Étienne Parizet
email: etienne.parizet@insa-lyon.fr

In situ surveys report some interactions between railway noise annoyance and the level of railway vibration on one hand, and between railway vibration annoyance and the level of railway noise on the other hand. Few studies have been conducted to investigate these interaction phenomena under laboratory conditions and their results are contradictory. During a laboratory experiment, recordings of noise and vibration from two train passages (1 freight train and 1 passenger train) were presented in combination to participants at different noise and vibration levels. The influence of noise level on participants' annoyance due to vibration, as well as the influence of vibration level on participants' noise annoyance was assessed in order to investigate two potential explanations for the contradictory results from the literature. Total annoyance responses due to combined noise and vibration were also analysed to further evaluate the influence of global noise and vibration levels on annoyance. No influence of vibration level on noise annoyance was detected. A weak influence of noise level on vibration annoyance was found, only when the vibration level was high (L Veq = 116dB). Several existing total annoyance models were tested. Among those, perceptual models showed good agreement with the laboratory data.

Introduction

Annoyance caused by railway noise has been widely studied, but it is still difficult to predict given the variability of results in the literature. Several studies have established dose-response relationships between sound energy-based indices and the percentage of people annoyed (%LA, %A or %HA; e. g. [START_REF] Miedema | Annoyance from transportation noise: relationships with exposure metrics dnl and denl and their confidence intervals[END_REF]). The European Commission recommends the use of such relationships for the estimation of annoyance due to railway noise although their predictive quality is quite low ( [START_REF] Ec | Position paper on dose response relationships between transportation noise and annoyance[END_REF]). In various socio-acoustic surveys, railway noise appears to be the least annoying transportation noise and as such receives a bonus in several regulations (e. g. in Germany, [START_REF] Gottlob | Regulations for community noise[END_REF]). However, this observation is questioned by more recent studies which have shown that ignoring simultaneous vibration exposure limits the accuracy of dose-effect relationships for railway noise (cf. [START_REF] Lercher | Combined noise exposure at home[END_REF] for a review on the topic of combined noise sources). In particular, during in situ surveys, the level of vibration due to railway traffic seems to have an influence on noise annoyance (e. g. [START_REF] Woodcock | Human response to vibration in residential environments: Establishing exposure-response relationships[END_REF], [START_REF] Gidlöf-Gunnarsson | Railway noise annoyance and the importance of number of trains, ground vibration, and building situational factors[END_REF]).

In order to study the influence of noise and vibration levels on annoyance, it is necessary to get insights into the perceptual mechanisms at stake in such combined exposure situations. To that end, few laboratory experiments have been conducted under controlled conditions during the past decades. Moreover, these investigations led to contradictory results.

Two laboratory experiments were conducted by Howarth and Griffin ([7]) and Paulsen and Kastka ([8]). Both used a similar protocol in which combinations of railway noise and vibration were presented to participants (24 participants for Howarth and Griffin and 16 participants for Paulsen and Kastka) at different levels. For each combination, participants were asked to evaluate (1) partial annoyance due to noise heard in the presence of vibration, (2) partial annoyance due to vibration felt in the presence of noise and (3) total annoyance due to combined noise and vibration.

The conclusions of the two studies differ as to the influence of vibration level on noise annoyance. Howarth and Griffin reported that no significant effect of vibration level on noise annoyance was detected while Paulsen and Kastka showed that low noise levels (below 33.4 dB(A)) were more annoying in the presence of strong vibration. Reciprocally, the influence of noise level on vibration annoyance was reported in different ways. According to [START_REF] Howarth | Subjective response to combined noise and vibration: summation and interaction effects[END_REF], noise level tends to increase vibration annoyance when vibration level is high (synergistic effect) and to decrease it when vibration level is low (antagonistic effect). On the other hand, Paulsen and Kastka reported that low vibration levels (0.03 mm.s -1 and 0.05 mm.s -1 ) were evaluated more annoying when combined with the highest noise levels (45.4 dB(A) and 59.9 dB(A)).

Comparisons between results of the two studies are difficult because of the differences in the measurement units used to express noise levels (A-weigthed sound exposure level, SEL A for [START_REF] Howarth | Subjective response to combined noise and vibration: summation and interaction effects[END_REF] and A-weighted equivalent sound pressure level, L Aeq , [START_REF] Paulsen | Effects of combined noise and vibration on annoyance[END_REF]) and vibration levels (W b -weighted average rms acceleration, a rms , and unweighted average rms velocity, v rms , respectively). However, it seems that, for both noise and vibration, the levels used by Howarth and Griffin were higher than those experienced by participants in Paulsen and Kastka's study (see table A.1 in appendix):

• The lowest noise level in [START_REF] Howarth | Subjective response to combined noise and vibration: summation and interaction effects[END_REF] was 54dB(A), which corresponds to the second highest level in [START_REF] Paulsen | Effects of combined noise and vibration on annoyance[END_REF], taking into account the duration of the freight train passage (24s).

• The lowest vibration level in Paulsen and Kastka's study was "just perceptible" while the first vibration level in Howarth and Griffin's experiment (W b -weighted a rms = 0.02 m.s -2 ) was well above the perception threshold (unweighted a rms ≈ 0.015 m.s -2 ).

A final difference between the two studies is the source of the excitation (freight train in one case, tramway in the other one), which leads to signals with very different frequency contents.

Two initial hypotheses can therefore be put forward to explain the different results obtained by [START_REF] Howarth | Subjective response to combined noise and vibration: summation and interaction effects[END_REF] and [START_REF] Paulsen | Effects of combined noise and vibration on annoyance[END_REF]:

Hypothesis H 1 : The results depend on the ranges of the selected noise and vibration levels. Indeed, stimuli used in [START_REF] Howarth | Subjective response to combined noise and vibration: summation and interaction effects[END_REF] and [START_REF] Paulsen | Effects of combined noise and vibration on annoyance[END_REF] had very different level ranges.

Hypothesis H 2 : The different types of trains used as stimuli (freight train for [START_REF] Howarth | Subjective response to combined noise and vibration: summation and interaction effects[END_REF] and tramway for [START_REF] Paulsen | Effects of combined noise and vibration on annoyance[END_REF]) had an influence on the obtained results. In particular, the spectral content of the vibration signal associated with the freight train ranged between 30Hz and 45Hz while the spectral content of the vibration signal associated with the tramway was wider band (between 16Hz and 60Hz).

An experiment is proposed to test these two hypotheses. Two train recordings (a freight train and a passenger train) whose generated vibrations showed differences in spectral content were presented to a panel of participants. The noise and vibration associated with each passage were presented in combination, at 5 different noise levels and 5 different vibration levels (25 possible combinations for each type of train), so as to cover as much as possible the ranges of noise and vibration levels involved in the two previously mentioned studies (resp. [START_REF] Howarth | Subjective response to combined noise and vibration: summation and interaction effects[END_REF] and [START_REF] Paulsen | Effects of combined noise and vibration on annoyance[END_REF]). Responses of noise annoyance, vibration annoyance and total annoyance were obtained for each combination. Furthermore, the experimental data were also used to evaluate several existing models of total annoyance due to railway noise and vibration and to build a relationship of subjective equivalence between noise annoyance and vibration annoyance.

Method

Participants

Forty adults (23 males, 17 females; mean age = 33.3 years, standard deviation = 14.3 years) participated in the experiment. They were naive concerning the goal of the study and their hearing was evaluated before the experiment by means of an audiogram. All participant had normal hearing abilities. Finally, participants' written consent was required before the experiment began and compensation was paid at the end of the experiment.

Apparatus

Vibration was generated in the vertical direction by an electrodynamic shaker LDS-V650 (B&K, Naerum, Denmark, www.bksv.com). Noise was reproduced using two Tapco S5 speakers.

Participants sat on a rigid stool attached to the vibration test bench which consisted in a platform secured to the shaker by means of a clamping screw. A guardrail was present around the platform as a precautionary measure for participants to avoid any risk of falling. Participants were instructed not to lean against the guardrail and to keep their backs straight during the experiment. The speakers were placed so that they formed an equilateral triangle with the participant's head, once the participant sat on the stool. Each loudspeaker was 2.25m away from the participant's head. A touch screen was placed in front of the participant to display instructions.

The experiment was carried out in a semi-anechoic chamber. The background noise in the chamber did not exceed 30dB(A) and was mainly due to the cooling system of the vibration test bench power supply.

The frequency response of the vibration test bench was compensated by filtering the vibration signals before their reproduction.

Stimuli

The noise and vibration due to train passages were recorded simultaneously inside a house located near a railway track in Caluire-et-Cuire (France).

The equipment used for recording vibration signals was provided by Acouphen (Lyon, France, www.acouphen.fr). Measurements were made in the vertical direction using a Piezotronics 393B12 accelerometer (PCB Piezotronics, Depew, NY, www.pcb.com) valid over the frequency range of interest (i.e., between 1Hz and 80Hz for whole body vibration). The noise recordings were made according to the ORTF technique, using a pair of cardioid microphones spaced 17cm apart and oriented to form a 110°angle . This technique allows a stereophonic capture of the train passages to be used with a stereophonic sound reproduction, as it has been done previously in [START_REF] Maigrot | Two laboratory methods of assessing annoyance due to railway noise and vibration (L)[END_REF] and by other researchers for sound sequences with moving sound sources, considering its good representation and overall quality of reproduction ( [START_REF] Guastavino | Spatial audio quality evaluation: comparing transaural, ambisonics and stereo[END_REF]).

For the experiment presented in this paper, noise and vibration recordings from two train passages were used. Several modifications were applied to the acoustic and vibration signals in order to avoid any potential influence of parameters such as stimulus duration on the results. In order to test this hypothesis, two vibration signals were selected among 20 recorded passages. The two train passages for which frequency content differences were greatest were a freight train passage and a passenger train passage (see figure 2.1). This choice of stimuli was relevant due to the nature of the trains. Indeed, Sharp and his colleagues showed that there were significant differences between annoyances caused by vibration generated by freight trains and by passenger train ( [START_REF] Sharp | Exposure-response relationships for annoyance due to freight and passenger railway vibration exposure in residential environments[END_REF]). The authors explained this result by the differences in average duration between the two types of trains and also by the higher low frequency content in the case of freight trains.

