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Abstract A hybrid system proposed by three different specifications for the equipment of a tourist lodge in the headland of south-west Morocco was sized by analysing the limits of load profile constraints, such as hour-to-hour variability (HHR), day-to-day variability (DDR) and the operating reserve rate (ROR). Based on the three-factor Doehlert matrix recommendations, the simulations employed an energy-sizing tool for hybrid renewable-energy systems. Testing was conducted with DDR at 5–30%, HHR at 10–30% and ROR at 0–20%. Under these conditions, a second-order polynomial relationship with a correlation rate of ~90% was found between the net present cost (NPC) of the system, the levelized cost of electricity and the various constraint factors. The first specification, SPC(1), composed of generators and batteries, was introduced to control and validate the simulation independently of renewable energy, which showed a positive manifestation with the imposed constraints. The analysis expanded by introducing solar and wind energy resources. The SPC(2) configuration added PV modules to the SPC(1) and the SPC(3) configuration added wind turbines to SPC(2). The effect of DDR, HHR and ROR in the trials was significant by linear regression. At the same time, only DDR had a significant quadratic regression. The others, with their pairwise interactions, were insignificant. The desirability procedure made it possible to calculate the maximum limits of load profile constraint variables leading to targets of LCOE = 0.41 US$/kWh and NPC = US$320 080.1 of the load profile constraints: the DDR = 15.47% and the HHR = 26.55% at an ROR rate of 17.77%. Open in new tabDownload slide hybrid system, wind and photovoltaic energies, HOMER software, variability in load profile, rate of non-load coverage, model, headland south-west Morocco Introduction Although renewable energy is booming around the world, it needs to be harnessed in various hybrid or straightforward configurations, whether coupled to conventional sources or not, to deal with the scarcity of conventional fuels, pollution, global warming and the enormous energy bill [1–3]. Furthermore, the configurations can be more expensive due to the improper size of the systems and the disregard for the environment surrounding renewable-energy projects [4, 5]. The calculations are numerous and complex for the dimensioning, the numerical simulation of hybrid systems. Therefore, the use of a specialized modelling and optimization tool is highly desirable. Fig. 1 shows the input data for the simulation operation. The various configurations proposed use load profile, technical characteristics data, renewable and non-renewable energy resources, and the constraints imposed on the systems. The simulations compare the costs throughout the life of the project. In addition to the performance study, it is also a support for the optimal configuration. Fig. 1: Open in new tabDownload slide The inputs and outputs of the hybrid system simulations around HOMER[6]. The simulations are essentially based on the criterion of the minimum cost of the system object of the project studied, generally perceived as a unique constraint. However, other criteria are important to consider in the quality of the approach relating to the proposed solutions: load profile of the consumer and its variability over the year; distribution rate between renewable and conventional sources; maximum annual capacity shortage and/or annual peak load applied; the reliability and viability of the project over its lifetime. Indeed, this work will begin with a bibliographic reading illustrating the latest studies and methods carried out in dimensioning hybrid systems. Then it will be linked to methods and means of computer simulations. The effects of the system constraints depend on the load profile in the region considered for the installation of the project. Then we will rebound the study of a simple case formed of the generator set and batteries to see the impact of stress factors on the response. This impact study will be based on a linear experimental design. Then it becomes a quadratic function model according to the three-variable Doehlert design. Finally, we are going to discuss the excellent factor rates, which lead to optimal sizing for renewable-energy systems. Literature review on hybrid systems sizing Reading the literature on hybrid systems, in order to study their sizing, several researchers studied specific configurations and tried to bring out the best performance from them. Others used more or less complex applications due to a large number of simulations of the cases, which may arise in order to be able to decide on the choice of the optimal configuration. Studies have proposed sizing approaches for hybrid systems based on economics; financial studies have been presented using MATLAB® and software specializing in the optimization of hybrid installations [7, 8]. The feasibility of autonomous hybrid renewable systems has also integrated wind power, photovoltaic fields and fuel-cell units. These electricity-production units have been applied to a residential or agricultural profile in different desert-like localities in the Middle East. In Egypt, the authors examined different configurations to opt for the criterion of the production efficiency of electrical energy to irrigate agricultural fields. Among the configurations and methods used, a hybrid system consisting of a photovoltaic field, a fuel cell and an electrolyser achieved very satisfactory performance and a very affordable economic cost [9, 10]. On the other hand, other studies have examined the reliability problems of hybrid systems in their various aspects and they have studied the optimal economic sizing, numerical modelling and control procedures. These authors have applied an evolutionary technique relating to the theory of games for better optimization of hybrid systems [11]. As for the semi-desert regions of Iran, the feasibility was studied for the installation of a hybrid system composed of wind turbines, a photovoltaic solar