Optimal sizing and energy management of a stand-alone photovoltaic/pumped storage hydropower/battery hybrid system using Genetic Algorithm for reducing cost and increasing reliability

Abstract

In this paper, a genetic algorithm is applied to optimize the sizing of an autonomous renewable energy multi-source system for reliable and economical supply of energy. The multi-source system is composed of a photovoltaic generator, a pumped storage hydropower system and a battery. The system will power public lighting and operate a garden fountain in the Botanical Garden, located in the Alexandre Aibéo Park in Covilhã (Portugal). Solar irradiance is initially simulated for a reference photovoltaic capacity (25 kWp) over one year by the PVsyst software for the city of Covilhã. Two objective functions are used for sizing optimization: the loss of power supply probability (LPSP) and the levelized cost of energy (LCE). The LCE takes into account the capital cost, the replacement cost and the cost of operation and maintenance. The genetic algorithm is used to determine the best configuration of the different subsystems (photovoltaic generator capacity, upper water reservoir capacity and battery capacity). The originality of this work lies in the combination of two storage elements with different dynamics, the introduction of an adapted energy management strategy (EMS) allowing to manage energy flows between the different subsystems and to control the process of charging/ discharging storage elements, and multi-objective optimization (considering technical and economic criteria) of the sizing of the autonomous photovoltaic/pumped storage hydropower/ battery hybrid system using genetic algorithm.

Keywords

Multi-objective optimization optimal sizing energy management photovoltaic battery pumped storage hydropower evolutionary algorithm genetic algorithm LCE LPSP

Introduction

The ambitious Global Energy Transition Plan aims to achieve a low-carbon climate-resilient future in a safe and cost-effective manner. In many countries, the phasing out of nuclear and coal-fired power plants generation has started with a shift towards new renewable sources including primarily solar energy for power generation. However, solar has variable energy supply and difficult to match with energy demand. Hydroelectricity, with untapped potential, has all the characteristics to support the integration of solar energy into microgrids through the flexibility of production via turbine as well as the vast potential for pumped storage.

High-performance stand-alone PV microgrids typically take advantage of a combination of hydroelectric and battery storage to ensure reliable and affordable energy supply: this combination is used according to the excess/ deficit of the amount of net energy (the difference between PV energy generation and consumption), to balance production demand and mitigate the intermittency of the photovoltaic source.

A stand-alone hybrid renewable energy system must be optimally designed to cover the desired load demand at a defined level of availability. This requires knowing certain parameters such as the potential of each energy source, mathematical models of system components, sizing methodologies and end-user requirements. This data helps designers reliably improve system efficiency to meet end-user needs at a desired level of availability and an acceptable cost range. Thus, the selection of evaluation criteria is one of the important steps in the optimal design of a multi-source systems. Several research works have introduced a multi-criteria approach making the process of selecting the optimal system design more flexible and transparent. This approach is based on criteria covering both technical and economic aspects. In Tables 1 and 2, we review several formulations of reliability and economic performance indicators.

Table 1.

Reliability performance indicators.

Indicator	Definition	Formula
Loss of Power Supply Probability (LPSP)	This is the percentage of unsatisfied energy demand. It is defined as the ratio of the energy deficit to the energy demanded (Diaf et al.;¹ Yang et al.²)	$L P S P (%) = \sum_{t = 1}^{T} \frac{E_{L} (t) - E_{s y s} (t)}{E_{L} (t)}$
Loss of Power Supply Probability (LPSP)		Where E_L (t) is the energy demand, E_sys (t) is the the total energy production (PV and storage), t is the sample of time (1 h) and T is the simulation period (one year, i.e. 8760h).
Loss Of Load Probability (LLP) (Abouzahr & Ramakumar;³ Kazem et al.,⁴) also called Loss Of Load Expected (LOLE) (Moghaddam et al.;⁵ Arun et al.⁶) or Equivalent Loss Factor (ELF) (Billinton.⁷)	It corresponds to the number of hours per year the load demand is unmet, due to insufficient generation capacity, lack of energy supply and/ or sudden increase in load demand (Ardakani et al.⁸)	$L O L E (%) = \frac{L O L H}{T}$
		where LOLH =
		$\sum_{t} {\begin{matrix} 1 & s i E_{L} (t) - E_{s y s} (t) > 0 \\ 0 & s i n o n . \end{matrix}$
Total energy loss (TEL)	It indicates the energy loss due to excess of energy production (Alsayed et al.⁹)	TEL = ${\begin{matrix} \sum_{t = 1}^{T} (E_{L} (t) < E_{E} (t)) i f E_{L} (t) < E_{E} (t) \\ 0 o t h e r w i s e \end{matrix}$
Total energy loss (TEL)		Where E_E (t) is the extra energy generated by the system.
Level of autonomy (LA)	It is the result of the number of hours the load demand is satisfied over the operating time of the system (Ekren & Ekren.¹⁰)	LA = 1 – LOLH

