Licínio Moreira

Sérgio Leitão
email: sleitao@utad.pt

Zita Vale

João Galvão
email: jrgalvao@ipleiria.pt

Use of Web Based Meters to Improve Energy Efficiency and Power Quality in Buildings

Keywords: Energy Efficiency, Cloud-based System, Energy Management Systems, Power Quality, Smart City

During the work conducted, several buildings were analysed, in terms of energy efficiency and power quality. Two case studies are here presented: an educational building and a museum. Most of the studies were conducted recurring to traditional measurement equipment, forcing the person to travel to the site to install equipment and every time he wanted to collect data. But one of the case studies, the museum, comprised the development of an analyser (hardware and software) able to measure electric energy, temperature and humidity. This analyser has the capability to register values on a database available in the internet and issue warnings to the building manager. This allows real-time information, supporting some energy efficiency actions. The objective is to improve this model and expand its use for several buildings, providing savings in terms of time and other resources, taking advantage of cloud-based systems.

Introduction

At present time, the availability of information on energy use for customers is, in most of the cases, limited to the monthly utility bills. The information provided by the utilities is generally limited to quantitative aspects, neglecting the qualitative issues. This diminutive information, along with the time gap between the effective consumption and the delivery of the bill constitute barriers to immediate actions. The widespread use of energy analysers, with metering and power quality analysis capabilities, connected to cloud-based systems would enable real-time knowledge and it could benefit the benchmarking of different building and processes.

The knowledge of individual data and the benchmarking of several similar processes or buildings, based on web systems, empowers the manager to the development of strategies for intervention to improve the energy efficiency of the building or process, within the concept of Smart City for sustainability.

This deals with a methodology shift in the energy auditing. It is intended to set off from the classic energy auditing, with individualized analysis requiring onsite data collection, to a more systematic approach, based on spread analysers dispatching data to a common database through the use of web-based systems.

Benefits from Cloud-based Engineering Systems

Data and programs are part of the world of computing in the desktop PCs, but the current trend is to relocate them and integrate the usually server room to the cloud computing service or on-demand computing/software. The platform used is the Internet with exceptional growth and the common element is a shift in the geography of computation. For example, each time someone uses a search engine service, the main software is lodged computers on unseen to the user, possibly distributed across different continents. [START_REF] Hayes | Cloud computing[END_REF] In a wider context we can say that cloud is a large-scale, distributed Information Technologies (IT) facilities available over the internet and is transforming the way intrinsic IT services are delivered and managed.

The use of cloud-based systems tends to reduce overall cost and increase efficiencies, especially when replacing an organization's locally operated system and supported with local servers. This detail is reflected in energy and environmental benefits. Also the cloud-based systems have a huge potential, improving efficiency and business agility, therefore contributing to a more sustainable world [START_REF] Abood | Cloud Computing and Sustainability: The Environmental Benefits of Moving to the Cloud[END_REF].

Industrial or services companies acting in energy audit, that use suitable equipment to collect energy consumption and/or power quality data variables will gather the inherent business benefits of this technology, mainly from the remote and possibly real-time data availability. The ease of data collection, data sharing and information delivery, boosted by the rising use of mobile devices, is another relevant benefit for users. Another impact of the use of this computing platform is the reduction of costs related to technical staff involvement in on-site data collection and system maintenance. All of this can play a crucial role in making IT more sustainable by significantly reducing energy consumption, raising levels of energy efficiency [START_REF] Mann | Cloud technology + mobile = a net positive impact on all businesses[END_REF].

Motivation of the Work

The energy data from multiple sites, such as industrial, services and residential buildings has to date been collected on an individualized approach and on site, recurring to temporary placement of portable energy analysers. Although many installations are already fitted with smart meters for electric energy, they are only used in remote metering by the utility and the data isn't usually delivered to the customer in a timely way. Also, they only measure total energy at the point of common coupling, therefore they don't allow the disaggregation of energy (electric and thermal) consumption by different sector or areas of the facility under study. This high volume of data collected is related to main energy consumers in the buildings, highlighting the appliances, machinery, HVAC, lighting, compressed air. Also, data related with the activity in the building (production, occupation, building structure ...). Also some other data is linked with consumer behaviour, market and technologies, measurement methods, public procurement, market transformation programs, end-use metering, demand response, smart meters, smart homes and smart appliance, consumer electronics, ICT, residential lighting and home automation.

On this field, the disaggregation of energy variables, with several consumers and several parameters, is necessary. In each case study, sampling intervals of 5, 10 or 15 minutes are used, resulting in a large collection of data a t the end of a campaign up to several weeks. This data requires to be treated and interpreted quickly, in order to promptly take actions, in terms of energy efficiency and/or power quality issues.

This individually collecting of data, along with individual data processing is time and resource consuming associated with the travelling to the site and losses of time due to computer media used and different software that perform the data processing. The main objective of this work is to demonstrate that the data management with resource to cloud-based systems can raise the performance in the analysis energy data.

Based on several case studies in urban and industrial environment, related with the researches developed on last years, to retrofit the energy systems and achieve better energy efficiency in these buildings and industrial activities, putting into practice the smart city concept. These studies are part of a set of actions to achieve the assimilation of the national programme which implements these requirements for greater energy efficiency (the 20/20/20 Plan) by the various economic and industrial players. This 20/20/20 Plan predicts a cut of 20% in GHG emissions for the EU by the year 2020, a share of 20% of energy from renewable sources and a 20% increase in energy efficiency and implementing smart grids and cities, for a low carbon a and sustainability [START_REF] De Wilde | The implications of a changing climate for buildings[END_REF] and [START_REF] Wada | Energy efficiency opportunities in the residential sector and their feasibility[END_REF].

These case studies included, among others, plastic and mould industries, public library, sports hall, museum, comprising a vast diversity of data (numerical data; thermal images) to be processed. Here, the cloud technology can play an important role in data processing and in the dissemination of results [START_REF] Moreira | Power Quality problems in the mould Industry[END_REF], [START_REF] Galvão | Sustainable Energy for Plastic Industry Plant[END_REF], [START_REF] Galvão | Smart City and Sustainable Renovation of Energy Systems for Efficiency[END_REF] and [START_REF] Moreira | Analysis of Power Quality Disturbances in Industry in the Centre Region of Portugal[END_REF].

Case Studies

The base of the studies consists of energy audits. The acquisition of existing energy consumption and other data was carried out with the use of various energy and power quality analysers, thermal camera and other equipment, aiming to characterize not only the energy consumptions, but in also the buildings structure and materials (walls, roof, warehouse and office). The energy audit consists of several aspects that will allow us to identify critical parts of this facility and that should be improved in order to achieve a higher level of performance. In this context, the energy facilities and activities associated with them were characterized according to the standard Energy Management Systems [START_REF]EMS -Energy Management Systems -requirements with guidance for use[END_REF] and [START_REF] Galvão | Hybrid Model for the Energy Efficiency of Building Services[END_REF].

The energy audit of all sectors and all forms of energy, and its pursuance requires knowledge of the electrical, thermal, mechanical and environmental areas of the building. Thus, energy audits provide specific information and identify the actual energy savings, consisting primarily of a critical examination of how energy is used based on the available records of energy consumption and costs. An energy analysis was carried out, leading to the characterization of energy consumption in recent years. This consisted in the use of existing energy bills from the utility and the use of several energy analysers.

In several audits, especially the ones in industrial facilities, power quality issues were also addressed. In some cases, prior to the studies, the building manager didn't relate the malfunction of some equipment to power quality events, while others hold responsible the electricity distributor for every malfunction, even if it was not to blame. In general, one can conclude that the awareness of power quality issues is short. In most cases, this work contributed to the rise of awareness among industrial managers.

Given the diversity of buildings and activities analyzed, only two cases in the service area (library and museum) are presented here, being a sample of the objectives to increase energy efficiency, sustainability in the context of Smart City. One of them was conducted in the traditional manner and the other includes the development of a web-based meter.

Public Library

Approximately three quarters of the population in EU lives in cities or nearby. It is necessary to improve the energy efficiency of buildings, since about 40% of the primary energy consumed in the European Union, results from energy use in buildings [START_REF] Carvalho | Energy Policies in EU, Energy Conference Lisbon[END_REF] and [START_REF]Report of the Public Consultation on the Smart Cities and Communities Initiative[END_REF]. Therefore, it is important to promote good practice in the application of renewable energy combined with energy efficiency measures. The EU has developing a long-term strategy to a low-carbon economy and to make better use of its energy systems and scarce resources. Urban areas consume 70% of the energy in the EU and emit about the same share of greenhouse gases. The Smart Cities Initiative is a new European task force, whose objective is to make Europe's cities more efficient and more sustainable in the area of energy.

This case study comes up with a new energy model that retrofits the present system in a public library building, as a way to the dissemination the Smart City concept and development of energy production based on a sustainable and autonomous process. Taking into account that to implement this concept, constant monitoring of energy data is essential and only installing measurement equipment, and consequent rapid dispatch data to be analyzed and stored in the cloud-based platform if able to achieve high levels of energy efficiency in buildings.