field and a hydrogen tank for fuel cells. The results of this study based on climatic and solar radiation data from the different sites were able to show that a locality achieved a competitive energy cost compared to other regions. In particular, the lowest level cost was (US$0.54/kWh) [12]. In addition, in North Africa, Morocco and Algeria are very advanced in the research and development of renewable energies [13, 14]. Specifications were presented to equip a school located in a rural area in Beni Mellal in central Morocco with an electric production station made up of a wind turbine and a backup generator set, and a battery stack for storage. The optimization software used for this study is the HOMER Pro 3.2.3 software [15]. The analysis of the configuration to serve the school was 23 kWh/day in alternating current, achieving a peak of 6.02 kW. The results of the simulation operation concluded an optimized power plant size of the generator set of 7.8 kW, a wind turbine with a power of 2 kW, a solar photovoltaic field of 5 kW and the levelled cost of optimized electricity was ~US$1.12/kWh [16]. The performance evaluation of hybrid systems was carried out in Algeria for the production of hydrogen, the objective of which was to model the hydrogen-generation system on the one hand numerically and to perform a benchmark between seven regions in different corners of the country. This study estimated that developing countries can produce between 20 and 30 m3 of hydrogen annually. The peak of production was in March and the lowest production was observed in July in the north [16]. Residential areas were targeted by a study which noted that current islanding detection methods and international standards have limitations related to local load and inverter [17]. Hydrogen-production technologies based on hybrid systems are still topical in Malaysia. Researchers have reported that the production of hydrogen by supercritical water can gasify biomass in a more economically viable thermochemical context. In addition, they concluded that the low yield achieved and the high production cost through the solar photovoltaic field remained the main obstacle in front of solar hydrogen, thanks to the variability in the production conditions [18]. In Algeria, a study of an integrated ethanol-production system operating with a solar-energy-based hydrogen-production design demonstrated a notable effect of temperature and electric current factors on the hydrogen-production process during electrolysis [19]. The studies and analyses reviewed in the literature show the involvement of researchers in the profitability of renewable resource systems subject to energy-consuming, environmental, technical and economic profile constraints, and this by hybridization with conventional resource systems for self-production of hydrogen. The sizing methods for hybrid wind–solar–battery hybrid systems are simplified or complex. First, the sizing of each source based on the wind and solar potential available determines a battery capacity capable of covering the load in the event of low energy output, then the size of the other components (regulator, inverter and so on) is determined. The disadvantages of this method based on simple analytical relations are generally the oversizing or undersizing of the system because it does not take into account the variation in climatic parameters and energy parameters. The second method considers the variation by step and reduces their energy quality, which leads to the development of models that consider these parameters. The use of complex sizing aims to optimize the hybrid systems of wind and solar sources, which are single-objective or multi-objective systems. When it comes to single-objective optimization, the goal is most often to minimize the cost of the system. However, the overall objective is to find an optimal solution for the multi-objective system according to two or more criteria [20]. By way of example, we can cite the following multi-objective systems: minimization of the cost of the system and the capacity of the shortage rate; minimization of the cost of the system and the quantity of CO2; minimization of the quantity of CO2 and minimizing the cost of the system; and increasing the reliability of the system [21–24]. The advantage of sizing via HOMER is a new approach that allows defining a precise optimal configuration. Its limitation is a focus on multi-criteria optimization (only one criterion among others on a case-at-once basis: cost of the system, capacity shortage of the load profile, CO2 emissions and so on) and it uses monthly averages of energy data. In an optimal configuration for a single-objective project aiming only at the net present cost (NPC) over the project’s life, HOMER proposes a classification by the different possible combinations of the significant components of the resources used either by categories or by cost over the lifetime. The simulation results window shows several technical and economic details about each system configuration that HOMER is simulating [25–27]. Review of the use of sizing tools for hybrid systems HOMER software is universally used to size hybrid systems to cover three kinds of load profiles: residential, commercial and industrial. An economic feasibility study was initiated to assess the profitability of a hybrid system by introducing a water electrolysis unit in the wind and solar power plant [28–33]. Based on the literature review, the studies mentioned above and others, the optimization of the systems did not consider the variability in load profiles. Random variability rates are usually fixed, which could lead to erroneous sizing results. No study was found in the locality of the white headland in south-west Morocco concerning the technical and economic feasibility of a hybrid power plant composed of photovoltaic modules, wind farms, generators and batteries as the construction of a mini-grid. In addition, no analysis was performed on the limits of the load-profile constraints, such as the operational reserve rate and the hourly and daily variability using a three-variable Doehlert matrix for optimization. Therefore, this is a gap from previous research. Fortunately, hybrid systems are designed, studied and produced in most scientific literature using HOMER. 