Optimal design and performance analysis of coastal microgrid using different optimization algorithms

In 2019, the number of people without access to electricity reached 770 million who mostly live in sub-Saharan Africa, rural areas, or developing Asia [1]. Despite the global efforts and progress for the energy access policies to achieve development and sustainable electricity for all, it is estimated that about 670 million people will still lack access to electricity by reaching 2030 [2, 3]. These developments were based only on fossil energy which causes a global fossil energy crisis and environmental problems [4, 5]. Consequently, much focus has been given renewable energy sources (RESs) such as wind, solar, wave, and hydroelectric due to their various advantages such as low running cost, clean, and rich characteristics [6, 7]. The huge development of RESs can be realized in Fig. 1a and b which describes the most recent indicators for both country and technology, respectively [8]. From Fig. 1a, energy generation from PV and wind technologies combined offer about 68% of the RESs. As China stays at the top of the PV market in the world, a significant reduction in new PV facility embellishments occurred in 2020 due to COVID-associated interruptions. RESs are expected to cover 99% of global demand growth by 2025 as shown in the last statistics offered by the IEA in Fig. 2 [7].

Although the wind and solar energies have fast growth, the randomness and intermittence make the system an excessive size when only one energy source is used [9]. Also, this randomness reduces the reliability of the standalone system since the generated energy is influenced by both solar irradiance and wind speed variabilities [10]. Moreover, RESs require a high cost of investment besides the large land area for construction. To overcome the problem of weather variability, energy storage systems (ESSs) are integrated with these sources to form hybrid renewable energy systems (HRESs). Although the use of ESS ensures a steady power supply for load leveling, they increase the total system cost and reduce the energy conversion efficiency [11, 12]. Also, to overcome the cost issue, optimal planning and capacities of systems’ components should be accomplished. Recently, HRESs are developed as a green and cost-effective solution for reliability, cost, land area issues, and techno-environmental challenges of conventional sources. The use of the HRESs in standalone or grid-connected applications has been addressed in many studies [15‐18]. The optimal capacity planning problem of HRES can be solved using different metaheuristic algorithms (MA) as reviewed in [19, 20], and [21] or via various commercial software tools such as Hybrid Optimization Model for Electric Renewables (HOMER) [22], Hybrid Optimization by Genetic Algorithms (iHOGA) [23], REopt [24], System Advisor Model (SAM) [25], PVWatts [26], and RETScreen [27].

Considering the scope of this paper, this survey focuses on studies that employed metaheuristic algorithms, commercial software, or both. Table 1 summarizes the different up-to-date studies that addressed the problem of HRES optimal planning. HOMER software has been widely used in countless research works employing different types of energy solutions for distinct kinds of load demand. For example, the floating PV units were utilized to feed a small electrical system in Bangladesh where the techno-enviro-economic investigations were discussed to present the mini-system profits [28]. In [29], the authors developed a systematic techno-enviro-economic design optimization for a PV, wind, diesel, and batteries energy production system using HOMER. The results revealed that the optimal solution has a TNPC of 351,223 $ and COE of 0.2262 $/kWh. In [30], HOMER was used to optimize the cost of 13 scenarios that consist of a hydrogen system, PV, wind, and grid. The authors in [31] used HOMER to investigate optimal solutions regarding the energy, economic, and environmental of an HRES connected with a desalination plant in the new capital airport in Egypt. In another study, the authors in [32] reported using the HOMER software to investigate the techno-economic sustainability of the HRESs using different elements such as PV, wind, pumped hydro storage, diesel, and batteries.

The MA have been broadly used in a wide range of applications in the electric power system; this is due to their various applicability merits [33, 34]. Nevertheless, the applications of the MA are not limited to the field of power systems. In [35], the cyclical parthenogenesis algorithm was employed for layout optimization of truss structures with frequency constraints. Also, the authors in [36] introduced plasma generation optimization as a new physically based metaheuristic algorithm for solving constrained optimization problems. In [37], the dolphin echolocation optimization algorithm was introduced to reduce the computational efforts and time which remain the main challenges that face the MA users. Another efficient metaheuristic optimization algorithm, namely colliding bodies optimization (CBO), was introduced in [38]. The presented algorithm developed straightforward formulation to discover minimum or maximum of functions and does not rely on any interior parameter. Besides, an enhanced version of the CBO algorithm was addressed in [39] for design problems with discrete and continuous variables as well as to escape from local optima dilemma. Likewise, another physically inspired non-gradient algorithm, namely water evaporation optimization (WEO), was developed for solution of global optimization problems to impersonator the evaporation of a small quantity of water particles on the solid exterior [40].

