Gabriela Demarchi
email: gabriela.demarchidias@inrae.fr

Julie Subervie
email: julie.subervie@inrae.fr

Fernando Palha Leite
email: fernando.leite@cenibra.com.br

Jean-Paul Laclau

Farmers' Preferences for Water-Saving Strategies in Brazilian Eucalypt Plantations *

Keywords: choice experiment, climate change, drought, water resources, adaptation, eucalyptus, Brazil

In a climate change context, changing temperature and precipitation pattern are expected to have strong impacts on Brazilian eucalyptus plantations. Implementing adaptive water-efficient management practices is thus becoming necessary to maintain high levels of productivity while preserving the water resources. This paper investigates the ability of eucalyptus farmers to modify their current silvicultural practices in order to adapt to drought in the near future. We ran a choice experiment in the state of Minas Gerais, among 80 eucalyptus producers, who were asked to choose from several management options associated with various financial supports. The results show that adaptation by reducing the length of the eucalyptus rotation proves to be by far the preferred option, despite the associated costs. On the contrary, reducing density appears to be the least chosen option by the respondents, which may suggest that they underestimate the benefits of this strategy. We moreover find a clear and relevant segmentation of farmers' choice behavior, the general preference for reducing the length of the eucalyptus rotation being driven by the most vulnerable farmers of the sample.

Introduction

The biophysical effects of climate change on natural and managed systems, agricultural productivity and food security are increasingly well-understood [START_REF] Ipcc | Climate Change 2014: Synthesis Report. Contribution of Working Groups I, II and III to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change[END_REF][START_REF] Moore | New science of climate change impacts on agriculture implies higher social cost of carbon[END_REF]. In many areas, management options for adaptation to climate change have already been developed. These adaptation measures include, for example, using scarce water resources more efficiently, developing drought-tolerant crops and choosing tree species and forestry practices that reduce vulnerability to storms and fires. Adaptation to climate change, however, requires the incorporation of this knowledge into management decisions [START_REF] Keenan | Climate change impacts and adaptation in forest management: a review[END_REF]. Several management options for adaptation in agriculture exist, but farmers differ in their individual preferences for time and risk as well as in the constraints they face. Adaptation in agriculture may therefore vary significantly across regions, depending on climatic, social, economic and institutional factors (Khanal2018; Below et al., 2012;Deressa et al., 2009).

How will farmers adapt to the effects of climate change in the near future thus remains hard to predict.

Several studies have explored the steps that farmers' can take in adapting to climate change [START_REF] Chen | Policy support, social capital, and farmers' adaptation to drought in China[END_REF]Deressa et al., 2009;[START_REF] Seo | Measuring impacts and adaptations to climate change: a structural Ricardian model of African livestock management[END_REF][START_REF] Alam | Influence of institutional access and social capital on adaptation decision: Empirical evidence from hazard-prone rural households in Bangladesh[END_REF][START_REF] Alauddin | Climate change and farm-level adaptation decisions and strategies in drought-prone and groundwater-depleted areas of Bangladesh: an empirical investigation[END_REF][START_REF] Ngigi | Gender Differences in Climate Change Adaptation Strategies and Participation in Group-based Approaches: An Intra-household Analysis From Rural Kenya[END_REF]. Most have analysed the determinants of adaptation decisions by comparing the characteristics of adapters and non-adapters. For example, Deressa et al. (2009) found that household characteristics and access to agricultural extension and credit can influence farmers' adaptation decisions in the Ethiopian context. A number of studies have analysed the impact of adaptation on crop yields (Deressa and Hassan, 2009;[START_REF] Di Falco | Does Adaptation to Climate Change Provide Food Security? A Micro-Perspective from Ethiopia[END_REF][START_REF] Di Falco | Estimating the Impact of Climate Change on Agriculture in Low-Income Countries: Household Level Evidence from the Nile Basin, Ethiopia[END_REF][START_REF] Huang | Farmers' Adaptation to Extreme Weather Events through Farm Management and Its Impacts on the Mean and Risk of Rice Yield in China[END_REF][START_REF] Khanal | Farmers' Adaptation to Climate Change, Its Determinants and Impacts on Rice Yield in Nepal[END_REF]. Although a growing number of studies employ choice experiments to estimate farmers' willingness to provide ecosystem services (see [START_REF] Kaczan | Designing a payments for ecosystem services (PES) program to reduce deforestation in Tanzania: An assessment of payment approaches[END_REF] and references therein), there exist few ex-ante evaluations of the ability of farmers to adapt to climate change. Such evaluations would assess farmers' willingness to adopt new agricultural strategies that sometimes require drastic changes in forest or crop management. This study aims to fill this gap by conducting a choice experiment on a sample of Brazilian managers of eucalypt plantations who were asked to choose among several climate change adaptation strategies on eucalypt plantations. 1Eucalypt is a prime source of low-cost woody biomass, which explains its popularity among both industrial firms and smallholders. Like many plants, however, drought is a major risk for eucalypt plantations in a context of climate change. In the Brazilian state of Mi-nas Gerais, recent droughts have caused significant loss of yields and tree mortality in highly productive eucalypt plantations [START_REF] Gonçalves | Eucalypt plantation management in regions with water stress[END_REF]. The sustainability of eucalypt plantations is now threatened by high water demand2 and the absorptive capacity of the fastgrowing genotypes that are increasingly used. In some areas, silvicultural practices also affect the availability of water, and consequently tree growth [START_REF] Gonçalves | Assessing the effects of early silvicultural management on long-term site productivity of fast-growing eucalypt plantations: the Brazilian experience[END_REF][START_REF] Gonçalves | Eucalypt plantation management in regions with water stress[END_REF]. In this study, we investigate what would be the adaptation strategies chosen by smallholder farmers who would have to deal with the consequences of climate change. Governments may intervene in this choice for at least two reasons. First, eucalypt plantations are intensive fast-wood plantations and the way they are managed may have negative effects on water resources. As in any standard negative externality problem, the social planner may want to subsidize the most water efficient strategies. For that reason, improving water use efficiency by adopting appropriate forest management practices has become a key challenge in ensuring ecologically sustainable levels of productivity [START_REF] Booth | Eucalypt plantations and climate change[END_REF]. Second, eucalypt plantations have an important role in the Brazilian economy. Since climate change threatens the development of this sector, the government may want to support farmersâ adaptation to climate change by subsidizing the switch to the most profitable adaptation strategies. Our study aims at studying farmers' preferences for water-saving strategies in Brazilian eucalypt plantations to avoid mortality during prolonged droughts. We ran a choice experiment (CE) among 80 eucalypt growers who were asked to choose from several hypothetical adaptation strategies, defined as a combination of attributes. Each strategy was represented as a forest management option in which they received monetary compensation for implementing specific practices on their farm. We examined growers' preferences for five different options that have been identified in the literature as promising strategies for reducing the susceptibility of trees to drought while maintaining either the same or slightly diminished yields. These options include: reducing the cutting cycle, adopting new hybrid plants, reducing tree density, reducing the use of fertilizers, and coppicing. In our framework, a respondent who chooses to adapt to climate change opts for one of these forest management options, may also receive (in addition to a financial support) free technical assistance to help him implement the proposed system and a weather insurance subsidized at 50 percent.

The way in which farmers choose between several different adaptation strategies, each with varying levels of individual attributes, is used to quantify their preferences for these attributes, as well as to quantify overall willingness to accept (WTA) values, i.e. the amount of money an average grower would require in order to adapt to climate change. We analyze the data following the same approach as Gevrek and Uyduranoglu (2015); [START_REF] Lienhoop | Agri-environmental policy valuation: Farmers' contract design preferences for afforestation schemes[END_REF]; [START_REF] Broch | Farmers' willingness to provide ecosystem services and effects of their spatial distribution[END_REF] and other recent studies. We use a mixed logit model, which allows for heterogeneity in growers' tastes. We moreover study the extent to which the socioeconomic and structural farm characteristics of the respondents may influence their answers using a latent class model. Altogether, our results indicate that respondents tend to overvalue both free technical assistance and subsidized insurance. Moreover, the strategy based on the reduction of the cutting cycle appears to be by far the preferred option, while the reduction of plantation density is the least selected option. In between these two options, the respondents appear to equally value the reduction of fertilizer, the introduction of hybrid plants and coppicing.

We also find that growers' preferences are highly heterogeneous and that the strongest preferences for reducing the cutting cycle are held by the most vulnerable farmers in the sample.

The remainder of this article is organized as follows. We first provide background information on the Brazilian eucalypt plantations and the possible management options for adaptation to climate change in Section 2. We present the methodology and the data used in Section 3. Thereafter we present the results of the analysis in Section 4 and discuss them in Section 5. Section 6 concludes.

Brazilian eucalypt plantations and climate change

Background

Cultivation of eucalypt trees began in the 19th century and spread throughout the next century as the most planted genus of broadleaf trees in the world. Today eucalypt plantations are spread over more than 20 million hectares around the world [START_REF] Booth | Eucalypt plantations and climate change[END_REF]. Extensive cultivation of this genus beyond its natural range began in the early 20th century in Brazil (FAO, 2011). Over the past decades, it has expanded rapidly in Brazil, mainly replacing degraded pastures [START_REF] Smethurst | Stream flow unaffected by Eucalyptus plantation harvesting implicates water use by the native forest streamside reserve[END_REF]. Nowadays, eucalypt is the primary and most productive planted forest in Brazil, covering around 5.6 million hectares [START_REF] Iba | Relatorio Anual IBA[END_REF]. Of all eucalypt plantations in Brazil, more than one-third belongs to companies in the pulp and paper sector. Independent farmers and farmers in outgrower schemes3 hold the second largest share of planted forests in Brazil (IBA, 2016). Short rotation eucalypt crops are a significant source of raw material for the pulp and paper industry in Brazil, and these plantations have been mostly established in areas where the climate favours high yields [START_REF] Gonçalves | Integrating genetic and silvicultural strategies to minimize abiotic and biotic constraints in Brazilian eucalypt plantations[END_REF]. In addition to their private plantations, timber-based companies encourage the establishment of new plantations through outgrower programs. In these programs, companies typically provide seedlings, cuttings, and other inputs in exchange for being given priority when purchasing wood after the harvest [START_REF] Rode | The economics and optimal management regimes of eucalyptus plantations: A case study of forestry outgrower schemes in Brazil[END_REF]. These contracts encourage farmers to consider cultivation of eucalypt as a complement to their agricultural income.

Plantation management options for adaptation to drought

Eucalypt plantations are predominantly clonally propagated due to the ability of the plant to adapt to regions with low to moderate water scarcity and low fertility soils [START_REF] Gonçalves | Assessing the effects of early silvicultural management on long-term site productivity of fast-growing eucalypt plantations: the Brazilian experience[END_REF]. The largest Brazilian plantations are found in the Central-West and Southeastern regions of the country, particularly in the states of Minas Gerais (containing 24 percent of the total area of planted eucalypt), Sao Paulo (17 percent) and Mato Grosso do Sul (15 percent) [START_REF] Iba | Relatorio Anual IBA[END_REF]. These clonal forests have been largely established on sites with water and nutrient restrictions, where they out-perform conventional seed-based silviculture. In a climate change scenario, however, the sustainability of these plantations is threatened. In this study, we focus on several potential management options, which are built based on results of a number of recent studies [START_REF] Christina | Importance of deep water uptake in tropical eucalypt forest[END_REF][START_REF] Battie-Laclau | Potassium fertilization increases water-use efficiency for stem biomass production without affecting intrinsic water-use efficiency in Eucalyptus grandis plantations[END_REF][START_REF] White | Managing for water-use efficient wood production in Eucalyptus globulus plantations[END_REF][START_REF] Matusick | Sudden forest canopy collapse corresponding with extreme drought and heat in a mediterranean-type eucalypt forest in southwestern Australia[END_REF]. We explored the agronomic literature in order to determine the most relevant adaptation strategies in the Brazilian context. We then inserted these strategies into an socio-economic framework allowing us to assess not only farmers' preferences for these strategies, but also the potential levers to guide these choices (monetary and non-monetary rewards), and the factors likely to explain the heterogeneity of these choices (the characteristics of the farmers themselves). In order to reduce the risks of tree susceptibility to drought resulting from climate change, several silvicultural systems for eucalypt production are currently under development. Management options to reduce the risk of tree mortality during exceptional droughts, however, have some disadvantages compared to current silvicultural practices. In particular, a loss of productivity may occur compared to the most productive clone, planted with a high stocking density and highly fertilized. Five silvicultural systems appear promising for reducing the risk of tree susceptibility to drought while either maintaining or slightly diminishing yields.

