Kévin Jean
email: k.jean@imperial.ac.uk

Adrian Puren
email: adrianp@nicd.ac.za

Ewalde Cutler
email: ewaldec@nicd.ac.zabeverley

Beverley Singh
email: beverleys@nicd.ac.za>

Julie Bouscaillou
email: bouscailloujulie.bouscaillou@gmail.com>

Reathe Rain-Taljaard

Dirk Taljaard

Eleanor Gouws
email: gouwse@unaids.org

Pascale Lissouba
email: plissouba@aol.com

David A Lewis
email: david.lewis2@sydney.edu.au

Gilles Peytavin
email: gilles.peytavin@bch.aphp.fr

Bertran Auvert
email: bertran.auvert@uvsq.fr

Level of viral suppression and the cascade of HIV care in a South-African semi-urban setting in 2012

Keywords: Africa, HIV, ARV, Viral load, Male circumcision, HIV testing, Cascade of HIV care

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Introduction

Antiretroviral treatment (ART) has been rapidly scaled-up in sub-Saharan Africa in the last decade. It was initially used to prevent HIV-related deaths, as well as for the prevention of mother-to-child transmission (PMTCT) [START_REF] Connor | Reduction of maternal-infant transmission of human immunodeficiency virus type 1 with zidovudine treatment. Pediatric AIDS Clinical Trials Group Protocol 076 Study Group[END_REF][START_REF] Who | Antiretroviral therapy for HIV infection in adults and adolescents. Recommendations for a public health approach: 2006 revision[END_REF]. More recently, different studies highlighted the preventive effect of ART on onward sexual transmission [START_REF] Cohen | Prevention of HIV-1 infection with early antiretroviral therapy[END_REF][START_REF] Tanser | High coverage of ART associated with decline in risk of HIV acquisition in rural KwaZulu-Natal, South Africa[END_REF][START_REF] Baggaley | Heterosexual HIV-1 infectiousness and antiretroviral use: systematic review of prospective studies of discordant couples[END_REF], which has led the World Health Organization (WHO) to recommend the use of ART for both individual and collective benefits [START_REF] Who | Consolidated guidelines on the use of antiretroviral drugs for treating and preventing HIV infection. Recommandations for a Public Health approach[END_REF]. However, in order to have an impact on HIV incidence at a population-level, the coverage of those receiving treatment and having a suppressed Viral Load (VL) (as a proportion of all people living with HIV) should be high [START_REF] Eaton | HIV treatment as prevention: systematic comparison of mathematical models of the potential impact of antiretroviral therapy on HIV incidence in South Africa[END_REF][START_REF] Hontelez | Elimination of HIV in South Africa through Expanded Access to Antiretroviral Therapy: A Model Comparison Study[END_REF]. Particularly, ART coverage and viral suppression should be high among the age groups representing the highest HIV incidence levels. Recently, the Joint United Nations Programme on HIV/AIDS (UNAIDS) proposed ambitious treatment targets for 2020, suggesting that 90% of all HIV-infected people should be diagnosed by 2020, 90% of all HIV-diagnosed people should be receiving sustained ART, and 90% of people receiving ART should be virally suppressed [9]. Meeting this "90-90-90" target would result in viral load suppression among 73% of all people living with HIV and would contribute significantly to the reduction of new infections and AIDSrelated deaths and the UNAIDS goal of ending the AIDS epidemic by 2030.

Information documented to date highlights many failures along the so-called cascade of HIV care, with suboptimal efficiency of HIV testing, linkage to HIV care, ART initiation and viral suppression [START_REF] Rosen | Retention in HIV Care between Testing and Treatment in Sub-Saharan Africa: A Systematic Review[END_REF][START_REF] Kranzer | Quantifying and addressing losses along the continuum of care for people living with HIV infection in sub-Saharan Africa: a systematic review[END_REF][START_REF]Global Report: UNAIDS report on the global AIDS epidemic 2013[END_REF]. Estimating the overall proportion of viral suppression and identifying failures along the cascade of care in specific settings is a starting point for strategically planning the way forward towards reaching the UNAIDS 2020 targets and for identifying ways to improve ART program efficiency. Moreover, the majority of the studies published to date are clinic based and thus did not provide insight into those not linked or retained in care [START_REF] Miller | Community viral load as a measure for assessment of HIV treatment as prevention[END_REF].

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Relying on a representative sample of the adult population from a South-African hyperendemic peri-urban setting where an intensified HIV prevention program has been conducted since 2008, our main objective was to estimate the proportion of HIV-infected adults with viral suppression, especially among the highly-exposed age groups. The secondary objectives were a) to document completion of each step of HIV cascade and to identify factors associated with their successful completion, and b) to assess the effectiveness of the ART program in preventing AIDS-related deaths between 2005 and 2012.

Methods

Study community

This study was conducted in the township of Orange Farm, located approximatively 40km from Johannesburg, South Africa. The adult population is estimated at around 110,000. The township is located in a district with one of the most severe HIV epidemics in the world, with HIV prevalence estimated at 30% among women attending antenatal clinics in 2011 [START_REF]The National Antenatal Sentinel HIV and Syphilis Prevalence Survey in South Africa[END_REF].

ART became available in 2004 in the community, but was only available throughout all Orange Farm's clinics in 2005. This later date was retained as the starting date of the ART program for the purpose of our study. Orange Farm was the setting of the first randomized controlled trial on voluntary male medical circumcision (VMMC), conducted between 2002 and 2004 [START_REF] Auvert | Randomized, controlled intervention trial of male circumcision for reduction of HIV infection risk: the ANRS 1265 Trial[END_REF], and of an intensified VMMC scale-up program conducted since 2008 [START_REF] Auvert | Association of the ANRS-12126 male circumcision project with HIV levels among men in a South African township: evaluation of effectiveness using cross-sectional surveys[END_REF]. This program includes community mobilization and free VMMC. In the clinics offering VMMC, free HIV counseling and testing (HCT) is also offered.

Survey

We used a one-stage self-weighting sampling design to select a representative random sample of households in the community. Between January and December 2012, every adult aged 18

Copyright © 2016 Wolters Kluwer Health, Inc. Unauthorized reproduction of this article is prohibited. years or older and having slept at least two nights in the selected households during the previous seven nights were invited to participate in the study. Informed consent was obtained from all participants, interviews were conducted using standardized questionnaires, a genital examination was performed and bloods were collected at the study site. The following information was collected through standardized questionnaires: age, ethnic group, marriage history, occupation, education level, alcohol consumption, age at sexual debut, lifetime number of sexual partners, condom use at last sexual intercourse, HIV testing history (ever/never tested and date of the first HIV test) and, among women, pregnancy history.

Among men, a genital examination was performed to determine male circumcision (MC) status. The date of circumcision was also collected.

Laboratory procedure

Each participant was invited to supply a venous blood sample. Samples were collected in plasma preparation tubes and centrifuged. A screening test for HIV (GenscreenTM HIV1/2 version 2, Bio-Rad, Marnes-la-Coquette, France) was performed on all plasma samples. For reactive samples, a confirmatory test was run (VironostikaTM, HIV Uni-Form II plus O, bioMérieux, Boxtel, Netherlands). If the sample reacted positively for both assays, a second confirmatory test was conducted (Murex HIV-1.2.O, Murex Biotech Ltd., Dartford, UK).

Plasma samples testing positive for HIV were also tested for the presence of the most common antiretroviral drugs (ARV) currently in use in South Africa (Lamivudine, Stavudine, Zidovudine, Nevirapine, Efavirenz, Ritonavir, Lopinavir, Emtricitabine, Tenofovir, Abacavir, Atazanavir) using ultra performance liquid chromatography coupled with tandem mass spectrometry according to a slightly modified previously published method [START_REF] Jung | Simultaneous determination of 17 antiretroviral drugs in human plasma for quantitative analysis with liquid Copyright[END_REF]. Plasma HIV-1 RNA load was determined by reverse-transcription PCR using an assay designed to detect

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all M-group subtypes (Amplicor HIV-1 Monitor Test V1.5, Roche Diagnostic System Ins., Branchburg, New Jersey, USA) [START_REF] Triques | Efficiencies of four versions of the AMPLICOR HIV-1 MONITOR test for quantification of different subtypes of human immunodeficiency virus type 1[END_REF].

Ethics

Ethical clearance for the surveys was granted by the Human Research Ethics Committee (Medical) of the University of the Witwatersrand on May 8, 2007 (M070367).

