H Wu

D Depernet

V Lanfranchi

A Survey of Synchronous Reluctance Machine used in Electric Vehicle

Keywords: Synchronous reluctance machine, Renewable energy, Electric vehicle, Permanent magnet assisted, Sensorless

Due to more environmental problems and more attentions paid on renewable energy, electric vehicle (EV) has been a hot research topic. As a key equipment in EV, various drives have been studied. Synchronous reluctance machine (SynRM) is also studied widely as a drive in EV for its advantages. This paper presents an extensive survey on the application of SynRM in EV and reviews its working principle, various structures and control strategies.

Introduction

Nowadays, environmental problems such as climate change, pollutions and acid rain have been one of the most important issues in the whole world. To change the situation and pursue sustainable and better future, renewable energy (RE) is getting more and more attentions [START_REF] Pelkonen | Trends in renewable energy production and media coverage: A comparative study[END_REF]. On the other hand, the emissions of greenhouse gas should be reduced while a main source of air pollution is caused by traffic. To meet the requirements of above two aspects, electric vehicle (EV, hybrid electric vehicle is also included in EV) is the best candidate. The electricity generated by renewable energy can be used by EV [START_REF] Longo | Eletric Vehicles Impact using Renewable Energy[END_REF] while EV has little air pollution.

During EV's development, no matter what specific types of EV are presented, electric drive occupies an important position. The requirements for machines used in EV can be concluded as high efficiency, wide speed range, high torque density and high reliability and accepted cost [START_REF] Zhu | Electrical machines and drives for electric, hybrid, and fuel cell vehicles[END_REF]. From the view of application in EV, SynRM which meets most of the above requirements has been researched and tested widely as drives in EV in recent years [START_REF] Malan | Reluctance synchronous machine drive for hybrid electric vehicle. Industrial Electronics[END_REF][START_REF] Ansari | Evaluation of a Reluctance Synchronous Motor: For use in an Electric Mine Shuttle Vehicle (EMSV)[END_REF][START_REF] Ruba | Analysis of maximum torque per ampere control strategy for variable reluctance synchronous machines for traction applications[END_REF][START_REF] Ferrari | Design of synchronous reluctance motor for hybrid electric vehicles[END_REF][START_REF] Staton | Maximising the saliency ratio of the synchronous reluctance motor. Electric power applications[END_REF][START_REF] Rasid | Simple lumped parameter thermal model with practical experimental fitting method for synchronous reluctance machine[END_REF][10][11][12]. [START_REF] Malan | Reluctance synchronous machine drive for hybrid electric vehicle. Industrial Electronics[END_REF] shows SynRM drive has almost advantages of IM in terms of cost, weight, cooling and efficiency. [START_REF] Ansari | Evaluation of a Reluctance Synchronous Motor: For use in an Electric Mine Shuttle Vehicle (EMSV)[END_REF] designs a SynRM used in electric mine shuttle vehicle and states that SynRM could produce 34% more torque than the IM with 29% more current. It proves that SynRM represents serious future direction in automotive industry [START_REF] Ruba | Analysis of maximum torque per ampere control strategy for variable reluctance synchronous machines for traction applications[END_REF].

With more and more research attentions paid on SynRM, this paper focuses on the application of SynRM in EV. The principle of SynRM is introduced. Design and optimization of various rotor topologies and control strategies of SynRM used in EV are also reviewed.

Principle of SynRM

Unlike IM or DC, SynRM follows the reluctance concept which means the rotor rotates thanks to flux variation in order to fulfill the minimum reluctance path rule. The mathematical model of SynRM has been derived and analyzed by many researchers, therefore the electromagnetic torque is given directly by equation ( 1), and more details can be found in [START_REF] Ruba | Analysis of maximum torque per ampere control strategy for variable reluctance synchronous machines for traction applications[END_REF].

    2 3 sin 2 2 2 e d q p T L L I    (1)
Where p is pole number, L d and L q represent inductances of d-axis and q-axis respectively, I is the stator magnetizing current RMS value and θ is current angle. A conclusion can be made that the torque is dependent on difference of L d and L q for certain stator current. So a key parameter, saliency ratio, is defined as L d /L q . A number of performances such as power factor, efficiency, torque density and the speed range at constant power are closely related to saliency ratio [START_REF] Staton | Maximising the saliency ratio of the synchronous reluctance motor. Electric power applications[END_REF]. To get high performance, L d should be as large as possible while L q should be as small as possible. All designs and optimizations of SynRM rotor topology are concerned about how to improve saliency ratio.

SynRM used in EV

The revival of SynRM is based on its high performance which is also important for SynRM applied in EV. This part presents researches about rotor topologies, optimization and control strategy.

