Kelly Ribeiro De Faria

Tanguy Phulpin

Daniel Sadarnac

Charif Karimi

Larbi Bendani

Larbi

Reliability, power losses and volume comparison for isolated

Keywords: DC-DC isolated converter, FIDES reliability guide, reliability models for GaN switches, MTTF, power density, power efficiency

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

The demand for lower CO 2 emissions increases the request for high power density converters and higher efficiencies. The isolated DC/DC converters are present in a wide range of applications such as low voltage power supply for electric and hybrid vehicles, but also in the more electrical aircrafts. Four of the most common isolated topologies used for these applications are the resonant LLC, the series resonant LC, the Dual Active Bridge (DAB) and the Phase-shift converters. The converter's power density is inherently associated with the switching frequency that can be increased by using wideband gap materials, such as GaN. In this scenario, the lifetime must also be considered in the conception process. Indeed, reliability is a big challenge for GaN power transistors and FIDES, considered in Europe as the best prediction for reliability in power electronic systems, allows take into account this parameter [START_REF] Fides Group | FIDES Guide 2009 Editon A Reliability Methodology for Electronic Systems[END_REF]. Some research has been focused on the comparison of isolated DC/DC converters [START_REF] Krismer | A comparitive Evaluation of Isolated DC/DC Converters with Wide Input and Output Votlage range[END_REF], but most of the studies do not focus on lifetime, which is relevant and should be evaluated in order to choose the best converter. In [START_REF] Bendali | Intégration de la fiabilité dans la conception sous constraintes multi-physiqes des conv. statiques[END_REF] the integration of reliability is also used in the pre-design of nonisolated interleaved Buck converter in order to help the selection of the most adapted converter. In [START_REF] Arifujjaman | Reliability comparison of power electronic converters used in grid-connected wind energy conversion system[END_REF] the reliability is used to compare different grid-connected converters composed by IGBT and diodes for wind energy conversion. The reliability applied for power converters connected to photovoltaic systems is discussed in [START_REF] Pryadarshini | Reliability of DC-DC converters used as MPPT in grid connected photovoltaic systems[END_REF]. These studies use the reliability as a tool to evaluate the converters in the pre-design stage, but use components that have a mature time life model, but, for components as GaN power transistors, the analysis becomes a little more complicated.

When higher power density is required, GaN transistors presents enormous advantages concerning not only volume but also efficiency; however, they present a challenge concerning time life because contrarily to Si MOSFET, there's no a well established accelerated lifetime model based on years of experience for those components. In [START_REF] Carton | New FIDES Models for Emerging Technologies[END_REF], it's discussed the construction of predictive models for the emerging technologies in FIDES, that are possible if the reliability tests are executed close to the extreme operating conditions. Despite the difficult in to identify the main failure mechanism in the new transistors, the use of activation energy seems to be a good parameter to include them in acceleration factors from reliability models [START_REF] Bahl | A comprehensive methodology to qualify the reliability of GaN products[END_REF].

The objective of this paper is to compare the efficiency, volume and time life of HV/LV isolated converters based on different power transistor technologies. These parameters normally can be used to help engineers to choose the best topology in a predesign stage. The analysis of reliability from GaN devices is then discussed and integrated in the FIDES methodology to evaluate the time life of these components. This paper is organized as follows: Section 2 present the main difference between the isolated DC/DC converters, the choice of the components required in each topology for a specific application and the total power losses and volume estimation. In section 3, the FIDES model is then used in order to estimate the failure rate of each component and the Mean time to failure of each topology. It's also explained how the new GaN power transistors can be integrated in the FIDES methodology taking into account the difference between the structures: a direct enhancement mode and a cascode structure. In section 4, time domain simulations are then carried on each topology with an equivalent model for the power switches. A script in Octave using FIDES model, inserts the power profile in the simulation environment and a comparison of the reliability for an output power demand profile is obtained and discussed in section 5.

DESIGN AND COMPARISON OF CONVERTER TOPOLOGIES

For this study, isolated DC/DC converters are designed for a 3kW high/low voltage, typical application presented in electric vehicles, according to The four studied converters are illustrated in (Fig. 1).

The LLC resonant converter (Fig. 1A) and the LC series resonant converter (Fig. 1B) are designed by using the equivalent First Harmonic model [START_REF] Yang | Design of a High Efficiency High Power Density DC/DC Converter for Low Voltage Power Supply in Electric and Hybrid Vehicles[END_REF]. The main difference between the two resonant converters is the role of the transformer magnetizing inductance: the LLC is composed by a series inductance (Lr) and a series resonant capacitor (Cr) but also it uses the magnetizing inductance (Lm) to obtain a second resonant frequency. In the case of the LC series resonant, only the series inductance Lr and capacitor Cr are used in the resonance; the magnetizing inductance could be considered infinite in this converter. In the design of the LLC converter (Fig. 1A), the series inductance and the magnetizing inductance have similar magnitudes characterizing two closers resonance frequencies, but in the LC (Fig. 1B) Lr is too small when compared with Lm and normally the frequency variation range to regulate the output voltage is higher. Both converters are designed to operate under variation of the switching frequency, but the main resonant frequency is fixed at 100 kHz for both converters in the application example.

The DAB converter (Fig. 1C) operates with a fixed switching frequency, but the output regulation is made by adding a phase delay angle between the voltages on the transformer sides. Different command modes can increase the efficiency of this converter by realizing Zero Voltage Switching (ZVS) over an expanded output voltage range [START_REF] Kumar Jain | PWM control of Dual Active Bridge: Comprehensive Analysis and Experiemental Verification[END_REF].

The Phase-shift converter (Fig. 1D) also operates under fixed switching frequency, but differently from the DAB, the output regulation is made by an internal phase delay angle used between the two half-bridges on the primary side. The secondary structure consists in a current double that also could be placed by a full-bridge as in the other topologies; however, the first structure allows reducing the conduction power losses and has a series of advantages over other structures [START_REF] Biela | Optimization of a 5kW Telecom Phase-shift DC-DC Converter with Magnetically Integrated Current Doubler[END_REF], being also recommended for high current operation. In the design of the LLC and the LC resonant converters, keeping the switching frequency always higher than the resonance frequency, is possible to ensure ZVS in the primary side and ZCS in the secondary side. In the case of the DAB converter, the converter is designed with the methodology presented in [START_REF] Zhao | Overview of Dual-Active Bridge Isolated Bidirectional DC-DC Converter for High-Frequency-Link Power Conversion System[END_REF] with optimal operation at nominal conditions; however, under light output power and high output voltage the converter loses the capability of soft-switching and the same occurs with the phase-shift converter.

The converter designs are presented in Tableau 2.

Tableau 2: The design parameters for 3.5 kW.

Volume and total power losses estimation

The total volume occupied by the converters is considered as the sum of the volume occupied by the output filter (capacitors, inductors), the volume occupied by the transformer, including the magnetizing inductance in the case of the LLC resonant converter (if the inductance is not integrated in the transformer), the volume of the series inductance, the power switches and the heat sink.

The output capacitor volume for each converter depends on the RMS current, capacitance and maximum voltage. For this example, solid tantalum capacitors are selected and used in parallel to reduce the current ripple. The Phase-shift converter is the converter that requires the smallest output capacitance due to the presence of the two inductors in the secondary side that smooth the output current. The power losses in the capacitors are presented in Table 3 and are calculated with the datasheet information:

(1)

The volume occupied by the transformer is estimated by the product between the effective magnetic core section area A e and the winding area A w . This product establishes the closest available magnetic core to construct the transformer and it's determined by knowing the applied voltage waveform, the RMS current in the windings, the number of turns, the peak flux density B max , the current density J, and a feasible window utilization factor Fu [START_REF] Pressman | Switching Power Supply Design» Second Edition[END_REF], that normally for discrete transformer can be settled between 0.35 and 0.40.