Outcomes

Additionally to the HIV status of participants, our outcomes included the successive steps of the cascade of HIV care, defined as: i) having been ever tested for HIV; ii) testing positive for the use of any ARV; and iii) having viral suppression, defined as VL<400copies/mL (alternative thresholds were also used: <50 or <1000copies/mL). We also calculated the ratio of ARV-positive people over those HIV-negative. At the community-level, we calculated the detectable viral load proportion, defined as the proportion of untreated or treated but not virally suppressed HIV-infected people , and as such representing the fraction of the population potentially exposing their sexual partners to HIV [START_REF] Miller | Community viral load as a measure for assessment of HIV treatment as prevention[END_REF][START_REF] Kelley | Measuring population transmission risk for HIV: an alternative metric of exposure risk in men who have sex with men (MSM) in the US[END_REF]).

For participants testing positive for the use of ARVs, the ART profile was categorized as definite/probable/possible 1 st -line regime, definite/probable/possible 2 nd -line regime, or undetermined (see Table S1, Supplemental Digital Content 1, http://links.lww.com/QAD/A932, which describes the ART profiles).

Statistical analysis

For each outcome, we calculate the percentage and 95% Confidence Interval. For HIVpositivity and the different steps of the treatment cascade, we identified associated factors through univariate and multivariate Poisson regression, which allowed the calculation of

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unadjusted and adjusted Prevalence Rate Ratio (respectively, PRR and aPRR) [START_REF] Barros | Alternatives for logistic regression in cross-sectional studies: an empirical comparison of models that directly estimate the prevalence ratio[END_REF]. Variables considered in the multivariate models included all covariates associated with the studied outcome with a p-value <0.2 in univariate analysis.

We conducted additional analyses restricted to the highly exposed age groups, defined as those age groups with a particularly high HIV incidence rate, including 18-29 year old women and 25-34 year old men [START_REF] Shisana | South African National HIV Prevalence, Incidence and Behaviour Survey[END_REF]. The outcomes were also studied in the sub-population of women reporting having been pregnant during the past 12 months.

The number of participants testing positive for ARVs was expressed as a ratio relative to the number of HIV-negative participants in the sample (number non-directly dependent on ART programs). Using a basic model, (see Text, Supplemental Digital Content 2, http://links.lww.com/QAD/A932, which describes the model), we estimated what this ratio would have been if every HIV-infected person in the community had received ART using the treatment threshold of CD4<200cells/ L (which since 2005, has corresponded to the 2006 WHO guidelines [START_REF] Who | Antiretroviral therapy for HIV infection in adults and adolescents. Recommendations for a public health approach: 2006 revision[END_REF]). This model assumed a stable population and a stable HIV epidemic (i.e.

HIV incidence roughly equals AIDS-related mortality).

Analyses were performed using the statistical software R [START_REF] Development | R: a language and environment for statistical computing[END_REF].

Results

Sample characteristics

A total of 3293 men and 3473 women participated in the study.

HIV prevalence and factors associated with HIV-positivity

HIV prevalence was 17.0% [15.7-18.3%] among men and 30.1% [28.5-31.6%] among women (overall: 23.7% [22.7-24.7%]). Age-specific HIV prevalence is presented in Figure 1. Results of the risk factor analysis of HIV-positivity are presented in a table (see Table S2, Supplemental Digital Content 3, http://links.lww.com/QAD/A932, which describes the data).

Uptake of HIV testing

Overall, 59.1%[57.4-60.8%] of men and 79.5%[78.2-80.9%] of women reported having been previously tested for HIV. These proportions were 65.7%[62.5-68.7%] and 84.2%[82. .0%], respectively, among the highly-exposed age groups.

Among men, independent predictors of lifetime uptake of HIV testing were having ever been married, being at school, being HIV-positive and being circumcised (Table 2). This latter factor was the strongest predictor of having ever been tested. Among circumcised men, [START_REF] Development | R: a language and environment for statistical computing[END_REF].7%[215/694, 20.9-26.6%] of those having ever been tested reported the date of the first HIV test as being within a month of the date of the VMMC. Among women, independent predictors of lifetime uptake of HIV testing were employment and having been pregnant during the past 12 months. Among women reporting having received prenatal care, 96.2%[93.4-97.9%] reported having been tested for HIV (it is not

Copyright © 2016 Wolters Kluwer Health, Inc. Unauthorized reproduction of this article is prohibited. known whether they were tested as part of prenatal care), and 33.8% [29.3-38.6%] of those reported that they underwent their first HIV test within the past 12 months. Among participants testing positive for HIV in this study, 33.9%[29.9-38.0%] of men and 13.2% [11.2-15.4%] of women reported having never been tested for HIV.

ART coverage

Among 558 men and 1041 women testing positive for HIV, 21.0% [17.7-24.6%] and 30.5% [27.7-33.3%], respectively, tested positive for one or more ARV (overall: 27.1%[25.0-29.4%]). Among untreated HIV-positive participants, 39.0% [34.4-43.7%] of men and 16.5% [13.8-19.4%] of women reported having never been tested for HIV.

Factors associated with the use of ARVs among both genders were age and condom use during their last sexual encounter (Table 3). Additionally, being unemployed (vs. employed) among men, and having a low alcohol consumption among women, were independently associated with ARVs-positivity. MC status was not associated with ARVs-positivity, while among women from highly-exposed age groups, recent pregnancy was associated with ARVspositivity (aPRR=2.08 [1.22-3.57]).

Among the 119 women testing positive for HIV and reporting having been pregnant during the past 12 months, 31.1%[22.9-40.2%] were using ARVs.

Among men testing positive for ARVs, 14.5%[8.7-22.2%] reported having never been tested for HIV. Among women, this figure was 5.7%[3.4-8.8%].

Among the 434 participants testing positive for any ARV, the majority were definitely (303; 69.8%), probably (87; 20.0%) or possibly (11; 2.5%) using first-line regimen ARVs; 16 (3.7%), 8 (1.8%) and 1 (0.2%), respectively, were definitely, probably or possibly using second-line regimen ARVs, while the remaining 8 (1.8%) presented an undetermined profile.

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Viral Load distribution among people receiving ART

Among the 432 participants testing positive for ARVs, 405 had an available VL measure. Among these, the proportion with viral load under the thresholds of 1000copies/mL, 400copies/mL and 50copies/mL were respectively 94.1%[91.3-96.2%]; 91.9%[88.7-94.3%] and 78.3%[73.9-82.2%]. In univariate analysis, none of the studied risk factors were found to be significantly associated with VL suppression (see Table S3, Supplemental Digital Content 4, http://links.lww.com/QAD/A932, which describes the results of the analysis). None of the participants with a count of VL>1000copies/mL was under a definite, probable or possible 2 nd -line ART regime, and thus potentially in need of a 3 rd -line regime.

Overall cascade of HIV care and viral suppression

Assessing the effectiveness of ART programs

We calculated the ratio of people using ARVs to those HIV-negative to be 0.084. Using the model described in Annex 1, we estimate that, if ART programs implemented in Orange Farm since 2005 were successful in averting every AIDS-related death, this ratio would be 0.184.

By comparing the observed ratio to that calculated under the hypothesis of maximum

Copyright © 2016 Wolters Kluwer Health, Inc. Unauthorized reproduction of this article is prohibited. effectiveness, we estimate the effectiveness of the ART program in preventing AIDS-related deaths to be 46%.

Discussion

Main results

In 2012, in a peri-urban South-African community hyper-endemic for HIV, 23.7% of all HIVinfected people were virally suppressed. Furthermore, this proportion was significantly lower among age groups most exposed to HIV infection. These levels can be considered as a starting point for developing strategic plans for reaching the proposed UNAIDS target for 2020, namely to achieve viral suppression among 73% of all people living with HIV. A large majority of the population reported having ever been tested for HIV, whereas just over one in four people living with HIV were receiving ART. When correctly taken, ART was highly effective in achieving viral suppression. Using a basic model, we also demonstrate that ART programs conducted until 2012 have had an effectiveness of 47 to 67% in preventing AIDSrelated deaths in this community.

Limitations

This study has several limitations. We defined steps along the cascade of HIV care that differ from those suggested in relation to the proposed UNAIDS target [9], with specific reference to the first two steps (percentage of lifetime HIV testing and proportion of those testing positive for the use of ARVs). We cannot infer the percentage of diagnosed HIV infections from information on lifetime uptake of HIV testing. However, the percentage of HIV-infected participants reported having never been tested for HIV may be interpreted as a lower boundry of the proportion of undiagnosed HIV infections. Furthermore, the proportion of HIV-infected participants testing positive for ARVs may underestimate the true proportion of participants

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having initiated ART, because participants receiving ART but not taking treatment at the time of the survey would test negative for ART. However, our third cascade indicator, the percentage of HIV-infected participants with suppressed VL, integrates information from previous steps and is comparable with that proposed by UNAIDS. Moreover, the results of this study do not rely on longitudinal data, and thus do not allow for a comprehensive understanding of the dynamics that may affect the different steps along the HIV cascade [START_REF] Hallett | A Side Door Into Care Cascade for HIV-Infected Patients?[END_REF].