Rotor topologies

According to the rotor topology types, SynRM can be classified into three main types: salient pole rotor (SP), axially laminated rotor (ALA) and transversally laminated rotor (TLA). SP rotor is now gained little attention for its structure with small saliency ratio which cannot make the SynRM compare with IM. SynRM with ALA and TLA rotor obtains close or even, in some aspects, better performance than IM. Complex structure and high manufacture cost of ALA limit its acceptability and applications in industry. Compared with ALA, TLA rotor has close performance with simpler structure and lower cost. And commercial SynRMs which apply TLA topology have come out. When it comes to drives used in EV as shown in Fig. 2, the main types of SynRM are TLA topology (TLASynRM) [START_REF] Ansari | Evaluation of a Reluctance Synchronous Motor: For use in an Electric Mine Shuttle Vehicle (EMSV)[END_REF][START_REF] Ruba | Analysis of maximum torque per ampere control strategy for variable reluctance synchronous machines for traction applications[END_REF][START_REF] Ferrari | Design of synchronous reluctance motor for hybrid electric vehicles[END_REF][10][11][12][13][14][15] and its redesigned topology namely permanent magnet assisted synchronous reluctance machine (PMaSynRM) [15][16][17][18][19][20]. TLA structure is manufactured by traditional punch processing method and the layers are connected to each other by ribs. The only difference between TLASynRM and PMaSynRM is that the latter has permanent magnets (PMs) placed in their barriers as shown in Fig. 3. As shown in Fig. 4, its rotor is manufactured combined by two parts which are ALA topology and surface mounted permanent magnet. Compared with interior-permanent magnet machine, it has equivalent performance. A similar rotor structure combined with two different flux barriers parts is also studied in [22] which reduces the torque ripple. The hybrid (with two different rotor structures) type rotor has been developed into another rotor structure, Machaon, which will be presented in next section because the evolution version can be viewed as TLASynRM.

Design and Optimization of rotor

Different researchers focus on different aspects to design and optimize SynRM. And this section will introduce the design and optimization of TLASynRM rotor, from flux barriers, stator slot and ribs. The design stage is the same for PMaSynRM and TLASynRM. The main difference is that designing and optimizing PMaSynRM has to consider the material of PM and how to place PMs. So the design and optimization process of TLASynRM can be applied to PMaSynRM directly.

Flux barriers can affect the saliency ratio and performance greatly and its number and its shape should be chose carefully. When the number varies from one to three, a rotor with three flux barriers per pole generates lowest torque ripple [START_REF] Ferrari | Design of synchronous reluctance motor for hybrid electric vehicles[END_REF]11] Fig. 5 Machaon configuration [START_REF] Ferrari | Design of synchronous reluctance motor for hybrid electric vehicles[END_REF] Other parameters which also can affect the performance of TLASynRM are analyzed. In the case of stator slot, it can also affect the performance of SynRM. With more stator slot and fixed pole pair, torque ripple can be reduced significantly but when stator slot number is more than 24, the effect will became slight [11]. In the case of rib, [13] studies the performances of SynRM with various ribs dimensions and it presents combination of different rib widths in a rotor which can also improve SynRM's performance. Besides, when stator and rotor are manufactured by various steels, comparisons are implemented and SynRM whose stator and rotor are manufactured by different steels has better performance [13].

PMaSynRM

To improve performance, another effective way is to add PMs to flux barriers of SynRM. For the application in EV, PMaSynRM can meet the requirements about high performance, space and cost. The torque for a PMaSynRM can be expressed as [20]:

      2 p 3 = s i n2 + 2 2 e d q q p T L L I i    (2)
Where ψ p is the flux linkage from PMs and I q is the current of q axis. It can be seen that PMaSynRM has two parts of torques: reluctance torque and magnet torque. More PMs can produce larger torque, but from the view of other performances, it may not be good. Effects of PMs placement on performances of PMaSynRM has been analyzed. Compared with concentrated PMs among flux barriers, average torque of distributed PMs is almost the same but torque ripple can be reduced greatly; when distributed PMs are placed along q axis, average torque can be slightly increased than that of distributed PMs along d-axis, while torque ripple will be increased significantly [24]. So distributing PMs in all flux barriers along d-axis can improve performance of PMaSynRM with lowest cost. According to the types of added permanent magnet, there are usually two different PMaSynRM shown in Fig. 2: ferrite-assisted SynRM (FaSynRM) and NdFeB-assisted SynRM (NdFeBaSynRM). PMaSynRM have better performance than TLASynRM in terms of average torque, power factor, power density, torque and power changing rate, efficiency and allowable speed range; however, torque ripple is also increased and for FaSynRM, torque ripple is not added obviously [15,20]. Instead of placing PMs among flux barriers, [12] designs another PMaSynRM topology as shown in Fig. 6. The PMs are placed outside the flux barriers. This rotor structure shows good performance with higher power factor and efficiency.