The HOMER and the MA were implemented in different articles to compare and assess their performances. In [41], the GWO was applied to achieve the optimal techno-economic PV/wind/battery system sizes for Ras Shaitan in Egypt. The obtained results achieved by GWO are compared with those of PSO, WHO, and GA. The study focused only on meeting the load requirements and minimizing the COE. In [42], fuzzy logic controller is used in the GSA to determine the effect of the batteries and diesel systems in the HRESs. In another relevant study [43], the economic and environmental aspects were compromised for hybrid PV/wind energy and batteries using the diesel generator as a spare source. The proposed method is achieved using GA and PSO, and the results are compared with HOMER. The optimal COE and CO₂, which GA and PSO accomplish, have the lowest values compared with that obtained using HOMER software. In [44], the authors proposed a method to optimize the PV, wind, and battery hybrid systems for a specific region in Manipur using a backtrack search algorithm. The obtained results are compared with HOMER by considering the number of wind turbines, PV units, batteries, cost, fluctuation rate, and LPSP. Meanwhile, the authors in [45] used demand–supply management with PSO to design the optimal off-grid system with PV, diesel generator, and battery to energize residential buildings. The results were compared with HOMER considering the economic, technical analyses, and sensitivity evaluation in terms of TNPC, COE, RF, and CO₂.

Recently, AVOA has been proposed and used to achieve different objectives such as tuning the gains, optimal reconfiguration, and optimal sizing [46‐48]. In [46], the AVOA is just proposed instead of the PSO to tune the gains of the proportional-integral (PI) controllers for extracting the maximum power from the PV and wind systems. Meanwhile, in [47], the AVOA is adopted in the PV system to overcome the partial shade condition (PSC) where this phenomenon has a negative effect on the PV array which increases the power loss, causes hot spots, and reduces the generated power. Further, in [48], the AVOA is presented to obtain the optimum configuration for a HRESs. The HRESs in this study consist of FC/wind/PV where the grid is the main factor in this investigation. The purpose of this study was to determine the optimal number of HRES components to achieve the lowest TNPC and LOPSP. Although the obtained results have been compared with other MAs, they have not been compared with any commercial software such as HOMER. In addition, the results are used for supplying a building in Ahvaz, Iran, although the main factor was the grid. In [49], an evaluation of PV/WT hybrid renewable energy system forecasting and sizing techniques has been presented.

To the best author's knowledge, the proposed AVOA has not been employed before in the optimal sizing of the ISOLATED SYSTEM, which is based on a PV/wind/battery/diesel energy system; different attempts have already been accomplished using distinct MA or commercial software (see Table 1). Besides, most existing studies focus only on economic, technical, or environmental objectives or a combination of them, ignoring reliability and emission penalty constraints, except [51]. In addition, there is a lack of depth analysis for both MA and commercial software in depth. Driven from the research gaps, the key contributions of the study can be summarized as follows:

Besides the introduction described in Sect. 1, the mathematical models of the proposed HRES components are presented in Sect. 2. The problem formulation and the employed AVOA-based metaheuristic optimization are discussed in Sects. 3 and 4. The obtained simulation and optimization results considering the adopted case study data used are discussed and analyzed in Sects. 5 and 6. Finally, the most important conclusions are summarized in Sect. 7.

The objective function for the optimal design of the HRES is formulated to minimize the TNPC in $ and penalty cost associated with the carbon emission (PnCE) in $, subject to maintaining various constraints. The summation of the two terms represents the overall cost incurred by the HRES throughout its lifetime period. The objective function for the optimal design of the HRES is formulated to minimize the TNPC and penalty cost associated with the carbon emission subject to various constraints. The objective function (ObjFn) principally hinges on four numeral decision parameters (i.e., number of PV panels (N_PV), wind turbines (N_WT), diesel generators (N_DslG), and batteries (N_BESS). The optimization formula is described in Eq. (17).

This approach is one of the metaheuristics that can solve various optimization problems. It has been inspired by the lifestyle of African vultures [63]. These vultures are considered environmentally beneficial animals that can prevent the carcass from stretching and infecting. Also, they play an important extra-terrestrial role, and their destruction poses several serious risks to human health. They are distributed around the world except in Australia and Antarctica. In recent years, their population has started to decline, and they are more popular in African countries and follow the same lifestyle to find food and sometimes fight each other for food [64]. The African vultures can be split into three categories [65]. The first category includes the vultures, such as the front-footed vulture, which are more likely to be preyed upon than others due to their healthy physical condition. The second category includes vultures that are physically weaker than the first type, such as white-backed African gyps. The last category includes vultures that are physically weaker than the other two categories, such as the Necrosyrtes monachus hooded vulture. The AVOA follows the behavior of the African vulture during the foraging and navigation behavior to find the optimal solution to a problem. The following subsections will present the steps in the AVOA optimization approach and how AVOA can be used to solve the design challenges of the HRESs in the city of Marsa Matruh.

