A Rahoui
email: adel-rahoui@live.fr

A Bechouche
email: ali_bechouche@yahoo.fr

H Seddiki

D Ould Abdeslam

Abstract-This paper proposes a new AC voltage sensorless control scheme for three-phase pulse-width modulation rectifier.

A new startup process to ensure a smooth starting of the system is also proposed. The sensorless control scheme uses an adaptive neural (AN) estimator inserted in voltage-oriented control to eliminate the grid voltage sensors. The developed AN estimator combines an adaptive neural network in series with an adaptive neural filter. The AN estimator structure leads to simple, accurate and fast grid voltages estimation, and makes it ideal for low cost digital signal processor implementation. Lyapunov based stability and parameters tuning of the AN estimator are performed. Simulation and experimental tests are carried out to verify the feasibility and effectiveness of the AN estimator. Obtained results show that; the proposed AN estimator presented faster convergence and better accuracy than the second order generalized integrator based estimator; the new startup procedure avoided the over-current and reduced the settling time; the AN estimator presented high performances even under distorted and unbalanced grid voltages.

Index Terms-AC voltage sensorless control, adaptive neural (AN) estimator, grid voltages estimation, neural networks (NNs), pulse-width modulation (PWM) rectifier, startup process, voltage-oriented control (VOC).

I. INTRODUCTION

OWADAYS, renewable energy sources such as photovoltaic and wind power generation systems are commonly connected to the grid through three-phase pulsewidth modulation (PWM) rectifier [START_REF] Teodorescu | Grid converters for photovoltaic and wind power systems[END_REF], [START_REF] Haitham | Power electronics for renewable energy systems, transportation and industrial applications[END_REF]. This converter topology has such advantages as low harmonic pollution, adjustable DC-link voltage, bidirectional energy flow and operation at unity power factor (UPF) [START_REF] Friedli | The essence of three-phase PFC rectifier systems-Parte II[END_REF]. In renewable energy generation systems, cost reduction is essential for increasing their attractiveness compared to other conventional energy sources [START_REF] Teodorescu | Grid converters for photovoltaic and wind power systems[END_REF], [START_REF] Ketzer | Sensorless control technique for PWM rectifiers with voltage disturbance rejection and adaptive power factor[END_REF]. So, decreasing the converters cost can leads to improve their competitiveness.

Usually, control scheme of the three-phase grid connected PWM rectifier consist of two control loops; one for tracking AC-line currents, and another to regulate the DC-link voltage [START_REF] Bechouche | Adaptive AC filter parameters identification for voltage-oriented control of three-phase voltage-source rectifiers[END_REF]. To perform this, at least five sensors are generally required; two grid voltage sensors, one DC-link voltage sensor, and two AC-line current sensors [START_REF] Gholami-Khesht | Low computational burden grid voltage estimation for grid connected voltage source converter-based power applications[END_REF]- [START_REF] Jorge | Low computational burden grid voltage sensorless current controller[END_REF]. However, operation with reduced number of sensors provides cost savings. Indeed, for mid-low power systems, the sensors cost covers a significant portion of the entire system cost [START_REF] Kukkola | State observer for grid-voltage sensorless control of a converter equipped with an LCL filter: direct discrete-time design[END_REF], [START_REF] Mallik | Control of a three-phase boost PFC converter using a single DC link voltage sensor[END_REF]. For high power systems, the sensors cost is less significant since the overall system cost is high. Nevertheless, even if sensors are installed, control scheme with sensorless operation ability is relevant [START_REF] Ketzer | Sensorless control technique for PWM rectifiers with voltage disturbance rejection and adaptive power factor[END_REF], [START_REF] Kukkola | State observer for grid-voltage sensorless control of a converter equipped with an LCL filter: direct discrete-time design[END_REF]. This ensures uninterrupted operation in case of sensors failure. Besides obvious benefits of sensors reduction, there are several other additional advantages like [START_REF] Ketzer | Sensorless control technique for PWM rectifiers with voltage disturbance rejection and adaptive power factor[END_REF], [START_REF] Ghodke | One-cycle-controlled bidirectional three-phase unity power factor ac-dc converter without having voltage sensors[END_REF], [START_REF] Jorge | Low computational burden grid voltage sensorless current controller[END_REF], [START_REF] Mallik | Control of a three-phase boost PFC converter using a single DC link voltage sensor[END_REF], [START_REF] Lee | Robust predictive current controller based on a disturbance estimator in a three-phase gridconnected inverter[END_REF]; elimination of noise, resolution limitations, offset and various disturbances related to sensors, and decrease of hardware complexity. ACline current sensors and DC-link voltage sensor are essential for proper operation of the control system since the AC-line currents and DC-link voltage are the controlled quantities [START_REF] Ketzer | Virtual flux sensorless control for shunt active power filters with quasi-resonant compensators[END_REF]. In addition, these sensors are employed for overcurrent and overvoltage protections [START_REF] Ketzer | Sensorless control technique for PWM rectifiers with voltage disturbance rejection and adaptive power factor[END_REF], [START_REF] Ketzer | Virtual flux sensorless control for shunt active power filters with quasi-resonant compensators[END_REF]. On the other hand, grid voltage sensors are mainly used for synchronization purposes. So, they can be replaced by software sensors. Various strategies for grid voltages sensorless control of PWM rectifiers have been developed. Some of them are discussed in what follow.

Sensorless control algorithm based on instantaneous power theory has been initially proposed in [START_REF] Noguchi | Direct power control of PWM converter without power-source voltage sensors[END_REF]. Grid voltages are estimated by adding the input voltages to the voltage drop on the AC filter. Despite its simplicity, the AC-line currents derivative is required. Since this solution presents high noise sensitivity, other methods have been developed using virtual flux (VF) concept [START_REF] Ketzer | Virtual flux sensorless control for shunt active power filters with quasi-resonant compensators[END_REF], [START_REF] Suul | Virtual-flux-based voltage-sensor-less power control for unbalanced grid conditions[END_REF], [START_REF] Cho | Virtual-flux-based predictive direct power control of three-phase PWM rectifiers with fast dynamic response[END_REF]- [START_REF] Tao | Voltage sensorless predictive direct power control of three-phase PWM converters[END_REF], Kalman filters [START_REF] Ahmed | Sensorless current control of three-phase inverter-based distributed generation[END_REF], [START_REF] Guzman | Model-based control for a three-phase shunt active power filter[END_REF], disturbance observers [START_REF] Lee | Robust predictive current controller based on a disturbance estimator in a three-phase gridconnected inverter[END_REF], [START_REF] Yoo | Sensorless operation of a PWM rectifier for a distributed generation[END_REF], hybrid parallel observers [START_REF] Liu | Robust model predictive current control of grid-connected converter without alternating current voltage sensors[END_REF] and Luenberger observers [START_REF] Gholami-Khesht | Deadbeat direct power control for grid connected inverters using a full-order observer[END_REF]. Adaptive fullorder observers [START_REF] Kukkola | State observer for grid-voltage sensorless control of a converter equipped with an LCL filter: direct discrete-time design[END_REF], [START_REF] Kukkola | Observer-Based State-Space Current Controller for a Grid Converter Equipped With an LCL Filter: Analytical Method for Direct Discrete-Time Design[END_REF] have been also proposed for grid voltage sensorless control. This strategy has been tested under unbalanced conditions by exploiting the filtering capabilities of reduced-order generalized integrators (ROGIs). In [START_REF] Jorge | Low computational burden grid voltage sensorless current controller[END_REF], ROGI based control scheme has been modified to achieve sensorless operation. One cycle control designed using hardware circuits instead of a digital algorithm has been presented in [START_REF] Ghodke | One-cycle-controlled bidirectional three-phase unity power factor ac-dc converter without having voltage sensors[END_REF]. Recent algorithms based on virtual impedance emulation [START_REF] Ketzer | Sensorless control technique for PWM rectifiers with voltage disturbance rejection and adaptive power factor[END_REF] and mathematical optimization [START_REF] Gholami-Khesht | Low computational burden grid voltage estimation for grid connected voltage source converter-based power applications[END_REF], [START_REF] Gholami-Khesht | Novel grid voltage estimation by means of the Newton-Raphson optimisation for three-phase grid connected voltage source converters[END_REF] have been investigated. Other alternatives using neural networks (NNs) have been proposed for grid voltages estimation [START_REF] -R | A robust natural-framebased interfacing scheme for grid-connected distributed generation inverters[END_REF], [START_REF] -R | Adaptive grid-voltage sensorless control scheme for inverter-based distributed generation[END_REF]. In [START_REF] -R | A robust natural-framebased interfacing scheme for grid-connected distributed generation inverters[END_REF], the authors have developed a sensorless deadbeat current control strategy based on a multilayer NN estimator. Accordingly, an uncertainty function containing the AC filter parameters variation, harmonics disturbances and grid voltages information, is used for Grid Voltages Estimation for Three-Phase PWM Rectifiers Control Without AC Voltage Sensors Adel Rahoui, Ali Bechouche, Hamid Seddiki, and Djaffar Ould Abdeslam, Senior Member, IEEE N synchronization and control purposes. Separate estimation of the AC filter parameters and grid voltages using a parallel NNs structure has been achieved in [START_REF] -R | Adaptive grid-voltage sensorless control scheme for inverter-based distributed generation[END_REF].

Although the cited strategies provide satisfactory results, some of them require specific control schemes [START_REF] Ghodke | One-cycle-controlled bidirectional three-phase unity power factor ac-dc converter without having voltage sensors[END_REF], [START_REF] Jorge | Low computational burden grid voltage sensorless current controller[END_REF], [START_REF] Lee | Robust predictive current controller based on a disturbance estimator in a three-phase gridconnected inverter[END_REF], [START_REF] Yoo | Sensorless operation of a PWM rectifier for a distributed generation[END_REF], [START_REF] -R | A robust natural-framebased interfacing scheme for grid-connected distributed generation inverters[END_REF]. Others are sensitive to load variation [START_REF] Ketzer | Sensorless control technique for PWM rectifiers with voltage disturbance rejection and adaptive power factor[END_REF], need initialization [START_REF] Gholami-Khesht | Novel grid voltage estimation by means of the Newton-Raphson optimisation for three-phase grid connected voltage source converters[END_REF] and present instability under grid voltages sag [START_REF] Ghodke | One-cycle-controlled bidirectional three-phase unity power factor ac-dc converter without having voltage sensors[END_REF] which deteriorate their robustness. The VF estimation through open loop integrators has limitations related to stability [START_REF] Ketzer | Virtual flux sensorless control for shunt active power filters with quasi-resonant compensators[END_REF]. The observers based approaches presented difficulty of tuning and high computational burden. Multilayer NNs estimators proposed in [START_REF] -R | A robust natural-framebased interfacing scheme for grid-connected distributed generation inverters[END_REF] and [START_REF] -R | Adaptive grid-voltage sensorless control scheme for inverter-based distributed generation[END_REF] have a complicated structure where over ten weights are online updated. The authors in [START_REF] -R | Adaptive grid-voltage sensorless control scheme for inverter-based distributed generation[END_REF] have presented only real time simulation results; therefore, the proposal has not been experimentally validated. Furthermore, several strategies have not been tested for unbalanced or distorted grid voltages [START_REF] Gholami-Khesht | Low computational burden grid voltage estimation for grid connected voltage source converter-based power applications[END_REF]- [START_REF] Ketzer | Virtual flux sensorless control for shunt active power filters with quasi-resonant compensators[END_REF], [START_REF] Jorge | Low computational burden grid voltage sensorless current controller[END_REF], [START_REF] Mallik | Control of a three-phase boost PFC converter using a single DC link voltage sensor[END_REF]- [START_REF] Noguchi | Direct power control of PWM converter without power-source voltage sensors[END_REF], [START_REF] Kulka | Sensorless digital control of grid connected three phase converters for renewable sources[END_REF]- [START_REF] Ahmed | Sensorless current control of three-phase inverter-based distributed generation[END_REF], [START_REF] Yoo | Sensorless operation of a PWM rectifier for a distributed generation[END_REF]- [START_REF] Gholami-Khesht | Deadbeat direct power control for grid connected inverters using a full-order observer[END_REF], [START_REF] -R | Adaptive grid-voltage sensorless control scheme for inverter-based distributed generation[END_REF]. On the other hand, complexity and high computational burden are the major drawbacks of the strategies tested under non-ideal conditions. Hence, their implementation requires expensive digital signal processors (DSPs). The cost reduction aspect is then lost. Another important consideration of sensorless operation is the startup process that guaranties smooth starting of the control algorithm. At the best of our knowledge, the startup process has not been considered in the majority of the published works.

