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An innovative technique for optimization and sensitivity analysis of a PV/DG/BESS based on converged Henry gas solubility optimizer: A case study

An innovative technique for optimization and sensitivity analysis of a PV/DG/BESS based on... INTRODUCTIONOff‐grid power production is one method of providing energy in industrial, commercial, residential, and remote (rural) areas, where it is impossible to connect to the grid in most cases due to the geographically impassable setting and the high transmission expense [1]. In such cases, utilizing local (green/renewable) energy can ease the progression of new systems in these regions. Using options with minimum supply cost is considered a stable and rational way for the expansion of new power systems in these regions [2]. The common off‐grid method of electricity production is to utilize a diesel generator [3–5]. The development of new technologies, however, has resulted in abilities in designing combined systems (the diesel generator in addition to green energy technologies) to provide the required power [6]. It fulfilled the need at a minimum cost.In the novel method, the system is a combination of the diesel generator and green energy resources, namely solar photovoltaic, biomass, biogas, small hydropower, fuel cell, and wind. This combined technology may also utilize a power storing unit (battery) [7]. Thus, in general, a combined system includes diesel generators, batteries, and one or more green energy resources.A hybrid system could be diverse and its application could be various [8]. Different factors affect each combination of the hybrid system, such as accessibility of green energy resources, the geographical setting, economic limitations, and technical restrictions [7]. In an off‐grid energy production unit, the combined system delivers the possibility of producing cost‐effective and green electricity, which is far cheaper than generating electricity with a diesel generator most of the time [9]. Accordingly, green energy resources are the desired way for off‐grid power production. Combined systems as a developing technology have captured imaginations around the world [10, 11]. Several logics for this tendency could be expressed as improving the reliability of electricity supply, improving energy services, emissions and noise reduction, continuous electric power generation, extending the service life of the system, electricity production costs reduction, and optimal energy consumption [12–14]. A hybrid power generation station usually includes the following components:A. Inverter unit with a nominal connected energy of about 60% of the max needed.B. One or two diesel engines with a size of 1 to 1.5 times greater than the size of the inverter.C. The lead‐acid battery storage system.D. Solar photovoltaic arrangement.E. Microprocessor with control unit for automatic system monitoring and management.In the optimization process of the hybrid energy systems, they usually searched for different power supply arrangements according to the limitations, to obtain the most economical mode for the life cycle cost [15, 16]. To model a system including photovoltaic cells, the information on the solar source of the area should be accessible [17, 18]. Then, based on simulations, the amount of energy from renewable resources according to 1‐h steps has been achieved, and for most types of small energy systems, especially those that include intermittent renewable energy sources, 1‐h steps seem to be an accurate scale for analysis.Agarwal et al. [19] examined the optimization of an off‐grid combined solar‐battery‐diesel plant for electricity production in Uttar Pradesh rural regions, India. In this study, a multi‐objective optimal model was developed to identify the appropriate size of the off‐grid combined system. The decision factors considered in the optimization procedure are the total area of photovoltaic panels, yearly fuel consumption, and the power of the diesel generator. An ideal autonomous system design includes a photovoltaic area of 300 m2, 60 photovoltaic panels with 600 Wp, and a diesel generator with 5‐kW output. $110,556 over 25 years LC cost; 1151/year fuel usage; and 0.0189 tCO2/capita carbon dioxide emissions.Lan et al. [20] extracted optimized combined solar panel/battery/diesel size in a ship's electricity system. An approach for finding the finest dimension of the diesel generator, photovoltaic (PV) system, and batteries were described in detail. The generation of power from solar panels on a ship is dependent on the time zone, local time, date, latitude, and longitude within a navigation path. For adjusting the output of PV modules, an algorithm is created that takes seasonal and geographical fluctuations in solar irradiance and temperature into account [21]. To simulate the entire shipload, the suggested technique takes five conditions along the navigation path into account. Four detailed scenarios are examined to illustrate the applicability of the suggested technique.Yahiaoui et al. [22] evaluated integrated solar panel‐diesel‐battery technologies developed for Algeria's remote, rural cities. a diesel generator in conjunction with a photovoltaic array panel power system In this article, battery cells and load are taken into account. The system's overall cost, CO2 emission, and load loss possibility (LLP) have all been reduced using the particle swarm optimizer (PSO). The significance of photovoltaic and battery energy systems is also revealed by this study [23]. Without them, the yearly cost of a diesel generator rises significantly. Eventually, the offered method outcomes were compared with software programs. The suggested technique is also useful for dealing with the reducing costs of a combined system under an unmet load or non‐existence circumstance.Ashraf et al. [24] designed an optimum combination utilizing metaheuristic algorithms for a combined solar energy/battery /diesel electricity production unit. The major goal of their work is to provide a brand‐new, ideal combined system for China's Gobi Desert. The simulation demonstrates that the suggested approach may deliver a dependable augmentation for load needs, with photovoltaic penetration having a significant influence on about 98% of the expenses. According to the outcomes, when compared with the results of the HOMER software and PSO‐based optimum system, the suggested cEHO algorithm's emission of CO2 gas, at 1735 kg/year, is at its lowest level. The system's net current cost is 48,680 dollars, which is less than its initial capital price of 48,680 dollars.Esan et al. [25] evaluated the dependability of an island‐based combined solar panel‐diesel‐battery system for an average Nigerian rural settlement. In this study, a unique method for evaluating the production stability of a combination mini‐grid system (HMS) based on the best design outcome from the HOMER program is presented. The least net existing cost of a solar photovoltaic array, diesel generators, and battery storage is $4,909,206, with a levellized energy rate of $0.396 per kWh. When all three were running, it was seen that the HMS had load losses of 0.769, 0.594, and 0.419 MW. An approximate 97% decrease in all CO2 emissions was seen when comparing the HMS to a diesel‐only system for the neighbourhood.Optimize the system while simultaneously reducing the unmet load, system capital cost, and emissions, the constraint technique, and a meta‐heuristic can be used. The method usually does not require as many additional procedures as Pareto‐based methods do, making it more convenient. The best optimum solution is selected from the obtained solutions for the hybrid system to be used as a sustainable power supply unit. To synthesize the impact of all three parts on the combined system, the research also does a sensitivity analysis. The outcomes of the proposed technique are then contrasted with those obtained using the HOMER environment and a PSO‐based technique from the literature.THE SOLUTION PROCEDUREIn this study, the main aim is to introduce an optimal arrangement of a combined energy source based on a photovoltaic system, diesel generator, and batteries to provide a proper electricity supplier for a remote area in Yarkant County, Taklamakan desert, China [26–28]. The idea is to use an improved version of a newly introduced algorithm, Henry gas solubility for this purpose. Over the next step, we will use the results of the proposed optimal arrangement to validate with some other state‐of‐the‐art methods to show its efficiency. The proposed method can be also utilized for use in different similar areas and also can be extended for use in a different environment. The Taklamakan Desert's meteorological information is gathered from NASA datasets and NREL (the National Renewable Energy Laboratory), and the area is recognized using information from some abandoned buildings and local climatic features. Then, considering the local load figures and datasets, the profiles for load profiles, PV radiation, and temperature fluctuations are created.The modelling of the hybrid system components uses a mathematical approach. Then, the hybrid Diesel/PV/Battery energy system has been optimized using the provided optimization strategy and the ε‐constraint method. The sensitivity analysis is used in the study to examine the effects of each component on the system. For providing easy and optimal results for the system, a metaheuristic technique, based on an improved version of the Henry gas solubility optimization (HGSO) algorithm, has been utilized. The literature study indicates that the original HGSO yields good outcomes for optimization problems, though the algorithm's early convergence may occasionally yield subpar findings. Two crucial changes have been made to the ongoing study to address this problem. The initial improvement has made use of the self‐adaptive weighting concept to control the propensity speed for finding the best solution. In light of this, the position updating model regulates the random value on the terms for the impact of gas exploration and exploitation. The HGSO algorithm begins with an upper distance of exploration, and at the last epochs, local exploration in the solution space reduces the exploration distance. This strikes a balance between the optimizer's exploitation and exploration. The aforementioned approach gradually changes the operator's weight value to narrow the difference between the worst and best solutions. The second development is the application of a chaotic approach to the local optimization problem. By considering the chaotic idea, the problem can occasionally change in terms of temporal complexity. The pseudo‐haphazard amounts of chaos operatives’ ergodic and sequence random properties are extremely advantageous to the method. The work being presented makes use of a scheme plan, a typical chaotic procedure.THE TAKLAMAKAN DESERTNorthwest China's southwestern Xinjiang region contains the Taklamakan Desert. It is bordered to the south by the Kunlun Mountains, to the west by the Pamir Mountains, to the north by the Tian Shan range, and to the east by the Gobi Desert.With a surface size of 337,000 km2, the Taklamakan Desert is just marginally larger than Germany. The Tarim Basin, which is 400 km (250 miles) broad and 1000 km (620 miles) long, includes the desert. Two branches of the Silk Road, used by travelers to bypass the dry wasteland, traverse it at its southern and northern boundaries. The Taklamakan Desert is the second ‐biggest desert with shifting sand globally. Yarkant is a county in the Xinjiang Uyghur Autonomous Region of China. It is situated in the Tarim Basin on the southern edge of the Taklamakan Desert. The total population of this county until 2015 is 851,374. The coordinates for this county are 38°23′27″N 77°13′24″E.The conditional electrical appliances, such as fluorescent lights, and fans, TV and refrigerator are part of the load shape electricity needed for the households in the community. The time interval is set at 1 h, and the daily load profile is taken into account for the two seasons of winter and summer. Figure 1 represents the bar plot for the indicated load figures.1FIGUREThe energy use (kW) bar graph on recommended load figures basis.From Figure 1, we can conclude that the system's minimal and highest demands are 1.05 and 5 kW.In the next phase, the NASA Surface Meteorological information on an hourly basis has been utilized to simplify the collection of meteorological data. Figures 2 and 3 depict the meteorological profile at the study site, which includes the temperature, index of clearness, and daily radiation.2FIGURECase study's clearness index and daily radiation.3FIGURECases study's daily temperature.THE SYSTEM MATHEMATICAL MODELThe suggested HRES's total energy flow design is seen in Figure 4. As can be seen, the suggested combined system includes PV modules, a battery storing bank, and a diesel generator. The PV modules make an effort to meet the necessary load need by holding radiation from the Sun and converting it