The Short Rotation (SR) option: This production system consists in reducing the length of the cutting cycle from 7 years (the current practice in our study area) to 4 years. Previous studies indeed show that an increase in the frequency of clearcutting would make it possible to store water in deeper soil layers over a greater proportion of the rotation [START_REF] Christina | Importance of deep water uptake in tropical eucalypt forest[END_REF]. As [START_REF] Stape | The Brazil Eucalyptus Potential Productivity Project: Influence of water, nutrients and stand uniformity on wood production[END_REF] showed, reducing the cutting cycle from 6 years to 4 years would not affect the mean annual increment (MAI). The main constraint to the farmers under this system is the higher frequency of harvesting operations, which implies increased total harvesting and replanting costs.

The New Hybrid (NH) option: This option consists in adopting new hybrid eucalypt trees that are more tolerant to drought, instead of the highly productive clones currently used.

Although these hybrids are less productive, they have a greater water use efficiency rate that reduces water use and tree mortality [START_REF] Booth | Eucalypt plantations and climate change[END_REF]. Therefore, the loss of MAI in this system compared to the most productive clones currently planted will depend on the expected risk of mortality during an exceptional drought period.

The Reduced Density (RD) option:This option consists in reducing the density of trees planted, switching from one tree per area of 3 meters by 3 meter to one tree per area of 3 meters by 4 meters. This would decrease tree stand evapotranspiration and competition for water resources [START_REF] White | Managing productivity and drought risk in Eucalyptus globulus plantations in south-western Australia[END_REF][START_REF] White | Managing for water-use efficient wood production in Eucalyptus globulus plantations[END_REF]. However, a decrease in leaf area is needed to reduce tree stand transpiration, which may slightly decrease the productivity.

The Reduced Fertilization (RF) option: This option consists in a reduction of fertilizer doses. Previous studies have pointed out that this strategy can diminish tree mortality risk in the event of extreme droughts, as a consequence of lower leaf areas (Battie- [START_REF] Battie-Laclau | Potassium fertilization increases water-use efficiency for stem biomass production without affecting intrinsic water-use efficiency in Eucalyptus grandis plantations[END_REF]. Additionally, the water stored in the deep soil layers during the rainy season is withdrawn early in the dry season in fertilized plantations, leading to greater water deficit, while unfertilized stands use the water more slowly, making more water available during the rest of the season [START_REF] Christina | Simulating the effects of different potassium and water supply regimes on soil water content and water table depth over a rotation of a tropical Eucalyptus grandis plantation[END_REF][START_REF] White | Managing for water-use efficient wood production in Eucalyptus globulus plantations[END_REF].

The Coppice Management (CM) option:

This option consists in coppicing, which enables already-established roots to access to water at great depths [START_REF] Laclau | Dynamics of soil exploration by fine roots down to a depth of 10 m throughout the entire rotation in Eucalyptus grandis plantations[END_REF][START_REF] Germon | Consequences of clear-cutting and drought on fine root dynamics down to 17m in coppice-managed eucalypt plantations[END_REF]. Coppicing after the first rotation is a common option in Brazilian eucalypt plantations. An average loss of 5 percent on MAI is expected under this option [START_REF] De Souza | Growth of intact plants and coppice in short rotation eucalypt plantations[END_REF]. In the field experiment presented below, these five management options are included in the strategies used for climate change adaptation.

Methodology and Materials

Statistical Models

We use the framework provided by Revelt and Train (1998), in which a sample of N respondents have the choice of J alternatives (strategies for climate change adaptation here) on T choice occasions. A farmer is assumed to choose an adaptation strategy if the utility from choosing that alternative is greater than choosing either no adaptation or any of the competing choices. The utility that farmer n gets from choosing alternative j is given by U nj = β n x nj + nj , where β n is a vector of individual-specific coefficients, x nj is a vector of observed attributes relating to individual n and alternative j , and nj is a random term. The probability that farmer n chooses alternative k is:

P nk = P (U nk > U nj ) = P ( nk -nj < β n x nk -β n x nj )∀k = j
Different discrete choice models are obtained from different assumptions about the distribution of the random terms . We first use a mixed logit model. 4 We assume that all the parameters, except the monetary attribute, follow a normal distribution. Our models also include an alternative specific constant (ASC) taking the value of one if the status quo alternative describing the current situation is chosen and zero otherwise [START_REF] Adamowicz | Stated Preference Approaches for Measuring Passive Use Values: Choice Experiments and Contingent Valuation[END_REF][START_REF] Scarpa | Applications of Simulation Methods in Environmental and Resource Economics[END_REF]. As β n is unknown, the unconditional probability for a sequence of choices d can be expressed by integrating over all values of β weighted by the density of its distribution, denoted f (β|θ), where θ are the parameters of the distribution:

S MXL n = T t =1 J j =1   exp(x njt β) J j =1 exp(x njt β)   y njt f (β|θ)d β
where y njt = 1 if the respondent chooses j in situation t and zero otherwise. The log likelihood for the model is given by LL(θ) = N n=1 ln P n (θ). This expression cannot be solved analytically, and it is therefore approximated using simulation methods. We estimate this model by employing maximum simulated likelihood using 500 Halton draws [START_REF] Hole | Fitting mixed logit models by using maximum simulated likelihood[END_REF].

Since the monetary attribute is assumed to be a fixed parameter in our model, we have the convenient result that the willingness-to-accept (WTA) attribute k, i.e. the average value the respondents put on attribute k, all other things being equal, is:

E (WTA k ) = - E (β k ) β money
where β money is the coefficient of the monetary attribute.

We then use a latent class model in order to provide some insights regarding the heterogeneity of farmers' preferences -if there is indeed any according to the results of the mixed logit model -and the importance of their characteristics in the decision-making process regarding climate adaptation practices. In this case, each respondent is assumed to belong to a class q, where preferences vary across, but not within classes. In this case, the probability of a particular sequence of choices is:

S LC n = Q q=1 H nq T t =1 J j =1   exp(x njt β) J j =1 exp(x njt β)   y njt
where H nq is the probability of belonging to class q. The log-likelihood for this model is LL = N n=1 ln S n . We maximise this expression using the expectation-maximization algorithm.

Design of the Choice Experiment

The selection of attributes for the study was based on a review of existing relevant literature on current agricultural and environmental policies and discussion groups involving scientists as well as Brazilian forest managers who participated in the project. The four attributes and their corresponding levels are presented in Table 1. The adaptation strategies are characterized by four attributes: a silvicultural management option, some level of monetary compensation, a weather insurance scheme that is 50 percent subsidized and the provision of free technical assistance to help the farmer implement the management option proposed.

The silvicultural management attribute consists of five levels, namely the five management options designed to reduce the risks of tree susceptibility to drought in a context of climate change: reducing the cutting cycle, adopting new hybrid plants, reducing the tree density, reducing of the use of fertilizers, and coppicing the trees (see Section 2.2). In our model, reducing tree density is the reference level of the silvicultural management attribute.

The level of monetary compensation, the attribute used to estimate the implicit values of the other attributes, was defined so as to be realistic for respondents. The starting point here was identifying a payment level that was in line with expected wood production losses when adopting one of the water-efficient management systems. We calculated that a loss in productivity of three cubic meters per hectare per year would cost about 100 Brazilian reais (BRL) The design moreover includes two non-cash reward attributes: the provision of a free technical assistance and a 50 percent subsidized weather insurance. It is generally assumed that the presence of a technical expert -also called agricultural extension in the literature -is likely to promote significant changes in farming practices and more effectively in the early stages of the process dissemination of the new technology, new practice or new system sought to be adopted [START_REF] Anderson | Agricultural extension[END_REF]. This is the reason why a number of recent studies from the farmer choice experiment literature include technical assistance as an ing the potential to reduce vulnerability of agricultural systems to climate-related risks to farm-level production, infrastructure and income [START_REF] Smit | Adaptation options in agriculture to climate change: a typology[END_REF]. This instrument seems less often offered than technical assistance as an attribute in the choice experiment literature, probably because it is not available in all contexts. However, a number of recent papers in the choice experiment literature have considered it as one of the more viable income smoothing strategies [START_REF] Prasada | Climate-Indexed Insurance as a Climate Service to Drought-Prone Farmers: Evidence from a Discrete Choice Experiment in Sri Lanka[END_REF] and references herein).

We followed a D-efficient design approach to construct the choice sets, using prior in-formation we had about the sign and relative values of the design attributes. 5 We used secondary data to construct prior values for the true parameters of the model. The value chosen for technical assistance was 600 BRL, which is the average price for hiring a specialist for one day in Minas Gerais region. The value chosen for weather insurance was 175 BRL for insuring one hectare of eucalypt plantation (after the 50 percent subsidy) and 35 BRL for the value of the equivalent of one meter cubic of wood.

The design was generated with the software package Ngene in order to produce 10 choice sets per respondent. In our study, a choice set consists of two alternative adaptation strategies and an option to decline both strategies (the status quo option). An example of a choice set is displayed in Figure 2.

Data

We collected original data from a total of 80 out-grower farmers 6 living in the state of Minas Gerais. In practice, we had access to the registry database of all the farmers enrolled in the contract-farming scheme of CENIBRA, an eucalypt pulp and paper company located in Ipatinga, on the eastern part of Rio Doce basin (Figure 1). There were several hundreds of farmers likely to participate in the experiment. Given the financial constraints of the research project, we targeted 200 of them, focusing on their geographic location so that we have respondents from all the different zones of the study area. After contacting them by phone, we ended up with 80 farmers who agreed to participate in the experiment.

In order to ensure that respondents would fully understand the questions and concepts used in the CE, the questionnaire was pre-tested with technical assistants from CENIBRA, who interacted frequently with the out-grower farmers. 7 The respondents had a 30-minute information session regarding the attributes and levels before beginning the survey. The monetary compensation levels were not mentioned, since it could result in anchoring at the highest offer. 8 A brief description of the choice task was provided to each respondent be-5 Efficient experimental designs can reduce confidence intervals for parameters of interest in choice models, or alternatively reduce required sample sizes. Informed priors can then be useful when trying to make strong inferences from small amounts of data, since these priors capture any assumptions the researcher makes about model parameters before observing the data [START_REF] Kruschke | Bayesian data analysis for newcomers[END_REF]. 6 According to the FAO, a contractual partnership between growers or landholders and a company for the production of commercial forest products. Out-grower schemes or partnerships vary considerably in the extent to which inputs, costs, risks and benefits are shared between growers/landholders and companies. Partnerships may be short or long-term (eg. 40 years), and may offer growers only financial benefits or a wider range of benefits. Also, growers may act individually or as a group in partnership with a company, and use private or communal land. Out-grower schemes are usually prescribed in formal contracts. 7 CENIBRA did not participate in the design of the choice experiment. But they provided access to the pool of potential participants and guided the sampling so that it is representative in terms of geographic areas. 8 The monetary compensation levels were not revealed during the 30-minute briefing that took place prior to the choice experiment, but of course they did appear explicitly on the choice cards. More precisely, the attribute of monetary compensation was presented during the information session through the following sentence: The fore each choice set. We moreover provided plausible values for average annual incremental loss for each scenario, based on expert estimates. 9 The participants first answered survey questions about themselves, their farm and their environmental perceptions, and then participated in the CE. Data collection took place between March and April 2017 through faceto-face interviews.

