Optimum Sizing Algorithm for an Off Grid Plant Considering Renewable Potentials and Load Profile

The energy demand in remote area cannot be satisfied unless renewable energy based plants are locally installed. In order to be efficient, such projects should be sized on the basis of maximizing the renewable energies exploitation and meeting the consumer needs. The aim of this work is to provide an algorithm-based calculation of the optimum sizing of a standalone hybrid plant composed of a wind generator, a photovoltaic panel, a lead acid-battery bank, and a water tank. The strategy consists of evaluating the renewable potentials (solar and wind). Obtained results are entered as inputs to established generators models in order to estimate the renewable generations. The developed optimal sizing algorithm which is based on iterative approach, computes plant components sizes for which load profile meet estimated renewable generations. The approach validation is conducted for A PV/Wind/Battery based farm located in Sfax, Tunisia. Obtained results proved that the energetic need is covered and only about 4% of the generated energy is not used. Also a cost investigation confirmed that the plant becomes profitable ten years after installation.Article History: Received June 24th 2017; Received in revised form September 26th 2017; Accepted Sept 30th 2017; Available onlineCitation: Brahmi, N., Charfi, S., and Chaabene, M. (2017) Optimum Sizing Algorithm for an off grid plant considering renewable potentials and load profile. Int. Journal of Renewable Energy Development, 6(3), 213-224.https://doi.org/10.14710/ijred.6.3.213-224


Introduction
Following the technological revolution that has marked the past century, fuel prices have raised. In addition, fuel will break off in the following few decades. Thus, the world has moved towards the use of renewable energy in its various forms to cover its needs and fill gaps in traditional sources (Glasnovic et al. 2011;Chowdhury et al. 2011). Researches on renewable energies have been strongly developed over recent years. Plants become decentralized to consume locally the generated energy and avoid energy transport. Considered as autonomous systems, these plants are usually installed in remote area (Cano et al. 2014). Furthermore, plants are designed to gather many renewable energy forms: wind, photovoltaic (PV), etc. The design takes into account the site potential and the energy need. Hence, the plant must be characterized then its components must be sized on the basis of the renewable potentials assessment and consumer need.
In literature, many techniques have been developed for sizing optimization. Gupta et al.(2007) carried out the development of a computational model for optimal * Corresponding author: brahminabiha@gmail.com sizing of a hybrid energy system. Renewable potentials are evaluated through mathematical models, merging real meteorological data and load profile. The sizing evaluation is done in terms of loss of power supply probability (Gupta et al. 2007). Also, the main attribute of a hybrid system is the capability to satisfy energetic plant needs. The over energy production is stored in order to be used while deficit circumstances (Silva et al. 2011). A hybrid system optimum sizing using discrete version of harmony search was published (Maleki et al. 2016). The algorithm is easy to implement and can escape from local optima. Likewise, an efficient Artificial Bee Swarm Optimization (ABSO) algorithm is proposed to minimize the objective function (Maleki et al. 2014). The total annual cost is computed then the maximum allowable loss of power supply probability (LPSPmax) is taken into account to improve the system effectiveness. Similarly, a sizing optimization approach of stand-alone hybrid wind/PV/diesel energy has been presented by minimizing the cost function of the system that offers the system energy availability (Belfkira et al. 2011). Equally, Diaf et al.(2007) fixed the optimal number and type of hybrid system units in terms of technical and economical concepts: the loss of power supply probability and the levelised cost of energy (Diaf et al. 2007). Other researchers developed various tools to solve the sizing adequacy such as Genetic Algorithms (Tina et al. 2006), probabilistic approach (Grimsmo et al. 2005;Zhou et al. 2010), iterative technique (Musgrove 1988), dynamic programming (Bashir et al. 2012), and Monte Carlo approach (Yang et al. 2002). Hence, in order to ensure a defined autonomy for the system, different case studies are performed. Likewise, using wind and solar measurements from a meteorological station installed in Ekren et al.(2009) investigated the performance of PV/Wind hybrid system under to distinct load demand profiles (Ekren et al. 2009). Kazem and al. (2013) proposed a novel sizing strategy to increase the system reliability and reduce energy cost for a stand-alone PV system as well as tilt angle for remote areas in Sohar, Oman (Kazem et al. 2013). Kaldellis et al. (2012) estimated the size of a combined PV / wind based hybrid system, located in the Greek territory, to provide the energy demand of typical remote consumers under the criterion of minimum first installation cost (Kaldellis et al. 2012).
This paper puts forward a concrete and pragmatic sizing optimization of a hybrid stand-alone PV/wind/battery plant which considers the energetic characterization of the site and the consumer need. A hybrid renewable energy grid is composed of Direct Current (DC) bus that gathers over inverters a photovoltaic panel and a wind turbine. Since renewable energy sources are intermittent, a storage system is included so as to store the unconsumed generated energy and to supply the load in case of energy deficiency. Thus, the considered plant becomes autonomous (Fig. 1).

