Techno-Economic Analysis and Optimization of Hybrid Renewable Energy System with Energy Storage under Two Operational Modes

Abstract

Access to cheap, clean energy has a significant impact on a country’s ability to develop sustainably. Fossil fuels have a major impact on global warming and are currently becoming less and less profitable when used to generate power. In order to replace the diesel generators that are connected to the university of Debre Markos’ electrical distribution network with hybrid renewable energy sources, this study presents optimization and techno-economic feasibility analyses of proposed hybrid renewable systems and their overall cost impact in stand-alone and grid-connected modes of operation. Metaheuristic optimization techniques such as enhanced whale optimization algorithm (EWOA), whale optimization algorithm (WOA), and African vultures’ optimization algorithm (AVOA) are used for the optimal sizing of the hybrid renewable energy sources according to financial and reliability evaluation parameters. After developing a MATLAB program to size hybrid systems, the total current cost (TCC) was calculated using the aforementioned metaheuristic optimization techniques (i.e., EWOA, WOA, and AVOA). In the grid-connected mode of operation, the TCC was 4.507 × 10⁶ EUR, 4.515 × 10⁶ EUR, and 4.538 × 10⁶ EUR, respectively, whereas in stand-alone mode, the TCC was 4.817 × 10⁶ EUR, 4.868 × 10⁶ EUR, and 4.885 × 10⁶ EUR, respectively. In the grid-connected mode of operation, EWOA outcomes lowered the TCC by 0.18% using WOA and 0.69% using AVOA, and by 1.05% using WOA and 1.39% using AVOA in stand-alone operational mode. In addition, when compared with different financial evaluation parameters such as net present cost (NPC) (EUR), cost of energy (COE) (EUR/kWh), and levelized cost of energy (LCOE) (EUR/kWh), and reliability parameters such as expected energy not supplied (EENS), loss of power supply probability (LPSP), reliability index (IR), loss of load probability (LOLP), and loss of load expectation (LOLE), EWOA efficiently reduced the overall current cost while fulfilling the constraints imposed by the objective function. According to the result comparison, EWOA outperformed the competition in terms of total current costs with reliability improvements.

1. Introduction

Due to the global energy crisis and the environment’s quickening decline, it is urgently necessary to develop renewable energies like solar and wind. Although renewable energy sources have many advantages, including being sustainable and environmentally friendly, their unpredictable and intermittent nature makes them unsuitable for power generation. The global acceptance of clean energy is rising. Long-term development, energy security, and environmental preservation frequently require technologies for renewable energy [1]. Fortunately, the complementary nature of solar and wind in different seasons and at different times of day allows for their combination, or a hybrid renewable energy system, to be able to lessen the effects of uncertainties and provide a more dependable source of power [2,3]. Wind and solar energy are particularly viable options for reducing carbon emissions and making the world safer and cleaner [4,5,6]. Renewable energy resources in Ethiopia, including solar [7,8,9], biomass [10,11], wind [12,13,14], and hybrid renewable energy sources [15,16], have recently undergone assessments in order to develop cleaner power generation and contribute to the energy security of this developing country in East Africa.

The era of distributed generation and hybrid renewable energy sources (HRES) is beginning to take hold in the energy sector [17]. By 2040, global energy consumption is expected to have increased by about 30.1% compared to 2015 levels [18]. Approximately 75% of the electricity in the world is produced using conventional energy sources like fossil fuels [19,20]. The best way to reduce the use of fossil fuels is widely acknowledged to be through energy efficiency and renewable energy sources [21,22]. The most popular energy sources that are integrated into the primary grid as distributed generators are solar PV cells and wind turbines [23,24,25,26,27]. Both stand-alone and interconnected modes of operation for HRES with the electrical grid are possible. HRES connect to the electric distribution networks when they are in the grid-connected mode and exchange energy using a bidirectional smart metering system [28,29,30]. Stand-alone power plants and generators are those that are run independently of regional and centralized electricity grids [31,32,33]. Due to the depletion of conventional energy sources (such as fossil fuels), as well as, specifically, environmental and economic challenges, researchers and energy planners are concentrating more and more on renewable energy resources [34,35,36]. Additionally, the load on transmission networks is unpredictably growing as the demand for electricity rises. Because building out transmission networks presents challenges from an economic standpoint, HRES have been seen as economically feasible choices [37,38].

Increasing energy reliability and efficiency is more crucial than ever in the current world, where electricity consumption is continually rising [39]. Numerous problems with current power systems are resolved by integrating HRES in various distributed generation units throughout the electrical network [40,41,42,43]. Many technological barriers must be overcome in order to successfully implement distributed generation, so that all of the benefits of distributed generation can be used and the current standards for reliability are not improved [44]. It is crucial to have a thorough understanding of study area viability, financial optimality, financial comparisons, and renewable potential before successfully implementing distributed generation. When using HRES in stand-alone and utility grid-connected modes, there are multiple advantages for the environment, performance, power quality, investment, marketing, and cost savings [45,46]. Network congestion and the requirement for bulk transmission systems can both be significantly reduced by enhancing the power quality and dependability of power suppliers. The proposed HRES work with both stand-alone and utility grid-connected modes of operation.

Numerous studies on maximizing the costs of renewable energy have been conducted. Researchers have previously studied subjects like HRES control trends [47], HRES control strategies in stand-alone systems [48,49,50], regulation methods of distributed generation [51], HRES current and voltage regulation techniques [52], and enhancements of HRES implementation during stand-alone mode with energy storage system. These studies have focused on HRES control strategies, increasing storage capacity, regulating current and voltage, and controlling distributed generation parameters. The complex cost analysis of stand-alone and grid-connected operational modes for HRES aims to address disparities and equity-related constraints, while lowering HRES production costs and carbon emission costs. With the development of renewable energy technology, stand-alone power generation has become a more cost-effective way to meet remote rural (which is very far from the national grid) needs without utilizing conventional resources [53]. The development of any nation’s economy could be impacted by renewable energy technology. Additionally, the importance of renewable resources has increased due to the rise in fuel prices and the issues brought on by the energy crises in developing countries.

