Optimal Design of an Isolated Hybrid Microgrid for Enhanced Deployment of Renewable Energy Sources in Saudi Arabia

: Hybrid microgrids are presented as a solution to many electrical energetic problems. These microgrids contain some renewable energy sources such as photovoltaic (PV), wind and biomass, or a hybrid of these sources, in addition to storage systems. Using these microgrids in electric power generation has many advantages such as clean energy, stability in supplying power, reduced grid congestion and a new investment ﬁeld. Despite all these microgrids advantages, they are not widely used due to some economic aspects. These aspects are represented in the net present cost (NPC) and the levelized cost of energy (LCOE). To handle these economic aspects, the proper microgrids conﬁguration according to the quantity, quality and availability of the sustainable source of energy in installing the microgrid as well as the optimal design of the microgrid components should be investigated. The objective of this paper is to design an economic microgrid system for the Yanbu region of Saudi Arabia. This design aims to select the best microgrid conﬁguration while minimizing both NPC and LCOE considering some technical conditions, including loss of power supply probability and availability index. The optimization algorithm used is Giza Pyramids Construction (GPC). To prove the GPC algorithm’s effectiveness in solving the studied optimization problem, artiﬁcial electric ﬁeld and grey wolf optimizer algorithms are used for comparison purposes. The obtained results demonstrate that the best conﬁguration for the selected area is a PV/biomass hybrid microgrid with a minimum NPC and LCOE of $319,219 and $0.208/kWh, respectively.


Introduction
The depletion of fuel, environmental problems and the danger of nuclear use oblige the international community to adopt renewable energy resources, mainly the isolated mode in the non-electrified areas where the extension of the grid is costly, and the power losses are very high. Otherwise, the intermittence of the renewable resources is managed using hybrid systems such as PV and wind, which are considered complementary.
The hybrid microgrid systems (HMGs) become essential electrification of rural areas. The hybrid renewable energy system (HRES) is investigated and proposed in many studies (e.g., [1][2][3][4][5][6][7]), which introduce all necessary information to design isolated HRES. The authors of [1] presented the design and financing of a microgrid on a small Koh Jik Island recent algorithms to reach these objectives, which proved to provide their feasibility to find the optimal solution. Khan and Javaid [23] proposed a hybrid algorithm named the JLBO composed of Jaya and teaching-learning-based optimization (TLBO), dedicated to finding optimal PV/WT/battery sizing for a microgrid system. Makhdoomi and Askarzadeh [24] proposed a hybrid of CSA and the adaptive chaotic awareness probability algorithms called CSAAC-AP to optimize PV/diesel/PHS microgrid system operation. Kharrich et al. [25] proposed an improvement of the Bonobo Optimizer (BO), using the quasi-oppositional technique for resolving the microgrid design problem that is based on PV, wind, battery, diesel and biomass, with four configurations, and the case study was Aswan, Egypt. The algorithm is compared with BO, Harris Hawks Optimization (HHO), Algorithm of Artificial Electric Field (AEFA) and IWO algorithms. Abo-Elyousr and Nozhy [26] developed a biobjective ant colony algorithm (BOACA) for the optimal size of several configurations of hybrid microgrids. A comprehensive summary of previous work considering microgrid design and operation is listed in Table 1.
In this paper, microgrid design and power management are investigated for two configurations, PV/biomass and PV/wind/diesel/battery, to feed an isolated area in the Yanbu region of Saudi Arabia. The main objective of this paper is minimizing NPC, considering technical factors. The optimization is applied using many meta-heuristic algorithms such as the Giza Pyramids Construction (GPC), AEFA and Grey Wolf Optimizer (GWO). In summary, the paper presents four contributions: • Optimal design of the microgrid system feeding a load in the Yanbu region in Saudi Arabia • Proposing and analyzing two configurations of microgrid systems considering their technical and operational features • Presenting the optimal design operation of the hybrid renewable microgrid system by selecting suitable renewable sources to meet the required objectives and constraints • Investigation and implementation of a recent GPC optimization algorithm and compared it with other algorithms The mathematical modeling of renewable systems (PV and wind), conventional diesel and battery systems are presented in Section 2. Section 3 presents the mathematical formulation of the objective function. Section 4 presents the mathematical modeling of GPC optimization algorithm. Section 5 presents the case study. Section 6 presents the results and discussions. Finally, Section 7 presents the main conclusions.