Selection of stimuli

Duration of acoustic and vibration signals

Duration of vibration stimulus seems to influence vibration annoyance. Griffin and Whitham have shown that duration influences vibration annoyance due to sinusoidal vibration signals, up to a duration of 32s ([12]

). Recently, Woodcock and his colleagues developed a model of vibration annoyance based on railway vibration recordings, in which the duration of the vibration stimulus is considered as a variable ( [START_REF] Woodcock | A multidimensional evaluation of the perception and annoyance caused by railway induced groundborne vibration[END_REF]). Sharp and colleagues also used the duration of the vibration signal in a model of total annoyance due to railway noise and vibration ( [START_REF] Sharp | Considering the perception of combined railway noise and vibration as a multidimensional phenomenon[END_REF]).

In contrast, several studies have shown that annoyance due to various environmental noises was not influenced by duration (e. g. [START_REF] Morel | Physical and perceptual characterization of road traffic noises in urban areas for a better noise annoyance assessment[END_REF] for stimuli of short duration and [START_REF] Paulsen | On the influence of the stimulus duration on psychophysical judgment of environmental noises taken in the laboratory[END_REF] for stimuli up to 80s duration). Trollé and his colleagues also indicated that duration does not influence noise annoyance due to tramway recordings from 8s to 25.5s ( [START_REF] Trollé | Short-term annoyance due to tramway noise: Determination of an acoustical indicator of annoyance via multilevel regression analysis[END_REF]). Finally, Vallin et al. also found no correlation between noise annoyance responses and stimulus duration for train recordings from 6s up to 47s ( [START_REF] Vallin | Railway noise annoyance modeling: Accounting for noise sensitivity and different acoustical features[END_REF]).

To avoid any potential influence of duration of the combined noise and vibration stimuli on annoyance, the signals were normalized to a 10s duration. The signal shortening process was performed using the free software Audacity® by truncating portions of the signals. To ensure realism, rise and decay were not deleted and a final check by ear was performed after modification of the signals.

Amplitude fluctuations

Amplitude fluctuations can have an influence on annoyance, at a fixed equivalent level. Indeed, indices such as the maximum A-weighted sound pressure level (L Amax ) or the sound pressure level exceeded during x% of the time (L x ) may be correlated with noise annoyance (e. g. [START_REF] Kim | Noise-induced annoyance from transportation noise: Short-term responses to a single noise source in a laboratory[END_REF], [START_REF] Sharp | Considering the perception of combined railway noise and vibration as a multidimensional phenomenon[END_REF]). Similarly, the maximum vibration level has been used as an indicator in some studies (e. g. [START_REF] Morihara | An experimental study on combined effects of high-speed railway noise and vibrations on activity disturbances[END_REF]).

In this study, the indicators used to quantify the energy of noise and vibration signals are the A-weighted equivalent sound pressure level (L Aeq ) and the average rms vibratory acceleration level (L Veq ). The second step was therefore to limit the amplitude fluctuations in the acoustic and vibration signals so that their energy contents could be represented only by these indicators.

Two gain functions, G n (t) and G v (t), were applied to noise and vibration signals, respectively, in order to satisfy criteria related to noise and vibration level fluctuations over time. The criterion for vibration signals was that the median value of the short-term rms acceleration, L V eq,125ms , should fall within the interval 90dB ± 1.5dB. The criterion for noise signals was that the difference between the L 10 and L 50 indices should be inferior to the value of 2dB(A). This step was performed using Matlab®.

Selection of noise and vibration levels

The H 1 hypothesis was that the ranges of variation of noise and vibration levels has an influence on the results obtained in [START_REF] Howarth | Subjective response to combined noise and vibration: summation and interaction effects[END_REF] and [START_REF] Paulsen | Effects of combined noise and vibration on annoyance[END_REF].

To test this hypothesis, the noise and vibration stimuli were presented at 5 different levels:

• The A-weighted equivalent sound pressure levels, L Aeq , of noise stimuli N 1 , N 2 , N 3 , N 4 and N 5 were 42, 50, 58, 66 and 74dB(A).

• The unweighted vibration levels, As a result, 25 combinations N i V j of noise and vibration could be formed (i = 1 : 5, j = 1 : 5) for each of the two selected train passages.

L Veq , of vibration stimuli V 1 , V 2 , V 3 , V
The two lowest sound pressure levels of the Paulsen and Kastka study (32.5 and 33.4dB(A)) were not selected, as they would not have emerged sufficiently from the background noise emitted by the experimental set-up. The equivalent sound pressure level of 74dB(A) may correspond to that of a train passage inside a dwelling with open windows or outside (e. g. terrace, balcony).

The range of variation of vibration levels was selected so as to cover as much as possible the ranges of vibration levels tested by [START_REF] Howarth | Subjective response to combined noise and vibration: summation and interaction effects[END_REF] and [START_REF] Paulsen | Effects of combined noise and vibration on annoyance[END_REF].

Procedure

The participants' task was to evaluate, for different combinations of noise and vibration, partial noise annoyance, partial vibration annoyance and total annoyance (3 responses per combination). The experiment consisted of 3 sessions A, B and C, each containing:

• Session A: the 25 combinations N i V j formed from the noise and vibration signals corresponding to the freight train.

• Session B: the 25 combinations N i V j formed from the noise and vibration signals corresponding to the passenger train.

• Session C: the combinations N 3 V 3 and N 4 V 4 formed from the noise and vibration signals corresponding to the freight train and passenger train (4 combinations in total).

For each combination, participants where asked to provide their responses using three continuous annoyance scales ranging from 0 ("not annoying at all") to 10 ("extremely annoying"), displayed on the touch screen in front of them. This methodology was validated in a previous laboratory study (cf. [START_REF] Maigrot | Two laboratory methods of assessing annoyance due to railway noise and vibration (L)[END_REF]).

The participants first performed sessions A and B (random order). Within each session, the order of stimuli was randomized. A training test was performed at the beginning of each of the two sessions. Four combinations of freight (resp. passenger) train noise and vibration were presented to participants during session A (resp. session B): a strong combination (N 5 V 5 ), a weak combination (N 1 V 1 ) and two intermediate combinations (N 1 V 5 and N 5 V 1 ).

Session C was conducted following sessions A and B. The purpose of this session was to evaluate the repeatability of the annoyance responses provided during the first two sessions in order to be able to make comparisons, if necessary, of these.

Results

Hypothesis testing

First, repeated-measures analysis of variance (RM-ANOVAs, [START_REF] Howell | Statistical methods for psychology[END_REF]) were conducted on partial noise annoyance (A N ), partial vibration annoyance (A V ) and total annoyance (A T ).

Six 1-factor RM-ANOVAs were conducted on A N , A V and A T due to the combinations N 3 V 3 and N 4 V 4 for freight and passenger train passages collected during sessions A and C respectively and during sessions B and C (see figure 3.1). The factor considered was the factor session (2 levels). The 6 RM-ANOVAs indicate that the effect of the factor session was not significant. The partial annoyance responses as well as the total annoyance responses due to noise and vibration of the freight train and passenger train could therefore be compared during the following analyses. Three 3-factors RM-ANOVAs were then conducted to evaluate the influence of factors noise and vibration (5 levels per factor) as well as factor train (2 levels) on partial annoyance due to noise (A N ), partial annoyance due to vibration (A V ) and total annoyance (A T ).

Effect of noise and vibration levels on A N

The effect of the noise level on A N was significant [F (4, 156) = 484.636, p < 0.001]. The percentage of variance η 2 explained by the factor noise level was 66.1%, giving information about the great size of the effect. The effect of the vibration level on A N was not significant [F (4, 156) = 0.522, p > 0.71]. No significant effect of the interaction between factors was observed.

Effect of noise and vibration levels on A V

The effect of the noise level on A V was not significant [F (4, 156) = 0.791, p > 0.53]. The effect of the vibration level on A V was significant with a large effect [F (4, 156) = 455.249, p < 0.001, η 2 = 70.0%]. The effect of the interaction between factors noise and vibration on A V was significant, although the effect size was very small [F (16, 624) = 3.134, p < 0.001, η 2 = 0.36%]. No effect of the interaction between other factors was detected.

The mean noise annoyance responses (sessions A and B aggregated) as a function of vibration level, and mean vibration annoyance responses (sessions A and B aggregated) as a function of noise level, are presented in figure 3.2.

Effect of noise and vibration levels on A T

The effect of the noise level on A T was significant with a large effect [F (4, 156) = 297.128, p < 0.001, η 2 = 40.1%]. The effect of the vibration level on A T was significant with a smaller effect [F (4, 156) = 98.898, p < 0.001, η 2 = 11.1%]. The effect of the interaction between the factors noise and vibration on A T was significant [F (4, 156) = 22.339, p < 0.001, η 2 = 3.4%]. No effect of the interaction between other factors was detected.

Effect of the train type on annoyance

The effect of the factor train on A N , A V and A T was not significant: [F (1.39) = 3.913, p > 0.055], [F (1.39) = 1.011, p > 0.32] and [F (1.39) = 3.847, p > 0.056] respectively.

Predictive quality of total annoyance models

The literature provides several models of total annoyance due to railway noise and vibration that need to be evaluated in terms of predictive quality. These models are of two kinds: in psychophysical models the independent variables are the global noise and vibration levels whereas in perceptual models the variables are the partial annoyances due to noise and vibration.

Psychophysical models

The first model was proposed by Howarth and Griffin ( [START_REF] Howarth | The annoyance caused by simultaneous noise and vibration from railways[END_REF]) and was based on the use of Stevens' power law for both modalities:

ψ = 22.7 + 243 • φ 1.18 v + 0.265 • φ 0.036 s (1)
where the variable φ v corresponds to the W b -weighted vibration dose value (V DV b ) and where log 10 (φ s ) is assimilated to the A-weighted Sound Exposure Level or SEL A .

Later on, the same authors proposed a second model ( [START_REF] Howarth | Subjective response to combined noise and vibration: summation and interaction effects[END_REF]) in which coefficients were relatively close to the previous ones:

ψ = 15.9 + 260 • φ 1.04 v + 0.167 • φ 0.039 s (2)
In these two studies, it was specified that the addition of an interaction term φ nv v • φ ns s did not significantly improve the correlation coefficient.