(

) 2
Ferrite core E shape from Magnetics is considered with a same magnetic material for the four converters. The inductor volume estimation is similar to that used for the transformer, but its effective magnetic core section area is directly proportional to the peak current, due to the maximum stored energy:

(

The power losses are estimated in the inductor and in the transformer. The magnetic core power losses are calculated by Steinmetz equation [START_REF] Herbert | User-friendly Data for Magnetic Core Loss Calculations[END_REF] and by using the information available on the datasheet considering the volume of the core. The winding power losses are estimated by the product between the RMS current and the equivalent resistance. In the case of the phase-shift converter, the output filter inductances are also considered, but in this case only the power loss due to the DC winding resistance is considered. In the case of the power transistors, the power losses are evaluated and a heat sink is calculated to prevent that the component has its junction temperature higher than the maximum allowed temperature. The total power losses, divided between conduction and switching power losses, are evaluated in Simetrix and compared with analytical expressions considering ZVS turn-on on the primary and ZCS on the secondary sides for the resonant converters and hard-switching at light load for the Phase-shift and DAB converter. It's also considered that the converters are synchronously rectified in order to prevent the reverse conduction power losses on the low voltage side. Reverse recovery energy is also considered for the ZVS turn-on condition.

(4)

(5)

The junction temperature is determined by the product between the total power losses produced by the device and its thermal resistance between case and junction Rthjc, added to the case temperature, Tc. If it's necessary, Tc is reduced by increasing the size of the heat sink. It's also considered individual's heat sinks for high and low voltage sides considering the ambient temperature of 40°C. The thermal and electrical main characteristics of the three different 650V power transistors are presented in the following table.

RELIABILITY USING FIDES GUIDE MODEL

In order to estimate the lifetime of the converters, FIDES methodology was investigated.

The methodology FIDES described in [START_REF]FIDES Guide 2004 Edition A -Reliability Methodology for Electronic Systems[END_REF] and [START_REF]FIDES Guide 2009 Edition A -Reliability Methodology for Electronic Systems[END_REF] is a result of a study began in 2001 by 8 companies in France and proposes a methodology for electronic system reliability. The methodology takes into account failure rates from the manufacturing process, design process and from the system's life profile, where the constraints as thermal, electrical and mechanical over stress are also evaluated. Its' also possible, include new technologies in the methodology because of its characteristic.

The failure rate ( ) is a constant and is based on the useful life of the system containing also the contribution of each individual component in the power converter, represented by the equation ( 7):

(7)
For each component, is the product of three factors, as represented in equation ( 8): the part manufacturer acceleration factor, π PartMan, representing the manufacturing quality of the component and the manufacturer qualification; the process acceleration factor, π Process , that includes quality and technical control in the product lifecycle; and the physical failure rate, Physical , which includes the base failure rate and physical constraints during its operational useful life, as temperature, humidity and mechanical vibrations [START_REF]FIDES Guide 2004 Edition A -Reliability Methodology for Electronic Systems[END_REF] [START_REF]FIDES Guide 2009 Edition A -Reliability Methodology for Electronic Systems[END_REF]. [START_REF] Singhal | Qualification Reliability of a GaN Process Platform[END_REF] The load profile presented in (Fig. 3) is used to determine the failure rate of the converters.

The failure rates obtained by the FIDES methodology are expressed in a calendar of a yearly profile (8760 hours) where each phase described in (Fig. 3) must be weighted by the phase's duration. It's considered in this application example that the demanded power profile applied on the converters occurs 365 times during a year. Three groups of components in each converter are submitted to the power load profile from (Fig. 3): the magnetic components consisting of the high frequency transformer, the resonant inductance and power inductors, as well the output filter inductances; the output capacitors and the semiconductors from high and low voltage sides. In the high voltage side are considered three different transistors: a 650V MOSFET CoolMOS technology (IPx65R099-TO247), a 650V GaN FET normally-off device in a cascode structure (TPH3205WSB-TO247) and a 650V enhancement mode GaN direct-driven power transistor (GS66516T topside cooled type package) presented in Tableau 5. On the low voltage side, a same Si MOSFET is considered for all the converters, the IPT007N06N.

The reliability of active components

In this section, the failure rates associated with the power transistors are determined. It consists in to find the elements described in [START_REF] Singhal | Qualification Reliability of a GaN Process Platform[END_REF] for the three different semiconductors.

The physical part has 3 contributions: [START_REF] Yang | Design of a High Efficiency High Power Density DC/DC Converter for Low Voltage Power Supply in Electric and Hybrid Vehicles[END_REF] Π induced is the overstress due to the physical position of the final converter, due to the most influence overstress on the application, due to the sensitivity to the overstress and the influence of the policy for taking into account those overstresses during the system development phase. These parameters are resumed in equation [START_REF] Biela | Optimization of a 5kW Telecom Phase-shift DC-DC Converter with Magnetically Integrated Current Doubler[END_REF]. The audit questionnaire proposed in FIDES [START_REF]FIDES Guide 2004 Edition A -Reliability Methodology for Electronic Systems[END_REF] (page: 50-54) is used to evaluate the criteria for mechanical and thermal overstresses being differentiated for the power transformer, capacitors and inductors, but not for the three different high voltage side power transistors. [START_REF] Kumar Jain | PWM control of Dual Active Bridge: Comprehensive Analysis and Experiemental Verification[END_REF] For each component presented in the power systems, the product between the acceleration factor (π acceleration ) and its base failure rate ( o ) has the influence of five constraints: the thermal constraints related to the junction temperature, casing and solder joints, respectively and the influence of humidity and mechanical vibrations, as presented in equation ( 12). [START_REF] Biela | Optimization of a 5kW Telecom Phase-shift DC-DC Converter with Magnetically Integrated Current Doubler[END_REF] The thermal acceleration factor π TH is modeled by Arrhenius and one of the physical tests associated with this model is the High Temperature Operating Life (HTOL) executed according to the JEDEC EIA JESD-22-A108A standard: [START_REF] Zhao | Overview of Dual-Active Bridge Isolated Bidirectional DC-DC Converter for High-Frequency-Link Power Conversion System[END_REF] In FIDES, Ea is assumed as 0.7eV because it's considered as the activation energy associated with the thermo-electrical failure mechanism for Si FETs; k is the Boltzmann constant, 8.617 x 10 -5 eV/K. T use is the reference temperature of the component and T stress is the temperature achieved due to the stress.

The thermal acceleration factor of the case π THCase and of the solder joints π THSolder use the Norris-Landzberg model and represents the fatigue mechanism due to temperature variation. In FIDES it appears with an equivalent Ea of 0.122 eV for both parts, case and solder joints: [START_REF] Pressman | Switching Power Supply Design» Second Edition[END_REF] N Cyannual and t annual are the annual n° of cycles and the annual duration of the phase respectively. Θ Cy is the cycle duration in hours.

T Cm , T o , ΔT o and ΔT Cy are the maximum cycle temperature, the reference temperature, the reference thermal amplitude and the thermal amplitude of the cycle respectively. m is the fatigue coefficient of the material P is the acceleration power of duration factor, 1/3 in FIDES.

The relative humidity π Hum and mechanical vibrations π Mech factors are based on Peck's and Basquin's models; and a same influence of those parameters is considered for the three power devices. The complete equation can be verified in [START_REF]FIDES Guide 2004 Edition A -Reliability Methodology for Electronic Systems[END_REF], [START_REF]FIDES Guide 2009 Edition A -Reliability Methodology for Electronic Systems[END_REF].

The information concerning the Silicon MOSFET reliability is a result of mature qualification experience and the particular MOSFET IPX65R099C is qualified according to the JEDEC (J-STD20 and JESD22). The qualification of Silicon power transistors normally consists of avalanche and Safe Operating Area testing, but the GaN materials have different failure modes which difficulties the development of a single evaluation methodology for those components.