However, the cross-sectional nature of our data presents a snapshot of the cascade of care in Orange Farm that may be representative at the community level. Moreover, as we rely on data collected from a representative sample of the population, our indicator has the advantage of being less affected by reporting or participation bias than results obtained in clinical settings [START_REF] Miller | Community viral load as a measure for assessment of HIV treatment as prevention[END_REF]. Other limitations were that a) we have used high incidence groups as a proxy for high transmitters and b) the questionnaire should have included questions about date of most recent HIV test, as well as date of the first test, and some indication of how many tests there were in between.

HIV testing

The proportions of the population having previously been tested for HIV in our study are very similar to those documented at the national level in South African [START_REF] Shisana | South African National HIV Prevalence, Incidence and Behaviour Survey[END_REF]. In particular, almost all women having recently been pregnant reported having ever been tested for HIV, which may reflect the impact of prevention of mother-to-child transmission programs [START_REF] Barron | Eliminating mother-to-child HIV transmission in South Africa[END_REF][START_REF] Goga | Unauthorized reproduction of this article is prohibited. transmission from mother to child, South Africa[END_REF]. The level of lifetime HIV testing documented in South Africa is among the highest in sub-Saharan Africa [START_REF] Staveteig | Demographic Patterns of HIV Testing Uptake in Sub-Saharan Africa -DHS Comparative Reports[END_REF]. However, in this study, at least 17% and 39% of HIV-infected women and men did not know their HIV status, which highlights the need to strengthen HIV testing programs.

More specifically, repeat HIV testing should be promoted to allow earlier linkage to care and ART initiation [START_REF] Gras | Lower mortality and earlier start of combination antiretroviral therapy in patients tested repeatedly for HIV than in those with a positive first test[END_REF]. Our data did not provide direct information on this issue, but results on

Copyright © 2016 Wolters Kluwer Health, Inc. Unauthorized reproduction of this article is prohibited. lifetime testing suggest that the proportion of people who have been repeatedly tested is low, especially among men. Previous studies conducted in South Africa suggest that the proportion of repeat testers among HIV test users ranges from 26% to 71%, depending on the local and testing context [START_REF] Kranzer | High prevalence of self-reported undiagnosed HIV despite high coverage of HIV testing: a cross-sectional population based sero-survey in South Africa[END_REF][START_REF] Regan | Factors associated with self-reported repeat HIV testing after a negative result in Durban, South Africa[END_REF][START_REF] Tabana | Testing Together Challenges the Relationship": Consequences of HIV Testing as a Couple in a High HIV Prevalence Setting in Rural South Africa[END_REF].

ART coverage

The proportion of HIV-infected people testing positive for the use of ARVs in our study was slightly lower than that estimated in a 2012 national population-based survey in South Africa (31.2%), with the proportion being consistently higher among women than men [START_REF] Shisana | South African National HIV Prevalence, Incidence and Behaviour Survey[END_REF]. In 2013, in a township in the Cape Town area, Kranzer et al reported that 33.5% of all HIV-infected individuals were receiving ART [START_REF] Kranzer | Community viral load and CD4 count distribution among people living with HIV in a South African Township: implications for treatment as prevention[END_REF]. This slightly higher estimate may be explained by overestimation due to self-reporting. The proportion of people on second-line treatment regimes in our study was close to the WHO projections for low-and middle-income countries [START_REF] Renaud-Théry | Utilization patterns and projected demand of antiretroviral drugs in low-and middleincome countries[END_REF].

Effect of VMMC campaigns

The study was conducted in a community where VMMC has been intensively promoted as part of a combined HIV prevention package, including HIV counseling and testing (HCT), since 2008 [START_REF] Auvert | Association of the ANRS-12126 male circumcision project with HIV levels among men in a South African township: evaluation of effectiveness using cross-sectional surveys[END_REF]. We therefore observed a probable secondary benefit of VMMC programs: circumcised men were more likely to have ever been tested for HIV than uncircumcised men. Moreover, among circumcised men, nearly one in four reported having undergone a first HIV test as part of the VMMC procedure.

Estimation of ART program effectiveness

While significant progress has been made in scaling up the provision of ART to eligible people living with HIV in sub-Saharan Africa, coverage remains sub-optimal. For example, in 2009, ART coverage in South Africa, using the 2006 WHO guidelines (CD4<200cells/µL) was estimated at around 56% [START_REF] Who | Toward universal access: Scaling up priority HIV/AIDS intervention in health Copyright[END_REF]. National-level coverage was estimated by UNAIDS using

Copyright © 2016 Wolters Kluwer Health, Inc. Unauthorized reproduction of this article is prohibited. a model which is based on national epidemiological data and assumptions on average survival rates with and without ART, and average time between sero-conversion and eligibility for treatment [START_REF] Stover | The Spectrum projection package: improvements in estimating mortality, ART needs, PMTCT impact and uncertainty bounds[END_REF]. Using a basic model and relying on the same kind of data and assumptions, we estimated that the effectiveness of ART programs was less than 50% in preventing AIDSrelated deaths in the Orange Farm community between 2005 and 2012. These results highlight the need for better efficiency in every step of the cascade of HIV care, from HIV testing and diagnosis, to ART initiation, retention in care and adherence to treatment [START_REF] Kranzer | Quantifying and addressing losses along the continuum of care for people living with HIV infection in sub-Saharan Africa: a systematic review[END_REF][START_REF] Fox | Patient retention in antiretroviral therapy programs up to three years on treatment in sub-Saharan Africa, 2007-2009: systematic review[END_REF].

Level of viral suppression and impact on HIV incidence

The level of viral suppression among the adult population infected with HIV in the Orange Farm community was found to be very similar to the 2013 UNAIDS estimate for Sub-Saharan Africa of 24% [START_REF]Global Report: UNAIDS report on the global AIDS epidemic 2013[END_REF]. A rough estimate of the impact of such a level of viral suppression might be obtained by comparing the detectable viral load proportion, i.e. the fraction of the population potentially exposing partners to HIV [START_REF] Miller | Community viral load as a measure for assessment of HIV treatment as prevention[END_REF][START_REF] Kelley | Measuring population transmission risk for HIV: an alternative metric of exposure risk in men who have sex with men (MSM) in the US[END_REF] to the crude HIV prevalence in the community. This basic calculation suggests a decrease in HIV incidence of 25% due to the preventive effect of ART. However, the true preventive effect of ART may have been lower, as lower levels of viral suppression were observed in the younger age groups among whom HIV incidence is at its highest levels. At the 2012 coverage level, we therefore cannot expect ART to have had a large impact on HIV incidence in this community.

Optimistic results

Our study shows that people receiving ART were more likely to report condom use at the last sexual encounter compared to untreated HIV-infected participants. This association may reflect the behavioral preventive effect of ART that has previously been described [START_REF] Kennedy | The impact of HIV treatment on risk behaviour in developing countries: a systematic review[END_REF][START_REF] Kaye | The impact of highly active antiretroviral therapy on high-risk behaviour of HIV-infected patients in sub-Saharan Africa[END_REF][START_REF] Berhan | Is the Sexual Behaviour of HIV Patients on Antiretroviral therapy safe or risky in Sub-Saharan Africa? Meta-Analysis and Meta-Regression[END_REF][START_REF] Jean | Decrease in sexual risk behaviours after early initiation of antiretroviral therapy: a 24-month prospective study in Côte d'Ivoire[END_REF].

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Another encouraging result from our study is that, when ARVs are correctly taken, and thus detectable in blood, their effectiveness in suppressing HIV viral load is high. Close to all treated participants presented a VL<1000copies/mL, which is the usual threshold of effective treatment. However, our results do not provide evidence to help understand why some patients interrupt or are insufficiently adherent to their treatment.

Conclusions

This study allowed the assessment of the gap between the 2012 level of viral suppression among the HIV-infected population of a hyper-endemic community in South Africa and the proposed UNAIDS treatment targets for 2020. The Orange Farm township is fairly representative of other semi-urban areas and our results may therefore be generalizable to those obtained in other sub-Saharan hyper-endemic semi-urban settings. While good progress has been made in the last decade in providing treatment to people living with HIV, the study shows that ART programs in 2012 were still suboptimal in delivering treatment to every person eligible for treatment according to the 2006 WHO treatment guidelines. Changing the HIV treatment eligibility criteria in itself will not be sufficient to reach the 2020 targets; there is an urgent need to improve the effectiveness of ART programs. Our results suggest that HIV testing and ART initiation, rather than ART effectiveness if actually taken, are crucial steps in need of improvement in order to achieve effective ART programs.