Paulsen and Kastka ( [START_REF] Paulsen | Effects of combined noise and vibration on annoyance[END_REF]) proposed a third model, based on the mean rms vibration velocity, v rms , and on the equivalent sound pressure level, L Aeq , in which the total annoyance was calculated by a multiple linear regression, and is expressed:

y = -0.15 + 1.58 • log 10 (v rms ) + 0.11 • L Aeq (3)
Finally, Sharp ([23]) proposed a fourth model in which the independent variables were the W b -weighted V DV index and the L Aeq index. The model obtained by means of a multiple linear regression is as follows:

A T = -12.8 + 30.7

• V DV b + 0.19 • L Aeq (4)

Perceptual models

Lee and Griffin ( [START_REF] Lee | Combined effect of noise and vibration produced by high-speed trains on annoyance in buildings[END_REF]) established two perceptual models, based on the perceptual models from the literature dealing with total annoyance due to combined noise sources. In the first model, called the independent effects model, the contributions of partial noise annoyance (A N ) and partial vibration annoyance (A V ) are summed:

A T = 2.742 + 0.25 • A V + 0.54 • A N (5)
In the second model, called the dominance model or strongest component model, only the most important partial annoyance is considered as the independent variable:

A T = 2.179 + 0.78 • A D ( 6
)
where

A D = max(A N , A V ).
The predictive quality of the above-mentioned models was evaluated using the data of the current study. Total annoyance, A T , was predicted using each model and the correlation coefficients between this predicted annoyance and the measured one are presented in table 3.1. Table 3.1: Values of correlation coefficient r P earson corresponding to the linear regressions between the values of A T predicted by the models from the literature and the values of A T measured during the experiment. * : p < 0.001.

Model

r P earson Howarth and Griffin [START_REF] Howarth | The annoyance caused by simultaneous noise and vibration from railways[END_REF] 0.76 * Psychophysical Howarth and Griffin [START_REF] Howarth | Subjective response to combined noise and vibration: summation and interaction effects[END_REF] 0.80 * models Paulsen and Kastka [START_REF] Paulsen | Effects of combined noise and vibration on annoyance[END_REF] 0.91 * Sharp [START_REF] Sharp | Human response to environmental noise and vibration from freight and passenger railway traffic[END_REF] 0.82 * Lee and Griffin [START_REF] Lee | Combined effect of noise and vibration produced by high-speed trains on annoyance in buildings[END_REF] 0.96 * Perceptual (independent effects) models Lee and Griffin [START_REF] Lee | Combined effect of noise and vibration produced by high-speed trains on annoyance in buildings[END_REF] 0.98 * (dominance model)

Subjective equivalence relationship determination

Based on the partial noise and vibration annoyance responses collected during the experiment, one can establish a subjective equivalence relationship between noise levels and vibration levels resulting in equivalent annoyance.

For stimuli of various kinds, Stevens' law links the perceived intensity of a stimulus, ψ, to its physical intensity, φ, by the following relationship:

ψ = k • φ n (7)
where k and n are constants ( [START_REF] Stevens | On the psychophysical law[END_REF]).

For noise and vibration stimuli, one can then write

ψ s = k s • φ ns s and ψ v = k v • φ nv v .
If one assumes that the annoyance due to noise (resp. vibration) is directly related to the perceived intensity of the noise (resp. vibration) stimulus, the two following equations can be obtained:

log 10 (A N ) = a s + b s • L Aeq (8) log 10 (A V ) = a v + b v • L Veq (9)
where a s = log 10 (k s ), Assuming that the perceived intensity of the noise and vibration stimuli is equal, a relationship between noise and vibration levels is given by:

a v = log 10 (k v ), b s = ns
L Aeq = a + n v n s • L Veq ( 10
)
where a is a constant.

To experimentally determine the subjective equivalence relationship corresponding to the data collected during the experiment, linear regressions were performed between the independent variable L Veq and the mean values of the dependent variable log 10 (A V ), obtained from the vibration annoyance responses given by participants exposed to each of the 5 noise levels. Table 3.2 presents the mean A V responses obtained for each combination of noise and vibration levels. The results of the linear regressions are presented in Table 3.3. For each of the 5 noise levels, the vibration level giving rise to a vibration annoyance equivalent to the specific noise annoyance due to the noise level alone was calculated. From equation ( 9), it was obtained as:

Table 3.2: Mean vibration annoyance responses

A V collected for each combination N i V j . A V V 1 = 72 V 2 = 92 V 3 = 100 V 4 = 108 V 5 = 116dB N 1 = 42 0.
L V eq,estim = log 10 (A N N i V 1 ) -a v b v ( 11
)
where A N N i V 1 represents the specific noise annoyance due to the noise level N i without the presence of vibration (vibration level V 1 ).

Table 3.3 shows the equivalent vibration levels calculated from the measured data.

According to the equation [START_REF] Guastavino | Spatial audio quality evaluation: comparing transaural, ambisonics and stereo[END_REF], a linear regression between the independent variable L V eq,estim and the dependent variable L Aeq leads to the following subjective equivalence relationship (r = 0.99, p = 0.001):

L Aeq = -134.5 + 1.7 • L V eq,estim (12)
Table 3.3: Coefficients a v and b v of the linear regressions between log 10 (A V ) and L Veq yielding the vibration level L V eq,estim equivalent in terms of annoyance to each noise level L Aeq . * : p < 0.001.

A V L Aeq A N N i V 1 Intercept Slope r P earson L V eq,estim = log 10 (A N N i V 1 )-av bv (dB) (dB(A)) (a v ) (b v ) 42 2.

Discussion

Verification of H 1 hypothesis

The studies conducted by Howarth and Griffin ([7]) and by Paulsen and Kastka ( [START_REF] Paulsen | Effects of combined noise and vibration on annoyance[END_REF]) both examined the influence of the global level on railway noise and vibration annoyances. But noise and vibration levels used in these two studies were significantly different, with the levels involved in Paulsen and Kastka's experiment being lower than those involved in Howarth and Griffin's study.

The H 1 hypothesis was that these experimental choices explained the different results between the two studies.

During the experiment presented in this paper, the ranges of noise and vibration levels approximated the ranges covered by the two studies. If the H 1 hypothesis was verified, then the results of Howarth and Griffin and those of Paulsen and Kastka should have been found, at high levels for the first study and at low and moderate levels for the second one.

The results of the 3-factor RM-ANOVA conducted on noise annoyance responses did not report any effect of the vibration level on noise annoyance. These results are consistent with those obtained by Howarth and Griffin ([7]). Similar results were also observed in a previous investigation where the tested noise levels ranged from 44 to 62 dB(A) and the tested vibration levels from 90 to 100 dB (ref. 10 -6 m.s -2 [START_REF] Maigrot | Two laboratory methods of assessing annoyance due to railway noise and vibration (L)[END_REF]). Yet, several studies have reported an effect of vibration level on railway noise annoyance. In laboratory, Morihara and Matsumoto ([20]) also found that vibration level influences noise annoyance felt during a thinking or a reading activity for maximum noise levels, L Amax , ranging from 50 to 70 dB(A) and for vibration levels ranging from 65 to 75 dB (ref. 10 -5 m.s -2 ).

However, it seems that this effect only occurs when the noise level is low. In particular, Paulsen and Kastka reported that vibration level influenced noise annoyance for noise levels less than or equal to 33.4 dB(A). As the background noise level during their experiment was close to this value (L Aeq = 32.5 dB(A)), a question may arise whether this equipment noise level may affect annoyance responses due to low levels of railway noise. In the current study, choice was made to test higher levels of railway noise in order to mask the noise from the cooling system due to the vibration test bench power supply.

The results of the 3-factor RM-ANOVA conducted on vibration annoyance responses did not report any effect of the noise level on A V . On the other hand, a significant effect of the interaction between noise and vibration levels was detected.

A t-test conducted between A V due to the combination N 1 V 5 and A V due to the combination N 5 V 5 yields a significant difference (p < 0.01). At high vibration level (L Veq = 116dB), the average response of A V goes from 7.1 when the noise level is low (L Aeq = 42dB(A)) to 7.9 when the noise level is high (L Aeq = 74dB(A) (see figure 3.2)).

Cohen's d is an estimate of the effect size shown by a t-test. According to this estimation, the effect of the noise level on annoyance due to the fifth vibration level V 5 is relatively small: d = 0.42. Indeed, Cohen specifies that an effect is considered weak when d = 0.2 and that it can be considered as average from d = 0.5 ([26]).

The result of the t-test is consistent with results presented in [START_REF] Howarth | Subjective response to combined noise and vibration: summation and interaction effects[END_REF]. This study showed that a synergistic effect of noise level on annoyance due to railway vibration may occur when the vibration level is high. This result is supported by the significant effect of the interaction of noise and vibration levels on A V , which could be related to the occurrence of a noise level effect above a certain vibration level.

There is a lack of consensus in the literature regarding the effect of vibration level on noise perception (and in particular on noise annoyance). On the other hand, the effect of noise level on vibration perception is more widely accepted (e. g. [START_REF] Gidlöf-Gunnarsson | Railway noise annoyance and the importance of number of trains, ground vibration, and building situational factors[END_REF] and [START_REF] Waddington | Human response to vibration in residential environments[END_REF], in situ). In the laboratory, Parizet and Marpe ( [START_REF] Parizet | Loudness estimation in the presence of vertical vibrations[END_REF]) showed that the perceived intensity of a sinusoidal vibration signal (28Hz) was significantly influenced by the presence of a tonal sound signal (28Hz).

Verification of H 2 hypothesis

Howarth and Griffin ( [START_REF] Howarth | Subjective response to combined noise and vibration: summation and interaction effects[END_REF]) and Paulsen and Kastka ( [START_REF] Paulsen | Effects of combined noise and vibration on annoyance[END_REF]) studied the influence of the global level on A V , A N and A T due to train passage recordings. The stimuli involved in these two studies were very different in nature: a freight train passage was presented to participants in the first case, and a tramway passage in the second one. In addition, the vibration associated with the two cases had very different frequency contents. The energy for the freight train vibration was mainly contained in the range [30Hz : 40Hz]. In the case of the tramway, the vibration spectrum was wider band ([16Hz : 60Hz]) with several energy peaks at 16Hz, 32Hz and 50Hz. The H 2 hypothesis was that these differences in frequency content influenced the results, explaining the differences between the two studies.

During the experiment presented in this paper, two passages of different natures and frequency contents were presented to the participants. Both stimuli had a wide band vibration spectrum (between 10Hz and 120Hz), but in the case of the freight train, the energy contained in the low frequencies (between 16Hz and 30Hz) was higher than in the case of the passenger train (about 10dB difference, see figure 2.1). If the H 2 hypothesis was verified, then the participants' responses should have been affected by the stimulus presented to them.