This work related to the ongoing research is based on an energy audit, comprising a survey on energy consumption by type: electrical and thermal (gas), recurring to portable energy analysers, as shown in Fig. 1, Another relevant aspect of this audit was the identification of anomalous situations in energy infrastructures: electrical and thermal, by means of a thermographic analysis of multiple parts of the installations, focused on electrical switchboards, as shown in Fig. 2, and thermal energy pinping. This consists of gathering information for determine energy savings from a perspective of energy determination of equipment that can induce forced stops away the power supply, for wear and tear or malfunction resulting from higher operating temperatures and lead to a rapid degradation. This energy of the building library consists of a photovoltaic (PV) plant and a biomass energy source to replace the gas that is currently used. As shown in Fig. 2, a spot with high temperature was detected on the bottom of a connection. This high temperature is due to a bad tightening and if this situation persists, the material would suffer a marked wear, leading to his destruction and possibly trigger a fire. The standards established by InterNational Electrical Testing Association (NETA) rule that a quick action is required, when the difference between electrical components exceeds 15ºC or the difference between air temperature and the electrical component exceeds 40ºC [14]. Besides bad electrical connections, thermal imaging can be used to detect the correct sizing of electrical components. An oversized (or underloaded) component would result in a low temperature, while an undersized (or overloaded) component would result in a high temperature. The innovative proposed model consists of a mix of energy production processes based on photovoltaic panels and biomass boilers. Economic analysis of the energy model already achieved some results regarding the payback of the investment, as well as to achieve decarbonisation of cities and a strategy for competitive and secure energy.

Museum

In the context of improvement of energy efficiency in public buildings, this case study comprised a small museum with an exhibition space of around 200 square meters and other areas (archive, administrative area, ...). This museum occupies a public building that was not built specifically for this purpose. The space underwent a minor retrofitting to receive the assets of the museum fifteen years ago. This implied some constraints on the use of the museum. Also, the energy bills were rising, becoming a major concern for the museum direction.

As a first approach, and after an energy audit conducted by the traditional method, the largest energy consumers were identified: lighting, dehumidifier and space heaters. The first step was the substitution of around 100 halogen spots (25, 35 and 50 W) by LEDs (4.4 W). The expected payback time is around 1.25 years, while increasing the light level in some spaces and minimizing the ultra-violet emission that fastens deterioration of some assets of the museum. Also, emissions of 1130 kgCO2e per year were avoided due to energy consumption reduction. In addition, some motion detectors were installed in the museum, mainly improving the convenience of the museum staff and, in addition, enabling additional energy savings in the lighting system.

The next step in this case study was the development of a low cost web-based meter, primarily for temperature and humidity supervision, but energy measurement features were included in the first iteration. The basic configuration of the system is shown in Fig. 3. A module with a humidity and temperature sensor and signal conditioning communicates with the central processing unit (CPU) using the wireless technology ZigBee ® . The energy measurement module is based on three current sensors and three 230/12 V and signal conditioning circuits that communicate with the CPU via a cable. The central unit, based on an Arduino processor, is responsible for processing the data received from the separate modules and record the data on a database. It is connected to the switch of the museum IT system via an Ethernet cable. The database created records the averaged values of temperature, humidity, voltage, current, active power, reactive power and power factor with an interval of 10 minutes. This data is available on an open web site. The system is also programmable with warning emission, by email, when the reference value of temperature and/or humidity is exceeded and anomalous energy consumption or power failures occur.

The central unit is scalable allowing to aggregate data from more temperatures and humidity modules or energy modules with slight changes in the software. Other changes, such as real-time power quality events recording are planned and possible without significant changes in the hardware of the meter.

The data recording and easy remote access to it, along with the warnings issued by the system, enables the manager of the building to take swift actions for a better energy efficiency.

Conclusions

With the increasing concerns for energy efficiency, a more efficient control of energy use is required. The timely availability of data, if possible in real time, constitutes a key factor in decision-making in all areas, including the energy management. Therefore, the traditional energy monitoring systems, sometimes limited to energy billing and periodic measures, constitute a barrier for the development of a proper energy management system focused on the best possible efficiency. Using the services provided by the cloud, the data could be attained more rapidly and the energy data handling can be simplified, using a common platform, optimizing processes for managing projects and opportunities. Also, with the use of cloud-based systems, the data may be available to different people wherever there is an internet connection.

As the efficiency of cloud computing increases, more services are developing, while each service or transaction tends to use less energy with several studies referring that cloud-based systems are more energy-efficient than on site IT systems. Bringing this energy saving together with the activity of energy auditing, further efficiency can be attained.

But sometimes the costs of buying and maintaining a system connected to the web can be an obstacle to the dissemination of these systems in buildings. The current work described here included the development of a low cost energy meter (including other parameter metering capabilities, such as power quality events, temperature and humidity). The dissemination of this kind of meters can play an important role in assisting the transition of locally available energy data to the web available data, allowing real-time information and benchmarking of different sites. These tools can play an important role in boosting the energy efficiency of buildings and processes.

Fig. 1 .

 1 Fig. 1. Measuring Equipment -Power Analyzer in the Collection of Consumptions.

Fig. 2 .

 2 Fig. 2. Thermografic image of switchboard and temperatures (maximum; average; minimum).

Fig. 3 .

 3 Fig. 3. Developed prototype of a web-based meter

Acknowledgment

This work has been partially supported by the Portuguese Foundation for Science and Technology under project grant PEst-OE/EEI/UI308/2014.


R Laia

H M I Pousinho
email: hpousinho@gmail.com

R Melício
email: ruimelicio@uevora.pt

V M F Mendes
email: vfmendes@deea.isel.pt

M Collares-Pereira
email: collarespereira@uevora.pt

Offering Strategies of Wind Power Producers in a Day-Ahead Electricity Market

Keywords: Mixed-integer linear programming, stochastic optimization, wind power, offering strategies

This paper presents a stochastic optimization-based approach applied to offer strategies of a wind power producer in a day-ahead electricity market. Further from facing the uncertainty on the wind power the market forces wind power producers to face the uncertainty of the market-clearing electricity price. Also, the producer faces penalties in case of being unable to fulfill the offer. An efficient mixed-integer linear program is presented to develop the offering strategies, having as a goal the maximization of profit. A case study with data from the Iberian Electricity Market is presented and results are discussed to show the effectiveness of the proposed approach.

Introduction

Renewable energy sources are viewed as of crucial usage for a sustainable society development [START_REF] Pousinho | Offering strategies for a wind power producer considering uncertainty through a stochastic model[END_REF] and the industry of conversion into electric energy is already exploiting these sources. Renewable energy sources can partly replace fossil fuel sources, avowing carbon emissions and reducing the fuel-import dependency on countries with rich fossil fuel stocks. Countries promote the usage of renewable energy sources by supporting mechanisms and policies to provide incentive or subsidy for renewable energy capturing [START_REF] Kongnam | Feed-in tariff scheme for promoting wind energy generation[END_REF]. Nowadays wind power is integrated into the electric power grid and there are encouragements by extra-market actions, involving, for instances, legislation, directives, feed-in tariffs, encouraging penalty pricing and guaranteed electric grid access [START_REF] Bitar | Selling wind power in electricity markets: the status today, the opportunities tomorrow[END_REF]. These actions runs at modest penetration levels in nowadays, but will become flawed as wind power penetration increases [START_REF] Bitar | Selling wind power in electricity markets: the status today, the opportunities tomorrow[END_REF]. This will force wind power producers (WPPs) to face the challenges of a day-ahead electricity market and bilateral contracting. For instance: in Portugal, WPPs are rewarded with a feed-in tariff in conditions of a limited amount of time or energy delivered, if one of these conditions fails, energy is sold either in the day-ahead electricity market or by bilateral contracts [START_REF] Barros | Feed-in tariffs for wind energy in Portugal: current status and prospective future[END_REF]; in United Kingdom, large WPPs are forced to participate in whole-sales markets and subjected to financial penalties in case of deviation from contracts in forward markets [START_REF] Barros | Feed-in tariffs for wind energy in Portugal: current status and prospective future[END_REF]. Intermittency and variability of wind power are WPP concerns of uncertainty in what regards imbalance penalties due to imbalance on the electric power delivered [START_REF] Al-Awami | Coordinated trading of wind and thermal energy[END_REF]. This paper is a contribution to deal with these concerns of uncertainty by using an approach based on stochastic optimization MILP to enable WPPs to optimize their offers having as a goal the maximization of profit in a day-ahead electricity market.

Relationship to Cloud-based Solutions

Cloud-based solutions can help the processing of approaches for helping trading in a day-ahead electricity market in order to take greater advantages of bids, requiring methodological approaches demanding computational effort not currently available to the WPP. Among these approaches the ones for the solution of the problems concerning with energy management, unit commitment and energy offers are particular vital for upholding a WPP business. The approaches to solve these problems have been limited by the available computational resources, i.e., details concerning some reality are disregard in view of the excessive use of computational requirements. These limitations are evident for large systems and lead to solutions not conveniently addressed in agreement with the reality, because the computational resources do not allow the usage of data or modeling for delivering more adequate solutions. Particularly, in what regards the fact that for WPP the market brings uncertainty and paying penalties due to uncertainty on wind power exploitation: the stochastic concern with scenarios data implies the processing of large sets of data requiring the use of reduction techniques to avoid the use of significant computational requirements.

Cloud-based solutions are able to contribute for upholding a WPP by setting out an adequate availability of computational resources needed to address those problems in due time. Although of the uncertainty on the wind power, i.e., intermittency and variability, cloud-based engineering systems will deal with problems approaching the full reality with gains in terms of profits for WPP's. Cloud-based solutions will help out smoothing the market-clearing electricity price due to the fact of having bids of wind power with higher level of energy and with more certainty in what regards the satisfaction on delivering the electric power accepted at the market-closing. Also, environmental benefits are expected with the increment in the ability of finding offers able to be fulfilled with a high level of being satisfied, i.e., integrating renewable energy into the electric grid with less deviation from the assumed compromises: less spinning reserved is needed, less thermal units are needed and less fossil fuel is used. Eventually, cloud-based solutions will allow processing approaches in order that when at a WPP site the renewable energy is available is all captured to be converted in electric energy to be injected without concerns on dynamic stability into the electric grid in due time.

