GENETIC ALGORITHMS APPROACH FOR OPTIMIZATION OF HYBRID POWER PLANT SIZING IN SAHELIAN ZONE: CASE STUDY IN BURKINA FASO

Electrification development in rural areas is essential in order to meet electricity needs at bearable cost, for rural areas population development. This work presents optimization of hybrid electric power plant composed of solar photovoltaic and biogas generators, without electrical energy storage, for low-cost electrification of rural and peri-urban areas, at four sites in Sahel region of Burkina Faso. Simulation results give electricity kilowatt-hour cost about 0.0616 dollar at Gorom-Gorom site, 0.0611 dollar at Dori site, 0.0616 dollar at Djibo site and 0.0616 dollar at Sebba site. Compared to kilowatt-hour cost charged by the national electricity distribution company, who is from 0.1345 dollar, produced electricity cost at these sites is very competitive and accessible for this region population. Use of biogas in addition to solar as an energy source for electrical hybrid power plant has made it possible to reduce significantly polluting and greenhouse gas emissions.

Hybrid system us is attractive solution for areas where electricity grid extension is not feasible, or requires relatively high cost. Hybrid electric systems development requires them to become more economically attractive. Dipama J. (2010), in his thesis, shows that industrial systems energy optimization offers enormous advantages, whether from economic or environmental point of view. Therefore, detailed techno-economic analysis, based on real observations (Belanger-Gravel, 2011), or on cost trends predictions of hybrid system various components is essential (Fathima and Palanisamy, 2015). Many studies have been carried out on hybrid power systems optimal sizing. Belatel and al. (2014) carried out hybrid wind-photovoltaic system with fuel cell technical and economic analysis.  have in turn proposed optimal configuration for micro-grid system using diesel as main source. Bao and al. (2013), on the optimal capacity of an autonomous wind-photovoltaic-diesel-battery system based on genetic algorithm, have carried out research. Olatomiwa and al. (2014) studied hybrid power system optimization for isolated site for telecommunication relay station in Nigeria. Li and al. (2015) carried out studies on mini distribution network optimal configuration, considering diesel generator as the main source. They made comparison between results obtained with Homer software and those obtained using genetic algorithm. It turns out that it is advantageous to use diesel generator as main source. For autonomous power, micro gas turbines are preferred over diesel generators because of their better dynamic performance and lower greenhouse gas emissions (Kanchev and al., 2015). The optimal definition of hybrid electric system generating elements includes steps of modeling available energy resources, optimization methodology definition, system each element modeling taking into account methodology objective and constraints definition (Kouam and Tchuen, 2015). Different criteria are used for hybrid electric system optimization, depending on installation site: electrical load loss probability, combination of minimal system cost and minimum harmful emissions, to which is added minimum unsatisfied load (Kaabeche and al., 2010;Ismail and al., 2012). Optimization procedures use either genetic algorithms, heuristic methods or commercial software such as Homer, DimHybrid or PVsyst (Ko and al., 2015;Kumar, 2016;Zhou and al., 2010). Ouedraogo (2018), in his thesis used genetic algorithm for multi-objective optimization of hybrid power plant, composed of solar photovoltaic, wind turbine and biogas generator.
The main objective of this work is to increase access to electricity supply and thus contribute to population development in rural and peri-urban areas in sahelian zone. Optimizing the sizing of hybrid power plant, composed of photovoltaic generator and biogas generator, will make it possible to offer produced electricity kilowatt hour cost cheapest and bearable by population

Material and methods:-
In this work, technical and economic optimization of hybrid electric power plant sizing is carried out by genetic algorithm, at four sites in Sahel region of Burkina Faso. For the hybrid power plant analysis, Matlab software is used.

Matlab presentation:
Matlab is an abbreviation of Matrix Laboratory. Matlab is an environment for scientific computing, which has several mathematical, scientific and technical functions. Matlab toolboxes solve problems in signal processing, automation, optimization, and more. Matlab has following particularities: easy programming, continuity among whole, real and complex values, the wide range of numbers and their precisions, very comprehensive mathematical library, graphical tool which includes graphical interface functions and utilities. Matlab allows links with other conventional programming languages (Zhang and al., 2019). In Matlab, no declaration of numbers is made. This feature makes the programming mode very easy and very fast.