The results obtained in the case of the freight train and the passenger train are similar. The H 2 hypothesis is therefore not verified.

One explanation may be that the vibration spectra did not show enough differences, compared to those found between the vibration stimuli used by [START_REF] Howarth | Subjective response to combined noise and vibration: summation and interaction effects[END_REF] and [START_REF] Paulsen | Effects of combined noise and vibration on annoyance[END_REF], to generate a difference in the results. Indeed, the stimuli used in this study were both extracted from recordings carried out inside the same dwelling. Although differences exist between the spectral contents of the freight train and passenger train vibration, both signals contained energy over a common range [16Hz : 120Hz].

Using measurements carried out at several sites, Sharp and his colleagues have shown that vibration emitted by a freight train are generally perceived as more annoying than those emitted by a passenger train, at equivalent average rms acceleration ( [START_REF] Sharp | Exposure-response relationships for annoyance due to freight and passenger railway vibration exposure in residential environments[END_REF]). This result was explained by differences in average duration (freight trains being generally longer) but also in frequency content (freight trains being generally heavier and therefore showing more energy at lower frequencies according to the authors).

Total annoyance models

Four psychophysical models and two perceptual models from the literature were evaluated in terms of predictive quality, using annoyance responses from the experiment.

For psychophysical models, the model providing the best predictive quality was the one established by Paulsen and Kastka ([8]) based on the average rms vibration velocity index.

Both perceptual models proved to be equally accurate. Other studies on noise annoyance due to combined noise sources have reported highest quality of perceptual models compared to psychophysical models, in terms of model fit with in situ data (e. g. [START_REF] Pierrette | Noise annoyance from industrial and road traffic combined noises: A survey and a total annoyance model comparison[END_REF], [START_REF] Pierrette | Corrigendum to "noise annoyance from industrial and road traffic combined noises: A survey and a total annoyance model comparison[END_REF]) and in terms of predictive quality for models tested using in situ data (e. g. [START_REF] Marquis-Favre | A simulated environment experiment on annoyance due to combined road traffic and industrial noises[END_REF]).

Subjective equivalence relationship

A relationship of subjective equivalence between noise annoyance and vibration annoyance was built in order to compare our results to those of other similar experiments.

The coefficient 1.7 obtained in equation ( 12) is quite close to what could be expected from existing data. Indeed, the exponent of Stevens' power law for loudness is known to be close to 0.6 (when physical intensity is expressed in Pascal, [START_REF] Stevens | The measurement of loudness[END_REF]).

In the meantime, the exponent for subjective intensity of whole-body vertical vibration is often reported as close to 1 (e. g. [START_REF] Shoenberger | Psychophysical assessment of whole-body vibration[END_REF], [START_REF] Jones | A scale of human reaction to whole body, vertical, sinusoidal vibration[END_REF]).

Therefore the ratio nv ns is equal to 1 0.6 ≈ 1.67 which is very close to the value appearing in equation [START_REF] Griffin | Discomfort produced by impulsive whole-body vibration[END_REF].

In order to compare the constructed subjective equivalence relationship with those obtained in the literature, it was necessary to establish a linear regression between the variable L Aeq and the estimated equivalent vibration levels expressed in terms of W b -weighted vibration dose value (V DV b ) (see table A.2 in appendix). This regression (r = 0.99, p = 0.001) yielded the following subjective equivalence relationship:

L Aeq = 89.7 + 40.4 • log 10 (V DV b,estim ) (13)
Huang and Griffin ( [START_REF] Huang | The effects of sound level and vibration magnitude on the relative discomfort of noise and vibration[END_REF]) conducted a study to determine the effects of noise and vibration levels on noise and vibration annoyances, resulting in the following subjective equivalence relationship (r = 0.99, p < 0.001):

L Aeq = 84.4 + 32.6 • log 10 (V DV b ) (14)
The authors also presented the relationships obtained by different studies which used various acoustic and vibration signals (not only railway traffic recordings):

• The values of the intercept range from 51.9 ([8]) to 93. 6 ([36]).

• The values of the slope vary between 14.4 ( [START_REF] Paulsen | Effects of combined noise and vibration on annoyance[END_REF]) and 40.0 ( [START_REF] Kjellberg | Whole-body vibration: exposure time and acute effects-experimental assessment of discomfort[END_REF]).

The coefficients of the relationship ( 13) are therefore consistent with those from the literature.

Conclusion

The objective of this work was first of all to study the influence of the global level (expressed by L Aeq for noise and L Veq for vibration) on partial noise annoyance (A N ), partial vibration annoyance (A V ) and total annoyance (A T ). The purpose of the experiment was also to get clues about the origins of the differences between the findings of two studies from the literature that previously addressed the same topic.

Two different train passages (1 freight train and 1 passenger train) were presented to participants in the form of combinations of noise and vibration at different levels. These passages have been selected from a set of recordings in order to maximize the differences in vibration frequency content. A similar modulation frequency for the two vibration signals was also a selection criterion.

Regardless of the train passage considered, it seems that participants assessed the annoyance due to the noise without taking care of the level of vibration. Partial vibration annoyance responses were slightly influenced by noise level, only when the vibration level was at least equal to 116dB. These results were also found by Howarth and Griffin ([7]) but not by Paulsen and Kastka ([8]).

From the current study, it seems that the different ranges of noise and vibration levels used by Howarth and Griffin and by Paulsen and Kastka can explain the differences observed between their results. The use of different trains and in particular the differences of vibration frequency content associated with the train passages, does not seem to have been the cause of the different results in their studies. Nevertheless, further laboratory experiments should be carried out to test the influence of vibration frequency on annoyance, using vibration recordings with more variability.

In the context of the signals used in the current work, noise was generally the most annoying component. Indeed, the variance of the total annoyance responses explained by noise was 40.1% compared to only 11.1% explained by vibration. The strongest component model (or dominance model) proposed in the literature allowed a good prediction of total annoyance due to combined railway noise and vibration.

A Appendix

Figure 2 . 1 :

 21 Figure 2.1: Frequency spectra of the selected vibration signals (sampling frequency 512Hz, 512 points Hanning window, overlap 50%).

  [START_REF] Lercher | Combined noise exposure at home[END_REF] and V 5 were 72 (no vibration), 92, 100, 108 and 116dB. They respectively corresponded to the W b -weighted vibration dose values, V DV b , 0.004, 0.022, 0.046, 0.127 and 0.316 m.s -1.75 .

Figure 3 . 1 :

 31 Figure 3.1: Mean annoyance responses and associated standard errors due to combinations N 3 V 3 and N 4 V 4 , collected: (a) during sessions A and C (freight) and (b) during sessions B and C (passenger train).

Figure 3 . 2 :

 32 Figure 3.2: Mean partial annoyance responses and associated standard errors due to (a) noise as a function of vibration level, (b) vibration as a function of noise level.

20 and b v = nv 20 ,

 20 and where L Aeq = 20 • log 10 (φ s ) and L Veq = 20 • log 10 (φ v ).

Table A .

 A 1: Noise and vibration levels tested byHowarth and Griffin ([7]) and byPaulsen and Kastka ([8]), background noise levels and stimulus duration for both studies. Table A.2: Coefficients a v and b v of the linear regressions between log 10 (A V ) and log 10 (V DV b ) yielding the vibration level log 10 (V DV b,estim ) equivalent in terms of annoyance to each noise level L Aeq . * : p < 0.001. Aeq A N N i V 1 Intercept Slope r P earson log 10 (V DV b,estim ) =

			Index	Howarth and Griffin	Index	Paulsen and Kastka
	Stimulus duration				24 seconds		16 seconds
	Tested noise levels		SEL A	54, 59, 64, 69, 74 and 79 dB(A)	L Aeq	32.5, 33.4, 45.4 and 59.9 dB(A)
	Tested vibration levels	a rms	0.02, 0.03, 0.04, 0.06 and 0.09 m.s -2	v rms	0.03, 0.05, 0.12 and 0.31 mm.s -1
		(W b weighting)			(no weighting)
	Background noise level	SEL A		42 dB(A)	L Aeq	32.5 dB(A)
					A V
	L log 10 (A N N i V 1 bv	)-av	(dB)
	(dB(A))		(a v )	(b v )
	42	2.7	1.31 *	0.72 *	0.99 *		-1.22
	50	4	1.31 *	0.73 *	0.99 *		-0.96
	58	5.7	1.24 *	0.67 *	0.99 *		-0.73
	66	7.3	1.22 *	0.63 *	0.99 *		-0.56
	74	9.2	1.29 *	0.72 *	0.99

* -0.45

Acknowledgments

The vibration measurements on site were made possible by Acouphen society (www.acouphen.fr). This work was supported by the LABEX CeLyA (ANR-10-LABX-0060) of Université de Lyon, within the program "Investissements d'Avenir" (ANR-16-IDEX-0005) operated by the French National Research Agency (ANR).


B Pichené

M Kabuth

F Braun

Ligier

Caroline Pham-Dinh

Vincent Laprevote

Raymund Schwan

Catherine Pichené

Bernard Kabuth

Marc Braun

Fabienne Ligier
email: fabienne.ligier@cpn-laxou.com

Quantifying efficacy of investigation during a simulated psychiatric interview

Keywords: simulation, psychiatry, suicide, standardized patient, psychiatry residents étudiant en psychiatrie, patient standardisé, psychiatrie, simulation, suicide

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

Résumé

Introduction : La simulation est un outil pédagogique très intéressant car il permet d'offrir une expérience clinique à l'étudiant en médecine, sans mise en jeu de la santé du patient. Cet outil peut être utilisé dans le champ de la psychiatrie et permettre l'acquisition de compétences d'entretien et d'évaluation spécifiques. C'est pourquoi nous nous appuyons de plus en plus sur la simulation dans notre Université dans l'enseignement destiné aux internes de psychiatrie. Cependant, il existe peu d'indicateurs objectifs permettant d'évaluer l'apprenant. Cette étude a pour objectif d'évaluer la pertinence d'une mesure quantitative de

Introduction

The practice of psychiatry is largely based on interhuman relations in both diagnosis and therapeutics. Hence psychiatric education cannot be based exclusively on theoretical lectures but has to involve clinical experience. Simulation offers the advantage of providing such experience without jeopardizing patients' health (for a review, see Brenner 2009 (1)). Possible uses of simulation in a psychiatry curriculum include semiology (2), use of standardized evaluations [START_REF] Birndorf | Teaching the mental status examination to medical students by using a standardized patient in a large group setting[END_REF], enhancement of focused interpersonal skills (4), and psychotherapeutic learning [START_REF] Coyle | Using standardized patients to teach and learn psychotherapy[END_REF]. Brenner [START_REF] Brenner | Uses and limitations of simulated patients in psychiatric education[END_REF] pointed out that simulation fits particularly well with the acquisition of focalized technical skills while it has several limits concerning the complex interhuman abilities that are mobilized in psychotherapeutics. The fact is that a psychiatric interview remains a technical action involving specific skills such as wording of the questions, paraverbal communication or time management, which can be enhanced using simulation [START_REF] Brenner | Uses and limitations of simulated patients in psychiatric education[END_REF].

