Optimizing a Green and Sustainable Off-Grid Energy-System Design: A Real Case

Abstract

In recent years, unquestionable warnings like the negative effects of CO₂ emissions, the necessity of utilizing sustainable energy sources, and the rising demand for municipal electrification have been issued. Therefore, users are encouraged to provide off-grid and sustainable energy systems for their own homes and businesses, especially if they are located rurally and far from grids. Hence, this study aims to design an off-grid hybrid energy system, in order to minimize both the baseline cost of energy and the net current expenditure in the desired system. To construct such a system, wind generators (WG), photovoltaic arrays (PV), battery banks, and bi-directional converters are considered in the real case of a supermarket with a 20-year lifespan in Malmö, Sweden. Some significant assumptions, such as the usage of renewable energy resources only, electricity production close to the business location, and a maximum allowance of 0.1% unmet are incorporated. To optimize the considered problem, a particle swarm optimization (PSO) approach as developed to provide the load requirements and establish the number of WGs, PVs, and other equipment. Moreover, to verify the obtained results, the developed system was simulated using HOMER Pro software, and the results are compared and discussed. The results indicated that the designed hybrid energy system is able to perform completely off-grid, while satisfying 99.9% of the yearly electricity demand. The best results obtained by the proposed PSO offered 160, 5, and 350 PVs, WGs, and batteries, respectively, while the best solution found by the simulation method was the use of 384 PVs, 5 WGs, and 189 batteries for the considered off-grid system. This study contributes to decentralized local electrification by utilizing renewable energy sources that have the potential to revolutionize green energy solutions.

1. Introduction

In most countries, the industrial and commercial sectors are the biggest consumers of electricity. The demand for the harnessing of renewable energy sources (RES) has increased significantly in the modern era because of rising populations and urbanization, as well as the ongoing depletion of fossil fuels [1,2]. Additionally, the negative effects on the environment may be decreased by adopting RES to reduce CO₂ emissions [3]. Moreover, the cost of power transmission may be anticipated, particularly for rural and isolated places, like islands [4]. To reduce the consumption of fossil fuels, certain steps need to be taken into consideration. Some solutions have been proposed to increase the flexibility in terms of how to produce electricity, such as the use of distributed generation (DG), future intelligent distribution grids (FIDG), and UNITED-GRID in Sweden, the Netherlands, and France for 2035 or 2050 [5], microgrid development [6], multi-grid joint-scenario generation [7], and decentralization. These are some examples of potentially important steps in resolving this issue [8]. In the decentralization approach, hybrid systems combine several power producers and energy sources to operate as a single entity [9,10,11].

Different component arrangements, such as solar panels, wind turbines, battery banks, hydrogen storage, etc., have been used to designi hybrid systems, using a variety of modeling techniques, ranging from sophisticated metaheuristics to exact solution methods, according to the literature [12]. Other cutting-edge approaches have been put forth, including the non-dominated sorting GA (NSGA-II) [13,14], Tabu Search (TS), fuzzy logic (FL) [15], Grey Wolf (GW), etc. A brief summary of some of the published studies in this field is listed in

Table 1. Literature review of hybrid-system-optimization methods.