into electricity. If there is an excess of electricity produced during energy generation beyond the amount needed to power the load, the additional energy can be saved in batteries.4FIGUREThe HRES's overall energy flow design.In contrast, the batteries will assist in meeting the remaining load requirement if the photovoltaic modules were unable to meet the need. Additionally, a diesel generator will be added to the system as a backup power resource to meet the remaining need if it becomes far more than the combined energy of the photovoltaic modules as well as the battery.The mathematical model of each element is described in depth in the upcoming sections.Diesel generatorThe following equation [29] determines the quantity of fuel consumed by the diesel generator (DG):1cfDG=αDG×PnDG+βDG×PoDG$$\begin{equation} c {f}^{DG} = {\alpha }^{DG}\ \times P_n^{DG} + {\beta }^{DG} \times P_o^{DG}\end{equation}$$where PnDG$P_n^{DG}$ and PoDG$P_o^{DG}$ provide the DG's nominal and output power (in kW) and αDG${\alpha }^{DG}$ and βDG${\beta }^{DG}$ indicate the consumption curve's coefficients (L/kWh).The following factors contribute to the diesel generator's performance:2ηDG=PoDGcfDG×LHVf$$\begin{equation}\ {\eta }^{DG} = \frac{{P_o^{DG}}}{{c{f}^{DG} \times LH{V}_f}}\ \end{equation}$$where LHVf$LH{V}_f$ signifies the fuel consumption heating value.Based on [29], in this study, LHVf is limited between 10 kWh/L and 11.6 kWh/L, and αDG and βDG are set 0.25  and 0.08L/kWh$0.08{\rm{\ L}}/{\rm{kWh}}$, respectively.Battery energy storage systemThe battery output current is directly influenced by the resulting energy of the control scheme, the renewable generators, and the SOC [16]. The key to increasing the capacity of the generating system is to regulate the discharging and charging processes of the battery while using the maximal energy of the photovoltaic cells. The equation below describes how much energy the battery system produced and absorbed between t−1$t - 1$ and t3PaBatt=PaBat×t−1×1−σ+Popvt−PoLoadtηin×ηbat$$\begin{eqnarray} P_a^{Bat}\ \left( t \right) &=& P_a^{Bat}\ \times \left( {t - 1} \right) \times \left( {1 - \sigma } \right)\nonumber\\ && +\, \left( {P_o^{pv}\left( t \right) - \frac{{P_o^{Load}\left( t \right)}}{{{\eta }_{in}}}} \right) \times {\eta }_{bat} \end{eqnarray}$$where4Charging:Popvt−PiLoadtηin>0andPaBatt−1<PaBatmaxDischarging:Popvt−PiLoadtηin<0andPaBatt−1>PaBatmin$$\begin{eqnarray}\left\{ { \def\eqcellsep{&}\begin{array}{@{}*{1}{c}@{}} {Charging\!:\ P_o^{pv}\left( t \right) - \dfrac{{P_i^{Load}\left( t \right)}}{{{\eta }_{in}}} &gt; 0\ and\ P_a^{Bat}\left( {t - 1} \right) &lt; \ P_a^{Ba{t}_{max}}}\\[11pt] {Discharging\!:\ P_o^{pv}\left( t \right) - \dfrac{{P_i^{Load}\left( t \right)}}{{{\eta }_{in}}}&lt; {0\ and\ P_a^{Bat}\left( {t - 1} \right)} &gt; \ P_a^{Ba{t}_{min}}} \end{array} } \right.\nonumber\\ \end{eqnarray}$$where PiLoad(t)$P_i^{Load}( t )$ specifies the load demand at time t, σ (here, 1 ×10‐3) describes the battery storage self‐discharge rate, ηbat${\eta }_{bat}$ (here, 0.7) and ηin${\eta }_{in}$ (here, 0.9) define the efficiency for batteries and inverter, respectively,PaBat(t)$\ P_a^{Bat}( t )$ and PaBat(t−1)$\ P_a^{Bat}( {t - 1} )$ represent the battery power availability at t and its previous time (t−1$t - 1$).To increase the lifespan of the battery energy storage system, the higher limitation, (SOCmax$SO{C}^{max}$) and the lower limitation SOCmin$SO{C}^{min}$ () are measured with the entire nominal capacity value in Ah by the following [30]:5SOCmax=PaBat×NBat$$\begin{equation}SO\ {C}^{max} = P_a^{Bat}\ \times {N}^{Bat}\end{equation}$$6SOCmin=PaBat×NBat×1−DoDmax$$\begin{equation}SO\ {C}^{min} = P_a^{Bat}\ \times {N}^{Bat} \times \left( {1 - Do{D}^{max}} \right)\end{equation}$$where DoDmax$Do{D}^{max}$ demonstrates the max deepness rate of the discharging.The battery's supreme lifecycle occurs, whenever the DOD is established from 0.3 to 0.5. As a result, DoDmax=0.3%$Do\ {D}^{max} = \ 0.3\% $.InverterThe inverter's output transmitted power required to meet the load requirement is as follows:7Pinv=PhDηinv$$\begin{equation}\ {P}^{inv} = \frac{{{P}^{hD}}}{{{\eta }_{inv}}}\ \end{equation}$$where ηinv${\eta }_{inv}$ and PhD${P}^{hD}$ represent the inverter efficiency and the hourly demand, respectively.Photovoltaic moduleThe solar system's output power is achieved by taking into account that the inverter has Max Power Point Tracking (MPPT) as follows [31]:8Popv(t)=Fd×Ps×Irrpvt1kWh/m2×1+α100×Tpvt−25$$\begin{eqnarray} P_o^{pv} ( t ) = {F}_d\ \times {P}_s \times \frac{{Ir{r}_{pv}\left( t \right)}}{{1kWh/{m}^2}} \times \left[ {1 + \frac{\alpha }{{100}} \times \left( {{T}_{pv}\left( t \right) - 25} \right)} \right]\nonumber\\ \end{eqnarray}$$where α describes the coefficient of the power temperature (°C), Irrpv(t) specifies the radiation over the curved area of the photovoltaic sheets, Ps${P}_s$ defines the resulted energy in standard testing circumstances (STC), Fd${F}_d\ $determines the factor of the power losses (0.9), and Tpv(t)${T}_{pv}( t )$ determines the PV cell temperature gained by Equation (9)9Tpv(t)=TNOC−200.8×Irrpvt1kWh/m2+Tambt$$\begin{equation}{T}_{pv} (t) = \left[ {\frac{{{T}_{NOC} - 20}}{{0.8}}} \right]\ \times \frac{{Ir{r}_{pv}\left( t \right)}}{{1kWh/{m}^2}} + {T}_{amb}\left( t \right)\end{equation}$$where Tamb(t)${T}_{amb}( t )$ and TNOC${T}_{NOC}$ describe the environmental temperature and the theoretical operating temperature of the cell.CONVERGED HENRY GAS SOLUBILITY OPTIMIZATION ALGORITHMStandard Henry gas solubility optimizer (HGSO)In this part, the mathematical expression of the HGSO is presented. The phases of mathematical are noted as follows:Stage 1: Operation of initialization. The swarm size (N) means the gases; quantity and the initialization for the location of the gases are based on the following equation:10Yi(t+1)=Ymin+r×Ymax−Ymin$$\begin{equation}{Y}_i ( {t + 1} ) = {Y}_{min}\ + r \times \left( {{Y}_{max} - {Y}_{min}} \right)\end{equation}$$where Yi${Y}_i$ defines the situation of the ith gas in N swarm, r indicates a random amount in the interval [0,1], and the limitations of the problem are represented by Ymax${Y}_{max}$, Ymin${Y}_{min}$; t indicates the iteration time. The initialization of the gas partial pressure Pi,j${P}_{i,j}$ in group j, ∇solE/R${\nabla }_{sol}E/R$ steady amount of the jth$j{\rm{th\ }}$type (Cj)$( {{C}_j} )$, and amounts of Henry's constant for jth$j{\rm{th\ }}$type (Hj(t))$( {{H}_j( t )} )$ are as follows:11Hj(t)=s1×rand(0,1),Pi,j=s2×rand0,1,Cj=s3×rand0,1$$\begin{eqnarray} {H}_j( t ) &=& {s}_1\ \times rand ( {0,1} ),{P}_{i,j} = {s}_2\ \times rand\left( {0,1} \right),\nonumber\\ {C}_j &=& {s}_3\ \times rand\left( {0,1} \right) \end{eqnarray}$$where s1=5E−02${s}_1 = \ 5E - 02$, s2=100${s}_2 = \ 100$, and s3=1E−02${s}_3 = \ 1E - 02$.Stage 2: Grouping. The factors of the swarm are split into identical groups equivalent to the numeral of gas kinds. Any group includes analogous gases and thus has the identical Hj${H}_j$(Henry's constant).Stage 3: Assessment. The gas that has the highest equilibrium condition among other gases of its kind is identified as the best gas through the assessment of any j cluster.Stage 4: Updating Henry's coefficient. The following equation is used to update Henry's coefficient:12Hj(t+1)=Hjt×exp−Cj×1Tt−1Tθ,T(t)=exp−titer$$\begin{eqnarray} {H}_j( {t + 1} ) &=& {H}_j\ \left( t \right) \times \exp \left( { - {C}_j \times \left( {\frac{1}{{T\left( t \right)}} - \frac{1}{{{T}^\theta }}} \right)} \right),\nonumber\\ T( t ) &=& {\rm{exp}}\left( { - \frac{t}{{iter}}} \right) \end{eqnarray}$$where Henry's coefficient related to cluster j is indicated by Hj${H}_j$; T and Tθ${T}^\theta $ define the temperature and a constant amount equal to 298.15; the whole numeral of iterations is described by iter$iter$.Stage 5: Updating of solubility. The following equation is used to update the solubility:13Ki,j=l×Hjt+1×Pi,jt$$\begin{equation}\ {K}_{i,j} = l \times {H}_j\left( {t + 1} \right) \times {P}_{i,j}\left( t \right)\end{equation}$$where Pi,j${P}_{i,j}$ and Ki,j${K}_{i,j}$ represent the partial pressure and solubility of gas i in the jth group; l indicates a constant.Stage 6: Updating of location. The following equation is used to update the location:Yi,j(t+1)=Yi,jt+F×r×γ×Yi,bt−Yi,jt+F×r×α×Ki,jt×Ybt−Yi,jt$$\begin{eqnarray*} {Y}_{i,j}( {t + 1} ) &=& {Y}_{i,j}\ \left( t \right) + F \times r \times \gamma \times \left( {{Y}_{i,b}\left( t \right) - {Y}_{i,j}\left( t \right)} \right)\nonumber\\ && +\, F \times r \times \alpha \times \left( {{K}_{i,j}\left( t \right) \times {Y}_b\left( t \right) - {Y}_{i,j}\left( t \right)} \right) \end{eqnarray*}$$14γ=β×exp−Fbt+εFi,jt+ε,ε=0.05$$\begin{equation}\gamma = \beta \times \exp \left( { - \frac{{{F}_b\left( t \right) + \varepsilon }}{{{F}_{i,j}\left( t \right) + \varepsilon }}} \right),\ \varepsilon = 0.05\end{equation}$$where Yi,j${Y}_{i,j}$ denotes the ith$i{\rm{th}}\ $gas situation in set j, t and r indicate the iteration time and a random constant. Yi,b${Y}_{i,b}$ is the finest gas i in the jth group, and Yb${Y}_b$ is the finest gas in the population. The capability of gas i in jth group for interacting with the gases in the same set is represented by γ. α=1$\alpha = 1$ which represents the effect of other gases on ith$i{\rm{th}}\ $gas in group j, β indicates a constant. The ith$i{\rm{th}}\ $gas fitness in set j is defined by fi,j${f}_{i,j}$; the finest gas fitness in the whole system is also indicated by Fb${F}_b$. For providing diversity ( =±$ = \ \pm $) and altering the direction of the search factor F (the flag) is used. Two variables that create stability between exploitation and exploration steps are expressed by Yi,b${Y}_{i,b}$ and Yb${Y}_b$, each of these two variables specifies the finest gas i in the jth group and the finest one in the whole swarm.Stage 7: Escaping from local optimum. This stage is utilized to avoid getting stuck in the local optimal answers. The worst factor's quantity (Nw${N}_w$) is classified and chosen as below15Nw=N×randc2−c1+c1,c1=0.1andc2=0.2$$\begin{eqnarray}\ {N}_w = \ N \times \left( {rand\left( {{c}_2 - {c}_1} \right) + {c}_1} \right),\ \ {c}_1 = \ 0.1\ and\ \ {c}_2 = \ 0.2\nonumber\\ \end{eqnarray}$$where N indicates the number of search factors.Stage 8: Updating the location of the worst factors.16D(i,j)=Dmin(i,j)+r×(Dmax(i,j)−Dmin(i,j)$$\begin{equation} {D}_{({i,j})} = {D}_{min}( {i,j} ) + r \times ({D}_{max}( {i,j}) - {D}_{min}({i,j} )\end{equation}$$Here, D(i,j)${D}_{( {i,j} )}$ represents the location of gas i in group j, r indicates a random amount, and Dmin${D}_{min}$, Dmax${D}_{max}$ illustrate the scope of the solution area.At last, the offered optimizer's pseudo‐code is given in Algorithm 1, containing the primary swarm, swarm assessment, and variables of updating.1ALGORITHMHGSO optimizer's pseudo‐code1:Initializing: Yi(i=1,2,…,N)${Y}_i( {i = 1,2, \ldots ,N} )$, number of gas kinds i, Hj${H}_j$, Pi,j${P}_{i,j}$, cj${c}_j$, s1, s2, and s3.2:Split the population factors into the gas kinds’ quantity (set) with the identical Hj${H}_j$.3:Assess any set j.4:Achieve the finest gas Yi,b${Y}_{i,b}$in any cluster and the finest search factor Yb${Y}_b$.5:Do until t<$t &lt; $max number of iterations6:do for any search factor7:Update the locations of whole search factors.8:end for9:Update Hj${H}_j$of any gas kind.10:Update the solubility of any gas.11:Categorize and select the worst factors’ number.12:Update the location of the worst factors.13:Update the finest gas Yi,b${Y}_{i,b}$, and the finest search factor Yb${Y}_b$.14:end while15:t=t+1$t = t + 1$16:return Yb${Y}_b$HGSO, SA (simulated annealing), and important observation employ the identical gas rule, while there have been distinctions in their systems. The modelling of the annealing operation of data is done in SA, and a novel location is created at any epoch at random. The space between the novel location and the present is based on the possibility distribution that is corresponding to the temperature. Therefore, SA is not able to permanently select the finest solution that results in a local optima getaway. In Henry gas solubility optimizer, the exploration factors are separated into classes and the constant of gas is identical for any class, the location alters proportionate to the value of solubility from the cost function utilizing expressed equation.Consider that the proposed algorithm comprises exploitation and exploration stages, as a global optimizer. Likewise, for easy understanding and the implementation of the algorithm, the number of set operators has been minimized. The calculation complication of the suggested procedure is O(tnd)$O( {tnd} )$ in which t displays the max numeral of epochs, n stands for the numeral of answers, and d denotes the numeral of variables. Each answer is homogeneous; this is the complicatedness of the optimizer irrespective of the cost function. Hence, the total complicatedness containing the cost function (obj)$( {obj} )$ is computed as O(tnd)∗O(obj).$O( {tnd} )*O( {obj} ).