The feasibility of various HRES options [54], as well as photovoltaic and biogas techno-economic analysis [55,56], are the topics of additional studies on techno-economic design that have been completed recently. The majority of these studies have been designed to work with HRES in both grid-connected and stand-alone modes of operation. Different financial and reliability evaluation parameters were taken into account for comparison. To enhance the reliability of the connected loads, energy storage systems are integrated into HRES systems. Renewable energy sources, however, have a number of disadvantages, one of which is that they are sporadic [57,58]. The production of solar and wind energy is also impacted by geographic factors and seasonal climate [59,60]. Hybrid renewable energy systems (HRES) have been developed to increase efficiency [61,62]. These systems have a number of benefits, including lower capital costs, increased power generation capacity, improved dependability and overall efficiency, and more design optimization flexibility. The unpredictability of renewable energy sources and the mismatch between supply and demand also have an effect on the stability of the power generation system. Energy storage systems (ESS) may be able to assist in finding solutions to these problems [63,64].

According to different systematic analyses of the economics of independent hybrid energy systems using various energy storage technologies [65,66,67], hydro-pumped storage has a significantly lower cost than conventional storage systems including battery storage banks and others [68,69,70]. A solar PV/pumped storage system’s modelling, size optimization, and economic analysis have also been studied in [71,72,73].

The optimum parameter sizing for a hybrid stand-alone microgrid has been the subject of numerous studies. Optimal sizing optimization for a hybrid PV/biomass with biogas and hydrogen blend system was investigated in [74]. In [75], the authors looked into the best way to size the parts of a hybrid solar PV/biogas energy storage system with PHES when it works on its own. The best size for a stand-alone microgrid that uses only renewable energy and energy storage systems is presented in [76,77]. In addition, grid-connected hybrid-only renewable energy sources with energy storage optimal sizing optimizations are investigated in [78,79,80].

The use of metaheuristic algorithms for hybrid microgrid optimal sizing has been very common because of their simple implementation, lack of dependence on gradient calculations, and capacity to escape from local optimal points [81,82,83]. These algorithms can successfully deal with the complexity and nonlinearity of optimization models. By handling non-convex optimization problems and having the potential to find and reach global optima, which is unusual when using traditional techniques, metaheuristic methods have an edge over traditional optimization techniques. According to the literature, many metaheuristic algorithms have been used, including the whale optimization algorithm (WOA) [84], genetic algorithm (NSGA-II) [85], particle swarm optimization (PSO) [86], teaching–learning-based optimization (TLBO) [87], chameleon swarm algorithm (CSA) [88], grey wolf optimization (GWO) [89], and seagull optimization algorithm (SOA) [90]. However, only one metaheuristic approach was used in those studies for the best sizing because metaheuristic approaches are stochastic, which is essential to assess and contrast how well these approaches perform in terms of optimal sizing.

Access to affordable, clean energy has a significant impact on a country’s ability to develop sustainably in the energy sector. The profitability of using fossil fuels to produce electricity is currently declining, and they have a significant impact on global warming. In order to switch out the diesel generators that are connected to the electrical grid of the university of Debre Markos with hybrid renewable energy sources, this study examines the financial implications of proposed hybrid renewable systems in stand-alone and grid-connected modes of operation, as well as their optimization and techno-economic feasibility. For the best sizing of the hybrid renewable energy sources in accordance with financial and reliability evaluation parameters, metaheuristic optimization techniques like the enhanced whale optimization algorithm (EWOA), whale optimization algorithm (WOA), and African vultures’ optimization algorithm (AVOA) are used. Three metaheuristic optimization techniques—the EWOA as the primary technique, and the WOA and AVOA as a comparison—were used to resolve the optimization problem, which had as its objective function minimizing the overall cost of the various components of renewable energy sources (RES). These three algorithms have already demonstrated their capability to solve challenging optimization issues. The best solutions were selected by comparing the results of the three algorithms, taking into account various constraints and a single objective function. Numerous study analyses have been developed and evaluated in order to decide how HRES, which is constructed close to the national grid power supply system, should operate.

After carefully looking at the above research works, this paper elaborates more about the following items that previous approaches did not cover:

✓

The best way to estimate a hybrid solar PV–biogas with SMES–PHES system is to use the lowest NPC possible while sticking to the assigned choice of the individual system’s upper and lower limit inequality constraints and cost comparisons for the system’s mode of operation.

✓

In grid-connected mode, figure out the costs of HRES energy exchange (excess to and deficit from the grid), and in stand-alone mode, figure out the costs of the variable dump load’s use of excess energy.

✓

The adopted EWOA technique, which was compared to WOA and AVOA for the optimal sizing of solar PV–biogas with SMES–PHES systems, has flaws that can be fixed in different operational modes.

The study’s objectives were to identify the cost-effectiveness of HRES in stand-alone and grid-connected modes of operation, as well as the optimal size of a hybrid PV–biogas with SMES–PHES system in order to decrease the nation’s high fuel costs, preserve the environment, and reduce the consumption of diesel generator fuel. To determine the optimal size for the suggested system while minimizing the total cost of the objective function, metaheuristic optimization methods including EWOA, WOA, and AVOA were applied.

The following is a statement of this work’s primary contribution:

✓

Minimizing the total cost through objective function optimization was conducted to assess the revenues of the operational modes of a HRES system in grid-connected and stand-alone configurations.

✓

To develop a mathematical model of HRES that shows how a system made up of solar PV, a biogas generator, a superconducting magnetic and a pumped hydro energy storage system works, whether it is connected to the grid or in stand-alone mode.

✓

To effectively and articulately minimize the total cost of the HRES system, EWOA was adopted as the main optimization technique, and WOA and AVOA were used for comparison, which suggests a workable approach based on the MATLAB program.

✓

Investigating and evaluating different evaluation parameters, such as financial and reliability evaluations, in a stand-alone and grid-connected mode of operation.