Optimization methods:
There are several optimization methods for multicriteria problems (Bokovi, 2013). It is question here of finding optimal solutions, which must be compromises between objective functions. Among these methods, genetic algorithms are widely used as optimization method. Genetic algorithms were proposed by Holland J. (1975) and then developed by other researchers (Fang and al., 2010). It is method based on Pareto approaches. For problem containing parameters with strong interactions resolution, genetic algorithms method was able to get closer to real front (Deb and al., 2002). Genetic algorithms method is chosen in this study. This method is also used by Ko and al. (2015) to minimize life cycle cost of electricity generation facility. Genetic algorithms structure used in this work is given.

Biogas production modeling:
Five (05) types of livestock waste are considered in this study (Weiland, 2013). These are pigs, cattle, goats, sheep and poultry. Digester sizing is made on basis of livestock number present at site. Depending on animal species, livestock number required for one (1) m 3 biogas production per day is given (Kamalan and al., 2011).
Where Q Slurry is slurry available quantity per day; N Cat is cattle number; N pig is pigs number; N She is sheep number; N Goa is goats number; N Pou is poultry number.
If livestock number at a site is known, biogas volume produced per day at this site is calculated (Ouedraogo and al., 2019).
where V Biogas is biogas volume per day; N Cat is cattle number; Npig is pigs number; N She is sheep number; N Goa is goats number; N Pou is poultry number.
The digester power is calculated according to methane content in biogas and this biogas calorific value (Levasseur and al., 2011).100% methane in biogas has calorific value of 12.67 kWh/m 3 . Biogas calorific value at methane content t is given (Beline and al., 2012).
where LCP t is biogas lower calorific power value at methane content t; t is methane content of biogas; LCP 100 is biogas lower calorific power value at 100% methane content.

Species
Cattle Pig  Sheep  Goat  Poultry  Number  1  3  11  11  93 420 Electrical energy produced from biogas at methane content t is calculated (Beline and al., 2012).
where E Biogas is digester electrical energy; LCP t is biogas lower calorific power value at methane content t; V Biogas is biogas volume per day. Digester electrical power is caculated (Beline and al., 2012).

) (
where P Dig is digester power; LCP t is biogas calorific value at methane content t; V Biogas biogas volume per day.

Biogas generator modeling:
Several parameters are used to describe biogas engines performance, including specific consumption and overall or effective efficiency.

Specific consumption:
Specific consumption (SC) is equal to consumed gas quantity during one hour to produce one kW electrical power. For biogas generator, specific consumption is expressed (Yamegueu NGuewo, 2012).
where a', b' and c' are generator characteristic constants, P(t) is power generated at given time by generator.

Generator overall efficiency:
The generator overall efficiency expresses the conversion efficiency of biogas chemical energy into electrical energy.It is directly linked to specific consumption (Yamegueu NGuewo, 2012).

SC LCP
where LCP (MJ/kg) is lower calorific power value of biogas; SC (g/kWh) is generator specific consumption.
Where P T-GBio is biogas generator total power, L max is load peak, X GBio is generator load rate.

Photovoltaic field modeling:
Photovoltaic field performance depends on solar radiation, temperature and load to supply. Photovoltaic field maximum output power is calculated (Bouharchouche and al., 2014).
where P mp is photovoltaic field maximum output power, A PV (m 2 ) is photovoltaic field area; G S (W/m 2 ) is solar irradiance; and η PV is photovoltaic modules efficiency.
Photovoltaic modules efficiency is given by equation (10).
where α is temperature coefficient for power correction (α = 0.0042), η ref is photovoltaic module reference efficiency and Ta is ambient temperature.

Inverter modeling:
Inverter input power is photovoltaic field maximum output power. Inverter output power can be expressed from his input power and his efficiency according.
where η Inv is inverter efficiency; p 0 and k are coefficients calculated from data supplied by manufacturer; p is reduced power.

Technical-economic analysis:
In techno-economic analysis process, investment, maintenance, operation and renewal costs, as well as generating elements residual value of hybrid plant are considered in produced electricity kilowatt-hour (kWh) cost calculation (Belatel and Ouazeta, 2014). It is proposed here, cost equation minimization expressed as function of each generating element optimal size (digester, biogas generator, photovoltaic field, inverters), while respecting hybrid power plant energy constraints (Bouharchouche and al., 2013).