According to [START_REF] Bahl | Application reliability validation of GaN power devices[END_REF] the qualification of the GaN transistors should be done differently for their specific failure modes instead of using the same tests used for Silicon transistors and a switching mode test should be used in order to evaluate the failure mechanisms in hard -switching. However, as can be verified by the reliability report from TPH3205WSB [START_REF] Brohlin | Direct-drive configurations for GaN devices[END_REF], the activation energy determined by JEDEC procedure matches with the activation energy determined by the acceleration high temperature switching operation test for this particular device. This result can be explained by the cascode structure of the device. In the cascode structure of the TPH3205WSB (Fig. 4A), the voltage drive is applied to the Si mosfet in series with the GaN transistor, contrarily the other GaN device (GS66516T receives directly the drive voltage). This characteristic helps to understand why the qualification tests applied to the first device present similar results, since the operating conditions in the offstate and on-state have more similarities with the Si mosfet behavior, contrarily of the enhancement mode direct drive device represented in (Fig. 4B). Furthermore, as explained in [START_REF] Brohlin | Direct-drive configurations for GaN devices[END_REF], the distribution of the voltage between the parasitic capacitances in off-state can generate an avalanche effect that also characterizes one of the failure mechanisms represented by the well established models.

Despite the difficult in to establish a model to describe the failure modes of GaN transistors, an attempt is made by considering only different thermal acceleration factors in the physical part for the three different power transistors. It consists in to determine different activation energies for π TH, π THCase and π THSolder .

The activation energy (Ea) in the three first acceleration factors is well defined for Silicon mosfets. For the qualified cascode GaN device, this information is available in the reliability report [START_REF] Brohlin | Direct-drive configurations for GaN devices[END_REF], as 1.84eV due to the thermal-electrical stress (used in the term π TH) and 0.09 eV for π THCase and π THSolder acceleration factors.

A previous study shows that the activation energy for GaN devices is between 1.05 and 2.5 eV [START_REF] Zanoni | AlGaN/GaN-Based HEMT Failure physics and reliability: mechanisms affecting gate edge and schottky junction[END_REF]. An equivalent energy of 2.0 eV is used for the non-qualified device. In [START_REF] Ejjabraoui | Arospace Optoelectronics reliability:Application of Multi-parametric BAZ model[END_REF], a multiparametric BAZ model shows the increasing in the probability of non-failure if the energy associated is also increased and the role of humidity and voltage are used to predict the necessary energy.

In order to differentiate the GaN and Si semiconductors, not only the physical part is evaluated, but also the manufacturer acceleration factor π PartMan in equation [START_REF] Singhal | Qualification Reliability of a GaN Process Platform[END_REF]. The part manufacturer acceleration factor is determined by using equation [START_REF] Herbert | User-friendly Data for Magnetic Core Loss Calculations[END_REF]. QA manuf is the description of the manufacturer quality assurance level, QA comp is the description of the component quality assurance level and RA comp is the risk level of the component associated with the test performed. For those three factors, the highest assurance level is equal to 3, when the assurance level obtained is higher than the reference state of the art or ultra passes the expectation; and 0 in the worst case, when there's no available information or when any qualification test was performed. [START_REF] Herbert | User-friendly Data for Magnetic Core Loss Calculations[END_REF] is the experience factor that the component buyer may have with his supplier and in the studying case is considered the same for all the three devices.

Capacitor, transformer and inductor reliability

The failure rates of capacitors, transformer and inductor are also determined according to equation [START_REF] Singhal | Qualification Reliability of a GaN Process Platform[END_REF].

For the output capacitors, the RMS current is one of the most important specifications for its reliability and it also affects the converter's efficiency resulting in a different impact for each topology studied. The most part of power converter designers combine technologies such as Tantalum, Aluminum and Tantalum Polymer in order to reduce cost and attend the requirements of current ripple and a lifetime; in some cases is necessary to investigate different combinations to find the best configuration. In this study only Tantalum capacitor is considered.

The part manufacturer factor and process are determined as in the case of active components. The physical part associated includes mechanical, thermal and thermo-electrical acceleration factors and in the induced factor, the relative sensitivity is defined for the solid tantalum capacitor for electrical, thermal and mechanical overstress as indicated in the FIDES guide [START_REF]FIDES Guide 2004 Edition A -Reliability Methodology for Electronic Systems[END_REF], [START_REF]FIDES Guide 2009 Edition A -Reliability Methodology for Electronic Systems[END_REF].

The physical failure rate is presented in equation [START_REF]FIDES Guide 2004 Edition A -Reliability Methodology for Electronic Systems[END_REF]. This same equation is also used for transformer and inductors. The voltage applied (Vapplied) on the capacitor, the maximum voltage specified by the supplier (Vrated) and the board temperature, are the factors contributing to physical stresses in the capacitors. The thermo-electrical acceleration factor is calculated in equation ( 16):

(15) (16) (17) (18)
The estimation of the magnetic component reliability, transformer and inductors are also described with the same acceleration factor models as in the capacitor study, but the temperature rise relative to the ambient temperature is used as recommended in the FIDES methodology (30°C for high power transformer), if there's no other available method. In order to evaluate the variation of temperature in the transformer due to the winding power losses, an equivalent thermal resistance was estimated considering the nominal power losses and the maximum allowed temperature. In [START_REF] Mulder | Application note on the design of low profile high frequency transformers[END_REF] has established an empirical formula to associate this thermal resistance with the volume of the magnetic core. It's also assumed that the core loss corresponds to the half of the total transformer loss, which is acceptable for a good designed transformer. [START_REF] Zanoni | AlGaN/GaN-Based HEMT Failure physics and reliability: mechanisms affecting gate edge and schottky junction[END_REF] In [START_REF] Markus Andresen | Thermal Stress Analysis of Medium-Voltage Converters for smart transformer[END_REF] the thermal stress in a power transformer is evaluated with a focus on a mission profile. A more precise analysis is recommended for planar transformers because the heat flow exchanged is not always performed as expected due to its physical placement on the board.

INTEGRATION OF THE RELIABILITY USING FIDES GUIDE

MODEL

For each power converter, the demanded power profile is inserted in Simetrix, where the converter is simulated for the different input conditions. The power profile is defined in a script in Octave environmental that runs the transient simulation in the first environmental and recovers the information after each cycle of the simulation. In Simetrix, the power switches are modeled by a switch that contains the information provided by the manufacturer. The model available on their websites could also be used for the simulations; however the simulation takes more time to achieve the steadystate. The simulation results, consisting of current and power losses in each power transistor and the current in the primary and secondary transformer winding are then loaded with Octave and the thermal equivalent model of the power switches and the reliability model for all the evaluated components, are used to determine the Mean Time to failure (MTTF) of the converter, presented on (Fig. 5). The total stress is derived from the rain flow counted cycles over a year [START_REF] Downing | Simple rainflow counting algorithms[END_REF].

After obtaining the failure rate of each component, the total failure rate of the converter is obtained by equation [START_REF] Carton | New FIDES Models for Emerging Technologies[END_REF]. This failure rate is the number of failures per unit of time. The equivalent Mean Time to failure in years is obtained by considering the FIT of the converter, which consists in the measure of failure rate in 10 9 device hours.

(20)

SIMULATION RESULTS AND LIMITATIONS

Results in (Fig. 6) and (Fig. 7) show the volume and efficiency for the different topologies considering the power profile presented in section 3. It's necessary to recall that the volume occupied by the resonant topologies and also for the DAB converter can be reduced by increasing the switching frequency without reducing the efficiency due to lower power losses generated in the GaN devices. Not only because the transformer can be reduced, but also the series inductance. The same does not occur with the same proportion for the Phaseshift converter due to the two output inductors. Comparing its efficiency with the LLC resonant converter, the first one has the smaller circulating energy and smaller rms currents justifying its better performance. Although the cascode GaN has better π PartMan than the E-mode GaN and can achieve the same T jmax as the other devices, the topologies DAB and LLC occupy more volume with the first device. Indeed, as its thermal resistance is higher, we need to increase the heat sink size in order to decrease its junction temperature and increase its lifetime. The LC series resonant and the DAB converters with HEMT GaN look the most efficient topologies for this configuration. Furthermore the LC presents the highest lifetime. In (Fig. 8) the failure rate obtained for a single power transistor connected at high voltage side is presented. It confirms the BAZ prediction model in [START_REF] Ejjabraoui | Arospace Optoelectronics reliability:Application of Multi-parametric BAZ model[END_REF] that the non-failure probability increases with the activation energy, but also shows the role of junction temperature in the failure rate. The higher the temperature elevation between junction and case of the device, higher needs to be the additional heat sink in order to reduce the probability of failure. Furthermore, the fact that the GaN transistors support higher temperature has an impact in their reliability model. It's necessary to remark that the reliability study is only applicable in the range for which the components are qualified. In the case of the non-qualified GaN power transistors, it's assumed that its characteristic assumptions are enough to this application range. The FIDES Guide is applicable only for ambient range temperature between -55°C and 125°C.