The remaining sections of the paper are structured as follows: The methodology is discussed in Section 2, optimization evaluation parameters like financial and reliability are discussed in Section 3, proposed problem formulations such as objective function and constraints are discussed in Section 4, proposed metaheuristic techniques are discussed in Section 5, result and discussions are discussed in Section 6, and, finally, conclusions are described in Section 7.

2. Methodology

The Meteorological Agency, which is in charge of rural electrification, started collecting data with secondary and primary sources because it has a wide range of information for numerous communities across the nation and intends to provide those communities with clean and affordable energy in the future. Resource information from the community was added to these data. The availability of solar, biomass, and water resources for the community’s energy generation was covered by the data collection. The following factors are taken into account when gathering data for the community: the current rate of energy access in the community, the current energy demand, the types of energy currently being used, the sources of energy supply at the moment, and the available renewable energy resources. A hybrid solar PV–biogas system with SMES–PHES was designed, simulated, and optimized using metaheuristic optimization techniques like EWOA, WOA, and AVOA in both a stand-alone and grid-connected mode of operation. Figure 1 shows Debre Markos University’s power distribution system’s hourly load profile.

As shown in Figure 2 the minimum, average, and maximum average monthly solar radiation and temperature data are 5.2, 6.4, and 7.1 kWh/m² and 16.2, 18.9, and 21.5 °C, respectively.

2.1. Schematic Layout of Proposed HRES System

Figure 3 and Figure 4 depicts the schematic diagram of the proposed hybrid power systems, mainly a solar PV–biogas system with an SMES–PHES system. The hybrid system consists of lower and upper reservoirs, a PV power plant, a biogas power plant, an SMES, a PHES, an inverter device, and variable dump loads. The operation of this system in stand-alone and grid-connected modes will be studied.

In Figure 3, the hybrid system is connected to the grid because it consumes any excess energy that is provided to the grid. In contrast, in Figure 4, the hybrid system is connected to a dump load system, which uses any extra energy that is not needed.

2.2. Mathematical Modeling of Each HRES Units

A brief overview of all mathematical models for the proposed hybrid system’s components is provided in the following sections.

2.2.1. Modeling of Solar PV Units

The following is how multiple PV cells are connected in series to produce electrical power [91,92]:

$$P_{PV}\left(t\right)=N_{PV}\times A_{PV}\times {\eta }_{PV}\times G\left(t\right)$$

(1)

where N_PV stands for the number of photovoltaic modules, A_PV for the area of the PV module, and η_PV for the efficiency of the PV system, while G(t) denotes the intensity of the ambient solar irradiation.

The following formula can be used to determine the PV system’s efficiency [93]:

$${\eta }_{PV}\left(t\right)={\eta }_r\times {\eta }_t\times \left[1-{\beta }_T\times \left(T_c\left(t\right)-25\right)-{\beta }_T\times G\left(t\right)\times \left(\frac{T_{nom}-20}{800}\right)\times \left(1-{\eta }_r\times {\eta }_t\right)\right]$$

(2)

where the terms η_r and η_t stand for the reference efficiency and the maximum power point tracking (MPPT) system’s efficiency, respectively. The temperature coefficient is denoted by β_T. The temperatures displayed by T_c and T_nom are the actual operating cell temperature and the current cell temperature, respectively.

2.2.2. Modeling of Biogas Generator Unit

Geographically, biogas is Ethiopia’s most important source of electricity, but it has not yet been fully utilized. However, Ethiopia’s energy industry has not yet adopted a specific strategy for producing electricity from biogas. Ethiopia’s capital city, Addis Ababa, established the first biogas plant to remove waste [94]. The amount of waste required for each bio-generator is calculated using the volume of biogas produced from 1 kg of cow dung and 1 kg of poultry waste, respectively, and the volume of biogas required to generate 1 kW of electricity [95]. Equation (3) can be used to figure out how much power the biogas generators are generating [96,97].

$$P_B\left(t\right)=\frac{B\times C_{VB}\times {\eta }_B}{3600}$$

(3)

where B stands for the amount of biogas, C_VB stands for the calorific value of biogas (kJ/kg), and η_B stands for the generator’s efficiency in producing biogas.

2.2.3. Modeling of SMES Unit

SMES technology enhances power quality and is applicable to uninterruptible power supplies. Due to the adaptable qualities it offers in exchanging real and reactive power, it has become popular for HRES applications [98,99]. In order to make this storage device very appealing to consumers, current studies on SMES devices are based on lowering the cost of coils and cooling systems. Additionally, a hybrid SMES system could be created to expand storage [100]. For SMES devices, the stored energy and power generated are most times specified and can be calculated in Equations (4) and (5) as follows [101]:

$$E=\frac{1}{2}{L}_{SMES}{I}_{coil}^2$$

(4)

$$P=\frac{dE}{dt}=L_{SMES}{I}_{SMES}\frac{d{I}_{SMES}}{dt}=V{I}_{SMES}$$

(5)

The SMES has three modes of operation, namely charging, discharging, and standby modes of operation. In this case, the standby mode of operation (ready to supply) is not considered for modeling SMES, as explained below.