1 Methods 1.1 Geographical characteristics of the white headland in south-west Morocco Fig. 2 shows the location map of the headland in south-west Morocco. The new town is positioned at the geographic coordinates of latitude and longitude of 20.8317°N and 17.0909°W, respectively. Fig. 2: Open in new tabDownload slide Location of the white headland in the south-west of Morocco. Source: Google/maps. 1.2 The specifications for the electrification of the tourist lodge For the tourist lodge that will be built on the white headland in south-west Morocco, three different options are available: generator–batteries (GE–B), generator–photovoltaic–batteries (GE–PV–B) and generator–wind power–photovoltaic–batteries (GE–WP–PV–B), which are described in specifications SPC(1), SPC(2) and SPC(3). The analysis of the various hybrid electric energy conversion chains proposes to cover the needs of this space, which could house an estimated tourist population of several dozen tourists per day. The energy consumption in the tourist lodge assumes a commercial load profile, with a daily electricity requirement of ~170 kWh/d. The proposed specifications of hybrid systems are detailed in Fig. 3: (i) SPC(1): GE–B; (ii) SPC(2): GE–PV–B; iii) SPC(3): GE–WP–PV–B. Fig. 3: Open in new tabDownload slide The proposed hybrid system specifications and layouts. SPC(1), containing only the generators and batteries among the specifications proposed in this work, has a unique and precise purpose. These are compliance testing and the validity of simulation results using HOMER software [34]. 1.3 Load profile: commercial Fig. 4 shows the expected load profile for the locality of the case study. The top-left subplot shows the commercial profile of a working population with a load of >150 kW from 8:00 a.m. to 4:00 p.m. and <25 kW from 8:00 p.m. to 7:00 a.m.: Fig. 4: Open in new tabDownload slide Commercial load profile with a daily load variability DDR of 10% and an hourly load variability of 20%. Pyr = (1 + HHR + DDR + HHR.DDR) ×Pwd×Nwd(1) where HHR and DDR are the rates of hourly and daily variability, respectively. The subplot on the right-hand side shows a profile of monthly variation during a year. The year returns an annual peak in July of ~26 kW. Furthermore, the bottom subplot indicates the variability in the load profile from hour to hour (HHR = 20%) and day to day (DDR = 10%). The graph style indicates that the variability in demanded power is concentrated during the day along a year between 200 and 400 kW. The rate of operating reserves (ROR) (in %) can also define a constant operating reserve energy requirement of the primary peak load. The hybrid system can now operate equipment requiring starting power (machine engines) without consuming power from the main load. The annual peak power reserve is derived from the hourly and daily variability rates (HHR and DDR). At the same time, the peak primary load rate (ROR) affects the NPC and the levelized cost of electricity (LCOE) of the best configuration. Each configuration’s energy production is ultimately determined by these three parameters. 1.4 Implementation of simulation In the context of ecological cities in the peninsula in south-west Morocco, electrification is being studied to establish a tourist lodge. Despite an annual variability in the commercial load profile, this study is to perform excellent sizing. The tourist project can be achieved by using a fundamental road axis that connects the North and South (Europe–Africa) at the Moroccan–Mauritanian border crossing of Gureguarate. The region is desert, sunny and windy, but the geography of the ground shows very variable roughness, characterized by the frequent uplift of sand and displacement of dunes; this can affect both renewable-energy availability and load-profile variability, and it specifically impacts the quality of solar photovoltaic panels and wind turbines. The suggested system is an optimized hybrid made up of generators using renewable and non-renewable resources, such as backup generators, photovoltaic panels, wind nacelles and storage batteries. We have provided the HOMER tool for the simulation of suggested and non-suggested configurations. The technical and commercial characteristics of the equipment of the hybrid systems of the three specifications proposed are presented in Tables 1 and 2. Table 1: Technical characteristics and commercial information of non-renewable equipment: generators Equipment . Mark . Settings . Value . Unit . Generators Generic (1 and 10 kW) [37] Frequency 50 Hz Voltage 230 V Nominal power 1/10 kW Maximal power 11 kW Fuel-tank capacity 25 L Lifetime 15 000 Hours Generators cost 500 $US/kW Project cost 25 Years Nominal interest rate 6 % System voltage 48 V Cost of a litre of diesel 1 $US Batteries SurrettS4KS25P [38] Battery cost 1000 $US Storage capacity 1350 Ah Battery lifetime 4 Years Inverter Xtender XTH6000W [39] Inverter cost 4000 $US Voltage 48 V Power 6000 W Inverter lifetime 10 Years Efficiency 90 % Maintenance and operations rate In relation to the capital of the equipment Inverter maintenance rate 1 %/yr Batteries maintenance rate 3 %/yr GE 0.2 %/h Environmental constraints Penalties on greenhouse gas emissions Carbon dioxide 14 $/t Carbon monoxide 7.5 $/t Sulphur dioxide 5.5 $/t Nitrogen oxide NOx 5 $/t Unburned hydrocarbons 4 $/t Particulate matter 3 $/t Equipment . Mark . Settings . Value . Unit . Generators Generic (1 and 10 kW) [37] Frequency 50 Hz Voltage 230 V Nominal power 1/10 kW Maximal power 11 kW Fuel-tank capacity 25 L Lifetime 15 000 Hours Generators cost 500 $US/kW Project cost 25 Years Nominal interest rate 6 % System voltage 48 V Cost of a litre of diesel 1 $US Batteries SurrettS4KS25P [38] Battery cost 1000 $US Storage capacity 1350 Ah Battery lifetime 4 Years Inverter Xtender XTH6000W [39] Inverter cost 4000 $US Voltage 48 V Power 6000 W Inverter lifetime 10 Years Efficiency 90 % Maintenance and operations