To address the previously cited issues, this paper proposes a new sensorless control scheme of grid connected three-phase PWM rectifier that offers acceptable tradeoff between estimation accuracy and system complexity. The proposed sensorless control scheme is composed with an adaptive neural (AN) estimator for grid voltages estimation feeding a voltage-oriented control (VOC) algorithm. The AN estimator combines an adaptive neural network (ANN) to estimate the grid voltages in series with an adaptive neural filter (ANF) to improve its harmonic rejection. The simple structure of the AN estimator offers low computational burden where only three weights are online updated. This leads to easy implementation in low cost DSPs [START_REF] Bechouche | Adaptive AC filter parameters identification for voltage-oriented control of three-phase voltage-source rectifiers[END_REF], [START_REF] Bechouche | A novel method for identifying parameters of induction motors at standstill using ADALINE[END_REF]. In addition, its online adaptation and filtering properties ensure robustness against periodic and time-varying disturbances related to the grid voltages. The AN estimator does not depend on the control structure; therefore it can be easily adapted to different control schemes [START_REF] Bechouche | AC voltage sensorless control of three-phase PWM rectifiers[END_REF]. Guidelines for optimal tuning of the AN estimator's parameters are also given here in. As the control scheme needs initialization in case of sensorless operation, a new startup process is introduced to perform a simultaneous starting of the DC-link voltage and AC-line currents control loops with minimum overcurrent and reduced settling time. The evaluation of the proposed estimator is performed through simulation and experimental tests. Several working conditions are considered including unbalanced and distorted grid voltages.

This paper is organized as follows. Section II presents the design of the proposed AN estimator. The startup process and overall structure of the proposed AC voltage sensorless control strategy are described in Section III. In Section IV, a comparison between the proposed estimation method and second order generalized integrator (SOGI) based method is performed. In Section V, experimental and simulation tests are conducted to verify the feasibility and effectiveness of the proposed AN estimator. Section VI concludes this paper.

II. NNS-BASED GRID VOLTAGES ESTIMATION

Accurate estimation of grid voltages is required for implementing a robust AC voltage sensorless control scheme. Accordingly, this section presents a novel estimation strategy based on NNs. This strategy permits to estimate online the grid voltages with low computational burden and high accuracy.

Fig. 1 describes the proposed AN estimator, which offers a reliable solution to online grid voltages estimation. It includes two simple NNs simultaneously working in series. First, an ANN is used to estimate the grid voltages. Second, an ANF is added in series for extracting fundamental components of the estimated grid voltages.

In this paper, the steepest descent and least mean square (LMS) algorithms are used for adaptive adjustment of the ANN and ANF weights, respectively. Their main advantages are low complexity, low computational demand, and highspeed convergence. Other online updating techniques like the total least squares EXIN neuron [START_REF] Cirrincione | A single-phase DG generation unit with shunt active power filter capability by adaptive neural filtering[END_REF] or recursive least square algorithm [START_REF] Astrom | Adaptive Control[END_REF] have been proposed to enhance NNs online learning capabilities. However, the use of these updating technics causes a significant increase of the complexity and computational demand of the estimator. Because this paper aims to propose a simple sensorless control scheme, steepest descent and LMS are selected as updating algorithms.

λ αβ (k) D W A.

ANN-Based Grid Voltages Estimation

The ANN topology is built from the model of the grid connected three-phase PWM rectifier shown in Fig. 2. L and R are, respectively, the inductance and resistance of the AC filter. C is the DC-link capacitance, V dc is the DC-link voltage and R L is the load resistance. i i , v in and e i (i=a,b,c) refer to the phase-i AC-line current, input voltage and grid voltage, respectively. S i (i=a,b,c) are the switching states of three converter legs. In the stationary α-β reference frame, the PWM rectifier can be modeled as follows:

n n e i i v d L R e i i v dt α α α α β β β β         = + +                 (1)
where i α , i β , e α and e β are, respectively, the αand β-axis components of the AC-line currents and the grid voltages. v αn and v βn are the αand β-axis components of the rectifier input voltages.

In the synchronous d-q frame, the model ( 1) is written as

d d d dn q q q qn e i i v R L d L e i i v L R dt ω ω         -   = + +                     (2)
where i d , i q , e d and e q are, respectively, the dand q-axis components of the AC-line currents and the grid voltages. ω is the grid angular frequency. v dn and v qn are the dand q-axis components of the rectifier input voltages.

Using the forward Euler method, the discrete-time form of (1) is obtained as follows:

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 1 1 . . 1 1 1 n n i k i k e k v k A B i k i k e k v k α α α α β β β β   - - -           = + -           - - -                   (3) with A 1 s T R L = - and B . s T L =
T s is the sampling period.

An ANN for estimating the grid voltages (e α , e β ) is designed using the following input/output combination:

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) , , , , 1 1 1 .
. . 1 1 1 est ANN n n est ANN i k e k i k v k A B B i k v k i k e k α α α α β β β β -     - -     = - +         - - -                 (4)
where e α,ANN , e β,ANN , i α,est and i β,est are the estimated grid voltages and the ANN outputs, respectively. As can be seen from the ANN architecture presented in Fig. 1, the updated weight is the estimated grid voltages.

The weight e αβ,ANN is adaptively adjusted using the steepest decent algorithm by exploiting the following estimation error:

( ) ( ) ( ) ( ) ( ) ( ) , ,
.

est est i k k i k k i k i k α α α β β β δ δ       = -                  (5)
Thus, a discrete-type quadratic error function can be deduced as follows:

( ) ( ) ( ) 2 2 . 2 k k E k α β δ δ + = (6)
The grid voltages are adaptively estimated by minimizing E(k). For this purpose, the following Jacobian is considered [START_REF] Widrow | Adaptive Inverse Control-A Signal Processing Approach[END_REF]:

( ) ( ) ( ) ( ) , , , , , , , , , , B
.

est est ANN ANN est est est ANN est ANN i E E i e e i k i k J i E i k i k E e i e α α α α α α β β β β β β ∂   ∂ ∂       ∂ ∂ ∂ -       = = = -      ∂ ∂ - ∂         ∂ ∂ ∂         (7)
According to the steepest descent algorithm, the weight at time (k + 1) is calculated as

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) , , , , , , , , , , 1 1 B
k i k e k i k α α α β β β α α α β β β µ + ∆       = +       + ∆                       = + -                       ( 8
)
where µ is a learning rate. Therefore, the simple iterative gradient algorithm ( 8) is used for minimizing [START_REF] Gholami-Khesht | Novel grid voltage estimation by means of the Newton-Raphson optimisation for three-phase grid connected voltage source converters[END_REF] online. It should be noticed that, under ideal condition, the ANN is sufficient for accurate grid voltages estimation. However, in case of non-ideal conditions, an additional filtering stage should be added in order to extract their fundamental components. This latter will be discussed in what follows.

B. ANF for Filtering the Estimated Grid Voltages

In this section, the estimated grid voltages e αβ,ANN are filtered. The time-varying magnitude and phase of the e αβ,ANN fundamental component are extracted using an ANF. In order to formulate this estimation problem, a suitable decomposition of e αβ,ANN is performed. This decomposition is given in a discrete-time as follows:

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) , 1 , 1 1 1 2 1 1 1 cos sin cos cos sin sin ANN n n s n n ANN n n s n s n n s n n s n n s n e k E kT e k E kT E kT E kT E kT E kT α β ω ϕ ω ϕ ω ϕ ω ϕ ω ϕ ω ϕ ∞ = ∞ =     +     =       +             + +       = +       + +           ∑ ∑ (9
) with E n is the magnitude of the n th term, φ n its initial phase angle and ω n its pulsation. From equation ( 9), the fundamental component of e α,ANN and e β,ANN can be obtained as

( ) ( ) ( ) ( ) , 1 1 1 , 1 1 1 cos . sin ANN s ANN s e k E kT e k E kT α β ω ϕ ω ϕ   +   =     +         (10)
This can be expressed yet in the following developed form:

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) , 1 1 1 1 1 1 , 1 1 1 1 1 1 cos cos sin sin . sin cos cos sin ANN s s ANN s s e k E kT E kT e k E kT E kT α β ϕ ω ϕ ω ϕ ω ϕ ω   -   =     +         (11
) Form equation [START_REF] Jorge | Low computational burden grid voltage sensorless current controller[END_REF], the following vectorial notation is obtained:

V dc - R L i abc R L e abc + C v abcn i C i L i dc PWM rectifier Sabc ( ) ( ) , ANN e k X D k αβ = (12)
where ( ) ( ) ( ) ( ) 12) is a linear combination that can be learned by one ANF with the adaptive weight W = [w αβ1 w αβ2 ]. The vector D(k) is represented by two generated sine waves which constitutes the ANF inputs (see Fig. 1). During the learning process, the weight W is adaptively updated to converge toward X. The weight W is updated using the LMS algorithm with the learning rate η [START_REF] Bechouche | Adaptive AC filter parameters identification for voltage-oriented control of three-phase voltage-source rectifiers[END_REF], [START_REF] Bechouche | A novel method for identifying parameters of induction motors at standstill using ADALINE[END_REF], [START_REF] Widrow | Adaptive Inverse Control-A Signal Processing Approach[END_REF] in the following way:

1 1 1 1 1 1 1 1 cos sin sin cos E E X E E ϕ ϕ ϕ ϕ  -  =     and D(k) = [cos(ω 1 kT s ) sin(ω 1 kT s )] T . Equation (
( ) ( ) ( ) ( ) ( ) ( ) 1 T k D k W k W k D k D k αβ ηλ ε + = + + ( 13
)
where ε is a sufficiently small and positive value used to avoid division by zero if

D T (k)D(k)=0. λ αβ =
( ) ( ) ( ) ( ) ( ) , 1 1 1 , , 1 1 1 cos
α αβ β ω ϕ ω ϕ   +   = =     +         (14)

C. Convergence Investigation of the AN Estimator and Learning Rates Tuning

The stability of the proposed AN estimator is investigated in this section regarding the ANN and ANF learning rates µ and η. Thus, Lyapunov's convergence criterion is exploited to establish the limits of µ and η that ensuring the AN estimator stability. The selected values of µ and η are then justified.