• When the hybrid system power exceeds the demand, the charging mode can operate.

$$P_{exch}\left(t\right)=\max \left\{-\left|\Delta P\left(t\right)\right|,\frac{\left((E_{exch}\left(t-1\right)-E_{exch-\max }\left(t\right)\right)}{\Delta t\times {\eta }_{ch}},-P_{exch-rated}\right\}$$

(6)

$$E_{exch}\left(t\right)=\min \left\{\left(E_{exch}\left(t-1\right)-P_{exch-ch}\left(t\right)\times \Delta t\times {\eta }_{ch}\right),E_{exch-\max }\right\}$$

(7)

• When the load demand is greater than hybrid power, then the charging mode can operate.

$$P_{exch}\left(t\right)=\max \left\{\left|\Delta P\left(t\right)\right|,\frac{\left((E_{exch}\left(t-1\right)-E_{exch-\min }\left(t\right)\right)\times {\eta }_{dis}}{\Delta t},P_{exch-rated}\right\}$$

(8)

$$E_{exch}\left(t\right)=\max \left\{\left(E_{exch}\left(t-1\right)-\frac{P_{exch,dis}\times \Delta t}{{\eta }_{dis}}\right),E_{exch-\min }\right\}$$

(9)

where P_exch is the SMES’s exchanged power at period t, which, during the charging, discharging, and idle modes of the SMES system, respectively, has a negative, positive, and equal to zero value. Additionally, η_cha and η_dis stand for the respective charging and discharging efficiencies. ∆P(t) represents the difference between the output of a hybrid power system and the load demand. E_exch-min and E_exch-max denote the SMES system’s minimum and maximum energy storage capacity limits, P_exch-rated denotes the SMES power rating, E_exch denotes the SMES capacity at period t, and ∆t denotes the time interval. For each SMES serving various load models, the initial value of the state of charge (SOC_initial), which is an index of the state of charge (SOC) energy stored within it, must be improved [102,103,104].

2.2.4. Modeling of PHES Unit

The volume of the upper reservoir and the height difference between the upper and lower reservoirs were found to be the two variables that have been shown in the literature to have the greatest impact on the design of pumped systems [105,106]. The lower reservoir, the penstock’s design, and the choice of pumps and turbines are additional design considerations [107]. PHES has two modes of operation, generating and pumping, which are explained in Equations (10)–(13) as follows:

• When solar PV cannot power the connected load, the output of the turbine generator unit can be used to make electricity. The generation mode can be expressed as:

$$P_{PHES-T}\left(t\right)=C_T\times q_T\left(t\right)$$

(10)

$$C_T={\eta }_T\times \rho \times g\times h$$

(11)

where q_T(t) is the volumetric flow rate of water going into the turbine, ρ is the specific density of water (1000 kg/m³), g is gravitational acceleration (9.81 m²/s), h is total dynamic height, η_T is the overall efficiency of the turbine generator unit, and C_T is the turbine generating coefficient.

The numerical values of the specific density of water (ρ) and Earth’s gravitational acceleration (g) are 1000 kg/m³ and 9.81 m²/s, respectively.

• The pumping station in this study consists of a number of parallel-operating variable-speed pumps. When the connected load is less than the solar PV power generated, the pumps only run when the solar power available is greater than the rated power. The pumping mode can be expressed as:

$$q_{PHES-P}\left(t\right)=C_P\times P_{P{V}_P}\left(t\right)$$

(12)

$$C_P=\frac{{\eta }_P}{\rho \times g\times h}$$

(13)

where P_PV is the input power to the solar pumps, C_P is the water pumping efficiency of the pump motor unit, and η_P is the overall pumping efficiency.

2.2.5. Modeling of Inverter

The alternating current voltage is delivered to customers using an electronic device called a DC/AC inverter [108]. When the inverter model is used, the load/AC bus can obtain the following amount of output power:

$$P_{inv-AC}\left(t\right)=\left(P_{SMES-inv}+P_{PV-inv}\right)\times {\eta }_{inv}$$

(14)

where P_inv-AC is the amount of AC power that the solar PV and SMES send to consumers and η_inv is a measure of how well the inverter works. In this work, η_inv is assumed 90% [109].

2.3. Proposed HRES Operating Strategy Flow Charts

Figure 5 and Figure 6 depict a flowchart outlining how the suggested stand-alone and grid-connected hybrid solar PV–biogas system with an SMES–PHES system operates.

The operation of a structural feature is covered in this section in order to minimize repetition and paper length. Based on the following operational scenarios, the proposed stand-alone and grid-connected hybrid solar PV–biogas with SMES–PHES power system is briefly introduced. According to Figure 5 and Figure 6, the flowchart’s operational scenarios are generalized as follows:

• In stand-alone and grid-connected operation modes, the electrical load is covered by renewable generation (solar PV) without the requirement for any power from the biogas, SMES, PHES, or national grid supply systems when the power supplied by photovoltaic energy resources, P_PV(t), equals the demand load, P_L(t).
• The water pump uses the difference to pump water into the upper reservoir and charge the SMES when the electrical energy provided by the RES is greater than the load, as shown by the equation Ppv (t) > PL (t). When the difference is greater than the capacity of those energy storage systems, the excess electrical energy is fed to the national grid in the grid-connected mode and to the variable dump load in the stand-alone mode of operation.
• The PHES system fills the gap in consumption when the load power is greater than the renewable energy-generated power, Ppv(t) > PL(t). Because of its quick response, SMES is recommended for the transition period from Ppv(t) to PHES.
• When the gap between generation and load exceeds the combined output power of Ppv(t) and PHES, the biogas generator can be used to fill the power gap. In the grid-connected mode of operation, when all hybrid energy generation is less than the connected load, the utility grid fills the gaps, but this does not happen in the stand-alone mode.

3. Optimization Evaluation Parameters

To ensure the excellent design of the HRES system, the three main evolution parameters—financial, reliability, and greenhouse gas emission—should be minimized. However, in this study, the reliability parameters and the financial parameters have been given more weight, and those are the two that will be discussed.