Descriptive statistics of the farms owned or managed by the survey respondents as well as their main socioeconomic characteristics are shown in Table 2. The sample is mainly composed of male growers, who have on average three household members, a secondary education and less than 15 years' worth of experience growing eucalypt. The majority of farmers interviewed grew eucalypt as a complementary source of revenue (less than 30 percent of their income). Less than seven percent of the sample has a plantation insurance that covers for fire and other weather-related damages. The average farm size is around 200 ha and the mean area of eucalypt plantations is around 90 ha (the median is 65 ha).

We find, however, that these figures mask a high level of heterogeneity. The interviewed farmers are spatially distributed into four distinct geographic zones (see Table 3). The zone near the municipality of Belo Oriente is characterized by the greatest climatic constraints and can be considered the zone that is most vulnerable to climate-change in our study. The main constraints in this region are: higher water deficit, lower altitude and smaller precipitation volumes, compared to other zones. 10 These characteristics explain the lower MAI among the sample in this region. Since these plantations are located in the vicinity of CENI-BRA's pulp mill, however, growing eucalypt in these areas remains economically viable for the time being. In contrast, plantations located in the area near the municipality of Cocais and Pecanha are characterized by the highest MAI rates, as a result of the greater annual precipitation levels, a higher altitude and soils with suitable properties to grow eucalypt trees.

Despite the fact that Pecanha is one of the most distantly located plantations, eucalypt cultivation in this area remains viable. Caratinga is characterized by a moderate MAI due to its climatic and topographical conditions and is located on an intermediate distance from

CENIBRA pulp mill. Although participants in the study were not randomly selected, our third proposed compensation consists of the remuneration of an amount per hectare that takes into account losses in productivity without mentioning the values per hectare. The participants discovered the values only when starting the choice experiment. 9 When presenting the choice experiment, we informed the participants various consequences of climate change, including loss of yields and tree mortality, through simple diagrams showing the relative advantages of the different adaptation strategies proposed. In particular, we ranked the proposed management options according to the likely loss in MAI: 1) SR option (no loss), 2) CM option, 3) RD and RF options, and 4) NH option (highest loss). We also clearly specified that the performance of these strategies was based solely on expert opinion and could not correspond to the reality that the farmer will face in the future. 10 The precipitation pattern in the basin is characterized by two distinct periods. The rainy period extends from October to March and precipitation in this period varies from 800 to 1300 mm. The dry period extends from April to September, with the most severe droughts occurring from June to August. Precipitation during the dry period ranges between 150 and 250 mm (Agência Nacional de Águas, 2010).

sample is quite representative of CENIBRA out-growers' dispersion in the country. 11

Results

In this section, we first provide the estimates of the mixed logit model parameters, along with the WTA estimates, and we discuss the apparent heterogeneity in farmers' preferences. We then turn to a latent class (LC) model in order to investigate to what extent heterogeneity in preferences is correlated with farmers' characteristics.

Mixed logit model

Our main results are displayed in Table 4. Consistent with economic theory, all reward-type attributes significantly increase the probability that farmers adapt to climate change. The coefficients of the cash payment variable, the free technical assistance variable and the subsidized insurance variable are statistically different from zero at the 1 percent level. From these coefficients, we calculate that 96 percent of farmers prefer adaptation strategies that provide free technical assistance and/or prefer subsidized insurance. These figures are given by 100 * Φ(β k /s k ) where Φ is the cumulative standard normal distribution, and β k and s k are the mean (Column 1) and standard deviation (Column 2), respectively, of the k th coefficient of the model.

Following [START_REF] Sheremet | Incentivising participation and spatial coordination in payment for ecosystem service schemes: forest disease control programs in Finland[END_REF], we moreover computed the simulated probabilities of adapting to climate change for the different management options (Figure 4). Although the levels shown in these graphs cannot be interpreted as such, especially because the adoption probabilities reported in choice experiments are generally overestimated [START_REF] List | What experimental protocol influence disparities between actual and hypothetical stated values?[END_REF], it is nonetheless interesting to note that an adaptation strategy that would include both technical assistance and weather insurance was the most likely to be accepted for any management option and cash payment, while a strategy that would offer none of these two non-cash rewards has the lowest chances to be chosen.

Regarding preferences about management options, our results suggest that farmers prefer adopting coppice management or shortening the cutting cycle rather than diminishing the plantation density (which is the reference management option in our model). We calculate from the estimated coefficients that 75 percent of farmers prefer adaptation strate- 11 We do not have quantitative data on those farmers who ultimately did not participate in the choice experiment. However, qualitative (informal) information collected from CENIBRA when the sample was drawn up suggests that the sample is representative in terms of zoning (the four geographical areas of CENIBRA farms are represented), but not in terms of farm size (participants in the survey are presumably larger on average than non-participants, according to CENIBRA staff). Moreover, as in any survey where respondents voluntarily choose to participate or not, we cannot exclude that participants differ from non-participants in terms of their allocation of leisure time or perhaps in terms of awareness of the likely impacts of climate change.

gies that involve a reduced cutting cycle and 69 percent prefer those that require coppice management (when confronting with diminishing the plantation density). Nevertheless, the WTA (Col 3) indicates that the farmers value reduced cutting cycles almost twice as much as coppicing: the average respondent is willing to receive 175 BRL to implement the density option instead of the cycle option, while he only requires 86 BRL to implement the density option instead of the coppice option. Finally, the results do not indicate any stronger (or lower) preference for the reduction of fertilizers or the adoption of drought-tolerant hybrids compared to the reference option. 12 Column 2 of Table 4 moreover suggests that there is significant heterogeneity in respondents' preferences for nearly all attributes of the proposed adaptation strategies. This is particularly the case for the two preferred management options -coppice and reduced cutting cycles -and for the ASC (alternative specific constant). As for the reduction of fertilizers, which is not significant on average, we find on the contrary that the standard deviation is statistically significant, suggesting that at least some respondents have stronger or lower preference for this management option. 13 .

In order to present this result about heterogeneity graphically, we estimate the individuallevel coefficients for each attribute using the approach suggested by [START_REF] Revelt | Customer-Specific Taste Parameters and Mixed Logit: Households' Choice of Electricity Supplier[END_REF] and using Stata software. The distribution of the individual-level coefficients associated with each management option for which β k and/or s k appear significant in Table 4 is displayed in Figure 3. In some cases, as for reduced cutting cycles and coppicing, the shape of the distribution of the coefficients suggests that we might have two different classes of farmers in our sample, which we investigate using a latent class model.

Latent Class model

The LC model provides an alternative approach to describing our data, in which farmers are expected to have different motivations and purposes for their respective choices regarding adaptation to climate change. To explore this possibility, the model assigns farmers to groups based on their preferences and other (latent) individual-specific variables. The LC model combines characteristics of the individual, such as socioeconomic characteristics with the 12 For the present study we opted for the practical solution to simply maximize the sample size given the research budget at hand, i.e., trying to overpower the study as much as possible (de [START_REF] De Bekker-Grob | Sample size requirements for discrete-choice experiments in healthcare: a practical guide[END_REF]. However, a limited sample size, like the one in our study, prevents detection of small effects. This is possibly the reason why we were not able to detect any effect for two adaptation options using the mixed logit model (the New Hybrid strategy and the Reduced Fertilization strategy). A consequence of this is that no conclusions should be drawn from insignificant results. 13 The fact that the standard errors are significant for most variables indicates that the Mixed logit model fits well with the presented data. As a robustness check we however ran the most standard Conditional logit model. Same results hold on the average estimates. They are displayed in supplementary material, as well as alternative mixed logit models, assuming the price to be a random parameter and using different probability density functions for the distribution of coefficients.

stated behavior in the choice sets [START_REF] Beck | Environmental attitudes and emissions charging: An example of policy implications for vehicle choice[END_REF]. Preferences are presumed to be homogeneous within each latent class but different between classes [START_REF] Colombo | Modeling preference heterogeneity in stated choice data: an analysis for public goods generated by agriculture[END_REF]. In this model, we focus on a selection of individual characteristics about the farmers and their farm [START_REF] Wilson | Factors influencing farmer participation in the environmentally sensitive areas scheme[END_REF][START_REF] Vanslembrouck | Determinants of the Willingness of Belgian Farmers to Participate in Agri-environmental Measures[END_REF][START_REF] Horne | Forest owners' acceptance of incentive based policy instruments in forest biodiversity conservation -A choice experiment based approach[END_REF][START_REF] Ruto | Investigating farmers' preferences for the design of agrienvironment schemes: a choice experiment approach[END_REF], as well as geographical features (Espinosa-Goded, [START_REF] Espinosa-Goded | What Do Farmers Want From Agri-Environmental Scheme Design? A Choice Experiment Approach[END_REF][START_REF] Broch | Farmers' willingness to provide ecosystem services and effects of their spatial distribution[END_REF].

We select the optimal number of latent classes in a model using the Bayesian information criterion (BIC) and the Akaike information criterion (AIC), both of which pointing to a two-class model (Table 5). Our main results are displayed in Table 6. The smaller class (21 percent of the sample) is mainly comprised of male farmers who engage in cattle ranching activity as their main source of revenue and possess large eucalypt plantations. These farmers are heavily dependent on the income from these plantations and are located in a region considered to be more sensitive to climate change (Table 3).

Results displayed in the upper part of Table 6 call for four comments. First, while both groups exhibit a strong (and comparable in magnitude) preference for the technical assistance attribute, insurance does not seem to play a decisive role anywhere other than in Class 1 (though this result lacks precision). Second, although preferences for the coppice option appears significant in both groups, they are stronger in Class 1. Third, the reduced cutting cycle option now appears to be the preferred option for Class 1 only and not Class 2.

Finally, the significant ASC in Class 1 suggests that a status quo effect occurs, the positive sign of the coefficient indicating that moving away from the current situation may have a negative effect on respondents' decisions to opt for adaptation in Class 1.14 Such an effect does not appear in Class 2.15

Discussion

Although the results of this study cannot be generalized, our findings enable us to identify three main takeaways.