$Exploration and exploitation stagesBy fine‐tuning the appropriate randomness amount, the stability among the exploitation and exploration stages is managed, and the algorithm can move out of each local optimum and starts searching globally. The Henry gas solubility optimizer has three principal managing variables: ki,j${k}_{i,j}$, γ, and F. (1) ki,j${k}_{i,j}$ indicates the ith$i{\rm{th}}\ $gas solubility in set j and is based on the time of repetition [32, 33]. Therefore, the exploration factors are transferred from the global to the local stage in addition to transferring to the finest location; thus, this gains the most suitable equilibrium among exploitation and exploration characteristics. (2) γ is the capability of gas i in the jth set for interacting with the same set of gases and intends to move the exploration factors from global to local step and vice versa following the condition of a specified case. (3) While the variable F represents a flag that alters the orientation of the exploration factor and supplies variety = ±, this offers a great option to alter the orientation of exploration for some factors to present the power to discover a certain area intently.The decreased mean value indicates exploitation and the increased mean distance in the dimensions of the population individual refers to exploration in this study. This means that the search factors are located near one another. In the circumstance of unimportance distinction in average diversity amounts throughout numerous repetitions, it could be stated that the optimizer has achieved a condition of convergence [34]. The measurement‐wise variety throughout the repetition of the exploration approach was estimated as below:171Divj=1N∑i=1Nmedianyj−yijDivt=1N∑j=1DDivj$$\begin{equation}\ \frac{1}{{Di{v}_j}} = \frac{1}{N}\ \mathop \sum \limits_{i = 1}^N median\left( {{y}^j} \right) - y_i^jDi{v}^t = \frac{1}{N}\ \mathop \sum \limits_{j = 1}^D Di{v}_j\end{equation}$$where yij$y_i^j$ indicates jth dimension of ith swarm individual and median (yj${y}^j$) denotes the median amount of jth dimension of total the swarm. Divi$Di{v}_i$ defines average diversity amount for measurement j. This measurement‐wise diversity is next balanced (Divt$Di{v}^t$) on whole D dimensions for epoch t and t=1,2,3,…,iter$t = 1,\ 2,\ 3,\ \ldots ,\ iter$. When swarm diversity is calculated for epochs iter$iter$, where iter$iter$ is the maximum epochs the search approaches were performed, then it is feasible to specify how much the explorative and exploitative features of the method were [35]. The mensuration of exploitation/exploration value could be specified utilizing the below formula:Exploration%=fracDivtDivmax×100$$\begin{equation*}Exploration\% = frac{{Di{v}^t}}{{Di{v}_{max}}}\ \times 100\end{equation*}$$18Exploitation%=fracDivt−DivmaxDivmax×100$$\begin{equation}Exploitation\% = frac{{\left| {Di{v}^t - Di{v}_{max}} \right|}}{{Di{v}_{max}}}\ \times 100\end{equation}$$where Divt$Di{v}^t$ describes swarm diversity of tth iteration and Divmax$Di{v}_{max}$ defines the maximum diversity located in every T iteration.Converged HGSO (cHGSO)According to the literature study, the original HGSO produces good results for optimization problems, although the algorithm's early convergence might occasionally provide unsatisfactory results. To address this issue, two key improvements have been made in the ongoing study. The self‐adaptive weighting idea has been used in the initial improvement in managing the tendency speed for arriving at the most optimal solution [36, 37]. Having this in mind, the model of location updating controls the random value on the terms for gas exploration and exploitation impact [38]. The initial rounds of the HGSO algorithm explore with an upper distance of exploring, and at the final epochs, the exploration distance is narrowed by a local exploration in the solution space. This balances the exploitation and exploration of the optimizer. The following equation applies this strategy to the random moving term:19Yi,jnew(t+1)=Yi,jnew(t+1)=Yi,j(t+1)+ζ×(Yi,jbest−Yi,j(t))×r,rand>0.5Yi,jnew(t+1)=Yi,j(t+1)−ζ×(Ycibest−Yi,j(t))×r,rand≤0.5$$\begin{equation} Y_{i,j}^{new}({t + 1}) = \left\{ \def\eqcellsep{&}\begin{array}{@{}*{1}{l}@{}} Y_{i,j}^{new} ({t\! +\! 1}) = {Y}_{i,j}({t\! +\! 1})+ \zeta \times ({Y_{i,j}^{best}\! -\! {Y}_{i,j}(t)})\\[5pt] \quad \times\, r,\ rand &gt; 0.5\\[5pt] Y_{i,j}^{new} ({t\! +\! 1}) = {Y}_{i,j} ({t\! +\! 1}) - \zeta \times\, ({Y_{ci}^{best}\! -\! {Y}_{i,j}(t)})\\[5pt] \quad \times\, r,\ rand \le 0.5 \end{array} \right. \end{equation}$$Here,20ζ=fYi,jbestfYi,jworst2,iffYi,jworst≠01,iffYi,jworst=0$$\begin{equation} \zeta = \left\{ \def\eqcellsep{&}\begin{array}{ll} {{\left( {\frac{{f\left( {Y_{i,j}^{best}} \right)}}{{f\left( {Y_{i,j}^{worst}} \right)}}} \right)}}^2, &\quad if\ f\left( {Y_{i,j}^{worst}} \right) \ne 0\\[11pt] 1,&\quad if\ f\left( {Y_{i,j}^{worst}} \right) = 0 \end{array} \right.\ \end{equation}$$where f(Yi,jbest)$f( {Y_{i,j}^{best}} )$, and f(Yi,jworst)$f( {Y_{i,j}^{worst}} )$, in turn, represent the worst and the finest answer of the cost function.To reduce the gap between the worst and best solutions, the aforementioned method progressively alters the operator's weight value. The adoption of a chaotic method to address the local optimization problem is the second advancement. Sometimes, the problem can be changed in terms of temporal complexity by taking the chaotic notion into account.The method can benefit greatly from the ergodic and sequence random properties of chaos operatives, which are pseudo‐haphazard amounts. The work that is being presented employs a strategy plan, a common chaotic technique. This method was developed by doing the following equation:21βi+1=βi+ϕi×βi$$\begin{equation}\ {\beta }^{i + 1} = {\beta }^i\ + {\phi }_i \times {\beta }^i\end{equation}$$where22ϕi+1=4ϕi1−ϕi$$\begin{equation}\ {\phi }_{i + 1} = \ 4{\phi }_i\left( {1 - {\phi }_i} \right)\end{equation}$$where ϕi${\phi }_i$ defines the value of the ith chaotic iteration. ϕ1 is considered the initial value that is equal to 0.5.Validation of the proposed converged HGSOThe proposed convergent HGSO is applied to 10 standard benchmark functions with unimodal and multimodal problems, to validate its accuracy and precision, and the results are compared with various published techniques. Owl Search Algorithm (OSA) [39], Squirrel search algorithm (SSA) [40], Pigeon‐Inspired optimizer [41], and original HGSO are the algorithms that are being compared. The technique was tested on a laptop with MATLAB version 2017b installed on windows 10 64‐bit version with AMD A4 3600 processor and 8 GB RAM.The main objective is to minimize any one of the 10 benchmark functions. As a result, each algorithm's lowest possible value proves that it is more effective than the others. Table 1 displays the set parameters for the investigated methods.1TABLESet parameters for the investigated methodsAlgorithmParameterValueOwl search algorithm (OSA) [39]Tdead${T}_{dead}$16|P|$| P |$8Acclow$Ac{c}_{low}$0.4Acchigh$Ac{c}_{high}$1Squirrel search algorithm (SSA) [40]Nfs${N}_{fs}$5Gc${G}_c$2.1Pdp${P}_{dp}$0.2Pigeon‐inspired optimization (PIO) algorithm [41]Space dimension15Map and compass factor0.1Map and compass operation limit160Landmark operation limit250w1C11.3C21.3Each optimizer is separately run 25 times on every function to test the efficacy of the algorithms, and the average value and STD value are validated based on these runs to generate reliable results. Table 2 lists the rankings of the benchmark functions among the algorithms.2TABLEEvaluations of the test functions for the proposed cHGSO algorithm and the other comparison algorithmsBenchmarkcHGSOHGSOOSA [39]SSA [40]PIO [41]f1AVG0.003.254.334.613.09STD0.001.543.083.211.06f2AVG0.914.155.124.834.25STD0.823.124.983.673.02f3AVG0.004.25 × 10−91.21 × 10−84.15 × 10−84.35 × 10−9STD0.000.002.34 × 10−64.41 × 10−43.25 × 10−6f4AVG0.000.004.25 × 10−85.17 × 10−75.31 × 10−8STD0.000.003.38 × 10−74.53 × 10−72.40 × 10−8F5AVG0.001.352.153.021.84STD0.002.513.384.272.34F6AVG0.033.254.514.103.80STD0.002.132.813.852.13F7AVG0.003.523.743.833.26STD0.221.041.781.381.08F8AVG0.000.270.730.650.21STD0.240.780.961.080.87F9AVG0.000.080.760.980.33STD0.000.010.511.070.13F10AVG0.001.251.031.121.1STD0.000.620.850.910.83As can be observed from Table 2, when compared to other comparable techniques, the converged HGSO algorithm yields the lowest value for the mean measure and exhibits greater accuracy. When compared to several runs by using various methodologies, the proposed optimizer also produces the lowest standard deviation (STD) value, demonstrating more reliability.THE ε‐CONSTRAINT PROCEDUREThis approach was first introduced in 1971. In this method, the goal is to optimize the objective functions in such a way that we choose one of the objective functions and to minimize this objective function, we convert the other objective functions into constraints. Note that these constraints (εi${\varepsilon }_i$) will be unequal. A multi‐objective problem is assumed for more explanation:23MinF1x,F2x,…,Fnx$$\begin{equation}Min\ \left( {{F}_1\left( x \right),\ {F}_2\left( x \right), \ldots ,\ {F}_n\left( x \right)} \right)\ \end{equation}$$where n specifies the number of objective functions, Fi|i=1,2,…,n${F}_{i|i = 1,2, \ldots ,n}$ illustrates the cost functions, and x demonstrates the optimization variables. x∗${x}^*$ is an optimal solution providing that no other practicable answer x exists that Fi(x)≤Fi(x∗)${F}_i( {\rm{x}} ) \le {F}_i( {{{\rm{x}}}^{\rm{*}}} )$.Therefore, by considering Fk|k=1,2,…,n${F}_{k|k = 1,2, \ldots ,n}$ as the key function and the others (Fi|i=1,2,…,n${F}_{i|i = 1,2, \ldots ,n}$) as constraints, we have24MinFkx$$\begin{equation}Min\ {F}_k\left( x \right)\ \end{equation}$$s.t.25Fix≤εi$$\begin{equation}{F}_i\left( x \right) \le {\varepsilon }_i\end{equation}$$where i≠k$i \ne k$, x describes the feasible solution, εi${\varepsilon }_i$ signifies the objective functions that do not exceed.PROBLEM FORMULATIONCost functionIn this study, for the optimal arrangement of the proposed combined system, the emission of CO2$C{O}_2$, the annual LLP, and ACS (annual cost of the system) have been considered for optimization. Based on the ε‐constraint method, we select ACS as the key cost function and the emission of CO2$C{O}_2$ and the LLP as the limitations of the optimization problem. Therefore, the cost function can be considered as follows:26ACS=Ccpt+Crpm+Co&m+Cfuel$$\begin{equation}ACS\ = {C}_{cpt}\ + {C}_{rpm} + {C}_{o\& m} + {C}_{fuel}\end{equation}$$where Ccpt${C}_{cpt}$, Co&m${C}_{o\& m}$, Crpm${C}_{rpm}$, and Cfuel${C}_{fuel}$ represent the yearly capital, maintenance and operational, replacement, and fuel costs, respectively.In the equation above, the annual replacement cost, including the battery storage replacement pending the lifetime, has been achieved by the equation below [42]:27Crpm=CrpmBat×Fsffrir,tR$$\begin{equation}\ {C}_{rpm} = C_{rpm}^{Bat}\ \times {F}_{sff}\left( {{r}_{ir},{t}_R} \right)\end{equation}$$where tR${t}_R$ and CrBat$C_r^{Bat}$ represent, in turn, the yearly lifespan of the battery storage, and the battery replacement cost. Fsf${F}_{sf}$ here describes the reducing fund coefficient and is calculated based on Equation (28) [42]:28Fsf=ri1+ritR−1$$\begin{equation}\ {F}_{sf} = \frac{{{r}_i}}{{{{\left( {1 + {r}_i} \right)}}^{{t}_R} - 1}}\ \end{equation}$$where ri${r}_i$ describes the interest rate on yearly basis and is achieved by the following formula:29rir=rir′−F1+F$$\begin{equation}\ {r}_{ir} = \frac{{\left( {r}_{ir}^{\prime} - F \right)}}{{\left( {1 + F} \right)}}\ \end{equation}$$where F and rir′${r}_{ir}^{\prime}$ define, in turn, the annual inflation rate and the nominal interest ratio, respectively.The annual capital cost can be achieved by the following equation:30Ccpt=Ccptd×Fcrfi,tl$$\begin{equation}\ {C}_{cpt} = C_{cpt}^d\ \times {F}_{crf}\left( {i,\ {t}_l} \right)\end{equation}$$where tl${t}_l$ and Ccptd$C_{cpt}^d$ represent, in turn, the annual project lifetime and the devices' capital cost, and Fcrf${F}_{crf}$ states the capital recovery element and is achieved as31FcR=ri×1+ritl1+ritl−1$$\begin{equation}\ {F}_{cR} = \frac{{{r}_i \times {{\left( {1 + {r}_i} \right)}}^{{t}_l}}}{{{{\left( {1 + {r}_i} \right)}}^{{t}_l} - 1}}\ \end{equation}$$where ri${r}_i$ demonstrates the real interest ratio within a year.Finally, the yearly operation and maintenance cost has been achieved as follows:32Co&m=Co&m1t×1+ritl$$\begin{equation}\ {C}_{o\& m} = C_{o\& m}^{1{\rm{t}}}\ \times {\left( {1 + {r}_i} \right)}^{{t}_l}\end{equation}$$where Co&m1t$C_{o\& m}^{1{\rm{t}}}$ describes the operation maintenance cost.Table 3 represents the parameter value of the proposed hybrid system for simulation.3TABLEParameters value of the proposed hybrid system for simulationParametersValueUnitParametersValueUnitMPPT efficiency90%Battery banks reliability0.82–Inflation rate7.75%Inverter reliability0.87–Yearly interest ratio8.05%Battery banks lifespan8YearsPV panel cost2.4$/kWProject lifetime22YearsDiesel generator cost361$/kWPhoto voltaic panel lifetime21YearsSingle inverter cost732$/kWInverter lifetime22YearsBattery expense327$/kWhFuel