System configuration
The work aims to characterize the plant components on the basis of the potentials assessment and the energetic needs. The PV array delivers a DC current function of solar irradiance and ambient temperature. A boost converter is used to increase the output voltage. As for the Wind Energy Conversion System (WECS), it is based on a Permanent Magnetic Synchronous Generator (PMSG) which is coupled to the DC bus via a rectifier. Finally, a battery is coupled to a bidirectional converter in order to store over generated energy and supply the plant in case of energy deficiency. Since loads are supplied by alternative current, a DC/AC inverter is added to the installation.
The system sizing is structured around three steps: the estimation of renewable energy potentials, the evaluation of renewable generations on the basis of energy sources models and the load profile characterization (Fig. 2). The monthly average of solar energy is given by: Where is the daily global solar radiation provided by the Tunisian National Meteorological Institute (INM).

Wind potential
The monthly wind energy is expressed by: The turbulence intensity characterizes the wind variability in high frequency (order of second). and are the two parameters of the Weibull distribution. This distribution is the most famous approach that permits to establish the wind potential assessment (Brahmi et al. 2012). The probability density function of the wind speed is defined as: The corresponding cumulative distribution function is given by: Many methods are used in the determination of k and c: the Least Squares Method (LSQ) (Seguro, et al. 2000), the Maximum Likelihood Method (MLM) (Yang et a.. 2003), and the Modified Maximum Likelihood Method (MMLM) (Arbaoui 2006). These methods are compiled to compute and using the available monthly meteorological database. In previous work Brahmi et al. (2012), the parameters and were determined by the MMLM method. The wind potential is calculated on the basis of the Weibull distribution using its shape and scales parameters. The characteristic speeds are expressed as follows: WhereΓ is the defined gamma function, for any real number x positive not null, by:

 
The Weibull distribution has the advantage of giving an excellent recovery of the experimental database and of envisaging the wind power for various heights (Parket al 2004). Indeed, knowing the mean speed ( ) at height , the mean speed ( ) at the height is given as:

PV system model
The common empirical model of an equivalent circuit photovoltaic cell is based on a one diode (Fig. 3).

Fig. 3.Electrical model of a solar cell
The output current of the PV cell can be described as (Gokcek et al.2007): The light-generated current of the PV cell ℎ depends linearly on the solar irradiance and the cell temperature according to the following equation: sc n on oc n v The PV array is composed of serial PV cells connected in parallel branches. The whole generated current is given by: The photovoltaic generated power is:

Wind Generator
The wind generator is composed of a wind turbine coupled to Permanent Magnetic Synchronous Generator (PMSG) (Fig.4).
Where is the nominal power of the PMSG and represents the mechanical power of the turbine. It is expressed by the following equation (Melício et al. 2011): is the power coefficient defining the aerodynamic efficiency of the wind turbine rotor. It depends on the wind velocity and the tip speed ratio . According to the Betz law, the power coefficient can never exceed 0.593, it is expressed by (Slootweg et al 2003):    Figure 5 shows the variation of the power coefficient versus the tip speed ratio for different pitch angle ( , ). It reaches a maximum value of 0.5 for an optimal of 8.2 and a null pitch angle.

Cost assessment
Eq. 20 gives the calculation formula of the global plant cost: Where : initial cost, : maintenance cost, : replacing cost

Initial cost
The initial cost function is expressed by Belmilin et al. (2014): Where _ : initial cost of the wind system, _ : initial cost of the photovoltaic system, _ : initial cost of the storage system, _ ℎ : initial cost of the inverter, : apparent power of the inverters.