Farmers' valuation of reward attributes

First, we found that farmers particularly value adaptation strategies based on free technical assistance and/or subsidized weather insurance. This result is consistent with results provided in previous studies conducted in other contexts [START_REF] Abebe | Contract farming configuration: Smallholders' preferences for contract design attributes[END_REF][START_REF] Andow | Heterogeneity in intention to adopt organic strawberry production practices among producers in the Federal District, Brazil[END_REF][START_REF] Minten | Global retail chains and poor farmers: Evidence from Madagascar[END_REF][START_REF] Kuhfuss | Nudging farmers to enrol land into agri-environmental schemes: the role of a collective bonus[END_REF][START_REF] Vignola | Negotiation analysis for mechanisms to deliver ecosystem services: The case of soil conservation in Costa Rica[END_REF][START_REF] Prasada | Climate-Indexed Insurance as a Climate Service to Drought-Prone Farmers: Evidence from a Discrete Choice Experiment in Sri Lanka[END_REF]. When confronting the values that respondents place on technical assistance and subsidized weather insurance with market prices, we can conclude that farmers tend to overestimate the value of both of these attributes. Indeed, a subsidized weather insurance incentive has a market value of approximately 175 BRL per hectare per year, which is approximately 42 BRL lower than the WTA of the farmers who participated in this study (217 BRL). We also find that growers value technical assistance at nearly 149 BRL per hectare per year, while the average cost of technical assistance, considering the average 7 year cycle, is about 36 BRL per hectare per year [START_REF] Rode | The economics and optimal management regimes of eucalyptus plantations: A case study of forestry outgrower schemes in Brazil[END_REF]. This result makes sense given that Brazilian eucalypt producers tend to be unaware of the existence of this sort of insurance; in our sample for example, less than seven percent of farmers had an insurance policy (Table 2). Note also that respondents are not irrational when they value technical assistance and insurance. The analysis of the choice experience simply indicates that they place a monetary value on these attributes that is higher than the real cost which would be incurred by the implementation of these instruments in reality.

Farmers' valuation of management options

Second, we found that farmers highly value adaptation strategies that bring them money today rather than in the future (shortening the cutting cycle, typically). This result is consistent with the standard hypothesis that economic agents value the present more than the future [START_REF] Samuelson | A note on measurement of utility[END_REF]. It is also in line with findings from the behavioural economics literature, which suggests that individuals may have present-biased preferences [START_REF] Laibson | Golden eggs and hyperbolic discounting[END_REF][START_REF] Cohen | Measuring time preferences[END_REF]. Moreover, if the rotation is shorter, then the exposure to the risk of drought is reduced. Moreover, if the rotation is shorter, then the exposure to the risk of drought is reduced. Such preferences, however, could have environmental as well as economic consequences. First, increasing the frequency of clearcuts could result in soil compaction and an increase in nutrient exports since nutrient remobilizations decrease the concentrations in stemwood throughout the rotation [START_REF] Sette | Source-driven remobilizations of nutrients within stem wood in Eucalyptusgrandis plantations[END_REF]. Harvesting young trees could therefore increase soil nutrient depletion and the need for fertilizers to maintain high yields. Second, the quality of the wood obtained from young trees wood may not be optimal for cellulose production because wood density increases with tree aging [START_REF] Sette | Efeito da idade e posição de amostragem na densidade e características anatômicas da madeira de Eucalyptus grandis[END_REF].

Additionally, increasing the frequency of harvesting operations could raise the final cost of a meter cubic of wood.

The marked preference for the coppice strategy (the second most preferred option of respondents) can be explained by the fact that a number of farmers already know this management practice and possibly employ it at least partially. 16 In such a case, adopting this 16 Such information was collected in the field as part of the informal discussion with farmers.

strategy could be done without a significant decrease in income. Additionally, the possibility of multiple earnings from more rotations combined with the smaller cultivation costs can also make the eucalypt coppice system more economically attractive than alternative options [START_REF] Ribeiro | Manejo por talha dias: estabelecimento das idades otimas de corte[END_REF].

Another important finding of our study is the reluctance of farmers to decrease the plantation density to cope with prolonged drought periods, while this option is often highlighted by researchers in ecophysiology and silviculture [START_REF] Booth | Eucalypt plantations and climate change[END_REF][START_REF] Gonçalves | Eucalypt plantation management in regions with water stress[END_REF]. One plausible reason for this is that switching from one tree per area of 3 meters by 3 meters to one tree per area of 3 meters by 4 meters would mean replacing the usual 1,111 trees per hectare by 833 trees per hectare -a loss that farmers would overestimate. Moreover, this option has some drawbacks, like the time needed to reach canopy closure, which would increase the need for weeding during the early growth stage.

Heterogeneity in farmers' preferences

Third, we found that farmersâ preferences for adaptation strategies are heterogenous. Our results from the mixed logit model indeed suggest that respondentsâ preferences are heterogeneous for a number of attributes, which include not only the rewards but also the adaptation strategies themselves. Our results from the latent class model moreover suggest that adaptation to climate change remains a major concern mainly for the most vulnerable out-growers (named Class 1), while other farmers who are less dependent on income from eucalypt plantations exhibit much less concern about it (named Class 2). These results are consistent with that highlighted by previous choice experiments involving farmers exposed to climate change in other regions of the world [START_REF] Nthambi | Quantifying Loss of Benefits from Poor Governance of Climate Change Adaptation Projects: A Discrete Choice Experiment with Farmers in Kenya[END_REF][START_REF] Khanal | Influence of payment modes on farmersâ contribution to climate change adaptation: understanding differences using a choice experiment in Nepal[END_REF][START_REF] Schaafsma | Assessing smallholder preferences for incentivised climate-smart agriculture using a discrete choice experiment[END_REF] just to cite some recent ones). Our findings moreover suggest that adaptation policies should target the most vulnerable smallholders first [START_REF] Donatti | Vulnerability of smallholder farmers to climate change in Central America and Mexico: current knowledge and research gaps[END_REF], whether with the objective of supporting the standard of living of households that depend on the cultivation of eucalypt or with the objective of preserving water resources. This is because our analysis shows that this category of the population displays more marked preferences for the proposed adaptation strategies.

Conclusion

This paper reports the results of a CE study that investigates how eucalypt farmers arbitrate between changes in silvicultural management practices and the monetary compensation offered in exchange for adopting these practices. Our approach compares several innovative silvicultural strategies, as well as a variety of "rewards" (or support) for undertaking these strategies.

A mixed logit model and latent class model were used to analyse the CE data. When we analyse farmers' preferences as a whole, we find that adaptation to climate change is more likely to occur by reducing the eucalypt cutting cycle, since the majority of farmers have a predilection for this adaptation strategy. However, this practice could entail negative environmental and economic impacts. Furthermore, the farmers in our survey were shown to be extremely averse to reducing the density of eucalypt trees on their plantations. Since reducing tree density could be a more sustainable strategy than reducing the length of the cutting cycle, governmental, non-governmental or private bodies may want to consider supporting this practice. This, however, this can only be done at a high cost.

When we analyse heterogeneity in farmers' preferences for adaptation strategies, a twoclass model explained the observed choices and provided a clear segmentation between farmer types. We detected that both groups are likely to adapt to the upcoming global changes, but not in the same way. In particular, a small group of the most vulnerable farmers appear to drive the result on the preference to adapt to climate change by reducing the cutting cycle. These results suggest that a customized approach to payments for ecosystem services 17 would make sense in this context.

Lastly, this study is only looking at one part of the problem (that of Eucalypt farmers) and not that of society as a whole (which would then include water consumers or other types of farmers). It gives us clues about farmers' willingness to adopt the proposed silvicultural changes and provides information regarding the order of magnitude, in monetary terms, with which farmers value each strategy. Overall, our results suggest that adaptation may not require complex or expensive changes. However, management should consider the maintenance and provision of environmental services across the landscape. One direction for further research is to better understand the divergence between private and social optima and define strategies for climate change adaptation that assure long-term sustainability for the planted forest sector. 17 PES have been generally defined as transfers of resources between stakeholders in order to encourage the agreement between individual and/or collective land use with the public interest in the management of natural resources [START_REF] Muradian | Reconciling theory and practice: An alternative conceptual framework for understanding payments for environmental services[END_REF]. Note: These diagrams show that an adaptation strategy that includes both technical assistance and weather insurance is the most likely to be accepted for any management option and cash payment, while a strategy that offers none of these two non-cash rewards has the lowest chances to be chosen.

Figures and Tables

  attribute of the options offered to respondents and generally show a marked preference of farmers for this type of non-cash rewards[START_REF] Abebe | Contract farming configuration: Smallholders' preferences for contract design attributes[END_REF];[START_REF] Andow | Heterogeneity in intention to adopt organic strawberry production practices among producers in the Federal District, Brazil[END_REF];[START_REF] Minten | Global retail chains and poor farmers: Evidence from Madagascar[END_REF];[START_REF] Kuhfuss | Nudging farmers to enrol land into agri-environmental schemes: the role of a collective bonus[END_REF];[START_REF] Vignola | Negotiation analysis for mechanisms to deliver ecosystem services: The case of soil conservation in Costa Rica[END_REF] to name just a few examples). Private climate insurance has also been seen as hav-

Figure 1 :

 1 Figure 1: Location of the study area

Figure 4 :

 4 Figure 4: Simulated probabilities of adapting to climate change for different management options

Table 1 :

 1 Description of attributes and levels

	Levels
	Attribute

Table 3 :

 3 Description of geographic zones in the study area

	Zone	Precipitation Water deficit Altitude	Major agronomic crops
	Belo Oriente	1094 mm	459 mm	220 m	Pasture (mostly overgrazed)
	Cocais	1348 mm	137 mm	791 m	Eucalypt
	Caratinga	1175 mm	324 mm	578 m	Coffee and Pasture
	Pecanha	1171 mm	209 mm	780 m	Eucalypt and Pasture
	Source: CENIBRA

Table 4 :

 4 Mixed logit model estimates **, ** and * indicate that the estimated coefficients are statistically significant at the 1%, 5%, and 10% levels, respectively. Standard errors are given in parentheses. Last column gives the willingnessto-accept (WTA) estimates. Confidence intervals of WTA are given in parentheses.

	Attribute	Mean	Std.Dev.	WTA
	money	0.009 ***
		(0.001)
	assistance	1.298 ***	0.758 **	-149
		(0.227)	(0.313)	(-95; -175)
	insurance	1.890 ***	1.053 **	-217
		(0.706)	(0.485)	(-25; -274)
	fertilizer	0.187	1.050 ***
		(0.671)	(0.355)
	hybrid	0.460	-0.281
		(0.649)	(0.934)
	cycle	1.529 ***	2.306 ***	-175
		(0.475)	(0.492)	(-51; -279)
	coppice	0.750 ***	1.482 ***	-86
		(0.263)	(0.343)	(-30; -135)
	ASC	-0.471	2.255 ***
		(0.796)	(0.519)
	Log-likelihood			-475.60
	LR χ 2			81.95
	P-value			0.00
	Nb. of observations			2,400
	Notes: *

Eucalypt plantations are not forests in the sense in which it is understood in temperate zones, since the average rotation is around 6-7 years. It should be seen as closer to the cultivation of permanent crops in tropical zones, like coffee for example.

Previous studies have shown that water use by eucalypt plantations depends on the particular territory, environmental conditions and land-use practices employed[START_REF] Poore | The ecological effects of eucalyptus[END_REF][START_REF] Cornish | The effects of logging and forest regeneration on water yields in a moist eucalypt forest in New South Wales, Australia[END_REF][START_REF] Calder | Water use by forests, limits and controls[END_REF][START_REF] Almeida | Comparação entre uso de água em plantações de Eucalyptus grandis e floresta ombrófila densa (Mata Atlântica) na costa leste do Brasil[END_REF][START_REF] Hubbard | Effects of irrigation on water use and water use efficiency in two fast growing Eucalyptus plantations[END_REF][START_REF] Ferraz | Managing forest plantation landscapes for water conservation[END_REF][START_REF] De Barros Ferraz | Effects of Eucalyptus plantations on streamflow in Brazil: Moving beyond the water use debate[END_REF].

Outgrower schemes, also known as contract farming, are broadly defined as binding arrangements through which a firm ensures its supply of agricultural products by individual or groups of farmers(FAO, 2001).