Model formulation:
Developed model is based on objective "cost" function definition. This function takes into account all expenses incurred by hybrid power plant, during its lifetime. This function definition goes through classic stages of engineering projects financial analysis. Objective function takes into account of investment, operation, maintenance and renewal costs, as well as residual value of hybrid plant generating elements.

 
where f(x) is objective function, C I is investment cost, C M is maintenance cost, C Op is operation cost, C R is renewal cost, V R is residual value.
Investment cost is express according to: where a 1 is the digester acquisition coefficient 1, a 2 is biogas generators investment coefficient 1, a 3 is PV field investment coefficient 1, a 4 is inverters investment coefficient 1, b 1 is digester investment coefficient 2, b 2 is biogas generators investment coefficient 2, b 3 is PV field investment coefficient 2, b 4 is inverters investment coefficient 2, 422 x 1 is digester peak power, x 2 is biogas generators peak power, x 3 is PV field peak power, x 4 is inverters peak power, L max is load maximum value, X GBio is biogas generators load rate.

Hybrid power plant maintenance cost equation is determined by:
where a 0 is biogas generators maintenance coefficient 1, b 0 is biogas generators maintenance coefficient 2, m Dig is digester maintenance cost coefficient, m GBio is biogas generator maintenance cost coefficient, m PV is PV field maintenance cost coefficient, N biogas generators number, A(a,n Dig ) is digester investment annualization factor, A(a,n PV ) is PV field investment annualization factor, P(i,a,d) is investment discounting factor, X t+4 is biogas generators number operating at time t, C I-PV is PV field investment cost, x 1 is digester peak power, x 2 is biogas generators peak power. .

Hybrid power plant operating cost is giving by:
where C 0 is 1 m 3 biogas cost, a 5 and 5 b are biogas generator consumption parameters, E Dig is digester operating cost coefficient, A(a,n Dig ) is digester investment cost annualization factor, PW(i,a,d) is investment discounting factor, x 1 is digester peak power, x 2 is biogas generators peak power. .
The hybrid power plant components renewal cost is given by: is adjusted discount rate for biogas generators replacement and   d a i PW , , 2 adjusted discount rate for inverters replacement, L max is maximum load, X GBio is biogas generators load rate, x 2 is biogas generators peak power, x 3 is PV field peak power, x 4 is inverters peak power, max L is load maximum value, GBio X is biogas generators load rate.   (24) where nr Dig is biogas plant remaining lifetime, n Dig is biogas plant total lifetime, nr GBio is biogas generators lifetime, n GBio is biogas generators total lifetime, nr PV is photovoltaic modules remaining lifetime, n PV is photovoltaic modules total lifetime, nr Inv is inverters remaining lifetime, n Inv is inverters total lifetime, L max is maximum load, X GBio is load 423 rate, x 1 is digester peak power, x 2 is biogas generators peak power, x 3 is PV field peak power, x 4 is inverters peak power. Hybrid power plant must be able to meet electric load power at all times. Problem formulation therefore boils down to constrained optimization problem, which can be expressed.

Hybrid plant residual value equation at project end is:
where x 1 is digester power, x 2 is biogas generators peak power, x 3 is photovoltaic field nominal power, x 4 is inverter nominal power, X t is biogas generators number in operation at time t, G(t) is solar radiation, L(t) is load power every hour, η Inv is inverter efficiency.

Carbon dioxide emissions analysis:
Photovoltaic generator, in its operation does not produce greenhouse gases. In our study, carbon dioxide (CO 2 ) equivalent quantity is calculated by considering only biogas consumed and gases emitted after combustion in biogas generators, taking into account their global warming potential. CO 2 equivalent quantity is calculated (Kanchev and al., 2015).  Parameters configuration file (GA.m) and evaluation file (evaluationFonction.m) must be modified for program easy use. Setting only two files allows obtaining very good results with reasonable computing time. Hybrid power plant model developed at each site, in this study has as input parameters solar radiation daily values, biogas quantity produced per day and load profile at each site.