CONCLUSIONS

The comparison of four different DC-DC isolated converters considering efficiency, reliability and volume was investigated. The comparison of three different power switches, including a Si CoolMOS, a cascode GaN and an E-mode GaN, showed the importance of its thermal characteristics in the lifetime prediction. At 100 kHz, the LC resonant followed by the DAB converter designed with the E-mode GaN transistor are most promising topologies considering efficiency, but the LC resonant seems more robust with respect of the lifetime. The difficulty in obtaining more data concerning the reliability of the non-qualified transistors can be surpassed using the FIDES guide and estimated base failure rates associated with the device. However, the activation energy and the use of the part manufacturer factor are not enough to estimate theirs reliability with accuracy comparing with Silicon mosfet. It could be used for comparing similar technologies, as used for both GaN structures, but it's necessary to include different acceleration factors to evaluate the most influent failure mode of a particular GaN structure, either for the cascode structure or for the directdrive enhancement mode transistor. From the results is also possible to verify that the MTTF is a compromise between volume and Tj and can be increased by using a larger heat sink.

Fig. 1 :

 1 Fig. 1: DC/DC isolated converter topologies.

( 6 )Fig. 2 :

 62 Fig. 2: Thermal equivalent model to estimate the mosfet junction temperature.

Fig. 3 :

 3 Fig. 3: Power load profile application required once by day.

Fig. 4 :

 4 Fig. 4: Enhancement mode device structures a) TBS3205WBS b) GS66516T.

Fig. 5 :

 5 Fig. 5: Flowchart of the platform that integrates the FIDES model with time dependent simulations.

Fig. 6 :

 6 Fig. 6: Estimated performance of the LLC, LC, DAB and Phase-shift. Converters designed with different power switches.

Fig. 7 :

 7 Fig. 7: Volume, MTTF-LLC, LC, DAB and Phase-shift. converters.

Fig. 8 :

 8 Fig. 8: Failure rate of a single power transistor connected at High Voltage side.

Table

Table 1 .

 1 1: DC/DC power converter requirements for the application example.

	Vin (V)	Vout (V)	Pout max (W)	Fsw nom (kHz)
	290-400	10-14	3500	100


Baoling Guo

Seddik Bacha

Mazen Alamir

Amgad Mohamed

Variable speed micro-hydro power generation system: Review and Experimental results *

Keywords: Micro-hydro power, variable speed operation, modelling, topology, 'Hill charts', dynamics

Micro-hydro power has a large potential in the renewable energy context. Variable speed technique is preferable to improve the hydraulic power profitability and optimise the hydraulic transient process. First, a review of hydraulic modelling approaches is addressed. In particular, an improved hydraulic modelling approach based on the 'Hill charts' measurements is presented. Furthermore, representative power topologies employed to variable speed micro-hydro power generation systems are reviewed. A direct drive permanent magnet synchronous generator topology is implemented in this paper. Experiments are provided to verify effectiveness of the hydraulic model built and its control algorithms. Conclusions are indicated in the end.

INTRODUCTION

Micro-hydro power is widely used in the renewable energy context [START_REF] Ansel | Modelling and simulation of an autonomous variable speed micro hydropower station[END_REF]- [START_REF] Yadav | Pond head level control in a run-of-river hydro power plant using fuzzy controller[END_REF]. Large applications to Micro-Hydro Power Plants (MHPPs) have proved that variable speed operations can gain more hydraulic power than the fixed speed case [START_REF] Ansel | Modelling and simulation of an autonomous variable speed micro hydropower station[END_REF][START_REF] Belhadji | Adaptive mppt applied to variable-speed microhydropower plant[END_REF][START_REF] Belhadji | Modeling and control of variable-speed micro-hydropower plant based on axial-flow turbine and permanent magnet synchronous generator (mhpp-pmsg)[END_REF][START_REF] Marcel Oliveira De Mesquita | Maximum power point tracking applied on small hydroelectric power plants[END_REF][START_REF] Marquez | Dynamic modeling, simulation and control design of an advanced micro-hydro power plant for distributed generation applications[END_REF][START_REF] Guo | Variable speed micro-hydro power plant : modelling, loss analysis, and experiment validation[END_REF]. Besides, variable speed techniques can improve the operation process such as mitigating the cavitation effects, alleviating water hammer disturbances, and optimizing transient processes [START_REF] Belhadji | Adaptive mppt applied to variable-speed microhydropower plant[END_REF][START_REF] Belhadji | Modeling and control of variable-speed micro-hydropower plant based on axial-flow turbine and permanent magnet synchronous generator (mhpp-pmsg)[END_REF]. Due to the benefits of variable speed operation, large efforts have been contributed.

Firstly, a practical hydraulic model is the key for control law test. However, unlike the well-developed case of wind turbines which has an optimal tip speed ratio to realize the maximum power efficiency, there is no general efficiency expression for hydraulic turbines [START_REF] Jiang | Power conversion system for grid connected micro hydro power system with maximum power point tracking[END_REF][START_REF] Marquez | Dynamic modeling, simulation and control design of an advanced micro-hydro power plant for distributed generation applications[END_REF]. The efficiency highly depends on both the geometry turbine design and its operating conditions, which are complex to be determined, numerous types of models are proposed in previous works. Some modelling approaches neglect the water flow rates variations caused by rotation speed changes [START_REF] Ansel | Modelling and simulation of an autonomous variable speed micro hydropower station[END_REF][START_REF] Marcel Oliveira De Mesquita | Maximum power point tracking applied on small hydroelectric power plants[END_REF][START_REF] Marquez | Dynamic modeling, simulation and control design of an advanced micro-hydro power plant for distributed generation applications[END_REF]. The application scope of [START_REF] Ansel | Modelling and simulation of an autonomous variable speed micro hydropower station[END_REF][START_REF] Borkowski | Laboratory model of small hydropower plant with variable speed operation[END_REF][START_REF] Marcel Oliveira De Mesquita | Maximum power point tracking applied on small hydroelectric power plants[END_REF][START_REF] Marquez | Dynamic modeling, simulation and control design of an advanced micro-hydro power plant for distributed generation applications[END_REF] is limited to particular hydraulic turbines. Some dynamic models can achieve more precise curves but not practical for variable speed implementations [START_REF] Borkowski | Maximum efficiency point tracking (mept) for variable speed small hydropower plant with neural network based estimation of turbine discharge[END_REF][START_REF] Mello | Hydraulic turbine and turbine control models for system dynamic studies[END_REF][START_REF] Mesnage | Hydraulic-turbine start-up with "s-shaped" characte-ristic[END_REF][START_REF] Souza | Study of hydraulic transients in hydropower plants through simulation of nonlinear model of penstock and hydraulic turbine model[END_REF]. Considering these drawbacks, an improved modelling approach based on static measurements is proposed in [START_REF] Guo | Variable speed micro-hydro power plant : modelling, loss analysis, and experiment validation[END_REF], which could be applied to a class of micro-hydro turbines with 'Hill Chart' efficiency characteristics. Therefore, a 'Hill charts' based model is used to achieve the real-time simulation study in this paper.

Furthermore, to achieve the efficient variable speed operation, various hydraulic energy conversion topologies based on Power Electronics (PE) are proposed in [START_REF] Belhadji | Modeling and control of variable-speed micro-hydropower plant based on axial-flow turbine and permanent magnet synchronous generator (mhpp-pmsg)[END_REF][START_REF] Benelghali | Comparison of pmsg and dfig for marine current turbine applications[END_REF][START_REF] Chen | Marine tidal current systems : State of the art[END_REF][START_REF] Sabar Nababan | An overview of power topologies for micro-hydro turbines[END_REF]. The topologies are different from several aspects : namely, generation units, mechanical coupling system, and PE connection. A review on available topologies is needed, which could help designers to make the right option.