The mixed logit model overcomes three drawbacks of the standard logit model by allowing for heterogeneity in tastes, correlation in unobserved factors over repeated choices made by each individual, and complete relaxation of the independence of irrelevant alternatives (IIA) assumption[START_REF] Train | Recreation Demand Models with Taste Differences over People[END_REF][START_REF] Greene | A latent class model for discrete choice analysis: contrasts with mixed logit[END_REF].

None of the 80 farmers who agreed to participate in the experiment opted for the status quo option in all cards.

These results can be found also using a mixed logit model that interacts farmersâ characteristics with attributes. Such a model is displayed in the supplementary material.

* Funding for this research was provided by the French National Research Agency (ANR-13-AGRO-0005). † French National Research Institute for Agriculture, Food and Environment (INRAE), Center for Environmental Economics of Montpellier (CEEM), for Agriculture, Food and Environment (INRAE), Center for Environ-


Benzaouia Soufyane
email: soufyane.benzaouia@gmail.com

Rabhi Abdelhamid

Zouggar Smail

M L Elhafyani

El Ahmed

Hajjaji

Fully Robust Sensorless Control of Direct-Drive PMSG Wind Turbine Feeding a Water Pumping System

Keywords: PMSG, PMDC, Centrifugal pump, Water pumping, Wind energy, P&O, MRAS observer, Fuzzy logic controller (FLC), Sliding mode controller (SMC), Variable gain super twisting algorithm

In this paper, we propose a fully sensorless control strategy that guarantees robustness and stability properties. The aim is to maximize the extracted power and to ensure an optimum control without mechanical sensors to reduce the cost. Firstly, a fuzzy logic technique has been used to estimate the wind speed information. Then an improved model reference based on adaptive sliding mode controller has been developed to estimate the permanent-magnet synchronous generator speed. The proposed control strategy includes two control loops, an outer control loop based on fuzzy super twisting algorithm to regulate the generator speed to its optimal value and to provide the optimum DC side current, and an internal control loop based on sliding mode controller to regulate the DC side current to its optimal value and provides the appropriate signal for the DC-DC boost converter. The considered system in this work is supposed supplying a water pumping system for a use in isolated areas. The proposed control strategy has been compared to the conventional MPPT control method based on the concept of perturbation and observation. The obtained results show, a good estimation performance for the wind speed estimator and the improved MRAS speed observer, a good tracking performance and a good stability around the maximum power point. Comparing to the classical MPPT strategy, the current technique can greatly reduce the ripples that can generate vibrations and significant noise on the generator and the motor-pump group.

INTRODUCTION

Wind energy has received a great deal of attention as an ideal alternative to conventional energy sources. Pumping water is one of the most promising application for wind energy conversion systems. Permanent magnet synchronous generator (PMSG) based wind turbines are the most preferred for standalone applications due to their high reliability and efficiency. Small commercial PMSG wind turbines already contain an internal rectifier. The accessible output provides a DC voltage. The connection of a DC motor driving a centrifugal pump is the most low cost solution, avoiding by that the need of an inverter in the case of using an AC motors [START_REF] Fernandez | Sliding mode control for efficiency optimization of wind electrical pumping systems[END_REF]. The final wind electric water pumping system configuration is illustrated in Figure (1). Its consists of permanent-magnet synchronous generator, an AC/DC converter, a DC-DC boost converter and a centrifugal pump driven by a permanent-magnet DC (PMDC) motor .This pumping system can operate autonomously; no additional power source is needed for the excitation circuit of the two machines.

The major drawback of wind turbine systems is the highly nonlinear behavior (Figure (2)). The main objective is to maximize the energy capture at every wind speed. Conventional MPPT control strategies have shown a poor performance and a low efficiency under random wind speed profile and external disturbances. In literature, several MPPT control strategies were developed and proposed in order to extract the maximum available power from the wind. The main problem is the use of mechanical sensors. According to [START_REF] Qiao | Wind speed and rotor position sensorless control for direct-drive PMG wind turbines[END_REF], the use of such sensors increases the overall cost of the wind system and the failure rate. The best alternative is to use an observer or an estimator. In [START_REF] Sitharthan | Adaptive hybrid intelligent MPPT controller to approximate effectual wind speed and optimal rotor speed of variable speed wind turbine[END_REF] an adaptive hybrid intelligent MPPT controller is proposed, the developed strategy allows to estimate the effective wind speed and the optimal rotor speed of the wind power generation system by the RBFNN technique. In [START_REF] Belmokhtar | Novel fuzzy logic based sensorless maximum power point tracking strategy for wind turbine systems driven DFIG (doubly-fed induction generator)[END_REF], a novel FLC MPPT method has been proposed, an MRAS observer based on fuzzy logic technique has been used to estimate the DFIG rotor's speed, and then the wind speed has been estimated from the mechanical power using the fuzzy logic technique. In [START_REF] Qiao | Wind speed and rotor position sensorless control for direct-drive PMG wind turbines[END_REF] a sensorless control strategy is proposed for a directly driving permanent magnetic generator, a sliding-mode observer is designed to estimate the generator rotor position and a back-propagation artificial neural network (BPANN) is designed to estimate the wind speed. In [START_REF] Mohamed | New hybrid sensorless speed of a nonsalient pole PMSG coupled to wind turbine using a modified switching algorithm[END_REF], a new hybrid sensorlees speed control is proposed for a non-salient pole PMSG wind turbine, the generator speed is estimated by a hybrid structure that combines two observers and a switching algorithm.

In this paper, the rotational generator speed is estimated through an improved MRAS observer based on a sliding mode controller adaptation mechanism and a fuzzy estimator is used to estimate the effective wind speed. The proposed control strategy includes two control loops, a speed controller to regulate the rotational speed to its optimal value and to provide the optimum (reference) DC side current as output and a current controller used to regulate the DC side current to its optimal value and to provide the appropriate duty cycle to the DC-DC boost converter. Unlike the considered conventional constant gain proportional integral (PI) controllers in [START_REF] Kot | Comparison of maximum peak power tracking algorithms for a small wind turbine[END_REF], this work proposes a robust variable gain super twisting algorithm assisted with a fuzzy logic controller and a sliding mode controller in order to improve the system stability and to reduce the convergence time. The effectiveness of the proposed control strategy is checked by several computer simulation tests using Matlab/Simulink software and compared to the conventional MPPT strategy. Characteristics 𝐶 𝑝 vs 𝜆 for different values of the pitch angle 𝛽.

MODELING OF WIND ELECTRIC WATER PUMPING SYSTEM 2.1 Modeling of the Wind Turbine

The model of the turbine is given by following equations:

𝑝 𝑣 = (𝜌. 𝐴. 𝑣 𝑤 3 )

2

(1) Where 𝑝 𝑣 is the wind power, 𝜌 is the air density, 𝐴 is the circular area, 𝑣 𝑤 is the wind speed, 𝑝 𝑚 is the mechanical power, 𝐶 𝑝 is the power coefficient, 𝛽 is the pitch angle, 𝜆 is the tip speed ratio, Ω 𝑚 𝐺 is the turbine rotor speed, 𝑅 is the turbine radius, 𝑇 𝑚 𝐺 is the mechanical torque, 𝑇 𝑒𝑚 𝐺 is the electromagnetic torque produced by the generator, 𝑓 is the friction coefficient and 𝐽 𝐺 is the total moment of inertia of the rotating parts.

𝑝 𝑚 = 1 2 𝐶 𝑝 (𝜆, 𝛽

Permanent Magnet Synchronous Generator (PMSG)

model d-q stator voltage equations of this generator are given by the following expressions: Where 𝐿 𝑑 , 𝐿 𝑞 are the inductances of the generator on the q and d axis, 𝑅 𝑠 is the stator resistance, 𝜓 0 is the permanent magnetic flux, ⍵ 𝑟 is the the electrical rotating speed of the PMSG which is given by ⍵ 𝑟 = 𝑝. Ω 𝑚 𝐺 and 𝑝 is the number of pole pairs. The load torque of the centrifugal pump is given by the following expression:

𝑇 𝐿 𝑀 = 𝑎. Ω 𝑚 𝑀 𝑛 + 𝑏 (12)
Where 𝑅 𝑎𝑀 is the armature winding resistance, 𝐿 𝑎𝑀 is the armature self-inductance, 𝐼 𝑎𝑀 is the motor armature current, 𝑉 𝑎𝑀 is the applied voltage, 𝑒 is the back e.m.f of the PMDC motor, 𝐾 𝑒 is the voltage constant, Ω 𝑚 𝑀 is the angular speed, 𝐾 𝑡 is the torque constant, 𝐽 𝑀 is the moment of inertia, 𝐵 𝑚 is the viscous torque constant, 𝑇 𝑓 𝑀 is the torque constant for rotational losses, 𝑇 𝑒 𝑀 , 𝑇 𝐿 𝑀 are the electromagnetic torque and load torque respectively, and 𝑎, 𝑏 are the constants of the pump.

3. FUZZY WIND SPEED ESTIMATOR The fuzzy inference system of the wind speed estimator receives the error between the estimated mechanical power 𝑃 ̂𝑚𝑜𝑝𝑡 and the calculated one 𝑃 𝑚 𝑐 𝑜𝑝𝑡 using the generated estimated wind speed 𝑣 ̂𝑤 provided by the FLC as a feedback. The error between the estimated mechanical power and the calculated one is multiplied to a scaling factor 𝜇 and then considered as input to the FIS, this error is calculated as follows:

𝜇. 𝑥 𝑝 𝑚 = 𝜇. (𝑃 ̂𝑚𝑜𝑝𝑡 -𝑃 𝑚 𝑐 𝑜𝑝𝑡 ) (13) 𝑊ℎ𝑒𝑟𝑒: 𝑃 𝑚 𝑐 𝑜𝑝𝑡 = 1 2 𝐶 𝑝 𝑚𝑎𝑥 (𝜆 𝑜𝑝𝑡 ). 𝜌. 𝐴. 𝑣 ̂𝑤3 (14)
The estimation process of the wind speed requires the turbine mechanical power information. This information can be estimated here using two ways. The first method by using equation ( 15), this technique is no longer recommendable because its requires the torque information, and it will causes an additional cost for installing a torque sensor, and the second method uses equations ( 16), which represents the conversion of the turbine mechanical power in the generator electrical power and consider power losses 𝑝 𝑙𝑜𝑠𝑠 in the model of the generator [START_REF] Qiao | Wind speed and rotor position sensorless control for direct-drive PMG wind turbines[END_REF]. Power losses 𝑝 𝑙𝑜𝑠𝑠 can be divided into four parts, copper loss 𝑝 𝑐𝑜𝑝𝑝𝑒𝑟 in the stator windings, which can be calculated using equation ( 18), the mechanical loss, which is assumed to be 1.0% of electrical power 𝑝 𝑒 , the core loss that depends on the flux linkage and the rotor speed, and the stray load loss that is also assumed to be 1.0% of electrical power 𝑝 𝑒 [START_REF] Qiao | Wind speed and rotor position sensorless control for direct-drive PMG wind turbines[END_REF]. , and the output of the FLC provides the change of the estimated wind speed (𝛥𝑣 ̂𝑤(𝑘)), and the estimated wind speed is obtained using the following equation:

𝑃
𝑣 ̂𝑤(𝑘) = 𝑣 ̂𝑤(𝑘 -1) + 𝛥𝑣 ̂𝑤(𝑘) (19)
Input error variable (𝜇. 𝑥 𝑝 𝑚 ) is described using five fuzzy subsets called membership functions: 𝑁 𝑖2 , 𝑁 𝑖1 , 𝑍 𝑖 , 𝑃 𝑖1 and 𝑃 𝑖2 , this input variable indicates two main information, the sign of error (𝜇. 𝑥 𝑝 𝑚 ) and its amplitude. Similarly, to output variable 𝛥𝑣 ̂𝑤(𝑘), we have five fuzzy subsets 𝑁 𝑜2 , 𝑁 𝑜1 , 𝑍 𝑜 , 𝑃 𝑜1 and 𝑃 𝑜2 . Triangular symmetrical memberships functions are selected for the input and output variables as shown in Figure (3). The designed FLC uses five fuzzy control rules. The used fuzzy rules here have the form of "If-Then"; and are designed and represented as below: The output of the FLC is a fuzzy subset of control. A nonfuzzy values are required for the control, that can be done by using a defuzzification method. Defuzzification is the process of converting a fuzzified output into a single crisp value. This operation is performed by using the centroid method. 4) is composed of two models, a reference model built from the 𝜓 𝑑𝑠 and 𝜓 𝑞𝑠 equations, and an adaptive model given by equations ( 20) and ( 21).