expense0.14$/LReliability of diesel generator0.81–Emission coefficient2.2kg/LPV modules reliability0.91–ConstraintsAs aforementioned, the LLP and the CO2$C{O}_2$ emissions are two functions that have been turned into constraints during the ε‐constraint method. The CO2$C{O}_2$ emission which is made by the diesel generator is the main reason for the pollution. So, considering this term is too important to design. This term can be mathematically considered by the following equation:33CO2emm=∑t=18800Fct×Fe$$\begin{equation}C O_2^{emm} = \mathop \sum \limits_{t = 1}^{8800} {F}_c\left( t \right) \times {F}_e\ \end{equation}$$where the CO2emm$CO_2^{emm}$ is limited and should have a value smaller than (or equivalent to) the permissible emission (εLLP${\varepsilon }_{LLP}$), and Fc${F}_c$ and Fe${F}_e$ represent the fuel consumption of the DG and the DG emission factor which is limited from 2.41 to 2.81 kg/L [43].The LLP is the second term as a limitation. The LLP phrase defines the generation likelihood that, at some moment over a specific time window, is insufficient to meet the load demand and is accomplished as follows [43, 44]:34LLP=frac∑t=18800Ult∑t=18800Det$$\begin{equation}LLP = frac{{\mathop \sum \nolimits_{t = 1}^{8800} {U}_l\left( t \right)}}{{\mathop \sum \nolimits_{t = 1}^{8800} {D}_e\left( t \right)}}\ \end{equation}$$where De(t)${D}_e( t )$ and Ul(t)${U}_l( t )$ represent the electricity demand and unfulfilled load throughout the time period t. It should be noted that the LLP term ought to be smaller than (or equal to) the permissible index of LLP reliability (εLLP${\varepsilon }_{LLP}$).Furthermore, the batteries number and the capacity of the battery storage are considered two other constraints, that is,35NBat,NPV,PnDG≥0$$\begin{equation}{N}^{Bat,}\ {N}^{PV},P_n^{DG} \ge 0\end{equation}$$36CminBat≤CBatt≤CmaxBat$$\begin{equation}C_{min}^{Bat} \le {C}^{Bat}\left( t \right) \le C_{max}^{Bat}\end{equation}$$Also, the constrained produced energy by the devices (Ej(t)${E}_j( t )$) can be considered by the following equation:37Ejt≤PjΔt$$\begin{equation}{E}_j\left( t \right) \le {P}_j{{\Delta}}t\end{equation}$$where Δt${{\Delta}}t$ describes the period (Δt=1h${{\Delta}}t = 1\ h$).Optimization methodologyBased on the explanations stated before, this work's main aim is to design an optimum arrangement for a combined battery/PV/ diesel generator system using an improved HGSO. Because of the problem complexity due to designing a multi‐objective strategy, the ε‐constraint technique is utilized. The three objectives of the study include CO2$C{O}_2$ emissions, the system's entire cost, and LLP.Here, based on the ε‐constraint method, the two first terms are considered as constraints and the third one is chosen as the cost function [45]. The decision variables for the mentioned optimization problem are a three‐variable vector, including the battery storage size, the DG valued volume, and the size of PV panels, that is: NPV${N}^{PV}$,NBat$\ {N}^{Bat}$, andPoDG$\ P_o^{DG}$, such that every different parameter shows a different pattern [46]. Figure 5 illustrates the diagram of the designed system in a flowchart for an optimum pattern of the hybrid using the improved HGSO algorithm and the ε‐constraint.5FIGUREGeneral diagram flowchart of the proposed optimal hybrid system.According to the annual undesired load, the annual fuel usage in the DG, and the pollution for each individual, the simulation model is assessed. After that, the produced values are sent to the improved HGSO algorithm to see if it can be done given the limitations. If the target under consideration is unsatisfactory, this amount is created and sent to the stage of optimization. After the stopping criterion has been reached, the optimum answers are likely to be returned.RESULTS AND DISCUSSIONSThe hourly modelling outcomes for the combined system are examined based on the proposed improved HGSO algorithm and a comparison is conducted among the results, HOMER, and PSO [47] under a specific load, and are discussed in this section. Here, if the photovoltaic system along with the battery energy storage system (backup system) could not fulfill the load need, the DG can be provided for supplying the remained demand. As a result, the DG can be utilized for supplying sufficient energy to meet the main load.During the simulation, the valued volume of DG is limited between 2 and 15 kW, the number of photovoltaic cells is limited between 5 and 110, and the number of battery cells is limited between 5 and 55. The main idea of using the combination of the ε‐constraint method and cHGSO algorithm is to optimum choice of the considered decision parameters to make the system yearly basis cost min as the main objective function and considering the CO2 emissions and LLP as constraints. The economical parameters of the modelling are illustrated in Table 4 (US$).4TABLEEconomical parameters of the simulation (US$)CcptCfuelCo&mCrpmACSConverter418.50201.4200.4852.4Diesel generator200.7115110.70475.8Battery bank1711.60805.618074429.7PV subsystem2854.90122.302827.3Total5185.711512402007.48585.2With regard to Table 4, the entire annual cost for the designed system is 8585.2 $. This system considers the variables’ optimal value as 10 kWp of PV generator, 8 kW of the DG, and 48 kWh of battery storage. Figures 6 and  7 show the rate of elements’ energy production and battery storage capacity during the intra‐hourly oscillation in winter (19th of Sep) and summer (the 5th of Mar) seasons, respectively.6FIGUREThe rate of elements’ energy production and battery storage capacity during the intra‐hourly oscillation in winter.7FIGUREThe rate of elements energy production and battery storage capacity during the intra‐hourly oscillation in summer.As previously stated, the battery storing bank is included as a backup system for solar PV due to the batteries’ SOC (situation of charge) providing that the electricity production based on the solar system is unable to deliver the needed load. The DG system has been included as a backup unit to satisfy the load requirement if these two power generators were unable to do so. The radiation of the Sun is a crucial factor that directly influences the energy output of the diesel generator. These radiations are plainly visible in cold weather and demonstrate that their magnitude is sufficient to meet the load requirement. Figure 8 shows monthly changes in the power production of elements.8FIGUREMonthly changes in the power production of elements.Regarding the results, the battery bank is directly impacted by the electricity generated by the photovoltaic system, and the diesel generator is adversely impacted. The storage system's maximum value is used in October and March.Sensitivity analysis is used to examine and pinpoint the changes that have the greatest impact on the system. The constraints are εLLP${\varepsilon }_{LLP}$, εCO2${\varepsilon }_{C{O}_2}$, and load consumption that was previously discussed are examined in this study.We make the assumption that the load fluctuates between 1 and 38 kWh per day while the other components—the size of the PV array, the battery bank, and the DG —remain unchanged for the sensitivity analysis of the load consumption. The presented system heavily leans on a diesel generator to make up for the lack of power caused by the increased load. Table 5 illustrates the system load variations.5TABLESystem load variationsThe additional load (kWh/day)PV penetration (%)LLP (%)Co2 (kg per year)COE ($/kWh)ACS (US$)195.1022570.378467.3392.8025190.368319.3590.5027370.358461.2787.1033420.358544.11184.3038170.348769.61382.4042550.348844.11581.9045340.338864.41777.4051590.338906.61974.8072460.328946.22271.30.7878210.318988.42569.61.981090.309149.33065.13.593150.279207.03563.75.898110.269276.63861.96.410,1420.259281.6As seen in Table 5, the specified reliance on the diesel generator backup system raises the system's yearly cost from 8467.3 to 9281.6 dollars (an increase of around 8.04%) through increasing fuel usage. Obviously, the LLP rises from zero to about 8.7% and the carbon dioxide emissions grow from 2257 to 10,142 kg per year.Additionally, it can be deduced that the drop in photovoltaic penetration from 95.1% to 61.9% causes the value of the cost of electricity to drop from 0.37 to 0.25 dollars per kilowatt‐hour. This decline shows that the cost of fuel has a greater impact on the cost of electricity than the cost of a photovoltaic system since traditional power generation is less expensive than power generation using a photovoltaic system.Table 6 shows how the size of the battery, the photovoltaic system, and the diesel generator are affected by the term, εCO2${\varepsilon }_{C{O}_2}$.6TABLEEffect of εCO2${{\rm{\varepsilon }}}_{{\rm{CO}}_2}$ on the three analyzed parametersεCO2${{\bm{\varepsilon }}}_{{\bm{C}}{{\bm{O}}}_2}{\bm{\ }}$(kg per year)Power of PV (kWp)Capacity of battery bank (kWh)DG capacity (kW)6018.64558018.145510017.944520017.444530016.844540015.543550015.2435100013.9425200012.4415300011.7395400010.837550009.336560009.131580008.7285As can be observed from Table 6, the battery bank capacity has grown from 28 to 45 kWh whenever εCO2${\varepsilon }_{C{O}_2}\ $rang varies from 8000 to 60 kg/year, which has a significant influence on battery bank dimensions. The consequence of εLLP${\varepsilon }_{LLP}$ on the three analyzed parameters is demonstrated in Table 7. The effect of the εLLP${\varepsilon }_{LLP}$ on the capacity of battery banks, the photovoltaic, and the diesel generator system has been illustrated. The size of battery banks also has a significant impact on the εLLP${\varepsilon }_{LLP}$, where it lessens from 21.8 to 16 kWh whenever it is placed in the range of zero to two. Table 8 illustrates the system's economical outcomes.7TABLEEffect of εLLP${{\rm{\varepsilon }}}_{{\rm{LLP}}}\ $on the three analyzed parametersεLLP${{\bm{\varepsilon }}}_{{\bm{LLP}}}{\bm{\ }}$(kg per year)Power of PV (kWp)Capacity of battery bank (kWh)DG capacity (kW)0621.830.16.41820.25.91820.35.71820.45.61620.55.81620.66.11620.76.31620.86.216215.91621.56.116226.11628TABLEThe system economical results ($)NPCElementInitialReplacementM&OFuelSalvageOverallPhotovoltaic26,485025340029,019Generator 12240019631265−1185350Hoppecke 10 OPzS 150016,245954812950−105526,033Converter514816243980−3236847System50,11811,17261901265−149667,249It is evident from Table 8’s economic findings that the system's original capital cost of $50118 was less than its net present value. The major cost is contained in the photovoltaic, which accounts for 52.84% of the system's overall cost.The suggested cHGSO algorithm's simulation results are shown in Table 9, along with a comparison with PSO and HOMER [47]. The outcomes of the simulation show that the HOMER platform is outperformed by the optimum combined system utilizing the cEHO algorithm, followed by the optimizer utilizing the PSO. With 95.1% PV penetration, it can also be said that the suggested cHGSO‐based system offers higher renewable penetration than the other approaches that were evaluated.9TABLEComparison of the offered cEHO with other analyzed algorithmsAlgorithmParameters per year (on yearly basis)CEHOPSO [47]HOMERDG power (kWh)50213952109PV power (kWh)23,19122,40821,846Overall power (kWh)23,14722,75923,450Fuel usage (L)802692795The batteries’ input power (kWh)941695089815The batteries’ output power (kWh)974697148540Co2 emissions (kg)169419052135Additionally, the cHGSO algorithm emits 1694 kg of CO2 each year, which is the lowest amount among the approaches and produces the cleanest results.CONCLUSIONSThe conventional method of producing electricity off the grid is to use a diesel generator; the appearance of new technologies, however, has created abilities that are a combined system design based on green energy resources alongside a diesel generator. For making the capability of supplying the required power with minimum cost, the present study introduced a modified metaheuristic technique using a novel modified Henry gas solubility optimizer for the optimum design of combined diesel/PV/ battery banks. The system's yearly cost, the loss of load probability, and the value of CO2 emissions were the three objective functions considered in the research. For streamlining the optimization process, the ε‐constraint approach was utilized. To demonstrate the approach's effectiveness, the data from the PSO‐based and HOMER optimum methods were compared with those of the proposed method. According to simulation findings, the proposed technique can fully meet load need such that photovoltaic penetration significantly affects prices by 95.1%.AUTHOR CONTRIBUTIONSNoradin Ghadimi: Investigation; Software; Validation; Writing ‐ original draft; Writing ‐ review & editing. 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An innovative technique for optimization and sensitivity analysis of a PV/DG/BESS based on converged Henry gas solubility optimizer: A case study

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Wiley
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© 2023 The Institution of Engineering and Technology.