EV can run at different driving cycles. An interesting research is how different driving cycles affect the design and optimization of PMaSynRM. New Europe Driving Cycle (NEDC) which is associated with suburban and highway driving and Artemis Urban which represents driving cycle with more accelerations and stop-and-go motions are considered for the design and optimization of PMaSynRM [29]. For the application in NEDC, reducing the high speed copper and iron loss should be paid more attention which results in lower split, insulation ratios and thicker tooth widths and thinner back iron. However, in the case of Artemis Urban, minimizing the copper and inverter loss at low speed region is more important which means larger split and insulation ratios and higher turn number. According to NEDC, a FaSynRM is designed for EV to maximize efficiency by finite element based tool GOT-It and a representation of energy distribution of NEDC is given for the optimization [17].

Control strategy

Control strategy is another important research aspect of SynRM. With different control objectives such as maximum torque per ampere (MTPA), maximum efficiency (ME) and maximum power factor, we can apply various control strategies. Actually, MTPA control can achieve the same goal than ME control with the same current angle of π/4 which also can conclude from expression [START_REF] Pelkonen | Trends in renewable energy production and media coverage: A comparative study[END_REF]. For SynRM used in EV, MTPA control is usually applied to improve efficiency. For a low power electric propulsion [START_REF] Ruba | Analysis of maximum torque per ampere control strategy for variable reluctance synchronous machines for traction applications[END_REF], MTPA control is used to simulate and control an analytical model of SynRM. A parameter estimator is proposed for MTPA control by considering high order harmonics equations of back EMF and eventually the controller is robust against load variation and average torque and is not affected by saturation effect [25].

Besides, SynRM is suitable to be controlled with saliency based position sensorless control (PSC) for its good saliency. However, saturation caused by adding loads decreases the inductance difference between d-axis and q-axis which can make PSC malfunction. Besides, mutual inductances between d-axis and q-axis caused by the asymmetrical saturation of rotor result in saliency shift which can make PSC works badly.

Conclusion

Comparisons between SynRM and other drives used in EV have proven that SynRM can be a better solution. And to meet the requirements of EV drives, further research can be undertaken from three aspects. One involves the design and optimization of rotor topology and especially optimization of asymmetrical rotor structure which could improve the performance including power converter. Another aspect is to improve PSC performance at small current and under loads. At last, future research on simultaneous designing of SynRM, power converter and innovative control, based on systemic optimization strategy will possibly get better performances of the whole system.

Fig. 2

 2 Fig.2 Classifications of SynRM used in EV

  . Adjusting flux barrier opening widths also succeeds in reducing torque ripple [18]. What's more, a Machaon configuration shown in Fig.5 is presented in [7]. It can be viewed as the evolution of hybrid rotor topology. Its flux barriers of adjacent poles have different shapes and are combined from two different barriers designs, what means that Machaon rotor can obtain advantages of two rotor topologies. Machaon configuration also decreases torque ripple [7]. Similarly, different tip shapes of flux barriers are also designed and studied to maximize average torque and minimize torque ripple. SynRM with full asymmetric flux barrier tips can reduce 50% torque ripples without losing average torque [23].

Fig. 6

 6 Fig.6 Rotor with PMs outside flux barriers [12]

Fig. 7

 7 Fig.7 Epoxy-filled rotor [14]: (a) design structure (b) rotor manufactured


K S Agbli

M Hilairet

F Gustin

O Bossard

BATTERY AND SUPER CAPACITORS-BASED SINGLE CONVERTER HYBRID 1 POWER PACK ENERGY MANAGEMENT 2

Dealing with the energy management of a single converter hybrid power pack involving battery and super capacitor, the real 10 condition simulation and the preliminary experimental results have been hereby given. Through of a suitable management of both 11 super capacitors (Scaps) state of charge and the dc bus voltage, smoothed power demand is assigned to the battery pack, whereas 12 high frequency power demand is managed by the Scaps pack. Because military vehicle application is the target of the related 13 application, security-based constraints namely battery pack temperature, current and voltages thresholds, are taken into account. 14 The developed energy management is applied through 16-bits Microchip microcontroller dsPIC33EP512MU810 by means of 15 CAN and CANopen communication. The presented results need to be refined owing to the sampling time issues of the used CAN 16 bus frames.

Introduction 19

The presented work is performed in the framework of a 20 partnership project involving E4V (Energy For Vehicle) and

29

presented in [1]. In fact, it is a one converter hybrid power 30 pack of battery and Super capacitors (Scaps).

31

One or two converters-based such a hybrid system has 32 already been developed involving fuel cell and Scaps [START_REF] Azib | [END_REF][3][4][5][6][7][8][9][10][11][12][13][14].

56

The highest sampling time is 100Hz and the lowest is 10Hz.

57

This kind of application based only on communication 58 through CAN bus is carried out in this paper.

59

The paper is organized as follow: firstly, the experimental text

76

The transient period is highlighted by the zoom on Fig. 6 (c).