This paper is organised as follows. Firstly, different modelling approaches applied to MHPPs are reviewed in Section 2. In particular, a modelling method based on the 'Hill Charts' measurements is described. Then, it is continued by a review on available energy conversion topologies in Section 3. The employed grid-connected architecture of a variable speed micro-power generation system and its global control design are also presented. Further more, experiments of variable speed operation and grid integration control are validated in a Power Hardware-In-the-Loop (PHIL) experiment benchmark in Section 4. Conclusions are indicated in the last section.

MICRO-HYDRAULIC TURBINE MODELLING

In this section, various hydraulic models are reviewed, the strengths and drawbacks of those models are remarked. Moreover, an improved modelling approach based on the so called 'Hill charts' is presented.

Hydraulic turbines

The hydraulic turbines can be classified into impulse turbine and reaction turbine as shown in Fig. 1. In fact, a large majority of MHPPs are based on "Run-of-river", which has a low head and high water flow rates [START_REF] Ansel | Modelling and simulation of an autonomous variable speed micro hydropower station[END_REF][START_REF] Belhadji | Adaptive mppt applied to variable-speed microhydropower plant[END_REF][START_REF] Marquez | Dynamic modeling, simulation and control design of an advanced micro-hydro power plant for distributed generation applications[END_REF][START_REF] Joachim | Hydro power the design, use and function of hydromechanical, hydraulic and electrical equipment[END_REF]. Therefore, a class of axial Micro-Hydraulic Turbines (MHTs) such as Kaplan [START_REF] Ansel | Modelling and simulation of an autonomous variable speed micro hydropower station[END_REF], Semi-Kaplan [START_REF] Belhadji | Adaptive mppt applied to variable-speed microhydropower plant[END_REF][START_REF] Belhadji | Modeling and control of variable-speed micro-hydropower plant based on axial-flow turbine and permanent magnet synchronous generator (mhpp-pmsg)[END_REF], Bulb [START_REF] Marcel Oliveira De Mesquita | Maximum power point tracking applied on small hydroelectric power plants[END_REF], or Propeller [START_REF] Borkowski | Maximum efficiency point tracking (mept) for variable speed small hydropower plant with neural network based estimation of turbine discharge[END_REF][START_REF] Marquez | Dynamic modeling, simulation and control design of an advanced micro-hydro power plant for distributed generation applications[END_REF] turbines and Cross flow turbines [START_REF] Vallet | Management and control of operating regimes of cross-flow water turbines[END_REF] become the most attractive prime movers because of their high efficiency under such conditions. The power absorbed from the hydraulic turbine depends on the net water head H(m) and the water flow rate Q w (m 3 /s) :

P h = ρ • g • H • Q w (1)
Hydraulic turbine efficiency η is defined as the ratio of mechanical power transmitted by the shaft to the absorbed hydraulic power, which strongly affects the net output mechanical power P m (watts) :

P m = η • ρ • g • H • Q w (2)
where ρ (kg/m 3 ) the volume density of water, g the acceleration due to gravity (m/s 2 ).

The mechanical torque could be given by

T m = P m ω (3)
where ω (rad/s) represents the turbine rotation speed.

Modelling approaches review

Simplified linear torque model

A Kaplan turbine submitted to fixed head is described in [START_REF] Ansel | Modelling and simulation of an autonomous variable speed micro hydropower station[END_REF], which has neither blade pitch control nor guide vane regulation. The hydraulic behaviour is described by a linear decreasing turbine torque (T m ) versus speed (ω) characteristic by

T m = T n (1.8 - ω ω n ) ( 4
)
where T n and ω n represent the rated values. This hydraulic behaviour for a fixed flow rate is presented in Fig. 2. It indicates that the torque becomes null for a rotating speed value ω e , which is called the runaway speed. The mechanical power is consequently a parabola.

n  e  Fig. 2. Simplified linear torque model [START_REF] Ansel | Modelling and simulation of an autonomous variable speed micro hydropower station[END_REF] However, the turbine used in [START_REF] Ansel | Modelling and simulation of an autonomous variable speed micro hydropower station[END_REF] includes neither blade pitch nor guide vane. Also, this paper assumes that water flow variations are very slow compared to the drive dynamics, the model in Fig. 2 only works under fixed flow rates conditions.

2-D efficiency model

In [START_REF] Marquez | Dynamic modeling, simulation and control design of an advanced micro-hydro power plant for distributed generation applications[END_REF], a Propeller type turbine modified from a Kaplan turbine has been modelled, numerical approximations are developed to calculate hydraulic turbine efficiency. The efficiency expression is described by

η(λ, Q w ) = 1 2 [( 90
λ i + Q w + 0.78)exp( -50 λ i )]3.33Q w ( 5
)
λ i = [ 1 λ + 0.089 -0.035] -1 (6)
where λ = RAω/Q w , R (m) is the radius of the hydraulic turbine, A (m 2 ) is the area swept by rotor blades, and ω (rad/s) is the hydraulic turbine rotational speed.

The efficiency curves are presented in Fig. 3. It can be observed that there always exists an optimal rotation speed to achieve the maximum efficiency under each water flow rate.

In another work [START_REF] Marcel Oliveira De Mesquita | Maximum power point tracking applied on small hydroelectric power plants[END_REF], based on some loss curves, the efficiency η of a Bulb type turbine is modelled by

η = 1 -|ω 11 -Q 11 | 1.25 (7)
where the turbine rotation speed ω 11 and the discharge of water Q 11 are both expressed in unitary values. The efficiency will vary under different operation conditions. The expression indicates that only when the unitary values of rotation speed and water flow rate are the same, the efficiency is maximized, namely to be 1.

These kinds of models are improved to be suitable for varying discharge conditions. According to [START_REF] Farell | Hydromechanics of variable speed turbines[END_REF], the flow rate can be increasing or decreasing as a function of the rotational speed, depending on the specific speed and the geometrical design parameters of the turbine, for both. While these 2-D models neglect the water flow rate variations caused by rotation speed changes. Also, they are only suitable for a hydraulic turbine of neither blade pitch control nor valve regulation.

Look-up table based model

In [START_REF] Fraile-Ardanuy | Neural networks for optimal operation of a run-of-river adjustable speed hydro power plant with axial-flow propeller turbine[END_REF], the look-up table is filled in by using a trained neural network. In order to fill in the statistic hydraulic lookup tables, it sweeps different combinations of different river flow and guide vanes position for constant water level, then the measurements under steady state are stored in the tables as shown in Fig. 4.

River flow

Guide vanes

Steady state reach?

No Yes Store in look-up table

1  n  11  1 Q 1 m  1n  m Q mn  ... ... . . . Q  Fig. 4
. Fill in the look-up table [START_REF] Fraile-Ardanuy | Neural networks for optimal operation of a run-of-river adjustable speed hydro power plant with axial-flow propeller turbine[END_REF] Maximum efficiency point tracking is discussed in [START_REF] Borghetti | Maximum efficiency point tracking for adjustable-speed small hydro power plant. 16th PSCC[END_REF]. The implemented turbine model is based on two look-up tables as illustrated in Fig. 5, where the angular position of the fixed and the rotating vanes (α and β), and the rotational speed n(r/min) are considered. These tables provide the efficiency η T and the discharge of the hydraulic turbine Q, respectively. The look-up tables have been obtained from experimental measurements carried out on a small hydro power plant.

The measured look-up table can provide a more complete model, more natural factors are considered including discharge of hydraulic turbine, guide vane opening, and pitch angle. However, a look-up table based model is not discontinuous. Besides, it is difficult to scale the obtained model to the laboratory level, consequently, the look-up tables have to be measured under a similar level MHPP.