 If 𝜇. 𝑥 𝑝 𝑚 is 𝑁 𝑖2 Then 𝛥𝑣 ̂𝑤(𝑘) is 𝑁 𝑜2  If 𝜇. 𝑥 𝑝 𝑚 is 𝑁 𝑖1 Then 𝛥𝑣 ̂𝑤(𝑘) is 𝑁 𝑜1  If 𝜇. 𝑥 𝑝 𝑚 is 𝑍 𝑖 Then 𝛥𝑣 ̂𝑤(𝑘) is 𝑍 𝑜  If 𝜇. 𝑥 𝑝 𝑚 is 𝑃 𝑖1 Then 𝛥𝑣 ̂𝑤(𝑘) is 𝑃 𝑜1  If 𝜇. 𝑥 𝑝 𝑚 is 𝑃 𝑖2 Then 𝛥𝑣 ̂𝑤(𝑘) is 𝑃 𝑜2

IMPROVED MRAS OBSERVER BASED ON SLIDING MODE CONTROLLER ADAPTATION MECHANISM A Model Reference Adaptive Speed (MRAS) observer as shown in Figure (

𝜓 ̂𝑑𝑠 = ∫(𝑉 𝑑𝑠 -𝑅 𝑠 𝐼 ̂𝑑𝑠 + 𝜔 ̂𝑟𝐿 𝑞 𝐼 ̂𝑞𝑠 )𝑑𝑡 + 𝜓 0 (20)

𝜓 ̂𝑞𝑠 = ∫(𝑉 𝑞𝑠 -𝑅 𝑠 𝐼 ̂𝑞𝑠 -𝜔 ̂𝑟𝐿 𝑑 𝐼 ̂𝑑𝑠 -𝜓 0 𝜔 ̂𝑟)𝑑𝑡 (21)
The used adaptation mechanism in the conventional MRAS observer is based on constant gain proportional integral (PI) controller; the objective is to drive the output error vector between the reference and the adaptive model to zero. The error in the d-q coordinates is defined as:

[𝜀 𝜔 𝑟1 , 𝜀 𝜔 𝑟2 ] 𝑇 = [𝜓 ̂𝑑𝑠 -𝜓 𝑑𝑠 , 𝜓 ̂𝑞𝑠 -𝜓 𝑞𝑠 ] 𝑇 .
The estimated speed is given as follows:

𝜔 ̂𝑟 = 𝑘 𝑝 (𝜀 𝜔 𝑟1 In order to improve the MRAS observer estimation performance, an adaptive mechanism based on sliding mode controller is considered [START_REF] Gadoue | MRAS sensorless vector control of an induction motor using new slidingmode and fuzzy-logic adaptation mechanisms[END_REF].

The sliding surface is defined as follows:

𝑆 = 𝜀 𝜔 𝑟 + ∫ 𝑘𝜀 𝜔 𝑟 𝑑𝑡, (𝑘 > 0) 𝑊ℎ𝑒𝑟𝑒: 𝜀 𝜔 𝑟 = 𝜓 ̂𝑑𝑠 𝜓 𝑞𝑠 -𝜓 ̂𝑞𝑠 𝜓 𝑑𝑠 (24)
The sliding surface is equal to zero (𝑆 = 0) when the system is in the sliding mode. The first derivative of 𝑆 gives:

𝑆 ̇= 𝜀̇𝜔 𝑟 + 𝑘𝜀 𝜔 𝑟 (25)

When the system reaches the sliding surface, we have 𝑆 ̇= 0, therefore the error dynamics can be expressed as:

𝜀ω 𝑟 = -𝑘𝜀 𝜔 𝑟 (26)
The sliding mode control law is determined using the Lyapunov theory, we have:

𝑣 = 1 2 𝑠 2 (27)
The system is globally stable, if the derivative of the Lyapunov function is negative (𝑣̇< 0). The derivative of the Lyapunov function gives:

𝑣̇= 𝑆𝑆 ̇ <=> 𝑆(𝜀̇𝜔 𝑟 + 𝑘𝜀 𝜔 𝑟 ) (28)
The derivation of error 𝜀 𝜔 𝑟 gives: Let 𝑓 1 and 𝑓 2 be defined as: The Lyapunov function derivative (𝑣) is negative if:

𝑓 1 = 𝜓
(𝑓 1 + 𝑓 2 𝜔 ̂𝑟 + 𝑘𝜀 𝜔 𝑟 ) < 0 𝑓𝑜𝑟 𝑆 > 0 = 0 𝑓𝑜𝑟 𝑆 = 0 > 0 𝑓𝑜𝑟 𝑆 < 0 (36)
The general SMC form contains an equivalent control 𝑢 𝑒𝑞 (𝑡) used to keep the system state on the sliding surface and a switching control 𝑢 𝑠 (𝑡) used to forces the system sliding on this surface. The SMC law is given as follows:

𝑢(𝑡) = 𝑢 𝑒𝑞 (𝑡) + 𝑢 𝑠 (𝑡) (37)
The equivalent and the switching control functions are expressed as follows:

𝑢 𝑠 (𝑡) = 𝑀𝑠𝑖𝑔𝑛(𝑆), 𝑀 > 0 (38) 𝑢 𝑒𝑞 (𝑡) = -𝑓 1 -𝑘𝜀 𝜔 𝑟 𝑓 2 (39)
Where M is the hitting control gain. The rotational speed can be estimated using the following law:

𝜔 ̂𝑟 = -𝑓 1 -𝑘𝜀 𝜔 𝑚 𝑓 2 + 𝑀𝑠𝑖𝑔𝑛(𝑆) (40) 𝑊ℎ𝑒𝑟𝑒: 𝑠𝑖𝑔𝑛(𝑆) = { -1 𝑓𝑜𝑟 𝑆 < 0 +1 𝑓𝑜𝑟 𝑆 > 0 (41)
The sign function in equation ( 40) has been replaced by the sigmoid function 𝐻(𝑠), in order to reduce the chattering phenomenon. Function 𝑓 2 may cause an estimation errors when its value approaches zero, because of its presence in the denominator of equivalent control 𝑢 𝑒𝑞 (𝑡), this problem is solved by adding a small positive constant to 𝑓 2 . The final estimated rotational speed expression is given as follows:

{ 𝜔 ̂𝑟 = -𝑓 1 -𝑘𝜀 𝜔 𝑚 𝑓 2 + 𝑀. 𝐻(𝑠) 𝐻(𝑠) = [ 2 (1 + 𝑒 -𝑠𝑥 )
] -1 8), an outer control loop based on fuzzy super twisting algorithm used to regulate the generator speed to its optimal value and to provide the optimum DC side current, and an internal control loop based on sliding mode controller used to regulate the DC side current to its optimal value and to provide the appropriate signal for the DC-DC boost converter.  Generalized Super-Twisting Algorithm According to [START_REF] Moreno | A Lyapunov approach to second-order sliding mode controllers and observers[END_REF], the generalized STA can be described by the following differential inclusion:

(42)
{ 𝜎̇= -𝑘 1 𝜙 1 (𝜎) + 𝓏 (𝜎 ∈ ℝ) 𝓏̇= -𝑘 2 𝜙 2 (𝜎) + 𝜚(𝑡) (𝓏 ∈ ℝ) (43)
The nonlinear stabilizing terms are given as follows:

{ 𝜙 1 (𝜎) = 𝜇 1 |𝜎| 1 2𝑠𝑔𝑛(𝜎) + 𝜇 2 𝜎, 𝑤𝑖𝑡ℎ 𝜇 1 , 𝜇 2 ≥ 0 𝜙 2 (𝜎) = 𝜇 1 2 2 𝑠𝑔𝑛(𝜎) + 3 2 𝜇 1 𝜇 2 |𝜎| 1 2𝑠𝑔𝑛(𝜎) +𝜇 2 2 𝜎 (44)
𝜇 1 can take only the value 𝜇 1 = 1 and 𝜇 1 = 0.  Fuzzy-VGSTA Speed Controller design for PMSG: The speed tracking error (sliding surface) and its reachability condition are defined as follows:

{ 𝑆 Ω 𝑚 𝐺 = 𝜀 𝑥 = Ω ̂𝑚𝑜𝑝𝑡 𝐺 -Ω ̂𝑚 𝐺 𝑆 Ω 𝑚 𝐺 𝑆 ̇Ω𝑚 𝐺 < 0 (45)
Where Ω ̂𝑚𝑜𝑝𝑡 𝐺 is the reference rotational speed ( Ω ̂𝑚𝑜𝑝𝑡 𝐺 = (𝑣 ̂𝑤. 𝜆 * ) 𝑅 ⁄ ) and 𝜆 * is the optimum tip-speed ratio. The first order and the second order sliding mode control for Ω 𝑚 𝐺 are given respectively by:

𝑆 ̇Ω𝑚 𝐺 = Ω ̂̇𝑚𝑜𝑝𝑡 𝐺 -[ 1 𝐽 𝐺 (𝑇 𝑚 𝐺 -𝑓. Ω ̂𝑚 𝐺 -𝑇 𝑒𝑚 𝐺 )] =Ω ̂̇𝑚𝑜𝑝𝑡 𝐺 -[ 1 𝐽 𝐺 (𝑇 𝑚 𝐺 -𝑓. Ω ̂𝑚 𝐺 -𝑘 𝑏 𝐼 𝑚 )] 𝑆 ̈Ω𝑚 𝐺 = Ω ̂̈𝑚𝑜𝑝𝑡 𝐺 + 𝑘 𝑏 𝐽 𝐺 𝐼 ̇𝑚 + 𝑓 𝐽 𝐺 Ω ̂̇𝑚 𝐺 - 𝑇 ̇𝑚 𝐺 𝐽 𝐺 (46)
According to [START_REF] Yin | A novel fuzzy integral sliding mode current control strategy for maximizing wind power extraction and eliminating voltage harmonics[END_REF] the electromagnetic torque can be approximated by: 𝑇 𝑒𝑚 𝐺 = 𝑘 𝑏 𝐼 𝑚 . Considering a single input and a single output nonlinear system [START_REF] Das | A ${H_\infty} $ Robust Active and Reactive Power Control Scheme for a PMSG-Based Wind Energy Conversion System[END_REF] 𝑆 ̇Ω𝑚 𝐺 = 𝑓(𝑡, 𝑆 Ω 𝑚 𝐺 ) + 𝑢, where 𝑓(𝑡, 𝑆 Ω 𝑚 𝐺 ) is unknown bounded perturbation term and globally bounded by

|𝑓(𝑡, 𝑆 Ω 𝑚 𝐺 )| ≤ 𝜕|𝑆 Ω 𝑚 𝐺 |
𝑝 for some constant 𝜕 > 0. The maximum sliding order as 2 can be reached by choosing 𝑝 as 0.5. Control input 𝐼 𝑚_𝑜𝑝𝑡 for Ω 𝑚 𝐺 by applying the variable gain super twisting algorithm is given as follows:

