue sword carp (type Nantes) ;

Figure 2 :

 2 Figure 2 : samples of copper alloy objects and fragments from the Keriero hoard (Morbihan). Photographs : F. Bordas

Figure 3 :

 3 Figure 3 : Keriero hoard (Bangor, Finistère) : summary of the proportions by number of remains and mass of each functional category. Despite a large number of undetermined remains and possible loss of objects, the composition of the Keriero hoard get close to those of mostly atlantic hoards.

Figure 1 :

 1 Figure 1 : Distribution of few carp's tongue sword hoards unpublished or little know, studied in our PhD Thesis. DAO : F. Bordas. Background map : Th. Vigneau.

Figure 6 :

 6 Figure 6 : Some hoards are known, in the current state of our research, only by few unpublished photographs. It concerns private collections, lost hoards or some resulting from illicit detections. Left : Lannilis hoard (Finistère), archives of the CReAAH-Archéosciences laboratory, Rennes. In the center: Saint-Germain-le-Gaillard hoard (Manche): informations -Cyril Marcigny. Right : fragments of one of the two cauldrons hooks of the Dunaverey type, discovered in the neighborhood of Léry (Eure) : information and study in progress -José Gomez de Soto.

Figure 4 :

 4 Figure 4 : Distribution of hoards associated with pottery during the Bronze final atlantic 3 (Bordas et al. forthcoming).