Maintenance cost
In the developed software a percentage of the initial cost for each compound is given for a period of a year (Belmilin et al. 2014).

Compounds replacing cost
The Compounds replacing cost is evaluated, specially, using the lifetimes of different components (Belmilin et al. 2014  life-time of the whole system, photovoltaic system, the wind system, the batteries, the chopper and the inverter.

Sizing Algorithm
The sizing algorithm is developed in order to ensure an autonomous system and to meet the established energy constraints. The algorithm inputs are the estimated available renewable energies, the load profile and the generators models ( Figure 6). The algorithm provides the photovoltaic panel surface, the surface of wind turbine blades, the tank volume and the battery capacity. The algorithm is composed of three steps: Step I: An ANN estimation of the photovoltaic potential implication coefficient (the ratio of solar and wind potentials). This coefficient depends on the geographical characteristics of the sites and on the ratio of 1kW prices produced by each type of energy.
Step II: Calculation of the initial surfaces of the PV and wind generators blades using the least squares method by ensuring the satisfaction of the yearly energy need by renewable generation: 12 12 Step III: Adjust the surfaces of PV and wind generator blades by iterative computing according to the monthly energy gap value( ) which is the difference between the generated and consumed energies. After convergence, the battery capacity is consequently calculated. Then the tank volume is computed on the basis of all previous sizes results.
A case study of an agriculture farm supplied by a PV/Wind/Battery system is considered. Fig. 6 shows the sizing algorithm. It computes the optimum sizes of the considered farm components: the surface of the wind generator blades, the PV array surface, the tank volume, and the battery capacity. The algorithm should ensure the load energy need throughout the year by maximizing the use of renewable energies (Brahmi et al. 2012).

Determination of photovoltaic implication coefficient
The ANN controller is used to estimate the optimum photovoltaic implication coefficient for a given solar and wind potentials. The architecture of the adopted Neural Network is composed of three layers (Fig. 7). The input layer contains two neurons as it disposes of two inputs (solar potential and wind potential: , ). The hidden layer includes five neurons, this number is fixed following the execution of empirical rules which start with a high number of neurons and eliminate the unnecessary ones on condition to reach network stability and output accuracy. The output layer contains one neuron that provides the optimum .
The activation function of neurons is defined by the hyperbolic tangent function (Haykin, 1998) are respectively the prices of 1 W produced by each generator (wind and photovoltaic), : Photovoltaic implication coefficient (without unit), : factor indicating the proportionality of the two renewable potentials: photovoltaic and wind (without unit), : the ratio of generation costs ofwind and photovoltaicenergies (without unit). Figure 8 shows the algorithm that determine the optimum implication coefficient . Fist the maximum number of PV modules is calculated on the basis of the estimated solar and wind potentials. Then, the number of PV modules is calculated thanks to an iterative loop starting with = 1 until = . For each iteration, the number of wind generator is determined in order to satisfy the load. Consequently, the whole renewable generation is established ( ) which yields to the calculation of the relative implication coefficient .  Step I Step II Step III

LSQ based estimation
The values of ̂ and ̂ are estimated using the LSQ method applied to measurements database vectors X, Y and Z are composed respectively of , , and monthly measures, by considering: The quadratic error between the generated and the required energies is expressed by:

Battery sizing
The stored energy in a battery is given by Eq. 30: The technology of the selected battery (Lead/Acid) allows 80% as Depth Of Discharge DODmax=80%. The usable energy usable E in the battery is expressed by Eq.

31
: is the number of autonomy days.
Hence, the battery capacity is given by the Eq. 32:

Tank sizing
The tank volume is calculated on the basis of the needed water and the excess in generated energy (Eq.33).
Where is the excess of the monthly energy, is the water density ( . −3 ), g is the gravity acceleration ( −2 ), and H is the height of rise (m).