State of the Art

Wind power and the market-clearing electricity price uncertainties are passed on the variables of the problems [START_REF] Cena | The impact of wind energy on the electricity price and on the balancing power costs: the Spanish case[END_REF][START_REF] El-Fouly | Impact of wind generation control strategies, penetration level and installation location on electricity market prices[END_REF] to be addressed by the WPP in order to know how much to produce in order to formulate realistic bids, because in case of excessive or moderate bids, other producers must reduce or increase production to fill the so-called deviation, implying penalties causing economic losses [START_REF] Pousinho | Offering strategies for a wind power producer considering uncertainty through a stochastic model[END_REF]. In order for upholding a WPP in a Offering Strategies of Wind Power Producers in a Day-Ahead Electricity Market 381 competitive environment, three main lines of action have been proposed in the technical literature: One of them is based on the use of wind power with energy storage technologies [START_REF] Angarita | Combined hydro wind generation bids in a poolbased electricity market[END_REF]- [START_REF] Gonzalez | Stochastic joint optimization of wind generation and pumped-storage units in an electricity market[END_REF]; another one is the use of financial options as a tool for WPP to hedge against wind power uncertainty [START_REF] Hedman | Comparing hedging methods for wind power: using pumped storage hydro units vs options purchasing[END_REF]; and the final one focuses on designing stochastic models intended to produce optimal offer strategies for WPP participating in an electricity market [START_REF] Bathurst | Trading wind generation in short term energy markets[END_REF]- [START_REF] Pinson | Trading wind generation from short-term probabilistic forecasts of wind power[END_REF], without depending on third-parties or governmental regulations. The third line of action is a stochastic formulation explicitly modeling the uncertainties faced by the scheduling activities of a WPP [START_REF] Ruiz | Wind power day-ahead uncertainty management through stochastic unit commitment policies[END_REF], using uncertain measures and multiple scenarios built by wind power forecast [START_REF] Fan | Forecasting the wind generation using a two-stage network based on meteorological information[END_REF]- [START_REF] Catalão | An artificial neural network approach for short-term wind power forecasting in Portugal[END_REF] and market-clearing electricity price forecast [START_REF] Catalão | Short-term electricity prices forecasting in a competitive market: a neural network approach[END_REF]- [START_REF] Amjady | Mixed price and load forecasting of electricity markets by a new iterative prediction method[END_REF] applications. Mixed integer linear programming (MILP) is one of the most successful explored methods for scheduling activities because of rigorousness, flexibility and extensive modeling capability [START_REF] Floudas | Mixed integer linear programming in process scheduling: modeling, algorithms, and applications[END_REF]. Hence, MILP is expected to be also a successful method for solving WPP problems in the context of the day-head electricity market and this paper aims at show the usefulness of this method for WPPs.

Problem Formulation

Wind energy conversion into electric energy for trading in a day-head market involves facing up uncertainties that must be taken into account in devising of the offer strategy. The uncertainties are due to the intermittence and variability on the available wind power and due to the market-clearing electricity price. These uncertainties if not conveniently addressed are capable of losses on profit due to the incurred imbalance penalties. The problem formulation in this paper is an addressing in a convenient way.

System imbalance is defined as a non-null difference on the trading between the delivered energy and the offered energy. If there is an excess of delivered energy in the power system, the system imbalance is positive; otherwise, the system imbalance is negative. The system operator seeks to minimize the absolute value of the imbalance in a power system through a mechanism based on prices penalization for the deviation of the delivered energy from the one offered by a producer in the day-ahead market. If the system imbalance is negative, the system operator keeps the price for the energy in excess for the producers with excess of offers, and pays a premium price for the energy produced above the offer. The prices are as follow

D t t λ λ = + (1) ) , max( UP t D t t λ λ λ = - (2)
In ( 1) and (2), + t λ and - t λ , are applied in the balancing market to the energy deviations, D t λ is the day-ahead market-clearing price and UP t λ is the price of the energy that needs to be added to the system. If the system imbalance is positive, the prices are as follow 382 R. Laia et al

) , min( DN t D t t λ λ λ = + (3) D t t λ λ = - (4)
In (3), DN t λ is the price of the energy of offers in exceeds. The uncertainties in the available wind power may result in differences between the energy offered by a WPP and the actual energy delivered. The revenue t R of the WPP for hour t is as follows

t D t D t t I P R + = λ (5)
In ( 5), D t P is the power traded by the WPP in the day-ahead market and t I is the imbalance income resulting from the balancing penalty. Since the total deviation for hour t is as follows

D t t t P P - = ∆ ( 6
)
where t P is the actual power for hour t . t I is given as follows

0 , ≥ ∆ ∆ = + t t t t I λ (7) 0 , < ∆ ∆ = - t t t t I λ (8)
In ( 6), a positive deviation means the actual production is higher than the traded in the day-ahead market and a negative deviation means an actual production lower than the traded, this way + t λ is the price paid to the WPP for its excess of generation and t λ the price to be charged for the deficit. Let

1 , ≤ = + + + t D t t t r r λ λ (9) 1 , ≥ = - - - t D t t t r r λ λ ( 10
)
Then 0 , ≥ = + t t t D t t r I ∆ ∆ λ (11) 0 , < = - t t t D t t r I ∆ ∆ λ (12)
Offering Strategies of Wind Power Producers in a Day-Ahead Electricity Market 383

A WPP that needs to correct the energy deviations in the balancing market incurs an opportunity cost because in the day-ahead market energy is traded at a more competitive price. Equation ( 5) can be rewritten to reflect the opportunity cost. Two cases have to be considered. If the energy deviation is positive, 0 > ∆ t , the revenue is given as follows

t t D t D t D t t r P R ∆ + = + λ λ ( 13
)
Using the total deviation expressed in equation ( 6), the revenue is given as follows

0 , ) 1 ( ≥ - - = + t t t D t D t D t t r P R ∆ ∆ λ λ ( 14
)
Similarly, if the energy deviation is negative, the revenue is given as follows

0 , ) 1 ( < - + = - t t t D t D t D t t r P R ∆ ∆ λ λ (15)
Equations ( 14) and ( 15) can be expressed in a general form as follows

t D t D t t C P R - = λ ( 16
)
where 0 , ) 1 ( ≥ ∆ ∆ - = + t t t D t t r C λ (17) 0 , ) 1 ( < ∆ ∆ - - = - t t t D t t r C λ (18)
In ( 16), the term

D t D t P λ
is the maximum revenue that the WPP can collect from trading the energy in a situation without wind power uncertainty. With wind power uncertainty a set of scenarios Ω is considered for wind power and system imbalances. Each scenario ω is weighted with a probability of occurrence π . The expected optimal revenue of the WPP over a time horizon is obtained be the maximization of the objective function given as follows ( )

∑∑ Ω = = - - + + ∆ - ∆ + N N t t t D t t t D t D t D t T r r P 1 1 ω ω ω ω ω ω ω ω ω λ λ λ π (19)
The maximization is subjected to constraints as follow

t P P D t ∀ ≤ ≤ , 0 max (20)

(

)

ω ω ω ∀ ∀ - = ∆ , , t P P D t t t (21) ω ω ω ω ∀ ∀ ∆ - ∆ = ∆ - + , , t t t t (22) ω ω ω ∀ ∀ ≤ ∆ ≤ + , , 0 t d P t t t (23)
In [START_REF] Catalão | Short-term electricity prices forecasting in a competitive market: a neural network approach[END_REF] the limit of offers to the maximum power installed in the wind farm is set. In [START_REF] Coelho | A RBF neural network model with GARCH errors: Application to electricity price forecasting[END_REF] to [START_REF] Floudas | Mixed integer linear programming in process scheduling: modeling, algorithms, and applications[END_REF]

is imposed 0 = ∆ + ω t when + ∆ ω t is negative, D t t P P < ω , and imposed 0 = ∆ - ω t when - ∆ ω t is negative, ω t D t P P <
. When the system balance is negative, the WPP is penalized for the deficit of energy generated below the energy traded in the day-ahead 384 R. Laia et al market, so the term

+ + ∆ ω ω ω λ t t D t r
is null and the term

- -∆ ω ω ω λ t t D t r
is subtracted from the revenue in the situation of no deviation,

D t D t P ω λ
. When the system balance is positive, the WPP is penalized for the energy generated above the energy traded in the day-ahead market, so the term

- -∆ ω ω ω λ t t D t r
is null and the term

+ + ∆ ω ω ω λ t t D t r
is subtracted from the revenue in the situation of no deviation.

Case Study

The effectiveness of the proposed stochastic MILP approach is illustrated by a case study using two sets of data from the Iberian electricity market [24]. The first data set comprises 10 days of November 2013 and the second 10 days of June 2014 as are respectively shown in Fig. 1. The energy produced is obtained using the total energy produced from wind scaled to the maximum power, MW P 120 max =

. The system operator matches the total energy

Offering Strategies of Wind Power Producers in a Day-Ahead Electricity Market 385 production to the system needs. This is achieved by defining the price multipliers + t r and - t r given by ( 9) and [START_REF] Bathurst | Value of combining energy storage and wind in short-term energy and balancing markets[END_REF]. The + t r and - t r in 2013 are respectively shown in Fig. 3. The optimal energy offer in conditions of maximizing a WPP revenue is determined by [START_REF] Catalão | An artificial neural network approach for short-term wind power forecasting in Portugal[END_REF] to [START_REF] Floudas | Mixed integer linear programming in process scheduling: modeling, algorithms, and applications[END_REF]. The optimal energy offer and the expected hourly revenue are respectively shown in Fig. 5 and Fig. 6. The forecasted revenue for the 24 hours is 52,861 € in 2013 and 39,656 € in 2014. The difference between the expected revenue and the revenue for each scenario, assuming that the 24 hours will behave exactly the same in each scenario is shown in Fig. In each year, the deviation for the worst case scenario is lower than the expected revenue, which means that if the condition during the day matches any one of the scenarios, the result would be always positive.