Reference	System Components						Objective(s)	Optimization Method	Modeling Span
	WG	PV	FC	HP	ST	Fs
Wang et al. [16]	●	●			●	●	Multi-objective problem	NSGA-II	1
Maleki et al. [17]		●			●	●	PSO with adaptive inertia weight	PSO	1
Maleki and Rosen [18]	●		●			●	Minimize system/total cost	PSO	1
Fadaee and Radzi [19]	●	●			●		Multi-objective optimization	EA	20
Isa et al. [20]		●	●		●		Lowest total cost/lowest levelized energy cost/Low pollutant gas	HOMER	25
Diaf et al. [21]	●	●			●		Power-supply-loss minimization/energy-cost minimization	PSO	1
Trivedi [22]	●				●		Lowest cost/lowest gas emission	GA	1 day
Elliston et al. [23]	●	●		●	●		Lowest yearly cost	GA	1
Ugirimbabazi [24]	●	●		●	●	●	Minimum LCOE and NPC	HOMER	25
Eke et al. [25]	●	●					Lowest total expense	LP	1
Garyfallos et al. [26]	●	●	●		●	●	Lowest total expense	PSA	10
Akella et al. [27]	●	●		●			Lowest total operational expense	LP	1
Hanane et al. [28]	●	●	●		●		Lowest difference in hydrogen supply and demand	MINLP	30 days
Kashefi et al. [29]	●	●	●		●		Minimize annualized expense	PSO	20
Lagorsea et al. [30]		●	●		●		Lowest total expense	Simulation	1
Orhan et al. [31]	●	●			●		Lowest total expense	SA	20
Raquel and Daniel [32]	●		●		●	●	Lowest LEC	LP and heuristic	1
Iniyan et al. [33]	●	●				●	Lowest cost/highest efficiency rate	LP	11
Juhari et al. [34]	●	●		●	●		Lowest energy expense	Simulation	1
Katsigiannis and Georgilakis [35]	●	●			●	●	Lowest energy expense	TS	20
Budischak et al. [36]	●	●	●		●	●	Lowest energy expense	Exact solution	20
Lorestani & Ardehali [37]	●	●			●		Minimum total cost while covering thermal and electrical loads	PSO	1
Abedi et al. [38]	●	●	●		●	●	Lowest total expense, Lowest gas emission, Lowest uncovered load	FL	1
Bernal and Dufo [39]	●	●	●	●	●	●	Lowest total expense	GA	1
Ahmarinezhad et al. [40]	●	●	●	●	●	●	Lowest total expense	PSO	20
Mohammadi et al. [41]	●	●			●		Minimum NPC with different unmet load	HOMER	20
Yuan et al. [42]		●			●	●	Lowest NPC & LCOE	HOMER	10
Rongjie Wang [43]	●	●			●	●	Minimum cost and load power shortage rate	FABC	20
Vatankhah et al. [44]	●	●	●		●		Lowest NPC & LCOE	GW	20

, where FC, HP, ST, Fs, and NPC stand for fuel cell, hydropower, storage, fuels, and net present cost, respectively.

As shown in Table 1, the uses of the PSO, HOMER simulation software, and the GA simulation method have been the most interesting approaches to optimizing hybrid systems. The PSO artificially models everyday life and the social interactions between animals and birds. It is a population-based evolutionary method that performs significantly better than GA in terms of CPU usage and the quantity of necessary parameters [45]. This method takes relatively few time steps, and is more stable than conventional techniques [46].

The presented study focuses on off-grid systems and the supply chain according to the concept of sustainable development, can benefit local populations in a various ways, e.g., lower road-building costs, improved energy-network management, and electrical power backup. Furthermore, the case study was selected to focus on the power supply for supermarkets and larger grocery stores, since small businesses have disappeared from towns and metropolitan areas in recent years. Moreover, in this study, a bi-objective problem is considered to supply the hourly required load for a supermarket located in Malmö, with peak loads of 115 kW and 2002 kWh per day. To supply the required electricity to run this supermarket annually, the optimization of an off-grid hybrid system was planned. In addition, to minimize the cost of long-distance energy transmission, it is suggested that this hybrid system is located near the supermarket. To solve the bi-objective problem, first, a PSO-based algorithm was developed [47] and, next, HOMER Pro software was used to simulate the considered hybrid system, since this software has been frequently used in the field of renewable energy systems. The HOMER Pro software uses sophisticated optimization algorithms, which simulate users’ defined systems in a single run. Finally, the results obtained from both solution approaches were compared.

The following summaries the content of the study. The system configuration and related elements are presented in Section 2; the problem definition is presented in Section 3, followed by the solution methods, in Section 4; Section 5 contains the obtained results and a discussion of the findings. The study is concluded in the last section.

2. System Configuration

Configurations of the considered potential hybrid systems are explained below.

2.1. Photovoltaic Array

Numerous mathematical models have been proposed in the literature for photovoltaic (PV)-array power generation [48]. For instance, maximum power-tracing efficiency and latitude and longitude parameters were used in Rui Wang et al.’s computations [16]. A linear model based on PV efficiency and solar irradiance was used because of simplicity of its convergence, and because it ignored temperature variations in numerical modeling [49,50,51], while other researchers used more complex models that also took temperature impact into account [52,53]. Each solar panel’s potential power production at a time step “t” is formulated in Equation (1).