21FEMTOS-

  ST (Franche-Comté Electronics Mechanics22Thermal and Optics -Sciences and Technologies). This

23

  research is funded by the French Government Armament 24 Procurement Agency (DGA -Direction Générale de 25 l'Armement). The main purpose is developing a control card 26 intending to manage energy within a hybrid power pack in 27 order to propel a vehicle. The theoretical description, of the 28 developed energy management strategy, has already been

33

  Whether the one converter-based energy management [2-34 3,12-13] or the two converters ones [4,6,14], it's often dealt 35 with ensuring smooth behaviour on the terminal of the low 36 frequency devices like fuel cell or the medium frequency ones 37 like batteries. The main benefit of one converter network is 38 consequently a saving purpose (reduce the hybrid power pack 39 price). Therefore, the most used energy management principle 40 tends to apply charge sustaining strategy to the Scaps by 41 smoothing energy of the battery [2-3,4,6,12-13,14]. Such an 42 approach requires three nested control loops: an inner current 43 control loop, then an inner voltage control one and an outer 44 voltage control loop called compensation loop. This latter one 45 serves to perform charge sustaining behaviour of the Scaps by 46 pursuing its reference voltage value.47 In this work, with the hybrid power pack involving one 48 converter, it is expected to also operate the Scaps in charge 49 sustaining mode by smoothing the battery power. Compare to 50 the previous performed works [2-3, 12-13] which are 51 implemented with real-time Dspace controller board with 25-52 kHz sampling frequency, our application uses CAN bus-based 53 CANopen protocol communication. In such a system like 54 ours with different sampling time of the involved devices, the 55 control become more complex than the former applications.

60

  bench is presented before provide the CAN bus and the 61 control structure characteristics. Afterwards, simulation 62 results based on real application characteristics (devices data 63 transmission sampling time, the control signal one, the real 64 response time of the control system) are provided. Finally, 65 before the conclusion some preliminary experimental results 66 are given.

67 2 .

 2 figure 1. Using MPLABX 2.6 Microchip software, the 71

1Fig. 1 . 7 Fig. 2 .

 172 Fig. 1. Electrical network of the system

Fig. 3 .25

 3 Fig. 3. Discretized PI (left) and IP (right) controllers'

A7 19 Fig. 4 .4. 2 46 50 Fig. 5 .

 1942505 Fig. 4. Real condition simulation results

64

  This section deals with the battery pack security-based current 65 limitation. The current bound in discharge is 15A and a load 66 pulse of 20A is applied as shown on Fig. 6(a).

Fig. 6 .

 6 Fig. 6. Current limitation mode in discharge: (a) ibt and isc, 69

77

  Before the Scaps react to the current set point sent by the 78 converter, the battery pack undergoes the load profile high 79 frequency component. Afterwards, the system converges 80 toward the desired behaviour point. From Fig. 6 (c), it 81 emerges that during a current drop, the current threshold in 82 The transient phase Paper Submitted to ICREGA'16 discharge is overcome. This is the main drawback of this 1 control in the current state.

4 9 Fig. 7 .

 97 Fig. 7. Current limitation mode in charge: (a) ibt and isc, (b) 10

  34

31 Table 1 .

 311 Data acquisition characteristics.

	32
	Measures	Sampling	Precision	Numbering
		[ms]		system
	vsc vb ibt	54.2 109 109	#0.05V #0.01V #0.1A	Float float Float

Regarding the set point current value (Table

2

), it appears that 33 to the DC-DC converter, it is provided 10ms sampling time 34 integer as current reference value. While we would need a 35 precision to the hundredth of the value of the current. It is a 36 constraint from which we cannot undo. This might introduce 37 some inaccuracies whether on Scaps voltage management or 38 on battery pack set point voltage management.

39

Table 2 .

 2 Set point variable characteristics.

	40
	Set point	Sampling	Precision	Numbering
	variable	[ms]		system
	iscref	10	#1A	Integer

The table

3

shows the controllers' parameters. Thanks to all 41 the provided parameters (from table 1 to table 4) the system 42 model is simulated. Then, preliminary experimentation has 43 been performed.

44

Table 3 .

 3 Controllers' coefficients.

	45
		Inner loop Outer loop	Sampling [ms]
	Proportional	1.7184	-0,375	10
	coefficient
	Integral	103.1	-0,0114	10
	coefficient

Table 4 .

 4 CAN bus features.

	46
		values
	Baud rate	250 kps
	Data frames on the CAN bus 10
	Minimum sampling time	0,5Hz
	Maximum sampling time	10Hz
	4. The simulation and experimental trials

47

As a result of the foregoing, the real conditions simulations 48 have been performed.