Moreover, French students have insufficient "know-how" [START_REF] Steichen | Evaluation du savoir-faire en sémiologie clinique des étudiants en 2ème cycle des études médicales[END_REF].

In order to learn about students' potential to progress on technical skills, several types of evaluation have been tested in the literature. In numerous publications, students' performance is rated by external observers. These evaluations may focus on simple clinical skills such as accuracy of diagnosis (2), or on more complex interpersonal skills [START_REF] Hodges | Validation of an objective structured clinical examination in psychiatry[END_REF], and may rely on specific scales [START_REF] Mcniel | An approach to evaluating competence in assessing and managing violence risk[END_REF]. Some publications prioritize self-evaluation by the student [START_REF] Fallucco | Teaching paediatric residents to assess adolescent suicide risk with a standardized patient module[END_REF]. By contrast, the patient may directly rate specific skills such as empathy [START_REF] Colliver | Assessment of Empathy in a Standardized-Patient Examination[END_REF]. However, Mc Lay et al. [START_REF] Mclay | Simulating a fulllength psychiatric interview with a complex patient: an OSCE for medical students[END_REF] and Brenner [START_REF] Brenner | Uses and limitations of simulated patients in psychiatric education[END_REF] pointed out marked differences between rating by an actor and by external observers. Providing objective and relevant measures on interpersonal skills may therefore improve students' capacity to evaluate their performance and their potential to progress.

A psychiatric interview in the emergency room is a common situation where taking the best decision at the best moment is crucial for the safety of the patient. Indeed, a clinician who precipitates the evaluation may miss decisive aspects which would generate an irrelevant decision. Conversely, an excessively long evaluation may imperil the quality of the therapeutic alliance or thwart the therapeutic process. In brief, such situations call on a specific skill: the capacity to identify a maximum amount of relevant information in a given short time. Young psychiatrists may encounter such emergency situations right from the beginning of their activity, and they are interested in this specific training. In this context, it seems useful to assess their capacity in investigating suicide risk and the evolution of this capacity through years. To avoid halo effect (12), we created an objective evaluation tool that we evaluated through simulation with an actor as patient, in order to have a reproducible situation.

This pilot study aims to evaluate the relevance of a quantified measure of the efficacy of investigation of suicide risk by psychiatry residents during a simulated psychiatric interview.

Our main hypothesis assumed that the efficacy of investigation may increase with trainees' professional experience.

Methods

Participants

Twenty psychiatric trainees were recruited at the Université de Lorraine between January 2012 and June 2014. The study was proposed during different psychiatry courses. Inclusion criteria were: a valid enrolment for the degree in psychiatry at the Université de Lorraine and at least six months of clinical work.

Written consent was obtained from all participants after being informed. No participant was paid for taking part in the study. No specific authorization was required for this kind of study.

There was no potential harm to participants. Anonymity of participants was guaranteed.

Procedure

The simulations took place in the Simulation Centre of the College of Medicine of the Université de Lorraine. Students were evaluated during four different sessions with five students per session (see Figure 1). They were first briefed about the objectives of the study and the method of simulation. We then provided standardized short information about the context of the clinical situation. The order in which students performed was randomized.

While waiting for the simulated interview, students could practice cardio pulmonary resuscitation with two experienced instructors. After the simulated interview, students had an immediate personal debriefing of the situation in order to take the emotional impact of the exercise into account. The students were then asked to answer different questionnaires about the simulation and to write a medical observation about the patient. At the end of the session all students met again with both experimenters (VL & FL) and the standardized patient for a general debriefing.

[Insert Figure 1 here] The scenario simulated the intervention of a psychiatric trainee in an emergency room. The situation involved two different actors who did not know each other: an emergency physician, played by an experienced psychiatrist, and the patient, played by an experienced psychiatric male nurse. The students were asked to evaluate the suicidal risk of a patient being offered medical care in an emergency room after deliberately causing a car crash. Trainees were asked to collect as much information as needed to be able to take a clinical decision. However, trainees were not required to formulate the precise decision, especially not during the consultation. This instruction was given in order to fit with the pedagogic objective of the simulation which was to evaluate the efficacy of investigation rather than negotiate therapeutic issues. The actor had memorized a complete description of the patient's biography and his medical and psychiatric history. He was asked to be uncooperative and to have as his sole objective to return home as soon as possible. The standardized time of simulation was obtained after ten minutes when the emergency physician entered the room requiring the psychiatric trainee to leave the room.

The simulation was video-and audio-transmitted into an adjacent room where two investigators and a technician were present. The experimenters could intervene immediately in the event of a major difficulty but which was not required at any time during the study.

The experimenters were teachers and not external ones who could be confronted with reallike evaluation situations.

Main measure: I²/Q ratio

During each consultation the investigators (VL and FL) noted the number of relevant items (I) in a list of 11 items relevant for a clinical decision which had been previously established based on the script by a panel of four different psychiatrists (BK, JPK, CP, and RS). These items were: social and familial support/financial situation/psychiatric care (history or actual)/actual mood/addiction/impulsivity/suicide attempt history/ dangerousness of disposable lethal means/suicidal intent/premeditation/criticism on suicidal gesture.

The video recordings of all the consultations were then re-examined by the same two investigators in order to calculate the total number of questions asked by the student during the consultation (Q) and to verify the number of relevant items (I).

The performance of each student was finally evaluated by the I²/Q ratio. The number of relevant information items was squared in order to standardize the range of both variables. Also, we assumed that this indicator remained relevant considering that the probability of obtaining relevant information in response to a question is maximal at the beginning of the consultation but decreases strongly during the time of consultation (Figure 2).

[Insert Figure 2 here]

Other measures

At the end of each consultation the patient was asked to score a visual analogue empathy scale graduated from 0 to 10, with 0 as minimal empathy and 10 as maximal empathy. He then noted his readiness to follow a therapeutic proposal from the psychiatrist he had just met and the appeasement of internal tension on a visual analogue scale.

At the end of their consultation, the students scored the appeasement of the patient's internal tension on a visual analogue scale ranging from a minimum of 0 to a maximum of 10. They filled in a questionnaire about their perception of the simulation and prepared a brief clinical summary, as generally required in French emergency rooms.

The investigators also scored a visual analogue empathy scale at the end of the consultation.

Statistical analysis

Statistical analyses were conducted with STATISTICA® 6.1 software (StatSoft Inc.). All the quantitative variables were described by their mean and standard error of the mean. The main variable was the I²/Q ratio, and a Pearson correlation analysis was conducted between I²/Q ratio and the clinical experience of the students to verify the main hypothesis. In order to explore the reproducibility of the I²/Q ratio, the quotation of I²/Q ratio was compared between the experimenters by the intraclass correlation coefficient. The other variables were analysed with Pearson correlations or Mann & Whitney tests when deemed appropriate.

Results

Students' experience ranged between 3 and 8 semesters (see Figure 3): 14 (70%) were women, 6 (30%) were men. Their mean experience was 5.3 semesters (SEM ± 0.37).

[Insert Figure 3 here] Main measure: I²/Q ratio The mean I²/Q ratio was 1.13 (SEM ± 0.2). The ratio ranged between 0.25 and 2.86. The mean value of I was 6.25. The mean value of Q was 39.45.

The statistical analysis found a positive correlation between I²/Q ratio and the clinical experience of the students with r = 0.46 and p = 0.04. As seen in Figure 4, the more experienced the students the higher the I²/Q ratio.

In order to evaluate the consistency of the ratio between the investigators, we calculated the interclass correlation coefficient (ICC) of the I²/Q ratio. In our study, the ICC was 0.94 across both investigators. Classically, the ICC ranges between 0 and 1, and a value greater than 0.6 is interpreted as good reproducibility of the indicator.

[Insert figure 4 here]

Other measures

The mean empathy score given by the standardized patient was 6.95 (SEM ± 0.32), ranging from 4 to 9. Interestingly, we found a trend towards a positive correlation between this score and the I²/Q ratio (r = 0.43, p = 0.06).

The mean empathy score given by the experimenters was 6.76 (SEM ± 0.32), ranging from 4.5 to 10. We found a significant positive correlation between this score and the empathy scored by the patient (r = 0.5, p < 0.05). However, this effect was mainly explained by the score of one investigator, as a separate analysis showed a strong inconsistency between the observers with a significant correlation for investigator FL (r = 0.64, p < 0.005), whereas there was no significant correlation for investigator VL (r = 0.13, p = 0.60).

The mean appeasement of the patient's internal tension evaluated by the students was 4.9 (SEM ± 0.56), ranging from 0 to 10. This score was positively correlated with the empathy score for the patient (r = 0.5, p < 0.05).

Discussion

This pilot study aimed to evaluate the relevance of the I²/Q ratio, a quantitative measure for objectivising the investigation efficiency of a suicidal risk in an emergency room. We showed that I²/Q ratio had an excellent inter-investigator reliability and was correlated with the student's clinical experience. In other words, the more experienced the student the more efficient was his investigation as measured by the I²/Q ratio.

Increasing the efficiency of the investigation is crucial in emergency psychiatry to support the medical reasoning (14). We chose here to evaluate the investigation by a ratio depicting the capacity of the clinician to bring out the relevant information from the "noise" contained in a clinical interview. The objectivity of the I²/Q ratio relies on the fact that both components are simply counted during the consultation or the video screening.