$$P_{PV\text{-}each}^t=\left\{\begin{array}{cc}\hfill P_{Rs}\left(\frac{r^2}{R_{SRS}·R_{CR}}\right)\hfill & if 0\le r<R_{CR}\hfill \\ P_{Rs}\frac{r}{R_{SRS}}\hfill & if R_{CR}\le r<R_{SRS}\hfill \\ \hfill P_{Rs}\hfill & if R_{SRS}\le r\hfill \end{array}\right.$$

(1)

where $P_{Rs}$ is the maximum allowable PV power, r is the solar irradiance, $R_{CR}$ is a predetermined set point for radiation (equivalent to 150 $\frac{\mathrm{W}}{{\mathrm{m}}^2}$), and $R_{SRS}$ is the solar radiation taken into account when the standard environment is 1000 $\frac{\mathrm{W}}{{\mathrm{m}}^2}$ in Equation (1). Additionally, a PV panel with the Kyocera KD-145SXUFU model was chosen for generating electricity. To produce approximately 1 kW of power from each PV array (in this study), 7 pieces of PV panels per array were assumed to generate the MPP voltage output ($U_{MPP}=145v$). Roof-mounted horizontal plates were utilized, even though tilted PV modules have superior solar-ray-absorption levels. According to Lindahl’s recommendation, the initial expenditure for commercial PV arrays erected on roofs, including converters, can be expected to be around 11.6 $\frac{SEK}{W_p}$ [54]. In this study, the data related to hourly global irradiance were obtained from a related website [55].

Numerous maintenance and repair tasks should be kept int consideration when estimating operation and maintenance (O&M) costs, to ensure these are realistic. These include the fact that, as indicated by Electric Power Research Institute (EPRI) in 2015, the yearly O&M of solar PV can be approximated at roughly 10.00–45.00 $\frac{\mathrm{\$}}{\mathrm{kW}.\mathrm{year}}$ [56]. Prices in this study are given in SEK; and USD 1 equals 8.22 SEK, and MSEK stands for SEK one million.

2.2. Wind Turbine

To calculate power output by each wind turbine at time step t, Equation (2) is used [57].

$$P_{WG\text{-}each}^t=\left\{\begin{array}{cc}\hfill 0\hfill & if \nu <{\nu }_{Cutin}\hfill \\ \frac{1}{2}{C}_P\rho A_{WG}{\nu \left(t\right)}^3\hfill & if {\nu }_{Cutin}\le \nu <{\nu }_{rated}\hfill \\ P_{WG,rated}\hfill & if {\nu }_{rated}\le \nu <{\nu }_{Cutout}\hfill \\ \hfill 0\hfill & if {\nu }_{Cutout}\le \nu \hfill \end{array}\right.$$

(2)

where $P_{WG,rated}=100 \mathrm{kW}$ is the rated power and $A_{WG}=468 {\mathrm{m}}^2$ is the turbine’s swept area. The Northern Power NPS 100C-24 wind turbine is 37 m above the ground, and $\nu \left(t\right)$ is the velocity of the wind at that height. The standard $C_P$ value for contemporary wind generators is approximately 0.40, which was verified using the NPS-100C-24 curve for its power. The rated wind speed was computed as $v_{rated}={{(2P}_{WG,rated}/\left(C_p\rho A_{WG}\right))}^{1/3}=9.6 \mathrm{m}/\mathrm{s}$ with the cut-in wind speed, $v_{Cut\text{-}in}$, as 3 m/s and the cut-out wind speed, $v_{Cutout}$, as 26 m/s. Recently, Liang et al. developed numerical models that aimed to efficiently simulate dynamic-behavior WGs [58].

In this study, the data related to hourly wind speed were obtained from the related website [59].

2.3. Battery Bank and Convertor

The proposed model of the battery bank’s charging and discharging scenarios was generated from Maleki et al.’s model [49] by using Equations (3) and (4), respectively. The investigation used a Gildemeister 10 kW–40 kWh CELLCUBE^® battery, USA.

$$E_{batt}^t=E_{batt}^{t-1}\times \left(1-\sigma \right)+\left[{(P}_{Wind}^t-P_{Load}^t\right).{\eta }_{conv}+P_{PV}^t].{\eta }_{BC}.\mathsf{\Delta }t$$

(3)

$$E_{batt}^t=E_{batt}^{t-1}\times \left(1-\sigma \right)-\left[\frac{P_{Load}^t-P_{Wind}^t-\frac{P_{PV}^t}{{\eta }_{conv}}}{{\eta }_{conv}·{\eta }_{BF}}\right].\mathsf{\Delta }t$$