The complete pseudocode of the AVOA is described in Algorithm 1. It is assumed that N vultures, representing the initial population of a problem, live in a particular environment. Vultures are physically divided into two groups in their natural environment. The first group was designed to compute the fitness function (i.e., objective function) for the entire original population and select the best positions for the first and second vultures. In contrast, the other group forms a population to shift or replace the best two vultures in each presentation. The AVOA optimization algorithm consists of four steps to find the optimal solution to a problem.

This part describes integrating the AVOA algorithm to determine the optimal solution to the current optimization problem. The AVOA is a new metaheuristic optimization algorithm motivated by the African vultures' social behavior, as mentioned earlier. The advantages of AVOA are as follows: easy to implement due to its simple structure, less storage and computational requirements, faster convergence due to continuous reduction of search space; its ability to avoid local minima; and having the ability to find the optimal solutions for problems with nonlinear relationships between its variables, hence better stability, and robustness.

The overall result of this optimization problem is to determine the optimal capacity planning for the city of Marsa Matruh operating in an isolation mode, given the constraints and minimal costs throughout the project lifecycle. An energy management strategy (EMS) is required to coordinate the flow of power between different distributed generations in the system. The proposed EMS is designed according to a cyclic charging strategy as shown in Fig. 6. In this strategy, renewable energy is fully utilized, where it always operates at the maximum power point under current climate conditions. It has a rule-based algorithm in the form of “if” and “then” implementation. Also, the diesel generator has two switched-on or switched-off positions. In this way, when the diesel is running (i.e., switched on), it produces its rated power according to the capacity obtained from the AVOA algorithm. The dummy load is used to absorb the surplus power in the system when charging the BESS to its maximum allowable capacity. The EMS algorithm starts by calculating the annual available power from the PV and WT based on the given mission profile at the DC bus. Then, the remaining power (ΔP), in the microgrid, can be calculated by subtracting the load, PV, and WT powers at the AC bus to check if the system needs additional power or if there is already surplus power in the system. In the case of ΔP > 0 (that is, extra power is needed), the diesel must operate at its rated capacity to meet the load requirements. At low RESs power and high loading demand, the design maybe not be sufficient to cover all the remaining load demands, which the available power of the BESS should cover. Furthermore, there could be a load shedding condition, in which the battery cannot deliver at minimum capacity due to lifetime consideration. In such a case, the HLPS should be computed, and it will be greater than zero.

The complete flow diagram clearly illustrating the proposed AVOA for the optimization problem under study is shown in Fig. 7. It starts by loading the input data, such as meteorological data (solar irradiance, ambient temperature, and wind speed) related to the location of the current study. Then, the load demand profile over the year, the technical and economic factors of the HRES components, and the desired limits are also loaded as specified in Sect. 2. The next step is to define the parameters associated with the optimization algorithms, as given in Table 2. The dimension of the current optimization problem consists of four variables: N_PV, N_WT, N_DslG, and N_BESS. Finally, the search space of the components’ capacity can be listed in Eq. (37).

Then, like any metaheuristic approach, a random population set is generated within the search space limit of each dimension. Then, the fitness function is evaluated for each possible candidate in this list to determine the best first and second positions of the vultures. The fitness function will include initial, maintenance, replacement, and salvage costs. Also, to act against climate change, we have included, within the fitness function, the penalty due to carbon emission. To check the feasibility of the proposed optimization method in solving this HRES capacity planning, we have compared it with up-to-date optimization approaches for this type of problem. The comparison algorithms include the GOA [67] and GPC [68]. Their parameters are given in Table 2.

The metaheuristic optimization algorithms are independently executed around 20 times to extract the statistics results, as summarized in Table 4. Therefore, it is obvious that the proposed AVOA for optimal HRES design provides the best values compared to GOA and GPC.

The convergence curves of the three adopted algorithms, including the proposed AVOA, GOA, and GPC, are shown in Fig. 10. It can be recognized that the proposed AVOA has a better convergence rate (i.e., the lowest value of the objective function) and statistical measures compared with the GOA and GPC approaches. The algorithms started with initial estimations and remained until the termination condition was fulfilled. Table 5 describes the optimal results of the three metaheuristics optimization algorithms and the HOMER optimizer with their relative ObjFn and execution time. It can be distinguished that the AVOA takes less time than other approaches and attains superior economic results at minimum lifecycle cost (346,614 $) and energy price (0.0947 $/kWh). The AVOA reached the optimal solution at the 17th iteration, while the GOA and GPC algorithms found the optimal solution at the 38th and 80th iteration, respectively. The GPC algorithm appears in the second rank, followed by GOA concerning ObjFn, despite taking a longer execution time than the GOA.