rate In relation to the capital of the equipment Inverter maintenance rate 1 %/yr Batteries maintenance rate 3 %/yr GE 0.2 %/h Environmental constraints Penalties on greenhouse gas emissions Carbon dioxide 14 $/t Carbon monoxide 7.5 $/t Sulphur dioxide 5.5 $/t Nitrogen oxide NOx 5 $/t Unburned hydrocarbons 4 $/t Particulate matter 3 $/t Open in new tab Table 1: Technical characteristics and commercial information of non-renewable equipment: generators Equipment . Mark . Settings . Value . Unit . Generators Generic (1 and 10 kW) [37] Frequency 50 Hz Voltage 230 V Nominal power 1/10 kW Maximal power 11 kW Fuel-tank capacity 25 L Lifetime 15 000 Hours Generators cost 500 $US/kW Project cost 25 Years Nominal interest rate 6 % System voltage 48 V Cost of a litre of diesel 1 $US Batteries SurrettS4KS25P [38] Battery cost 1000 $US Storage capacity 1350 Ah Battery lifetime 4 Years Inverter Xtender XTH6000W [39] Inverter cost 4000 $US Voltage 48 V Power 6000 W Inverter lifetime 10 Years Efficiency 90 % Maintenance and operations rate In relation to the capital of the equipment Inverter maintenance rate 1 %/yr Batteries maintenance rate 3 %/yr GE 0.2 %/h Environmental constraints Penalties on greenhouse gas emissions Carbon dioxide 14 $/t Carbon monoxide 7.5 $/t Sulphur dioxide 5.5 $/t Nitrogen oxide NOx 5 $/t Unburned hydrocarbons 4 $/t Particulate matter 3 $/t Equipment . Mark . Settings . Value . Unit . Generators Generic (1 and 10 kW) [37] Frequency 50 Hz Voltage 230 V Nominal power 1/10 kW Maximal power 11 kW Fuel-tank capacity 25 L Lifetime 15 000 Hours Generators cost 500 $US/kW Project cost 25 Years Nominal interest rate 6 % System voltage 48 V Cost of a litre of diesel 1 $US Batteries SurrettS4KS25P [38] Battery cost 1000 $US Storage capacity 1350 Ah Battery lifetime 4 Years Inverter Xtender XTH6000W [39] Inverter cost 4000 $US Voltage 48 V Power 6000 W Inverter lifetime 10 Years Efficiency 90 % Maintenance and operations rate In relation to the capital of the equipment Inverter maintenance rate 1 %/yr Batteries maintenance rate 3 %/yr GE 0.2 %/h Environmental constraints Penalties on greenhouse gas emissions Carbon dioxide 14 $/t Carbon monoxide 7.5 $/t Sulphur dioxide 5.5 $/t Nitrogen oxide NOx 5 $/t Unburned hydrocarbons 4 $/t Particulate matter 3 $/t Open in new tab Table 2: Technical characteristics and commercial information of renewable equipment: PV and wind turbine Equipment . Mark . Settings . Value . Unit . Photovoltaic Generic flat-plate PV [40] Nominal power 1 kW Nominal temperature of standard cell NOCT 47 °C Effect of temperature on power –0.5 %/°C Efficiency under standard conditions 13 % 1-kW cost 3000 $US Wind Power AWS HC 10 kW AWS HC 3.3 kW [41] Nominal power 3.3 and 10 kW Height 12 m Lifetime 20 Years 10 and 3.3 kW cost 5000 $ US/kW Equipment . Mark . Settings . Value . Unit . Photovoltaic Generic flat-plate PV [40] Nominal power 1 kW Nominal temperature of standard cell NOCT 47 °C Effect of temperature on power –0.5 %/°C Efficiency under standard conditions 13 % 1-kW cost 3000 $US Wind Power AWS HC 10 kW AWS HC 3.3 kW [41] Nominal power 3.3 and 10 kW Height 12 m Lifetime 20 Years 10 and 3.3 kW cost 5000 $ US/kW Open in new tab Table 2: Technical characteristics and commercial information of renewable equipment: PV and wind turbine Equipment . Mark . Settings . Value . Unit . Photovoltaic Generic flat-plate PV [40] Nominal power 1 kW Nominal temperature of standard cell NOCT 47 °C Effect of temperature on power –0.5 %/°C Efficiency under standard conditions 13 % 1-kW cost 3000 $US Wind Power AWS HC 10 kW AWS HC 3.3 kW [41] Nominal power 3.3 and 10 kW Height 12 m Lifetime 20 Years 10 and 3.3 kW cost 5000 $ US/kW Equipment . Mark . Settings . Value . Unit . Photovoltaic Generic flat-plate PV [40] Nominal power 1 kW Nominal temperature of standard cell NOCT 47 °C Effect of temperature on power –0.5 %/°C Efficiency under standard conditions 13 % 1-kW cost 3000 $US Wind Power AWS HC 10 kW AWS HC 3.3 kW [41] Nominal power 3.3 and 10 kW Height 12 m Lifetime 20 Years 10 and 3.3 kW cost 5000 $ US/kW Open in new tab 1.5 General procedure for carrying out experiments (simulations) The approach followed, and the same as that used in the dimensioning plan, precedes GE–B. The postulated mathematical model is a spherical model with interaction: Y=a0+a1X1+a2X2+a3X3+a11X12+a22X22+a33X32+a12X1X2+…+a13X1X3+a23X2X3+ε(2) where a0 represents the mean; a1, a2 and a3 represent the average effects of X1, X2 and X3; a11, a22 and a33 represent the interactions of each factor on itself; and a12, a13 and a23 represent the first-order interactions. 2 Results and discussion In this section, concerning the feasibility study of the hybrid system project indicated above through the proposed specifications presented, at first glance, the effect of the factors on the responses will be highlighted. As shown in Table 3, the elements are the rate of variability in the load profile from day to day (DDR), the rate of variability in the load profile from hour to hour (HHR) and the effect of the third one, the ROR. The responses are the net present cost (NPC) and the LCOE. Before evaluating the influence of the experimental conditions (simulation) of hybrid renewable resource systems on the NPC, the validity of the simulated results must examine a priori by SPC(1) because the operating reserve comes from this amount not consumed and stored in batteries. This situation in the SPC(1) case can be noticed for the possible starting of some machines. The hybrid system uses only conventional resources. Indeed, we have analysed the experimental design (simulations) to optimize a hybrid installation comprising diesel generators; in this first measure, the screening study shows a distinct dependence of the HHR factor and the DDR factor, and the ROR factor on the response parameters NPC and the LCOE. Fig. 5 shows that the ROR factor has not had some sensible effect on NPC, but it depends directly on the hourly and daily load variability and no interaction between both couples ROR.HHR and ROR.DDR. Fig. 5: Open in new tabDownload slide Graphical study of the effects