Table 2.

Economic performance indicators.

Indicator		Definition	Formula
Life cycle cost (LCC)		It is defined as the sum of the investment costs, the maintenance costs and the replacement costs of the system components (Kazem et al.;⁴ Ibrahim et al.¹¹)	$L C C = \sum_{i = 1}^{n} C I_{i} (1 + N R_{i}) + C M_{i} (R_{p r o j} - N R_{i})$
Life cycle cost (LCC)			where i is the summation index of all components in the system, n is the total number of components in the energy system, CI_i is the initial capital cost of the i-th component, NR_i is the expected number of replacements of the i-th component over the lifetime of the system, CM_i is the maintenance cost per year of the i-th component, R_proj is the lifetime of the energy system.
Salvage Value (SV)		It presents the estimated value of a power system component at the end of the project lifetime (Energy.¹²)	$S V = C_{r e p} (\frac{R_{r e m}}{R_{c o m p}})$ , where C_rep is the replacement cost of the component, R_comp is its lifetime (years), and R_rem is the remaining lifetime of the component at the end of the project lifetime, given by R_rem = R_comp−(R_proj−R_rep), where R_proj is the project life and $R_{r e p} = R_{c o m p} . I N T (\frac{R_{p r o j}}{R_{c o m p}})$ R_rep is the replacement life, given by ,Where INT is a function that returns the integer quantity of a real number.
Total cycle (TLCC)	Life cost	It is the total cost of the system over its life cycle (including its residual value at the end of its lifetime) (Mohamed et al.;¹³ Semassou et al.¹⁴)	LTCC = LCC − SV_sys
Total cycle (TLCC)	Life cost		Where SV_sys is the residual value of the system at the end of the project life time. Typically, the SV_sys is a percentage of the LCC.
Annualized cost of a system (ACS)		It is the total cost of the system over a year (Yang et al.²)	$A C S = \frac{T L C C}{R_{p r o j}}$
Levelized cost of energy (LCE)		It is defined as the ratio of the total annual cost of the system components to the total annual energy generated by the system (Lazou & Papatsoris;¹⁵ Yang et al.¹⁶)	$L C E = \frac{A C S}{E_{s y s}}$
Levelized cost of energy (LCE)			Where E_tot is the total energy generated by the system during one year.

Many studies have been carried out to develop different algorithms to optimize the design of stand-alone hybrid PV systems in order to select the optimum capacities of the PV generator and storage systems. These algorithms can be classified into two categories: evolutionary numerical and analytical algorithms.

Evolutionary algorithms (EA), inspired by Darwin's biological evolution, are optimal numerical research techniques based on the concepts of natural selection and survival of the fittest They work with a fixed-size population of possible solutions to a problem, called individuals, which evolve over time to converge to an optimal solution that meets identified criteria. There are three main steps in all EAs. The first step is the initialization process where the initial population of individuals is randomly generated according to an initial estimate. Each individual represents, directly or indirectly, a solution. In the second step, each solution in the population is evaluated according to the performance criteria. This evaluation process is used to calculate the suitability of the population or to rank the individual solution within the population. The third step is the generation of a new population by disturbing the solutions in the existing population (e.g. setting a reliability criteria). Evolutionary numerical methods offer the advantage of accuracy and the ability to improve by incorporating more complex models of the system components. In these methods, reliability is defined in a systematic way as a predetermined range of PV/ storage system capacities is linearly swept. Numerical algorithms provide accurate results when using rigorous stand-alone PV system models, small step changes, and hourly profiles for weather and load data.