(c) The transient phase


C Damour

M Benne

Y Gangate

D Payet

M Hilairet

ECONOMIC PERFORMANCE OPTIMIZATION OF A HYBRID PV-BESS 1 POWER GENERATOR: A CASE STUDY LA REUNION ISLAND 2

This paper proposes an economic performance optimization strategy for a PV plant coupled with a battery energy 10 storage system (BESS). The case study of La Reunion Island, a non-interconnected zone (NIZ) with a high level of renewable 11 energy sources (RES), is considered. This last decade, to reach the ambitious target of electricity autonomy by 2030 set by the 12 local authorities, local and national plans have been launched to promote RES integration that led to a noticeable development of 13 photovoltaic (PV) systems. To avoid a decrease of the grid reliability due to a large integration of intermittent energy sources 14 into a non-interconnected grid, the authorities have introduced new regulatory rules for RES producers. The proposed 15 optimization strategy relies on a these new regulatory rules and takes into account the energy market data, the amount of PV 16 production subject to penalties for imbalance, the batteries and the PV technological characteristics together with a PV 17 production forecast model. The effectiveness and relevance of the proposed strategy are assessed on experimental data collected 18 on a real PV power plant. An economical analysis demonstrates that the proposed optimization strategy is able to fulfill the new 19 regulatory rules requirements while increasing the economic performance of the system.

20 21 35 strongly based on imported fuels. In this context, local 36 authorities have set the ambitious objective of reaching 37 electricity autonomy by 2030. This last decade, to reach this 38 target, local and national plans have been launched to 39 promote RES integration [3-4]. Thus, supported by incentive 40 mechanisms such as tax exemptions, direct subsidies or feed-41 in tariffs, photovoltaic (PV) systems have experienced a rapid 42 and noticeable development [5]. However, a large integration 43 of intermittent sources into a non-interconnected grid raises 44 critical technical issues due to the uncertainties of the energy 45 production. The intermittency and unreliability of solar-46 generated power may reduce the network stability and lead to 47 load shedding or to the interruption of electric service [6]. To 48 avoid such situations, the authorities have set a limit of 30% 49 of intermittent sources in the instantaneous electricity 50 production and have introduced new regulatory rules for RES 51 development. Henceforth, RES producers have to declare to 52 the grid operator, a day in advance, the power profile that will 53 be injected to the grid. Then, if the power plants do not meet 54 the submitted schedule for injected power, they face financial 55 penalties. In La Reunion Island, if mismatches between actual 56 and scheduled power injection exceed a given tolerance, RES 57 producers are charged with imbalance penalties. In order to 58 address the problem related to the intermittency of solar-59 generated electricity while reducing the amount of PV 60 production subject to penalties for imbalance, energy storage 61 systems (ESSs) appears as one of the most relevant option. 62 Recently, several works related to the applicability, 63 advantages and disadvantages of various ESS technologies 64 for RES integration have been reported [7]. As regards PV 65 power plants coupling with ESS, several works dealing with 66 technical issues and economic feasibility have been 67 conducted [8-11]. However, from a regulatory point of view 68 (incentive schemes and economic feasibility), nearly all 69 works reported in the literature focus on the determination of 70 the optimal sizing of the ESS [12-15]. 71 72 In the case of La Reunion, and according to our best 73 knowledge, none work has been conducted to optimize the 74 economical performance of existing hybrid photovoltaic-75 battery energy storage system (BESS) power generators, 76 based on the latest regulatory rules. In this paper, an 77 economical optimization of a hybrid PV-BESS power 78 generator is developed. The proposed methodology relies on a 79 metaheuristic optimization algorithm taking into account the 80 energy market data, the amount of PV-generated energy

Introduction 22

To date, reducing carbon emission has become a major 23 concerned. Among possible options, increasing shares of

32

In this study, the case of La Reunion Island, a non-

8

The rest of this paper is organized as follows. The regulatory 9 rules applied in La Reunion are presented in Section 2.

𝑃 !"_! Measured PV power [kW] 𝑃 !"_! Forecasted PV power [kW] 𝑃 !"_!"#$ Installed PV power capacity [kW p ] 𝑃 !"# Storage power [kW] (>0 charge, <0 discharge) 𝑃 !"#_!"
Storage power exchanged with the AC bus

- P ! Maximal power in discharge [kW] P ! Maximal power in charge [kW] 𝑃 ! Imbalance power [kW] E !"#_!"#$ Amount of energy dedicated to evening peak [kWh] 𝐸 !"_!_!"!#$ Estimated total energy produced by PV plant [kWh] α !"#$ Parameter to be estimated β !"#$%&'(

43

The electricity tariff system relies on peak and off-peak hours.

44

During peak hours, 7PM to 9PM, the electricity feed-in tariff 45 is more attractive. However, during this time period,

46

producers have to guarantee a constant power injection to the 47 grid comprise between 20 % and 70 % of 𝑃 !"_!"#$ . The 48 current electricity tariff system applied to PV power 49 producers in La Reunion, including peak and off-peak feed-in 50 tariffs, is summarized in Table 2.

52

𝑝𝑒𝑛𝑎𝑙𝑡𝑖𝑒𝑠 = 𝐶 ! 60 𝑃 !"# 𝑃 !"# 𝑃 !! !"#$ -0.1 + 2𝑃 !"# 𝑃 !! !"#$ 𝑃 !"# + 𝑃 !"# -0.05𝑃 !"_!"#$ 0.015 - 𝑃 !"# 𝑃 !! !"#$
where P bid denotes the day-ahead schedule power profile to be 79 injected to the grid.