Conclusion

A stochastic MILP approach for solving the offering strategy of a WPP in a deregulated market is discussed in this paper and envisaged as potential convenient for the producers with the help of cloud-based solutions. The main result is the bidding strategy for a WPP facing the wind power and price uncertainties, as well the system imbalances which affect the price in case of deviations between the energy traded in the day-ahead market and the actual energy produced by the WPP.

Stochastic programming is a suitable approach to address parameter uncertainty in modeling via scenarios. The proposed stochastic MILP approach proved both to be accurate and computationally acceptable, since the computation time scales up linearly with number of price scenarios, units and hours over the time horizon. Since the bids in the pool-based electricity market are made one day before, this approach is a helpful tool for the decision-maker.

Fig 1 .

 1 Fig 1. Price scenarios; left: November 2013, right: June 2014. The total energy produced in 2013 and 2014 are respectively shown in Fig. 2.

Fig 2 .

 2 Fig 2. Energy from wind; left: November 2013, right: June 2014.

Fig 3 .

 3 Fig 3. Imbalance price multipliers 2013; left: + t r , right: - t r .

Fig 4 .

 4 Fig 4. Imbalance price multipliers 2014; left: + t r , right: - t r .

Fig 5 .

 5 Fig 5. Energy traded day-ahead market; dashed-line: 2013, solid line: 2014.

Fig 6 .

 6 Fig 6. Expected hourly revenue; dashed-line: 2013, solid line: 2014

7

 7

Fig 7 .

 7 Fig 7. Revenue deviation; left: 2013, right: 2014.


Sérgio F Santos

Nikolaos G Paterakis

João P S Catalão
email: catalao@ubi.pt

New Multi-Objective Decision Support Methodology to Solve Problems of Reconfiguration in the Electric Distribution Systems

Keywords: Distribution system reconfiguration, ε-constraint method, switching cost, multi-objective optimization

The distribution systems (DS) reconfiguration problem is formulated in this paper as a multi-objective mixed-integer linear programming (MILP) multi-period problem, enforcing that the obtained topology is radial in order to exploit several advantages those configurations offer. The effects of distributed generation (DG) and energy storage systems (ESS) are also investigated. To address the multi-objective problem, an improved implementation of the ε-constraint method (AUGMECON-2) is used, providing an adequate representation of the Pareto set. The objective functions considered stand for the minimization of active power losses and the minimization of switching operations. The proposed methodology is tested using a real system based on the S. Miguel Island, Azores, Portugal. The potential uses of cloud-based engineering systems, both in terms of exploiting the enhanced decentralized computational opportunities they offer and of utilizing them in order to achieve communication and coordination between several entities that are engaged in DS, are thoroughly discussed.

Introduction

The reconfiguration of power distribution systems (DS) is the process of opening and closing switches, changing the network topology, in order to achieve several operating advantages. The problem is to find a configuration that presents the least amount of active power losses, subject to the following restrictions: voltage levels, power transfer capability of branches, the rated power of transformers and often the radial configuration of the obtained system. A classification of the DS problems together with a literature survey can be found in [START_REF] Thakur | Study and Characterization of Power Distribution Network Reconfiguration[END_REF].

Systems with meshed structures are not recommended for power distribution networks, because their protection schemes are more complex in comparison with radial distribution systems. The reconfiguration problem is typically a nonlinear, multiobjective, combinatorial problem, subject to operational constraints of loads. Some of these configurations are not allowed, or because they lead to a disconnected system (with several islands) or non-radial systems. Others are not feasible, because they violate operational and load restrictions. Various objective functions have been used, but the most common one is the minimization of the active power losses [START_REF] Jabr | Minimum Loss Network Reconfiguration Using Mixed-Integer Convex Programming[END_REF].

Multi-objective approaches try to optimize a combination of the previous objective functions [START_REF] Zidan | Long-term multi-objective distribution network planning by DG allocation and feeders' reconfiguration[END_REF], [START_REF] Amanulla | Reconfiguration of Power Distribution Systems Considering Reliability and Power Loss[END_REF]. In the emerging Smart Grid scheme, Distributed Generation (DG) and Energy Storage Systems (ESS) play a key role and pose new challenges in the operation of the DS [START_REF] Wu | Study of Reconfiguration for the Distribution System With Distributed Generators[END_REF], [START_REF] Malekpour | Multi-Objective Stochastic Distribution Feeder Reconfiguration in Systems With Wind Power Generators and Fuel Cells Using the Point Estimate Method[END_REF].

The majority of the related studies in the literature treat the problems using solution techniques based on meta-heuristics, mainly because they are easily applicable to the problem and offer computational advantages, especially in the case of the multiobjective formulations. There are also studies that try to solve the DS reconfiguration problem through the linearization of the AC power flow constraints [START_REF] Franco | A mixed-integer LP model for the reconfiguration of radial electric distribution systems considering distributed generation[END_REF], formulating it as a Mixed-Integer Linear Programming (MILP) problem.

However, treating the DS reconfiguration with a Multi-Objective Mathematical Programming (MOMP) approach poses difficulties, mainly due to the computational effort that is required and the need to guarantee that the obtained solution is the best possible [START_REF] Mavrotas | Effective implementation of the ε-constraint method in Multi-Objective Mathematical Programming problems[END_REF]. Although solving a Single-Objective Mathematical Programming problem is a procedure that will return the maximum or the minimum solution among the feasible ones, the solution of a MOMP problem is not a trivial task, since there is not, in general, a single solution that optimizes every objective function simultaneously. In MOMP, the required result is the set of the relatively optimal solutions, called the Pareto set.

The aim of this work is to develop tools that contribute to the quality of service to the end-users at a minimal cost to the companies responsible for power distribution. Therefore, the novel contributions of this work are twofold. The first contribution is the formulation of the radial DS reconfiguration as a multi-period MOMP problem, considering the effects of DG and ESS with two objective functions: minimization of the active power losses and minimization of the total switching cost. The second contribution comes from the solution of the problem using an improved version of the ε-constraint method, namely the Augmented ε-constraint Method (AUGMECON-2), a state-of-the-art methodology introduced by Mavrotas in [START_REF] Mavrotas | Effective implementation of the ε-constraint method in Multi-Objective Mathematical Programming problems[END_REF] and further improved in [START_REF] Mavrotas | An improved version of the augment ε-constraint method (AUGMECON2) for finding the exact pareto set in multi-objective integer programming problems[END_REF], in order to generate an adequate representation of the Pareto optimal solutions of the problem.

Contribution to Cloud-based Engineering Systems

The DS reconfiguration (DSR) problem has been a topic of intensive research that has led to several applications during the past decades. Nevertheless, recent changes in the characteristics of the DS, such as the introduction of DG, ESS and flexible demand, as well as the introduction of various stakeholders that utilize the DS, require the revaluation of the DSR problem using innovative solutions.

In this respect, cloud-based engineering solutions may prove invaluable in several ways. Illustratively, several applications that can immediately benefit the distribution system operator with respect to the DSR problem are:

1. Optimal DSR is formulated as a complex optimization problem. Given emerging elements that have to be considered in optimization procedures, the complexity of the DSR problem dramatically increases. The high computational burden, especially for a large-scale DS, may force distribution system operators to upgrade the informatics infrastructure, incurring high investment costs. A cloud-based engineering system could be used in order to solve the problem in a de-centralized fashion using cloud computing.

2. The introduction of several entities (e.g. load aggregators and DG unit's owners) that utilize the DS to materialize their purposes, imposes the need of transparency regarding the DSR decisions. The configuration of the DS affects several DS operating parameters, such as losses and quality of service, which in turn may affect the allocation of operating costs. A cloud-based engineering system (e.g. an on-line portal) may be used in order to allow stakeholders to access relevant information, promoting the fair allocation of costs. 3. Internet is a utility that is available virtually everywhere since there are many wired and wireless options to access the internet. A cloud-based engineering system may be utilized in order to monitor data, even at remote nodes of the DS at an affordable cost. In this way, better analytics may be obtained and exploited in the development of more accurate optimization problems and real-time operation (e.g. fault detection). Also, commands such as switching actions may be given remotely, eliminating constraints such as crew availability. Finally, advanced control schemes may be performed automatically (e.g. automated reconfiguration after the detection of a fault).