Artificial intelligence (AI) is the latest concept in numerical algorithms, used to overcome the unavailability and non-linearity of weather data in the design of multi-source systems. The most widespread AI techniques for PV system sizing are (Mellit et al.¹⁷): Particle Swarm Optimization (PSO), artificial neural networks, genetic algorithms (GA), Artificial bee colony algorithms (ABC) and Ant colony optimization algorithms (ACO). It has been shown, in Fadaee & Radzi;¹⁸ Fezai & Belhadj,¹⁹ that GAs are the most appropriate optimization techniques to apply when designing multi-source renewable energy systems. It has also been shown that these scalable algorithms are very effective in solving nonlinear optimization problems with discrete and continuous variables offering a number of exclusive advantages: robust and reliable performance, global search capability, no information requirements and reduced computational time. A summary of some research works for the sizing of a stand-alone hybrid PV system using GA is listed in the Table 3.

Table 3.

Summary of research work using GA for sizing standalone PV systems.

Ref.	Reliability indicator	Economic indicator	System
Aihara et al.²⁰	LLP	LCC	PV-Pumped storage hydropower (PSH) system
Chen²¹	LLP	ACS	PV-battery system
Kazem et al.⁴	LLP	TLCC	PV system
Semaoui et al.²²	LPSP	LCE	PV-battery system
Dufo-Lo'pez et al.²³	SOC	LCE	PV-battery system
Ma et al.²⁴	LPSP	LCE	PV-PSH system
Bouabdallah et al.²⁵	LPSP	ACS	PV-battery system
Nordin & Rahman²⁶	LPSP	LCE	PV-battery system
Ibrahim et al.¹¹	LLP	TLCC	PV-battery system
Alvarez et al.²⁷	LLP	LCC	PV-wind-battery-diesel-PSH system
Sarhan et al.²⁸	LLP	LCE	PV-battery
Rathish et al.²⁹	LPSP	LCE	PV-wind-battery-diesel system
Khatib & Muhsen³⁰	LLP	LCC	PV-battery
Xu et al.³¹	LPSP	LCE	PV-wind-PSH
Suresh & Meenakumari³²	LPSP	LCE	PV-wind-diesel-battery system
Das et al.³³	LPSP	LCE	PV-wind-biogas-battery system

In this paper, multiobjective optimization using the GA is applied for optimal sizing of a hybrid stand-alone PV/ PSH/ battery system. The performance indicators LPSP and LCE are employed for energetic and economic evaluation of the system. An energy management strategy (EMS) is also developed in order to maintain the balance between energy production and consumption and to improve energy efficiency: reduce storage and production losses, guarantee energy availability and optimize the system sizing to reduce installation and maintenance costs.

Methodology

System modelling

The implemented autonomous hybrid electricity production system is mainly composed of a solar photovoltaic generator, a PSH power plant and batteries. The main objective of the implementation of such a system is to optimize the efficiency of the energy produced in regard to the energy consumed. During the day, solar energy is produced to operate a garden fountain from 8am to 2pm. The excess of solar energy is stored by hydraulic pumping and batteries. The stored energy is used to power the public lighting of a park during the night from 9pm to 5am and to operate the fountain in case of a deficit in solar production during the day. Figures 1 and 2 illustrate the energy system implemented in the Alexandre Aibéo Park (Botanical Garden) and the daily energy consumption profile. The designations of the symbols in Figure 1 are listed in Table 4. To simplify this study, we have assumed the case where h_t = h_p.

Figure 1.

Basic architecture of the implemented energy system in the Alexandra Aibeo Park (Botanical Garden).

Figure 2.