(4)

where the battery bank’s charging and discharging efficiencies, respectively, were ${\eta }_{BC}$ and ${\eta }_{BF}$. Both were taken to be 95%. The $E_{batt}^t$ is the quantity of electricity that is stored at the current time step t, and $\sigma =0.0002$ is the rate of hourly self-discharge. It should be noted that each battery has its own minimum and maximum storage limits. The battery cannot be discharged below a particular threshold; in this study, zero and 40 kWh of electrical energy were used as the lower and upper limits, respectively. Of course, the rated battery capacity cannot be exceeded. As a result, more batteries must be prepared for the system design to store a larger amount of electricity. Furthermore, the rectifier and inverter systems were both chosen with ${\eta }_{conv}$ equal to 95%.

2.4. Systems Architecture

The suggested system is shown in Figure 1, where the battery bank and PV arrays are linked to the DC busbar and converters have connections to the AC and DC busbars in both directions.

3. Problem Definition

In order to obtain the ideal number of components, such as PV arrays and wind turbines, minimal LCOE and NPC during a 20-year operational lifespan were taken into consideration. Additionally, it should be assumed that all refrigerators and freezers that are in operation are always turned on to prevent food contamination in grocery stores. Therefore, only over 0.1% were permitted; as a result, with this setting and RES only, a small amount of ${\mathrm{CO}}_2$ was produced. Equations (5) and (6) are used to determine the LCOE and NPC, respectively.

$$\mathrm{LCOE}=\frac{C_{0,total}.a}{E_0}$$

(5)

$$\mathrm{NPC}=\sum _{i=1}^n\frac{C_{cashflow}}{{(1+p)}^n}-A_0$$

(6)

where $a$ is the annuity factor, $C_{0,total}$ is the entire annualized cost, and $E_0$ is the annual energy yield (kWh) in Equation (5). Equation (6) is used to determine the NPC in SEK, where $C_{cashflow}$ is the annual net cost for the designed project, $A_0$ is the initial cost, and p is the interest rate. All the limitations are listed below:

$$0\le N_{PV}\le 400$$

(7)

$$0\le N_{WG}\le 15$$

(8)

$$0\le N_{batt}\le 350$$

(9)

$$0\le N_{conv}\le 300$$

(10)

$${0=E}_{batt}^{min}\le E_{batt}^t\le E_{batt}^{max}=40 \mathrm{kWh}$$

(11)

$$\mathrm{If} E_{batt}^t<E_{batt}^{min} \to E_{batt}^t=E_{batt}^{min} \left(\mathrm{kWh}\right)$$

(12)

$$\mathrm{If} E_{batt}^{max}<E_{batt}^t \to E_{batt}^t=E_{batt}^{max} \left(\mathrm{kWh}\right)$$

(13)

At most 0.1% shortage is accepted

(14)

Constraint (7) denotes that the number of PV arrays cannot be more than 400, and each of these arrays has an installed power of 1 kW. Similarly, constraints (8) to (10) limit the number of wind turbines, batteries, and convertors to 15, 350, and 300, respectively. Constraints (11) to (13) show that the stored electricity at time t cannot be less than zero, or more than 40 kWh. The maximum number of PV arrays and batteries was determined in order to keep the project’s overall cost from becoming excessively high. Access to a load-demand profile is the first piece of information needed to execute each optimization and simulation of the hybrid system. Finally, constraint (14) considers the allowance of shortage in the satisfaction of the demand, which should be a maximum 0.1%.

Equation (15) can be used to define the hourly electricity-consumption indicator (HECI, unit W/m²) in accordance with the non-linear correlation suggested by Noren and Pyrko [60].

$$\mathrm{HECI}=C_0+C_1\times \mathrm{SFA}+C_2\times T^2$$

(15)

where $C_0$, $C_1$, and $C_2$ are constant coefficients that were discovered by monthly regression. The daily average temperature in the specified area for this study is shown by $T$, in degrees Celsius. Noren and Pyrko [60,61] presumptively included grocery retailers’ gross floor area (GFA) and sales floor area (SFA). Through the analysis of the data, it became clear that SFA consumes significantly more electricity than GFA. The existence of numerous refrigerators in SFA is the primary cause of this discrepancy. Therefore, all the aforementioned equations were programmed in MATLAB software, taking into account a supermarket measuring 1000 m² situated in Malmö. Figure 2 illustrates the average real hourly load profile in January and August 2010 for the area of 1000 m² on weekends and working days. The estimation was based on the outdoor-temperature data [59].