First, the ANN stability is analyzed. A positive definite Lyapunov function candidate for ( 5) is chosen and expressed as ( ) ( ) ( )

2 2 1 . 2 k k V k α β δ δ + = (15)
The Lyapunov's convergence criterion must be satisfied such that ( ) ( )

1 1 0 V k V k ∆ < (16)
where the Lyapunov function variation ∆V 1 (k) is given by 16) is satisfied when ∆V 1 (k)<0. Since the grid voltages can be considered as continuous signals and their period is much higher than the estimation period, the error variation (∆δ α (k), ∆δ β (k)) due to the learning rate of the ANN is given as

( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 1 1 1 , 1 , 0. V k V k k V k k α β α β δ δ δ δ ∆ = + + - < (17) As V 1 (k) is a positive definite function, the stability criterion in (
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) , , , , , , , , , , 1 1 ANN
ANN ANN ANN ANN ANN ANN ANN ANN ANN k k k k k k k e k e k e k e i k k k e e k i k k e e α α α β β β α α α β β β α α α α α β β β β β δ δ δ δ δ δ δ δ δ δ µ δ δ ∆ +       = -       ∆ +             ∂   ∆   ∂   =   ∂   ∆   ∂   ∂   ∂   ∂ ∂   =   ∂ ∂     ∂ ∂   (18)
By replacing ( 18) in ( 17), ∆V 1 (k) is calculated as follows:

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 1 2 2 , , , , , , 2 2 2 2 , , , 2 2 2 , , , 1 2
2 5) and ( 6), the following equality can be assumed:

est est ANN ANN ANN ANN est ANN ANN est ANN ANN V k k k k k k k k i k i k k k k e e e e i k k k e e k i k k e e α α β β α β β β α α α β α α β β α α α α α β β β β β δ δ δ δ δ δ δ δ µ δ δ δ µ δ δ δ     ∆ = ∆ + ∆ + +       ∂ ∂ ∂ ∂   = +   ∂ ∂ ∂ ∂      ∂ ∂  +  ∂ ∂    ∂ ∂  +  ∂ ∂   (19) where ||•|| is the Euclidian norm in n ℜ . From (
( ) ( ) ( ) ( ) , , , , , ,
.

est ANN ANN est ANN ANN i k k e e k i k e e α α α α β β β β δ δ ∂   ∂       ∂ ∂     = -     ∂ ∂         ∂ ∂     (20)
The expression of ∆V 1 (k) is obtained by replacing (20) in [START_REF] Kulka | Sensorless digital control of grid connected three phase converters for renewable sources[END_REF] in the following way:

( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 4 2 , , 1 , , 2 4 2 , , , , 2 . 2
est est ANN ANN est est ANN ANN i k i k V k k e e i k i k k e e α α α α α β β β β β µ µ δ µ µ δ   ∂ ∂   ∆ = - -   ∂ ∂       ∂ ∂   - -   ∂ ∂     (21)
The ANN convergence is guaranteed when the stability condition in ( 16) is satisfied. Hence, the learning rate µ must be selected according to the following inequality:

( ) ( ) 2 2 , , , , 2 0 .
max ,

est est k ANN ANN i k i k e e β α α β µ < <   ∂ ∂   ∂ ∂     (22)
Secondly, the ANF stability is investigated. As the weight W computed by the ANF algorithm is an estimate of X, a positive definite Lyapunov function candidate for the ANF estimation error can be defined as

( ) ( ) ( ) 2 W W T V k k k = ɶ ɶ (23)
where ( )

W k ɶ is the ANF estimation error , defined as ( ) ( ) ( ) W W . k X k k ≡ - ɶ (24)
The Lyapunov's convergence criterion must be satisfied such that ( ) ( )

2 2 0 V k V k ∆ < ( 25
)
where ∆V 2 (k) is the Lyapunov function variation. As illustrated in [START_REF] Guzman | Model-based control for a three-phase shunt active power filter[END_REF], V 2 (k) is a positive definite function. Therefore, the stability criterion ( 25) is satisfied when ∆V 2 (k) < 0. The Lyapunov function variation is established as

( ) ( ) ( ) ( ) ( ) 2 2 2 W 1 W 0. V k V k V k ∆ = + - < ɶ ɶ (26)
By using the ANF estimation error dynamics, obtained from [START_REF] Yoo | Sensorless operation of a PWM rectifier for a distributed generation[END_REF], with the update law (13), ∆V 2 (k) can be assessed as 26) is satisfied if the bracketed term in ( 27) is negative which means that the learning rate satisfy the inequality given below:

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 1 1 W W 1 1 W W W 1 1 1 2 1 1 1 1 T T T T T T T D k D k k V k k D k D k k k k D k D k D k D k D k D k D k η ε η η ε ε - - ∆ = - + - - -   -   - -   = -+   + - - + - -     ɶ ɶ ɶ ɶ ɶ (
0 2 η < < (28)
The following convergence properties are also satisfied:

( ) ( ) ( ) 0 0 0 W W W 1 W W 0 W , 1 k k k - ≤ -- ≤ - ≥ (29.a) ( ) ( ) ( ) ( ) W 1 lim 0 1 1 T k k D k D k D k ε →∞ - = + - - ɶ (29.b)
where W 0 is obtained at perfect convergence of the ANF.

According to [START_REF] -R | A robust natural-framebased interfacing scheme for grid-connected distributed generation inverters[END_REF], the augmented error is monotonically nonincreasing, hence, the convergence is guaranteed. If the learning rates µ and η are chosen according to the intervals given by ( 22) and [START_REF] -R | A robust natural-framebased interfacing scheme for grid-connected distributed generation inverters[END_REF], respectively, the AN estimator stability is guaranteed. The µ and η values affect directly the accuracy, convergence speed and stability of the AN estimator [START_REF] Cirrincione | A single-phase DG generation unit with shunt active power filter capability by adaptive neural filtering[END_REF]. Indeed, low values of µ and η lead to increase the accuracy and the stability at cost of slower convergence speed. On the other hand, high values of µ and η lead to high convergence speed but with less accuracy and stability. Therefore, correct choice of the learning rates is a tradeoff between the convergence speed and stability of the AN estimator.

III. STARTUP PROCESS OF THE AC VOLTAGE SENSORLESS CONTROL SCHEME

Startup procedure of control algorithms is a common problem in case of grid voltages sensorless operation of PWM rectifiers [START_REF] Suul | Virtual-flux-based voltage-sensor-less power control for unbalanced grid conditions[END_REF]. During the startup, the initial value of the grid voltages phase angle θ is needed. In case of VOC, initial values of e d and e q are also required. With these satisfactions, the over current can be reduced and stability of the control scheme is guaranteed.

Few startup algorithms have been proposed in the literature [START_REF] Kulka | Sensorless digital control of grid connected three phase converters for renewable sources[END_REF], [START_REF] Yoo | Sensorless operation of a PWM rectifier for a distributed generation[END_REF], [START_REF] Liu | Robust model predictive current control of grid-connected converter without alternating current voltage sensors[END_REF], [START_REF] Lee | AC voltage and current sensorless control of three-phase PWM rectifiers[END_REF], [START_REF] Jung | Initial voltage angle detection method of a PWM converter without any grid voltage measurement using conduction state of diodes for smooth starting[END_REF]. A common method based on the application of short zero-voltage-vector pulses at the rectifier input is proposed in [START_REF] Kulka | Sensorless digital control of grid connected three phase converters for renewable sources[END_REF], [START_REF] Yoo | Sensorless operation of a PWM rectifier for a distributed generation[END_REF], [START_REF] Lee | AC voltage and current sensorless control of three-phase PWM rectifiers[END_REF]. The grid voltages angle is then deduced from the AC currents variation. However, such a technic short circuit the converters AC side. Therefore, an important over current is occurred. Extracting the initial value of θ during the diode rectifier operation mode has been also proposed in recent papers. In [START_REF] Jung | Initial voltage angle detection method of a PWM converter without any grid voltage measurement using conduction state of diodes for smooth starting[END_REF], the signs of the AC currents flowing during the diode rectifier operation are exploited to deduce an approximated value of θ using a look up table. Current signs detection based method is also proposed in [START_REF] Liu | Robust model predictive current control of grid-connected converter without alternating current voltage sensors[END_REF] to detect the zero crossing interval of θ. However, both strategies start with an imprecise grid voltages position, which lead to an increased settling time. The diode rectifier operation mode (when all the IGBTs are switched off) is exploited in this paper to propose a new strategy for initial values estimation of θ, e d and e q at the startup. Indeed, the proposed AN estimator is applied to estimate the grid voltages by exploiting the similarity between the PWM rectifier and the diode rectifier models. Since the AN estimator needs the input voltages v αβn , three Heaviside functions are then used to their computation in diode rectifier operation mode. The Heaviside functions determine if the diodes are conducting or in blocking state [START_REF] Marques | A simple and accurate system simulation of three-phase diode rectifiers[END_REF]. Assuming ideal diode bridge switches, the input voltages v αβn are expressed as

1 1 1 2 2 2 3 3 3 0 2 2 a n dc b n c g v V g v g α β     - -         =           -       (30)
where g i = {+1 if i i ≥ 0; 0 if i i < 0} for i=a,b,c. It should be noticed that, by replacing [START_REF] Bechouche | A novel method for identifying parameters of induction motors at standstill using ADALINE[END_REF] in [START_REF] Teodorescu | Grid converters for photovoltaic and wind power systems[END_REF], the diode rectifier model can be obtained. Fig. 3 presents the AC-line currents and the reconstructed input voltages from (30) during diode rectifier operation mode. The overall sensorless control scheme is depicted in Fig. 4. It consists of a control unit and an estimation unit. The control unit based on VOC maintains a constant DC-link voltage under a UPF operation [START_REF] Bechouche | Adaptive AC filter parameters identification for voltage-oriented control of three-phase voltage-source rectifiers[END_REF]. The estimated parameters θ est , e d,est and e q,est are obtained from the AN estimator through a phase locked loop (PLL). The estimation unit ensures grid voltages estimation and a smooth starting of the VOC. The equation ( 30) is used to compute the input voltages during the diode rectifier operation mode. The obtained input voltages are injected in the AN estimator. Thus, the grid voltages are accurately estimated under diode rectifier operation. Thereafter, the estimated grid voltages are used in a PLL to obtain initial values of θ, e d and e q . The VOC is finally started and initialized by the PLL outputs (θ est , e d,est and e q,est ). Simultaneously, the input voltages obtained from [START_REF] Bechouche | A novel method for identifying parameters of induction motors at standstill using ADALINE[END_REF] are switched to the actual input voltages (see Fig. 4). Note that, in PWM operation mode, the actual input voltages are obtained from the current controller outputs. This leads to avoiding direct measurements that are affected by the modulation and acquisition noise [START_REF] Gholami-Khesht | Novel grid voltage estimation by means of the Newton-Raphson optimisation for three-phase grid connected voltage source converters[END_REF], [START_REF] -R | A robust natural-framebased interfacing scheme for grid-connected distributed generation inverters[END_REF].

IV. COMPARISON BETWEEN THE PROPOSED ESTIMATION METHOD AND SOGI BASED ESTIMATION METHOD

To prove the superiority of the proposed AC voltage sensorless control algorithm, comparative study between the AN estimator and the recently developed SOGI based estimation method [START_REF] Ketzer | Virtual flux sensorless control for shunt active power filters with quasi-resonant compensators[END_REF], [START_REF] Suul | Virtual-flux-based voltage-sensor-less power control for unbalanced grid conditions[END_REF] has been performed. First, the SOGI method is presented. Thereafter, simulation tests are carried out in MATLAB/Simulink environment.