Mathematical Modeling
In this case study, two configurations of the HMG systems are presented. The systems are composed of PV, wind, diesel, biomass and battery systems, as presented in Figure 1. The first configuration considers the PV/biomass microgrid system with the power management strategy presented in Figure 2. The second configuration considers the PV/wind/diesel/battery system with the power management shown in Figure 3. The main sequence of the microgrid operation is as follows: • The PV and wind turbine supply energy as a pillar of the system. • The battery operates when there is a shortage of power from renewable sources.

•
The diesel generator works and supplies power when the battery is at its min SOC.

PV Modeling
The power of the PV panel can be represented as [27]: where I represents solar irradiation, A pv represents the area of PV panel and η pv represents the efficiency of the PV system, which is calculated by: where NOCT represents nominal operating of the cell temperature ( • C), η r represents the reference efficiency, η t represents MPPT equipment efficiency, β is temperature coefficient, T a represents ambient temperature ( • C) and T r represents cell reference temperature ( • C).

Wind Generator Modeling
The wind power depends on wind speed, which can be presented as [28]: where V represents wind speed; P r represents wind rated power; V ci , V co and V r are cut-in, cut-out and rated wind speeds, respectively; and a and b represent two constants that are calculated as: The rated power of wind is calculated as: where ρ represents the air density, A wind represents the wind turbine swept area and C p represents the max power coefficient, which is limited between 0.25% and 0.45%.

Biomass System Modeling
The biomass produces power as [29]: where Total bio is the total organic material of biomass which is from the date palm waste, CV bio represents the calorific value of the organic material (≈20 MJ/kg), η bio is the biomass efficiency and O time is the operating hour for each day. The procedure of converting the biomass to electricity is presented in Figure 4.

Diesel Generator System Modeling
The rated power of diesel generator (P dg ) is represented as [30]: where F dg is fuel consumption, P dg,out is the output power and A g and B g are two constants that represent the linear curve of the fuel consumption.

Battery Energy Storage System Modeling
The battery is an essential element in isolated microgrid systems. The battery capacity (kWh) can be expressed as [30]: where E l represents the total energy load that should be transferred to the HRES; AD represents the battery autonomy; DOD is the depth of discharge (%), which should avoid dominating the storage to the minimum state of the battery; and η inv and η b are the efficiency of inverter and battery (%), respectively, which consider the losses in the transfer of energy.

Net Present Cost
The objective preserved in this paper is to minimize the Net Present Cost (NPC), which represents the total investment project cost. It contains the sum of all systems capital (C), operation and maintenance (OM) and replacement (R) costs, as well as the fuel cost of the diesel FC dg when it is added to the system. This paper also considers the interest rate (i r ), inflation rate (δ), escalation rate (µ) and the project lifetime (N). In summary, the NPC can be calculated as follows [31]:

Costs of PV and Wind
The concept of cost calculation for PV and WT is generally similar. Their capital costs are based on the initial cost (λ PV,WT ) and the area (A PV,WT ). The capital cost of PV and/or wind is calculated as [32]: The OM costs are [32]: where θ PV,WT represents the annual operation and maintenance cost.

Costs of Diesel Generation
The diesel generator costs are calculated as [31]: where C dg is capital cost, λ dg represents initial cost of the diesel for each KW, OM dg is the actual O&M cost, θ dg represents annual O&M cost, N run represents operating hours number of diesel generator per year, R diesel is the diesel generator replacement cost, R dg is annual replacement cost, p f represents the fuel cost, F dg is annual fuel consumption and FC dg represents total fuel cost.