The hybrid system’s structure is shown in Figure 3. In this figure, it is shown that the wind turbines and electric loads are linked to the AC busbars, whereas the PV panels and batteries are linked to the DC busbars. Moreover, a pair of bi-directional converters was used to connect two busbars.

4. Solution Methods

Both solution approaches for the problem presented in this study are scrutinized in the following ways:

4.1. Metaheuristic-Solution Approach

To find the best solution to the proposed NP hard problem, a metaheuristic-solution approach based on the PSO method was developed [62,63]. In general, PSO locates each swarm by first producing a random population. In each iteration, the best answer is kept in its memory while it continues to converge on the optimal solution to change each person’s velocity. Initialization, encoding, parent choice, and position update are crucial PSO processes. The size of the population (PS), the factor of constriction in a swarm to limit the speed (CF), maximum iterations (MI), and coefficients for acceleration, noted by $c_1$ and $c_2$, are all included in the initialization step.

Evaluations of the starting population and the fitness function were carried out at the encoding step. The method maintains and saves the finest position of every detected particle within iterations and records the best as the global position during the parent selection stage. All positions in the list were examined, and the velocity factor of this algorithm was changed after each iteration. Two equations, (16) and (17), were used to update the swarms’ positions; the swarm’s velocity ($V_i$) and related position ($X_i$) were updated while taking into account the coefficient of control ($\omega$) and acceleration coefficients ($c_1$ and $c_2$).

$$V_i^{\left(t+1\right)}=\omega \ast V_i^{\left(t\right)}+c_1{r}_1\left(P_i^{\left(t\right)}-X_i^{\left(t\right)}\right)+c_2{r}_2\left(X_G^{\left(t\right)}-X_i^{\left(t\right)}\right)$$

(16)

$$X_i^{\left(t+1\right)}=X_i^{\left(t\right)}+\chi {\ast V}_i^{\left(t+1\right)}$$

(17)

where $X_G\left(t\right)$ is the best recorded global position and $P_i\left(t\right)$ is the best position at the time step t. In Equations (16) and (17), velocity-limit coefficient is shown by χ, and $r_1$ and $r_2$ are uniformly generated random values (with 0 and 1 as their endpoints in a closed interval). These parameters are either replaced with new positions in each phase or kept in the best position thus far after comparison to the best global position. When the PSO algorithm completes the MI, it is terminated. Algorithm 1 provides the proposed PSO method’s pseudocode.

Algorithm 1. Pseudocode of the proposed PSO algorithm.
Step	Description
0	Initialization of PSO parameters
1	Generating of population
2	Fitness function calculation for initial individuals
3	Initial individuals recorded in $P_i$
4	The best individual registered in $X_G$
5	No. of Iteration as 0
6	While (Iteration < MI) do
7	By using Equations (16) and (17) update recorded positions
8	Calculate fitness value for new members
9	if value in step #8 is less than at $P_i$
10	Position of that individual must be replaced by $P_i$
11	if value in step #8 is less than at $X_G$
12	Position of that individual must be replaced by $X_G$
13	End
14	End
15	No. of Iteration + 1 restore in No. of Iteration
16	end while
17	Return $X_G$

4.2. Simulation Method

In addition to the developed metaheuristic approach, a simulation method is considered to optimize the proposed hybrid system using HOMER Pro software. According to the hourly outdoor temperature that HOMER uses, the load demand for a supermarket measuring 1000 m², located in Malmö, in 2010, is shown in Figure 4.

The Swedish Meteorological and Hydrological Institute (SMHI)’s data bank was used to gather the real sun-irradiance, wind-speed, and ambient-temperature data [59]. Figure 5 displays the heat map of horizontal solar radiation in Malmö. The greatest and the minimum daily irradiances 23re reported in July and December, and the average annual global irradiance was 2.73 $\frac{\mathrm{kWh}}{{\mathrm{m}}^2.\mathrm{day}}$.

The heat map of wind speed in Malmö for the year 2010 is depicted in Figure 6. In 2010, the annual mean value for the wind speed was 4.88 (m/s). For more information regarding the wind-power forecasting, the methods reported by Sun et al. [64] and Li et al. [65] might be.