for all responses: summarized graph of NPC and LCOE parameters. Fig. 6 presents the Pareto graph, which shows that the DDR, HHR factors and both DDR.HHR interacted with each of NPC or LCOE with >90%. On the other side, from Figs 5 and 6, the DDR and HHR factors positively affect the NPC response and the DDR.HHR rate negatively affects the NPC response. This situation shows a dependence of the load-profile parameters on NPC and LCOE. Furthermore, the ROR factor has an ambiguous effect on them. Therefore, the effect of the last factor ROR may appear more clearly in the renewable-system cases. Fig. 6: Open in new tabDownload slide Pareto diagram: graphical study of the effects for all responses (NPC/LCOE). The rest of the study, which aims to upgrade to the second-degree model, kept the three factors: DDR, HHR and ROR. The Doehlert design was chosen [35, 36]. The latter requires 12 trials and 3 trials in the centre have been added to assess the experimental error and analyse the variance of the model postulated a priori, bringing the number of trials to 15 for each specification (Table 4). The Doehlert design is a response-surface plane. Its main characteristic is to have a uniform distribution of the experimental points in the experimental domain (simulation). Moreover, it is characterized by a regularity concerning the factors, which allows the experimenter to add additional experience points and find an arrangement identical to the starting one. Among 45 different simulations (15 × 3), the 9 case-centred results are identical as described by the Doehlert model. The variable load-profile conditions imposed by the location of the tourist lodge and its environment affect the investment cost and the operating cost. A zero test is conducted (all factors are set to code 0). Before HOMER processing, all necessary costs are initialized, including the equipment capital, replacement, maintenance and operation, and penalties specified for greenhouse gas emissions. When the HOMER software processing has been completed, the average values of NPC and LCOE are obtained for all cases under the different test conditions of DDR, HHR and ROR, which are specified in Fig. 3 for the three specifications indicated above. For the case of SPC(1), the generator case of 3.3 kW was found to be more optimal than 10 kW to cover a load of 165.59 kWh/day, with a total NPC and an LCOE cost of US$311 728 and US$0.420/kWh, respectively. This test concludes that HOMER can choose between two generators: one with high optimal power and the other with low optimal power. The generator set plays an essential role in hybrid systems. It intervenes during periods of non-coverage of the load. The capacity shortage tolerance rate (3%) is imposed on the tool, which reduces the small generator sets to 1 without impacting other components, which leads to the conclusion that ±3% of load can influence the number more or less of the main components of the hybrid system that can increase or decrease the LCOE and NPC. The standard deviation parameter is much more centred for SPC(1) with the generator set and more dispersed for SPC(2) with coupling to the solar photovoltaic field. This famous statistical parameter is reduced for SPC(3) by adding a wind turbine. This state can be explained by the comparison of the production fleet specifications, where the nine parameters represent the coefficients of their model, according to their corresponding linear parameters HHR, DDR and ROR quadratic parameters HHR2, DDR2 and ROR2, and the parameters of the interaction HHR.DDR, DDR.ROR and ROR.HHR. The load-profile parameter of the average response a0 has been omitted so as not to bias the others. These parameters look almost identical between the generator set and the farm with the wind turbine, unlike the PV–farm specification. Table 5 presents the analysis of variance analysis for NPC outcomes of the two specifications containing the renewable technologies CPS(2) and CPS(3) relating to the proposed generating facilities. The standard deviation parameter is much more centred for SPC(2) with the generator set coupled to the solar photovoltaic field and more dispersed for SPC(3) after adding a wind turbine. The regression coefficients, R2, were almost equal to 99.9% and 99.1% for the specifications using renewables SPC(2) and SPC(3), respectively, and 97% for SPC(1) using fossil energy. Table 5: Correlation rates of models, estimates and statistical coefficients Statistical parameters . LCOE . . NPC . . . CPS(2) . CPS(3) . CPS(2) . CPS(3) . Standard deviation 0.00104 0.002 36 606.22 2 158.91 R2 0.999 0.993 0.999 0.991 R2 adjusted 0.995 0.973 0.997 0.963 R2 predicted ~1 ~1 ~1 ~1 Number of degrees of freedom 3 3 3 3 Statistical parameters . LCOE . . NPC . . . CPS(2) . CPS(3) . CPS(2) . CPS(3) . Standard deviation 0.00104 0.002 36 606.22 2 158.91 R2 0.999 0.993 0.999 0.991 R2 adjusted 0.995 0.973 0.997 0.963 R2 predicted ~1 ~1 ~1 ~1 Number of degrees of freedom 3 3 3 3 Open in new tab Table 5: Correlation rates of models, estimates and statistical coefficients Statistical parameters . LCOE . . NPC . . . CPS(2) . CPS(3) . CPS(2) . CPS(3) . Standard deviation 0.00104 0.002 36 606.22 2 158.91 R2 0.999 0.993 0.999 0.991 R2 adjusted 0.995 0.973 0.997 0.963 R2 predicted ~1 ~1 ~1 ~1 Number of degrees of freedom 3 3 3 3 Statistical parameters . LCOE . . NPC . . . CPS(2) . CPS(3) . CPS(2) . CPS(3) . Standard deviation 0.00104 0.002 36 606.22 2 158.91 R2 0.999 0.993 0.999 0.991 R2 adjusted 0.995 0.973 0.997 0.963 R2 predicted ~1 ~1 ~1 ~1 Number of degrees of freedom 3 3 3 3 Open in new tab We can verify that the mean response coefficients, a0, are the same as the experimental values (simulations) of NPC obtained when all the factors are weighted at coded level 0, test 1 (ROR = 10%, DDR = 20% and HHR = 20%). Therefore, we can conclude apparently that this location has more stable solar energy available than wind energy. This state can be explained by Table 6 relative to the comparison of the production-layout specifications, where the nine coefficients of the model, according to their corresponding linear parameters