Costs of Battery System
The capital with OM (which contains the replacement) costs of battery are as follows [32]: where λ bat is the battery initial cost and θ bat represents battery annual O&M cost.

Costs of Biomass System
The biomass costs are calculated as [27]: where λ bg represents initial cost of biomass, θ 1 is annual fixed O&M cost, θ 2 represents variable O&M cost and P w is the annual generated energy (kWh/Year).

Costs of Inverter
The capital and O&M costs of the inverter are calculated as [31]: where λ inv is the inverter initial cost and θ Inv is annual O&M cost of inverter.

Levelized Cost of Energy
The Levelized Cost of Energy (LCOE) is calculated as follows [30]: where P load is the load demand and CRF is the capital recovery factor that converts the initial to annual capital cost, which is calculated as follows: where R represents the lifetime of the project.

Loss of Power Supply Probability
The loss of power supply probability represents the reliability of microgrid system. LPSP is calculated as [30]: where P SOC, bmin is the minimum state of charge of battery.

Availability Index
The availability index (A) is calculated to confirm the ability of the designed system as follows [32]: where P b represent the battery power. u is equal to 1 if the load is not satisfied; otherwise, it is equal to 0.

Optimization Algorithm
The HMG design needs an efficient meta-heuristic algorithm that can help to resolve the system's complex operations. In a recent paper, we proposed a new optimization algorithm called Giza Pyramids construction. The effeteness of GPC is investigated through the hybrid microgrid design of two scenarios: PV/biomass and PV/wind/diesel/battery. Moreover, the GPC is compared with two other optimization algorithms to prove its ability to find the optimal solutions.
Harifi et al. [33] initially proposed the GPC algorithm, simulating the building process of the pyramids in Giza. The GPC optimization is a new population-based metaheuristic optimization algorithm that is inspired by the movement of workers and stone blocks during the pyramid building. The GPC is dedicated to several areas, including engineering applications.
To prove the effectiveness of the GPC, it is compared with two other algorithms, AEFA and GWO, which are presented in Appendices A.1 and A.2, respectively. Appendix A.3 represents the parameters of the algorithms declared above.
The GPC pseudocode is listed in Algorithm 1.

Algorithm 1: Giza Pyramids construction [33]
Step 1: Initialize a set of random stone block or workers X i w = X 1 w , X 2 w , . . . , X N w within the limits X i min ≤ X i B ≤ X i max . Initialize the GPC parameters. Evaluate the objective function of all populations.
Step 2: for iter = 1 to Max_iter, do if new_fitness < Pharaoh's agent cost then set new_fitness as Pharaoh's agent cost. end if end Sort solution for next iteration. end

Yanbu Case Study of the Hybrid Microgrid System
The case study is proposed for the Yanbu region of Saudi Arabia, as shown Figure 5. The project is dedicated to feed a domestic load with the coordinate latitude 24.265 • and longitude 38.06 • . A heat dump system is used to dump power.
The hourly load demand is presented in Figure 6 where the peak is about 43 kW. The metrological data [34], including solar radiation, temperature, wind speed and pressure, are presented in Figures 7-10, respectively. The project economic and technical data are presented in Table 2 for PV, wind, biomass, diesel and battery systems.