3.1. Financial Parameters

Evaluations of financial parameters begin with the system’s total annual cost (C_an−tot) of investment. Individuals can express C_an−tot using the following formula [111]:

$$C_{an-tot}=C_{an-cap}+C_{an-rep}+C_{an-O\&M}$$

(15)

The capital recovery factor (CRF) is used to turn the initial investment into annual capital costs. It is based on the following equation [110]:

$$CRF\left(r,M_{sys}\right)=\frac{r\times {\left(1+r\right)}^{M_{sys}}}{{\left(1+r\right)}^{M_{sys}}-1}$$

(16)

The following formulas are used to figure out the annual cost of capital for each subsystem:

$$\left.\begin{array}{l}{C}_{an-cap-PV}=C_{cap-PV}\times CRF\left(r,M_{PV}\right)\\ C_{an-cap-B}=C_{cap-B}\times CRF\left(r,M_B\right)\\ C_{an-cap-SMES}=C_{cap-SMES}\times CRF\left(r,M_{SMES}\right)\\ C_{an-cap-PHES}=C_{cap-PHES}\times CRF\left(r,M_{PHES}\right)\\ C_{an-cap-inv}=C_{cap-inv}\times CRF\left(r,M_{inv}\right)\end{array}\right\}$$

(17)

As a result, the hybrid system’s annual capital investment cost is calculated as follows:

$$C_{an-cap}=C_{an-cap-PV}+C_{an-cap-B}+C_{an-cap-SMES}+C_{an-cap-PHES}+C_{an-cap-inv}$$

(18)

The proposed scheme’s estimated operation and maintenance costs take the following form:

$$C_{O\&M}=C_{O\&M-PV}\times T_{PV}+C_{O\&M-B}\times T_B+C_{O\&M-SMES}\times T_{SMES}+C_{O\&M-PHES}\times T_{PHES}+C_{O\&M-inv}\times T_{inv}$$

(19)

The following formula calculates the lifetime cost of component replacement for a hybrid system [112].

$$C_{rep}={\displaystyle \sum _{j=}^{n_{rep}}{K}_{C_{rep}}\times C_u{\left(\frac{1+i}{1+r}\right)}^{\raisebox{1ex}{$j{M}_{sys}$}\!\left/ \!\raisebox{-1ex}{$\left(n_{rep}+1\right)$}\right.}}$$

(20)

The grid-connected mode is the only one taken into consideration when calculating the cost of energy exchange with the utility grid. When there is a shortage of energy, the cost of power purchased from the grid (C_GP) and the cost of power supplied to the grid (C_GS), which occurs when generation outpaces load demand, are determined by [113]:

$$C_{GP}=N_{GP}\times C_P$$

(21)

$$C_{GS}=N_{GS}\times C_S$$

(22)

Based on the estimated investment cost, the annual cost of the hybrid renewable system is calculated. This cost can be expressed as follows:

$$C_{an-tot}=C_{an-cap}+C_{an-rep}+C_{an-O\&M}+C_{GP}-C_{GS}$$

(23)

The current cost values of each component over the course of the project are the total current cost (TCC) of the system. This includes the component values for Ccap, Crep, and CO&M for the stand-alone mode and includes CGP and CGS for the grid-connected mode of operation while accounting for the time value of money. TCC can be calculated utilizing [114]:

$$TCC=\frac{C_{an-tot}(€/year)}{CRF\left(r,M_{sys}\right)}$$

(24)

The following equation represents the cost of energy (COE) from the hybrid system in terms of EUR/kWh:

$$COE=\frac{C_{an-tot}(€/year)}{{\displaystyle \sum _{t=1}^{8760}{P}_L}}=\frac{TCC(€/year)}{{\displaystyle \sum _{t=1}^{8760}{P}_L}}\times CRF\left(r,M_{sys}\right)$$

(25)

The ratio of the annualized total cost of the hybrid system to the total load demand over a year (kWh/year) yields the levelized cost of energy (LCOE), which is expressed in dollars per kWh. The LCOE calculates the average price per kWh of the actual electricity generated by the HRES system, which may consist of a utility grid. It could be calculated using the formula [115]:

$$LCOE=\frac{TCC(€/year)}{\mathrm{Total} \mathrm{Energy} \mathrm{production} \mathrm{of} \mathrm{HRES} (\mathrm{kWh}/\mathrm{year})}\times CRF\left(r,M_{sys}\right)$$

(26)

3.2. Reliability Parameters

The ability of an electrical power system to provide enough energy to a specific load without a shortage or interruption in service is referred to as reliability. In this study, some of the reliability evaluation parameters for systems, including the loss of load probability (LOLP) [17], loss of load expectation (LOLE), expected energy not supplied (EENS) and reliability index (IR) [45], are considered. As shown in Equations (27), (28), (29) and (30), respectively, the reliability evaluation parameters LOLP, LOLE, EENS, and IR provide the ability of the designed HRES to satisfy the load demand without any shortage in service.

$$LOLP=\frac{{\displaystyle \sum _{t=1}^{8760}hours\#at\left[\left(P_L\left(t\right)+P_{PHES\&SMES}^{cha}\left(t\right)\right)>\left(P_{PV}\left(t\right)+P_B\left(t\right)+P_{PHES\&SMES}^{dis}\left(t\right)+P_{GP}\left(t\right)\right)\right]}}{8760}$$

(27)

$$LOLE=LOLP\times 365$$

(28)

$$EENS={\displaystyle \sum _{t=1}^{8760}\left[\left(P_L\left(t\right)+P_{PHES\&SMES}^{cha}\left(t\right)\right)-\left(P_{PV}\left(t\right)+P_B\left(t\right)+P_{PHES\&SMES}^{dis}\left(t\right)+P_{GP}\left(t\right)\right)\right]}$$

(29)

$$IR=1-\frac{EENS}{{\displaystyle \sum _{t=1}^{8760}{P}_L\left(t\right)}}$$

(30)

4. Problem Formulation

The objective function and design constraints in the optimization model, as well as the case study for the optimal sizing of solar PV–biogas with SMES–PHES systems, are covered in this section. It is important to remember that the optimization framework makes decisions based on the capacities of the parts.