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Figure legend

Figure 2

 2 Figure 2 summarizes the cascade of HIV care in Orange Farm. Overall, 23.7%[21.6-25.9%]

Fig. 1 :

 1 Fig. 1: HIV prevalence across age groups among men and women in Orange Farm,

Fig. 2 .

 2 Fig. 2. Percentage of ART-positivity and suppressed VL in Orange Farm, 2012.

  HIV testing characteristics of the population are presented in Table1. Among 18-49 year old men (age group targeted for VMMC), the prevalence of MC was 46.2%[95% Confidence Interval: 44.3-48.0%]. Among women, 12.9%[11.8-14.0%] reported having been pregnant during the past 12 months, among whom 93.8%[91.1-96.0%] reported having seen a health provider in relation to the pregnancy.

The overall participation rate was 60%. The mean age (median[Inter-Quartile Range]) was 31.8 years (27.0[22.0-38.6]) among men and 36.0 years (32.6[23.7-46.2]) among women. Background, behavioral and Copyright © 2016 Wolters Kluwer Health, Inc. Unauthorized reproduction of this article is prohibited.

Table 2 . Factor associated with lifetime uptake of HIV testing among men and women in Orange Farm, 2012.

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			Men (N=3291)			Women (N=3471)
		% ever tested			% ever tested
			PRR[95%IC]	aPRR[95%IC]		PRR[95%IC]	aPRR[95%IC]
		(n)			(n)
	Age
	18-24	52.6% (1366)	1	1	81.2% (1052)	1	1
	25-29	64.2% (606)	1.22[1.08-1.38]	1.13[0.99-1.30]	95.6% (481)	1.18[1.05-1.32]	1.09[0.97-1.23]
	30-34	68.4% (326)	1.30[1.12-1.51]	1.21[1.02-1.43]	92.8% (373)	1.14[1.01-1.29]	1.06[0.92-1.21]
	35-39	61.5% (239)	1.17[0.98-1.39]	1.06[0.86-1.30]	90.8% (347)	1.12[0.98-1.27]	1.04[0.90-1.20]
	≥40	61.9% (754)	1.18[1.05-1.32]	1.13[0.96-1.32]	64.5% (1218)	0.79[0.72-0.88]	0.79[0.70-0.89]
	Ethnic group
	Sotho	57.0% (1119)	1		78.3% (1295)	1
				Not entered			Not entered
	Zulu	60.0% (1349)	1.05[0.95-1.17]		82.8% (1305)	1.06[0.97-1.15]
	Other	60.5% (822)	1.06[0.94-1.19]		76.6% (870)	0.98[0.89-1.08]
	Occupation
	Employed	61.5% (1470)	1	1	83.5% (926)	1	1
	Unemployed	59.7% (1148)	0.97[0.88-1.07]	1.02[0.92-1.12]	82.5% (1924)	0.99[0.91-1.08]	0.94[0.86-1.03]
	Other	52.8% (671)	0.86[0.76-0.97]	0.98[0.83-1.14]	64.6% (621)	0.77[0.69-0.87]	0.76[0.66-0.88]

PRR: unadjusted Prevalence Rate Ratio. 95%CI: 95% Confidence Interval. aPRR: adjusted Prevalence Rate Ratio. PRR and aPRR were computed from univariate and multivariate Poisson regression. The multivariate models included all covariate associated with the outcome with a p-value <0.2 in univariate analysis.

Table 3 . Factor associated with positivity to ARV among HIV-infected men and women in Orange Farm, 2012.

 3 : Antiretroviral drugs. PRR: unadjusted Prevalence Rate Ratio. 95%CI: 95% Confidence Interval. aPRR: adjusted Prevalence Rate Ratio. PRR and aPRR were computed from univariate and multivariate Poisson regression. The multivariate models included all covariate associated with the outcome with a p-value <0.2 in univariate analysis.

	Men (N=558)		Women (N=1041)
	% positive	% positive
	PRR[95%IC]	aPRR[95%IC]	PRR[95%IC]	aPRR[95%IC]
	to ART (n)	to ART (n)

Copyright © 2016 Wolters Kluwer Health, Inc. Unauthorized reproduction of this article is prohibited.

Copyright © 2016 Wolters Kluwer Health, Inc. Unauthorized reproduction of this article is prohibited.

ARV

Acknowledgements

We would like to thank the entire research team of Progressus Research and Development and specifically Agenda Gumbo for organizing the data entry of this study. We would like to thank Gaph Phatedi and Audrey Mkwanazi for support. We would like to thank the community of Orange Farm and specifically the Community Advisory Board of Orange Farm chaired by Portia Ntshangase.

Source of funding

We acknowledge support from the French Research Agency ANRS (Grant 12285).

Competing interests

The authors declare that they have no competing interests.

Authors' contribution

All authors have read and approved the manuscript. Substantial contributions to conception and design: BA, JB, RRT, DT and PL Preformed the acquisition of data: RRT, DT, JB and PL. Conducted the biological analysis of samples: EC, BS, AP, DAL and AP. Preformed the statistical analysis: KJ, BA. Interpretation of data: KJ, BA, GP, AP, PL, JB and EG. Wrote the first draft: KJ and BA.

Contributed to writing the paper: AP, JB, EG, DAL and GP. Copyright © 2016 Wolters Kluwer Health, Inc. Unauthorized reproduction of this article is prohibited.

Previous presentation


Waleed Nwesaty

Antoneta Iuliana Bratcu

Olivier Sename

Power sources coordination through multivariable LP V /H ∞ control with application to multi-source electric vehicles

Keywords: H∞ control, LPV systems, power source coordination, reduced-order controller, frequency separation, electric vehicle

Power sources coordination through multivariable LPV/Hinf control with application to multi-source electric vehicles

Waleed Nwesaty, Antoneta Iuliana Bratcu, Olivier

INTRODUCTION

Global warming and increased need of petroleum products are main issues nowadays. Lots of research works focus on decreasing CO 2 emission by developing hybrid vehicles or electric ones equipped with a convenient solution that replaces combustion engines [START_REF] Van Mierlo | Which energy source for road transport in the future? a comparison of battery, hybrid and fuel cell vehicles[END_REF][START_REF] Garcia | Fuel cell-battery hybrid system for transport applications[END_REF]. Hybrid power supply systems use combination of fuel cell, battery and supercapacitor in order to satisfy power demand within electric vehicles. However, fuel cell could be combined with battery and supercapacitor in order to achieve power and energy density values similar to an ordinary engine [START_REF] Hannan | Analysis of multi-power sources energy management system for electric hybrid vehicle[END_REF], and it is expected that fuel cell/battery/supercapacitor hybrid could result in improved system performances and energy efficiency [START_REF] Thounthong | Energy management of fuel cell/battery/supercapacitor hybrid power source for vehicle applications[END_REF].

Fuel cell is a promising energy system for sustainable future due to its environment friendliness and modularity. The main drawback of a fuel cell power generation system is its slow dynamics because the fuel cell current slope must be limited to prevent fuel starvation and to improve its performance and lifetime. Besides, high cost per power unit and inability to allow bi-directional power flow are some drawbacks [START_REF] Nayeripour | Frequency deviation control by coordination control of FC and double-layer in an autonomous hybrid renewable energy power generation system[END_REF][START_REF] Yu | An innovative optimal power allocation strategy for fuel cell, battery and supercapacitor hybrid electric vehicle[END_REF]. Batteries also enable an important pollutant emission reduction and fuel consumption, but have some drawbacks such as low power density in comparison with supercapacitors (long charging time), low energy density in comparison with fuel cell (limited range), a high cost per power unit and a shorter lifetime [START_REF] Allegre | Flexible real-time control of a hybrid energy storage system for electric vehicles[END_REF]. According to Ragone's plot [START_REF] Kuperman | Battery/ultracapacitor hybrids for pulsed current loads: A review[END_REF], sources can be classified into two main classes: high-energy-density sources that can supply power for long duration of time (e.g., fuel cells), and high-power-density sources, which can provide relatively high power for short period of time (e.g., supercapacitors). Batteries are classified in between the two classes depending on the battery type.

In order to achieve hybridization between the three power sources (fuel cell is main power source, battery and supercapacitor are auxiliary power sources), many configuration topologies are proposed regarding the number of components, energy management complexity and performance reliability. There are three main topological architectures: series, parallel, and cascaded [START_REF] Azib | Online energy management strategy of a hybrid fuel cell/battery/ultracapacitor vehicular power system[END_REF][START_REF] Tie | A review of energy sources and energy management system in electric vehicles[END_REF][START_REF] Aharon | Topological overview of powertrains for battery-powered vehicles with range extenders[END_REF]. In this paper, the parallel structure is chosen due to its flexibility to adapt the system parameters such that DC-bus value, sources' independence, and even the facility to replace or to add more power sources (photovoltaic panels, grid electricity, etc...).