Comparison between empathy scored by experimenters and by the standardized patient is interesting. Despite a close correlation between the mean empathy score of both experimenters and the empathy scored by the patient, a separate analysis of the empathy scores of each experimenter revealed that these scores had poor reproducibility. Indeed, empathy scored by one of the experimenters showed no correlation with empathy scored by the standardized patient. This result underlies the utility of highly reproducible and objective scores such as I²/Q ratio. We assume that using I²/Q ratio fits particularly well with clinical situations such as emergency situations because they require being both rapid and efficient while keeping good quality of the relationship. Using this indicator may help a student evaluate his own progression potential, especially if simulations using this indicator are repeated during the curriculum. However, we also identify some restrictions in its use. Since this ratio mainly evaluates the efficiency of investigation, we consider that it is not relevant enough to evaluate other relational skills of a psychiatrist such as empathy or psychotherapeutic capacities. Also, although this ratio constitutes an interesting and quasi-automatic evaluation, an experimented human follow-up remains irreplaceable.

This study has several limits. The evaluation of our indicator is not based on a comparison of means but on a correlation analysis which could be constructed as an indirect method of measure. We made this choice because there is to our knowledge no similar indicator that could have been used as a comparator. Moreover, the I²/Q ratio was tested with only one clinical situation in this study. Further studies are thus now needed to evaluate its reliability in different clinical environments.

Conclusions

Simulation with standardized patients is a consistent tool that offers vivid experience to psychiatry students without directly exposing a patient. Evaluation through simulation is very interesting because simulation assesses the "show how" (13). In order to progress students also need to evaluate their own performance. Here we provide a consistent, reproducible tool to evaluate efficiency of investigation. Development of other similar tools is now needed to provide students with a multi-criteria evaluation of their performance.

12. Thorndike EL. A constant error on psychological ratings. Journal of Applied Psychology. 1920; 4: 25-29. number of questions asked by the student during the consultation (Q)

  13. Sadolvelli GL, Naik VN, Joo HS, Houston PL, Graham M, Yee B, et al. Evaluation of patient simulator performance as an adjunct to the oral examination for senior anesthesia residents. Anesthesiology. 2006;104:475-81. 14. Micoulaud-Franchi JA, Geoffroy PA, Amad A, Quiles C. [The gardener and the botanist. Proposition of a minimal organisation of psychiatric semiology for medical students]. Annales Médico-psychologiques, revue psychiatrique. 2015; 173 (5): 460-469.

Figure 1 :

 1 Figure 1: Study design

Figure 2 :

 2 Figure 2: Mathematical function of I²/Q ratio. The rapid progression of I²/Q at the first questions reflects the higher probability of obtaining important information during the first questions in an intervention.

Figure 3 :Figure 4 :

 34 Figure 3: Trainees semesters distribution (N=20) Figure 4: Scatter plot of I²/Q ratio (vertical axis) and the clinical experience of the students (in semesters, horizontal axis).A positive correlation was found, indicating that the more experienced the students were, the higher the I²/Q ratio.

Acknowledgements 10

The authors are particularly grateful to Mr Olivier Beaudoin, who played the role of the standardized patient with a constant talent. We also thank the CUESim team and especially H.

Hani, Dr C. Varoqui and J.-M. Kleffer for their commitment.

Declaration/conflict of interest

All authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as potential conflicts of interest.


-F Benkhoris

K Ghedamsi

S Bella
email: saad.bella@univ-msila.dz&saad.bella@univ-nantes.fr

A Houari

A Djerioui

A Chouder

M Machmoum

M-F Benkhoris

Robust Model Predictive Control (MPC) for Large-Scale PV Plant Based on Paralleled Three-Phase Inverters

Keywords: Grid-connected inverter, parallel operation, circulating current, PV power plant, model predictive control, Hardware-In-the-Loop

est destinée au dépôt

Introduction

Large-scale photovoltaic plants (LSPPs) are being a viable solution to handle the growth of green energy sources integration as they provide an interesting mid-term return of investment (" IEA PVPS report, 2018";[START_REF] Tang | Large-scale photovoltaic system on green ship and its MPPT controlling[END_REF][START_REF] Tobar | Large scale photovoltaic power plants: configuration, integration and control[END_REF]. This is essentially due to the decrease of the manufacturing cost of PV modules as reported by the International Energy Agency (IEA).

Actually, PV modules prices have fallen by nearly 70% and are expected to continue to decline for future large-scale PV systems (" IEA report," 2018.). LSPPs are capable to generate power in range of megawatts such that installed in Australia in 2018 which is the largest one in the country with the capacity of 220 MW (" M. [START_REF] Maisch | Bungala Solar Farm goes fully online as Australia's biggest solar project to date[END_REF]. As the produced energy by these PV plants is intended to be injected in the main grid, some challenges will arise due to the necessity of feeding it in a smooth and efficient way. Besides, due to the power rating limitations of the existing power inverters and economic issues, it is difficult to deliver this power to the main grid with a single central inverter. For such systems, in which efficiency and power quality should comply with international standards [START_REF] Ouai | Control and energy management of a large scale gridconnected PV system for power quality improvement[END_REF][START_REF] Wu | Standards and Guidelines for Grid-Connected Photovoltaic Generation Systems: A Review and Comparison[END_REF][START_REF] Xu | A novel adaptive command-filtered backstepping sliding mode control for PV grid-connected system with energy storage[END_REF], paralleling inverters seem to be a promising solution. This topology, based on paralleled threephase inverters, allows energy availability of the system even in case of partial failure. Furthermore, they ensure the improvement of efficiency since components are less stressed (Bella et al., 2018a(Bella et al., , 2018b;;[START_REF] Zhang | Circulating Current Suppression of Parallel Photovoltaic Grid-Connected Converters[END_REF]. However, when parallel inverters are connected in the same DC and AC buses, undesired current known as zero-sequence circulating current (ZSCC) appears through inverters. Basically, the main reason of emerging such a problem is the disparities between the parameters of inverters, tolerance of hardware devices, unequal filters, dead-time, and asynchronous switching frequencies [START_REF] Wang | Investigation of Zero Sequence Circulating Current Suppression for Parallel Three-Phase Grid-Connected Converters Without Communication[END_REF][START_REF] Wei | A Circulating-Current Suppression Method for Parallel-Connected Voltage-Source Inverters With Common DC and AC Buses[END_REF]. The existence of this current might lead to the distortion of the line-currents of each inverter, increases power losses, and decreases the efficiency of the whole system.

Various methods have been reported to solve this issue. For instance, some industrials suggest to install multi-port isolating transformers in the AC side of the central inverter [START_REF] Ji | Operation analysis and new current control of parallel connected dual converter system without interphase reactors[END_REF][START_REF] Ji | Operation analysis and new current control of parallel connected dual converter system without interphase reactors[END_REF], such that PVS800 solar inverter (" ABB, PVS800"), and SGI 500/750XTM solar inverter ("SGI 500/750XTM "). This method can definitely stop the ZSCC from flowing through inverters. However, it is expensive, bulky, and transformers suffer from losses; which make this solution usually limited to two paralleled inverters. In [START_REF] Xueguang | Bandwidth Expansion Method for Circulating Current Control in Parallel Three-phase PWM Converter Connection System[END_REF][START_REF] Ye | Control of circulating current in two parallel threephase boost rectifiers[END_REF], a PI controller has been introduced to modify the distribution of zero vectors at each switching period of space vector modulation (PWM). However, the PI controller is sensitive to the change of parameters which leads to poor performance. Other research has investigated that the emerging of circulating currents (CCs) is due to the asynchronized PWM and the interaction between inverters. Therefore, in order to eliminate (CCs) two parallel two-level inverters are controlled as one three-level inverter [START_REF] Ogasawara | A novel control scheme of a parallel current-controlled PWM inverter[END_REF][START_REF] Quan | A Three-Level Space Vector Modulation Scheme for Paralleled Converters to Reduce Circulating Current and Common-Mode Voltage[END_REF]. This method is capable to eliminate ZSCC. But, if more than two inverters are connected in parallel the control becomes too complicated. Further, it does bring unwanted currents called cross currents. To deal with this last issue, a control method was proposed for minimizing cross currents by introducing a control variable to adjust the duration time of the switching vectors [START_REF] Zorig | Novel Differential Current Control Strategy Based on a Modified Three-Level SVPWM for Two Parallel-Connected Inverters[END_REF]. However, it is still complicated, and difficult to implement in more than two parallel inverters.

Several studies have shown that the ZSCC is closely related to the difference of common mode voltage (CMV) between VSIs. Therefore, the suppression of circulating current is achieved by injecting the same CMV in each inverter of the parallel system or by synchronizing their PWM carriers [START_REF] Chen | Dual-Modulator Compensation Technique for Parallel Inverters Using Space-Vector Modulation[END_REF][START_REF] Jiang | Suppression of Zero Sequence Circulating Current for Parallel Three-Phase Grid-Connected Converters Using Hybrid Modulation Strategy[END_REF][START_REF] Prasad | Common-Mode Injection PWM for Parallel Converters[END_REF]. However, even they will have the same CMV, ZSCC will still possible circulate if the fundamental component of CMV of inverters are different.

Today, the power electronic application community has begun adopting the concept of MPC from control system theory [START_REF] Lim | A Comparative Study of Synchronous Current Control Schemes Based on FCS-MPC and PI-PWM for a Two-Motor Three-Phase Drive[END_REF]. Indeed, predictive control is largely used to control power electronics based applications [START_REF] Chai | Model predictive control of a permanent magnet synchronous motor with experimental validation[END_REF][START_REF] Lim | A Comparative Study of Synchronous Current Control Schemes Based on FCS-MPC and PI-PWM for a Two-Motor Three-Phase Drive[END_REF][START_REF] Yaramasu | Model Predictive Current Control of Two-Level Four-Leg Inverters-Part I: Concept, Algorithm, and Simulation Analysis[END_REF]. This is due to its proprieties that make it suitable for the control of power inverters: simple concept, possibility of including nonlinearities, it considers multivariable approach, and the implementation is easy with the development of processors. Many algorithms are applied in power electronics, amongst them model predictive control (MPC) was proposed for electric drives-based application, where it is applied to control PMSM [START_REF] Chai | Model predictive control of a permanent magnet synchronous motor with experimental validation[END_REF]. Another variety of MPC called finite set control model predictive (FSC-MPC) is applied to control gridconnected converters [START_REF] Yaramasu | Model Predictive Current Control of Two-Level Four-Leg Inverters-Part I: Concept, Algorithm, and Simulation Analysis[END_REF][START_REF] Xing | Model predictive control for parallel three-level T-type gridconnected inverters in renewable power generations[END_REF][START_REF] Wang | Model Predictive Control System Design and Implementation Using MATLAB®[END_REF][START_REF] Kazmierkowski | Predictive Control of Power Converters and Electrical Drives [Book News[END_REF]. For instance, a Lyapunov function based FSC-MPC was proposed to control PV gridconnected inverter [START_REF] Boukezata | Predictive current control in multifunctional grid connected inverter interfaced by PV system[END_REF][START_REF] Golzari | A Lyapunov function based model predictive control for three phase grid connected photovoltaic converters[END_REF]. However, greater is the number of switches used, greater is the computational burden. Also, the switching frequency is variable which might produce a large distributed current spectrum, causing resonances, audible noise, and poor steady-state behavior.