81

Every time P inj is outside the tolerance band, the system is 82 said to be in faulty condition and financial penalties are Paper Submitted to ICREGA'16

In this work, the economic effectiveness of the system is 1 assessed using two criteria, which are the revenue and the 2 daily fault rate (DFR). This last criterion defines the ratio of 3 time where the system is in faulty condition each day:

4 5 DFR = 𝜏 !"#$% 1440 6 7
With 1440 minutes per day, 𝜏 !"#$% represents the cumulated 8 time of fault condition in minute.

10

To fulfill the requirements of the new regulatory rule, PV 36 37

𝑃 !"_! 𝑡 = 𝑃 !"_! 𝑡 -1440 (2)
38 39

where 𝑃 !"_! and 𝑃 !"_! denotes respectively the measured and 40 forecast PV output power at time 𝑡.

42

Even if this method does not take into account the intra-day 62 63

𝑆𝑂𝐶 𝑡 = 𝑆𝑂𝐶 𝑡 -∆𝑡 + 𝑃 !"# 𝑡 ∆𝑡 𝐶 !"# (3)
64 65

Subjected to constraints on power and capacity:

66 67

! ≤ 𝑃 !"# 𝑡 ≤ 𝑃 ! 𝑆𝑂𝐶 !"# ≤ 𝑆𝑂𝐶 𝑡 ≤ 𝑆𝑂𝐶 !"# (4)
68 69

where 𝑃 !"# 𝑡 is the storage power at time t. 𝑃 ! < 0, - 𝑃 ! 70 represents the maximum battery discharging power, and

71

𝑃 ! > 0 the maximum battery charging power.

80

The PV, battery, grid, and loads are all connected to an AC 81 bus. Since the battery is operated on DC, an AC-to-DC

82

(respectively DC-to-AC) converter is necessary when 83 charging (respectively discharging) the battery. Therefore,

84

considering the storage charge and discharge efficiencies (η ! 85 and η ! respectively), the storage power exchanged with the

86

AC bus 𝑃 !"#_!" 𝑡 is expressed as follows:

87 88

P !"#_!" t = P !"# t η ! if P !"# t < 0 discharge P !"! !" t = P !"# t /η ! if P !"# t ≥ 0 charge (5)
89 90 Paper Submitted to ICREGA'16 energy dedicated to the evening peak hours (E !"#_!"#$ ), which 1 have to be stored in the BESS meanwhile, and is written as a 2 fraction of the estimated total energy produced by the PV

3 plant (𝐸 !"_!_!"!#$ ): 4 5 𝐸 !"#_!"#$ = 𝛼 !"#$ 𝐸 !"_!_!"!#$ (6) 6 7 Here E !"_!_!"!#$ = P !"_! 𝑑𝑡 !""# ! . The

23

PV/BESS control rules

24

The power injected to the grid is defined as the sum of the

25

PV output power and the storage power exchanged with the

26

AC bus:

27 28

𝑃 !"# = 𝑃 !"_! + P !"#_!" (8)
29 30

The BESS is used to adjust the PV power plant 𝑃 !"_! to 31 maintain, as much as possible, the difference between the 32 day-ahead announcement 𝑃 !"# and the actual power injected

33

𝑃 !"# to the grid within the tolerance band. If 𝑃 !"_! is above

34

(respectively below) the tolerance limit, the BESS can be 35 used, when it is possible, to store (respectively deliver) the 36 imbalance power 𝑃 ! . Depending on whether the measured 37 output PV is within, below or above the tolerance band, 𝑃 ! is 38 defined as follows:

39 40

P ! = 0 within P ! = 𝑃 !!_! -𝑃 !"# + 0.05 𝑃 !!!"#$ above charge P ! = 𝑃 !!_! -𝑃 !"# -0.05 𝑃 !!!"#$ below discharge
with 𝐽 = 𝑃 !" !,! 𝐶 ! 60 -𝑃 !"# !,! 𝐶 ! 60 - 𝑃𝑒𝑛𝑎𝑙𝑡𝑖𝑒𝑠 !,! !""# !!! !"# !!! and 19 subjected to p ∈ 𝑝 !"# , 𝑝 !"# ; 𝑝 !"# = 0 0 ! ; 𝑝 !"# = 1 0.8 ! .