In the literature, many works are dedicated to design high-performance and efficient energy management systems for a variety of application with two or three different power sources. A significant number of strategies can be found such as switching strategy [START_REF] Hannan | Test bench model and algorithms for multi-sources light electric vehicle energy management system[END_REF], equivalent consumption minimization strategy [START_REF] Aiteur | Energy management and control of a fuel cell/supercapacitor multi-source system for electric vehicles[END_REF], proportional-integral controllers [START_REF] Wong | A parallel energy-sharing control for fuel cell-battery-ultracapacitor hybrid vehicle[END_REF], fuzzy logic control [START_REF] Erdinc | A wavelet-fuzzy logic based energy management strategy for a fuel cell/battery/ultra-capacitor hybrid vehicular power system[END_REF][START_REF] Fadel | An experimental and analytical comparison study of power management methodologies of fuel cell, battery hybrid vehicles[END_REF], filtering strategy [START_REF] Silva | Application of a decoupling method based on online filtering technique for multi-source electric vehicles[END_REF][START_REF] Florescu | Frequency-separation-based energy management control strategy of power flows within electric vehicles using ultracapacitors[END_REF][START_REF] Florescu | Adaptive frequency-separation-based energy management system for electric vehicles[END_REF], sliding mode control [START_REF] Liu | Observer-based higher order sliding mode control of power factor in three-phase ac/dc converter for hybrid electric vehicle applications[END_REF], and LQG optimal control [START_REF] Florescu | LQG optimal control applied to on-board energy management system of all-electric vehicles[END_REF].

This paper deals with on-board energy management for a three-power-source power supply system (fuel cell, battery and supercapacitor) used in a parallel structure, where each source is controlled by means of a DC-DC converter. The sources are connected in parallel to the load (consisting of an electrical motor with its associated converter) through a DC-bus (Fig. 1). The main power source is the fuel cell connected to a 1-quadrant boost converter, whereas auxiliary sources are the battery and the supercapacitor; their role is to respond to power demand variations placed in relatively high frequency and to collect the reversed power (during braking phase). Each auxiliary source is connected to a 2-quadrant converter which allows charging/discharging. The sources are coordinated in a manner related to the frequency characterization of each one, which protects fuel cell and battery from high variation in power demand and in consequence prolong their lifetimes. The proposed strategy is formulated in the LP V /H ∞ framework methodology which leads to robust stability of the closed-loop behaviour.

This paper extends the authors' work in [22] by using a reduced-order version of the LP V /H ∞ controller, which is compared with the original one. Moreover, the control system is tested here using the driving cycle of IFSTTAR (Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux) that represents suburban driving features. This cycle has been preferred here because it has richer frequency content than, for example, the Normalized European Driving Cycle (NEDC), and, thus, it is more illustrative for the frequency separation validation. Steady-state source's behaviours are also examined.

The paper main contributions can be summarized in the following points:

• This paper proposes a generic solution that can be used as energy management system for power supply systems with potentially any number of power sources.

• The solution can handle the variations in system parameters due to LPV approach used in modeling and control design.

• An original frequency separation technique is proposed based on the choice of weighting functions associated to H ∞ control design. This can be applied to solve several power sources coordination problems.

• From application point of view, MORE toolbox [START_REF] Poussot-Vassal | Introduction to MORE: A MOdel REduction toolbox[END_REF] can be used to perform order-reduction for the LPV controller within specified frequency intervals. It is the method of LPV controller order reduction that is used here in order to reduce the computational burden when it is about practical implementation.

• The use of H ∞ control design allows to handle the load power demand without any prediction or estimation of its behavior. However, load current can be measured to modify the setpoint of the fuel cell and the battery steady-state behaviors.

• Detailed nonlinear models of the different parts of the studied system are used for simulation purpose in order to achieve and study the closed-loop behavior under as realistic as possible conditions.

This paper is organized as follows: Section 2 details power sources, converters and DC-bus models. The control problem is formulated in Section 3. The proposed solution is presented in Section 4, along with a method to reduce the controller order. Section 5 details the simulation results, including a comparison with a classical-PI-based filtering strategy taken as base-line. Section 6 concludes the paper.

MODELLING

This section is dedicated to present the system model starting from ordinary differential equations that represent physical laws. In general, vehicle's power supply system may be divided into three stages:

• Input stage: this stage represents the power sources in the vehicle. The main power source is assumed to be the fuel cell, whereas the auxiliary ones are the battery and the supercapacitor. Fig. 1 shows the electrical models of the three power sources.

The dynamics of the fuel cell and the battery are not considered in the LPV/H ∞ control problem. However more detailed models will be used for simulation purposes [START_REF] Hernandez | A robust multivariable approach for hybrid fuel cell supercapacitor power generation system[END_REF][START_REF] Ceraolo | New dynamical models of lead-acid batteries[END_REF].

The supercapacitor state of charge is chosen to be controlled to handle the response to load variations during acceleration/braking phases. Supercapacitor electrical model shown in Fig. 1 leads to following equations [START_REF] Wu | On-line supercapacitor dynamic models for energy conversion and management[END_REF]:

                     dV 0 dt = -1 C 0 I sc dV 1 dt = -1 C 1 R 1 V 1 - 1 C 1 I sc dV 2 dt = -1 C 2 R 2 V 2 - 1 C 2 I sc V sc = -I sc R 0 + V 0 + V 1 + V 2 (1)
where I sc is the supercapacitor current, V sc is supercapacitor voltage, R 0 , C 0 , R 1 , C 1 , R 2 , and C 2 are constant parameters of supercapacitor model, V 0 , V 1 and V 2 are sub-voltages represented in supercapacitor model (Fig. 1).

• Output stage: usually called DC-bus, which supplies power to load (vehicle's DC or AC motor with its associated power converter whose model is out of scope of this paper). Without any loss of generality, the DC-bus dynamic is investigated by using an output capacitor, which leads to the following equation:

dV dc dt = 1 C dc [ -1 R dc V dc -I Load + I f c (1 -α f c ) + I bat α bat + I sc α sc ] (2)
where I Load is the load current, V dc is the DC-bus voltage, C dc and R dc are the DC-bus capacitor and resistance, respectively.

• Conversion stage: it represents all converters used to adapt the inputs to the output. Each power source is attached to DC-DC power converter with respect to source type, i.e., the fuel cell is connected to 1-quadrant which allows power flow in one direction, whereas battery and supercapacitor are connected to 2-quadrant converters that are able to charge/discharge the sources. All converters are connected in parallel to the output stage (load) Fig. 1. Averaged models are considered [START_REF] Bacha | Power Electronics Converters Modelling and Control : With Case Studies[END_REF], which leads to following equations:

               dI f c dt = 1 L f c [V f c -R f c I f c -V dc (1 -α f c )] dI sc dt = 1 L sc [V sc -R sc I sc -V dc α sc ] dI bat dt = 1 L bat [V bat -R bat I bat -V dc α bat ] (3)
where I f c , I bat , and I sc are the currents of fuel cell, battery, and supercapacitor sources, respectively. α f c , α bat , and α sc are the corresponding converter averaged duty ratios (averaged pulse-width-modulation control signals). V f c and V bat are fuel cell and battery voltages, respectively. L f c , L bat , L sc , R f c , R bat and R sc are the inductances and resistances of smoothing inductors for each power converter, respectively.

This conversion stage is treated separately from the paper problem. To this end, low level current-control loops are used to handle the dynamics represented in (3), as explained in Section 3.2.

The system (1),(2) may be rewritten in LPV form as follows:

ẋ = A • x + B 1 • w + B 2 (ρ) • u y = C • x + D • u (4)
where the state vector is

x = [V DC V 1 V 2 V 0 ] T , w = I Load is the load current which represents the disturbance input, u = [I f c I bat I sc ]
T is the control input vector composed of fuel cell, battery and supercapacitor currents, respectively, and

ρ = [ρ 1 ρ 2 ρ 3 ] T = [α f c α bat α sc ]
T is the varying parameter vector. Matrices in (4) are:

A =       -1 C dc R dc 0 0 0 0 -1 C1R1 0 0 0 0 -1 C2R2 0 0 0 0 0       B 1 =       -1 C dc 0 0 0       , B 2 =       1-ρ1 C dc ρ2 C dc ρ3 C dc 0 0 -1 C1 0 0 -1 C2 0 0 -1 C0       C = 1 0 0 0 0 1 1 1 , D = 0 0 0 0 0 -R 0
In the considered approach each parameter ρ i is assumed to be bounded by [0.1, 0.9] (this corresponds to the averaged duty ratio accepted variation from 10% to 90%). Each parameter is supposed to be independent from the other parameters.