The average hourly temperatures in 2010 are shown in Figure 7, with an annual average temperature of 7.37 (°C).

5. Results and Discussion

With no annual shortage and considering separate operational reserves, the proposed system will be operational for a period of 20 years.

5.1. Results of PSO Method

The PSO method was programmed in MATLAB (R2017b) software using a laptop with an Intel (R) Core (TM) i5-4200U CPU running at 2.30 GHz and with 4.0 GB of RAM. In this method, some parameters should be first defined, and their preliminary values should be set . The parameters are the control coefficient, the velocity-limit coefficient, and two constant coefficients, which are shown by ω, χ, $c_1$, and $c_2$, respectively. Maleki et al. [17] set the values of the mentioned parameters as 1, 1, 2, and 2, respectively. Kaviani et al. [29] set these as 1, 0.7, 2.5, and 1.5, respectively, while $c_1$ and $c_2$ gradually change to 1.5 and 2.5, respectively. In this study, the latter case was used to set the parameters because it was predominant in the first case and also covered that set. All the used and defined parameters and their starting values are shown in

Table 2. Initial values of parameters considered in PSO method.

PSO Parameters	Values
ω	1
χ	0.7
$c_1$	2.5
$c_2$	1.5
Lifespan (year)	20
Number of particles	200
Maximum iterations	200
Number of bi-directional converters	199

. In addition, as mentioned previously, the life span considered for this project is 20 years. The maximum number of particles active in the PSO was 200, and the number of iterations was also 200. Finally, the number of bi-directional converters was considered as 199, which was the best solution found by the simulation approach.

The number of particles represents the number of search agents.

Table 3. Results of the heuristic method used.

Methods	Number of PVs	Number of WGs	Number of Batteries	Number of Convertors	LCOE	NPC
PSO	160	5	350	199	0.4768	4.7347

lists the optimal outcomes from the generated PSO modeling. In this table, the unit of the PV and the converter is kW, the unit of the WG and the batteries is number, and the units of the LCOE and NPC are measured in USD/kWh, and USD millions, respectively.

According to the results presented in Table 3, the best solution found by the PSO method was 160 kW of PV arrays, five wind turbines, 350 batteries, and 199 kW of converters, with a LCOE of around 0.48 $/kWh and around USD 4.7 million as the NPC.

5.2. Results of Simulation Method

In the next step, to solve the problem with the simulation method, HOMER Pro was used, and the best configuration for the hybrid system was designed in

Table 4. Results of simulation method used.

Methods	Number of PV	Number of WG	Number of Batteries	Number of Convertors	LCOE	NPC
Simulation	384	5	189	199	0.3796	3.7682

, where the explanations for each column are similar to the information in Table 3.

The results in Table 4 show that in the best solution, 384 kW of PV arrays, five wind turbines, 189 batteries, and 199 kW of converters were needed, which led to an LCOE of around 0.38 USD/kWh and an NPC of less than USD 3.77 million.

The findings are remarkably comparable to one another; as we expected to find dissimilarities between them, these equal outcomes were not anticipated. In terms of the convergence to equivalent optimal values, it is obvious that the coded metaheuristic method and the simulation approach were compatible. The selection of several alternatives in the optimization considerations may have been another cause of the discrepancies in the results. The low solar irradiation during six months of the year (in Sweden) was taken into account during the optimization with the PSO. As a result, the employment of batteries rather than the addition of more PV panels was the main focus. In addition, the hybrid system’s design needed solar panels to take advantage of the solar energy, particularly during the summer. The supermarket was seen as entirely self-sufficient, even in the periods of limited sunshine in Sweden.

According to is the information presented in Table 3 and Table 4 for the batteries, 350 batteries equaled 14 MWh of storage, while 189 batteries equaled 7.6 MWh of storage. The average annual load was 850 MWh, or 2.3 MWh/day; therefore, the smaller battery can cover the load for about 3 days, and the larger battery can cover it for 6 days. Both sizes seem appropriate for an off-grid system with significant unmet load demand.

Table 5. Net present costs.

Component	Capital ($)	Operating ($)	Replacement ($)	Total ($)
Gildemeister 10 kW–40 kWh	755,474.5	312,652.1	510,948.9	1,581,508.5
Kyocera KD 145 SX-UFU	467,153.3	95,315.9	0.00	563,260.3
Northern Power NPS 100C-24	1,423,357.7	82,666.2	0.00	1,508,515.8
System Converter	38,717.6	32,886.6	0.00	71,604.4
Hybrid System Total Costs	2,712,895.4	546,228.7	510,948.9	3,771,289.5

outlines the NPC for each component in the designed RES.