The SOGI based estimation method uses the VF concept where a virtual AC motor is assumed from the behavior of the grid voltages and the AC filter. Then, the grid voltages are induced by a virtual magnetic flux [START_REF] Ketzer | Virtual flux sensorless control for shunt active power filters with quasi-resonant compensators[END_REF], [START_REF] Suul | Virtual-flux-based voltage-sensor-less power control for unbalanced grid conditions[END_REF], [START_REF] Norniella | Improving the dynamics of virtualflux-based control of three-phase active rectifiers[END_REF]. In α-β reference frame, the VF ϕ αβ can be estimated from the integration of the grid voltages as follows: The integration in (31) induces saturation and DC offset in the estimated VF. To overcome this, the authors in [START_REF] Ketzer | Virtual flux sensorless control for shunt active power filters with quasi-resonant compensators[END_REF] and [START_REF] Suul | Virtual-flux-based voltage-sensor-less power control for unbalanced grid conditions[END_REF] proposed a SOGI based adaptive filter with a cutoff frequency ω. The SOGI transfer function is given by

( ) ( ) ( ) 2 2 nf e n e s k s F s s s k s αβ αβ φ ω φ ω ω = = + + (32)
where ϕ αβnf is the filtered quantity of ϕ αβn and k e is a parameter that influences the SOGI filter speed convergence. Note that since no grid voltages information is available from the SOGI method, the estimated VF is utilized to derive the estimated grid voltages used in VOC control scheme [START_REF] Zhang | Predictive control with novel virtual-flux estimation for back-to-back power converters[END_REF]. This is performed in the following way:

-     =           (33)
In the present comparative study, k e is optimally tuned according to [START_REF] Rodriguez | A stationary reference frame grid synchronization system for three-phase grid-connected power converters under adverse grid conditions[END_REF] and the AN estimator learning rates (µ, η) are tuned according to the criterions established in Section II-C. Thus, both the AN estimator and the SOGI based estimator are tuned to their best. To perform the comparison, the two estimation methods are simulated in the same conditions where two tests are carried out. The simulation parameters are summarized in Table I Performances comparison between the AN estimator and the SOGI based estimator in term of tracking speed of the grid voltages is illustrated in Fig. 5. In this simulation, R L is set to 55Ω and V dc ref is fixed to 190 V. Both estimators are started without initialization. Fig. 5(a) shows the actual grid voltage e α and its estimations e α,ANE and e α,SOGI provided by the AN estimator and the SOGI based estimator, respectively. In Fig. 5(b) the corresponding estimation errors are presented. These results show that, compared to the SOGI based estimator, the AN estimator exhibits faster convergence and low estimation error. Fig. 6 illustrates the actual AC-line currents i α,ANE and i α,SOGI corresponding to the sensorless control methods based on AN estimator and the SOGI based estimator, respectively. From this result, it is clear that the control method based SOGI estimator causes higher overshoots and longer settling time. Furthermore, this test shows the necessity of using initial values of the grid voltages at the startup. Performances comparison between the control methods based on AN estimator and SOGI estimator under V dc ref step change is given in Fig. 7. In this test, R L is set to 55Ω. At time t=1s, a step change of 20V in V dc ref is applied (V dc ref passes from 190V to 210V). The actual grid voltage e α and the estimated voltages e α,ANE and e α,SOGI are shown in Fig. 7(a). The corresponding estimation errors are illustrated in Fig. 7(b). From these figures, it is clear that the AN estimator is not affected by V dc ref step change unlike the SOGI estimator where an estimation error has occurred. This is mainly due to the SOGI filter which is not applied to the whole estimated flux. As shown in [START_REF] Bechouche | AC voltage sensorless control of three-phase PWM rectifiers[END_REF] and [START_REF] Cirrincione | A single-phase DG generation unit with shunt active power filter capability by adaptive neural filtering[END_REF], the current through L is not filtered. Indeed, in transient phase, the SOGI estimator may lose information of Li αβ being not sinusoidal or having a different frequency than ω. However, in our proposed estimation method, all the quantities used in the estimation are processed by the AN estimator. This leads to robust estimation during V dc ref step change. Controlled DC-Link voltages corresponding to each estimation strategy are presented in Fig. 7(c). It can be observed that the DC-Link voltages follow correctly V dc ref .

Grid voltages estimation

From the obtained results, the AN estimator presented faster convergence and better accuracy compared to the SOGI based estimator. In order to verify the feasibility, robustness and accuracy of the proposed AC voltage sensorless control scheme, experimental and simulation tests are carried out in the following section.

V. RESULTS

The laboratory setup used for experimenting the developed AC voltage sensorless control algorithm, illustrated in Fig. 4, is presented in Fig. 8. It consists of a three-phase insulategate-bipolar-transistor based PWM rectifier with antiparalleling diodes. Two current sensors and one voltage sensor are used to measure two input currents (i a and i b ) and DC-link voltage V dc , respectively. It should be noted that, three voltage sensors are used for measuring the grid voltages. These measured voltages are not used in the closed-loop control scheme. Therefore, they are only used to perform comparison between the estimated grid voltages and the actual ones. The developed AC voltage sensorless control algorithm is implemented in MATLAB-Simulink environment and executed on a dSPACE DS1104 board using Euler resolution method. The experimental platform specifications can be found in Table I. The AN estimator is implemented with the learning rates µ=9520 and η=0.04 which are experimentally adjusted to ensure stability and optimal convergence speed according to the criterions established in section II-C. Thus, these learning rate values are both used in simulation and experiment tests. During all tests, the PWM rectifier operates at UPF since the current i q ref is fixed to zero.

In the following subsections, experimental (from Fig. 9 to Fig. 20) and simulation (Figs. 21 and22) tests are carried out. The AN estimator is experimentally tested in different operating conditions such as diode rectifier operation mode, startup process, V dc ref variation, R L variation, symmetrical grid voltages sag and unbalanced grid voltages. Finally, the AN estimator is simulated under distorted grid voltages. The simulation test is done in a MATLAB-Simulink environment using the parameters listed in Table I.

A. Performances of the AN estimator in Diode Rectifier Operation Mode

Experimental results of the grid voltages estimation in diode rectifier operation mode are presented in Figs. 9 and10. In this experiment, the load resistance is set to 55 Ω. So, the DC-link voltage is around 117 V. Figs. 9(a) and 9(b) illustrate the signals used as inputs of the AN estimator. The input voltages (v αn , v βn ) are obtained from [START_REF] Bechouche | A novel method for identifying parameters of induction motors at standstill using ADALINE[END_REF]. From Fig. 9(c) and 9(d), the αβ-axes components of the grid voltages are accurately estimated. After the estimation process, e α,est and e β,est are inserted in the PLL (see Fig. 4). In Fig. 10, the estimated dq-axes components (e d,est , e q,est ) and the phase angle (θ est ) of the grid voltages are illustrated. Therefore, the estimated quantities (e d,est , e q,est and θ est ) will be used as initial values in order to achieve smooth startup of the sensorless control scheme.

B. Startup Process

Figs. 11 and 12 present obtained experimental results of the proposed sensorless control strategy at startup. In this experiment, V dc ref is fixed to 190 V and R L is set to 55 Ω. The input voltages v αn and v βn are shown in Fig. 11(a). The VOC strategy is started at t = 1.34s. Simultaneously, the input voltages computed from [START_REF] Bechouche | A novel method for identifying parameters of induction motors at standstill using ADALINE[END_REF] are switched to αβ-axes components of the current controller outputs (v αn ref and v βn ref ) (see Fig. 4). As illustrated in Figs. 11(b) and (c), the proposed startup process prevents the over-current trip and reduces the commissioning time of the controlled system. So, V dc rapidly follows its reference. It passes from 117V to 190V in about 0.1s. This settling time is due to the time constant of the external control loop. The actual and estimated grid voltages are shown in Fig. 11(d) and (e). It is clear that the estimated voltages are close to the actual ones and present a minimum estimation error at startup. For comparison purpose, two PLLs are computed with actual and estimated grid voltages. The obtained results are presented in Fig. 12. Reduced oscillations and noises are obtained from the PLL computed with

C. Robustness Analysis

To verify the robustness of the proposed sensorless control strategy several tests have been conducted under different working conditions. The results are given in Figs. 13141516171819202122.

1) V dc ref variation: In this experiment, R L is set to 55Ω. A step change of 20V in V dc ref is applied at t = 1.287 s (V dc ref passes from 190V to 210V). As shown in Fig. 13(a) and (b), the actual and estimated grid voltages are superimposed. During the step change in V dc ref , the currents rise from 6A to 8A (see Fig. 13(c)). This increases the flowed power from the AC side to the DC side. V dc is given in Fig. 13(d). It follows accurately its reference before and after the step change. From Fig. 14, the PLL gives great performances with the estimated grid voltages where the computed quantities are not affected by the V dc ref step change. The actual phase angle is also well tracked. 2) Load resistance variation: In this test, a variation of 35% in R L is applied during 0.23s. V dc ref is fixed to 190V. In Figs. 15(a) and (b), the actual grid voltages are well tracked with low estimation errors. Thus, R L variation seems not affect the estimation algorithm. From Fig. 15(c), the currents vary from 6A to 10A. Transient performances of the PLL are shown in Fig. 16. Actually, the PLL provides good performances with the estimated grid voltages. The actual phase angle remains well tracked. 3) Symmetrical grid voltages sag: In this experiment, V dc ref is fixed to 190V and R L is set to 55Ω. Symmetrical grid voltages sag of 16% is applied during 0.25s by adding threephase resistance of 1.5Ω in the AC side (see Fig. 8). As shown in Fig. 17, the AN estimator stability is ensured and the grid voltages are rapidly estimated during the symmetrical grid voltages sag. An increase in the AC-line currents due to the power flow variation is observed during the sag. In Fig. 18

i β i α V dc ref V dc

4) Unbalanced grid voltages:

In this experiment, V dc ref is maintained to 190V and R L is set to 55Ω. Two-phase sag is applied during 0.25s. As presented in Fig. 19(a) and (b), the AN estimator is not affected by the grid voltage unbalance. The estimation error remains very close to zero. Fig. 19(c) shows the currents i α and i β . Although grid voltage unbalance causes AC-line currents distortion, a stable operation of the overall control strategy is guaranteed. Clearly, the computed components with actual and estimated grid voltages shown in Fig. 20 are distorted. This is only due to limitation of the used PLL against unbalanced conditions. Therefore, it cannot be considered as an issue of the proposed estimation strategy. θ e q,est e q θ est grid voltages unbalance Fig. 20. Transient performances of the PLL under grid voltages unbalance (experiment): computed dq components (ed, eq) with actual grid voltages and computed dq components (ed,est, eq,est) with estimated grid voltages and (b) computed angles θ and θest with actual and estimated grid voltages, respectively.

5) Distorted grid voltages:

In this simulation, R L is set to 55Ω, V dc ref is fixed to 190V and the grid voltages contain the 5 th and 7 th harmonic components (5% of the 5 th harmonic and 5% of the 7 th harmonic). As can be seen from Figs. 21(a) and (b), the estimated voltages are well filtered without any influence of the actual grid voltages distortion on the estimation process. This is due to the ANF designed at the fundamental grid voltages frequency. This leads to fundamental components estimation of the grid voltages even under distorted conditions. It should be mentioned that the distortions observed in i α and i β (see Fig. 21(c)) are caused by the used current controllers (simple PI controllers) and not by the AN estimator. Fig. 22 shows performances of the PLL. The computed quantities (e d , e q and θ) using the actual grid voltages present large ripples which are due to the limited PLL performances against harmonic distortions. As the distortions do not appear on the estimated grid voltages, the quantities (e d,est , e q,est and θ est ) do not present significant oscillations.