FORMULATION OF THE CONTROL PROBLEM

CONTROL OBJECTIVES

This section summarizes the main goals of the proposed energy management system. Basically, some electrical constrains should be achieved with respect to power sources characteristics. The objectives are:

1. Keep the DC-bus voltage around 150V within an error of ±10% regardless of the load current variations.

2. Apply frequency separation to power sources, i.e., each power source supplies power with respect to its characteristic frequency according to Ragone's classification [START_REF] Kuperman | Battery/ultracapacitor hybrids for pulsed current loads: A review[END_REF]. This helps to protect the fuel cell and battery from harmful fast changes of load current. Frequency separation is achieved due to some suitable choice of weighting functions associated to H ∞ control design.

3. Maintain the supercapacitor state of charge (SOC) slowly around 50%, which allows to absorb/provide power to fulfil instantaneous load power demand.

4. Impose a desired steady-state behaviour for the rest of the power sources (fuel cell and battery) that corresponds to some desired power sharing between sources in steady state. This allows to operate the fuel cell at desired working point, e.g., which corresponds to maximum efficiency. Steady-state behaviour could be used to determine battery charging cycle for long term with respect to its type. Battery charging could be achieved by using the main power source (fuel cell).

The hierarchical control strategy proposed in this paper consists of two loops: the current control loops on a lower level, and the energy management strategy corresponding to the LP V /H ∞ control loop shown in Fig. 2.a. This latter loop provides references for the lower-level loop.

For sake of comparison, the block diagram of an energy management system using a PI-based filtering strategy is given in Fig. 2.b. It consists of a cascade structure where the DC-link voltage regulation controller provides total current reference, whose components obtained by appropriate filtering are sent as references for the sources' current control loops. The filters' types and their cut-off frequencies are chosen in an empirical way depending on the desired dynamic behaviour of the associated power source in regulating the DC-bus voltage. For each power source, the desired behaviour is related to reliability and exploitation constraints recommended by the manufacturer. Therefore in this application, the fuel cell current reference is obtained by using a low-pass filter, which leads to slow variation of fuel cell current, while the battery current is filtered by using a bandpass filter, and finally the supercapacitor current is filtered using a high-pass filter, thus corresponding to supercapacitor ability in providing a fast-variable contribution to DC-bus regulation.. A supercapacitor SOC controller is also present, which provides a low-frequency component current reference to the supercapacitor, thus allowing to keep the SOC slowly around a desired setpoint (50%).

Performances of the two strategies will be comparatively assessed by numerical simulation in Section 5.

CURRENT CONTROL LOOPS (LOWER-LEVEL CONTROL)

Each power source current must be controlled and prevented from exceeding admissible limits. Therefore, three classical PI controllers are used to control the converters' dynamics represented in [START_REF] Hannan | Analysis of multi-power sources energy management system for electric hybrid vehicle[END_REF]. These classical loops are designed [START_REF] Åström | PID Controllers: Theory, Design, and Tuning[END_REF] to be transparent to the outer level (have faster dynamics), and to satisfy tracking of all current references generated by LP V /H ∞ controller placed on the upper level (Fig.

LP V /H ∞ CONTROL DESIGN (UPPER-LEVEL CONTROL)

The LPV controller K(ρ) in Fig. 2.a should satisfy the performance requirements given in Section 3.1. The controller design is tackled in the H ∞ framework applied to LPV systems. The control design scheme is given in Fig. 3, where usual forms of the weighting functions are considered to represent the performance objectives, as explained below: 1. DC-bus voltage (V DC ) tracking: W eV dc is in charge to ensure both desired time response and acceptable tracking error range. To this end, a first-order weighting function is used.

2. Supercapacitor state of charge (SOC) regulation: a first-order function W eV sc is used to maintain supercapacitor state of charge (SOC) around 50%. Consequently, the supercapacitor's SOC is a direct image of its voltage V sc and can be calculated by using the following equation:

SOC = V sc -V sc,min V sc,max -V sc,min × 100%, (5)
where V sc,max is the maximum allowed supercapacitor's voltage corresponding to SOC=100% and V sc,min is the minimum allowed supercapacitor's voltage corresponding to SOC=0%. Note that V sc,min must be different from zero and it is decided regarding the minimum allowed voltage input for the supercapacitor DC-DC converter.

3. Power sources separation with respect to their characteristic frequencies: W uIf c , W uIbat and W uIsc shape the dynamic behaviour of current references of the fuel cell, the battery and the supercapacitor, respectively, according to some prespecified frequency ranges. Both W uIbat and W uIsc are chosen as fourth-order transfer functions in order to achieve better dynamic separation within narrow frequency range, while W uIf c is used in form of a first-order function.

4. Fuel cell and battery steady-state behaviours: W eI f c and W eI bat are used as constant values to determine fuel cell and battery long-term behaviours, respectively. In this way a desired steady-state power sharing can be imposed by using I f c steadystate and I batsteadystate exogenous inputs. According to Fig. 3, the considered control problem is to find an LPV controller K(ρ) that ensures the closed-loop stability for all parameter variations and satisfies

CONTROL DESIGN SOLUTION

In order to obtain a controller that meets the control objectives, a set of Linear Matrix Inequalities (LMI) is solved [START_REF] Scherer | Multiobjective output-feedback control via LMI optimization[END_REF] in the context of LP V /H ∞ control synthesis. The choice of weighting functions (associated to H ∞ control problem) is essential to meet frequency separation according to sources' characteristics. This is not a trivial process since there exist 19 parameters to be determined. Different approaches can be used in order to find a suitable parameter set such that heuristic methods, neural networks or some evolutionary algorithm. One of the most known class of evolutionary algorithms is genetic algorithms, which can be used to facilitate the weighting functions parameter choice in an automatic way. Because convergence to optimality is guaranteed, progress of iterations can be stopped when the solution is considered sufficiently good in relation to the predefined objective functions. An arbitrary stop criterion like maximum number of iterations may thus be used. Fig. 4.a shows the steps followed to find the LP V /H ∞ controller.

LPV/H ∞ CONTROLLER

System in (4) can be rewritten under a polytopic form with 2 3 = 8 vertices (since the parameter vector ρ has three bounded elements between [0.1,0.9]). The generalized LPV MIMO system is represented as following:

   ẋ z y    =    A B 1 B 2 (ρ) C 1 D 11 D 12 C 2 D 21 D 22       x w u    (6)
The polytopic approach [START_REF] Scherer | Multiobjective output-feedback control via LMI optimization[END_REF] is used to find the desired LP V /H ∞ controller. According to the methodology in the framework of quadratic stabilization described in [START_REF] Apkarian | Self-scheduled h ∞ control of linear parameter-varying systems: a design example[END_REF][START_REF] Do | Lpv modeling and control of semi-active dampers in automotive systems[END_REF], the problem is treated off line by solving a set of LMIs using Yalmip/Sedumi solver (convex optimisation using single Lyapunov function, i.e., quadratic stabilization) at each vertices of the polytope, which leads to vertex controllers

K i = A i B i C i D i with 1 ≤ i ≤ 8.
The LPV controller K(ρ) is computed on line as a convex combination of the vertices controllers K i as follows:

K(ρ) = 8 1 α i (ρ)K i (7)
with: where w i are the vertices of the polytope corresponding to the extreme values of the parameter vector ρ. C(w i ) j is the j th component of the vector C(w i ) defined as:

α i (ρ) = 3 j=1 |ρ j -C(w i ) j )| 3 j=1 ρ j -ρ j ) > 0, 8 1 α i = 1
C(w i ) j = ρ j if w i = ρ j ρ j otherwise
where in this application ρ j = max(ρ j ) = 0.9, ρ j = min(ρ j ) = 0.1

SELECTION OF WEIGHTING FUNCTIONS USING GENETIC ALGORITHMS

Genetic algorithms (GA) are used to find weighting functions' parameters used in LP V /H ∞ synthesis. As shown in Fig. 4.b, this method develops generations of parameters to satisfy desired criteria, where objective (cost) functions are required to be minimized in order to meet optimal performance [START_REF] Goldberg | Genetic algorithms and machine learning[END_REF][START_REF] Zitzler | SPEA2: Improving the strength Pareto evolutionary algorithm[END_REF]. In our case, the genetic algorithm minimizes two objective functions:

• Objective function 1 (closed-loop stability): certain combinations of weighting functions' parameters lead to no solution during H ∞ control optimization, this is considered as unstable generation. On the contrary, if good parameters are found the solution is stable by the nature of optimality process, and this cost function allows to search for more stable solution in the sense that the real parts of closed-loop eigenvalues are smaller than a certain desired value δ. Objective function 1 is expressed as:

min{f 1 = max i (Re(λ i )) < -δ : δ > 0} (8)
where Re(λ i ) is the real part of the closed-loop eigenvalue λ i .