4.1. Objective Function

Minimizing the total cost over a 25-year lifetime is taken into consideration as the objective function. The component costs, fuel consumption, and maintenance and replacement costs are used to determine the TCC. The capital costs, as well as major and minor maintenance costs of the components, are used to calculate the TCC of the components over the course of the project. These steps are used to calculate the total TCC:

$$F_{Grid-Connected}=\min \left\{TCC\right\}=\min \left\{\frac{C_{an-cap}+C_{an-rep}+C_{an-O\&M}+C_{GP}-C_{GS}}{CRF\left(r,M_{sys}\right)}\right\}$$

(31)

$$F_{S\tan d-alone}=\min \left\{TCC\right\}=\min \left\{\frac{C_{an-cap}+C_{an-rep}+C_{an-O\&M}}{CRF\left(r,M_{sys}\right)}\right\}$$

(32)

4.2. Constraints

The following constraints related to the optimization model are taken into consideration when designing a hybrid solar PV–biogas system with SMES–PHES systems:

$$N_{PV}^{\min }\le N_{PV}\le N_{PV}^{\max }$$

(33)

$$P_{Bio}^{\min }(t)\le P_{Bio}(t)\le P_{Bio}^{\max }(t)$$

(34)

$$P_{PHES}^{\min }(t)\le P_{PHES}(t)\le P_{PHES}^{\max }(t)$$

(35)

$$P_{SMES}^{\min }(t)\le P_{SMES}(t)\le P_{SMES}^{\max }(t)$$

(36)

$$P_{inv}(t)\ge P_{PV\_peak}(t)+P_{SMES-dis}(t)$$

(37)

$$LPSP\le {\beta }_L$$

(38)

where $N_{PV}^{min}$ & $N_{PV}^{max}$ represents the minimum and maximum limits of PV panels and $P_{Bio}^{\min }(t)$ & $P_{Bio}^{\max }(t)$ represents the minimum and maximum limits of the capacity of biogas generator and with high reliability or minimum. In this study, loss of power supply probability is predefined as β_L ≤ 0.01.

5. Optimization Techniques

The enhanced whale optimization algorithm (EWOA), one of the suggested metaheuristic optimization methods, is covered in detail in this section. Comparisons are made between the outcomes of the selected algorithm and those of the WOA and AVOA metaheuristic optimization algorithms. MATLAB is used to run the algorithms.

Mirjalili and Lewis’ (2016) [116,117] work is where the whale optimization algorithm (WOA) was initially proposed. Of the enormous baleen whales, the humpback whale is one. Their hunting method, known as the bubble-net feeding method, is how WOA was established. The algorithm was constructed using the bubble-net hunting technique. The global optimal solution to multimodal problems with many local optimal solutions cannot be found using WOA, despite its rapid rate of convergence. Shahraki et al., in 2022 [118], discovered the enhanced whale optimization algorithm (EWOA) to enhance the capability of global search. EWOA enhances the performance of the conventional WOA by utilizing three effective search techniques and a pooling mechanism. These tactics include migration, preferred prey selection, and improving the local prey. The worst responses from each iteration are crossed with the best responses from the pooling technique in order to maintain the population’s genetic diversity. EWOA is adopted to use for the optimal sizing of HRES for stand-alone and grid-connected mode of operation. The proposed EWOA is compared with the most popularly used metaheuristic optimization techniques such as WOA and AVOA. With the help of metaheuristic algorithms, Figure 7 shows how to optimize HRES for both stand-alone and grid-connected mode operations. With the input data, the optimization process begins. Finally, using metaheuristic methods, the component sizes are randomly generated. Following that, a year’s worth of operations of the grid-connected and stand-alone HRES systems are assessed.

6. Result and Discussions

The objective function solution puts forth the aim of maintaining the total cost of the hybrid components as low as possible. Charging or discharging can take place in stand-alone or grid-connected mode of operation during peak or off-peak hours, depending on how full the PHES and SMES are and how much power the associated load requires for long-term power supply. During the selection process, consideration is given to the HRES’ rating, cost, and type. The proposed system includes a solar PV and biogas generator along with an SMES and PHES system, which is used as a backup system to provide a steady supply of electricity at night or during cloudy days. The proposed HRES is intended to supply a specific region in the north as a means of addressing the issue of a lack of electricity caused by dependence on expensive fuel and transportation costs. MATLAB software is used to determine the best configuration for the proposed system’s size and operation. In Appendix A 

Table A1. Technical and financial specifications for the HRES system’s components.

Solar panel [126]
Max power	380 Wp
Length width	1.976 × 0.991 m
Efficiency	19.41%
Temperature coefficient	0.41%
Initial cost	145.845 EUR/kW
O M cost	1%
Life span	25 Years
SMES [127]
Energy, ESMES	1 MJ
Inductance, LSMES	0.5 H
Current, ISMES	1 KA
Voltage, Vdc-link	2 KV
Capacitance, Cdc-link	0.01 F
PHES [128,129]
Overall efficiency	77%
Cost of power conversion	165–740 EUR/kW
Fixe OM cost	8.5 EUR/kW
Variable OM	0.8 EUR/MWh
Life Span	30 years
Biogas generator [130]
Initial Cost	1342.5 EUR/kW
Fixed OM cost	71.65 EUR/kW
Variable OM	20.7 EUR/MWh
Inverter [131,132]
Model	Understand Solar
Initial cost	172 EUR/kW
OM cost	1%
Efficiency	95%
Economic parameters
Real discount rate	12%
Lifetime of the project	years

, the system’s component specifications and economic parameters are listed. Using different sizes and configurations of the desired components in stand-alone and grid-connected modes of operation, metaheuristic optimization will carry out energy balance calculations based on the input parameters.

In this study, the mathematical model requires different hourly data inputs. As shown in Figure 8a,b, these inputs are the solar horizontal irradiance in W/m², the ambient temperature in °C, and the load demand in MW for a full year (a) and one typical day (b). The minimum, maximum, and average numerical values for solar PV horizontal global irradiance are 0, 1195.8, and 273.98 W/m², respectively. In addition, ambient temperature values are 16.5, 21.25, and 26 °C, and connected load demand values are 662.68, 1185.04, and 1707.40 kW. Figure 8b is a representation of one typical full day, with graphical representation taken from Figure 8a to show clearly the dynamic variations of the connected load, solar irradiation, and ambient temperature.