An electricity summary, including both the excess and the electricity shortage, as well as the production summary, is listed in

Table 6. Electricity summary.

Excess and Unmet Load ($\frac{\mathbf{kWh}}{\mathbf{year}}$)		Production Summary ($\frac{\mathbf{kWh}}{\mathbf{year}}$)
Excess electricity	751,913	Kyocera KD 145 SX-UFU	454,867
Unmet electric load	727	Northern Power NPS 100C-24	1,143,688
Capacity shortage	727	Total	1,598,554

.

The annual state of charge (SOC) of the system’s battery bank is depicted in Figure 8.

The PSO was modeled with space limitations for the solar-panel installation (placed on the roof of the supermarket), while the space limitations were not considered in the simulation in HOMER Pro. In this case study, there were no limitations in terms of the available area near the supermarket in which to locate the facilities. In addition, interestingly, the two different solution methods, i.e., the PSO and the HOMER Pro simulation, obtained different numbers of facilities, but with similar costs. The PSO suggested 160 PV arrays with 350 batteries, and the HOMER Pro showed 384 PVs and 189 batteries. If there is insufficient space available in the location, the latter solution is suggested (with a greater number of PV panels). Solar panels can be installed on the roof or in the parking area, meaning they can provide shade and function as shelters for cars. Moreover, it is clear from the data analysis and the comparison of the two planned models that the results suggested by the PSO method had relatively high expenses, because the PSO method requires more batteries than the simulation method by Homer Pro application.

It is conceivable and profitable to sell the extra electricity to the grid. Levels of profitability may differ based on the price per kWh for selling the electricity. In terms of low carbon emissions, this approach would enhance the reputation of the supermarket’s brand, while the supermarket would be completely self-sufficient in terms of energy supply. This aspect may generate advertising value.

As changes in the use of different renewable energy sources are possible, the hybrid system, in this research, will have more flexibility. The system might be even better supported, encouraging a higher share of renewables, if the storage is allowed to integrate with the grid even further by charging from electricity purchased at low prices.

6. Conclusions

In both emerging and wealthy nations, the decentralization of local electrification by utilizing renewable energy sources has the potential to revolutionize green energy solutions. The decentralized electrical supply for a real-world small supermarket with a 20-year lifespan in Malmö was the focus of this study based. To solve the considered problem, two approaches—metaheuristic and simulation methods—were utilized.

The best solution found by the proposed PSO algorithm offered 160 PV arrays, five wind turbines, 350 batteries, and 199 bi-directional system converters. However, when using HOMER Pro to simulate the hybrid system, the suggested off-grid system was made up of 384 PV arrays, five wind turbines, 189 batteries, and 199 converters. It should be noted that in this investigation, a shortfall of no more than 0.1% at peak load was permitted. It would be simple to manage and deal with the continued shortage because the store may have a few non-critical loads. However, for the supermarket under study, it would be reasonable to remain connected to the grid, so the shortfall would not be a problem. The grid can also receive significant help regarding grid connectivity. From the supermarket’s perspective, it is obvious that the system is not immediately lucrative, but that it will have high promotional values.

The HOMER simulation and the PSO method, like any other software, have their own limitations. For instance, any time-series data in the form of daily average might not be imported to HOMER, or the software does not rank the hybrid systems according to the cost of energy. In addition, it does not consider the factor of intra-hour variability (in version 2017). On the other hand, as PSO is not ready software, any data, objective function, etc. must be coded. In this regard, comparing different systems, or obtaining different graphs, is time-consuming, and an expert is needed to define and to code them.

To delve deeper into research in this area, the salvage price can also be considered in the optimization model, which might give a more realistic perspective to project consultants. The recent study performed by Liao et al. related to the recycling of end-of-life PVs [66] might be considered in relation to this issue. Furthermore, tilting PV panels that are carefully tuned are preferable to horizontal panels.

Regarding excess electricity, it is recommended that it is either used in another operation, sold to the grid, or stored in hydrogen tanks. Therefore, the stored energy can be used again when more energy (whether electricity or heat via fuel cells) is required, especially during the winter, when the solar irradiation is insufficient.