• Objective function 2: this is used to ensure frequency splitting ability of weighting functions. It is based on minimizing the following criterion:

min f 2 = J 1 + J 2 + J 3 3 (9)
with

J 1 = I f c I load ∞,(ω1,ω2) I f c I load ∞ J 2 = 1 2 .
I bat I load ∞,(ω3,ω4)

I bat I load ∞ + 1 2 .
I bat I load ∞,(ω5,ω6)

I bat I load ∞
Figure 5: Frequency comparison between full-order and reduced-order vertex controllers.

J 3 = Isc I load ∞,(ω7,ω8) Isc I load ∞
where . ∞,(ωi,ωj ) is the H ∞ norm calculated within [ω i , ω j ] frequency interval. These criteria allow minimize the H ∞ -norm for each power source outside the desired working frequency interval of this source.

The criteria ( 8),( 9) guarantees an arbitrary imposed degree of closed-loop stability and allow to size a desired frequency separation between power sources according to requirements of each application. GA gives the following weighting functions used in LP V /H ∞ synthesis:

                                                       1 W eV dc = s + ω b • s/M s + ω b = s + 0.05 0.5363s + 500 1 W eI f c =3 1 W eI bat =1.9 1 W eV sc = s + ω b • s/M s + ω b = s + 0.0005 0.5263s + 0.05 1 W uI f c = • s + ω BC s + ω BC /M u = 0.9091s + 0.07 s + 0.0007 1 W uI bat = • s + ω BC s + ω BC /M × s + ω b • s/M + ω b 2 =
s 4 + 57.14s 3 + 816.3s 2 + 0.005714s + 10 -8 0.34s 4 + 0.01721s 3 + 2.858 × 10 -4 s 2 + 1.721 × 10 -6 s + 3.4 × 10 -9

1 W uI sc = • s + ω BC s + ω BC /M × s + ω b • s/M + ω b 2 = s 4 + 395s 3 + 3.

CONTROLLER ORDER REDUCTION

The full order LP V /H ∞ controller is a convex combination of eight controllers at the vertices of the polytope. Each of them is an LTI system with 18 states in its state-space representation. Model reduction is investigated in this work in order to reduce the complexity of the solution from practical implementation point of view. To this end, the MORE toolbox [START_REF] Poussot-Vassal | Introduction to MORE: A MOdel REduction toolbox[END_REF] is used to find a reduced-order model that fits the original controller for bounded frequency range. More precisely, Iterative SVD Tangential Krylov Algorithm (ISTIA) is applied on each vertex controller for a frequency range that contains all power sources characteristics, that is, for the whole bandwidth of the closed-loop system. The reduced-order vertex controllers are then found to be tenth-order dynamical systems. The controller's transfer matrix contains 12 transfer functions that correspond to 4 inputs and 3 outputs (Fig. 2.a). Fig. 5 shows frequency fitness between original and reduced-order controller for some input/output transfer functions, whereas some other terms vanish due to reduction process (they have negligible values).

The performance of the full order LP V /H ∞ controller is compared with that of the reduced-order one. To this end, the considered criterion is the cost function in [START_REF] Azib | Online energy management strategy of a hybrid fuel cell/battery/ultracapacitor vehicular power system[END_REF] and both H ∞ , and H 2 norms of the closed-loop system. The comparison is done using the maximum obtained values among all vertices of the polytope and shown in Table 1. One can notice that the values are close in view of the chosen criterion, even though the complexity is highly reduced.

SIMULATION

Numerical simulations are carried out using nonlinear electrical models for different system parts shown in Fig. 1, where all dynamics of DC-DC converters, fuel cell and battery are taken into consideration (12 differential equations in total). The detailed models of different system parts have been validated on real-world data, being thus considered sufficiently accurate to represent the system behaviour in a numerical simulation context, as reported in previous works [START_REF] Florescu | Adaptive frequency-separation-based energy management system for electric vehicles[END_REF][START_REF] Hernandez | A robust multivariable approach for hybrid fuel cell supercapacitor power generation system[END_REF]. IFSTTAR driving cycle [START_REF] Barlow | A reference book of driving cycles for use in the measurement of road vehicle emissions[END_REF] is chosen to prove the closed-loop system capability to cope with various driving modes and satisfy the required control objectives. This driving cycle is used next to represent the load demands in supporting a numerical-simulation comparison between the obtained reduced-order LPV controller and a base-line PI-based filtering strategy, as represented in Fig. 2.b.

IFSTTAR TEST

The IFSTTAR profile represents various driving conditions, i.e., acceleration, deceleration, fixed speed and full brake, which allow assessing performance of DC-bus voltage regulation and the way how the three sources are coordinated to satisfy the power demand. For this scenario, it is considered that load current is served exclusively by fuel cell in steady-state, hence no change demand for battery's SOC. For this reason, exogenous input references are fixed to I f c steady-state = I load 1-α f c and I batsteady-state = 0, respectively, where α f c corresponds to the imposed steady state.

This load profile is rich in frequency content and challenges the vehicle's power supply management system in a way corresponding to urban driving conditions (Fig. 6.a), where the DC-link current is an image of the vehicle speed. In the sequel, DC-link current is called load current for sake of simplicity.

The energy management system satisfy the control objectives as shown in Fig. 6, where the DC-bus voltage is well regulated at voltage reference 150 V within accepted tracking error of ±10% (Fig. 6.b). Power sources' currents are provided to the system the manner of fuel cell supplying average current and supercapacitor handling peak variations, while the battery provides the midrange current variations as shown in Fig. 6.d. In order to complete the analysis, the power spectral density of each source current is computed, then it is normalized with respect to the maximum power delivered by each source. According to Fig. 8.a, each power source is used in distinct frequency zone according to the criteria choice J 1 , J 2 and J 3 in genetic algorithm design (Section 4.2). Fuel cell is used in low-frequency range all the time, in contrast supercapacitor serves the relatively high-frequency load current variation, and finally battery is operated in between the other two sources. Another control objective is satisfied, where the supercapacitor state of charge is always kept within reasonable limits (avoiding extreme states, completely empty or completely full)(Fig. 6.c).

For sake of comparison, the PI-based filtering strategy shown in Fig. 2.b is also run in simulation. Note that it has a lot of parameters to be tuned manually; its cascade structure imposes in fact constraints on some of these parameters and prevents control objectives from being independently achieved. In particular, a relation between the imposed closed-loop bandwidth of the DC-link voltage regulation and filters' cut-off frequencies should a priori be set. Thus, a good combination of parameters for such strategy is difficult to be found while satisfying all control objectives. As clearly seen in Fig. 6.b, the filtering strategy fails to regulate the DC-bus voltage within the accepted tracking error, whereas it has good performance regarding the frequency separation between power sources, according to Fig. 8.b. Finally, there is no guarantee for the closedloop stability. Different from this approach, the proposed LPV MIMO control strategy finds automatically the appropriate parameters of weighting functions using a genetic algorithm procedure that takes into account all control objectives (Section 3.1).

In a broader sense, the proposed strategy is a generalized filtering strategy in a MIMO context, i.e., completed with certain degrees of freedom to meet a multitude of control goals, and optimized according to some user-defined criteria.

Important remark: The previous results are found using the reduced-order controller version (see Section 4.3). The original LP V /H ∞ controller leads to slightly better performance, but its practical implementation is more difficult because of its complexity.

Table 2 presents comparatively the values of the same optimization criteria as in Table 1, but this time for the reducedorder controller and for the filtering strategy, respectively. One can see that, manually parameter tuning without any systematic improvement or optimization approach makes the filtering strategy to performs worse.

STEADY-STATE TEST

Another simulation scenario is tested when the load has a step variation, in order to assess system steady-state behaviour. This scenario illustrates how the two proposed external inputs, I f c steadystate and I batsteadystate , determine the steady-state load sharing between fuel cell and battery. Negative battery current value can be used in order to charge it in long term.