6.1. Results on Optimal Sizing of HRES Components

This section presents the findings of the optimal sizing for various configurations that can meet the load demand. In this study, it is recommended to use metaheuristic optimization techniques like EWOA, WOA, and AVOA to find a compromise solution that is regarded as reliable and affordable. In this case, the decision variables used in a grid-connected system are the number of solar PV panels, the capacity of the biogas generator, the capacity of the PHES system, the capacity of the SMES system, and the capacity of the upper reservoir. A Pareto front displayed TCC vs. iteration in a stand-alone and grid-connected HRES with a PHES-SMES system. This objective function is taken into consideration when sizing HRES system components. In both grid-connected and stand-alone modes of operation,

Table 1. HRES component sizing by using metaheuristic optimization techniques.

Mode of Operation	Methods	Type of Renewable Energy Resources
		No. of PV Panel	PHES Capacity (kW)	Reservoir Capacity (m3)	Capacity of Biogas (kW)	SMES Capacity (kWh)
Grid- Connected	EWOA	5496	400.67	26,798.34	860.29	142.28
	WOA	5120	397.92	26,599.85	865.34	142.28
	AVOA	2951	356.85	25,350.88	995.65	142.28
Stand-alone	EWOA	5510	400.35	26,803.72	850.46	158.25
	WOA	5121	390.28	26,509.45	870.62	158.25
	AVOA	2938	360.46	25,875.52	1000.68	158.25

displays the capacity of components that have been optimized using various metaheuristic optimization algorithms.

The minimum TCC at the proposed location was evaluated using the EWOA optimization algorithm. As shown in Table 1, the estimated values of 5496 and 5510 PV modules, 860.29 and 850.46 kW biogas generator capacity, 142.28 and 158.25 kWh for the SMES capacity, 400.67 and 400.35 kW for the PHES capacity, and 26,798.34 and 26,803.72 m³ for the upper reservoir’s maximum capacity were all calculated for grid-connected and stand-alone modes of operations, respectively. In addition, an estimated 5120 and 2951 PV modules, 865.34 and 995.65 kW biogas generator capacity, 142.28 and 142.28 kWh for the SMES capacity, 397.92 and 356.85 kW for the PHES capacity, and 26,599.85 and 25,350.88 m³ for the upper reservoir’s maximum capacity were all calculated for grid-connected operation modes by using WOA and AVOA, respectively. In grid-connected operation mode, an estimated 5121 and 2938 PV modules, 870.62 and 1000.68 kW biogas generator capacity, 158.25 and 158.25 kWh for the SMES capacity, 390.28 and 360.46 kW for the PHES capacity, and 26,509.45 and 25,875.52 m³ for the upper reservoir’s maximum capacity were all calculated in grid-connected operation mode by using WOA and AVOA, respectively.

6.2. Economic and Reliability Results of HRES

As shown in Figure 9, EWOA reached the best solution of 4.507 × 10⁶ and 4.817 × 10⁶ EURin grid-connected and stand-alone modes of operations, while staying within the predetermined operation limits. WOA reached the best result of 4.515 × 10⁶ and 4.868 × 10⁶ EURin grid-connected and stand-alone modes of operations, staying within the predetermined operation limits, and, finally, the objective function value for the worst technique, AVOA, is 4.538 × 10⁶ and 4.885 × 10⁶ EURin grid-connected and stand-alone modes of operations while staying within the predetermined operation limits.

The financial and reliability evaluation parameters are recorded in

Table 2. Optimal settings for cost and dependability in the proposed optimization methods.

	Techniques	Grid-Connected Mode			Stand-Alone Mode
Evaluation Parameters		EWOA	WOA	AVOA	EWOA	WOA	AVOA
	NPC (EUR)	7.001 × 106	7.006 × 106	7.012 × 106	7.189 × 106	7.193 × 106	7.202 × 106
Financial	COE (EUR/kWh)	0.053513	0.053561	0.053817	0.059713	0.059781	0.059827
	LCOE (EUR/kWh)	0.042351	0.045237	0.046175	0.043251	0.045814	0.046765
	EENS	1.124 × 105	1.174 × 105	1.186 × 105	1.124 × 105	1.174 × 105	1.186 × 105
	LPSP	0.0085	0.0089	0.0092	0.0085	0.0089	0.0092
Reliability	IR	0.9915	0.9911	0.9908	0.9915	0.9911	0.9908
	LOLP	2.892	3.145	3.864	2.892	3.145	3.864
	LOLE	10.555	11.479	14.104	10.555	11.479	14.104

.

As shown in Table 2, according to the findings, the EWOA predicts that the system with the lowest COE also has the lowest NPV and LPSP in both modes of operation. The best COE, predicted using the EWOA method, is 0.053513 and 0.059713 EUR/kWh, yielding a net present value of 7.001 × 10⁶ and 7.189 × 10⁶ dollars and guaranteeing that the LPSP value, predicted by the method to be 0.0085 and 0.0085, is in accordance with the target value (<0.01) in grid-connected and stand-alone modes of operations, respectively. In addition, according to this finding, the COE predicted using the WOA and AVOA approaches is 0.053561 and 0.053817 EUR/kWh, yielding a net present value of 7.006 × 10⁶ and 7.012 × 10⁶ dollars, and the LPSP value predicted is 0.0089 and 0.0092, which are in accordance with the target value (<0.01) in the grid-connected mode of operations, respectively. In the stand-alone mode of operation, the estimation of COE is 0.059781 and 0.059827 EUR/kWh, yielding a net present value of 7.193 × 10⁶ and 7.202 × 10⁶ dollars, and the LPSP value predicted is 0.0089 and 0.0092 by utilizing the WOA and AVOA optimization techniques, respectively.

6.3. Application of the Optimal Solutions of HRES

The generated power for each of the proposed hybrid system’s parts in the EWOA optimal cases are displayed for one full year and one day hourly in both stand-alone and grid-connected modes of operations in Figure 10a,b. The Figure shows the total power produced by solar PV (P_PV), the total power produced by a biogas generator (P_PB), and the total power difference (P_diff) between renewable generation (P_PV) and load over the course of a full year. Figure 10b is a representation of one typical full day, with graphical representation taken from Figure 10a to show clearly the dynamic variations of the proposed hybrid system outputs of solar PV, biogas, and the difference in P_PV-P_load.