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1751-8695
DOI
10.1049/gtd2.12773
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Abstract

INTRODUCTIONOff‐grid power production is one method of providing energy in industrial, commercial, residential, and remote (rural) areas, where it is impossible to connect to the grid in most cases due to the geographically impassable setting and the high transmission expense [1]. In such cases, utilizing local (green/renewable) energy can ease the progression of new systems in these regions. Using options with minimum supply cost is considered a stable and rational way for the expansion of new power systems in these regions [2]. The common off‐grid method of electricity production is to utilize a diesel generator [3–5]. The development of new technologies, however, has resulted in abilities in designing combined systems (the diesel generator in addition to green energy technologies) to provide the required power [6]. It fulfilled the need at a minimum cost.In the novel method, the system is a combination of the diesel generator and green energy resources, namely solar photovoltaic, biomass, biogas, small hydropower, fuel cell, and wind. This combined technology may also utilize a power storing unit (battery) [7]. Thus, in general, a combined system includes diesel generators, batteries, and one or more green energy resources.A hybrid system could be diverse and its application could be various [8]. Different factors affect each combination of the hybrid system, such as accessibility of green energy resources, the geographical setting, economic limitations, and technical restrictions [7]. In an off‐grid energy production unit, the combined system delivers the possibility of producing cost‐effective and green electricity, which is far cheaper than generating electricity with a diesel generator most of the time [9]. Accordingly, green energy resources are the desired way for off‐grid power production. Combined systems as a developing technology have captured imaginations around the world [10, 11]. Several logics for this tendency could be expressed as improving the reliability of electricity supply, improving energy services, emissions and noise reduction, continuous electric power generation, extending the service life of the system, electricity production costs reduction, and optimal energy consumption [12–14]. A hybrid power generation station usually includes the following components:A. Inverter unit with a nominal connected energy of about 60% of the max needed.B. One or two diesel engines with a size of 1 to 1.5 times greater than the size of the inverter.C. The lead‐acid battery storage system.D. Solar photovoltaic arrangement.E. Microprocessor with control unit for automatic system monitoring and management.In the optimization process of the hybrid energy systems, they usually searched for different power supply arrangements according to the limitations, to obtain the most economical mode for the life cycle cost [15, 16]. To model a system including photovoltaic cells, the information on the solar source of the area should be accessible [17, 18]. Then, based on simulations, the amount of energy from renewable resources according to 1‐h steps has been achieved, and for most types of small energy systems, especially those that include intermittent renewable energy sources, 1‐h steps seem to be an accurate scale for analysis.Agarwal et al. [19] examined the optimization of an off‐grid combined solar‐battery‐diesel plant for electricity production in Uttar Pradesh rural regions, India. In this study, a multi‐objective optimal model was developed to identify the appropriate size of the off‐grid combined system. The decision factors considered in the optimization procedure are the total area of photovoltaic panels, yearly fuel consumption, and the power of the diesel generator. An ideal autonomous system design includes a photovoltaic area of 300 m2, 60 photovoltaic panels with 600 Wp, and a diesel generator with 5‐kW output. $110,556 over 25 years LC cost; 1151/year fuel usage; and 0.0189 tCO2/capita carbon dioxide emissions.Lan et al. [20] extracted optimized combined solar panel/battery/diesel size in a ship's electricity system. An approach for finding the finest dimension of the diesel generator, photovoltaic (PV) system, and batteries were described in detail. The generation of power from solar panels on a ship is dependent on the time zone, local time, date, latitude, and longitude within a navigation path. For adjusting the output of PV modules, an algorithm is created that takes seasonal and geographical fluctuations in solar irradiance and temperature into account [21]. To simulate the entire shipload, the suggested technique takes five conditions along the navigation path into account. Four detailed scenarios are examined to illustrate the applicability of the suggested technique.Yahiaoui et al. [22] evaluated integrated solar panel‐diesel‐battery technologies developed for Algeria's remote, rural cities. a diesel generator in conjunction with a photovoltaic array panel power system In this article, battery cells and load are taken into account. The system's overall cost, CO2 emission, and load loss possibility (LLP) have all been reduced using the particle swarm optimizer (PSO). The significance of photovoltaic and battery energy systems is also revealed by this study [23]. Without them, the yearly cost of a diesel generator rises significantly. Eventually, the offered method outcomes were compared with software programs. The suggested technique is also useful for dealing with the reducing costs of a combined system under an unmet load or non‐existence circumstance.Ashraf et al. [24] designed an optimum combination utilizing metaheuristic algorithms for a combined solar energy/battery /diesel electricity production unit. The major goal of their work is to provide a brand‐new, ideal combined system for China's Gobi Desert. The simulation demonstrates that the suggested approach may deliver a dependable augmentation for load needs, with photovoltaic penetration having a significant influence on about 98% of the expenses. According to the outcomes, when compared with the results of the HOMER software and PSO‐based optimum system, the suggested cEHO algorithm's emission of CO2 gas, at 1735 kg/year, is at its lowest level. The system's net current cost is 48,680 dollars, which is less than its initial capital price of 48,680 dollars.Esan et al. [25] evaluated the dependability of an island‐based combined solar panel‐diesel‐battery system for an average Nigerian rural settlement. In this study, a unique method for evaluating the production stability of a combination mini‐grid system (HMS) based on the best design outcome from the HOMER program is presented. The least net existing cost of a solar photovoltaic array, diesel generators, and battery storage is $4,909,206, with a levellized energy rate of $0.396 per kWh. When all three were running, it was seen that the HMS had load losses of 0.769, 0.594, and 0.419 MW. An approximate 97% decrease in all CO2 emissions was seen when comparing the HMS to a diesel‐only system for the neighbourhood.Optimize the system while simultaneously reducing the unmet load, system capital cost, and emissions, the constraint technique, and a meta‐heuristic can be used. The method usually does not require as many additional procedures as Pareto‐based methods do, making it more convenient. The best optimum solution is selected from the obtained solutions for the hybrid system to be used as a sustainable power supply unit. To synthesize the impact of all three parts on the combined system, the research also does a sensitivity analysis. The outcomes of the proposed technique are then contrasted with those obtained using the HOMER environment and a PSO‐based technique from the literature.THE SOLUTION PROCEDUREIn this study, the main aim is to introduce an optimal arrangement of a combined energy source based on a photovoltaic system, diesel generator, and batteries to provide a proper electricity supplier for a remote area in Yarkant County, Taklamakan desert, China [26–28]. The idea is to use an improved version of a newly introduced algorithm, Henry gas solubility for this purpose. Over the next step, we will use the results of the proposed optimal arrangement to validate with some other state‐of‐the‐art methods to show its efficiency. The proposed method can be also utilized for use in different similar areas and also can be extended for use in a different environment. The Taklamakan Desert's meteorological information is gathered from NASA datasets and NREL (the National Renewable Energy Laboratory), and the area is recognized using information from some abandoned buildings and local climatic features. Then, considering the local load figures and datasets, the profiles for load profiles, PV radiation, and temperature fluctuations are created.The modelling of the hybrid system components uses a mathematical approach. Then, the hybrid Diesel/PV/Battery energy system has been optimized using the provided optimization strategy and the ε‐constraint method. The sensitivity analysis is used in the study to examine the effects of each component on the system. For providing easy and optimal results for the system, a metaheuristic technique, based on an improved version of the Henry gas solubility optimization (HGSO) algorithm, has been utilized. The literature study indicates that the original HGSO yields good outcomes for optimization problems, though the algorithm's early convergence may occasionally yield subpar findings. Two crucial changes have been made to the ongoing study to address this problem. The initial improvement has made use of the self‐adaptive weighting concept to control the propensity speed for finding the best solution. In light of this, the position updating model regulates the random value on the terms for the impact of gas exploration and exploitation. The HGSO algorithm begins with an upper distance of exploration, and at the last epochs, local exploration in the solution space reduces the exploration distance. This strikes a balance between the optimizer's exploitation and exploration. The aforementioned approach gradually changes the operator's weight value to narrow the difference between the worst and best solutions. The second development is the application of a chaotic approach to the local optimization problem. By considering the chaotic idea, the problem can occasionally change in terms of temporal complexity. The pseudo‐haphazard amounts of chaos operatives’ ergodic and sequence random properties are extremely advantageous to the method. The work being presented makes use of a scheme plan, a typical chaotic procedure.THE TAKLAMAKAN DESERTNorthwest China's southwestern Xinjiang region contains the Taklamakan Desert. It is bordered to the south by the Kunlun Mountains, to the west by the Pamir Mountains, to the north by the Tian Shan range, and to the east by the Gobi Desert.With a surface size of 337,000 km2, the Taklamakan Desert is just marginally larger than Germany. The Tarim Basin, which is 400 km (250 miles) broad and 1000 km (620 miles) long, includes the desert. Two branches of the Silk Road, used by travelers to bypass the dry wasteland, traverse it at its southern and northern boundaries. The Taklamakan Desert is the second ‐biggest desert with shifting sand globally. Yarkant is a county in the Xinjiang Uyghur Autonomous Region of China. It is situated in the Tarim Basin on the southern edge of the Taklamakan Desert. The total population of this county until 2015 is 851,374. The coordinates for this county are 38°23′27″N 77°13′24″E.The conditional electrical appliances, such as fluorescent lights, and fans, TV and refrigerator are part of the load shape electricity needed for the households in the community. The time interval is set at 1 h, and the daily load profile is taken into account for the two seasons of winter and summer. Figure 1 represents the bar plot for the indicated load figures.1FIGUREThe energy use (kW) bar graph on recommended load figures basis.From Figure 1, we can conclude that the system's minimal and highest demands are 1.05 and 5 kW.In the next phase, the NASA Surface Meteorological information on an hourly basis has been utilized to simplify the collection of meteorological data. Figures 2 and 3 depict the meteorological profile at the study site, which includes the temperature, index of clearness, and daily radiation.2FIGURECase study's clearness index and daily radiation.3FIGURECases study's daily temperature.THE SYSTEM MATHEMATICAL MODELThe suggested HRES's total energy flow design is seen in Figure 4. As can be seen, the suggested combined system includes PV modules, a battery storing bank, and a diesel