In this work, a robust predictive algorithm is proposed to handle power quality requirement in large scale PV plant based on paralleled three-phase inverters. The main motivation is related to the promising performance of predictive control to handle complex control issues.

The main purpose is to assess the performance of paralleled inverters in order to remove the undesired circulating current and ensure power quality requirements. The main contribution and the novelty of the present work can be summarized in the following points:

• Parallel inverter structure is used to export power from large-scale PV plant to the main grid which offers high efficiency and availability under existing failure.

• Robust Model Predictive Control MPC is proposed to ensure the proper control of delivered power to meet the requirement of grid integration code. This algorithm is extended in such way to provide an appropriate augmented model which adds an integral action that allows to achieve good tracking, a good steady state, and rejection of unknown disturbances.

• The optimization approach is used to make the control accurate which gives a smooth power and a smaller ripple.

• The z-axis component is included in the cost function for minimizing circulating currents flowing through inverter units

• The proposed MPC control is validated through MatLab Simulink and its real-time feasibility is verified via a Hardware-In-the-Loop (HIL) setup based on Opal-RT and dSPACE rapid prototyping systems.

The proposed MPC is based on an optimization approach which allows minimizing circulating currents with ensuring the standard requirements for the grid. This technique can be generalized to be applied on n-inverters allowing power sharing; which seems to be interesting from industrial point of view given the limitation of central inverter structures. Hence, in order to demonstrate the effectiveness of the proposed control, the performance of the proposed MPC is compared to that of PI controller in terms of power quality, power ripple, perturbation rejection, and good dynamic response.

The rest of this paper is arranged as follows. In Section II, modeling of parallel inverters is analyzed, and, in Section III, designing the proposed MPC controller is presented. Section IV presents simulation results to validate the effectiveness of control scheme. Section V presents the HIL architecture and the obtained results. Finally, section VI is dedicated to the conclusion. In ideal conditions, if the parallel inverters are composed of similar modules and inductances, no circulating current will be generated. However, in practice the existence of a small difference in the inverter parameters can lead to a large circulating current through them.

System modeling

The equations of the system in the three-phases % -' -( frame can be given as:

) ( ) * ( ) *+ = ( ) - -- ( ) (1)
where ( ) are the output voltages of the inverter ( ; = 1,2, . . 4). and ( ) represent the grid voltages and phase currents of the inverter ( ) respectively; ) ( ) ,are the inductance and the resistance of the output filters.

In the calculation of predicted currents, a mathematical model in * -5 -6 is helpful to describe the relationship between the system inputs 78( ) , and the system outputs 78( ) . model of the parallel system in the * -5 -6 frame can be written as:

9 ) ( ) * 78( ) *+ = 78( ) -78 --78( ) -:) ( ) 78( ) ) ( ) * ;( ) *+ = [ ;( ) --;( ) ] (2)
where ;( ) is the common voltage of the inverter ( );

The sum of ZSCC for n-inverters can be written as

> ; ? @A = >( + + )/√3 ? @A = 0 (3)
For two inverters, we obtain

; = ;A = -;F = ( + + )/√3 (4)
This equation indicates that only one of the two currents is needed to have zero sequence current control.

For three inverters, the expression given by (3) becomes

;H = -( ;A + ;F ) (5)
This equation indicates that in three parallel inverters only two currents are needed to have zero sequence current control. The dynamic model of the zero-sequence circulating current for two and three parallel inverters can also be deduced from (2). This fact is revealed in Fig. 2 and Fig.

Designing of the proposed MPC controller

This section presents in detail the procedure of designing the proposed MPC control strategy.

As illustrated in Fig. 4, the MPC algorithms consist of controlling the line-currents injected to the main grid and minimizing circulating currents through inverters.

L 1 ,r 6 Inv #2 Inv #1 i abc1 i abc2
d i k + + P PV - Eqs (1) & (2)
--

1 d i z i 2 q i 2 d i 1 q i 1/2 * 0 z i = * 2 q i * 2 d i * 1 q i * 1 d i Fig. 4. Block diagram of proposed control scheme for two parallel inverters.
The proposed MPC control is designed, on one side to ensure the proper control of the injected currents and on the other side to remove the undesired circulating current in parallel inverters.

The mathematical fundamentals of this control concept is presented in [START_REF] Wang | Model Predictive Control System Design and Implementation Using MATLAB®[END_REF].

Actually, the model predictive control is formulated to solve an optimal control problem. Fig. 5 shows the basis of model predictive control. Based on the measured variable, the controller predicts the future dynamic behavior of the system over a prediction horizon . By using a cost function, the objective is to minimize the error between the predicted output and the reference where the objective function is made small as possible. Thus, the control algorithm optimizes over a time period to determine the immediate and best control action that brings the predicted output closer to the desired objective. Once the control is applied, then the controller reinitializes the optimization over the moving horizon to find next control inputs and this keeps marching forward and forward in time. To build the desired control, it is needed: i) state prediction, ii) optimization of the cost function.

i) State prediction

According to inverter model given above, the dynamic model of the parallel inverters can be written in the following form:

J K (+) = L (+) + M "(+) + * N(+) = O (+) (6)
where

(+) = [ 7A 8A 7F 8F ; ] Q "(+) = R 7A 8A 7F 8F ; S Q , N(+) = [ 7A 8A 7F 8F ; ] Q
and the matrices L , M , O are defined as:

L = T U V --/) A 0 - --/) A 0 0 0 0 0 0 0 --/) F 0 0 - 0 0 0 0 --/) F 0 0 --/) FW X Y M = T U V 1/) A 0 0 0 1/) A 0 0 Z 0 0 0 0 1/) F 0 0 0 0 0 1/) F 0 0 0 0 0 1/) F W X Y O = T U V 1 0 0 0 1 0 0 Z 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 W X Y * = [ 7 /) A 8 /) A 7 /) A 8 /) A 0 ] Q
The state-space model for the parallel grid connected system has to be discretized for the purpose of designing the discrete MPC controller. In this work, Euler approach is used which implies that:

L 7 \ ] + L & M 7 \ M & O 7 = O .
where is the sampling time.

To overcome the uncertainties of unknown parameters, * is assumed to be constant in order to be removed when handling the incremental model. By taking the difference between two consecutive samples, the incremental model is given as:

∆ ( + 1) = L 7 ∆ ( ) + M 7 ∆"( ) (7)
where ∆ ( ) = ( ) -( -1) is the difference of state variable and ∆"( ) = "( ) -"( -1) is the difference of control variable also,

N( + 1) -N( ) = O 7 ∆ ( + 1) = O 7 L 7 ∆ ( ) + O 7 M 7 ∆"( ) (8) then:
N( + 1) = N( ) + O 7 L 7 ∆ ( ) + O 7 M 7 ∆"( ) (9)

The augmented system can be given as

J ( + 1) = L ( ) + M"( ) N( ) = O ( ) (10)
where

( ) = a ∆ ( ) N( ) b , L = a L 7 0 c×c O 7 L 7 ] c×c b, M = a M 7 O 7 M 7 b, O = (0 c×c ] c×c )
where 0 c×c , and ] c×c , are the zero and identity matrices respectively, their dimensions are denoted by sub-indices.

This MPC algorithm is used to track the reference signals N where for two parallel inverters, the outputs are: Then, dividing them over two in order to make the two inverters sharing the same currents.

N = R 7A 8A 7F
The reference currents for each inverter are then calculated as follows:

7A = 7F = 7 2 & 8A = 8F = 8 2 (12)
The design of MPC algorithm needs the predicted future outputs for a number of coming steps.

The future state vectors predicted for samples from one to instants can be given as

( + 1) = L ( ) + M∆"( ) ( + 2) = L F ( ) + LM∆"( ) + M∆"( + 1) ⋮ ( + ) = L o p ( ) + L o p qA M o p qA ∆"( ) + ⋯ + L o p qo s M∆"( + -1),
where and are named the control and prediction horizon ( t ) , respectively.

Assuming that the incremental control ∆" becomes zero after samples. The predicted output vectors for the next instants are written in a compact matrix and vector form, as

u = v w ( ) + Φ∆# ( 13
)
where

v w = y L L F ⋮ L o p z; Φ = { | | | } M 0 ⋯ 0 LM M ⋯ 0 L F M LM ⋯ 0 ⋮ L o p qA M ⋮ L o p qF M ⋮ ⋯ ⋮ L o p qo s M • • • € ∆# = [∆"( ) ∆"( + 1) ⋯ ∆"( + -1)] Q ; ( + 1) = [ ( + 1| ) Q ⋯ ( + | ) Q ] Q

2) Optimization of the cost function

To find the control vector, the following cost function is proposed to be minimized

' = u Q ƒ u + ∆# Q " ƒ ∆# ( 14
)
where ƒ and " ƒ are scalar matrices that have identical components. The dimension of the ƒ , and " ƒ matrices are (5 × ) × (5 × ) and (5 × ) × (5 × ) for the application of two parallel system. The optimal solution can be given by

…' …∆# = 0
Solving this equation gives the optimal control vector as

∆# = -Ω qA Ψ ( )
where data matrices are defined as

Ω = (Φ Q ƒ Φ + " ƒ ) %4* Ψ = Φ Q ƒ v w
using receding horizon control, the control components to be applied at the next sampling time (first five rows) is

∆"(+ ) = -[I 0 … 0]Ω qA Ψ Š‹‹‹‹‹‹OE‹‹‹‹‹‹• Ž ••' ( ) = -K ( ),
Therefore, the control law to be applied to the plant is

"( ) = ∆"( ) + "( -1)
It is worth to say that the proposed predictive MPC controller can be generalized to be applied on n-inverters. As equation ( 3) indicates, to control the circulating currents flowing through nparallel inverters, only n-1 inverters are needed to have ZSCC control.

Designing comparative controller

In order to demonstrate the effectiveness of the proposed control, the performance of the proposed MPC is compared to that of PI linear controller. In the following, the design of the PI controller is presented.