Methodology

Overview of Augmented ε-constraint Method

The ε-constraint method is a "generation method" that is used to construct an adequate representation of the Pareto-optimal set of solutions, and does not consider the Decision Maker's preferences a priori. Among the different objective functions, one is used as the objective function of the problem, while the others are treated as inequality constraints. Their bounding values are varied parametrically in order to produce the Pareto-optimal set of solutions. The application of the ε-constraint method requires the knowledge of the range of objective functions that are used as constraints. The range is usually calculated using the pay-off table that contains the values of the objective functions, resulting from the individual optimization of each single objective function [START_REF] Cohon | Multiobjective Programming and Planning[END_REF]. The pay-off table alone does not guarantee that the range always provides the efficient set. AUGMECON addresses this issue through the utilization of lexicographic optimization. Lexicographic optimization is performed by optimizing the objective functions according to their priority. The highest priority objective function is optimized first and its optimal value is incorporated as an equality constraint in the optimization of all the less priority objective functions. This procedure is repeated for all the objective functions. After lexicographic optimization, the ranges of the objective functions are divided in equal intervals and + 1 grid points are used to parametrically vary the bound of the objective functions used as inequality constraints in the classical ε-constraint method. This method is guaranteed to provide only efficient solutions [START_REF] Mavrotas | Effective implementation of the ε-constraint method in Multi-Objective Mathematical Programming problems[END_REF]. The number of grid points is adjustable and is directly linked to the density of the Pareto-optimal set representation. It also allows determining the desired trade-off between quality of the representation and computational burden. To reduce the computational burden, power flow equations are not incorporated as constraints of the optimization problem. Through a linear approximation of the active power flow losses (using Special Ordered Sets of Type 2-SOS2) a least-losses equivalent topology may be obtained. If required, branch currents, node voltages and the exact amount of losses may be calculated afterwards for the obtained topology using any available power-flow algorithms. The linearization through SOS2 variables offers computational advantages when using Branch-and-Bound based solution algorithms (e.g. CPLEX).

Mathematical Formulation

In this section, the proposed mathematical formulation is presented. To simplify the application of the aforementioned multi-objective optimization method and in order to reduce the computational burden, constraints that typically appear in DS reconfiguration problems in the literature, such as node voltage limits, line currents, reactive power, etc. are not considered, assuming that sufficient reactive power compensation is available locally (at the nodes) and that an advanced metering infrastructure (AMI) provides enough information regarding the state of voltage magnitude and angle. The nomenclature used in the formulation is presented in the Nomenclature at the end of the paper.

1) Objective Function a) Minimization of the Total Operating Costs

Objective function (1) stands for the minimization of the total power losses over the total time period.

The two objective functions are conflicting. As the load at the different nodes of the DS varies with time, the flows through the branches change, so do the losses. Thus, by reconfiguring the DS in order to minimize the losses at a specific time period, switching operations are contributing in the total switching-cost.

2) Constraints a) Radiality Constraints

The radial configuration of the system is ensured by (3)- [START_REF] Wu | Study of Reconfiguration for the Distribution System With Distributed Generators[END_REF]. Constraints (4) and (5) consider transfer nodes, i.e. nodes without production or consumption.

, ∈ = - - (1 -, ) ∈ : ∈( ∪ " # ) (3)
, ≤ , ∀' ∈ (, ) ∈ (* ∪ * ∪ * + ), , ∈

,

∈ : ∈( ∪ " ∪ " # ) ≥ 2 • , ∀) ∈ * , , ∈ (5)
A DS topology is radial if and only if it constitutes a tree-graph (no loops) and all the nodes are connected.

b) Constraints ensuring the Connection of Nodes with Distributed Elements

The following constraints prevent islanding. Thus, they do not allow a part of the network to be fed from distributed elements (i.e. storage systems, DG). For intentional islanding (e.g. for back-up reasons) these constraints could be handled in order to allow some nodes to play the role of a substation.

0 , ∈ : ∈ " # - 0 , ∈ : ∈ " + 0 , 1 = 0 2 ∀) ∈ 3, , ∈ (6)
-24 • , ≤ 0 , ≤ 24 • , ∀' ∈ (, , ∈

k 6,7 8 ≥ 0 ∀i ∈ Ω 6 < , t ∈ T (8) 0 , 1 = 0 ∀) ∉ * , , ∈ (7)
0 2 = 1∀) ∈ * 24 (9)
)

0 2 = 0∀) ∉ * 24 (11)
c) Node Power Balance, Branch Flow Limits, Substation Limits and Distributed Generation Limits Constraints (12)-(15) stand for the power equilibrium at each node of the distribution system and set the appropriate values for the respective decision variables. @ , ∈ : ∈ " # -@ , ∈ : ∈ "

+ , + , 21 + , 2 = A , + , BC ∀) ∈ 3, , ∈ (12)
-@ DEF • , ≤ @ , ≤ @ DEF • , ∀' ∈ (, , ∈

) d) Linear Approximation of the losses

The power losses on a branch are approximated using a quadratic function of the power that flows through the branch. The units of the coefficients b and c are [.] and [MW -1 ], respectively.

, = ' • G@ , G + H • @ , I ∀' ∈ (, ∀, ∈ (16)
The expression of the losses can be linearized using the concept of Special Order Sets of Type 2 (SOS2). This is described by ( 17)-( 19). It should be noted that variables J are positive and continuous.

J , ,K K∈L = 1 ∀' ∈ (, ∀, ∈ (17)
@ , = M K K∈L • J , ,K ∀' ∈ (, ∀, ∈ (18)
N , = O K K∈L • J , ,K ∀' ∈ (, ∀, ∈ (19)
By the definition of SOS2, it is also stipulated that no more than two adjacent values of z can be greater than zero. The accuracy of the approximation depends on the sampling of the non-linear function, i.e. the number of samples and the intervals that are used.

It is also reported that the linearization of a function using this method has computational advantages when using the Branch-And-Bound algorithm that is implemented in many commercial solvers.

e) Switching Cost Equations ( 20)-( 22) define the switching cost by following the change of status of every line. Through the parameter SC R a different switching cost can be attached to every branch representing the cost emerging from this operation, considering several factors such as equipment degradation costs and crew constraints.

, = ( , -, ST ) • ∀' ∈ (, , ∈ |, V 1 )@ , = 1 (20) , = ( , ST -, ) • ∀' ∈ (, , ∈ |, V 1 )@ , = 0 (21) , = 0 ∀' ∈ ( )@ , = 1 (22

) f) Energy Storage System Constraints

Energy Storage Systems (ESS) are an important asset of the smart-grid. Promising technologies such as Sodium-Sulfur batteries (NAS) have been already used in practice and can efficiently store large amounts of energy. Their primary goal is to support demand response activities, balancing volatile renewable energy sources production and offer back-up and other ancillary services. In this study, a general formulation of an ESS is considered through (23) to (28), in order to investigate their ability to facilitate the operating goals of the DS.

WX , = WX , ST + , BC . X - , 2 AX ∀) ∈ * Z , , ∈ (23)
, BC ≤ [ • , Z ∀) ∈ * Z , , ∈ (24)
,

Z + J , Z ≤ 1 ∀) ∈ * Z , , ∈ (28)

Tests and Results

The proposed methodology has been coded using General Algebraic Modeling System (GAMS) and the solver CPLEX. The system used to illustrate the presented methodology is adapted from [START_REF] Açores | ^). PARAMETERS: -number of nodes; -number of substation nodes; 24 -number of nodes[END_REF] and is presented in Fig. However, at this point, an assumption is made about the decision maker's final selection. It can be noticed that, as the switching cost decreases, the active power losses increase. Furthermore, it can be noticed that the first four solutions slightly increase the active power losses, while the switching cost is significantly decreased. Thus, the final selection considered is the 4-th efficient solution.

The configurations for this solution during the horizon are shown in Figs. 3 and4. The first reconfiguration occurs at the beginning of period T4-T3 and T7 where the branches L49, L50, L51 and L45 open. At the beginning of period T4 the branch L50 and L45 closes and the branch L10 and L27 opens. The DG units provide power at their maximum capacity during all the periods. In Fig. 5 the ESS state-of-energy is presented. During period T4 the ESS is charging. This stored energy is used during periods T5 and T6 in order to serve the increased demand needs.

Conclusions

In this work the application of a new method to handle the DS reconfiguration problem was presented. The problem was formulated as a multi-period multi-objective mixed-integer linear problem, solved using the augmented ε-constraint method in order to produce an adequate representation of Pareto efficient solutions set. The objective of the proposed formulation was to find the DS configuration that has as a result the minimum losses and switching operations. DG and ESS have also been considered in the proposed mathematical formulation. Applying the ε-constraint method in order to solve multi-objective problems related to the DS, considering also power flow

  of the Total Switching Costs Objective function (2) stands for the total cost emerging from the switching operations required throughout the horizon in order to change the DS configuration. = ,

, 2 ≤

 2 A[ • J , Z ∀) ∈ * Z , , ∈ (25) WX , ≤ WX DEF ∀) ∈ * Z , , ∈(26)WX , ≥ WX D \ ∀) ∈ * Z , , ∈

  respectively, and 11811 kW at the São Roque power node. The Pareto efficient set of solutions obtained by the AUGMECON method is shown in Fig.2.Five grid points are used and the CPU time needed is 54.8 seconds on a laptop with an 8-core processor and 4GB of RAM, running a windows 64-bit distribution. Using more grid points, no more efficient solutions are discovered, thus Fig.2provides the complete Pareto efficient solution set. After acquiring an adequate representation of the Pareto efficient solution set, a decision making procedure should be applied, such as the Analytic Hierarchy Process (AHP) or the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), in order to make the final decision.

Fig. 1 .

 1 Fig. 1. Single-line diagram of Test System Network MT 10kV Interconnection São Roque -Lagoa adapted [11].

Fig. 2 .

 2 Fig. 2. The Pareto efficient solution set.

Fig. 3 .

 3 Fig. 3. Configuration of the distribution system during periods T1-T3 and T7.

Fig. 4 .

 4 Fig. 4. Configuration of the distribution system during period T4-T6.

Fig. 5 .

 5 Fig. 5. ESS State-of-energy during the time horizon.

Acknowledgment. This work was supported by FEDER funds (European Union) through COMPETE and by Portuguese funds through FCT, under Projects FCOMP-01-0124-FEDER-020282 (Ref. PTDC/EEA-EEL/118519/2010) and PEst-OE/EEI/LA0021/2013. Also, the research leading to these results has received funding from the EU Seventh Framework Programme FP7/2007-2013 under grant agreement no. 309048

equations, such as optimal placement and sizing of DG units and ESS, reliability and other quality of distribution issues, will be the subject of future works by the authors.