VI. CONCLUSION

In this work, a new AN estimator for eliminating the grid voltage sensors in VOC of three-phase PWM rectifier has been proposed. The developed AN estimator combines estimation capability of the ANN and filtering property of the ANF. Lyapunov's theory based stability analysis has been exploited for optimal tuning of the AN estimator. Hence, simple, accurate and fast grid voltages estimation has been obtained. To avoid current overshoot and to reduce the settling time at the startup, a new startup process has been proposed to initialize the VOC. The effectiveness of the proposed procedure has been experimentally demonstrated. A comparison between the proposed AN estimator and the recently developed SOGI based estimator has been conducted. This comparison has clearly indicated faster convergence and better accuracy of the proposed estimator. Finally, robustness of the AN estimator regarding to step change in DC-link voltage reference, load resistance variation and non-ideal grid voltages conditions (symmetrical sag, unbalance, distortion) has been investigated through simulation and experimental tests. The obtained results have demonstrated high performances of the proposed AN estimator within the analyzed working conditions.

Fig. 1 .

 1 Fig. 1. Architecture of the proposed AN estimator.

Fig. 2 .

 2 Fig. 2. Schematic diagram of the controlled three-phase PWM rectifier.

  27) where ||• || is the Euclidian norm in n ℜ . Since ε >0, the stability condition in (

Fig. 3 .

 3 Fig. 3. Sensed AC-line currents (ia, ib and ic) and computed input voltages (vαn and vβn) during diode rectifier operation mode (experiment).

Fig. 4 .

 4 Fig. 4. Overall structure of the developed AC voltage sensorless control.

Fig. 5 .Fig. 6 .

 56 Fig. 5. Comparison between the AN estimator and the SOGI estimator at startup (simulation): (a) actual grid voltage eα and estimated grid voltages (eα,ANE, eα,SOGI), (b) estimation errors.

Fig. 7 .

 7 Fig. 7. Performances comparison under Vdc ref step change (simulation): (a) actual grid voltage eα and estimated grid voltages (eα,ANE, eα,SOGI), (b) estimation errors and (c) reference DC-link voltage Vdc ref and measured DClink voltages (Vdc,ANE, Vdc,SOGI).

Fig. 8 .

 8 Fig. 8. Photograph of the implemented test bench: 1) three-phase PWM rectifier, 2) interconnecting inductances, 3) interconnecting resistances, 4) isolating transformer, 5) PC-Pentium + dSPACE board + ControlDesk, 6) dSPACE input/output connectors, 7) load resistance, 8) additional resistances, 9) current sensors, 10) voltage sensors.

Fig. 9 .

 9 Fig. 9. Steady-state performances of the AN estimator in diode rectifier operation mode (experiment): (a) computed input voltages vαn and vβn, (b) actual AC-line currents iα and iβ, (c) actual grid voltage eα, estimated grid voltage eα,est and estimation error and (d) actual grid voltage eβ, estimated grid voltage eβ,est and estimation error.

Fig. 10 .

 10 Fig. 10. Steady-state performances of the PLL in diode rectifier operation mode (experiment): (a) computed dq components (ed, eq) with actual grid voltages and computed dq components (ed,est, eq,est) with estimated grid voltages and (b) computed angles θ and θest with actual and estimated grid voltages, respectively.

Fig. 11 .

 11 Fig. 11. Performances of the AN estimator at startup (experiment): (a) input voltages vαn and vβn, (b) actual AC-line currents iα and iβ, (c) reference and measured DC-link voltages (Vdc ref, Vdc), (d) actual grid voltage eα, estimated grid voltage eα,est and estimation error and (d) actual grid voltage eβ, estimated grid voltage eβ,est and estimation error.

Fig. 12 .

 12 Fig.[START_REF] Kukkola | State observer for grid-voltage sensorless control of a converter equipped with an LCL filter: direct discrete-time design[END_REF]. Performances of the PLL at startup (experiment): (a) computed dq components (ed, eq) with actual grid voltages and computed dq components (ed,est, eq,est) with estimated grid voltages and (b) computed angles θ and θest with actual and estimated grid voltages, respectively.

Fig. 13 .

 13 Fig. 13. Transient performances of the AN estimator under Vdc ref step change (experiment): (a) actual grid voltage eα, estimated grid voltage eα,est and estimation error, (b) actual grid voltage eβ, estimated grid voltage eβ,est and estimation error, (c) actual AC-line currents iα and iβ and (d) reference and measured DC-link voltages.

Fig. 14 .

 14 Fig. 14. Transient performances of the PLL under Vdc ref step change (experiment): (a) computed dq components (ed, eq) with actual grid voltages and computed dq components (ed,est, eq,est) with estimated grid voltages and (b) computed angles θ and θest with actual and estimated grid voltages, respectively.

Fig. 15 .

 15 Fig. 15. Transient performances of the AN estimator under load resistance variation (experiment): (a) actual grid voltage eα, estimated grid voltage eα,est and estimation error, (b) actual grid voltage eβ, estimated grid voltage eβ,est and estimation error and (c) actual AC-line currents.

Fig. 16 .

 16 Fig.[START_REF] Cho | Virtual-flux-based predictive direct power control of three-phase PWM rectifiers with fast dynamic response[END_REF]. Transient performances of the PLL under load resistance variation (experiment): (a) computed dq components (ed, eq) with actual grid voltages and computed dq components (ed,est, eq,est) with estimated grid voltages and (b) computed angles θ and θest with actual and estimated grid voltages, respectively.

Fig. 17 .

 17 Fig. 17. Transient performances of the AN estimator under symmetric grid voltages sag (experiment): (a) actual grid voltage eα, estimated grid voltage eα,est and estimation error and (b) actual grid voltage eβ, estimated grid voltage eβ,est and estimation error and (c) actual AC-line currents.

Fig. 19 .

 19 Fig. 19. Transient performances of the AN estimator under grid voltages unbalance (experiment): (a) actual grid voltage eα, estimated grid voltage eα,est and estimation error and (b) actual grid voltage eβ, estimated grid voltage eβ,est and estimation error and (c) actual AC-line currents.

Fig. 21 .

 21 Fig. 21. Transient performances of the AN estimator under distorted grid voltages (simulation): (a) actual grid voltage eα and estimated grid voltage eα,est, (b) actual grid voltage eβ and estimated grid voltage eβ,est and (c) actual AC-line currents.

Fig. 22 .

 22 Fig.[START_REF] Ahmed | Sensorless current control of three-phase inverter-based distributed generation[END_REF]. Transient performances of the PLL under distorted grid voltages (simulation): computed dq components (ed, eq) with actual grid voltages and computed dq components (ed,est, eq,est) with estimated grid voltages and (b) computed angles θ and θest with actual and estimated grid voltages respectively.

+ - A ∑

	i αβ (k)	z -1
	v αβn (k)	z -1		-B	i αβ,est (k)
		B	e αβ,ANN
				Learning rule	δ αβ (k)
		ANN		Equ. (8)
					e αβ,ANN (k)
		cos (ω1kTs)	w αβ1	+
				∑	-	e αβ,est (k)
		sin (ω1kTs)		w αβ2
				Learning rule
		ANF		Equ. (13)
					AN estimator

  .

														R L
										e d,est
	Vdc ref VOC	-+	DC-link voltage regulation i q ref =0	i d ref i q i d + +	i q i d	--	current controller current controller abc/dq L ω	--	+ vqn ref vdn ref + e q,est θ est dq/abc -+	van ref vbn ref vcn ref	PWM block	S abc	PWM rectifier
		θ est	e d,est e q,est conventional PLL	e α,est e β,est		AN estimator (Fig. 1)		i α i β	abc/αβ
							v αn	v βn
			startup
			switcher
				abc/αβ		Equ. (30)
				v an ref v bn ref v cn ref	V dc

  , transient performances of the PLL are presented under symmetrical grid voltages sag. The dq-axes components of the grid voltages and phase angle are well estimated. Fig.18. Transient performances of the PLL under symmetric grid voltages sag (experiment): (a) computed dq components (ed, eq) with actual grid voltages and computed dq components (ed,est, eq,est) with estimated grid voltages and (b) computed angles θ and θest with actual and estimated grid voltages, respectively.

						symmetrical grid voltages sag
	Voltage (V)	50 100			e d	e q			e q,est	e d,est	(a)
			0
		Angle (V)	2 4 6 8			θ est		θ			(b)
			0	2.25	2.3	2.35	2.4	2.45	2.5	2.55	2.6	2.65
							Time (s)

Since 1993, he has been with the Mouloud Mammeri University of Tizi-Ouzou, where he is currently an Associate Professor. His main interests include power electronics and electrical drives.


Sébastien Rigourd

Stephane Carras

Benoît Agnus

Blaise Ravelo
email: blaise.ravelo@yahoo.fr

Serge De Blasi

Water Wave Micro-Energy Mini-Boat Harvester

Keywords: Water wave, micro-energy harvester, piezoelectric, electrical circuit, experimentation, electromechanical energy transducer

This paper introduces an original research work on experimental demonstration of micro-energy harvesting from water wave. To implement this demonstrator, commercial piezo-electric elements are used as an electromechanical aquatic energy transducer. The proof-of-concept is constituted by electrical micro-energy sensor circuit implemented on a mini-boat external surface. The water wave is generated by the valve oscillating motion placed in a water tank. Because of the wave interaction with the piezo, it was shown that the electrical circuit placed on the micro-boat surface generates instantaneous electrical power with microwatt amplitude under some Volts amplitude instantaneous voltage. The influence of the boat orientation in function of the water wave propagation direction is investigated.

Introduction

The future embedded and wearable electronic devices trend to operate permanently with smart networks as 5G technology [START_REF] Zhang | The numerical investigation on the turbulent heat transfer[END_REF][START_REF] Patankar | Numerical Heat Transfer and Fluid Flow[END_REF]. These modern electronic infrastructures still require technological challenges notably on the power supply design and implementation. One of the deployed solutions to overcome this challenging roadblock is focused on the micro-energy harvester development [START_REF] Kays | Heat transfer[END_REF]. Since two decades, different natures of energy harvesters available in the urban cities and environments have been identified and investigated in function of available ambient sources [START_REF] Kays | Heat transfer[END_REF]. With the technological progress, some of classical energy scavengers, as the hybrid energy harvesting device for generating electricity from heat and light from Fujitsu® are so far, industrialized [START_REF] Kawaguchi | Experimental and numerical investigations of turbulent drag reduction phenomena by additives[END_REF]. Because of the generated electrical power level, the piezoelectric based mechanical harvester is the most popular according to different surveys as reported by IDTechEx® [5]. Different piezoelectric based harvesters have been implemented and commercialized. For example, the walking harvester device is industrialized by PowerWalk® [START_REF] Nordmann | Converging technologies -Shaping the future of European societies[END_REF].