𝜎 = 𝑧 1 𝑆 ̇Ω𝑚 𝐺 + 𝑧 2 |𝑆 Ω 𝑚 𝐺 | 1 2 𝑠𝑔𝑛(𝑆 Ω 𝑚 𝐺 ), 𝑤𝑖𝑡ℎ 𝑧 1 , 𝑧 2 > 0 ℒ ̃= -𝑘 1 (𝜎, 𝑡)𝜙 1 (𝜎) -∫ 𝑘 2 (𝜎, 𝑡)𝜙 2 (𝜎)𝑑𝑡 𝑡 0 { 𝜙 1 (𝜎) = |𝜎| 1 2𝑠𝑔𝑛(𝜎) + 𝜇 2 𝜎, 𝑤𝑖𝑡ℎ 𝜇 2 > 0 𝜙 2 (𝜎) = 1 2 𝑠𝑔𝑛(𝜎) + 3 2 𝜇 2 |𝜎| 1 2𝑠𝑔𝑛(𝜎) + 𝜇 2 2 𝜎 𝑘 1 = 𝜕 |𝑧 1 𝜀ẋ + 𝑧 2 |𝜀 𝑥 | 1 2𝑠𝑔𝑛(𝜀 𝑥 )| 𝑛 = 𝜕|𝜎| 𝑛 𝑘 2 = 𝜂 |𝑧 1 𝜀ẋ + 𝑧 2 |𝜀 𝑥 | 1 2𝑠𝑔𝑛(𝜀 𝑥 )| 𝑚 = 𝜂|𝜎| 𝑚 (47)
When STA gains 𝑘 1 and 𝑘 2 are constant and 𝜇 2 = 0 the standard STA is recovered. 𝜇 2 > 0 allows to handle with disturbances and perturbations that grow outside the sliding surface and the variable gains 𝑘 1 and 𝑘 2 make possible to render the sliding surface insensitive to bounded perturbations. 𝜕 and 𝜂 are super twisting algorithm tuning parameters. To allow a good dealing with the random wind speed nature, 𝜕 has been considered here as an additional adaptive parameter. The 𝜕 value should vary according to the wind speed (𝑣 𝑤 ) variation. A sugeno FLC is selected for this purpose. The input of the considered FLC has two inputs. The first one is the estimated wind speed value provided by the fuzzy wind speed estimator (𝑣 ̂𝑤(𝑘)) and the second one is the change of the estimated wind speed (∆𝑣 ̂𝑤(𝑘) = 𝑣 ̂𝑤(𝑘) -𝑣 ̂𝑤(𝑘 -1)). The FLC provides as output the VGSTA tuning parameter (𝜕(𝑘)). FLC input variables have been divided and assigned to the linguistic variables using nine fuzzy membership functions: 𝑟 1 , 𝑟 2 , 𝑟 3 , 𝑟 4 , 𝑟 5 , 𝑟 6 , 𝑟 7 , 𝑟 8 and 𝑟 9 for the estimated wind speed variable, and three linguistic variables 𝑁, 𝑍 and 𝑃 for the estimated wind speed change. The output variable 𝜕(𝑘) has been also divided and assigned to the linguistic variables using seven fuzzy subsets 𝑂 𝑖1 , 𝑂 𝑖2 , 𝑂 𝑖3 , 𝑂 𝑖4 , 𝑂 𝑖5 , 𝑂 𝑖6 , 𝑂 𝑖7 , 𝑂 𝑖8 and 𝑂 𝑖9 . The common triangular symmetrical memberships functions have been used for the FLC variables (Figures ( 5),( 6) and ( 7)). The fuzzy rules have the form of "If-Then" with "and" logical operator, and are represented as below:

{ 𝐼 ̇𝑚 = - 𝑟 𝑚 𝐿 𝑚 𝐼 𝑚 + 1 𝐿 𝑚 𝑉 𝑑𝑐 - (1 -𝑞) 𝐿 𝑚 𝑉 𝑎𝑀 𝑉 ̇𝑑𝑐 = 1 𝐶 𝑒 𝐼 𝑑𝑐 - 1 𝐶 𝑒 𝐼 𝑚 (48)
Where 𝐼 𝑚 is the input current, 𝑉 𝑎𝑀 is the output voltage, 𝑉 𝑑𝑐 is the input voltage, 𝑞 is the switch state, 𝐿 𝑚 and 𝐶 𝑒 are energy storage elements and 𝑟 𝑚 is the internal resistance of the boost inductance 𝐿 𝑚 .

The DC-DC boost converter is forced to bring up the PMSG to operate at the optimum DC-side current 𝐼 𝑚_𝑜𝑝𝑡 and therefore at the maximum power working point (MPP). The sliding surface 𝜎 𝐼 𝑚 and the control law are defined as follows: 9) represents the applied random wind speed profile and the estimated one by the fuzzy wind speed estimator using the second input information, the fuzzy wind speed estimator shows a high estimation performance with a very small error. Figure ( 10) depicts the response of the MRAS speed observer, we can notice, a high estimation accuracy of the generator speed at dynamic and steady state regime. Figure ( 11) depicts the variation of the power coefficient (𝐶 𝑝 ) of the proposed fully sensorless MPPT strategy. As can be seen the power coefficient is kept close to its optimum value 0.48 even under arbitrary wind speed profile. The proposed control strategy has been compared to the conventional simple sensorless MPPT strategy presented in many research papers [START_REF] Hussein | Simple sensorless control technique of permanent magnet synchronous generator wind turbine[END_REF]. The concept of this latter is based on perturbing the control variable ( duty-cycle of the DC-DC boost converter) using a fixed step-size and observing the resulting power changes until achieving the maximum power point. Even that this technique is simple, flexible and does not require any knowledge about the wind turbine characteristic; its main drawback is the poor stability around the MPP and it fails to achieve the maximum power under sudden wind variations. These drawbacks has been observed on the studied system when applying this technique, the obtained power coefficient (𝐶 𝑝 ) using the conventional method is shown in Figure ( 11), we notice large oscillations around the maximum power coefficient, the thing which lead to affect the captured mechanical power (Figure ( 12)) and causes a vibration and noise of the machines. Figures ( 13) and ( 14) shows the motor-pump performances using the proposed and conventional MPPT strategy, the first one depict the variation of the absorbed power by the motor-pump group and the second one represents the variation of the electrical torque and the load torque opposed by the centrifugal pump. From the obtained results, it can be noted that under random wind speed profile, the conventional control strategy gives higher ripple in power and torques of the motor pump group caused due to oscillation around the maximum power point, it can be also noted that this oscillations are almost negligible using the proposed MPPT control strategy and applying this latter will ensure a stable working of the pumping system without any vibrations or noises of the motors. CONCLUSIONS A fully robust sensorless control strategy has been proposed in this paper for a direct-drive PMSG wind turbine. The studied

𝜎 𝐼 𝑚 = 𝐼 𝑚_𝑜𝑝𝑡 -𝐼 𝑚 𝑞 = 1 2 [1 + 𝑆𝑖𝑔𝑛(𝜎 𝐼 𝑚 )], 𝑤𝑖𝑡ℎ 𝑞 = { 1 𝜎 𝐼 𝑚 > 0 0 𝜎 𝐼 𝑚 < 0 (49)

Figure 1 .

 1 Figure 1. Studied wind electric water pumping system

{

  𝑉 𝑑𝑠 = 𝑅 𝑠 𝐼 𝑑𝑠 + 𝐿 𝑑 𝐼 ̇𝑑𝑠 -⍵ 𝑟 𝜓 𝑞𝑠 𝑉 𝑞𝑠 = 𝑅 𝑠 𝐼 𝑞𝑠 + 𝐿 𝑞 𝐼 ̇𝑞𝑠 + ⍵ 𝑟 𝜓 𝑑𝑠 𝜓 𝑑𝑠 = 𝐿 𝑑 𝐼 𝑑𝑠 + 𝜓 0 𝜓 𝑞𝑠 = 𝐿 𝑞 𝐼 𝑞𝑠 (7) Differential equations of the PMSG can be obtained as follows: { 𝐿 𝑑 𝐼 ̇𝑑𝑠 = 𝑉 𝑑𝑠 -𝑅 𝑠 𝐼 𝑑𝑠 + ⍵ 𝑟 𝐿 𝑞 𝐼 𝑞𝑠 𝐿 𝑞 𝐼 ̇𝑞𝑠 = 𝑉 𝑞𝑠 -𝑅 𝑠 𝐼 𝑞𝑠 -⍵ 𝑟 𝐿 𝑑 𝐼 𝑑𝑠 -𝜓 0 𝑑 -𝐿 𝑞 )𝐼 𝑑𝑠 𝐼 𝑞𝑠 + 𝜓 0 𝐼 𝑞𝑠 ]

2. 3

 3 Permanent-Magnet DC Motor (PMDC) and Centrifugal pump model The model of the PMDC motor is represented by the following equations: { 𝑉 𝑎𝑀 = 𝑅 𝑎𝑀 𝐼 𝑎𝑀 + 𝐿 𝑎𝑀 𝐼 ̇𝑎𝑀 + 𝑒 𝑇 𝑒 𝑀 = 𝐾 𝑡 𝐼 𝑎𝑀 𝑒 = 𝐾 𝑒 Ω 𝑚 𝑀 𝑇 𝑒 𝑀 -𝑇 𝐿 𝑀 = 𝐽 𝑀 Ω ̇𝑚 𝑀 + 𝐵 𝑚 . Ω 𝑚 𝑀 + 𝑇 𝑓 𝑀 (11)

Figure 3

 3 Figure 3. a. Input variable membership functions, b. Change of the estimated wind speed (𝛥𝑣 ̂𝑤(𝑘)) membership functions

  𝜀ω 𝑟 = 𝜓 ̂ḋ𝑠 𝜓 𝑞𝑠 + 𝜓 ̂𝑑𝑠 𝜓 ̇𝑞𝑠 -𝜓 ̂q𝑠 𝜓 𝑑𝑠 -𝜓 ̂𝑞𝑠 𝜓 ̇𝑑𝑠 (29) By replacing Equations (20) and (21) into Equation (29), error derivative (𝜀̇𝜔 𝑟 ) becomes: 𝜀̇𝜔 𝑟 = 𝜓 ̂𝑑𝑠 𝜓 ̇𝑞𝑠 -𝜓 ̂𝑞𝑠 𝜓 ̇𝑑𝑠 +𝑉 𝑑𝑠 𝜓 𝑞𝑠 -𝑅 𝑠 𝐼 ̂𝑑𝑠 𝜓 𝑞𝑠 + 𝜔 ̂𝑟𝐿 𝑞 𝐼 ̂𝑞𝑠 𝜓 𝑞𝑠 -𝑉 𝑞𝑠 𝜓 𝑑𝑠 + 𝑅 𝑠 𝐼 ̂𝑞𝑠 𝜓 𝑑𝑠 + 𝜔 ̂𝑟𝐿 𝑑 𝐼 ̂𝑑𝑠 𝜓 𝑑𝑠 + 𝜓 𝑑𝑠 𝜔 ̂𝑟𝜓 0 𝜀ω 𝑟 = 𝜓 ̂𝑑𝑠 𝜓 ̇𝑞𝑠 -𝜓 ̂𝑞𝑠 𝜓 ̇𝑑𝑠 +𝜓 𝑞𝑠 (𝑉 𝑑𝑠 -𝑅 𝑠 𝐼 ̂𝑑𝑠 ) -𝜓 𝑑𝑠 (𝑉 𝑞𝑠 -𝑅 𝑠 𝐼 ̂𝑞𝑠 ) + 𝜔 ̂𝑟(𝐿 𝑞 𝐼 ̂𝑞𝑠 𝜓 𝑞𝑠 + 𝐿 𝑑 𝐼 ̂𝑑𝑠 𝜓 𝑑𝑠 + 𝜓 𝑑𝑠 𝜓 0 ) (30)

Figure 4 .