Results and discussion
As previously mentioned, the main aim is to optimize the sizing of a standalone hybrid plant on the basis of renewable potentials assessment, well characteristics, and load profile. In order to validate the developed algorithm, a farm located in Sfax is considered as a case study. It is located in the South-EST of Tunisia, at latitude of 34°43 ′ and longitude of 10°41 ′ . The approach is based on the establishment of monthly energies audit already published inBrahmi et al. 2012.
A one year of a saved meteorological data base at Sfax airport station is used.
The daily wind speed at height of 12 m is presented by Fig. 9. The wind speed varies between 1 m/s and 8.5 m/s, April is the windiest month with an average of 4 m/s. The INM offers a data base of solar potential characteristics for 10 years. The monthly average solar irradiation is depicted in Fig. 10. It reaches its maximum from May to September. The curves were plotted thanks to the wind and PV models. Fig. 11 shows the curves of the monthly renewable energies generated per 2 in Sfax, Tunisia. The wind potential in Sfax is more important than the solar potential. This is due to the availability of wind throughout the day 24h / 24h, while the sun is available only during daylight.

Fig. 11. Renewable potentials in Sfax
The wind speed and the solar radiation are used as inputs for the algorithm. Load profiles (in per unit of kWh) are defined for quarter-hour time-step for each day over one year. Official and floating holidays, all seasonal, weekly and daily influences (Friedl et al. 2007) are considered. Figure 12 shows a daily farm energetic consumption profiles. The curves present two peaks: at the morning (6 am) and at the evening (7 pm).  Referring to the algorithm of Figure 7, the produced renewable energy to supply a typical load of 1 KWh is plotted for each month function of the implication coefficient (Fig 14). Then, considering the algorithm of Figure 8. The optimum implication coefficient is deduced on the basis to achieve no lost energy.
Consequently The initial estimated surfaces are entered as inputs to the sizing algorithm of Figure 6.
Following the achievement of iterations, the obtained rounded surfaces for PV panels and wind blades are: The PPV surface is larger than the turbine wind blades surface because the wind turbine supplies energy all the time thanks to the wind conditions availability, contrary to the solar energy which is available only during daylight. Also, as well known the wind turbine efficiency is largely higher than the PPV efficiency. The difference in the dominance of two potentials allows the calculations of the implication coefficient. For a typical load of 1 kW, Figure 15 shows the lost energy function of the implication coefficient. In order to evaluate the sizing performance, monthly need and generated energies have been analyzed by computing the energy balance over the year. Figure 16 shows the energy balance of the system during the year. An energy deficit is noticed during the 8 th and the 1 st month but this deficit is covered during the rest of the year. In fact, the yearly energy loss is evaluated at 4% using Eq.34: Referring to section §3.3 the battery capacity and lifetime are vital in system optimization process. By computing the luck of energy during all the year, the plant needs a battery bank of a capacity equal to 1200Ah.Therefore, using equation 28, the obtained tank volume is = 270.2296 3 .

Profitability
An investigation on the plant cost is carried out in order to determine the plant profitability (Belmilin al. 2014) (Eq.20). All cost parameters are described in Table 1 and Table 2 Table 2 Cost parameters for the installation components (Eftichios, et al. 2006). The different cost percentages are summarized in Fig. 17. It is obvious that the PV system cost part occupies 55% of the total installation cost. The batteries take 21% of the overall cost as they must cover the load need during night. As for the wind system, it occupies only 16% because Tunisia does not have an important wind potential. The effectiveness of the system sizing and the economic study request a computing of the system profitability.

Parameters
Referring to Tunisian prices of electricity provided in the electric power provider company (Tunisian Company of Electricity and Gas: STEG), the cost of 1 kwh is 0.167 dt and the license fees are 2.6 (dt/kW/Month) and taxes are 30% of the whole charges. As the installation need is 30834 Kwh/year, the total cost of the yearly consumption is 8722.0614 dt. Hence the profitability is calculated as follows: Cost of the renewable plant Profitability= =10.3203years price of the yearly consumption 55% 16% 21% 8% Ppv Wind system Batteries Converters

Conclusion
An optimum sizing algorithm is proposed so as to provide the sizes of renewable generators (PVP/ Wind/ battery) supplying an autonomous agriculture farm. The sizing is based on renewable potentials, generators models and the load profile. A case study is considered in order to validate obtained results. Referring to the calculated energy balance over the year, the algorithm offers generators' sizes and water tank volume that are able to cover the farm energy need. .