Despite the progressive industrialization of mechanical harvesters, most of the sensational and prominent harvester concept as human motion based micro-energy harvesters are still under laboratory research concept study and test [START_REF] Harb | Energy harvesting: State-of-the-art[END_REF][START_REF] Fujitsu | Fujitsu develops hybrid energy harvesting device for generating electricity from heat and light[END_REF][START_REF]Piezoelectric energy harvesting 2013-2023: Forecasts, Technologies[END_REF]. Such wearable electronic devices are classified in the biomechanical energy harvesting technologies [START_REF] Powerwalk® | [END_REF]. Various types of mechanical energy sensors as electrostatic conversion concept for vibration energy harvesting [START_REF] Riemer | Biomechanical energy harvesting from human motion: theory, state of the art, design guidelines, and future directions[END_REF], piezoelectric microfiber composite actuators [START_REF] Bassani | Human motion energy harvesting using a piezoelectric MFC patch[END_REF], ultrasound flow sensor based on arrays of piezoelectric transducers [START_REF] Dagdeviren | Conformal piezoelectric energy harvesting and storage from motions of the heart, lung, and diaphragm[END_REF], PZT nanofiber based nanogenerator [START_REF] Choi | Wearable biomechanical energy harvesting technologies[END_REF] and textile-reinforced thermoplastic sensors [START_REF] Boisseau | Electrostatic conversion for vibration energy harvesting[END_REF] were proposed. In order to integrate the mechanical harvesters for certain applications as human motion [START_REF] Harb | Energy harvesting: State-of-the-art[END_REF][START_REF] Fujitsu | Fujitsu develops hybrid energy harvesting device for generating electricity from heat and light[END_REF][START_REF]Piezoelectric energy harvesting 2013-2023: Forecasts, Technologies[END_REF], the flexible technology generator was introduced [START_REF] Usher | Piezoelectric microfiber composite actuators for morphing wings[END_REF]. Among the flexible harvester solutions, because of its adaptability to 3D geometrical shape variation, the threads and textile-based structures [START_REF] Kunadt | Ultrasound flow sensor based on arrays of piezoelectric transducers integrated in a composite[END_REF][START_REF] Chen | 1.6 V Nanogenerator for mechanical energy harvesting using PZT nanofibers[END_REF][START_REF] Hufenbacha | Effect of integrated sensor networks on the mechanical behaviour of textile-reinforced thermoplastics[END_REF][START_REF] Fan | Flexible triboelectric generator[END_REF] remain the most integrable to the human body environment. Currently, it can be pointed out with the reported energy harvester state of the art [START_REF] Kays | Heat transfer[END_REF]5] that the most popular mechanical harvesters operate with classical direct contacts.

However, among the existing mechanical harvesters available in the research literature, few works were available about the fluidic liquid motion and water-based energy harvesters [START_REF] Valentini | Flexible triboelectric generator and pressure sensor based on poly[(R)-3-hydroxybutyric acid] biopolymer[END_REF][START_REF] Hufenbach | Development and investigation of a textile-reinforced thermoplastic leaf spring with integrated sensor networks[END_REF][START_REF] Buckley | Woven piezoelectric yarns lead to 3D textile energy harvester[END_REF]. The existing concept about this fluidic pressure based micro-energy harvester are still under laboratory research concept study and test [START_REF] Valentini | Flexible triboelectric generator and pressure sensor based on poly[(R)-3-hydroxybutyric acid] biopolymer[END_REF][START_REF] Choi | Corrugated textile based triboelectric generator for wearable energy harvesting[END_REF]. For this reason, the present paper is focused on the development of miniboat proof-of-concept (PoC) dedicated to the water wave micro-energy harvesting.

For the better understanding, the paper is organized in three main sections. Section 2 describes the design principle of the mini-boat harvester PoC. Section 3 deals with the experimental setup of the demonstrator and discusses about the electrical generated energy obtained results. Then, Section 4 summarizes the paper with a conclusion.

Description of the mini-boat electromechanical micro-energy harvester

The present section describes the operation principle of the proposed mini-boat water wave energy harvester. It is explained by introducing the synoptic system. Then, the specifications of each constituting block of the harvester are described. The proposed energy harvester PoC is comprised of:

General description of the water wave energy harvester PoC

• An oscillating valve or leaf system generating the water wave which moves with controlled frequency;

• The quantity of water wave pressure;

• The mini-boat geometrical surface and positioning with respect to the water wave propagation direction;

• The piezo-electric sensor acting as a transducer element which ensures the electromechanical energy conversion;

• And the generated electrical energy E from the water wave motion is intuitively proportional to the water wave amplitude force Fw and impacting on sensor velocity vw:

( , ) w w E F v ∝ .
(1)

Description of the water wave source

The experimental protocol of the proposed energy harvester PoC is performed in an aquatic water tank. Fig. 2 In order to be realistic, we have designed and fabricated by ourselves on the example of a speedboat. The fabricated PoC is a very common type of boat. Its particularities are that its length is three times greater than its width, that the "ventral" curvature primer ends at 30% of the front-rear distance from the bow and that the width decreases from 40% of the front-rear distance from the stern. The following dimensions have been adapted to the dimensions of the tank, indicated below, the boat will be 24 cm long and 8 cm wide, the reduction in width starts at 10 cm from the stern and the bow curvature starts at 7.5 cm from the same bow. By deeming the transport purposes, we have established that the tank would be 70 cm × 30 cm × 30 cm.

The water level filling the mini-boat would be of about 15 cm. The plate making the beats would be located 9 cm from the rear wall of the tank, would be fixed 7.5 cm opposite the top of the tank and would stop at 4.5 cm from the bottom. The plexiglass plate creating the waves is driven by a motor equipped with a dimmer which will then allow us to manage the frequency and intensity of the waves. The overall characteristics of the employed piezoelectric sensors are addressed in Table 1. For the present study, our main focus is on the following sensor element parameters: piezo surface, buzzer diameter, operating frequency and the output impedance. According to the manufacturer model, the latter behaves as an RC-parallel network.

2.3.Mini-boat design

Discussion on the experimental results with micro-energy harvesting from water wave source

The present section is focused on the description the experimental setup and the discussion on the obtained electrical signal generated results.

3.1.Experimental setup description

Fig. 6 illustrates the photograph of the performed wave water electromechanical micro-energy conversion. The Filix® maintenance team has developed a system to reproduce the effect of the motor (holding a fixed heading). The wave generator system consists of a plexiglass part that is fixed in the boat hull and allows 360° rotation. The system also allows to manage the height at which the boat is fixed.

The photographs of the mini-boat oriented in the parallel direction with the water wave propagation direction are shown in profile view of Fig. 7.

3.2.Discussion on the harvested electrical energy

This leaf system topped by a variable speed drive motor allows us to create waves with a frequency of appearance of one wave every second at most and one wave every five seconds.

Piezo-electric single test with water constant rate

To make the connections, without damaging the piezoelectric cells, the wires were soldered on copper tape. The experimentations have been performed in different steps. First of all, we wanted to characterize the piezoelectric cells. To do this, we release an object without initial velocity of known mass and contact surface into a tube of known height. We will not obtain any results during this characterization attempt since the observed phenomenon is a shock and not a pressure, the phenomenon must last a minimum in time for there to be a physical deformation of the piezoelectric cell. Then, we empirically characterized each piezo sensor sensitivity. This characterization will potentially bring us closer to the strength of a wave whose flow rate we can control. It is noteworthy that the tests in aqueous medium with straightening did not yield concluding result. The characterization experimental setup is therefore highlighted by Fig. 8. A massive object was fallen on the piezo sensor with height of about h=30 cm.

Then, the induced electrical energy is measured with the voltage indicated by the multimeter. The present study is essentially focused on the fluctuating induced voltage amplitude. Table 2 presents the measured results with ten piezo sensors. To determine the optimal characteristics for our sensors, we have chosen a panel of 10 sensors that will allow us to evaluate the characteristics that influence the performance of the sensors in terms of energy recovery.

The values obtained were recorded in an experiment in which the different piezoelectric cells were placed under a continuous flow of known and stable flow and force. Thus, all the cells were exposed, previously covered in a waterproof manner, to a perpendicular flow rate of 0.2 l/s. In order to determine

White Paper 2019

Page 14 by 24 the influence of the resonance frequency on the efficiency, we used four cells with the same diameter but different frequencies. Fig. 9 plots the obtained results from experimental measurements. We would like

to propose an empirical model with low relative errors in term of standard deviation. By using Matlab forth degree polynomial fitting, the empirical efficiency can be approximated as:

4 4 3 2 10 (12 202 948 909) f f f ξ - = - + - (2)
It should be emphasized that this forth degree enables to achieve reduce considerably the standard deviation from the measured data and the fitting model.

In addition, we can observe that the cell surface is the parameter that most influences the yield. Indeed, the first cell is both the largest in terms of surface area but also has the lowest resonance frequency, yet it is the cell with the best efficiency. It should be pointed out that the sensor operating at 4.1 kHz frequency cell is actually defective. We therefore used only the 41 mm diameter cell presenting a resonance frequency of 1.3 kHz.

Figure 9: Piezo-electric efficiency versus resonance frequency with water rate 0.2 l/s with propagating direction perpendicular to the piezo surface.

Dynamic wave harvesting test results

This leaf system topped by a variable speed drive motor allows us to create waves with a frequency of appearance of one wave every second at most one wave every five seconds.

During the present study, we attended to look at the different circuits that may be used in the future. It seems that signal rectification system is needed. It should be noted that the signal of a piezoelectric cell is a continuous signal that alternates sign according to the action performed on the cell. When a pressure is applied, the signal is positive and when the cell is relaxed, the signal is negative, so that the internal loads of the cell are rebalanced and are ready for use again.

We can therefore see that the direct addition of induced voltage by connecting two cells together in series has a lower efficiency than indirect addition. This finding is because of the fact that the two cells are independent of about 4 mV against 6 mV. But in terms of gross recovery, the indirect addition is not optimal for our system. Indeed, although there is an improvement, when performing an indirect additive assembly with six piezoelectric cells, we find that the growth curve of energy recovery takes the form of a logarithmic curve presented in Fig. 11.

Influence of water wave propagation and mini-boat orientation

This leaf system topped by a variable speed drive motor allows us to create waves with a frequency of appearance of one wave every second at most and one wave every five seconds. We have tried to map the efficiency of energy recovery as a function of the sensor position and the orientation of the boat. This will allow us to optimize the monitoring afterwards. (i.e. define predefined areas of analysis and monitoring on the hull). We studied empirically the influence of the boat's orientation on the energy recovery of the different positions.

In this experiment, we wanted to highlight the influence of the boat's orientation on the energy recovery of each position independently of each other.

The experimental protocol was to place the boat halfway between the bottom of the aquarium and the wave creating sash as explained by Fig. 12. Then, the boat was oriented according to the angles θ={0°, 45° 90° 135°, 180° 225°, 270°, 315°}. Table 3 presents the measured electric voltage maximal amplitude of each of the positions. The wave flow created is constant and regular and moves in the 0°-180° axis.

Conclusions

An innovative harvesting technique of water wave electromechanical energy is investigated. The energy harvesting proof of concept was designed with a mini-boat placed in a water tank filled with water. The design method of the mini-boat prototype integrating piezo cells is described. The energy harvesting experimental setup is originally introduced.

The empirical test results were obtained under laboratory conditions, which implies low values and therefore limited analysis. The harvested electric power range depends on the piezoelectric technology performance. Further investigation is also performed to highlight the influence of the piezo cell positioning and the boat orientation. The amplitude of the harvested electric power is mapped in function of the board orientation compared to the wave propagation direction. We have determined which direction leads to the best performance.