Results and Discussions
In this paper, GPC is chosen and implemented to design an HMG system. PV, wind turbine, biomass system, diesel generator and battery storage system are used for two scenarios: (A) PV/biomass hybrid microgrid system (B) PV/wind/diesel/battery microgrid system The results obtained by GPC are compared with those of the AEFA and GWO algorithms to validate its ability and effectiveness in achieving the best optimal design with high reliability and minimum investment costs. The simulations were performed using MATLAB editor R2018a. The convergence of the three optimization algorithms (GPC, AEFA and GWO) are shown in Figures 11-13, which display the convergence curves of all algorithms. It is clear that the GPC algorithm achieves the best optimal designs for both configurations. Figure 11 presents the PV/biomass system convergence curves, which show that the GPC has the best results compared to those of the AEFA and GWO algorithms. Figure 12 presents the convergence curve of PV/diesel/battery system, using GPC, AEFA and GWO. Figure 13 presents the convergence of PV/wind/diesel/battery system, proving that GPC is the best algorithm. Thus, GPC needs less computational time to find the optimal system, which reduces the computer source usage, as well as reduces the system cost. The AEFA and GWO algorithms need more time for convergence. The best value of convergence is found in Iterations 59 (GPC), 87 (AEFA) and 75 (GWO) for the first PV/biomass microgrid system. For the second system, the best value is found at Iterations 54(GPC), 88 (AEFA) and 47 (GWO). For the third configuration, the optimal is found at Iterations 53 (GPC), 55 (AEFA) and 12 (GWO). Typically, in microgrid design problems, 100 iterations are sufficient.   The objective functions (NPC) and other technical and economical calculated parameters for both hybrid microgrid systems are listed in Table 3. From the obtained results, the best optimal microgrid design in this study is found for the first scenario of PV/biomass system with NPC of $319,219 and LCOE of $0.208/kWh for cost of energy. The associated LPSP limit is 0.049 and the availability is about 96%. The optimal results are obtained using the GPC algorithm in both configurations, where the computational time of GPC is the shortest compared with those of AEFA and GWO as shown in Table 4. This project's optimal microgrid system is to install 265,870 m 2 of PV panel with a 1000 ton/year biomass generator.  Figure 14 presents the annual contribution of the optimal microgrid system using the proposed GPC algorithm, while Figure 15 presents the time response of PV and biomass. Figures 16 and 17 present the annual contribution and the time response of PV/diesel/battery. Figure 18 presents the annual contribution of PV/wind/diesel/battery using the GPC algorithm, while Figure 19 presents the time response of the PV and wind systems. Figure 20 shows the required costs of PV, biomass and inverter, considering the capital, operation/maintenance, replacement and resale costs. All costs are expressed in dollars. Figures 21 and 22 show the detailed costs of the two studied configurations, PV/diesel/battery and PV/wind/diesel/battery, respectively, where PV is the least expensive in both configurations. The cost of fuel is the highest during the project lifetime at $287,549 in the second configuration. Figure 23 presents the percent of total annual contribution, of which PV is the first contributor with 85%; similarly, PV represents 71.73% in the second configuration. The wind is the most important contributor in the PV/wind/diesel/battery with 59.75%.

Conclusions
The hybrid microgrid isolated systems is a cost-effective system, especially in Saudi Arabia, where solar radiation is significant. The paper presents the design of three hybrid microgrid systems in Yanbu region. The minimum cost of investment is obtained using the PV/biomass system by applying the recent GPC optimization algorithm. The developed algorithm is compared with the AEFA and GWO algorithms. The objective function is to minimize the net present cost respecting some technical constraints. The best optimal system has 265,870 m 2 of PV and 1000 ton/year biomass generator. The NPC is $319,219 and LCOE is $0.208/kWh. In future work, the proposal and implementation of new optimization algorithms and new microgrid system configurations will be the main focus. A new framework containing an efficient algorithm and a good power management helps to find a cost-effective microgrid system.  Rated power of the diesel generator (kW) λ bat Initial cost of the battery system ($/kWh) P f Fuel price ($/L) λ bg Biomass initial cost ($/kW) P bg Generated power of the biogas plant (kW) λ dg Diesel generator initial cost ($/kW) P BM Biomass power (kW) λ PV,WT Initial cost of PV and WT ($/m 2 ) P pv Output power of the PV (kW) δ Inflation rate (%) P r Rated power (kW) µ Escalation rate (%) P re Power from renewable energy systems θ 1 Biomass annual fixed O&M cost ($/kW/year) P w Annual working of biomass (kWh/Year) θ 2 Biomass variable O&M cost ($/kW h)