Results and Discussions:-
Chosen sites for this study are those of Gorom-Gorom, Dori, Djibo and Sebba located in the Sahel region of Burkina Faso. The aim is to increase access to electricity supply in this zone, by exploiting endogenous renewable resources, in particular solar photovoltaic and biogas. Study is carried out for 25 years project lifetime.
Electricity load profile at studied sites: According to population growth forecasts at studied sites, electricity load profile to be satisfied by hybrid power plants is estimated. Biogas production assessment at studied sites: Livestock number at each site makes it possible to determine biogas daily quantity that be produced at each site. High livestock number at these four sites means that biogas production potential is enormous. Studied sites have very high potential for biogas production. However, it is at Djibo site that the highest biogas production potential is observed. This is due to animals' total number at this site, which is higher than in other sites.

Solar radiation profile at four studied sites:
Solar radiation profile at four studied sites is represented. The best solar radiation curve at studied sites is that March month. This solar radiation is used in this study to better understand hybrid power plants dynamics. Solar energy is the most abundant endogenous renewable resource at study sites. Daily average solar radiation is 5.5 kWh/d, for 3,000 to 3,500 hours per year and average production estimated at 1,620 kWh per kWp installed (PNDES, 2016).

Hybrid power plant technical and economic optimization:
Optimization simulation is done with program developed with genetic algorithm, in Matlab 8 environment. Several trials were necessary to arrive at overall optimum. Four optimal values of decision variables: x 1 , x 2 , x 3 and x 4 , corresponding respectively to digester power, biogas generator nominal power, photovoltaic field peak power and inverters nominal power are calculated. The highest digester power is at Dori site, with power of 15,484 kW, while the smallest is at Sebba site, which records 14,852 kW power. The same is true for hybrid system other generating elements at all sites. Dori site records the largest hybrid power plant power. Animals' number at Dori site explains this, which is higher than at other sites. Optimal value of fval, obtained by implementing objective function over project lifetime (25 years), corresponding to electricity produced kWh cost at each site is determined by simulation in program developed with genetic algorithm.  3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 24

Carbon dioxide emissions analysis:
Biogas combustion in generator engines produces carbon dioxide, carbon monoxide, nitrogen oxides, unburned biogas and particulate matter. These gases carbon dioxide (CO 2 ) equivalent quantity is calculated by considering each gas effect on global warming. Consumed biogas and emitted gases by generators quantities as well as CO 2 equivalent quantity avoided at each site are calculated. Consumed biogas total CO 2 equivalent for biogas generators operation at four sites is one hundred and thirty-four million three hundred and two thousand four hundred and eighty (134,302,480) tons per year. This CO 2 quantity could be emitted into atmosphere, if it was not converted into electricity. CO 2 equivalent avoided is then one hundred and thirty-four million two hundred and forty-four thousand eight hundred and eighteen (134,244,818) tons per year.

Conclusion:-
This study main objective is to increase access to electricity supply, at lower cost, for daily electricity needs at four sites in the Sahel region of Burkina Faso, thus contributing to improvement of populations living conditions. The simulation results give electricity kWh cost at four studied sites: 0.0616 $ at Gorom-Gorom site, 0.0611 $ at Dori site, 0.0616 $ at Djibo site and 0.0616 $ at Sebba site. Compared to per kilowatt-hour cost practiced by national electricity distribution company, which is on average 0.1345 $, hybrid power plants sizing optimization has resulted in very competitive kWh costs. Electricity production from these low-cost hybrid power plants will thus sustainably boost socio-economic development in Sahel region. Upgrading animals waste into biogas, used as gaseous fuel, has significantly reduced producing electricity cost and producing fertilizer for crops. Use of biogas in addition to solar energy for hybrid power plants has reduced polluting and greenhouse gas emissions very significantly. Developed model with genetic algorithm is model which, in addition to giving system overall configuration, also simulate system dynamics. This model can be used as decision support tool for decentralized electrification operators. This project expected socio-economic impact is jobs creation and local wealth. Parameters similarity of studied sites which are located in Liptako-Gourma zone, orders that this study results be applicable to Liptako-Gourma zone, which covers large part of North-East Mali, North-East and East Burkina Faso, and South Niger, as well as to entire Africa Sahelian zone.