Daily electricity consumption profile (kWh): fountain (2 kWh) and public lighting (2.6 kWh).

Table 4.

Designation of the symbols in Figure 1.

Symbol	Designation
h_t	The drop height, which represents the vertical distance of the waterfall.
h_r	The discharge head, which is the vertical distance from the centre of the pump impeller to the point where the discharge pipe reaches its maximum height.
h_a	The suction lift, which represents the vertical distance between the surface of the water to be pumped and the centre of the pump impeller.
h_p = h_r + h_a	The total discharge head, which is the sum of the discharge head h_r and the suction lift h_a.
P_pv	The power supplied by the PV generator.
P_cons	The power demanded by the DC load.
P_fournbatt	The power supplied by the batteries.
P_stockbatt	The power stored by the batteries.
P_fourntur	The power produced by the turbine upon water fall.
P_conspomp	The power consumed by the pump to pump water into the upper tank.

Estimation of the hydraulic storage potential

The required capacity of the upper water reservoir is described by the following equation (Ma et al.³⁴):

C_{r e s} = \frac{E_{L} .3, {6.10}^{6}}{η_{t u r} . ρ . g . h_{t u r}}

(1)

where C_{r es} is the installation capacity of the upper reservoir in m³, E_L (kWh) is the daily energy consumption of the load (here equal to 36.8 kWh), h_t is the drop height of the water turbine (here equal to 15 m³), η_tur (%) is the global efficiency of the water turbine generator (here equal to 70%), ρ = 1000kg/m³ is the density of water and g = 9.81m/s² is the acceleration of gravity. Using the previous formula, we can preliminarily estimate the capacity of the upper water reservoir at C_{r es} = 1279m³.

Estimation of the solar potential

The capacity of the photovoltaic generator required to power the entire system can be estimated using the following equation (Ma et al.³⁵):

C_{p v e s} = \frac{E_{L}}{η_{c} . T_{p s} . (1 - e)}

(2)

Where C_{pv es} is the desired installation capacity of the photovoltaic array, η_c is the overall conversion efficiency estimated at 80% in this study, T_ps is the average number of hours of sunlight per day and e is the overall loss factor for the photovoltaic array (high temperature, dirt, dust, shading,…) estimated at 15% in this study. The average sunshine hours per day in the area where the system is implemented (Castelo Branco) is equal to 5 h per day. Therefore, the photovoltaic capacity required to power the entire system is estimated to be C_{pv es} = 11kWp.

Estimation of the electrochemical potential

The storage capacity of batteries can be described by the following equation (Chel et al.³⁶):

C_{b e s} = \frac{n_{B} . E_{L}}{η_{b a t t} . D O D_{max}}

(3)

where C_{b es} is the battery capacity (kWh), n_B is the number of days of battery autonomy, η_batt(%) is the efficiency of the battery system, and DOD_max(%) is the maximum depth of discharge of the battery system, set to 80% in our study. The number of days of battery life is usually set to n_B = 1day (Muselli et al.;³⁷ Rajkumar et al.³⁸) In our case, the battery will be mainly used to supply the consumption demand at night (16 h per day).

n_{B} = \frac{16}{24}

Thus, A Lithium-ion battery bank with an efficiency η_batt = 95% will be adopted in our study. Thus, the capacity of the battery bank is estimated at C_b = 32kWh.

Energy management strategy

First, the hourly power difference P_diff between the hourly power supplied by the PV generator P_pv and the hourly consumption power P_cons will be calculated. Depending on its state of charge, nominal operating range and the sign of P_diff, the storage system is called to supply (P_diff > 0) or store (P_diff < 0) energy. In our study, there are two strategies:

Strategy 1: Storage and production priority to the PSH system;

Strategy 2: Storage and production priority to the battery system.

In this paper, we propose to discuss only strategy 1. Here we assign the priority of energy storage and production to the PSH system. The principle of this EMS is summarized in the diagram of Figure 3.