In Figure 11a,b, the energy exchange with the external grid is depicted, showing the energy surplus and deficit during the annual and one full day hourly operational period for a configuration that is connected to the external grid. The variable dump loads, which range in size from zero to 0.5285 GWh annually, can use the excess energy in the stand-alone configuration mode. Figure 11b is a representation of one typical full-day, with graphical representation taken from Figure 11a to show clearly the dynamic variations of the power exchange in a specified time (energy balance), power deficits, and surplus power from the hybrid system.

The hourly power used by the SMES set coils to charge (P_SMES-ch), the hourly power generated from the SMES set coils (P_SMES-dis), and the state of charge (SOC) to store energy on the set of coils as a percentage of its capacity are all displayed in Figure 12 in one full year (a) and one typical days (b). Figure 12b is a representation of one typical full day, with graphical representation taken from Figure 12a to show clearly the dynamic variations of the discharging and charging power of SMES, as well as the state of charge of the SMES system in a hybrid system.

Figure 13a,b display the annual and daily power used by the pump-motor set (P_Pump), the power generated hourly by the turbine-generator set (P_Turbine), the volume of water raised to the upper reservoir (Q_ch), the volume of water discharged (Q_dis), and the upper reservoir’s SOC as a percentage of its capacity. The optimization requirements must be met while maintaining zero energy exchange with the grid, which is very challenging due to design constraints. The figure makes it abundantly clear that nearly all of the electric energy is required for meeting the load demand flows to and from the external grid. The water is raised to the upper tank during periods of high renewable energy production, increasing the volume of water in the tank as a result. Figure 13b is a representation of one typical full day, with graphical representation taken from Figure 13a to show clearly the dynamic variations of the consuming and generating power by/from PHES, the discharging and charging of water from the upper reservoir, and the state of charge of the upper reservoir in a hybrid system.

Annual energy production and financial cases based on the proposed stand-alone and grid-connected HRES are presented in the above sections. Each renewable energy system is represented as a percentage of the overall project cost and energy production in stand-alone and grid-connected modes of operation in Figure 14 and Figure 15, respectively. In the stand-alone mode of operation, the PV system pays for 1.2895 × 10⁶ (27%), the biogas generator system pays for 1.4738 × 10⁶ (32%), the SMES system pays for 7.2085 × 10⁵ (16%), and the PHES system covers the remaining 1.1098 × 10⁶ (25%) of the entire project’s cost. In grid-connected operation mode, the PV system pays for 1.2828 × 10⁶ (28%), the biogas generator system pays for 1.4757 × 10⁶ (32%), the SMES system pays for 7.1853 × 10⁵ (16%), and the PHES system covers the remaining 1.0941 × 10⁶ (24%) of the entire project’s cost.

In addition, based on the biases of energy production share, in the stand-alone mode of operation, the PV system covers 42%, the biogas generator system covers 45%, the SMES system covers 1%, and the PHES system covers the remaining 12% of the project’s cost. In the grid-connected operation mode, the PV system covers 42%, the biogas generator system covers 42%, the SMES system and the national grid cover 1%, and the PHES system covers the remaining 12% of the total energy production from the HRES system.

As a result, comparisons of financial parameters such as NPC and COE have been evaluated with other researchers’ work. Barhoumi et al. [119] discuss the comparison of the techno-economic parameters of NPC and COE in two modes of operation. The NPC of grid-connected modes was lower by 19.22% compared to stand-alone modes of operation. In addition, COE grid-connected modes were 9.8% less efficient than stand-alone modes of operation. As compared to the results of NPC and COE recorded in this paper, they are 19.87% and 10.08% lower than those of grid-connected modes of operation, respectively. In addition, in a study by Ahmed S. et al. [80], the results clarify that the algorithms succeeded in obtaining the best design for the selected hybrid renewable energy system with the minimum COE of 0.25 EUR/kWh and a NPC of 7.3703 × 10⁶ EUR, which is greater than the proposed work by 19.65% and 36.93% of COE and NPC, respectively. As shown by the discussed results, the proposed grid-connected system is better than stand-alone modes of operation, even if the results achieved by this work are smaller than the mentioned researcher’s results.

7. Conclusions

This study looks at the optimization and techno-economic feasibility of hybrid renewable sources and their overall cost effects in both stand-alone and grid-connected modes of operation. For this study, data from Debre Markos, Ethiopia, about real-time community and commercial loads and climate parameters were used. The optimal size of the hybrid solar PV–biogas with SMES and PHES system was obtained using EWOA, WOA, and AVOA optimization techniques, and the capacity of each component in the hybrid system and different types of costs were analyzed in a detailed design parameter manner. Thus, optimization techniques are applied in two modes of operation cases, i.e., grid-connected and stand-alone modes of operation. After developing a MATLAB program for sizing the hybrid system, the TCC obtained by utilizing EWOA, WOA, and AVOA were 4.507 ×10⁶ EUR, 4.515 × 10⁶ EUR, and 4.538 × 10⁶ EUR, respectively, in grid-connected modes of operation. In stand-alone modes, the TCC obtained by utilizing EWOA, WOA, and AVOA were 4.817 × 10⁶ EUR, 4.868 × 10⁶ EUR, and 4.885 × 10⁶ EUR, respectively. In both modes of operation, EWOA does a good job of minimizing the total current cost while meeting the requirements of the objective function. Based on the comparison of results, EWOA did better than the competition in terms of total current costs and reliability.

This technique is proposed as a standard for the following stage of study in order to provide comparable findings in other applications, notably for varied distribution networks and remote places with meteorological circumstances. The recommended method can be modified to incorporate other latest meta-optimization techniques [120,121,122,123,124,125] and include more sustainable criteria, such as hybrid power system control, which can help with the development of rural networks, smart towns, and expected demand prediction.