/ n n D H   rotor speed net head     11 n   11 n 60 2 T T g Q H n     2 11 Q Q D H  Q flow rate torque T n H 11 Q T  11 11 11 ( , , ) Q Q n    11 ( , , ) T T n      3-D table 3-D table Fig. 5. Look-up table based modelling [5]

Real-time efficiency model

The efficiency is calculated in real-time in [START_REF] Borkowski | Maximum efficiency point tracking (mept) for variable speed small hydropower plant with neural network based estimation of turbine discharge[END_REF] by

η = P out 9.81 • Q est • H (8)
The active output power P out is easy to be measured. Therefore, precise estimation Q est for water flow rates becomes the key for its successful application. An accurate measurement of the flow rate in low head schemes is still challenging as shown in Fig. 6. The neural-network-based estimator is used to solve the troublesome measurement of the turbine discharge in [START_REF] Borkowski | Maximum efficiency point tracking (mept) for variable speed small hydropower plant with neural network based estimation of turbine discharge[END_REF]. Compared with a look-up table based model, it achieves more accurate and smoother efficiency curve. However, the estimating method is very complicated for a real-time implementation.

Dynamic hydraulic model

A complete model of micro-hydro plant contains many modelling like penstock, wicket gate, hydraulics behaviour, and mechanical connection as shown in Fig. 8. Dynamic models are frequently discussed in the hydraulic research field [START_REF] Fraile-Ardanuy | Speed optimisation module of a hydraulic francis turbine based on artificial neural networks. application to the dynamic analysis and control of an adjustable speed hydro plant[END_REF][START_REF] Nand Kishor | A review on hydropower plant models and control[END_REF][START_REF] Mello | Hydraulic turbine and turbine control models for system dynamic studies[END_REF][START_REF] Souza | Study of hydraulic transients in hydropower plants through simulation of nonlinear model of penstock and hydraulic turbine model[END_REF]. A complete control design considering large non-linear hydraulic dynamics are presented in Fig. 8. The dynamic models can be divided into linear and non-linear models as shown in Fig. 11, this classification is based on the complexity of the modelling [START_REF] Nand Kishor | A review on hydropower plant models and control[END_REF]. The choosing rules of these turbine models depends on different control objectives.

Hydro plant model

Mechanicalhydraulic Governor

Hydraulic dynamic system Electrical dynamic system Fig. 8. Dynamic model of micro-hydraulic turbine [START_REF] Mello | Hydraulic turbine and turbine control models for system dynamic studies[END_REF] they are studied mostly under the off-line simulation environment. But the computation burden of these non-linear dynamic models makes it too heavy to achieve real-time simulation experiments in laboratory. Also, increasing the calculation burden would deteriorate the control system behaviour. In fact, the transient hydraulic process are much longer in terms of the electrical control, therefore, the dynamics of penstock could be neglected if the implementation is dedicated to electrical control algorithms validation.

Regression model

Regression methods have been widely applied to obtain the hydraulic models. In [START_REF] Borkowski | Laboratory model of small hydropower plant with variable speed operation[END_REF], the hydraulic turbine torque is expressed by a function of speed n(r/min) for different values of the guide vanes angle α as ( 9) presented in Fig. 9. The hydraulic behaviour is approximated by [START_REF] Farell | Hydromechanics of variable speed turbines[END_REF] shown in Fig. 10.

T r m = -1.2 • n r • H r • (0.237 • α 0.544 ) (9)
Q = 0.0166 • α • n r (10)
where Fig. 10. Turbine flow in relation to speed [START_REF] Borkowski | Laboratory model of small hydropower plant with variable speed operation[END_REF] In another case [START_REF] Jiang | Power conversion system for grid connected micro hydro power system with maximum power point tracking[END_REF], the obtained experimental power curve has a similar shape with the parabola, Matlab function 'polyfit' Fig. 11. Overview of hydropower plant models [START_REF] Nand Kishor | A review on hydropower plant models and control[END_REF] was used to regress power-speed relationship. The power is expressed by the rotation speed in a quadratic equation by [START_REF] Fraile-Ardanuy | Speed optimisation module of a hydraulic francis turbine based on artificial neural networks. application to the dynamic analysis and control of an adjustable speed hydro plant[END_REF]. The torque could be computed according to the equation [START_REF] Belhadji | Modeling and control of variable-speed micro-hydropower plant based on axial-flow turbine and permanent magnet synchronous generator (mhpp-pmsg)[END_REF].

T r m = T t /T tN relative torque, n r = n/n N relative speed, H r = H/H N relative head, Q r = Q/Q N relative flow rate, index N represents nominal value.
P m = -1.23ω 2 + 223.1ω -2623.2 (11)
The hydraulic features in [START_REF] Borkowski | Laboratory model of small hydropower plant with variable speed operation[END_REF] are considered to be proportional to the turbine speed for a given guide vanes angle (see Fig. 10), however, according to [START_REF] Farell | Hydromechanics of variable speed turbines[END_REF], the flow rate can be increasing or decreasing with speed increasing. To simplify the modelling, the model used in [START_REF] Jiang | Power conversion system for grid connected micro hydro power system with maximum power point tracking[END_REF] neglects a factor of varying water flow rates. These models still have a limitation for its applications. But the regression method is still an efficient way to obtain the hydraulic mathematical model. The key in a successful implementation is how to make use of the obtained data. Conventionally, a class of hydraulic turbines make use of the so called 'Hill Charts' (see Fig. 12) to describe the steady-state relationships among the rotational velocity N (rpm), if exists the guide vanes opening γ(ratio) , the pressure head H(m), the volumetric flow rate Q(m 3 /sec) and the turbine's mechanical torque T (N.m). The 'Hill Chart' is used to determine the maximum efficiency operating point in [START_REF] Fraile-Ardanuy | Speed optimisation module of a hydraulic francis turbine based on artificial neural networks. application to the dynamic analysis and control of an adjustable speed hydro plant[END_REF][START_REF] Tessarolo | Traditional hydropower plant revamping based on a variable-speed surface permanent-magnet high-torque-density generator[END_REF]. From the control viewpoint, however, it is difficult to extract a useful model from these curves [START_REF] Belhadji | Adaptive mppt applied to variable-speed microhydropower plant[END_REF]. Based on 'Hill charts' measurements, a regression method is proposed to obtain a 3-D hydraulic mathematical model in [START_REF] Guo | Variable speed micro-hydro power plant : modelling, loss analysis, and experiment validation[END_REF], it is well employed into Maximum Power Point Tracking (MPPT) and variable speed control. Because a systematic modelling procedure has been detailed in [START_REF] Guo | Variable speed micro-hydro power plant : modelling, loss analysis, and experiment validation[END_REF], main steps are briefly reviewed here.

11 Q 11 N 1  2  3  max  1 2 3      11 ' Q 11 '' Q 11 ' N 11 '' N '' ' 2 1       

'Hill Charts' based hydraulic modelling

Due to the unavailability of micro-turbine's 'Hill Charts' data, we made use of GE's provided 'Hill Charts' of a Francis turbine which after processing, according to General Electric (GE) engineers, could be down-scaled to approximate the behaviour of a micro-turbine, for example tuning the data points using the new turbine's diameter D, maximum values of (N, γ, H, Q, and T ), in addition, the unstable region (S-region) of the 'Hill Charts' of the Francis turbine can be removed which helps in smoothing the 'Hill Charts' to facilitate the model generation.

Model generation

The 'Hill charts' are generally represented using unitary variables N 11 , Q 11 and T 11 for each γ opening, where :

N 11 = N D √ H ; Q 11 = Q D 2 √ H ; T 11 = T D 3 H
Thus, by using provided data points for (Q 11 , T 11 , N 11 , γ) and by defining the mathematical models Q11 and T11 as shown in equations ( 14)-( 15), non-linear optimization routines can be used to solve the optimization problems ( 12)-( 13 Hence, the torque and volumetric flow rate could be computed using equations ( 14)- [START_REF] Jiang | Power conversion system for grid connected micro hydro power system with maximum power point tracking[END_REF] and by combining them with the definitions of the unitary variables, we get :

Q = Q11 D 2 √ H (16)
T = T11 D 3 H (17)
So, once the pressure head is specified, ( 14)-( 17) could be used to compute Q and T for a given N and γ.