A) PI controller design

The main purpose of the PI controller is to allow tracking the reference currents. The reference voltages of each single inverter can be calculated as:

' 7 = " (")• 7 -7 --) 8 + 7 8 = " (")• 8 -8 -+ ) 7 + 7 (15) and ; = " (")• ; -; - (16)
where " (") is the transfer function of the PI controller. The closed loop transfer function, where the inner loop is considered as a first order function, is expressed as:

O)(") = ) " + ) " F + •-+ - ) " + ) (17)
Comparing this function to canonic form of a second order transfer function, we find:

J = 2) $ -- = ) F

Simulation results

In order to validate the proposed control strategy, a simulation of a PV system connected to the main grid with two parallel inverters is built on MATLAB/Simulink environment. The characteristics of the PV plant are shown in Fig. 6 where the generated power is about 1MW in standard conditions (1000 W/m 2 and 25 °C). The parameters used in the simulation of the studied system are listed in Table 1. Simulations are carried out during steady and transient state for the proposed MPC controller.

Also, assessment and comparison of its robustness with filter parameter variations are investigated and the results of circulating current proposed are presented.

PV side power flow

Fig. 8 shows the chosen irradiation when temperature is set at 25 °C. At the beginning, the irradiation is set to 1000 W/m² and the maximum power injected to the grid is about 1.0056 MW as indicated in Fig. 6. Fig. 9 shows the power extracted by the MPPT block using the well-known P&O algorithm. It is observed that in the two methods, the maximum power available is properly tracked with respect to irradiation changes. As it is shown in the results, the power ripple in case of MPC controller is less than that in case of linear controller. The percentage of the ripple in each case is respectively 0.7%, and 2.8%.

Fig. 10 illustrates the dc-link voltage; we notice that, in the two control strategies, it is kept equal to the voltage at MPP. However, the amount of the voltage ripples, in case of the proposed controller, is smaller and its value is about Ÿ 7 = 45 ™, whereas its value in case of PI controller is Ÿ 7 = 82 ™.

Fig. 11 shows the DC input current for the parallel inverters ( 7 ) which is equal to the sum of ( 7 A ) and ( 7 F ). We notice that the input power of parallel inverters is equal to the DC current times the DC link voltage.

Grid side power flow

This scenario is aimed to assess the performance of the proposed predictive controller in injecting maximum available power with respect to irradiation variations. From Fig. 12 it can be seen that the system rapidly reaches steady-state for both controllers. As it is shown, the ability of sharing power among various units is well achieved. In fact, the injected power is the sum of the power of the two inverters. One can observe that the instantaneous active and reactive power of grid side in case of the proposed controller contain smaller undesirable oscillating part which came from the power ripple that flows between DC link and RL filters. The ripple value in case of MPC is about 4.3% which is less than that in case of the PI controller which is 7.7%.

Voltage (V)

Voltage (V) Fig. 11 The DC input current of paralleled inverters and of each inverter. To understand well what happens in closed loop control of the PV system, either dq-current loops or circulating current loop, the next section focuses on the assessment the performance of the predictive controllers in regulating currents and suppressing circulating currents.

Current regulation performance

In this section, the performance of predictive MPC controller is investigated and compared to PI controller. The transient analysis has been carried out with = 20 oe". A step change in the irradiation is applied (600 -1000 -800 /š²). The obtained results are depicted in Fig. 13 where a good dynamic response of injected currents is observed. The rising time is the same in both controllers, which is about 3.7ms. Moreover, the rejection of the disturbance using MPC is faster than that obtained by the classical controller. In terms of total harmonic distortion (THD), its value is 0.82 % with MPC, whereas it is about 2.23 % with PI controller (see Fig. 14.). one can notice that the THD values, for both controllers, comply with IEEE 1547 standard which must be lower than 5%.

Zero-sequence circulating current minimization

The goal of this section is to minimize the circulating current in order to increase the whole efficiency of the parallel inverters and to protect them. This is achieved by including the zcomponent to the cost function of controller as modelled in section 2. Fig. 15 shows the a-phase current of each unit of the parallel inverters. It can be seen that a-phase currents are shifted from each other by ZSCC component. As depicted in the same figure, the amplitude of the ZSCC component using MPC is less even without applying ZSCC control part. Its value is ; = 75L which is about 6.85% of the injected current. Whereas its recorded value is about 53.4% when using PI controller.

As mentioned before, to handle this undesired current we need to force the z-component current to be zero and the ZSCC will track this reference. After applying zero-sequence current control, Fig. 16 reveals that a-phase currents are not shifted and ZSCC is minimized, as well as the power sharing is enhanced where the value of the a-current ( % ) is the sum of a-phase currents ( %1 , F ). Fig. 17 shows the minimized ZSCC component, the circulating current ripple using MPC is smaller compared to that using classical controller, and minimized better.

Current (A)

Current (A)

Parameter variations & Robustness analysis

This test is aimed to investigate the robustness of the proposed predictive control against filter parameter variations and compare the compensation ability for such variations. The filters are considered to change from 25% to 250% of the nominal value of the filter inductances. Fig. 19 shows the performance of the proposed predictive controller compared to PI controller in terms of harmonic contents. The Simulation confirms that both controllers are fairly good in the range of nominal value. Because MPC naturally includes uncertainties, it continues to perform properly current control for a wide range of filter parameters comparing to PI controller. Despites of 25 % of the variations from the nominal value, the THD value in MPC controller is still comply with international standards. This result confirms the high performance in terms of power quality of the proposed control against filter variations.

The summary of these tests is presented in Table 2 where this plus "+" means better performance.

Real-time implementation in a HIL setup

A. Setup architicture

The HIL simulation prototype is built based on Opal-RT RT-LAB platform integrated with MATLAB/Simulink and dSPACE control desk. Fig. 20 describes the prepared setup used to validate the MPC control. In this setup, the physical power system is emulated in the Opal-RT OP4510 simulator and the proposed control is implemented by using a dSPACE DS 1007. The RT-LAB consists of a 3.5GHz core, and has 128 high performance analogue/digital channels. It is controlled via windows host computer using TCP/IP connection.

B. Results

Fig. 21 shows the a-phase currents of the two parallel inverters denoted ( %1 , F ) and the grid current with their zoom. As it can be seen in Fig. 21(a), the presence of circulating currents results in shifting between a-phase current waveforms when the zero-sequence circulating current is uncontrolled. This undesired issue is then cancelled when activating the ZSCC control part as presented in Fig. 21(b).

The general view of the system behavior is presented in Fig. 22 where the grid voltage, the three-phase currents of the two paralleled inverters are displayed.

Conclusion

In this paper, a robust model predictive control MPC based on state-space is proposed to ensure power quality of PV plant connected to the grid with parallel inverters. The proposed control uses the optimization process in order to compute the next control which enhance the injected currents and minimize the circulating current. More, a detail designing of the proposed algorithm is presented. The proposed MPC is assessed and compared with PI control.

Fig. 1

 1 Fig. 1 depicts a PV plant connected to the main grid through parallel inverters. The structure of the system comprises several three-phase voltage source inverters connected in parallel with common DC and AC buses.

Fig. 1 .

 1 Fig. 1. Structure of the studied system.

  Fig. 2. Dynamic model of ZSCC in two parallel inverters.

  Fig. 5. Principle of the proposed model predictive.

Fig. 6 .

 6 Fig. 6. Characteristics of the PV plant.

Fig. 7

 7 Fig. 7 presents the Simulink block-diagram of the studied PV plant. Simpower-system Library is used to build the power part which consists of PV arrays, the paralleled inverters and connecting passive filters to the main grid. The control part consists of an MPPT algorithm and the proposed MPC controller.

Fig. 7 .

 7 Fig. 7. Simulink block diagram of parallel inverter system.

Fig. 8 .

 8 Fig. 8. Variations of irradiations.

Fig. 9 .

 9 Fig. 9. Comparison of extracted power at MPP. (a) the proposed modulated MPC, (b) PI controller.

Fig. 10 .

 10 Fig. 10. Comparison of dc-link voltage. (a) the proposed MPC, (b) PI controller.

Fig. 12 .

 12 Fig. 12. Comparison of injected power into the grid: (a) the proposed modulated MPC, (b) PI controller.

Fig. 13 .Fig. 14

 1314 Fig. 13. Comparative simulation results of transient response in d-q frame: (a) the proposed modulated MPC, (b) PI controller.

Fig. 18 Fig. 15 .

 1815 Fig.18illustrates the three-phase currents of each inverter of the studied structure after applying the ZSCC control part.

Fig. 16 .Fig. 17 .

 1617 Fig. 16. The a-phase currents with zero-sequence current part; inverter line currents A , F and the a-phase voltage. (a) the proposed modulated MPC, (b) PI controller.

Fig. 18 .

 18 Fig. 18. The three-phase currents of each inverter of the paralleled structure.

Fig. 20 .

 20 Fig. 20. HIL setup.

  Fig. 22(a) shows that the presence of circulating currents results in unbalanced inverter currents. Meanwhile, the activation of the ZSCC control enhances the current waveform quality and ensures equal current sharing between the two inverters Fig.22(b).

Fig. 21 .Fig. 22 .

 2122 Fig. 21. HIL results of the a -phase current waveforms and their zoom: (a) without, and (b) with activating ZSCC control part.

Table 1

 1

	Power (W)
	System parameters
	Parameters	Value
	Maximum Power of plant Voltage at maximum power point of w	1,0056 MW
	plant filter resistance -filter inductance ) A filter inductance ) F	1015 ™ 1 š› 300oe• 340oe•

Table 2

 2 Performance comparison

	Methods	Linear control	MPC control
	Criteria
	THD	2.23%	0.82%
	Rising edge time	3.7ms.	3.7ms.
	Circulating current ripple Power ripple percentage	Ÿ ; \ 48L 7.7%	Ÿ ; \ 18L. 4.3%
	Disturbance rejection	+	++
	Robustness to model parameters	+	++
	variations

Simulation results demonstrate that the proposed control provides good property and high performance. In case of step change, the rejection perturbation using MPC is fast. Also, the minimization of ZSCC is better where the amount of circulating current ripple is less. Moreover, MPC compensates for filter variation changes better than the linear controllers. The implementation under Hardware-In-the-Loop (HIL) setup based on Opal-RT and dSPACE rapid prototyping systems demonstrates the real-time feasibility of the proposed approach.