HHR, DDR and ROR, the quadratic parameters HHR2, DDR2 and ROR2, and the interaction parameters of HHR.DDR, DDR.ROR and ROR.HHR. The independent coefficient of the multivariate regression a0 is the average response of the load profile. As verified above, it is the mean response of NPC and LCOE obtained when all the factors are weighted at coded level 0, conforming the test 1 (ROR = 10%, DDR = 20% and HHR = 20%). Table 6: Model coefficients were obtained from the hybrid system and with generators and batteries Coefficient name . C . Values . . . . Signification (P-value) . . . . . . LCOE ($/kWh) . . NPC($US) . . LCOE (%) . . NPC (%) . . . . SPC(2) . SPC(3) . SPC(2) . SPC(3) . SPC(2) . SPC(3) . SPC(2) . SPC(3) . Average responses a0 0.41 0.41 317 919.00 322 818 <0.01*** <0.01*** <0.01*** <0.01*** ROR a1 0.01 0.01 6207.13 4253.63 0.0571*** 1.87* 0.0255*** 2.91* DDR a2 0.02 0.02 17 463.81 16 847.21 <0.01*** 0.0362*** <0.01*** 0.0572*** HHR a3 0.01 0.01 7156.90 6903.38 0.0396*** 0.505** 0.0166*** 0.774** ROR2 a1-1 –0.00 –0.00 117.50 –3595.50 100 21.8 88.4 26.7 DDR2 a2-2 0.01 0.01 5972.10 6676.76 0.921** 5.5 0.401** 8.6 HHR2 a3-3 0.00 0.00 1361.58 388.66 23.5 82.8 15.6 88.9 ROR. DDR a1-2 0.00 –0.00 316.39 –724.57 66.4 70.1 68.2 79 ROR.HHR a1-3 0.00 0.00 586.85 1525.01 50.3 63 50.8 62.2 DDR.HHR a2-3 –0.00 –0.00 –2471.48 –121.56 7.3 94.3 5.1 96.8 Coefficient name . C . Values . . . . Signification (P-value) . . . . . . LCOE ($/kWh) . . NPC($US) . . LCOE (%) . . NPC (%) . . . . SPC(2) . SPC(3) . SPC(2) . SPC(3) . SPC(2) . SPC(3) . SPC(2) . SPC(3) . Average responses a0 0.41 0.41 317 919.00 322 818 <0.01*** <0.01*** <0.01*** <0.01*** ROR a1 0.01 0.01 6207.13 4253.63 0.0571*** 1.87* 0.0255*** 2.91* DDR a2 0.02 0.02 17 463.81 16 847.21 <0.01*** 0.0362*** <0.01*** 0.0572*** HHR a3 0.01 0.01 7156.90 6903.38 0.0396*** 0.505** 0.0166*** 0.774** ROR2 a1-1 –0.00 –0.00 117.50 –3595.50 100 21.8 88.4 26.7 DDR2 a2-2 0.01 0.01 5972.10 6676.76 0.921** 5.5 0.401** 8.6 HHR2 a3-3 0.00 0.00 1361.58 388.66 23.5 82.8 15.6 88.9 ROR. DDR a1-2 0.00 –0.00 316.39 –724.57 66.4 70.1 68.2 79 ROR.HHR a1-3 0.00 0.00 586.85 1525.01 50.3 63 50.8 62.2 DDR.HHR a2-3 –0.00 –0.00 –2471.48 –121.56 7.3 94.3 5.1 96.8 C, coefficients. Open in new tab Table 6: Model coefficients were obtained from the hybrid system and with generators and batteries Coefficient name . C . Values . . . . Signification (P-value) . . . . . . LCOE ($/kWh) . . NPC($US) . . LCOE (%) . . NPC (%) . . . . SPC(2) . SPC(3) . SPC(2) . SPC(3) . SPC(2) . SPC(3) . SPC(2) . SPC(3) . Average responses a0 0.41 0.41 317 919.00 322 818 <0.01*** <0.01*** <0.01*** <0.01*** ROR a1 0.01 0.01 6207.13 4253.63 0.0571*** 1.87* 0.0255*** 2.91* DDR a2 0.02 0.02 17 463.81 16 847.21 <0.01*** 0.0362*** <0.01*** 0.0572*** HHR a3 0.01 0.01 7156.90 6903.38 0.0396*** 0.505** 0.0166*** 0.774** ROR2 a1-1 –0.00 –0.00 117.50 –3595.50 100 21.8 88.4 26.7 DDR2 a2-2 0.01 0.01 5972.10 6676.76 0.921** 5.5 0.401** 8.6 HHR2 a3-3 0.00 0.00 1361.58 388.66 23.5 82.8 15.6 88.9 ROR. DDR a1-2 0.00 –0.00 316.39 –724.57 66.4 70.1 68.2 79 ROR.HHR a1-3 0.00 0.00 586.85 1525.01 50.3 63 50.8 62.2 DDR.HHR a2-3 –0.00 –0.00 –2471.48 –121.56 7.3 94.3 5.1 96.8 Coefficient name . C . Values . . . . Signification (P-value) . . . . . . LCOE ($/kWh) . . NPC($US) . . LCOE (%) . . NPC (%) . . . . SPC(2) . SPC(3) . SPC(2) . SPC(3) . SPC(2) . SPC(3) . SPC(2) . SPC(3) . Average responses a0 0.41 0.41 317 919.00 322 818 <0.01*** <0.01*** <0.01*** <0.01*** ROR a1 0.01 0.01 6207.13 4253.63 0.0571*** 1.87* 0.0255*** 2.91* DDR a2 0.02 0.02 17 463.81 16 847.21 <0.01*** 0.0362*** <0.01*** 0.0572*** HHR a3 0.01 0.01 7156.90 6903.38 0.0396*** 0.505** 0.0166*** 0.774** ROR2 a1-1 –0.00 –0.00 117.50 –3595.50 100 21.8 88.4 26.7 DDR2 a2-2 0.01 0.01 5972.10 6676.76 0.921** 5.5 0.401** 8.6 HHR2 a3-3 0.00 0.00 1361.58 388.66 23.5 82.8 15.6 88.9 ROR. DDR a1-2 0.00 –0.00 316.39 –724.57 66.4 70.1 68.2 79 ROR.HHR a1-3 0.00 0.00 586.85 1525.01 50.3 63 50.8 62.2 DDR.HHR a2-3 –0.00 –0.00 –2471.48 –121.56 7.3 94.3 5.1 96.8 C, coefficients. Open in new tab The coefficients of the multivariate regression analysis superscripted with three stars have P-value < 0.1, which is a high signification; those superscripted with two stars have 0.1 < P-value < 1, which is a medium signification; those superscripted with one star have 1 < P-value < 10, which is a low signification; and those with no star have 10 < P-value, which is not significant. Indeed, the P-value signification basis can qualify the three linear regression parameters (a1, a2 and a3), which inform the intensity of dependency of the respective variables of the load profile ROR, DDR and HHR to their responses, NPC and LCOE. So they designate a full dependence on CPS(2). However, on CPS(3) with the introduction of the wind turbine, those parameters have a low dependence with the ROR variable, medium dependence with HHR and the dependence remains crucial with the DDR variable. On the other hand, the quadratic parameter (a22), a coefficient of the only variable DDR2, has a moderate dependency on NPC and LCOE for SPC(2). Nevertheless, it is not significant for SPC(3). Figs 7 and 8 show the iso-response curves from Doehlert through NemrodW® processing, which constitute a projection of the response surface in the horizontal plane. They are interpreted as contour lines onto which the value of the response is projected. Beyond two factors, it is necessary to maintain a constant level of the factors whose variations are insignificant in the horizontal plane. The main factors influencing the NPC amount and the LCOE are the ROR factor corresponding to the reserve rate below peak power (X1) and the DDR factor of the variability in the day-to-day load profile (X2). An increase in ROR in CPS(3) leads to a significant increase in NPC and LCOE and high divergence for DDR < 20%, while DDR almost remains a soft constant elsewhere, showing the same results along with the variation in ROR. However, in CPS(2), the iso-responses in NPC and LCOE are a linear equidistant for increasing ROR and decreasing DDR. Fig. 7: Open in new tabDownload slide Contour plots (top: LCOE, bottom: NPC, HHR left 20% right 10%). Fig. 8: Open in new tabDownload slide Contour plots (top: LCOE, bottom: NPC, HHR left 20% right 10%). On the other hand, they are delimited by contours at HHR at 10% and 20%. The illustrations show the compromise between the NPC amount and the LCOE for the two specifications. They were obtained when the DDR and ROR rates were respectively between two rates DDRmin and DDRmax and RORmin and RORmax, corresponding to a value of LCOE, the cost of the kilowatt-hour unit of produced electricity. So we have imposed a desirable LCOE of US$0.41/kWh as the maximum cost estimated under the variability constraints of the load profile. To determine an acceptable compromise zone, we introduced the desirability in Table 7. The responses were simultaneously optimized using the desirability function approach included in the NemrodW®software (2000-D, LPRAI Corporation, France) [42]. Therefore, the optimal operating conditions that have been obtained for the specifications SPC(2) and SPC(3) studied were chosen for an LCOE cost of US$0.41/kWh and NPC of ~US$320 000 with maximum parameters of DDR = 15.47%, ROR = 17.77% and HHR = 26.55%. Table 7: Results of desirability: maximum coordinates generated from NemrodW® software Variable . Value code . Factors . Value . X1 0.776 088 ROR 17.760 9 X2 –0.453 46 DDR 15.465 4 X3 0.436 92 HHR 26.553 8 Variable . Value code . Factors . Value . X1 0.776 088 ROR 17.760 9 X2 –0.453 46 DDR 15.465 4 X3 0.436 92 HHR 26.553 8 Open in new tab Table 7: Results of desirability: maximum coordinates generated from NemrodW® software Variable . Value code . Factors . Value . X1 0.776 088 ROR 17.760 9 X2 –0.453 46 DDR 15.465 4 X3 0.436 92 HHR 26.553 8 Variable . Value code . Factors . Value . X1 0.776 088 ROR 17.760 9 X2 –0.453 46 DDR 15.465 4 X3 0.436 92 HHR 26.553 8 Open in new tab The boundary conditions are now known. For our application in the tourist accommodation in southern Morocco, we have considered DDR = 15%, ROR = 15% and HHR = 20%. When combining renewable resources with conventional resources, the simulations favoured renewable-energy solutions, with a rate of 98% in the case of CPS(2) and 97% in the case of CPS(3) by the addition of wind power. Wind energy production is available continuously throughout the year because the region is very windy. In the case of the coupling of GE and the GPV in SPC(2), the solar potential is lower during the autumn season between October and January, and a period of capacity shortage dramatically exceeds the capacity of the batteries, hence the intervention of the GE with a rate of 3% (days 9 and 10 June and 18 and 19 December). The introduction of wind power in the SPC(2) configuration has reduced the capacity of the storage system by half. The wind potential begins to decrease from June until November, and seeing that HOMER proposed a storage system of 12 batteries, which is insufficient to cover the energy need, this choice was fixed by the assignment of the string for a step change in the number of batteries. In order to minimize fuel consumption and gas emissions, a readjustment by removing the string (1, which corresponds to a step of 12 V) filled this shortage of renewables by storage in batteries, but with a higher NPC expense. Thus, the proposed scenario is that by readjusting string batteries, there will be no need for generators, thereby reducing fuel consumption to zero, for the benefit of the environment, but NPC expenditures will rise. The latter corresponds well to the previous configuration with a lower-cost NPC of US$320 080.1. 3 Summary and conclusions Hybrid systems have two primary purposes: the total availability of quantitative and qualitative electrical energy at a lower cost, and saving the environment by favouring renewable over conventional energy sources. In light of these objectives, the HOMER tool was designed to make life easier for those involved in the field to have an optimal configuration of a hybrid system combining conventional energy with clean energies with respect for the environment. Design of experiments (simulations) according to the Doehlert matrix was carried out to limit the adequate conditions in terms of the constraints of load-profile variability and reserves to be added in the optimal model and sizing of hybrid systems. This methodological approach is satisfactory for predictive dimensioning work and pre-project studies in the context of urbanizing ecological localities. Therefore, to obtain a competitive cost of LCOE and NPC, fixed respectively at 0.41 US$/kWh and US$320 000 when applying the desirability approach, the limits of the parameters had the following constraints: DDR = 15.47%, ROR = 17.77% and HHR = 26.55%. Therefore, according to the study, we were able to bring out the results of the simulations: The operating reserve ratio and the load-profile variability rates were taken under the limit conditions: DDR = 15%, ROR = 15% and HHR = 20%. Renewable energies in the two specifications SPC(2) and SPC(3) contributed with a rate of >97%. Wind energy and photovoltaics shared this proportion (wind generator 54%, PV 43%). In comparison with SPC(1) composed of generators and batteries, the excess of energy generated through SPC(2) was 22% by adding a photovoltaic field, and 36% for SPC(3) after the addition of a wind generator to SPC(2). The addition of a wind turbine reduced the storage fleet by half. The energy produced only by renewable components covered the load by 84% for wind and 100% for PV. GE produced more than double with the GE–PV–WP system than with GE–PV, replacing the reduction in the battery count from 24 to 12 units. In perspective, these rates will be taken into account for a sizing study of hybrid wind and solar power plants to produce hydrogen. Table 3: Spherical model with interaction parameters Criteria . Test area . Parameters . Number of variables 3 ROR, DDR and HHR Number of tests 15 Number of coefficients 10 a0, a1, a2, a3, a11, a22, a33, a12, a13 and a23 Number of responses 1 LCOE, NPC Criteria . Test area . Parameters . Number of variables 3 ROR, DDR and HHR Number of