The turbine's efficiency (η) shown in Fig. [START_REF] Jiang | Power conversion system for grid connected micro hydro power system with maximum power point tracking[END_REF] is given by

η = T (γ, ω, H)N ρgHQ(γ, ω, H) (18)
where ρ is the water's density, g is the gravitational acceleration and ω = 2πN 60 . Consequently, the mechanical power (P m ) shown in figure [START_REF] Nand Kishor | A review on hydropower plant models and control[END_REF] could be computed by This section provides a general philosophy on obtaining the mathematical model for a class of hydraulic turbines with 'Hill Charts' efficiency characteristics. Different definitions of Q11 and T11 could be used depending on the provided 'Hill Charts'.

P m = η(γ, ω, H)ρgHQ(γ, ω, H) (19)

'Hill Chart' scaling

It is important to note that the 'Hill charts' could be obtained under different operation conditions. In order to scale it to match the requirement of the laboratory benchmark, the diameter of the turbine and the pressure head could be changed to compute Q and T , in addition to re-scaling the resulting regression models to get equations ( 20)- [START_REF] Munteanu | Hardware-in-the-loop-based simulator for a class of variable-speed wind energy conversion systems : Design and performance assessment[END_REF].

Qs 11 (γ, ζ × N 11 ) = α × Q11 (20) T s 11 (γ, ζ × N 11 ) = β × T11 (21)
where the scaling coefficients α, β, ζ > 0

Remarks on modelling approaches

Compared with simplified linear model [START_REF] Ansel | Modelling and simulation of an autonomous variable speed micro hydropower station[END_REF], look-up table based model [START_REF] Borghetti | Maximum efficiency point tracking for adjustable-speed small hydro power plant. 16th PSCC[END_REF][START_REF] Fraile-Ardanuy | Neural networks for optimal operation of a run-of-river adjustable speed hydro power plant with axial-flow propeller turbine[END_REF], and 2-D efficiency models [START_REF] Marcel Oliveira De Mesquita | Maximum power point tracking applied on small hydroelectric power plants[END_REF][START_REF] Marquez | Dynamic modeling, simulation and control design of an advanced micro-hydro power plant for distributed generation applications[END_REF], the accuracy of this novel modelling approach is improved, because the chosen regression functions lead to capturing the main patterns in the 'Hill Charts'. Furthermore, the scaling operation makes it flexible to adapt to different experiment environments, the practicability is thus improved. Even the model is less complete than [START_REF] Fraile-Ardanuy | Speed optimisation module of a hydraulic francis turbine based on artificial neural networks. application to the dynamic analysis and control of an adjustable speed hydro plant[END_REF][START_REF] Souza | Study of hydraulic transients in hydropower plants through simulation of nonlinear model of penstock and hydraulic turbine model[END_REF], it benefits from lighter computation burden than the dynamic model. This approach could be applied to a class of micro-hydro turbines with 'Hill Chart' efficiency characteristics, which means that it has a wider application range [START_REF] Guo | Variable speed micro-hydro power plant : modelling, loss analysis, and experiment validation[END_REF]. A comparison of the hydraulic modelling approaches is presented in Table 1.

ENERGY CONVERSION CHAINS TOPOLOGIES

Topologies review

A classification of representative power topologies for varible speed Micro-Hydro Power Generation System (MHPGS) is shown in Fig. 17. The topologies are differed from three aspects, namely generators used, mechanical coupling system, and power electronics connection. A. The generation units can be equipped with either Doubly Feedback Induction Generator (DFIG) [START_REF] Benelghali | Comparison of pmsg and dfig for marine current turbine applications[END_REF][START_REF] Sabar Nababan | An overview of power topologies for micro-hydro turbines[END_REF] or Permanent Magnet Synchronous Generator (PMSG) [START_REF] Belhadji | Adaptive mppt applied to variable-speed microhydropower plant[END_REF][START_REF] Guo | Variable speed micro-hydro power plant : modelling, loss analysis, and experiment validation[END_REF], PMSG can be replaced by Electrically Excitation Synchronous Generator (EESG) [START_REF] Chen | Marine tidal current systems : State of the art[END_REF][START_REF] Sabar Nababan | An overview of power topologies for micro-hydro turbines[END_REF]. B. Regarding the mechanical connection [START_REF] Chen | Marine tidal current systems : State of the art[END_REF][START_REF] Sabar Nababan | An overview of power topologies for micro-hydro turbines[END_REF], a gearbox is essentially needed for DFIG. Both the system equipped with gearbox and direct drive system have been used in the PMSG and the EESG. C. Also, PE connection has great differences for various topologies, DFIG has a direct connection between stator and grid, and a back-to-back Voltage Source Converter (VSC) is connected to rotor and stator [START_REF] Belhadji | Adaptive mppt applied to variable-speed microhydropower plant[END_REF][START_REF] Benelghali | Comparison of pmsg and dfig for marine current turbine applications[END_REF]. This inverter The more '+' the better, the more '-' less better.

carries only a fraction of the full scale power by sacrificing the control ability. PMSG has PE units connected to stator and grid, the converter decouples the generator from the grid [START_REF] Guo | Variable speed micro-hydro power plant : modelling, loss analysis, and experiment validation[END_REF]. An excitation converter is needed for EESG [START_REF] Chen | Marine tidal current systems : State of the art[END_REF]. In terms of their costs and maintenances [START_REF] Belhadji | Adaptive mppt applied to variable-speed microhydropower plant[END_REF][START_REF] Benelghali | Comparison of pmsg and dfig for marine current turbine applications[END_REF][START_REF] Chen | Marine tidal current systems : State of the art[END_REF][START_REF] Sabar Nababan | An overview of power topologies for micro-hydro turbines[END_REF], large maintenances for DFIG are needed for its gearbox and the slip rings, but the costs of induction generator are normally cheaper than PMSG, particular for large capacity. Additionally, direct drive systems now are used widely, as a direct-drive PMSG without gearbox requires less maintenance. While the low rotational speed leads to more pole pairs generator design, resulting in bigger generator volume and higher cost.

Implemented architecture and its control design

A direct drive PMSG topology is extensively employed in variable speed hydraulic systems for the following reasons [START_REF] Belhadji | Adaptive mppt applied to variable-speed microhydropower plant[END_REF][START_REF] Guo | Variable speed micro-hydro power plant : modelling, loss analysis, and experiment validation[END_REF][START_REF] Sabar Nababan | An overview of power topologies for micro-hydro turbines[END_REF] : firstly, a PMSG has excellent electric driven capabilities on account of its high efficiency and the high power density ; moreover, the converter decouples the generator from the grid, resulting in less effects of grid disturbances ; moreover, PMSGs with full power converters have an extended speed regulation range. A variable speed grid-connected MHPGS is shown in Fig. 18. It is composed of a micro-hydraulic turbine such as Propeller, Kaplan, or Bulb, a PMSG, double back-toback voltage source converters with PWM interacting with the three-phase grid. Some ancillary devices such as the voltage, current, and position sensors are also presented. 18. Architecture of a variable speed MHPGS and its control design [START_REF] Guo | Variable speed micro-hydro power plant : modelling, loss analysis, and experiment validation[END_REF] The global control objectives of a variable speed MHPGS involve two aspects : the generator side control and the grid side control [START_REF] Belhadji | Adaptive mppt applied to variable-speed microhydropower plant[END_REF][START_REF] Belhadji | Modeling and control of variable-speed micro-hydropower plant based on axial-flow turbine and permanent magnet synchronous generator (mhpp-pmsg)[END_REF][START_REF] Guo | Variable speed micro-hydro power plant : modelling, loss analysis, and experiment validation[END_REF].