Ioana Andreea Stănescu
email: ioana.stanescu@ats.com.ro

Antoniu Ștefan
email: antoniu.stefan@ats.com.ro

Florin Gheorghe

Cloud-Based Decision Support Ecosystem for Renewable Energy Providers

Keywords: dynamic architecture, cloud computing, renewable energy

The increasing complexity of decision making environments requires new approaches that can improve the efficiency, the effectiveness and the quality of the decision making processes. Cloud-based Decision Support Ecosystems (DSE) create the premises for the next generation of DSS, by modeling dynamic system architectures and customizable decision layers that instantiate a new level of independence at end-user level. End-users are able to connect new data sources to the decision making processes without assistance from software developers, while maintain consistency, to build more relevant decision environments. The authors discuss key challenges associated with the DSE and present the design premises of a cloud-based DSE for renewable energy providers.

Introduction

A Decision Support System (DSS) should enable decision makers to efficiently manage the increasing complexity, rapid changes and emergent risks of today's business environments. However, while it is easy to highlight the potential benefits of DSSs, it is often harder to deliver them in practice. Technology and knowledge advance at a rapid pace, but the complexity of the decision making environments also increases. The speed and the quality of decision making processes have to be enhanced at a faster rate. Beside context specific issues, decision makers also have to overcome collateral challenges associated with information overload and information distortion.

Nowadays, decision making does not rely on a single tool, but on a heterogeneous mix of systems of systems that support decision making processes. However, even if these systems are integrated and interoperable, they still reply on a static architecture that end-users cannot customize according to their needs. The unified management of all these DSSs coupled with the reduction of redundancies and end-user development represent a significant challenge. How can existing decision support technologies be improved considering emerging technologies and practices?

Web technologies and mobile communication, increased processing power, cloud infrastructures, and intelligent devices have created the premises for DSSs that enable decision makers better their performance. There are many opportunities to employ new information technologies to improve decision making processes.

In this context, the authors advance the notion of Decision Support Ecosystems (DSE) that fundament the design and development of dynamic system architectures, and that introduces for end-users a new level of independence from system developers. The design premises of a cloud-based DSE for renewable energy providers are presented, and related challenges are discussed.

Cloud-based Decision Support Ecosystems

The approach proposed in this paper builds upon cloud computing developments that enables the delivery of computing resources as a service. Cloud solutions implement horizontal scalable architectures, dynamic sizing (automatically adding and removing server instances), zero downtime architectures, dynamic failure detection and recovery architecture, etc [START_REF] Gregg | Systems Performance: Enterprise and the Cloud[END_REF], [START_REF] Mahmood | Cloud Computing: Concepts, Technology & Architecture[END_REF]. Cloud capabilities, especially dynamic sizing, answer to a critical issue that concern the use of the term "ecosystem" in connection to software: absence of intention [START_REF] Stallman | Free Software, Free Society: The Selected Essays of Richard M. Stallman[END_REF]. Cloud services are key to building autoadaptable software ecosystems. Because cloud environments are able to use as many servers as necessary to optimally respond to the cost and the timing constraints of an application [START_REF] Marinescu | Cloud Computing[END_REF], they are able to nurture the natural evolution of DSEs.

In the case of a dynamic system architecture, end-users are able to integrate their own data sources and they are able to customize the decision flows to integrate them. The authors have considered an Intelligent Decision Support and Control System for Low Voltage Grids with Distributed Power Generation from Renewable Energy Sources (INDESEN) to validate their premises. The system is designed as a cloud centric solution that stores and processed data centrally. This approach increases the adoption by lowering upfront costs and overall Total Cost of Ownership. Another contributing factor in choosing a cloud based solution is the large geographical distribution of renewable energy power plants which can only be efficiently managed through a centralized solution.

For data collection purposes, the system defined a set of API functions that can be used by third-party developers, as well as a set of standard software agents that can be deployed on site and feed data from proprietary hardware to the cloud.

State-of-the-Art

Decision capabilities have been supported by a large range of systems ranging from Executive Information Systems, Expert Systems and Decision Support Systems to Business Intelligence, Business Analytics, Business Activity Monitoring, Business Performance Monitoring [START_REF] Power | Decision Support Basics[END_REF], Knowledge Based Systems [START_REF] Zaraté | Integrated and Strategic Advancements in Decision Making Support Systems[END_REF], Creativity Enhancing Systems [START_REF] Delen | Real-World Data Mining: Applied Business Analytics and Decision Making[END_REF], etc.

Advances in Information Technology (IT) have brought solutions to many DSS issues and at the same time they also generated new opportunities and challenges for DSS developers. System integration and interoperability have significantly enhanced the performance, efficiency and quality of decision processes [START_REF] Stanescu | Interoperability Scenarios in Serious Games Ecosystems: The Impact on FInES[END_REF].

For the purpose of this paper, decision support tools used in the electrical energy field have been considered. In this context, Supervisory Control and Data Acquisition (SCADA) based solutions have been the first to be designed and developed to monitor and control renewable energy plants [START_REF] Mccrady | Practical Procedures for SCADA Software Development[END_REF]. The early developments of such systems offered a friendly interface for controlling systems that contain Programmable Logic Controllers (PLC) and mainly aimed to assist the human operators in routine processes [START_REF] Khedkar | SCADA based Integrated Operation of Renewable Energy Sources[END_REF]. More complex solutions have followed providing functions that were able to provide monitoring and operational evaluation of remote Renewable Energy Sources [START_REF] Papadakis | A server database system for remote monitoring and operational evaluation of renewable energy sources plants[END_REF].

Considering the specific requirements related to renewable energy production, storage, and distribution, research efforts in recent years have focuses on more advanced solutions able to facilitate renewable energy management and decisionmaking for independent or connected to public supply networks. Research has been carried out on renewable energy monitoring [START_REF] Villasevil | Plug-in driven architecture for renewable energy generation monitoring[END_REF]; interoperability issues [START_REF] Stanescu | Interoperability Scenarios in Serious Games Ecosystems: The Impact on FInES[END_REF]; algorithms for fast oscillation detection [START_REF] Vanfretti | Monitoring and Control of Renewable Energy Sources using Synchronized Phasor Measurements[END_REF]; environmental monitoring [START_REF] Garel | Applicability of the "Frame of Reference" approach for environmental monitoring of offshore renewable energy projects[END_REF], linear and non-linear optimization algorithms used in renewable energy sources [START_REF] Iqbal | Optimization classification, algorithms and tools for renewable energy: A review[END_REF]; production of scientific knowledge on renewable energy [START_REF] Rizzi | The production of scientific knowledge on renewable energies: Worldwide trends, dynamics and challenges and implications for management[END_REF]. Research addressing decision-making concerned energy availability for consumers, safety power supplying; reducing costs and maximizing generation [START_REF] Dumitru | SCADA Based Software for Renewable Energy Management System[END_REF].

Decision Support Ecosystems

Perspectives on Ecosystems

In recent years, ecosystems have gained momentum as an important field of research fueled by new business models [START_REF] Hanssen | Theoretical foundations of software ecosystems[END_REF]. A wide variety of ecosystems ranging from software to business and social ecosystems have been modeled. For the purpose of this research software and business ecosystems have been considered.

Software ecosystems are defined as a set of software solutions that enable, support and automate the activities and the transactions of the actors that operate in a business environment [START_REF] Bosch | From Software Product Lines to Software Ecosystems[END_REF]. Considering the multitude of devices and applications that are used in a renewable energy plant, the adoption of an ecosystem approach has the potential to provide the prerequisites for better decision-making processes.

Companies have changed the focus from rear-view mirror analysis (studying data from the past) to looking through the windshield practices (using data to predict future patterns) because the ability to anticipate can bring significant advantages [START_REF] Pring | Code Halos: How the Digital Lives of People, Things, and Organizations are Changing the Rules of Business[END_REF]. For renewable energy providers the ability to predict is even more relevant, as based on prediction they can better estimate energy prediction (based on more accurate weather patterns), deploy resources more effectively, reduce downtime, adjust staff levels, etc. Building business analytics ecosystems stands out as an essential component of future applications.

Key Challenges for DSE End-Users

The complexity of the decision-making environments has increased due to information overload, distortion of information, the need for faster, more accurate decisions, the challenging business environments, increased costs, etc. The capacity to access the right information at the right time, to retrieve knowledge, to analyse data and documents, as well as the ability to anticipate have become crucial for managers.

The premises for the DSE design have emerged from a set of challenges associated with existing DSSs. Power [START_REF] Power | Decision Support Basics[END_REF] has identified that:

1) DSS employ complex hardware and software technologies, and decision makers need computing and software knowledge to be able to operate such systems; 2) Decision makers need to manage rapidly changing environments, including changes associated with context environments and technology evolution; 3) There is a growing need for end-user development of DSS. 4) Decision makers need to understand the upside benefits, the downside risks, and the possibilities of further development. Currently, DSS have a static architecture that translates into a limited flexibility at end user level. End users cannot perform changes in the system without assistance from developers even if they have advanced IT skills. Even if end users are able to connect to external data sources, the system logic is not customizable and the new sources cannot be integrated into decisional flows.

DSE for Renewable Energy Providers

The decision-making processes in the renewable energy field are extremely challenging as they are based on masses of details concerning many different issues that require analysis and management. Therefore, decision makers use different tools to monitor and control, to carry out diagnosis and prediction, and to make decisions. They also rely on a wide range of data sources to fundament their decisions. These data sources are difficult to predict when the decision support tool is developed. Even if initial, generic data sources exist, for better decisions DSE end users need to connect to more data sources.