If P_diff (t) < 0, the PSH system is called to provide |P_diff (t)| by water turbining. There are two possible cases:

In case the power demand |P_diff(t)| is greater than the minimum turbine operating power P_mintur = 0.59kW and the upper reservoir is filled with water, then water is turbined down to produce P_fourntur(t), which is less than or equal to the maximum turbine operating power P_maxtur = 3 kW. The state of charge of the upper reservoir SOC_res(t) must not reach the minimum state of charge SOC_minres = 10%.

In case the demand is not fully satisfied by the turbine, the battery system is called to provide |P_fourntur (t) − P_diff (t)|. If the batteries are full, then they will be discharged to provide P_fournbatt(t), Which is less than or equal to the nominal power of the battery system P_nombatt = DOD_max.C_b. The state of charge of the battery system SOC_batt (t) must not reach the minimum state of charge SOC_minbatt = 20%.

If P_diff > 0, the PSH system is called to store P_diff (t) by pumping water. There are two possible cases:

In case the power to be stored P_diff (t) is greater than the minimum pump operating power P_minpomp = 7.5 kW and the upper reservoir is empty, then the pump will consume the power P_conspomp (t), which is less than or equal to the maximum pump operating power P_maxpomp = 12.19kW, in order to pump water to the upper reservoir. The state of charge of the upper reservoir SOC_res (t) must not exceed the maximum state of charge SOC_maxres = 90%.

In case the PSH system is unable to store all the available energy P_diff (t), the battery system will be called upon to store |P_conspomp (t) − P_diff (t)|. If the batteries are empty, then they will be charging to store power P_stockbatt (t), which is less than or equal to the nominal power of the battery system P_namebatt. The state of charge of the battery system SOC_batt (t) must not exceed the maximum state of charge SOC_maxbatt = 90%.

Figure 3.

Energy management strategy 1: priority to the PSH system.

The system cost

In this work, the project lifetime is fixed at R_proj = 25 years. Table 5 presents the economic specifications for each component of the studied standalone hybrid system (Solar;³⁹ HydroWires;⁴⁰ OpenEI.org.⁴¹)

Table 5.

Economic specifications of stand-alone PV system components.

Component	Initial capital cost	Operation and maintenance cost	Lifetime (years)
Photovoltaic panels	0.156 e/kWc	6.5 e/kWc-year	30
MPPT solar controller	1140 e/unit'e	-	10
Battery system	356.5 e/kWh	6.5 e/kWh-year	10
Solar installation system	31 e/kWc	-	30
PSH system (including power conversion system)	2 180 e/kW	13.14 e/kW-year	30
Upper reservoir	123 e/m³	0.5 e/kW-year	35

Optimization algorithm: Ga

The proposed methodology for the optimal sizing of the PV/PSH/battery stand-alone system of Figure 1, consists in using the genetic algorithm and the combination of tools (LPSP, LCE) to evaluate the energetic and economic aspects of the system. This methodology is given by the flowchart in Figure 4.

Figure 4.

Flowchart of the optimization of the PV/PSH/battery autonomous system sizing using the genetic algorithm.

We have previously estimated in a preliminary step the capacities of the PV generator C_{PV es}, of the batteries C_{b es}, and of the upper water tank C_{r es}. From those estimated capacities, we have built, for each energy source, a search space of optimal capacities, namely C_{pv prob}, C_{b prob} and C_{r prob} respectively. Each search space is delimited by two max and min values given respectively by twice the capacity of the considered energy source and half capacity of the considered energy source. To cover the search spaces, we have set a variation step for each search space. This step is called the selection operation.

From these 3 search spaces, we have determined several possible combinations called possible configurations of the system. A possible configuration is marked by 3 parameters (the capacity of the PV generator, the capacity of the batteries, and the capacity of the upper water tank). For each configuration, the EMS is simulated over a year (equivalent to 8784 h), the hourly energy balance of the system is calculated and ranked and the performance indicators (LPSP and LCE) are calculated and stored in matrices. At this stage, we obtain two matrices having the same size and containing respectively the possible values of the LPSP and LCE indicators according to the possible configurations. This step is called crossover and mutation operations.