21

The procedure, performed on experimental data

41

The analysis of the forecast error reveals the same periodicity 42 of 366 days, which means that the forecast error is linked to 43 the season. Indeed, as illustrated on Fig. 4

10

The analysis of the total energy produced by the PV plant 11 each day (𝐸 !"_!_!"!#$ ) reveals a seasonal component that is 12 due to the yearly solar irradiance variability (Cf. Fig. 5). The

36

The BESS is used during off-peak to compensate PV 37 production forecast error and during peak hours to inject 38 power to the grid. Therefore, two parameters have been

39

introduced. The first one is related to amount of energy to 40 store for the evening peak hours whereas the second one 41 represents the fraction of the storage capacity that is dedicated 42 to compensate power imbalance due to forecast errors. The 43 optimization goal is to find the optimal value of these 44 parameters that maximizing the revenue while taking into

24

  renewable energy sources (RES) such as solar, wind or 25 biomass resources appears as a promising solution for a 26 cleaner power generation. High shares of RES may then 27 become a critical aspect of future energy systems. In this 28 context, small islands that mainly rely on imported fossil fuels 29 for energy production are likely to be pioneers in the 30 development of decarbonized electricity production [1-2].

  33 interconnected zone (NIZ), is considered. Even if the territory 34 has a high level of RES, its electricity production remains Paper Submitted to ICREGA'16 technological characteristics together with a PV production 1 forecast model. To assess the effectiveness and relevance of 2 the proposed strategy, the economic analyses are performed 3 on data measured on a real power plant. Indeed, a one-year 4 experimental data, collected from August 2013 to August 5 2014 on a 57 kWp PV farm coupled with a 78.5kWh BESS, 6 are considered.

10

  Section 3 is dedicated to model design. In this section the PV 11 production forecast model and the energy storage model are 12 detailed. The performance of the proposed optimization 13 strategy in terms of economical efficiency improvement is 14 demonstrated in Section 4.15 16

20 intermittent

 20 sources raises critical technical issues related to 21 the reliability of power supply. The reliability of an electrical 22 grid can be defined by its ability to supply the aggregate 23 electrical demand and energy requirements of the customers 24 at all times, while withstanding sudden disturbances such as 25 unanticipated loss of system elements (e.g. load or production 26 fluctuations) [16-18]. Currently the sustainability of power 27 supply in La Reunion is already lower than in Metropolitan 28 France, with an average power outage duration estimated at 29 4 h/year/consumer vs 73 min [5]. In this context, and 30 considering the rapid and important growth of PV systems in 31 La Reunion the last decade, the authorities have recently 32 decided to set up new regulatory rules to ensure the reliability 33 of the power supply. Henceforth, producers have to declare a 34 one minute based profile that represents the day-ahead 35 forecasted power to be injected by their plants. If the 36 mismatches between the actual injected power and the 37 announced power exceed the admitted tolerance, financial 38 penalties are applied. According to this regulatory framework, 39 energy imbalance is calculated with minutely resolution, and 40 the tolerance band is taken equal to ± 5% of the installed PV 41 power capacity (𝑃 !"_!"#$ ).

  11 power producers have to announce a day in advance the 12 power profile to be injected to the grid, which requires a PV 13 production forecast model. Besides, regardless of the 14 accuracy of the PV production forecast model, financial 15 penalties due to imbalance are unavoidable. Therefore, to 16 reduce financial penalties and above all take advantage of 17 peak hours feed-in tariff, the use of ESS appears to be a 18 relevant option.

22

 22 In the literature, a wide variety of parametric and non-23 parametric forecast models have been reported [19]. 24 Parametric models require a wide set of information about the 25 PV power plant technology and its installation configuration. 26 Non-parametric models are generally based on weather 27 forecast models [20]. These limitations make the reliability 28 and the suitability for "on field" uses of parametric and non-29 parametric forecast models questionable. 30 31 In this study, regarding practical purposes, the widely used 32 persistence model is chosen to forecast the PV output power 33 at a minute basis. This is a simple model based on the 34 assumption that the PV production of today is the same as 35 yesterday [21]:

Fig. 1 :Fig. 2 :

 12 Fig. 1: Effects of 𝛽 !"#$%&'( on the revenue and the DRF (with 2

22 collectedFig. 3 :

 223 Fig. 3: Daily revenue and DRF obtain over one year

  Paper Submitted toICREGA'16 This can be mainly explained by the fact that the forecast 1 model does not take into account the intra-day variability of 2 solar irradiance and that in La Reunion Island the intra-day 3 variability is higher in summer. In this context, when the 4 intra-day variability increases the error modeling increases 5 too, which leads to an increase of the DFR. In other worlds, 6 the seasonality of the solar irradiance variability introduces a 7 seasonal component into the forecast error that is transmitted 8 to the DFR.

13

  amount of energy dedicated to the peak hours (𝐸 !"#_!"#$ ), 14 which could have a strong influence on the revenue, is taken 15 as a fraction of 𝐸 !"_!_!"!#$ using α !"#$ . In context, the16 seasonal component contained into 𝐸 !"_!_!"!#$ is transmitted 17 to 𝐸 !"#_!"#$ .A thorough study of intra-day and yearly 18 irradiance variability in La Reunion can be consulted in[23].