The research reported in this paper addresses the above-mentioned challenge and documents the decision-making processes associated with the management of renewable energy plants with the purpose of supporting the design of a cloud-and knowledge-based Intelligent Decision Support and Control System for Low Voltage Grids with Distributed Power Generation from Renewable Energy Sources (INDESEN) where end users can integrate into decision flows any data sources that comply to accepted formats (Fig. 2). INDESEN is designed to integrate the following modules:

• The Monitoring Module. Enables real-time tracking of the parameters that monitor the electric energy quality and the environmental factors. The data will be stored in the INDESEN database and will fundament the development of the knowledge base and the diagnosis of the hardware equipment.

•

The Diagnosis Module. The diagnosis of the equipment and of the causes that led to dysfunctions is carried out in the Diagnoses Module against reference standard values collected from the equipment specifications, the regulatory requirements issued by competent authorities, standards, national and European legislation, etc.

• The Prediction Module. The short-, medium, and long-term prediction is based on internal and external data sources. Data are constantly collected from the equipment and sensors installed in the renewable energy parks and from external weather services. The analysis takes into account the historical data and expert knowledge collected in the system. The capacity to produce electric energy is determined based on factors such as: the periodicity (day/ night; summer/ winter) of the environmental factors (solar radiation, temperature, wind speed), the equipment wear in time, etc.

• The Decision Module. The system will generate alternative decision scenarios that the decision-makers can choose from. For each scenario the system will present a synthesis of the rationale behind it build on historical data, current state of the equipment, weather prediction services, expert knowledge, etc.

• The Control Module. The system will allow real-time control of the equipment, in order to increase their efficiency. Decision-makers can intervene to optimize the energy supply/ storage ratio.

End users are able to integrate their own data sources in any of the above mentioned modules of INDESEN. The customizable decision layer maintains the consistency across the system, as end users can define correlations between the new data sources and the decision flows supported by the system. As INDESEN is designed as a cloud-based system, this enables the solution to scale according to the demands. End users will not encounter hardware or software capabilities issues when connected to a large number of new data sources.

Discussion and Conclusion

The increasing complexity of the decision-making processes in a globalized economy created the need for advanced computerized decision-support ecosystems that enable fact-based decisions, improve decision quality, enhance the efficiency and effectiveness of decision processes, and are able to provide competitive advantage while addresses rapid changes, and emerging risks. Wide access to knowledge management architectures, worldwide real-time access, increased performance and quality, user friendliness, standardized structures, and an easily administered controlling system represent key requirements for DSS. However, without an ecosystem perspective that is based on dynamic software architectures and that integrates cloud-based solutions and end user customizable decision support tools, decision support remain limited.

The authors present the key challenges of current DSS and the premises for the design of an end user customizable cloud-and knowledge-based Intelligent Decision Support and Control System for Low Voltage Grids with Distributed Power Generation from Renewable Energy Sources that is able to enhance decision-making processes within future enterprises.

This approach implements a new level of flexibility as end users can integrate data and knowledge sources independently from the system developers and they can reconfigure decision making process to accommodate the sources also without support from developers.

Future work includes the development and testing of the customization features of the DSE at end user level.

Fig. 1 .

 1 Fig. 1. Cloud-centric data flow.

Fig. 2 .

 2 Fig. 2. INDESEN end user customizable decision layer.

Acknowledgments. This research has been carried out within the INDESEN Project "Intelligent decision support and control system for low voltage grids with distributed power generation from renewable energy resources", Contract No. 42/2011, funded through the Romanian Partnership Program.

The paper builds upon the PhD research carried out within the INDESEN Project, funded by Unitatea Executiva pentru Finantarea Invatamantului Superior, a Cercetării


L Fialho

R Melício
email: ruimelicio@gmail.com

V F Mendes

M Collares-Pereira

V M F Mendes

Simulation of a-Si PV System Linked to the Grid by DC Boost and Three-Level Inverter Under Cloud Scope

Keywords: PV system, DC-DC boost, three-level inverter, simulation

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Introduction

The increment on the use of scarce fossil-fuel sources, the society wariness about the anthropogenic gas emissions and the increasing energy demand have strongly impelled the development of the use of renewable energy sources during the last decades [START_REF] López | Implementation of Wireless Remote Monitoring and Control of Solar Photovoltaic (PV) System[END_REF]. For instance, the growth of the annual market regarding exploitation of solar energy is an evidentiary fact during the last decade. Particularly, a growing expansion is to be expected over the coming decade in what regards the deployment of photovoltaic (PV) systems.

The European Commission has launched a line of attack for the Europe to become a highly energy-efficient and a low-carbon economy with a set of proposals to create a new Energy Policy for Europe, reducing the anthropogenic gas emissions by 20% by 2020 and 50% until 2050, raising the overall share of conversion from renewable energy sources. Solar energy exploitation is expected to be significant on the European Energy Policy. Also, European Commission points out a future significant advance towards a more active role of the consumer by the implementation of the concept of smart grid (SG), improving integration into the grid for renewable energy sources and increasing energy efficiency. An advance thought to have a significant impact on mitigation of anthropogenic gas emissions, job and technology development [START_REF] Fialho | PV System Modeling by Five Parameters and in Situ Test[END_REF].

A PV system directly converts solar energy into electric energy. The main device of a PV system is the solar cell. Solar cells are grouped to form PV arrays. An array is either a panel or a set of panels connected in series or parallel to form large PV systems. Simulation of PV systems is vital to assist in exporting energy, anticipating bad performances and deciding convenient measures to avoid malfunctions and my significant benefit in real-time application from cloud-based solutions.

Power electronic converters have been developed for assisting in the integration of renewable energy conversion into the electric grid. Historically, low power PV systems use single-phase inverters, but in three-phase grid linking the use of only one single-phase inverter produces unwanted imbalance between the phase currents due to the injection of energy into only one phase of the grid. As reported in [START_REF] Rampinelli | Mathematical Models for Efficiency of Inverters Used in Grid Connected Photovoltaic Systems[END_REF] a maximum power of 4.6 kW with 10 % of tolerance is possible to link to only one phase of a three-phase grid. Three single-phase inverters are needed for linking power greater than 5 kW to ensure a convenient balanced energy distribution between the phases.

Relationship to Cloud-based Solutions

A Cloud-based solution is significant support for launching a line of attack for a future highly energy-efficient management of energy conversion and usage. As the global energy demand increases with the growing world population, alternative sources of energy turn out to be attractive for exploitation in what regards a sustainable society's development. Within this attractive exploitation, the renewable energy from PV systems exploitation is considered one promising and reliable energy source for distributed generation (DG). DG and the increase usage of electric energy, for instances, the expected significant usage of electrical vehicles, will drive upcoming concerns on nowadays electrical grid about the ability to encompass with the future. So, a hatching thought about the electric grid is needed and the SG conception is on the way. A SG will benefit from cloud-based solutions allowing data interchange between end users and producers for transparency on energy consumption and on energy conversion of other forms of energy into electric energy. A Cloudbased solution allows the wanted consumer commitment in the management within the SG scope. The SG will be a source of information able to interact with other kinds of data, not only monitoring the flow of electric energy, but also an entire set of environments, leading to a foreseen increase data to be processed by SG management systems. So, the SG architecture has to be implemented with ensured security and reliability. A layered framework is one option gathering information about the SG components offering an awareness of the behavior, enabling people or machines to act accordingly over a services platform. The engineered software framework can be transposed to a Cloud architecture system, taking advantages of the existing internet cloud services to process with reduced operational costs the data storage and data transfer in real-time with reduced operational costs. For instance, as depicted in Fig. 1 for the PV system in study in this paper. This framework facilitates the integration of sensors and actuators with bidirectional data exchange [START_REF] Batista | Layered Smart Grid Architecture Approach and Field Tests by ZigBee Technology[END_REF], [START_REF] Papageorgas | Smart Solar Panels: In-situ monitoring of photovoltaic panels based on wired and wireless sensor networks[END_REF], [START_REF] Ayodele | Challenges of Grid Integration of Wind Power on Power System Grid Integrity: a Review[END_REF], allowing real-time simulations speeding up the integration PV system energy into Smart Grid.

Modeling

The solar cell is modeled by the five parameter equivalent circuit: a photo electric current controlled source giving s I , a shunt single-diode D draining the current Dj i , a shunt resistance p R draining the leakage current p I , a series resistances s R delivering the output current j I of the cell having the output voltage j V . As a normal assumption, assume that the cells associated within the module are equally subjected to the same irradiance and the junctions are at the same temperature, then the equivalent circuit for the PV module is same of the cell, but with a suitable numerical transformation in the values for the parameters. The PV system under study is formed by a PV module, a DC-DC boost and a three-level power inverter linking the system to an electric grid. The PV system is shown in Fig. 1. In Fig. 1, G is the solar irradiance, T is the cell p-n junction temperature in [K] and the current j i [2] is given by:

p j s j j j R I R V I i ) ( + + ≡ (1)
where j is a condition index: , maximum power point (MPP) condition. From (1), finding s R at short circuit and at MPP conditions, holds the equations [2] given by:

0 I I i V I i V I I i V sc sc sc oc mx oc mx mx mx mx oc = - - - - (2)
The MPP of a PV system depends on G and T , at the MPP the conversion is at the highest efficiency and satisfies the relation [START_REF] Fialho | PV System Modeling by Five Parameters and in Situ Test[END_REF] given by:

0 e ) R R ( I V ) 1 e )( I R V ( i R mx sc p s mx mx mx mx s mx sc mx p = + - + + - γ (3)
The input parameters for the MPPT algorithm are the values of the voltage and the current of the PV system. The condition to be satisfied is given by 0 = ∂ ∂ V P , i.e., if the condition is met, then the algorithm has found the MPP point. But typically in practice the algorithm iterates around that condition until eventually converges. The iteration procedures are as follows; if

0 V P > ∂ ∂
, an incremental adjustment is set in order to increase the out voltage, i.e., in the direction of the MPP; if

0 V P < ∂ ∂
, an adjustment is set in order to decrease the out voltage in the direction of the MPP [START_REF] Raj | A Two Stage Successive Estimation Based Maximum Power Point Tracking Technique for Photovoltaic Modules[END_REF].