 4 Figure 4. Model reference adaptive speed (MRAS) Observer 5. CONTROLLER DESIGN Two control loops were designed (Figure8), an outer control loop based on fuzzy super twisting algorithm used to regulate the generator speed to its optimal value and to provide the optimum DC side current, and an internal control loop based on sliding mode controller used to regulate the DC side current to its optimal value and to provide the appropriate signal for the DC-DC boost converter.  Generalized Super-Twisting Algorithm According to[START_REF] Moreno | A Lyapunov approach to second-order sliding mode controllers and observers[END_REF], the generalized STA can be described by the following differential inclusion:

Figure 5 .Figure 7 .

 57 Figure 5. Estimated wind speed (𝑣 ̂𝑤(𝑘)) membership functions

Figure 8 .

 8 Figure 8. Proposed sensorless control strategy 6. RESULTS & DISCUSSION The test has been performed by replacing the physical sensors by the improved MRAS speed observer and the fuzzy wind speed estimator. The overall fully sensorless control strategy have been investigated under random wind speed profile. The wind speed was modeled as a sum of deterministic several harmonics. Figure (9) represents the applied random wind speed profile and the estimated one by the fuzzy wind speed estimator using the second input information, the fuzzy wind speed estimator shows a high estimation performance with a very small error. Figure (10) depicts the response of the MRAS speed observer, we can notice, a high estimation accuracy of the generator speed at dynamic and steady state regime. Figure (11) depicts the variation of the power coefficient (𝐶 𝑝 ) of the proposed fully sensorless MPPT strategy. As can be seen the power coefficient is kept close to its optimum value 0.48 even under arbitrary wind speed profile. The proposed control strategy has been compared to the conventional simple sensorless MPPT strategy presented in many research papers[START_REF] Hussein | Simple sensorless control technique of permanent magnet synchronous generator wind turbine[END_REF]. The concept of this latter is based on perturbing the control variable ( duty-cycle of the DC-DC boost converter) using a fixed step-size and observing the resulting power changes until achieving the maximum power point. Even that this technique is simple, flexible and does not require any knowledge about the wind turbine characteristic; its main drawback is the poor stability around the MPP and it fails to achieve the maximum power under sudden wind variations. These drawbacks has been observed on the studied system when applying this technique, the obtained power coefficient (𝐶 𝑝 ) using the conventional method is shown in Figure (11), we notice large oscillations around the maximum power coefficient, the thing which lead to affect the captured mechanical power (Figure (12)) and causes a vibration and noise of the machines. Figures (13) and (14) shows the motor-pump performances using the proposed and conventional MPPT strategy, the first one depict the variation of the absorbed power by the motor-pump group and the second one represents the variation of the electrical torque and the load torque opposed by the centrifugal pump. From the obtained results, it can be noted that under random wind speed profile, the conventional control strategy gives higher ripple in power and torques of the motor pump group caused due to oscillation around the maximum power point, it can be also noted that this oscillations are almost negligible using the proposed MPPT control strategy and applying this latter will ensure a stable working of the pumping system without any vibrations or noises of the motors. CONCLUSIONS A fully robust sensorless control strategy has been proposed in this paper for a direct-drive PMSG wind turbine. The studied

Figure 9 .

 9 Figure 9. Actual and estimated wind speed profile Figure 10. Actual and estimated rotational speed

  Ω ̂𝑚 𝐺 represents the estimated generator rotational speed provided by the improved MRAS observer. Details about this observer will be discussed in the next section. The basic structure of the FLC controller consists of Fuzzification process, an Inference engine, a knowledge base and a Defuzzification process. The used FLC here is composed of one input and one output variable. The FLC input receive error (𝜇. 𝑥 𝑝 𝑚 ) between 𝑃 ̂𝑚𝑜𝑝𝑡 and 𝑃 𝑚

	̂𝑚𝑜𝑝𝑡 = 𝑇 𝑚 𝐺	𝑟𝑒𝑓 Ω ̂𝑚 𝐺	(15)
	𝑃 ̂𝑚𝑜𝑝𝑡 = 𝐽 𝐺 Ω ̂𝑚 𝐺 . Ω ̂̇𝑚 𝐺 + 𝑝 𝑒 𝑜𝑝𝑡 + 𝑝 𝑙𝑜𝑠𝑠 + 𝑓Ω ̂𝑚 𝐺 2	(16)
	𝑝 𝑒 = 𝑝 𝑐𝑜𝑝𝑝𝑒𝑟 = 3 (𝑉 𝑑𝑠 𝐼 𝑑𝑠 + 𝑉 𝑞𝑠 𝐼 𝑞𝑠 ) 2 3 2 (𝐼 𝑞𝑠 2 𝑅 𝑠 + 𝐼 𝑑𝑠 2 𝑅 𝑠 )	(17) (18)
		𝑐
		𝑜𝑝𝑡

  . 𝜓 ̂𝑞𝑠 -𝜀 𝜔 𝑟2 . 𝜓 ̂𝑑𝑠 ) +𝑘 𝑖 ∫(𝜀 𝜔 𝑟1 . 𝜓 ̂𝑞𝑠 -𝜀 𝜔 𝑟2 . 𝜓 ̂𝑑𝑠 )𝑑𝑡 + 𝜔 𝑟 (0) (22) 𝑊ℎ𝑒𝑟𝑒: 𝜀 𝜔 𝑟1 . 𝜓 ̂𝑞𝑠 -𝜀 𝜔 𝑟2 . 𝜓 ̂𝑑𝑠 = 𝜓 𝑞𝑠 . 𝜓 ̂𝑑𝑠 -𝜓 𝑑𝑠 . 𝜓 ̂𝑞𝑠 (23)

  𝑆 ̇= 𝜀ω 𝑟 + 𝑘𝜀 𝜔 𝑟 = 𝑓 1 + 𝑓 2 𝜔 ̂𝑟 + 𝑘𝜀 𝜔 𝑟(34)

	By substituting Equation (34) into Equation (28), we obtain
	the final expression of the Lyapunov function derivative(𝑣):
	𝑣̇= 𝑆𝑆 ̇= 𝑆(𝑓 1 + 𝑓 2 𝜔 ̂𝑟 + 𝑘𝜀 𝜔 𝑟 )	(35)

̂𝑑𝑠 𝜓 ̇𝑞𝑠 -𝜓 ̂𝑞𝑠 𝜓 ̇𝑑𝑠 + 𝜓 𝑞𝑠 (𝑉 𝑑𝑠 -𝑅 𝑠 𝐼 ̂𝑑𝑠 ) -𝜓 𝑑𝑠 (𝑉 𝑞𝑠 -𝑅 𝑠 𝐼 ̂𝑞𝑠 ) (31) 𝑓 2 = 𝐿 𝑞 𝐼 ̂𝑞𝑠 𝜓 𝑞𝑠 + 𝐿 𝑑 𝐼 ̂𝑑𝑠 𝜓 𝑑𝑠 + 𝜓 𝑑𝑠 𝜓 0 = 𝜓 ̂𝑞𝑠 𝜓 𝑞𝑠 + 𝜓 ̂𝑑𝑠 𝜓 𝑑𝑠 (32) Where: 𝜓 ̂𝑞𝑠 = 𝐿 𝑞 𝐼 ̂𝑞𝑠 And 𝜓 ̂𝑑𝑠 = 𝐿 𝑑 𝐼 ̂𝑑𝑠 + 𝜓 0 (33)



  If 𝑣 ̂𝑤(𝑘) is 𝑟 1 and 𝛥𝑣 ̂𝑤(𝑘) is ( 𝑁 Or 𝑍) Then 𝜕(𝑘) is 𝑂 𝑖1  If 𝑣 ̂𝑤(𝑘) is 𝑟 1 and 𝛥𝑣 ̂𝑤(𝑘) is 𝑃 Then 𝜕(𝑘) is 𝑂 𝑖2  If 𝑣 ̂𝑤(𝑘) is 𝑟 2 and 𝛥𝑣 ̂𝑤(𝑘) is ( 𝑁 Or 𝑍) Then 𝜕(𝑘) is 𝑂 𝑖2  If 𝑣 ̂𝑤(𝑘) is 𝑟 2 and 𝛥𝑣 ̂𝑤(𝑘) is 𝑃 Then 𝜕(𝑘) is 𝑂 𝑖3  If 𝑣 ̂𝑤(𝑘) is 𝑟 3 and 𝛥𝑣 ̂𝑤(𝑘) is ( 𝑁 Or 𝑍) Then 𝜕(𝑘) is 𝑂 𝑖3  If 𝑣 ̂𝑤(𝑘) is 𝑟 3 and 𝛥𝑣 ̂𝑤(𝑘) is 𝑃 Then 𝜕(𝑘) is 𝑂 𝑖4  If 𝑣 ̂𝑤(𝑘) is 𝑟 4 and 𝛥𝑣 ̂𝑤(𝑘) is ( 𝑁 Or 𝑍) Then 𝜕(𝑘) is 𝑂 𝑖4  If 𝑣 ̂𝑤(𝑘) is 𝑟 4 and 𝛥𝑣 ̂𝑤(𝑘) is 𝑃 Then 𝜕(𝑘) is 𝑂 𝑖5  If 𝑣 ̂𝑤(𝑘) is 𝑟 5 and 𝛥𝑣 ̂𝑤(𝑘) is ( 𝑁 Or 𝑍) Then 𝜕(𝑘) is 𝑂 𝑖5  If 𝑣 ̂𝑤(𝑘) is 𝑟 5 and 𝛥𝑣 ̂𝑤(𝑘) is 𝑃 Then 𝜕(𝑘) is 𝑂 𝑖6  If 𝑣 ̂𝑤(𝑘) is 𝑟 6 and 𝛥𝑣 ̂𝑤(𝑘) is ( 𝑁 Or 𝑍) Then 𝜕(𝑘) is 𝑂 𝑖6  If 𝑣 ̂𝑤(𝑘) is 𝑟 6 and 𝛥𝑣 ̂𝑤(𝑘) is 𝑃 Then 𝜕(𝑘) is 𝑂 𝑖7  If 𝑣 ̂𝑤(𝑘) is 𝑟 7 and 𝛥𝑣 ̂𝑤(𝑘) is ( 𝑁 Or 𝑍) Then 𝜕(𝑘) is 𝑂 𝑖7  If 𝑣 ̂𝑤(𝑘) is 𝑟 7 and 𝛥𝑣 ̂𝑤(𝑘) is 𝑃 Then 𝜕(𝑘) is 𝑂 𝑖8  If 𝑣 ̂𝑤(𝑘) is 𝑟 8 and 𝛥𝑣 ̂𝑤(𝑘) is ( 𝑁 Or 𝑍) Then 𝜕(𝑘) is 𝑂 𝑖8  If 𝑣 ̂𝑤(𝑘) is 𝑟 8 and 𝛥𝑣 ̂𝑤(𝑘) is 𝑃 Then 𝜕(𝑘) is 𝑂 𝑖9  If 𝑣̂𝑤(𝑘) is 𝑟 9 and 𝛥𝑣 ̂𝑤(𝑘) is ( 𝑁 Or 𝑍 Or 𝑃) Then 𝜕(𝑘) is 𝑂 𝑖9