In outlook of this research work, the proposed harvester will be transposed to more realistic conditions to be able to evaluate the higher amount of real recoverable energy. The present experimental investigation is prominent in the future for the development of energy storage technique in wider scale as in the marine environment.

Fig. 1

 1 Fig. 1 represents the global diagram of the water wave micro-energy PoC under investigation. It can

Figure 1 :

 1 Figure 1: Synoptic diagram of the mini-boat electromechanical micro-energy harvester.

  (a) and Fig. 2(b) show the photographs of the aquatic water tank and the valve controller module respectively.

Figure 2 :

 2 Figure 2: (a) Aquatic water tank and (b) control interface of valve oscillation frequency.

Fig. 3 (

 3 Fig. 3(a) and Fig. 3(b) introduce the SolidWorks® 3D design and the photograph of the fabricated

Figure 3 :

 3 Figure 3: (a) SolidWorks® 3D design and (b) photograph of the fabricated mini-boat prototype.

Figure 4 :

 4 Figure 4: Photograph of the fabricated mini-boat prototype: (a) top and (b) bottom views.

Figure 5 :

 5 Figure 5: Geometrical dimensions of piezo placement on the mini-boat surface.

Figure 6 :

 6 Figure 6: Photographs of the water wave harvester experimental setup: (a) rear and (b) profile.

Figure 7 :

 7 Figure 7: Profile view of the boat oriented in the parallel direction to the water wave propagation

Figure 8 :

 8 Figure 8: Piezo-electric single test configuration.

Figure 10 :

 10 Figure 10: (a) Signals emitted by two piezoelectric cells (Signal 1: 150 mV Signal 2: 250 mV)

Figure 11 :

 11 Figure 11: Generated electrical voltage average value in function of piezo-electric quantity.

Figure 12 :

 12 Figure 12: Mini-boat orientation reference.

Figure 13 :

 13 Figure 13: Radar maps of test results in function of water wave propagation direction and

Table 1 :

 1 Piezo-electric sensor characteristics.

		Piezo	Buzzer		Output
	Name	Ref. no.		Frequency
		surface	diameter		impedance
		AB4113B/668-1017-
	P1		24.6 mm²	1.3 kHz	200 Ω / 150 nF
		ND
		41 mm
		AB4141B/668-1624-
	P2		16.6 mm²	4.1 kHz	1 kΩ / 100 nF
		ND

Table 2 :

 2 Piezo-electric generated voltage amplitude simulated the test case of water constant rate.

	Piezo	P1	P2	P3	P4	P5	P6	P7	P8	P9
	VP (V)	1.78	0.54	1.54 0.47 0.37 0.17 0.29 0.43 0.43

Table 3 :

 3 Measured electric voltage maximal amplitude (in mV) in function of the mini-boat orientation.

		0°	45°	90°	135° 180° 225°	270°	315°
	Position	180	150	200	300 200	220	300	200
	1
	Position	250	280	400	400 300	370	450	300
	2
	Position	40	50	60	60	50	80	80	50
	3
	Position	120	200	350	200 150	250	200	150
	4
	Position	300	320	500	300 300	420	380	350
	5
	Position	200	200	300	200 220	200	220
	6

Acknowledgements

Acknowledgement is made to the France Normandy Region for the "FIL HARMONIQUE" project grant no. 18E00151 2017-2019 support of this research work, research and publication of the present article.

The authors declare that there is no conflict of interest regarding the publication of this paper.


A Poro

S Memarzadeh

A Halavati

M Pakravananfar

I Safaei

A Sojoudizadeh

S Hamedian

S Ebadi

J Ebrahimzadeh

A Roshanaei

M Piri

M H Kaboli

A Mohandes

H Khezri

P Eisvandi

M Shojaatalhosseini

A Shahdadi

M Hesampoor

A Gardi

K Gholizadeh

Z Tavangar

S Hesampoor

S Sarabi

M Kazemipour

H Hadianpour

F Chahooshizadeh

A Baghipour

F Hasheminasab

C Morris

Cape S Africa

S J Turner

CA Val Verde

F A Anet

S H Davies

G Goodman

Durban A Cousins

Johannes J Churms

Arizona D D Tucson

Nye

D Dunham

T Hanzawa

H Tomioka

M Sochan

V N De Gaia

J P Osorio

G Walters

Auckland M F Stoker

Taylor Range

Obs P E Anderson

Blenheim B Loader

Upper Hutt

J O'kane

J O'

Kane Camponovo

Rd3 Thornton

Nzl D Whakatane

Watson

J Tebbutt

M Schmid

England

R Noack

P Svoboda

D Ewald

Ziar Nad

Nikolaev Obs

Voronenkov

O Klinting

Las Spain

Juan J Cabezas De San

Fernandez

Rodovre

P B Denmark

Darnell

Juan F Cabezas De San

Gutierrez

Denmark C Virum

Grunnet

Juan F Cabezas De San

Denmark W Tisvildeleje

-Knudsen

Juan L Cabezas De San

Quijano

Denmark O Ronne

Olesen

Juan Cabezas De San

Salazar

K W Fabrin

M Szulc

De Cabezas

Juan A San

Orte

R Kurianowicz

A Malinowski

Cabezas

J Bourgeois

P Abbott

P Lipski

H J J Bulder

T Weiland

R Goncalves

J Pazder

M Micek

F Seidel

V Pribyl

O S Correa

Desna P E Anderson

Birmenst T Switzerland

Winiger

Obs S Kaneko

Wald E Switzerland

Kharadse

Yamagata Y Oba

Abastumani A Smith

Yamagata T Funakoshi

E Eichmann

Yamagata T Kaminoyama

Kurokawa

Hacienda Heig

S Baba

Lubeck O Sandor

Chofu S Shibasaki

Kaneko

Teplice P Stastka

Chiba T Sakura

Huzisawa

Teplice E Belda

Sirahama H Obs

Noda

Simosato H Obs

T Hayamizu

Kagoshima M Sendai

Szulc

Lubeck D Ewald

Melchow M Zawilski

Bisei T Obs

Oono

Lodz P Ossowski

Hiroshima K Nakaku

Iino

Ostrow Wielkopolski

J Speil

Walbrzych -Ksiaz

E D Speil

H Noda

Zilina A Siser

E Belda

Desna M Znasik

Lubeck R Buggenthien

Zilina R Sandy

K Iino

Saitama S Urawa

Baba

O-C Study of 545 Lunar Occultations from 13 Double Stars

Keywords: Lunar Occultation, Occult 4, O-C

In this article, we have studied the reports of lunar occultations by this project observation's teams (named APTO) in comparison with other observations of the objects. Thirteen binary stars were selected for this study. All the previous observations of these stars were also collected. Finally, an analysis of O-C of all reports were performed.

Introduction

A lunar occultation occurs when the Moon passes in front of stars, planets or other objects in the sky. Many astronomers have been observing occultations over the past two centuries. However, observations made from the Earth has its limitations. Larger telescopes are able to provide data on fainter stars, thus the more the optical device is capable of collecting the light and the higher its resolution, the more stars and fainter objects can be observed. However, it would also depend on the degree of the sky darkness, atmospheric extinction, and seeing conditions. Apart from that, the lower amount of humidity or dust along the horizon or sky during the observation would lead to a better recognition of fainter objects [START_REF] Poro | Introducing some effective parameters in the types of Occultations[END_REF]. The higher the lunar elevation the better the sky conditions might be expected.

The accurate timing of lunar occultations is performed regularly by astronomers using different methods. Visual observations are the least accurate but can be timed to an accuracy of a few tenths of a second. These so have a benefit in helping to refine our knowledge of lunar topography. Since human reaction time is involved, a personal equation (PE) needs to be developed and incorporated for each observer.

Our measurements of the Moon's topography is related to those made by a spacecraft called KAGUYA. The Japanese lunar explorer KAGUYA (also called SELENE) was launched successfully on September 14th, 2007 by the Japan Aerospace Exploration Agency. KAGUYA is in polar orbit around the Moon and uses onboard sensors to research gravity and topography (S. [START_REF] Sasaki | KAGUYA topography gravity team, Global Topography and Gravity of the Moon Observed by KAGUYA[END_REF].

Since the "edge of the Moon" is what is being observed from the Earth when an occultation occurs, it is possible that due to erosion, there are likely to be some very minor changes over long periods of time. The amount of change is calculated from the profiles produced by KAGUYA. Therefore, the calculations are based on the occultation timing by observations compared against KAGUYA profiles which is shown by what we refer to as the O-C parameter. O-C (Observed minus Calculated) implies a temporal aspect which is used when discussing cyclic phenomena where the times of occurrence of a given event are subject to irregularities (C. [START_REF] Sterken | The O-C Diagram: Basic Procedures[END_REF]. Before KAGUYA profiles began being provided, the reference for calculated O-C for lunar occultation reports was from a document popularly known as the Watt's charts published in 1963. They are presented in the form of charts of the liberation frame each 0.2 degrees of position angle measured from the Moon's axis of rotation. Since the Moon is not a sphere but presents a roughly spherical shape with continuing limb irregularities, these features are presented to the Earth at different aspect angles over time.

Occult 4 software is used to make predictions for the occultation observation as well as the reporting and O-C calculation based on KAGUYA profile. Occult 4 is a software program for predicting the circumstances of many types of astronomical occultations. Occult 4 will predict the circumstances of lunar occultations (total and grazing), asteroid occultations, occultations of planetary moons, etc. [START_REF] Poro | Astronomical Occultation Book[END_REF]. This openaccess software was developed by David Herald. This article is based on the results of a project called "Astronomical Project on Timing Occultation" (APTO). The project was started in February 2019 in partnership with nine Iranian teams and observatories. The first purpose of this project was to time lunar occultations comparing O-C with previous timing reports of those stars. For this purpose, we selected thirteen binary stars as targets. We extracted observations and timing reports from Occult 4 software going back in time to the year 1833 to compare against APTO's observations.

Data Sets

The following targets for the APTO observations are: SAO 139834, SAO 139794, SAO 187426, SAO 118892, SAO 98511, SAO 99185, SAO 98265, SAO 98488, SAO 139427, SAO 98673, SAO 79480, SAO 119447, XZ 43302. These targets and their occultation opportunities were selected given the following limitations: The stars are defined to be double (Table 1); the lunar phase for predictions is between 10% to 90% and -90% to -10%; lunar elevation above the local horizon during the occultation period should be more than 20 degrees; star visual magnitudes are between +5 and +9; only the occultation disappearances were timed (reappearances were not measured). Comparative observations based on selected double stars collected from Occult 4 (Version 4.7.2.0) software. These 528 observation reports are from 1833 to 2018 (Table 3). Details of the selected observation reports are also included in appendix A.

Timing Method

Lunar occultation timing measurements can be useful when there is an overall accuracy of a few tenths of a second in order to provide confirmation or improvement of knowledge of lunar topography. The methods of timing used by the APTO teams and observatories who gathered this data were primarily visual though there were a few video observations.

The base time references used in this project have been both the Network Time Protocol (NTP) and The Global Positioning System (GPS). NTP observers used the North American Asteroidal Occultation Program website2 and the SkyTiming.1 mobile application3 was used for GPS based time. Timing for a successful observation of occultation events has a long history. Since the early 1960s, scientists were using cassette tape recorders to record the sound of short-wave time signal broadcasts from radio station WWV, WWVB, CHU, WWVH or some other stations as well as the sound of their voice calls as occultations were seen to occur. Stopwatches were also used. Today, there are other methods for timing an occultation such as using NTP servers or GPS as time references. However, each one has some problems [START_REF] Lesani | SkyTiming; A New Mobile Application for Submit and Timing[END_REF].