tests 15 Number of coefficients 10 a0, a1, a2, a3, a11, a22, a33, a12, a13 and a23 Number of responses 1 LCOE, NPC Open in new tab Table 3: Spherical model with interaction parameters Criteria . Test area . Parameters . Number of variables 3 ROR, DDR and HHR Number of tests 15 Number of coefficients 10 a0, a1, a2, a3, a11, a22, a33, a12, a13 and a23 Number of responses 1 LCOE, NPC Criteria . Test area . Parameters . Number of variables 3 ROR, DDR and HHR Number of tests 15 Number of coefficients 10 a0, a1, a2, a3, a11, a22, a33, a12, a13 and a23 Number of responses 1 LCOE, NPC Open in new tab Table 4: Doehlert experiment matrix and corresponding results Number . Standardized variables . . Variables studied . . . . Specifications . . . . . . . . . . . . . SPC(1) GE–B . . SPC(2) BE–PV–B . . SPC(3) BE–PV–WP–B . . . X1 . X2 . X3 . ROR . DDR . HHR . LCOE . NPC . LCOE . NPC . LCOE . NPC . . . . . (%) . (%) . (%) . $/kWh . $US . $/kWh . $US . $/kWh . $US . 1 1 0 0 20 20 20 0.420 311 728 0.415 324 062 0.412 321 631 2 –1 0 0 0 20 20 0.437 339 252 0.399 312 011 0.405 316 814 3 1╱2 3/2 0 15 29 20 0.428 321 808 0.437 341 166 0.440 344 064 4 −1╱2 −3/2 0 5 11 20 0.421 323 315 0.389 303 963 0.396 309 162 5 1╱2 −3/2 0 15 11 20 0.418 313 137 0.398 310 756 0.404 315 466 6 −1╱2 3/2 0 5 29 20 0.439 337 430 0.427 333 825 0.434 339 015 7 1╱2 3╱6 6/3 15 23 32 0.428 321 187 0.426 332 853 0.431 336 962 8 −1╱2 −3╱6 −6/3 5 17 8 0.422 323 222 0.391 305 260 0.396 309 486 9 1╱2 −3╱6 −6/3 15 17 8 0.416 313 242 0.397 310 400 0.403 314 971 10 0 3╱3 −6/3 10 26 8 0.425 321 919 0.418 326 334 0.422 329 405 11 −1╱2 3╱6 6/3 5 23 32 0.441 340 484 0.418 326 572 0.422 329 405 12 0 −3╱3 6/3 10 14 32 0.426 323 180 0.407 317 631 0.411 321 315 13 0 0 0 10 20 20 0.424 321 755 0.407 317 919 0.413 322 818 14 0 0 0 10 20 20 0.424 321 755 0.407 317 919 0.413 322 818 15 0 0 0 10 20 20 0.424 321 755 0.407 317 919 0.413 322 818 Number . Standardized variables . . Variables studied . . . . Specifications . . . . . . . . . . . . . SPC(1) GE–B . . SPC(2) BE–PV–B . . SPC(3) BE–PV–WP–B . . . X1 . X2 . X3 . ROR . DDR . HHR . LCOE . NPC . LCOE . NPC . LCOE . NPC . . . . . (%) . (%) . (%) . $/kWh . $US . $/kWh . $US . $/kWh . $US . 1 1 0 0 20 20 20 0.420 311 728 0.415 324 062 0.412 321 631 2 –1 0 0 0 20 20 0.437 339 252 0.399 312 011 0.405 316 814 3 1╱2 3/2 0 15 29 20 0.428 321 808 0.437 341 166 0.440 344 064 4 −1╱2 −3/2 0 5 11 20 0.421 323 315 0.389 303 963 0.396 309 162 5 1╱2 −3/2 0 15 11 20 0.418 313 137 0.398 310 756 0.404 315 466 6 −1╱2 3/2 0 5 29 20 0.439 337 430 0.427 333 825 0.434 339 015 7 1╱2 3╱6 6/3 15 23 32 0.428 321 187 0.426 332 853 0.431 336 962 8 −1╱2 −3╱6 −6/3 5 17 8 0.422 323 222 0.391 305 260 0.396 309 486 9 1╱2 −3╱6 −6/3 15 17 8 0.416 313 242 0.397 310 400 0.403 314 971 10 0 3╱3 −6/3 10 26 8 0.425 321 919 0.418 326 334 0.422 329 405 11 −1╱2 3╱6 6/3 5 23 32 0.441 340 484 0.418 326 572 0.422 329 405 12 0 −3╱3 6/3 10 14 32 0.426 323 180 0.407 317 631 0.411 321 315 13 0 0 0 10 20 20 0.424 321 755 0.407 317 919 0.413 322 818 14 0 0 0 10 20 20 0.424 321 755 0.407 317 919 0.413 322 818 15 0 0 0 10 20 20 0.424 321 755 0.407 317 919 0.413 322 818 Open in new tab Table 4: Doehlert experiment matrix and corresponding results Number . Standardized variables . . Variables studied . . . . Specifications . . . . . . . . . . . . . SPC(1) GE–B . . SPC(2) BE–PV–B . . SPC(3) BE–PV–WP–B . . . X1 . X2 . X3 . ROR . DDR . HHR . LCOE . NPC . LCOE . NPC . LCOE . NPC . . . . . (%) . (%) . (%) . $/kWh . $US . $/kWh . $US . $/kWh . $US . 1 1 0 0 20 20 20 0.420 311 728 0.415 324 062 0.412 321 631 2 –1 0 0 0 20 20 0.437 339 252 0.399 312 011 0.405 316 814 3 1╱2 3/2 0 15 29 20 0.428 321 808 0.437 341 166 0.440 344 064 4 −1╱2 −3/2 0 5 11 20 0.421 323 315 0.389 303 963 0.396 309 162 5 1╱2 −3/2 0 15 11 20 0.418 313 137 0.398 310 756 0.404 315 466 6 −1╱2 3/2 0 5 29 20 0.439 337 430 0.427 333 825 0.434 339 015 7 1╱2 3╱6 6/3 15 23 32 0.428 321 187 0.426 332 853 0.431 336 962 8 −1╱2 −3╱6 −6/3 5 17 8 0.422 323 222 0.391 305 260 0.396 309 486 9 1╱2 −3╱6 −6/3 15 17 8 0.416 313 242 0.397 310 400 0.403 314 971 10 0 3╱3 −6/3 10 26 8 0.425 321 919 0.418 326 334 0.422 329 405 11 −1╱2 3╱6 6/3 5 23 32 0.441 340 484 0.418 326 572 0.422 329 405 12 0 −3╱3 6/3 10 14 32 0.426 323 180 0.407 317 631 0.411 321 315 13 0 0 0 10 20 20 0.424 321 755 0.407 317 919 0.413 322 818 14 0 0 0 10 20 20 0.424 321 755 0.407 317 919 0.413 322 818 15 0 0 0 10 20 20 0.424 321 755 0.407 317 919 0.413 322 818 Number . Standardized variables . . Variables studied . . . . Specifications . . . . . . . . . . . . . SPC(1) GE–B . . SPC(2) BE–PV–B . . SPC(3) BE–PV–WP–B . . . X1 . X2 . X3 . ROR . DDR . HHR . LCOE . NPC . LCOE . NPC . LCOE . NPC . . . . . (%) . (%) . (%) . $/kWh . $US . $/kWh . $US . $/kWh . $US . 1 1 0 0 20 20 20 0.420 311 728 0.415 324 062 0.412 321 631 2 –1 0 0 0 20 20 0.437 339 252 0.399 312 011 0.405 316 814 3 1╱2 3/2 0 15 29 20 0.428 321 808 0.437 341 166 0.440 344 064 4 −1╱2 −3/2 0 5 11 20 0.421 323 315 0.389 303 963 0.396 309 162 5 1╱2 −3/2 0 15 11 20 0.418 313 137 0.398 310 756 0.404 315 466 6 −1╱2 3/2 0 5 29 20 0.439 337 430 0.427 333 825 0.434 339 015 7 1╱2 3╱6 6/3 15 23 32 0.428 321 187 0.426 332 853 0.431 336 962 8 −1╱2 −3╱6 −6/3 5 17 8 0.422 323 222 0.391 305 260 0.396 309 486 9 1╱2 −3╱6 −6/3 15 17 8 0.416 313 242 0.397 310 400 0.403 314 971 10 0 3╱3 −6/3 10 26 8 0.425 321 919 0.418 326 334 0.422 329 405 11 −1╱2 3╱6 6/3 5 23 32 0.441 340 484 0.418 326 572 0.422 329 405 12 0 −3╱3 6/3 10 14 32 0.426 323 180 0.407 317 631 0.411 321 315 13 0 0 0 10 20 20 0.424 321 755 0.407 317 919 0.413 322 818 14 0 0 0 10 20 20 0.424 321 755 0.407 317 919 0.413 322 818 15 0 0 0 10 20 20 0.424 321 755 0.407 317 919 0.413 322 818 Open in new tab Acknowledgements This study could not have been successful without the Soda-Pro platform, which provided useful wind and solar irradiation data. 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Published by Oxford University Press on behalf of National Institute of Clean-and-Low-Carbon Energy
Clean Energy – Oxford University Press
Published: Jun 1, 2022
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