Meanwhile, the three optimization algorithms show better financial performance than the HOMER, which gives the highest ObjFn among all methods. For further explanation, Fig. 11 displays the optimal capacities of the different components obtained by the different metaheuristics optimization algorithms and the HOMER software. It can be noticed that the three metaheuristic algorithms did not consider employing WTs in the optimal solution, contrary to the HOMER, which considered 6 × 2.6 kW WTs. Also, HOMER requires the highest number of batteries (104 units), and thus, the ObjFn resulting from the HOMER will be higher than the other optimization algorithms. Besides, the GOA ranked third due to the high rating required for the PV units (62 kW) and 87 batteries compared to the other metaheuristic algorithms.

The detailed economic analysis of the metaheuristic algorithms and HOMER is summarized in Table 6 and portrayed in Fig. 12 for further demonstration. It can be seen that the proposed AVOA has the best optimal cost distribution among all optimizers with the lowest TNPC and LCOE of 346,614 $ and 0.0947 $/kWh, respectively. The initial cost of the AVOA optimal configuration is fewer than that of HOMER at 40.5%. Besides, the TNPC using the AVOA is reduced by 6.5% compared to HOMER. The optimal configuration suggested by HOMER has an LCOE of 0.239 $/kWh, while that suggested by the AVOA is 0.0947 $/kWh, recording a 60.3% reduction. Besides, the suggested LCOE by both the GOA and GPC algorithms is almost the same. It can be distinguished from the obtained results that the AVOA is more efficient than the HOMER and both the GOA and the GPC algorithms. It is worth mentioning that besides the results convergence of the metaheuristic algorithms with HOMER, the former is further accommodating in control preferences and model advancements. The cost summary of each component in the optimal configuration is also generated from the different optimizers, as summarized in Table 7. It should be noticed that there are no data generated from the metaheuristic algorithms regarding the WT cost since the optimal solution with each algorithm was reached at zero number of WTs. In contrast, the use of HOMER has resulted in six turbines in the optimal solution (see Table 5).

The average monthly energy production from the optimized HRES configuration with both the AVOA and HOMER is displayed in Fig. 13. The optimal capacity planning achieved with the AVOA promotes 37.5 and 62.5% energy share from the PV and the DslG, respectively. Meanwhile, the contributions of the PV units, WTs, and DslG in the case of HOMER are 40.1, 25.7, and 34.1% of the total energy produced. As anticipated, it is indicated that the energy production curves for solar and wind generation match the wind speed and solar irradiance profiles in the investigated locality. The figure also reveals that the load demand is efficiently fulfilled using both optimization methods, and the surplus energy is transferred to the batteries.

Moreover, Fig. 14a demonstrates the hourly profile of energy share of the optimal system components and batteries SOC during a year. From Fig. 14a and aided with Fig. 13a, it can be seen that the optimal system candidates by the AVOA share the produced power between the PV system (high share in summertime) and the diesel generator (higher share in wintertime). Besides, samples of two consecutive days during the wintertime and the summertime are indicated in Fig. 14b and c, respectively, from which the energy management and power flow within the optimal system can be verified. Similarly, the hourly profile of energy share using HOMER Pro is indicated in Fig. 15. With a closer view of the yearly profile in Fig. 15a, the SOC of the battery does not have a full charge state which discovers that occasionally the extra power does not transfer to the batteries. The main reason behind this is the kinetic model of batteries utilized by HOMER that relies on the charging/discharging record of the batteries.

Furthermore, the reliability and renewable penetration of the optimal HRES were assessed using three major parameters by the different optimizers: the loss of power supply possibility, the renewable fraction, and the unmet load ratio. Figure 16 shows the results of the different optimizers regarding the discussed parameters. It can be recognized that the three metaheuristic algorithms efficiently served the load demand with zero unmet load ratio, while for HOMER, there is a small portion of the load demand still unserved (0.0669%). Because the optimization problem is constrained by a zero-capacity shortage or a zero LPSP, the different optimizers successfully maintained the reliability limits by 0.0067, 0.0002, 0, and 0.0978% for the AVOA, GOA, GPC, and HOMER, respectively. Since the optimal HRES was attained at the highest PV capacity share, the GAO algorithm has the highest renewable fraction ratio (59.6%) among all optimization approaches. A similar value (59.3%) was reached in the case of HOMER owing to the integration of both PV units and WTs in the derived optimal HRES configuration (see Fig. 13). The AVOA and GPC methods have nearly renewable fractions of 40.38 and 44.23%, respectively, due to the conjunction of the PV rating in both methods.

The impact on the environment is also assessed based on the amount of produced CO₂ by the optimal HRES configuration with each solution approach. Table 8 indicates the diesel generator and corresponding CO₂ emission data. The annual amount of CO₂ obtained using the AVOA is estimated at 79,089.1 kg, almost the same resulting from the GPC algorithm. Besides, the amount of CO₂ estimated by HOMER is the lowest at 47,778 kg/year since the projected diesel has the lowest fuel rate consumption with 18,251 L every year.