generator. The PV modules make an effort to meet the necessary load need by holding radiation from the Sun and converting it into electricity. If there is an excess of electricity produced during energy generation beyond the amount needed to power the load, the additional energy can be saved in batteries.4FIGUREThe HRES's overall energy flow design.In contrast, the batteries will assist in meeting the remaining load requirement if the photovoltaic modules were unable to meet the need. Additionally, a diesel generator will be added to the system as a backup power resource to meet the remaining need if it becomes far more than the combined energy of the photovoltaic modules as well as the battery.The mathematical model of each element is described in depth in the upcoming sections.Diesel generatorThe following equation [29] determines the quantity of fuel consumed by the diesel generator (DG):1cfDG=αDG×PnDG+βDG×PoDG$$\begin{equation} c {f}^{DG} = {\alpha }^{DG}\ \times P_n^{DG} + {\beta }^{DG} \times P_o^{DG}\end{equation}$$where PnDG$P_n^{DG}$ and PoDG$P_o^{DG}$ provide the DG's nominal and output power (in kW) and αDG${\alpha }^{DG}$ and βDG${\beta }^{DG}$ indicate the consumption curve's coefficients (L/kWh).The following factors contribute to the diesel generator's performance:2ηDG=PoDGcfDG×LHVf$$\begin{equation}\ {\eta }^{DG} = \frac{{P_o^{DG}}}{{c{f}^{DG} \times LH{V}_f}}\ \end{equation}$$where LHVf$LH{V}_f$ signifies the fuel consumption heating value.Based on [29], in this study, LHVf is limited between 10 kWh/L and 11.6 kWh/L, and αDG and βDG are set 0.25  and 0.08L/kWh$0.08{\rm{\ L}}/{\rm{kWh}}$, respectively.Battery energy storage systemThe battery output current is directly influenced by the resulting energy of the control scheme, the renewable generators, and the SOC [16]. The key to increasing the capacity of the generating system is to regulate the discharging and charging processes of the battery while using the maximal energy of the photovoltaic cells. The equation below describes how much energy the battery system produced and absorbed between t−1$t - 1$ and t3PaBatt=PaBat×t−1×1−σ+Popvt−PoLoadtηin×ηbat$$\begin{eqnarray} P_a^{Bat}\ \left( t \right) &=& P_a^{Bat}\ \times \left( {t - 1} \right) \times \left( {1 - \sigma } \right)\nonumber\\ && +\, \left( {P_o^{pv}\left( t \right) - \frac{{P_o^{Load}\left( t \right)}}{{{\eta }_{in}}}} \right) \times {\eta }_{bat} \end{eqnarray}$$where4Charging:Popvt−PiLoadtηin>0andPaBatt−1<PaBatmaxDischarging:Popvt−PiLoadtηin<0andPaBatt−1>PaBatmin$$\begin{eqnarray}\left\{ { \def\eqcellsep{&}\begin{array}{@{}*{1}{c}@{}} {Charging\!:\ P_o^{pv}\left( t \right) - \dfrac{{P_i^{Load}\left( t \right)}}{{{\eta }_{in}}} &gt; 0\ and\ P_a^{Bat}\left( {t - 1} \right) &lt; \ P_a^{Ba{t}_{max}}}\\[11pt] {Discharging\!:\ P_o^{pv}\left( t \right) - \dfrac{{P_i^{Load}\left( t \right)}}{{{\eta }_{in}}}&lt; {0\ and\ P_a^{Bat}\left( {t - 1} \right)} &gt; \ P_a^{Ba{t}_{min}}} \end{array} } \right.\nonumber\\ \end{eqnarray}$$where PiLoad(t)$P_i^{Load}( t )$ specifies the load demand at time t, σ (here, 1 ×10‐3) describes the battery storage self‐discharge rate, ηbat${\eta }_{bat}$ (here, 0.7) and ηin${\eta }_{in}$ (here, 0.9) define the efficiency for batteries and inverter, respectively,PaBat(t)$\ P_a^{Bat}( t )$ and PaBat(t−1)$\ P_a^{Bat}( {t - 1} )$ represent the battery power availability at t and its previous time (t−1$t - 1$).To increase the lifespan of the battery energy storage system, the higher limitation, (SOCmax$SO{C}^{max}$) and the lower limitation SOCmin$SO{C}^{min}$ () are measured with the entire nominal capacity value in Ah by the following [30]:5SOCmax=PaBat×NBat$$\begin{equation}SO\ {C}^{max} = P_a^{Bat}\ \times {N}^{Bat}\end{equation}$$6SOCmin=PaBat×NBat×1−DoDmax$$\begin{equation}SO\ {C}^{min} = P_a^{Bat}\ \times {N}^{Bat} \times \left( {1 - Do{D}^{max}} \right)\end{equation}$$where DoDmax$Do{D}^{max}$ demonstrates the max deepness rate of the discharging.The battery's supreme lifecycle occurs, whenever the DOD is established from 0.3 to 0.5. As a result, DoDmax=0.3%$Do\ {D}^{max} = \ 0.3\% $.InverterThe inverter's output transmitted power required to meet the load requirement is as follows:7Pinv=PhDηinv$$\begin{equation}\ {P}^{inv} = \frac{{{P}^{hD}}}{{{\eta }_{inv}}}\ \end{equation}$$where ηinv${\eta }_{inv}$ and PhD${P}^{hD}$ represent the inverter efficiency and the hourly demand, respectively.Photovoltaic moduleThe solar system's output power is achieved by taking into account that the inverter has Max Power Point Tracking (MPPT) as follows [31]:8Popv(t)=Fd×Ps×Irrpvt1kWh/m2×1+α100×Tpvt−25$$\begin{eqnarray} P_o^{pv} ( t ) = {F}_d\ \times {P}_s \times \frac{{Ir{r}_{pv}\left( t \right)}}{{1kWh/{m}^2}} \times \left[ {1 + \frac{\alpha }{{100}} \times \left( {{T}_{pv}\left( t \right) - 25} \right)} \right]\nonumber\\ \end{eqnarray}$$where α describes the coefficient of the power temperature (°C), Irrpv(t) specifies the radiation over the curved area of the photovoltaic sheets, Ps${P}_s$ defines the resulted energy in standard testing circumstances (STC), Fd${F}_d\ $determines the factor of the power losses (0.9), and Tpv(t)${T}_{pv}( t )$ determines the PV cell temperature gained by Equation (9)9Tpv(t)=TNOC−200.8×Irrpvt1kWh/m2+Tambt$$\begin{equation}{T}_{pv} (t) = \left[ {\frac{{{T}_{NOC} - 20}}{{0.8}}} \right]\ \times \frac{{Ir{r}_{pv}\left( t \right)}}{{1kWh/{m}^2}} + {T}_{amb}\left( t \right)\end{equation}$$where Tamb(t)${T}_{amb}( t )$ and TNOC${T}_{NOC}$ describe the environmental temperature and the theoretical operating temperature of the cell.CONVERGED HENRY GAS SOLUBILITY OPTIMIZATION ALGORITHMStandard Henry gas solubility optimizer (HGSO)In this part, the mathematical expression of the HGSO is presented. The phases of mathematical are noted as follows:Stage 1: Operation of initialization. The swarm size (N) means the gases; quantity and the initialization for the location of the gases are based on the following equation:10Yi(t+1)=Ymin+r×Ymax−Ymin$$\begin{equation}{Y}_i ( {t + 1} ) = {Y}_{min}\ + r \times \left( {{Y}_{max} - {Y}_{min}} \right)\end{equation}$$where Yi${Y}_i$ defines the situation of the ith gas in N swarm, r indicates a random amount in the interval [0,1], and the limitations of the problem are represented by Ymax${Y}_{max}$, Ymin${Y}_{min}$; t indicates the iteration time. The initialization of the gas partial pressure Pi,j${P}_{i,j}$ in group j, ∇solE/R${\nabla }_{sol}E/R$ steady amount of the jth$j{\rm{th\ }}$type (Cj)$( {{C}_j} )$, and amounts of Henry's constant for jth$j{\rm{th\ }}$type (Hj(t))$( {{H}_j( t )} )$ are as follows:11Hj(t)=s1×rand(0,1),Pi,j=s2×rand0,1,Cj=s3×rand0,1$$\begin{eqnarray} {H}_j( t ) &=& {s}_1\ \times rand ( {0,1} ),{P}_{i,j} = {s}_2\ \times rand\left( {0,1} \right),\nonumber\\ {C}_j &=& {s}_3\ \times rand\left( {0,1} \right) \end{eqnarray}$$where s1=5E−02${s}_1 = \ 5E - 02$, s2=100${s}_2 = \ 100$, and s3=1E−02${s}_3 = \ 1E - 02$.Stage 2: Grouping. The factors of the swarm are split into identical groups equivalent to the numeral of gas kinds. Any group includes analogous gases and thus has the identical Hj${H}_j$(Henry's constant).Stage 3: Assessment. The gas that has the highest equilibrium condition among other gases of its kind is identified as the best gas through the assessment of any j cluster.Stage 4: Updating Henry's coefficient. The following equation is used to update Henry's coefficient:12Hj(t+1)=Hjt×exp−Cj×1Tt−1Tθ,T(t)=exp−titer$$\begin{eqnarray} {H}_j( {t + 1} ) &=& {H}_j\ \left( t \right) \times \exp \left( { - {C}_j \times \left( {\frac{1}{{T\left( t \right)}} - \frac{1}{{{T}^\theta }}} \right)} \right),\nonumber\\ T( t ) &=& {\rm{exp}}\left( { - \frac{t}{{iter}}} \right) \end{eqnarray}$$where Henry's coefficient related to cluster j is indicated by Hj${H}_j$; T and Tθ${T}^\theta $ define the temperature and a constant amount equal to 298.15; the whole numeral of iterations is described by iter$iter$.Stage 5: Updating of solubility. The following equation is used to update the solubility:13Ki,j=l×Hjt+1×Pi,jt$$\begin{equation}\ {K}_{i,j} = l \times {H}_j\left( {t + 1} \right) \times {P}_{i,j}\left( t \right)\end{equation}$$where Pi,j${P}_{i,j}$ and Ki,j${K}_{i,j}$ represent the partial pressure and solubility of gas i in the jth group; l indicates a constant.Stage 6: Updating of location. The following equation is used to update the location:Yi,j(t+1)=Yi,jt+F×r×γ×Yi,bt−Yi,jt+F×r×α×Ki,jt×Ybt−Yi,jt$$\begin{eqnarray*} {Y}_{i,j}( {t + 1} ) &=& {Y}_{i,j}\ \left( t \right) + F \times r \times \gamma \times \left( {{Y}_{i,b}\left( t \right) - {Y}_{i,j}\left( t \right)} \right)\nonumber\\ && +\, F \times r \times \alpha \times \left( {{K}_{i,j}\left( t \right) \times {Y}_b\left( t \right) - {Y}_{i,j}\left( t \right)} \right) \end{eqnarray*}$$14γ=β×exp−Fbt+εFi,jt+ε,ε=0.05$$\begin{equation}\gamma = \beta \times \exp \left( { - \frac{{{F}_b\left( t \right) + \varepsilon }}{{{F}_{i,j}\left( t \right) + \varepsilon }}} \right),\ \varepsilon = 0.05\end{equation}$$where Yi,j${Y}_{i,j}$ denotes the ith$i{\rm{th}}\ $gas situation in set j, t and r indicate the iteration time and a random constant. Yi,b${Y}_{i,b}$ is the finest gas i in the jth group, and Yb${Y}_b$ is the finest gas in the population. The capability of gas i in jth group for interacting with the gases in the same set is represented by γ. α=1$\alpha = 1$ which represents the effect of other gases on ith$i{\rm{th}}\ $gas in group j, β indicates a constant. The ith$i{\rm{th}}\ $gas fitness in set j is defined by fi,j${f}_{i,j}$; the finest gas fitness in the whole system is also indicated by Fb${F}_b$. For providing diversity ( =±$ = \ \pm $) and altering the direction of the search factor F (the flag) is used. Two variables that create stability between exploitation and exploration steps are expressed by Yi,b${Y}_{i,b}$ and Yb${Y}_b$, each of these two variables specifies the finest gas i in the jth group and the finest one in the whole swarm.Stage 7: Escaping from local optimum. This stage is utilized to avoid getting stuck in the local optimal answers. The worst factor's quantity (Nw${N}_w$) is classified and chosen as below15Nw=N×randc2−c1+c1,c1=0.1andc2=0.2$$\begin{eqnarray}\ {N}_w = \ N \times \left( {rand\left( {{c}_2 - {c}_1} \right) + {c}_1} \right),\ \ {c}_1 = \ 0.1\ and\ \ {c}_2 = \ 0.2\nonumber\\ \end{eqnarray}$$where N indicates the number of search factors.Stage 8: Updating the location of the worst factors.16D(i,j)=Dmin(i,j)+r×(Dmax(i,j)−Dmin(i,j)$$\begin{equation} {D}_{({i,j})} = {D}_{min}( {i,j} ) + r \times ({D}_{max}( {i,j}) - {D}_{min}({i,j} )\end{equation}$$Here, D(i,j)${D}_{( {i,j} )}$ represents the location of gas i in group j, r indicates a random amount, and Dmin${D}_{min}$, Dmax${D}_{max}$ illustrate the scope of the solution area.At last, the offered optimizer's pseudo‐code is given in Algorithm 1, containing the primary swarm, swarm assessment, and variables of updating.1ALGORITHMHGSO optimizer's pseudo‐code1:Initializing: Yi(i=1,2,…,N)${Y}_i( {i = 1,2, \ldots ,N} )$, number of gas kinds i, Hj${H}_j$, Pi,j${P}_{i,j}$, cj${c}_j$, s1, s2, and s3.2:Split the population factors into the gas kinds’ quantity (set) with the identical Hj${H}_j$.3:Assess any set j.4:Achieve the finest gas Yi,b${Y}_{i,b}$in any cluster and the finest search factor Yb${Y}_b$.5:Do until t<$t &lt; $max number of iterations6:do for any search factor7:Update the locations of whole search factors.8:end for9:Update Hj${H}_j$of any gas kind.10:Update the solubility of any gas.11:Categorize and select the worst factors’ number.12:Update the location of the worst factors.13:Update the finest gas Yi,b${Y}_{i,b}$, and the finest search factor Yb${Y}_b$.14:end while15:t=t+1$t = t + 1$16:return Yb${Y}_b$HGSO, SA (simulated annealing), and important observation employ the identical gas rule, while there have been distinctions in their systems. The modelling of the annealing operation of data is done in SA, and a novel location is created at any epoch at random. The space between the novel location and the present is based on the possibility distribution that is corresponding to the temperature. Therefore, SA is not able to permanently select the finest solution that results in a local optima getaway. In Henry gas solubility optimizer, the exploration factors are separated into classes and the constant of gas is identical for any class, the location alters proportionate to the value of solubility from the cost function utilizing expressed equation.Consider that the proposed algorithm comprises exploitation and exploration stages, as a global optimizer. Likewise, for easy understanding and the implementation of the algorithm, the number of set operators has been minimized. The calculation complication of the suggested procedure is O(tnd)$O( {tnd} )$ in which t displays the max numeral of epochs, n stands for the numeral of answers, and d denotes the numeral of variables. Each answer is homogeneous; this is the complicatedness of the optimizer irrespective of the cost function. Hence, the total complicatedness containing the cost function (obj)$( {obj} )$ is computed as O(tnd)∗O(obj).