A. Generator side control : its main objective is to achieve the MPPT by controlling the turbine shaft to run at the optimal rotation speed. The speed is determined by the dynamic function of input hydraulic driven torque and the electromagnetic torque of PMSG, which are achieved by current components control. In this paper, an adaptive MPPT technique proposed in [START_REF] Belhadji | Adaptive mppt applied to variable-speed microhydropower plant[END_REF] is employed. The generator is vector-controlled upon the PMSG Park model. Double PI controllers are applied in both the speed control and current speed control loops [START_REF] Belhadji | Modeling and control of variable-speed micro-hydropower plant based on axial-flow turbine and permanent magnet synchronous generator (mhpp-pmsg)[END_REF][START_REF] Guo | Variable speed micro-hydro power plant : modelling, loss analysis, and experiment validation[END_REF]. B. Grid side control : it includes double closed control loops, namely, the inner grid current control loop and the outer DC bus voltage loop. DC voltage control ensures the stability of DC bus voltage. The current control achieves high quality current of less harmonics, no distortion, and small frequency vibrations, as well as the power factor to be 1 [START_REF] Guo | Variable speed micro-hydro power plant : modelling, loss analysis, and experiment validation[END_REF]. In this paper, the PI controller is used to maintain constant DC bus voltage ; the grid side current is controlled through three Proportion Resonant (PR) controllers upon the abc three phase frame [START_REF] Belhadji | Modeling and control of variable-speed micro-hydropower plant based on axial-flow turbine and permanent magnet synchronous generator (mhpp-pmsg)[END_REF].

EXPERIMENTAL RESULTS

Experiment benchmark

Experiments are conducted in a PHIL experiment benchmark as shown in Fig. 19. The hydraulic turbine is emulated by a realtime physical simulator. The hydraulic mathematical model established in Section 2.3 is achieved in the dSPACE hardware (DS1005). Then, the physical replication of the hydro power operation is achieved by a torque-controlled Direct Current Motor (DCM), the torque tracking control of DCM is implemented into a TMS320F240 digital signal processor. The PMSG is physically coupled to the shaft of DCM, and the generator is connected to the power grid via double back-to-back VSC. The control algorithms of the energy conversion chains are also achieved by the dSPACE modular of DS1005 board, which is built under the Matlab/Simulink environment. The analog measurements and digital variables could be exchanged through the I/O interface [START_REF] Munteanu | A new method of real-time physical simulation of prime movers used in energy conversion chains[END_REF][START_REF] Munteanu | Hardware-in-the-loop-based simulator for a class of variable-speed wind energy conversion systems : Design and performance assessment[END_REF].

Variable speed control

To start the hydraulic turbine smoothly, a soft starting process is employed as shown in Fig. 20. Firstly, a small initial torque is added to overcome the friction torque, the speed increases slowly ; Then the controllers start working under no-load state ; Finally, the actuator acts and MPPT mode is enabled, the mechanical power is sent to the generator. The optimal rotation speed reference is updated by the MPPT, when the valve opening is adjusted. Then, by controlling the q axis current components, the rotation speed could follow the speed reference to maximize the output mechanical power. The d axis current is controlled to be zero.

Grid integration control

Grid integration performance is presented in Fig. 22. In the soft staring process, the DC bus voltage increases smoothly until it reaches the reference value, meanwhile, the hydraulic power is sent to the grid when the valve actuator starts acting as shown in 22a. The active power and reactive power (controlled to be zero) injected to the power grid vary with the guide valve opening in the MPPT process, and DC bus voltage keeps nearly constant as shown in Fig. 22b. Fig. 23 indicates that the injected grid current is well controlled, which works in phase with the grid voltage.

CONCLUSIONS

In this paper, numerous modelling approaches of MHPPs are reviewed. An improved modelling approach is presented, which could be applied to a class of micro-hydro turbines with 'Hill Chart' efficiency characteristics. This approach provides preciser 3-D model, and the scaling operation makes it flexible to adapt to different experiment environments. The model benefits from lighter computation burden by sacrificing the non-linear dynamics. A direct drive PMSG architecture is employed in this paper, because its has a wider speed operation range and great anti-disturbance capacity. Experiments results indicates that the variable speed technique can obtain more power from the hydraulic turbine ; the grid side integration is effectively control-

Fig. 1 .

 1 Fig. 1. Classification of hydraulic turbines

Fig. 3 . 2 -

 32 Fig.3. 2-D efficiency model[START_REF] Marquez | Dynamic modeling, simulation and control design of an advanced micro-hydro power plant for distributed generation applications[END_REF]

Fig. 6 .

 6 Fig.6. Water flow measurement in a pipe[START_REF] Borkowski | Maximum efficiency point tracking (mept) for variable speed small hydropower plant with neural network based estimation of turbine discharge[END_REF]

Fig. 7 .

 7 Fig. 7. Schematic of a hydro power plantGenerally, these complicated dynamic models are used in the hydraulic dynamics control study or transient process test[START_REF] Mello | Hydraulic turbine and turbine control models for system dynamic studies[END_REF],

Fig. 9 .

 9 Fig.9. Turbine torque characteristics[START_REF] Borkowski | Laboratory model of small hydropower plant with variable speed operation[END_REF]

Fig. 12 .

 12 Fig. 12. 'Hill Chart' diagram and the variable speed operation, N 11 and Q 11 represents unit values of the turbine rotation speed and flow rates, η is the hydraulic efficiency.

1 2 Q 11 - 11 - 2 ( 13 )-d 5 e (d6N11+d7N 2 11 +d8γ+d9γ 2 +d10γ 3 ) 11 T11Fig.

 12111121352311 Figs. (13)-[START_REF] Guo | Variable speed micro-hydro power plant : modelling, loss analysis, and experiment validation[END_REF] show the resulting regression models.

Fig. 15 .Fig. 16 .

 1516 Fig. 15. Efficiency (η) vs ω and γ for H = 0.35m and D = 0.5m, where negative efficiency values are set to zero

Fig. 17 .

 17 Fig. 17. Available architectures for variable speed MHPGS

  Fig.18. Architecture of a variable speed MHPGS and its control design[START_REF] Guo | Variable speed micro-hydro power plant : modelling, loss analysis, and experiment validation[END_REF]

Fig. 19 .

 19 Fig. 19. PHIL experiment benchmark Parameters of the benchmark used are listed in table 2.

  ω (20rad/s/div) the rotation speed, T hdy (2N.m/div) the hydraulic torque, Q (0.1m 3 /s/div) the water flow rate, time (4s/div) Pm (200W/div) the output mechanical power, iq (10A/div) the q axis current, i d (10A/div) the d axis current, time (4s/div) Fig. 20. Starting process of the generator side control

Fig. 21

 21 Fig.21shows MPPT process with valve opening ratios γ = [0.4, 0.5, 0.4]. The optimal rotation speed reference is updated by the MPPT, when the valve opening is adjusted. Then, by controlling the q axis current components, the rotation speed could follow the speed reference to maximize the output mechanical power. The d axis current is controlled to be zero.

  ω (20rad/s/div) the rotation speed, T hdy (2N.m/div) the hydraulic torque reference, Q (0.1m 3 /s/div) the water flow rate, time (4s/div) Pm (200W/div) the output mechanical power, iq (10A/div) the q axis current, i d (10A/div) the d axis current, time (4s/div) Fig.21. MPPT process of the generator side control led. The hydraulic model established could be used in various hydraulic operating regimes and control study.

Fig. 22 .Fig. 23 .

 2223 Fig. 22. Grid integration performance, with U dc (100v/div) the DC bus voltage, Qg (200var/div) the injected reactive power, Pg (200W/div) the injected active power, time (4s/div)

Table 1 .

 1 Comparison of different modelling approaches for Micro-hydro power plants

	Model types	Accuracy	Practicality	Less computation burden	Scope of application
	Linear torque model	-	+	+++	-
	2-D efficiency model	+	++	++	+
	Real-time efficiency model	+++	+	-	++
	Dynamic hydraulic model	+++	++	--	++
	Previous Regression model	+	+	+	+
	'Hill chats' based model	++	++	++	++

Table 2 .

 2 Parameters of the experiment benchmark

	Parameters	Value	Parameters	Value
	Armature Rs	0.17 Ω	Pole pairs	4
	d-axis Lq	0.0017 H	Switch frequency	10 kHz
	q-axis L d	0.0019 H	Friction factor	0.01 N.m.s
	Magnet flux	0.11 W b	Total inertia	0.03Kg.m 2

* This paper is supported by PSPC Innov'hydro project, which specifically brings together GE Renewable, EDF (Electricity of France), Grenoble INP and other key players in the hydroelectric sector, in France