The General Algebraic Modeling System (GAMS) is used to code a mathematical programming problem to identify the five parameters for the equivalent circuit of the PV system, using data information from the tests of open circuit, short circuit, maximum power point (MPP) conditions. The free solver COUENNE-Convex Over and Under Envelopes for Nonlinear Estimation for global optimization is used as a convenient option, due to the involvedness on the problem of identification of parameters [START_REF] Fialho | PV System Modeling by Five Parameters and in Situ Test[END_REF]. The DC-DC boost converter has one unidirectional commanded IGBT, 0 S . This converter is linked between the PV module and capacity banks, which in turn is linked to a three-level inverter. The modeling for the DC-DC boost converter is given by the switching variable λ used to identify the state of 0 S and the switching variable λ used to identify the state of the diode 0 D . These variables have to satisfy the switching condition [START_REF] Fialho | Simulation of a-Si PV System Linked to the Grid by DC-DC Boost and Two-Level Converter[END_REF] given by: The module current I is modeled by the state equation given by: ]

   = = = = = = = =
) ( [V 1 0 dc D s v v L dt dI + - = λ (5)
where 0 D v is the diode forward voltage at direct current and dc v is the voltage at the capacity banks.

The three-level inverter is linked between capacity banks and a second order filter, which in turn is linked to the electric grid, modeled by a three-phase active symmetrical circuit. The DC-AC inverter is a three-level inverter, having twelve unidirectional commanded IGBT identified by hy S , used as an inverter. The groups of four IGBT's linked to the same phase constitute the leg y of the inverter with identifies the IGBT. The three conditions to be satisfied for the switching voltage level variable of a leg y , at each level [START_REF] Seixas | Fifth Harmonic and Sag Impact with a Balancing New Strategy for Capacitor Voltages[END_REF], are given by: The inverter output voltage sy u in function of dc v [START_REF] Seixas | Fifth Harmonic and Sag Impact with a Balancing New Strategy for Capacitor Voltages[END_REF] is given by:

     = = = = = = = 0 ) or (
dc c y j a j j y sy v n n u ) 2 ( 6 1 ∑ ≠ = - = } , , { c b a y ∈ ; } 2 , 1 , 0 { ∈ n ( 7
)
The voltage at the capacity banks dc v appearing in ( 5) is a function of the electric charge stored or discharged from the capacitors by the action of the control of the converters. Hence, the state equation for this voltage is a function of the currents each capacitor cj i [START_REF] Seixas | Fifth Harmonic and Sag Impact with a Balancing New Strategy for Capacitor Voltages[END_REF] and is given by:

∑ - = = 1 1 1 p j cj j dc i C dt dv } 1 , . . . , 1 { - ∈ p j (8)
The current cj i [START_REF] Seixas | Fifth Harmonic and Sag Impact with a Balancing New Strategy for Capacitor Voltages[END_REF] is given by:

y c a y ny I cj i i i ∑ = - = δ } 1 , . . . , 1 { - ∈ p j (9)
where the auxiliary variable ny δ [START_REF] Seixas | Fifth Harmonic and Sag Impact with a Balancing New Strategy for Capacitor Voltages[END_REF] is given by:

   ≤ > = y y ny n j n j 1 0 δ } 2 , 1 , 0 { ∈ n ; } 1 , . . . , 1 { - ∈ p j (10)
The electric grid is modeled by an equivalent three-phase active symmetrical circuit, having a resistance and an inductance in series. Hence, for the electric current injected into the electric grid the state equation is given by:

) ( 1 y fy n fy n fy u i R u L dt di - - = (11)
where n L and n R are the electrical grid inductance and resistance, respectively, fy u is the voltage at the filter, y u is the voltage at the electric grid.

Control Method

The three-level inverter is a variable structure due to on/off switching states of the IGBT's. PI control and PWM by space vector modulation associated with sliding mode is used for controlling the inverter with the output vectors levels 0, 1 and 2 in the β α plane [START_REF] Seixas | Fifth Harmonic and Sag Impact with a Balancing New Strategy for Capacitor Voltages[END_REF] shown in Fig. 2. The sliding mode control strategy is an option known by the advantage of having attractive considerable robustness to parametric uncertainties [START_REF] Seixas | Fifth Harmonic and Sag Impact with a Balancing New Strategy for Capacitor Voltages[END_REF] due to partial shading or electric grid disturbances. Sliding mode control is particularly attractive in systems with variable structure, such as inverters, ensuring the choice of space vectors. The aim is to let the system slide along a predefined sliding surface ) , ( t e A αβ by changing the system structure. All transistors have a physical limitation due to the switch of finite frequency. So, an error exists between the control and the reference αβ e values. The sliding along the surface ) , ( t e A αβ is ensured by a state trajectory near the surfaces satisfying the condition [START_REF] Seixas | Fifth Harmonic and Sag Impact with a Balancing New Strategy for Capacitor Voltages[END_REF] given by: 0

) , ( ) , ( < dt t e dA t e A αβ αβ (12)
The control for the MPPT is a simple adjustments over the DC-DC boost converter in order to follow the condition given by 0 = ∂ ∂ V P .

Case Study

The mathematical modeling for the solar cell with single-diode, shunt and series resistances, for the MPPT algorithm and for the PV system with the DC-DC boost and the three-level topology is implemented in Matlab/Simulink without the use of Power System Blockset. This case study presents a simulation concerned with the data measured [START_REF]Photovoltaic devices -Part 1: Measurement of Photovoltaic (PV) Current-Voltage Characteristics[END_REF] from PV a-Si solar modules Kaneka KA58 provided in [START_REF] Giacobbe | Validação de Modelos Matemáticos de Componentes de Sistemas Fotovoltaicos[END_REF]. The irradiation is 800 W/m 2 , module temperature is 13 ºC and nominal AC power is 6 kW. The data for the a-Si solar module Kaneka KA58 at STC [START_REF]Kaneka Photovoltaic Products Information[END_REF] are shown in Table 1. Table 2 shows the data results for the PV modelling simulation. The current injected into the grid is shown in Fig. 3. The total harmonic distortion (THD) given by the DFT for the current injected into the electric grid is shown in Fig. 4. Fig. 4 allows concluding that the percentage of the fundamental harmonic component calculated by the DFT for the current injected into the grid has a very favorable result, about 93 %. Additionally, the observation of Fig. 4 is in favor that the current injected into the electric grid for the PV system with classical PI control presents a content of interharmonics relatively low and the higher order harmonics of the output current are filtered out by the second order filter. The THD of the current injected into the electric grid has a very favorable result, about 2.4 %. Hence, the PV system with DC-DC boost and three-level power inverter topology has an adequate performance in what regards the fact that the THD of the output current is being lower than 5% limit imposed by IEEE-519 standard.

Conclusions

Simulation studies of PV systems are essential to assist engineers not only in the design phase, but also in real-time operation where cloud-base solutions may allow enough computer resources for a better management in what regards extracting of energy, anticipating performance and deciding convenient measures to avoid malfunctions. The increased integration of PV system into the electric grids leads to technical challenges implying research for more realistic physical models able of giving a better understanding of what concerns the eventually disturbance caused by PV systems, allowing to circumvent loss of energy quality and undesirable instability problems.

The paper proposes an integrated model for PV systems linked to the electric grid through power converters. The integrated model allows a more accurate description of the dynamic of the system. The model includes a maximum power point tracking and power-electronic modeling for the power converters: DC-DC boost converter and the three-level convert linked to the electric grid. The control strategy used in the simulation is based on the use of classical PI controllers, PWM by SVM associated with sliding mode control and power factor control is introduced at the output of the inverter. Although more complex, this integrated model is justified for more realistic results. The application of this modeling to a case study on a-Si solar modules Kaneka KA 58 with a convenient filtering allows to anticipate that the THD for the output current is lower than the 5% limit imposed by IEEE-519 standard for this PV system with DC-DC boost and three-level power inverter topology.

Fig. 1 .

 1 Fig. 1. PV system linked to the electric grid through power converters.

Fig. 2 .

 2 Fig. 2. Output space vectors for modeling of the three-level inverter.

Fig. 3 .

 3 Fig. 3. Current injected into the electric grid.

Fig. 4 .

 4 Fig. 4. Harmonics and interharmonics for the current injected into the electric grid.

Table 1 .

 1 Data for the Kaneka KA58 solar module at STC

	Technology	* m V	I	* m	* oc V	I	* sc	β	oc	α	sc
	Amorphous	63 V	0.92 A	85 V	1.12 A	-206 mV/ ºC 1.3 mA/ ºC

Table 2 .

 2 Data results for the Kaneka KA58 solar module

	Parameter	s R	p R	m	I	PV	I	0
	Kaneka KA58	6.28 Ω	976.02 Ω	243.08	1.11 A	1.18 ×10 -6 A

Acknowledgments. This work was partially supported by Fundação para a Ciência e a Tecnologia, through IDMEC/LAETA, Instituto Superior Técnico, University of Lisbon and by Universidade of Évora.