If we set the LPSP to a desired value LPSP_d (for example an LPSP = 5%, which corresponds to an annual energy satisfaction of 95%), several configurations will meet this desired criteria. This step is called the generation of a new and more suitable population. Among the configurations meeting the desired reliability LPSP_d, only one configuration (C_pv, C_r, C_b) allows to have a minimum cost LCE_opt = min (LCE_d). This configuration is thus chosen as the optimal configuration of the system.

Results and discussion

The hourly PV power profile P_{pv ref} over the year 2016 is provided by the PVsyst software for a reference capacity of 25 kWp (Figure 5). Thus, for each capacity C_{PV es} in the first search sub-space, the PV output profile will be given by:

P_{p v p r o d} = \frac{C_{P V e s}}{25} P_{p v r e f} .

(4)

Figure 5.

Annual profile of photovoltaic production.

The stand-alone hybrid PV/PSH/battery system is simulated in MATLAB for the EMS prioritizing storage and generation for the PSH system. In the following, the variations of the system parameters with LPSP are represented up to LPSP = 15% with a variation step of 1%.

The variation of the LCE indicator with LPSP is shown in Figure 6. According to this figure, the minimum of energy unsatisfaction (LPSP) that can be reached is 4.32%. It can also be observed that the LCE decreases exponentially with increasing LPSP. However, according to Figure 6, the LCE has increased for LPSP of 14% and 15%. This result shows that there is only one minimum cost of the system, which corresponds to the value of LPSP = 13%. Beyond this value, the LCE increases very slightly with increasing of LPSP.

Figure 6.

Variations of the LCE (e/kWh) with the LPSP (%).

The distribution of the optimal configurations (PV array capacity, battery capacity, upper water reservoir capacity) with the LPSP, is shown in Figure 7. It can be seen from this figure that the optimal capacities of the PV generator, the batteries and the upper water reservoir decrease exponentially with increasing LPSP. The variation of C_{b opt} is rather slow compared to the variation of C_{res opt}.

Figure 7.

Variation of optimal configurations (C_{pv opt}, C_{b opt}, C_{res opt}) with the LPSP (%).

In the remaining part of this paper, we will study the energetic behaviour of the subsystems (PV generator, batteries and PSH system) for the optimal solution corresponding to an energetic satisfaction of 95% (i.e. LPSP = 5%).

By setting the desired energy reliability indicator LPSP = 5%, we can obtain several possible configurations, as shown in Figure 8. The optimal solution corresponds to the configuration offering the lowest cost According to Figure.8, the optimal solution is as: C_{pv opt} = 22 kWp, C_{b opt} = 63 kWh, C_{res opt} = 760 m³, LCE = 0.61 e/kWh.

Figure 8.

The possible configurations for LPSP = 5%.

Figures 9-10 represent the hourly distribution (kWh) in 2016 and the annual distribution (%) of photovoltaic generation between load and storage systems. The aim of Figure 9 is to represent the distribution of the total photovoltaic production between the demand, the batteries and the pumped storage over the year and to show the surplus of unexploited PV power.

Figure 9.

Annual profiles of the distribution of photovoltaic production (kWh).

Figure 10.

Distribution (%) of the total annual photovoltaic production.

It can be seen from the two figures that a large part of the total annual power produced by the PV generator is unused (about 55%). This is due to the following facts:

The required power by the load during the day (2 kWh) is quite lower than the maximal PV power production (17.7 kWh);

maximum PV output is greater than the maximal operating power of the PSH (12.19 kW);

upper reservoir is frequently full, because the power demanded by the load is low compared to the power stored by PSH;

Batteries are not used during the summer because they are full and the turbine has the priority to provide the load with energy in the evening.

In addition, battery storage is rarely used compared to PSH (5% vs. 23%).

Figures 11-12 show the hourly (kWh) and annual (%) contribution of the different energy sources to satisfy 95% of the consumption demand.

Figure 11.

Annual profiles of subsystems power contribution (kWh).

Figure 12.

Distribution (%) of the annual power contribution of the subsystems.