$O( {tnd} )*O( {obj} ).$Exploration and exploitation stagesBy fine‐tuning the appropriate randomness amount, the stability among the exploitation and exploration stages is managed, and the algorithm can move out of each local optimum and starts searching globally. The Henry gas solubility optimizer has three principal managing variables: ki,j${k}_{i,j}$, γ, and F. (1) ki,j${k}_{i,j}$ indicates the ith$i{\rm{th}}\ $gas solubility in set j and is based on the time of repetition [32, 33]. Therefore, the exploration factors are transferred from the global to the local stage in addition to transferring to the finest location; thus, this gains the most suitable equilibrium among exploitation and exploration characteristics. (2) γ is the capability of gas i in the jth set for interacting with the same set of gases and intends to move the exploration factors from global to local step and vice versa following the condition of a specified case. (3) While the variable F represents a flag that alters the orientation of the exploration factor and supplies variety = ±, this offers a great option to alter the orientation of exploration for some factors to present the power to discover a certain area intently.The decreased mean value indicates exploitation and the increased mean distance in the dimensions of the population individual refers to exploration in this study. This means that the search factors are located near one another. In the circumstance of unimportance distinction in average diversity amounts throughout numerous repetitions, it could be stated that the optimizer has achieved a condition of convergence [34]. The measurement‐wise variety throughout the repetition of the exploration approach was estimated as below:171Divj=1N∑i=1Nmedianyj−yijDivt=1N∑j=1DDivj$$\begin{equation}\ \frac{1}{{Di{v}_j}} = \frac{1}{N}\ \mathop \sum \limits_{i = 1}^N median\left( {{y}^j} \right) - y_i^jDi{v}^t = \frac{1}{N}\ \mathop \sum \limits_{j = 1}^D Di{v}_j\end{equation}$$where yij$y_i^j$ indicates jth dimension of ith swarm individual and median (yj${y}^j$) denotes the median amount of jth dimension of total the swarm. Divi$Di{v}_i$ defines average diversity amount for measurement j. This measurement‐wise diversity is next balanced (Divt$Di{v}^t$) on whole D dimensions for epoch t and t=1,2,3,…,iter$t = 1,\ 2,\ 3,\ \ldots ,\ iter$. When swarm diversity is calculated for epochs iter$iter$, where iter$iter$ is the maximum epochs the search approaches were performed, then it is feasible to specify how much the explorative and exploitative features of the method were [35]. The mensuration of exploitation/exploration value could be specified utilizing the below formula:Exploration%=fracDivtDivmax×100$$\begin{equation*}Exploration\% = frac{{Di{v}^t}}{{Di{v}_{max}}}\ \times 100\end{equation*}$$18Exploitation%=fracDivt−DivmaxDivmax×100$$\begin{equation}Exploitation\% = frac{{\left| {Di{v}^t - Di{v}_{max}} \right|}}{{Di{v}_{max}}}\ \times 100\end{equation}$$where Divt$Di{v}^t$ describes swarm diversity of tth iteration and Divmax$Di{v}_{max}$ defines the maximum diversity located in every T iteration.Converged HGSO (cHGSO)According to the literature study, the original HGSO produces good results for optimization problems, although the algorithm's early convergence might occasionally provide unsatisfactory results. To address this issue, two key improvements have been made in the ongoing study. The self‐adaptive weighting idea has been used in the initial improvement in managing the tendency speed for arriving at the most optimal solution [36, 37]. Having this in mind, the model of location updating controls the random value on the terms for gas exploration and exploitation impact [38]. The initial rounds of the HGSO algorithm explore with an upper distance of exploring, and at the final epochs, the exploration distance is narrowed by a local exploration in the solution space. This balances the exploitation and exploration of the optimizer. The following equation applies this strategy to the random moving term:19Yi,jnew(t+1)=Yi,jnew(t+1)=Yi,j(t+1)+ζ×(Yi,jbest−Yi,j(t))×r,rand>0.5Yi,jnew(t+1)=Yi,j(t+1)−ζ×(Ycibest−Yi,j(t))×r,rand≤0.5$$\begin{equation} Y_{i,j}^{new}({t + 1}) = \left\{ \def\eqcellsep{&}\begin{array}{@{}*{1}{l}@{}} Y_{i,j}^{new} ({t\! +\! 1}) = {Y}_{i,j}({t\! +\! 1})+ \zeta \times ({Y_{i,j}^{best}\! -\! {Y}_{i,j}(t)})\\[5pt] \quad \times\, r,\ rand &gt; 0.5\\[5pt] Y_{i,j}^{new} ({t\! +\! 1}) = {Y}_{i,j} ({t\! +\! 1}) - \zeta \times\, ({Y_{ci}^{best}\! -\! {Y}_{i,j}(t)})\\[5pt] \quad \times\, r,\ rand \le 0.5 \end{array} \right. \end{equation}$$Here,20ζ=fYi,jbestfYi,jworst2,iffYi,jworst≠01,iffYi,jworst=0$$\begin{equation} \zeta = \left\{ \def\eqcellsep{&}\begin{array}{ll} {{\left( {\frac{{f\left( {Y_{i,j}^{best}} \right)}}{{f\left( {Y_{i,j}^{worst}} \right)}}} \right)}}^2, &\quad if\ f\left( {Y_{i,j}^{worst}} \right) \ne 0\\[11pt] 1,&\quad if\ f\left( {Y_{i,j}^{worst}} \right) = 0 \end{array} \right.\ \end{equation}$$where f(Yi,jbest)$f( {Y_{i,j}^{best}} )$, and f(Yi,jworst)$f( {Y_{i,j}^{worst}} )$, in turn, represent the worst and the finest answer of the cost function.To reduce the gap between the worst and best solutions, the aforementioned method progressively alters the operator's weight value. The adoption of a chaotic method to address the local optimization problem is the second advancement. Sometimes, the problem can be changed in terms of temporal complexity by taking the chaotic notion into account.The method can benefit greatly from the ergodic and sequence random properties of chaos operatives, which are pseudo‐haphazard amounts. The work that is being presented employs a strategy plan, a common chaotic technique. This method was developed by doing the following equation:21βi+1=βi+ϕi×βi$$\begin{equation}\ {\beta }^{i + 1} = {\beta }^i\ + {\phi }_i \times {\beta }^i\end{equation}$$where22ϕi+1=4ϕi1−ϕi$$\begin{equation}\ {\phi }_{i + 1} = \ 4{\phi }_i\left( {1 - {\phi }_i} \right)\end{equation}$$where ϕi${\phi }_i$ defines the value of the ith chaotic iteration. ϕ1 is considered the initial value that is equal to 0.5.Validation of the proposed converged HGSOThe proposed convergent HGSO is applied to 10 standard benchmark functions with unimodal and multimodal problems, to validate its accuracy and precision, and the results are compared with various published techniques. Owl Search Algorithm (OSA) [39], Squirrel search algorithm (SSA) [40], Pigeon‐Inspired optimizer [41], and original HGSO are the algorithms that are being compared. The technique was tested on a laptop with MATLAB version 2017b installed on windows 10 64‐bit version with AMD A4 3600 processor and 8 GB RAM.The main objective is to minimize any one of the 10 benchmark functions. As a result, each algorithm's lowest possible value proves that it is more effective than the others. Table 1 displays the set parameters for the investigated methods.1TABLESet parameters for the investigated methodsAlgorithmParameterValueOwl search algorithm (OSA) [39]Tdead${T}_{dead}$16|P|$| P |$8Acclow$Ac{c}_{low}$0.4Acchigh$Ac{c}_{high}$1Squirrel search algorithm (SSA) [40]Nfs${N}_{fs}$5Gc${G}_c$2.1Pdp${P}_{dp}$0.2Pigeon‐inspired optimization (PIO) algorithm [41]Space dimension15Map and compass factor0.1Map and compass operation limit160Landmark operation limit250w1C11.3C21.3Each optimizer is separately run 25 times on every function to test the efficacy of the algorithms, and the average value and STD value are validated based on these runs to generate reliable results. Table 2 lists the rankings of the benchmark functions among the algorithms.2TABLEEvaluations of the test functions for the proposed cHGSO algorithm and the other comparison algorithmsBenchmarkcHGSOHGSOOSA [39]SSA [40]PIO [41]f1AVG0.003.254.334.613.09STD0.001.543.083.211.06f2AVG0.914.155.124.834.25STD0.823.124.983.673.02f3AVG0.004.25 × 10−91.21 × 10−84.15 × 10−84.35 × 10−9STD0.000.002.34 × 10−64.41 × 10−43.25 × 10−6f4AVG0.000.004.25 × 10−85.17 × 10−75.31 × 10−8STD0.000.003.38 × 10−74.53 × 10−72.40 × 10−8F5AVG0.001.352.153.021.84STD0.002.513.384.272.34F6AVG0.033.254.514.103.80STD0.002.132.813.852.13F7AVG0.003.523.743.833.26STD0.221.041.781.381.08F8AVG0.000.270.730.650.21STD0.240.780.961.080.87F9AVG0.000.080.760.980.33STD0.000.010.511.070.13F10AVG0.001.251.031.121.1STD0.000.620.850.910.83As can be observed from Table 2, when compared to other comparable techniques, the converged HGSO algorithm yields the lowest value for the mean measure and exhibits greater accuracy. When compared to several runs by using various methodologies, the proposed optimizer also produces the lowest standard deviation (STD) value, demonstrating more reliability.THE ε‐CONSTRAINT PROCEDUREThis approach was first introduced in 1971. In this method, the goal is to optimize the objective functions in such a way that we choose one of the objective functions and to minimize this objective function, we convert the other objective functions into constraints. Note that these constraints (εi${\varepsilon }_i$) will be unequal. A multi‐objective problem is assumed for more explanation:23MinF1x,F2x,…,Fnx$$\begin{equation}Min\ \left( {{F}_1\left( x \right),\ {F}_2\left( x \right), \ldots ,\ {F}_n\left( x \right)} \right)\ \end{equation}$$where n specifies the number of objective functions, Fi|i=1,2,…,n${F}_{i|i = 1,2, \ldots ,n}$ illustrates the cost functions, and x demonstrates the optimization variables. x∗${x}^*$ is an optimal solution providing that no other practicable answer x exists that Fi(x)≤Fi(x∗)${F}_i( {\rm{x}} ) \le {F}_i( {{{\rm{x}}}^{\rm{*}}} )$.Therefore, by considering Fk|k=1,2,…,n${F}_{k|k = 1,2, \ldots ,n}$ as the key function and the others (Fi|i=1,2,…,n${F}_{i|i = 1,2, \ldots ,n}$) as constraints, we have24MinFkx$$\begin{equation}Min\ {F}_k\left( x \right)\ \end{equation}$$s.t.25Fix≤εi$$\begin{equation}{F}_i\left( x \right) \le {\varepsilon }_i\end{equation}$$where i≠k$i \ne k$, x describes the feasible solution, εi${\varepsilon }_i$ signifies the objective functions that do not exceed.PROBLEM FORMULATIONCost functionIn this study, for the optimal arrangement of the proposed combined system, the emission of CO2$C{O}_2$, the annual LLP, and ACS (annual cost of the system) have been considered for optimization. Based on the ε‐constraint method, we select ACS as the key cost function and the emission of CO2$C{O}_2$ and the LLP as the limitations of the optimization problem. Therefore, the cost function can be considered as follows:26ACS=Ccpt+Crpm+Co&m+Cfuel$$\begin{equation}ACS\ = {C}_{cpt}\ + {C}_{rpm} + {C}_{o\& m} + {C}_{fuel}\end{equation}$$where Ccpt${C}_{cpt}$, Co&m${C}_{o\& m}$, Crpm${C}_{rpm}$, and Cfuel${C}_{fuel}$ represent the yearly capital, maintenance and operational, replacement, and fuel costs, respectively.In the equation above, the annual replacement cost, including the battery storage replacement pending the lifetime, has been achieved by the equation below [42]:27Crpm=CrpmBat×Fsffrir,tR$$\begin{equation}\ {C}_{rpm} = C_{rpm}^{Bat}\ \times {F}_{sff}\left( {{r}_{ir},{t}_R} \right)\end{equation}$$where tR${t}_R$ and CrBat$C_r^{Bat}$ represent, in turn, the yearly lifespan of the battery storage, and the battery replacement cost. Fsf${F}_{sf}$ here describes the reducing fund coefficient and is calculated based on Equation (28) [42]:28Fsf=ri1+ritR−1$$\begin{equation}\ {F}_{sf} = \frac{{{r}_i}}{{{{\left( {1 + {r}_i} \right)}}^{{t}_R} - 1}}\ \end{equation}$$where ri${r}_i$ describes the interest rate on yearly basis and is achieved by the following formula:29rir=rir′−F1+F$$\begin{equation}\ {r}_{ir} = \frac{{\left( {r}_{ir}^{\prime} - F \right)}}{{\left( {1 + F} \right)}}\ \end{equation}$$where F and rir′${r}_{ir}^{\prime}$ define, in turn, the annual inflation rate and the nominal interest ratio, respectively.The annual capital cost can be achieved by the following equation:30Ccpt=Ccptd×Fcrfi,tl$$\begin{equation}\ {C}_{cpt} = C_{cpt}^d\ \times {F}_{crf}\left( {i,\ {t}_l} \right)\end{equation}$$where tl${t}_l$ and Ccptd$C_{cpt}^d$ represent, in turn, the annual project lifetime and the devices' capital cost, and Fcrf${F}_{crf}$ states the capital recovery element and is achieved as31FcR=ri×1+ritl1+ritl−1$$\begin{equation}\ {F}_{cR} = \frac{{{r}_i \times {{\left( {1 + {r}_i} \right)}}^{{t}_l}}}{{{{\left( {1 + {r}_i} \right)}}^{{t}_l} - 1}}\ \end{equation}$$where ri${r}_i$ demonstrates the real interest ratio within a year.Finally, the yearly operation and maintenance cost has been achieved as follows:32Co&m=Co&m1t×1+ritl$$\begin{equation}\ {C}_{o\& m} = C_{o\& m}^{1{\rm{t}}}\ \times {\left( {1 + {r}_i} \right)}^{{t}_l}\end{equation}$$where Co&m1t$C_{o\& m}^{1{\rm{t}}}$ describes the operation maintenance cost.Table 3 represents the parameter value of the proposed hybrid system for simulation.3TABLEParameters value of the proposed hybrid system for simulationParametersValueUnitParametersValueUnitMPPT efficiency90%Battery banks reliability0.82–Inflation rate7.75%Inverter reliability0.87–Yearly interest ratio8.05%Battery banks lifespan8YearsPV panel cost2.4$/kWProject lifetime22YearsDiesel generator cost361$/kWPhoto voltaic panel lifetime21YearsSingle inverter cost732$/kWInverter lifetime22YearsBattery expense327$/kWhFuel expense0.14$/LReliability of diesel generator0.81–Emission coefficient2.2kg/LPV modules reliability0.91–ConstraintsAs aforementioned, the LLP and the CO2$C{O}_2$ emissions are two functions that have been turned into constraints during the ε‐constraint method. The CO2$C{O}_2$ emission which is made by the diesel generator is the main reason for the pollution. So, considering this term is too important to design. This term can be mathematically considered by the following equation:33CO2emm=∑t=18800Fct×Fe$$\begin{equation}C O_2^{emm} = \mathop \sum \limits_{t = 1}^{8800} {F}_c\left( t \right) \times {F}_e\ \end{equation}$$where the CO2emm$CO_2^{emm}$ is limited and should have a value smaller than (or equivalent to) the permissible emission (εLLP${\varepsilon }_{LLP}$), and Fc${F}_c$ and Fe${F}_e$ represent the fuel consumption of the DG and the DG emission factor which is limited from 2.41 to 2.81 kg/L [43].The LLP is the second term as a limitation. The LLP phrase defines the generation likelihood that, at some moment over a specific time window, is insufficient to meet the load demand and is accomplished as follows [43, 44]:34LLP=frac∑t=18800Ult∑t=18800Det$$\begin{equation}LLP = frac{{\mathop \sum \nolimits_{t = 1}^{8800} {U}_l\left( t \right)}}{{\mathop \sum \nolimits_{t = 1}^{8800} {D}_e\left( t \right)}}\ \end{equation}$$where De(t)${D}_e( t )$ and Ul(t)${U}_l( t )$ represent the electricity demand and unfulfilled load throughout the time period t. It should be noted that the LLP term ought to be smaller than (or equal to) the permissible index of LLP reliability (εLLP${\varepsilon }_{LLP}$).Furthermore, the batteries number and the capacity of the battery storage are considered two other constraints, that is,35NBat,NPV,PnDG≥0$$\begin{equation}{N}^{Bat,}\ {N}^{PV},P_n^{DG} \ge 0\end{equation}$$36CminBat≤CBatt≤CmaxBat$$\begin{equation}C_{min}^{Bat} \le {C}^{Bat}\left( t \right) \le C_{max}^{Bat}\end{equation}$$Also, the constrained produced energy by the devices (Ej(t)${E}_j( t )$) can be considered by the following equation:37Ejt≤PjΔt$$\begin{equation}{E}_j\left( t \right) \le {P}_j{{\Delta}}t\end{equation}$$where Δt${{\Delta}}t$ describes the period (Δt=1h${{\Delta}}t = 1\ h$).Optimization methodologyBased on the explanations stated before, this work's main aim is to design an optimum arrangement for a combined battery/PV/ diesel generator system using an improved HGSO. Because of the problem complexity due to designing a multi‐objective strategy, the ε‐constraint technique is utilized. The three objectives of the study include CO2$C{O}_2$ emissions, the system's entire cost, and LLP.Here, based on the ε‐constraint method, the two first terms are considered as constraints and the third one is chosen as the cost function [45]. The decision variables for the mentioned optimization problem are a three‐variable vector, including the battery storage size, the DG valued volume, and the size of PV panels, that is: NPV${N}^{PV}$,NBat$\ {N}^{Bat}$, andPoDG$\ P_o^{DG}$, such that every different parameter shows a different pattern [46]. Figure 5 illustrates the diagram of the designed system in a flowchart for an optimum pattern of the hybrid using the improved HGSO algorithm and the ε‐constraint.5FIGUREGeneral diagram flowchart of the proposed optimal hybrid system.According to the annual undesired load, the annual fuel usage in the DG, and the pollution for each individual, the simulation model is assessed. After that, the produced values are sent to the improved HGSO algorithm to see if it can be done given the limitations. If the target under consideration is unsatisfactory, this amount is created and sent to the stage of optimization. After the stopping criterion has been reached, the optimum answers are likely to be returned.RESULTS AND DISCUSSIONSThe hourly modelling outcomes for the combined system are examined based on the proposed improved HGSO algorithm and a comparison is conducted among the results, HOMER, and PSO [47] under a specific load, and are discussed in this section. Here, if the photovoltaic system along with the battery energy storage system (backup system) could not fulfill the load need, the DG can be provided for supplying the remained demand. As a result, the DG can be utilized for supplying sufficient energy to meet the main load.During the simulation, the valued volume of DG is limited between 2 and 15 kW, the number of photovoltaic cells is limited between 5 and 110, and the number of battery cells is limited between 5 and 55. The main idea of using the combination of the ε‐constraint method and cHGSO algorithm is to optimum choice of the considered decision parameters to make the system yearly basis cost min as the main objective function and considering the CO2 emissions and LLP as constraints. The economical parameters of the modelling are illustrated in Table 4 (US$).4TABLEEconomical parameters of the simulation (US$)CcptCfuelCo&mCrpmACSConverter418.50201.4200.4852.4Diesel generator200.7115110.70475.8Battery bank1711.60805.618074429.7PV subsystem2854.90122.302827.3Total5185.711512402007.48585.2With regard to Table 4, the entire annual cost for the designed system is 8585.2 $. This system considers the variables’ optimal value as 10 kWp of PV generator, 8 kW of the DG, and 48 kWh of battery storage. Figures 6 and  7 show the rate of elements’ energy production and battery storage capacity during the intra‐hourly oscillation in winter (19th of Sep) and summer (the 5th of Mar) seasons, respectively.6FIGUREThe rate of elements’ energy production and battery storage capacity during the intra‐hourly oscillation in winter.7FIGUREThe rate of elements energy production and battery storage capacity during the intra‐hourly oscillation in summer.As previously stated, the battery storing bank is included as a backup system for solar PV due to the batteries’ SOC (situation of charge) providing that the electricity production based on the solar system is unable to deliver the needed load. The DG system has been included as a backup unit to satisfy the load requirement if these two power generators were unable to do so. The radiation of the Sun is a crucial factor that directly influences the energy output of the diesel generator. These radiations are plainly visible in cold weather and demonstrate that their magnitude is sufficient to meet the load requirement. Figure 8 shows monthly changes in the power production of elements.8FIGUREMonthly changes in the power production of elements.Regarding the results, the battery bank is directly impacted by the electricity generated by the photovoltaic system, and the diesel generator is adversely impacted. The storage system's maximum value is used in October and March.Sensitivity analysis is used to examine and pinpoint the changes that have the greatest impact on the system. The constraints are εLLP${\varepsilon }_{LLP}$, εCO2${\varepsilon }_{C{O}_2}$, and load consumption that was previously discussed are examined in this study.We make the assumption that the load fluctuates between 1 and 38 kWh per day while the other components—the size of the PV array, the battery bank, and the DG —remain unchanged for the sensitivity analysis of the load consumption. The presented system heavily leans on a diesel generator to make up for the lack of power caused by the increased load. Table 5 illustrates the system load variations.5TABLESystem load variationsThe additional load (kWh/day)PV penetration (%)LLP (%)Co2 (kg per year)COE ($/kWh)ACS (US$)195.1022570.378467.3392.8025190.368319.3590.5027370.358461.2787.1033420.358544.11184.3038170.348769.61382.4042550.348844.11581.9045340.338864.41777.4051590.338906.61974.8072460.328946.22271.30.7878210.318988.42569.61.981090.309149.33065.13.593150.279207.03563.75.898110.269276.63861.96.410,1420.259281.6As seen in Table 5, the specified reliance on the diesel generator backup system raises the system's yearly cost from 8467.3 to 9281.6 dollars (an increase of around 8.04%) through increasing fuel usage. Obviously, the LLP rises from zero to about 8.7% and the carbon dioxide emissions grow from 2257 to 10,142 kg per year.Additionally, it can be deduced that the drop in photovoltaic penetration from 95.1% to 61.9% causes the value of the cost of electricity to drop from 0.37 to 0.25 dollars per kilowatt‐hour. This decline shows that the cost of fuel has a greater impact on the cost of electricity than the cost of a photovoltaic system since traditional power generation is less expensive than power generation using a photovoltaic system.Table 6 shows how the size of the battery, the photovoltaic system, and the diesel generator are affected by the term, εCO2${\varepsilon }_{C{O}_2}$.6TABLEEffect of εCO2${{\rm{\varepsilon }}}_{{\rm{CO}}_2}$ on the three analyzed parametersεCO2${{\bm{\varepsilon }}}_{{\bm{C}}{{\bm{O}}}_2}{\bm{\ }}$(kg per year)Power of PV (kWp)Capacity of battery bank (kWh)DG capacity (kW)6018.64558018.145510017.944520017.444530016.844540015.543550015.2435100013.9425200012.4415300011.7395400010.837550009.336560009.131580008.7285As can be observed from Table 6, the battery bank capacity has grown from 28 to 45 kWh whenever εCO2${\varepsilon }_{C{O}_2}\ $rang varies from 8000 to 60 kg/year, which has a significant influence on battery bank dimensions. The consequence of εLLP${\varepsilon }_{LLP}$ on the three analyzed parameters is demonstrated in Table 7. The effect of the εLLP${\varepsilon }_{LLP}$ on the capacity of battery banks, the photovoltaic, and the diesel generator system has been illustrated. The size of battery banks also has a significant impact on the εLLP${\varepsilon }_{LLP}$, where it lessens from 21.8 to 16 kWh whenever it is placed in the range of zero to two. Table 8 illustrates the system's economical outcomes.7TABLEEffect of εLLP${{\rm{\varepsilon }}}_{{\rm{LLP}}}\ $on the three analyzed parametersεLLP${{\bm{\varepsilon }}}_{{\bm{LLP}}}{\bm{\ }}$(kg per year)Power of PV (kWp)Capacity of battery bank (kWh)DG capacity (kW)0621.830.16.41820.25.91820.35.71820.45.61620.55.81620.66.11620.76.31620.86.216215.91621.56.116226.11628TABLEThe system economical results ($)NPCElementInitialReplacementM&OFuelSalvageOverallPhotovoltaic26,485025340029,019Generator 12240019631265−1185350Hoppecke 10 OPzS 150016,245954812950−105526,033Converter514816243980−3236847System50,11811,17261901265−149667,249It is evident from Table 8’s economic findings that the system's original capital cost of $50118 was less than its net present value. The major cost is contained in the photovoltaic, which accounts for 52.84% of the system's overall cost.The suggested cHGSO algorithm's simulation results are shown in Table 9, along with a comparison with PSO and HOMER [47]. The outcomes of the simulation show that the HOMER platform is outperformed by the optimum combined system utilizing the cEHO algorithm, followed by the optimizer utilizing the PSO. With 95.1% PV penetration, it can also be said that the suggested cHGSO‐based system offers higher renewable penetration than the other approaches that were evaluated.9TABLEComparison of the offered cEHO with other analyzed algorithmsAlgorithmParameters per year (on yearly basis)CEHOPSO [47]HOMERDG power (kWh)50213952109PV power (kWh)23,19122,40821,846Overall power (kWh)23,14722,75923,450Fuel usage (L)802692795The batteries’ input power (kWh)941695089815The batteries’ output power (kWh)974697148540Co2 emissions (kg)169419052135Additionally, the cHGSO algorithm emits 1694 kg of CO2 each year, which is the lowest amount among the approaches and produces the cleanest results.CONCLUSIONSThe conventional method of producing electricity off the grid is to use a diesel generator; the appearance of new technologies, however, has created abilities that are a combined system design based on green energy resources alongside a diesel generator. 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Journal

IET Generation Transmission & DistributionWiley

Published: Nov 1, 2023

Keywords: converged Henry gas solubility optimization algorithm; hybrid renewable energy system; multi‐objective optimization; sensitivity analysis; Taklamakan desert; ε‐constraint method

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