This test is used in order to illustrate the 4 th control objective (Section 3.1). A simple simulation scenario is given here, where the external reference inputs define steady-state distribution of the fuel cell and the battery currents. Therefore, a constant load current is applied which permits to reach steady-state equilibrium. Two different distributions are used to satisfy same constant load current (35 A): α batsteadystate = -24.5A; this corresponds to 130% I load supplied by the fuel cell and -30% by the battery, meaning that the fuel cell is managed to supply load current and to charge the battery in the same time (Fig. 8.b). Fig. 8 shows the slowly varying I f c and I bat currents corresponding to the constant load. From an application point of view, these two external inputs are useful to impose a desired steady-state operating point. Note that there exists a slight tracking error which could be reduced by using more complex weighting functions W eI f c and W eI bat .

• I f c

CONCLUSION

In this paper, an energy management strategy based on multi-variable LP V /H ∞ control is presented. This approach allows to coordinate power sources of different types within off-grid applications. The studied system is based on three different kinds of power sources -fuel cell, battery and supercapacitor -on board of an electric vehicle. Current-controlled sources are connected in parallel with their associated DC-DC boost converters on a common DC-bus. The DC-bus voltage is regulated in spite of load power variations that represent the image of driving cycle. Fuel cell and battery are protected from sudden power variations in order to prolong their lives. Thus, each source is operated in the frequency range which best suits its characteristics as either high-energy-density or high-power-density source, according to Ragone's taxonomy. Therefore, fuel cell is managed to provide low-frequency current (mean power), supercapacitor provides/absorbs sudden variations in power demand, while battery operation is placed in between the other two sources. Frequency-separation requirements are cast into an optimization criterion used to guide computation of H ∞ weighting functions by means of a genetic algorithm. The LP V /H ∞ controller based on the polytopic approach guarantees the quadratic-stability of the closed-loop system for all parameter variations. A reduced-order version of the full-order controller is also presented, which is a valuable step to reduce complexity from a practical implementation point of view.

The parallel configuration and use of MIMO control strategy allow to generalize this concept to any system equipped with potentially any number of power sources. The proposed strategy is generic and results in a systematic way while guaranteeing stability and robustness performance for the entire operating range. The possibility of imposing a desired steady-state behaviour is another advantage. For example, fuel cell operation at the maximum-efficiency point may be allowed in this way, thus increasing the total system autonomy. Applying frequency separation protects the fuel cell and the battery from sudden variation in current demand; therefore these sources are operated in better conditions and this helps to prolong their lifetimes. Ageing models must be considered in future study to quantitatively assess the advantage of frequency separation on power source lifetime.

Nonlinear electrical system is simulated using the IFSTTAR standardized driving profile, whose frequency content is rich and allows to properly illustrate the frequency separation ability of the proposed approach. Numerical simulation results show good performance in meeting the vehicle's power demand according to the frequency-separation power sharing regime imposed by user, all by regulating the DC-bus voltage at a desired setpoint.

This work can be extended to smart-grid applications, wherever different technologies are used to supply and/or store energy. Therefore, generalization of the proposed power sharing control strategy within multi-source application potentially containing any number of power sources, can easily be envisaged. An experimental validation on a dedicated test bench is in progress in collaboration with Systèmes Et Transports (SET) Laboratory in Belfort, France.

Appendix

Figure 1 :

 1 Figure 1: Considered system structure.

  2.a). These current references are fuel cell current reference I f c * , battery current reference I bat * , and supercapacitor current reference I sc * . As consequence, we will consider in the sequel I f c * =I f c , I bat * =I bat and I sc * =I sc .

  (a) Global control block diagram using LPV strategy. (b) Control block diagram using a classical-PI-based filtering strategy.

Figure 2 :

 2 Figure 2: Different control strategies used to implement the energy management system: (a) the proposed LPV control diagram, (b) a classical-PI-based filtering strategy used for comparison.

Figure 3 :

 3 Figure 3: H∞ Robust control design block diagram.

e 2 w 2 <

 2 γ ∞ , where w is the exogenous input vector w = [V dc ref , I f c steadystate , I batsteadystate , V sc ref , I load ], and e is the controlled output vector e = [e 1 , e 2 , ..., e 7 ].

Figure 4 :

 4 Figure 4: LPV/H∞ controller design procedure.

  steadystate = 0.70 * 35 1-α f c steadystate = 81A and I batsteadystate = 0.30 * 35 α batsteadystate = 30A; this corresponds to 70%I load supplied by the fuel cell and 30% by the battery (Fig.8.a). • I f c steadystate = 1.30 * 35 1-α f c steadystate = 190A and I batsteadystate = -0.30 * 35

Figure 6 :

 6 Figure 6: Performance of the proposed reduced-order controller strategy compared to ordinary filtering strategy (shown in Fig.2.b) and corresponding to the IFSTTAR scenario.

  Normalized power spectral density of sources' currents corresponding to reduced-order LPV strategy Ifc Normalized-PSD Isc Normalized-PSD Ibat (b) Normalized power spectral density of sources' currents corresponding to filterring strategy

Figure 7 :

 7 Figure 7: Frequency-domain spectral analysis corresponding to: a) proposed reduced-order LPV controller, b) filtering strategy (shown in Fig.2.b) and corresponding to the IFSTTAR scenario.

  Both fuel cell and battery have positive currents while satisfying the load demand and corresponding to the desired current reference setpoints.

  Fuel cell has positive current while satisfying the load demand and charging the battery (negative current) corresponding to the desired current reference setpoints.

Figure 8 :

 8 Figure 8: Steady-state scenarii for both fuel cell and battery (as described in Section 5.2) corresponding to a step of 35 A in load current demand.

  907 × 10 4 s 2 + 1.185 × 10 4 s + 900 0.1413s 4 + 19.91s 3 + 709.5s 2 + 597.2s + 127.2

	(10)

Table 1 :

 1 The cost function represented in (9) with H 2 , H∞ Norms calculations for both reduced and full-order controllers.

		J 1	J 2	J 3	H 2	H ∞
	Full-order controller O(18)	0.362 0.762 0.645 59.555 0.090
	Reduced-order controller O(10) 0.371 0.794 0.624 59.082 1.099

Table 2 :

 2 A comparison between the reduced-order controller and the filtering strategy (shown in Fig.2.b) with respect to the cost function represented in[START_REF] Azib | Online energy management strategy of a hybrid fuel cell/battery/ultracapacitor vehicular power system[END_REF] with H 2 , H∞ Norms calculations.

		J 1	J 2	J 3	H 2	H ∞
	Reduced-order controller	0.371 0.794 0.624 59.082 1.099
	Compared filtering strategy 0.740 0.818 0.801 66.474 7.201

Table 3 :

 3 Electrical system parameters used for simulation results.

	Parameter	description	simulation value
	DC-bus
	V DC	DC-bus voltage	150 V
	C DC	DC-bus capacitor	2.0 × 10 -3 F
	R DC	DC-bus discharging resistor	10.0 × 10 +3 Ω
	Fuel cell
	L f c	Fuel cell converter's inductor	2.0 × 10 -3 H
	E 0	Fuel cell open-circuit voltage	50 V
	R m	Fuel cell model's resistor	7.63 × 10 -2 Ω
	R ta	Fuel cell model's resistor	2.0 × 10 -3 Ω
	R tc	Fuel cell model's resistor	4.72 × 10 -4 Ω
	C a	Fuel cell model's capacitor	2.12 × 10 -3 F
	C c	Fuel cell model's capacitor	2.12 × 10 -2 F
	Battery
	L bat	Battery converter's inductor	1.0 × 10 -3 H
	Q n	Initial SOC of battery	70 %
	C 1	Battery model's capacitor	2.92 × 10 -4 F
	R 1	Battery model's resistor	13.4 × 10 -3 Ω
	C 2	Battery model's capacitor	2.92 × 10 -4 F
	R 2	Battery model's resistor	13.4 × 10 -3 Ω
	Nominal V bat	The nominal battery's voltage	48 V
	Supercapacitor
	L sc	Supercapacitor converter's inductor	1.0 × 10 -3 H
	R s	Supercapacitor model's resistor	0.8 × 10 -3 Ω
	C 0	Supercapacitor model's capacitor	56.0 F
	C 1	Supercapacitor model's capacitor	1.0 F
	C 2	Supercapacitor model's capacitor	1.0 F
	R 1	Supercapacitor model's resistor	6.0 × 10 -4 Ω
	R 2	Supercapacitor model's resistor	4.5 × 10 -4 Ω
	V sc,max	Supercapacitor maximum voltage corresponds to SOC=100%	42 V
	V sc,min	Supercapacitor minimum voltage corresponds to SOC=0%	32 V
	PIs local control loops
	Kp f c , Ki f c	PI parameters used for fuel cell current control loop	0.5 , 0.1
	Kp bat , Ki bat	PI parameters used for battery current control loop	0.01 , 0.8
	Kp sc , Ki sc	PI parameters used for supercapacitor current control loop	0.01 , 0.4