The NTP and GPS based time was used for visual timing. Observers in this project used each of them for timing by stopwatch or voice record ways. In many of the observations, both have been used by observers to reduce the error rate. In two reports, the video method was used by Kerman team. This method uses a DSLR camera. Both NTP and SkyTiming application (GPS) were used for the base time, which it was found that the SkyTiming application based GPS time was less error.

The GPS is the best time reference base. The whole system's rationale is based on time. Most (but not all) GPS receivers have a feature called One Pulse Per Second (1PPS) referenced to Universal Time (UT) to an accuracy measured in microseconds and that if this signal is used appropriately, a GPS receiver can be used to give times to an accuracy of ±0.001 seconds or better [START_REF] Gault | Applying UT to Visual Timing in Occultation Observations[END_REF]. However, even video measurements cannot achieve an accuracy better than .033 based on frame rate recording and this has no impact on visual measurement accuracies.

The most important errors in observation and timing are the base time error and the Personal Equation (PE) error. PE is the time the observer takes to react to the occultation. It is required for visual observers. Typical values are 0.3 to 0.5 for a disappearance as the star is first occulted by the Moon. The term D (or d) is used for disappearance and R (or r) for reappearance. Experienced observers always try to improve PE in their visual timing. If the star is not easily visible, or the observer is inexperienced, the value will be at the larger end. A visual observer should enter into the PE field a numerical value, which is a best estimate of their personal reaction time. It is only an estimate and not 100% accurate.

The estimated uncertainty (± time range) in the reported time, after any PE, has been applied. Usually, the uncertainty will be smaller than the PE. The ultimate goal is to decrease PE in visual observations. Initially, for observers to gain experience, they must use visual methods to see an occultation with their eyes as it takes place. This is the reason for understanding the concept of PE since it demonstrates that no matter how 'good' an observer thinks he or she is, there is always a delay in estimating a D or (especially an R) in lunar occultations. To eliminate PE entirely one must transition to a more accurate method that does not require the human eye to interpret when a D or R has taken place. Nowadays, video timing methods are used with GPS time embedded in each frame. As mentioned here, two reports of this project used a creative approach based on video timing, based on available facilities [START_REF] Poro | Introducing some effective parameters in the types of Occultations[END_REF].

Analyses and results

The most important problem in the visual observation part of the project was the reduction of the PE for each observer. This error can occur for a variety of reasons. Some of the things that have been reported to have caused this error, according to observers, are: -Effect of cold temperatures lowering the timing accuracy -Response of the eye/brain to an occultation impacted by the age of the observer -Observer's hands are not free for controlling the telescope.

-Observer cannot comment on some conditions concerning the observation directly.

-Eye fatigue and lack of consistent focus -PE even for the same observer can vary -Other problems which reduce the accuracy of timing such as instrumentation issues Despite the low experience of observers at the beginning of this project, the average PE for the observations is calculated: 0.3901. This error rate is within the range of 0.3 to 0.5.

Once we have found that the PE of reports was acceptable for this project, we proceeded to comparative study of O-C. As mentioned earlier, O-C can be an indicator of timing accuracy, according to the KAGUYA satellite profile. If this parameter's range for visual timing is between +0.1 to -0.1 it means that the observer has done an accurate time measuring.

Figure 1 shows O-C parameters during over years for all of the reports that studied in this project. This chart is based on a fit where a "Curve-Fit Robust Straight Line" was drawn. We analyzed the reports of this project, and a similar fit was done to obtain the line equation (figure 2).

According to this fit for our observation, it started at +0.07 and ended at -0.16. The specifications of the fits of figures 1 and 2 are given in Table 4.

Conclusion

Thirteen binary stars were selected for observation and comparison. Only disappearances were timed. Apart from the observations by the teams involved in this project, historical observational reports on these 13 stars were also collected from the Occult 4 software. As with other observations extracted from Occult 4, different timing methods were used, though 89.5% of these observations were visual with 0.3901 Personal Equations. In all the observations of this project, we used NTP or GPS for based time.

Based on the fits and calculations for O-C (table 4), the mean error of deviation from zero for total observations (figure 1) is 0.255 and for observations in this project (figure 2) is 0.115. Therefore, given a similar fit, it can be concluded that the average timing accuracy in this project reports was acceptable than average timing accuracy for total O-C diagram for previous observations. It should be noted that although total previous observations have used more of the visual timing type, the average error rate of them is acceptable.

Appendix

Figure 1 .

 1 Figure 1. O-C parameter for all reports over time

Figure 2 .

 2 Figure 2. O-C changes derived from this project reports

Table 1 . Details of all observed stars collected from the Simbad database 1

 1

	Star	RA.	Dec.	M(v)	Sp.	Dia. (")
	SAO 139794	14 13 18.6579408076	-08 26 40.683175535	7.15	K0	0.0007
	SAO 187426	18 54 10.1776767186	-22 44 41.427261350	4.84	K1	0.0035
	SAO 98673	09 37 02.5811258036	+16 26 16.627284928	5.73	K1	0.0011
	SAO 119447	12 31 14.61	+01 19 37.0	7.63	A5	0.0002
	SAO 79480	07 32 22.7663411126	+21 06 15.249116287	8.11	A2	0.0001
	SAO 139427	13 35 24.48454	-04 56 03.5580	8.7	F3	0.0001
	SAO 98488	09 18 58.8570535656	+17 42 18.952268371	6.64	F5	0.0003
	SAO 98511	09 20 38.1911603913	+17 07 38.430767874	7.76	F2	0.0002
	XZ 43302	18 4 17.4234	-22 29 39.961	8.71	B3	0.0001
	SAO 118892	11 29 39.9952266114	+07 35 57.748681014	6.73	F5	0.0003
	SAO 98265	08 58 18.2919146861	+18 18 29.789018923	6.55	A0	0.0002
	SAO 99185	10 34 07.2818934159	+12 22 27.974286167	7.86	A3	0.0001
	SAO 139834	14 16 48.7344774535	-08 53 04.109883483	6.47	K1	0.0012

Based on these limitations, predictions and observations for the 13 target stars by the teams and observatories from March to July 2019 were made in different parts of Iran. A total of 19 observations were report (Table

2

).

Table 2 . Details of lunar occultation observations during APTO

 2

	Date	Star	Observer	City	Location Longitude	Latitude	Alt. (m)	Tel. (cm)	Timing method	Time source	O-C	PE or Accuracy
	2019 3 17	SAO 98265	I. Safaei	Kashan	+ 51 8 26.9	+33 58 19.3 1774	25	Stopwatch	NTP	-0.08	0.4
	2019 4 12	SAO 79480	I. Safaei	Kashan	+ 51 8 26.9	+33 58 19.3 1774	25	Stopwatch	NTP	-0.14	0.5
	2019 4 14	SAO 98673	S. Paknejad	Tabriz	+ 46 19 44.8	+37 52 23.8 2343	20	Tape recorder	GPS	0.19	0.4
	2019 4 14	SAO 98673	S. Memarzadeh	Tabriz	+ 46 19 44.8	+37 52 23.8 2343	20	Stopwatch	GPS	0.11	0.4
	2019 4 15	SAO 99185	I. Safaei	Kashan	+ 51 8 26.9	+33 58 19.3 1774	25	Stopwatch	NTP	-0.17	0.5
	2019 4 16	SAO 118892	A. Halavati	Kerman	+ 57 1 11.8	+30 16 56.0 1782	25	Video	GPS	0.08	0.016
	2019 4 16	SAO 118892	H. Khezri	Bushehr	+ 51 3 21.1	+28 56 53.4	15	41	Stopwatch	NTP	-0.66	0.5
	2019 4 24	XZ 43302	S. Hamedian	Tabriz	+ 46 19 37.0	+38 3 5.3	1500	18	Tape recorder	GPS	0.35	0.3
	2019 4 24	SAO 187426	A. Halavati	Kerman	+ 57 1 11.8	+30 16 56.0 1782	25	Video	GPS	-0.16	0.016
	2019 4 24	XZ 43302	J. Ebrahimzadeh	Tabriz	+ 46 19 37.0	+38 3 5.3	1500	18	Stopwatch	GPS	0.38	0.4
	2019 5 11	SAO 98488	M. Piri	Tabriz	+ 46 19 36.3	+38 3 5.2	1524	15	Tape recorder	GPS	0.60	0.3
	2019 5 11	SAO 98488	J. Ebrahimzadeh	Tabriz	+ 46 19 36.3	+38 3 5.2	1524	18	Tape recorder	GPS	0.37	0.3
	2019 5 11	SAO 98511	S. Ebadi	Tabriz	+ 46 19 36.3	+38 3 5.2	1524	18	Tape recorder	GPS	-0.25	0.3
	2019 5 11	SAO 98511	S. Hamedian	Tabriz	+ 46 19 36.3	+38 3 5.2	1524	18	Stopwatch	GPS	-0.28	0.3
	2019 6 12	SAO 139427	H. Khezri	Bushehr	+ 51 3 21.1	+28 56 53.4	15	41	Stopwatch	NTP	-0.04	0.3
	2019 7 8	SAO 119447	A. Mohandes	Kashan	+ 51 8 26.9	+33 58 19.3 1774	25	Stopwatch	NTP	-0.32	0.4
	2019 7 8	SAO 119447	H. Khezri	Bushehr	+ 51 3 21.1	+28 56 53.4	15	41	Stopwatch	NTP	-0.22	0.4
	2019 7 10	SAO 139794	M. Kazemi	Ahvaz	+ 48 42 10.5	+31 21 54.8	30	25	Stopwatch	NTP	-0.18	0.5
	2019 7 10	SAO 139834	F. Hesampor	Shiraz	+ 52 34 50.	+29 34 19.	1528	20	Stopwatch	NTP	-0.04	0.4

Table 3 . List of occultation reports based on Occult 4 without APTO observations reports

 3

	Star	Mv	Number of Reports	Year of First Report	Year of Last Report
	SAO 139794 7.15	39	1944	2001
	SAO 187426 4.84	85	1898	2010
	SAO 98673	5.73	81	1833	1988
	SAO 119447 7.63	30	1927	2002
	SAO 79480	8.12	30	1982	1991
	SAO 139427 8.70	10	1998	2001
	SAO 98488	6.64	35	1852	2007
	SAO 98511	7.77	8	1970	1981
	XZ 43302	8.71	8	1982	1982
	SAO 118892 6.73	48	1926	2018
	SAO 98265	6.56	92	1934	2008
	SAO 99185	7.87	5	1968	1982
	SAO 139834 6.47	57	1907	2001

Table 4 . Fit specifications for data

 4

	Reports	Line equation	r 2	Adj r 2	FitStdErr
	Total	Y= -0.0027803391 x + 5.4629043	0.0049850001	0.0013268567	1.0292405
	This project	Y= -0.048778689 x + 0.22512559	0.050501821	0	0.303635

http://simbad.u-strasbg.fr/simbad/

www.asteroidoccultation.com/observations/NA

http://iota-me.com/skytiming.html

Acknowledgments

This manuscript was prepared by the International Occultation Timing Association Middle East section (IOTA/ME) and APTO teams. We would like to thank Paul D. Maley for his scientific guidance and editing of this article.