Figure 11 shows that the daily power demand (2 kWh) is mostly met by the PV generator, that the night-time power demand (2.6 kWh) is usually met by the turbine, and that in summer the batteries are not used. It can be seen from Figure 12 that the two PV-hydroelectricity contributions are equal (41%).

Figure 13 shows the hourly variations of the amount of water stored in the upper reservoir (m³) and the energy stored in the batteries (kWh).

Figure 13.

States of charge of the upper water reservoir (m³) and of the batteries (kWh).

It can be seen from Figure 13 that the batteries are almost at their maximum capacity in the summer because of the high PV production, while the upper reservoir is regularly charged/discharged to store the excess of PV energy and to power the load during the night. In winter, when the PV production is low, the discharge of the batteries is higher than the water reservoir.This is because the maximum power output of the batteries (DOD_max.C_{b max} = 0.8 × 64 = 51.2 kW) is much higher than the maximal operating power of the turbine (3 kW).

Figure 14 shows the annual profiles of PV generation, consumption demand, and storage element charging/discharging. It is clear that the batteries have a very low power flow compared to the PSH system because the priority of energy storage/production is reserved for the PSH system. The considerable difference between the charging and discharging profiles of the PSH system is due to the fact that the maximal operating power of the pump (12.9 kW) is much higher than maximal operating power of the turbine (3 kW) and the excess of the PV generation is important. It can also be noted that the batteries are not used during the summer months (June, July, August and September) because they are full and the PSH system is used to store the high PV production and to regularly power the load during the night (Figure 13).

Figure 14.

States of charge of the upper water reservoir (m³) and of the batteries (kWh).

Conclusion

In this paper, we have optimized, using GA and under reliability and cost constraints, the sizing and energy management within a stand-alone multisource hybrid renewable energy system composed of a photovoltaic generator, batteries and a PSH system. We detailed the implementation of GA, which includes three phases: selection, crossover and mutation. Two energy management strategies are possible: the priority of energy storage/production is reserved to the batteries or to the PSH system. In this paper, we have discussed only the strategy giving priority to the PSH system.

The last part of this paper was devoted to the simulation results of the system and its interpretations. The results showed that, by using the GA, the best configuration for the considered energy scenario at a desired LPSP of 5% is to have a photovoltaic generator of 22 kwp capacity, a 63 kwh battery bank and a 760 m³ water tank. The convergence time (number of iterations) of the GA depends on the choice of the initial population (the 3 search spaces).

Through these results, we could also conclude that the performance of a photovoltaic installation does not depend only on the efficiency of the PV panels, but also depends on the restricted power ranges of the pump, turbine and batteries.

Other solutions to reduce the surplus of PV energy can be discussed in the future: increasing the number of autonomous days of the storage devices, designing the PSH system and the batteries as a storage system and not as a production system, designing the entire system in two seasons (winter and summer), integrating the system into the grid, etc.

It may also be interesting to discuss, eventually, the second EMS giving priority to batteries and to compare the two strategies regarding reliability and cost

In the end, it is important to mention that the genetic algorithm has some drawbacks. The main disadvantage of the genetic algorithm is that it relies on a random approach, which can occasionally make the convergence to an optimal solution very slow. The setting of the population size, and the choice of the selection criteria for the new population must therefore be done with care.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Chaima Ghanjati

Chaima Ghanjati is a researcher at the Laboratory of Computer Science and Automatic Control for Systems -University of Poitiers, France. She is a Mechatronics Engineer (2017) from the University of Carthage, Tunisia. She obtained her doctoral thesis in Electrical Engineering from the University of Poitier (2021). Her research focuses on the optimization and control of hybrid energy storage systems in DC microgrid with renewable energies.

Slim Tnani is an associate professor with HDR at the University of Poitiers since 1999. He is a Doctor-Engineer in Electrical Systems. He is a researcher coordinator of optimizing electrical systems group at the laboratory of Computer Science and Automatic Control for Systems. His research interests are in electrical systems control and energetic efficiency in hybrid systems.

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