Fig. 5 :30

 5 Fig. 5: Energy produced by the PV plant

Table 1 :

 1 Nomenclature.

Table 2 :

 2 Summary of tariff system in La Reunion.

	53
		Peak hours (7PM to 9PM)	Off-peak hours
		[€ ct/kWh]	[€ ct/kWh]
		Selling price (𝐶 ! )	60	40
		Buying price (𝐶 ! )	40	40
	54
	71 72	penalties = 0
	73 74	elseif P inj > P bid + 0.05 P PV_peak	then
	75 76	penalties = P inj C S /60

Note that producers have the possibility to buy electricity 55 from the grid. In some very specific cases, it could be 56 interesting to buy electricity from the grid during off-peak, 57 store the energy in an ESS, and sell it back during peak hours.

58 59

The producer's revenue is calculated each minute using the 60 following expression: 61 62 revenue = P inj C S /60 -P out C b /60 -penalties (1) 63 64 where P inj denotes the power injected to the grid and P out the 65 power extracted from the grid. The financial penalties are 66 calculated as follows: 67 68 if P bid -0.05 P PV_peak < P inj < P bid + 0.05 P PV_peak then 69 70 else 77 78

  𝑆𝑂𝐶 !"# and 72 𝑆𝑂𝐶 !"# are the minimum and maximum battery state of 73 charge, respectively. 𝐶 !"# denotes the maximum usable

	74
	75	storage capacity of the ESS. Note that the battery aging and
	76	self-discharge rate, which obviously affect 𝐶 !"# , has not been
	77	considered. Besides, powers are considered constant during

the time interval t; t + ∆t . In this work, ∆t is equal to one 78 minute.

Table 3 :

 3 Storage system parameter values.

	91
		Variable	Description [unity]	Value
		𝐶 !"#	Maximum storage capacity [kWh]	78.5
		𝑆𝑂𝐶 !"#	Min. energy storage level [%𝐶 !"# ]	20
		𝑆𝑂𝐶 !"# Max. energy storage level [%𝐶 !"# ]	99
		η !	Efficiency of storage in charge	0.9
		η !	Efficiency of storage in discharge	0.9
		- 𝑃 !	Maximal power in discharge [kW]	36.1
		𝑃 !	Maximal power in charge [kW]	17.2
		DOD max	Maximal depth of discharge [%]	80
	92
	93	4. Economic performance optimization
	94	In this work, a minute dispatch strategy for a 57 kWp PV
	95	farm with 78.5 kWh BESS is implemented and an economical
	96	optimization of the dispatch strategy is proposed. BESS has
	97	two main applications: first, compensate PV production
	98	forecast errors during off-peak and thus reduce financial
	99	penalty due to imbalance. Second, inject power to the grid
	100	during peak hours and thus take advantage of the attractive
		feed-in tariff. In this context, two parameters are introduced.

subject to penalties for imbalance, the PV and the batteries

applied.

The first one, denoted α !"#$ , is related to the amount of

value of 𝛽 !"#$%&'( , there is an optimal amount of energy to

store in the BESS for the evening peak hours.

account the new regulatory rules constraints. The proposed

enough energy stored in the BESS for the evening peak. In 47 this aim, a tolerance band control strategy is proposed and a 48 specific control rules is designed for each zone: above, within 49 and below the band.

51

Above the upper limit

52

When 𝑃 !"_! is above the tolerance band, the BESS is used to 53 compensate the imbalance power and store the excess of 54 energy whenever possible. Indeed, the imbalance power 55 cannot always be compensated. Several conditions related to 56 operational and technical limits of the BESS have to be 57 verified (i.e state of charge, charge/discharge rate limits). In 58 this case, the storage power is computed as follows:

59 60

62

where P !"#_!"# = SOC !"# -SOC t C !"# ∆t 63 64

Below the lower limit

65

When 𝑃 !"_! is below the tolerance band, the imbalance 66 power due to forecast error can be compensated using the 67 energy stored in the BESS. However, this energy has to be 68 manipulated very wisely in order to ensure that enough 69 energy remains to guarantee peak hours. The storage power is 70 calculated according to operational and technical limits of the

71

BESS and subjected to constraints on 𝐸 !"#_!"#$ and 72 𝐶 !"#$%&%'( : 73 74

76 77

where 78

80

Within the tolerance band

81

When 𝑃 !"_! is within the tolerance band, the power 82 imbalance is equal to zero and there is not need to 83 absorb/inject power from/to the grid through the BESS:

84 85

86 87

Economic performance improvement

88

The economical performance improvement relies on the 89 estimation of two parameters α !"#$ and 𝛽 !"#$%&'( . The effects 90 of these parameters on the annual revenue and the average 91 annual DRF are illustrated on Fig. 1 and2.

93

As expected, while 𝛽 !"#$%&'( is increasing the DRF is

87

[5] Drouineau, M., Assoumou, E., Mazauric, V., Maïzi, N.

88

Increasing shares of intermittent sources in Reunion Island:

89

Impacts on the future reliability of power supply. Renewable

13

[11] Hill CA, Such MC, Chen D, Gonzalez J, Grady WM. Battery