Optimal energy management system for the design of off grid hybrid renewable energy systems: A hybrid technique

Abstract

This manuscript proposes an efficient hybrid strategy to obtain the optimal solution of operational cost reduction, size reduction of hybrid renewable energy sources and optimal power flow control for off-grid system. Here, off-grid is incorporated with photovoltaic array, wind turbine, Diesel generator, and battery energy storage system. The hybrid method is joint execution of Giza Pyramids Construction (GPC) and Billiards-inspired optimization algorithm (BOA) hence it is named GPC-BOA technique. The major purpose of proposed method is minimizing the operational cost as well as size of hybrid renewable energy sources and improves the power flow of system. In this energy management system of off-grid provides cost reduction which includes the generation, replacement, operating and maintenance, cost of fuel consumption, cost of exchanged power with grid, and the penalty for emissions. Here, the GPC method is employed for forecasting the load requirement of system. The BOA technique optimizes the off-grid system through the deliberation of forecasted load requirement. At last, the proposed approach is performed on MATLAB platform and the performance is assessed using existing techniques.

Keywords

Energy management system cost power flow photovoltaic array wind turbine Diesel generator battery energy storage system

Nomenclature and abbreviations

r ^F

Module de-rating factor

g _STC

Solar radiation under Standard test conditions

t ^C

Cell temperature

t ^A

Ambient temperature

t ^C,NOCT

Nominal operating photovoltaic cell temperature

g ^t,NOCT

Solar radiation at which NOCT condition

P_{T}^{WT}

Rated power output of wind turbine

P _ra

Rated power of single WT

f _CONS

Usage of power

p_OUT and p_IN

Output and input power

L_{tot}^{indu}

Total inductive load

e₁ (T)

Energy demand

μ_bd

Discharging efficiency

Self-discharging factor

dod

Depth of discharge

c_pv, c_wt, c_dg, c_bS, c_cNV

Cost of PV, WT, DG battery and converter

p_pv, p_wt, p_dg, eB_MIN and p_LOAD

Power of PV, WT, DG, load and battery

e _SERVED

annual served cost

Real Interest rate

Gravity of earth

η _K

Kinetic friction coefficient

angle

p_pv, p_wt, p_dg

generated power from PV, WT, and DG

number of workers

motion of stone block

{\vec{P}}_{I}

current position

φ _K

generated solution

V_{1}^{'}

and

V_{2}^{'}

velocity of balls 1 and 2 after impact

{VAR}_{M}^{MAX}

minimum and maximum

{VAR}_{M}^{MIN}

permitable value

selection pressure

number of pockets

precision rate

Error Rate

HRES

hybrid renewable energy sources

BOA

Billiards-inspired optimization algorithm

BESS

battery energy storage system

NOCT

normal operating cell temperature

TNPC

Total Net Present Cost

COE

Cost of energy

PSO

particle swarm optimization

solar radiation

β^P

temperature coefficient

t ^STC

solar panel cell temperature standard test condition

t ^A,NOCT

ambient temperature at which normal operating cell temperature (NOCT) condition

g ^t

solar radiation on PV

μ_{pv}^{mpp}

efficiency of photovoltaic array at MPP

P ^WT

power output of wind turbine

v, v_N, v_cin, v_cout

wind speed at wind unit hub height, wind speed rated, cut in and cut out wind speed

p _{dg_R}

rated power

Con ^R

rating of inverter

L_{tot}^{non - indu}

total non-inductive load

e_G (T)

generated energy

μ_bc

charging efficiency

μ_cNV

efficiency of converter

p_{pv_R}, p_{wt_R}, p_{dg_R}eB_MAX, and p_{cNV_R}

rated power of PV, WT, DG converter with battery

FUEL _CONS

consumption of fuel

c _ANUALIZED

total annualized cost

processing time of the system

mass of stone

angle

gravity of earth

V ₀

velocity of stone

number of stone blocks

P (t)

power and voltages of the system

motion of workers

ϑ _K

primary solution

V₁ and V₂

velocity of balls 1 and 2 before impact

M₁ and M₂

mass of the balls N and M number of balls and position

objective function

b_{N, M}^{NEW}

and

b_{N, M}^{OLD}

new positions as well as old position values of balls

RAND _[-er.er]

random values

ITER and ITER_MAX

recent iteration and maximum iteration

GPC

Giza Pyramids Construction

photovoltaic

MAS

Multi Agent Systems

DSM

Demand supply Management

LPSP

Loss of power supply probability

Genetic algorithm

WFSA

Wing fly suit algorithm

1 Introduction

In recent days, the number of distributed generation (DG) systems depending on Renewable Energy Sources (RES) like solar, wind, battery, etc. is utilized in multiple applications. But the coupling of RES with basic distribution networks is the difficult task due to these RES are intermittent, and provides lower quality of power [1]. To overcome this drawback, the smart micro-grids are introduced in many applications that coupled the renewable power generation, energy storage, and energy usage nearly via optimal communication and control techniques [2 –4]. For this operation, power electronic converters with the ability of bidirectional power transmission a well as four-quadrant function is needed [5]. The different types of control techniques are utilized in the power converter controller as well as micro-grid control stations for the reliable power delivery and keep the voltage level as well as frequency level to be constant [6]. Residential users as the main part of power users are varying passive energy users with active small-scale power distributors [7].

The maximum number of constructions in India is grid-connected [8 –12], where contains more amount of small as well as rural groups. Because of the large distance from cities, that places are not able to obtain the power from national power grid. The coupling of which places with the national power grid is complex task, so the Diesel Generator (DG) is one of the possible solution for providing the power to rural places [13 –15]. But the continuous increment of Diesel Fuel cost, more amounts of transmission cost, and worry about the power leakage problems will affect the proper power delivery through the Diesel generator [16]. The number of PV system placed in the residential as well as commercial areas is higher at past decades but currently which is slowly reduced even if, the size of PV systems is reaches the maximum of 5.5 kW from 1 kW [13, 14]. Natheless their benefits, the intermittency characteristics of RES denotes challenge that may be overcome through hybridization [17, 18]. The battery is required to store these renewable energy which helps to achieve the power demand at the time of unavailability of sources [19, 20]. The storage device may employed to smooth the transmission as one source to another source as well as maintain the power transmission utilizing sources through small dynamic response like fuel cells [21, 22].

The cost-effective hybrid renewable energy system (HRES) likes (PV) [23] and Biogas Generator (BG) with battery becomes a hopeful off-grid energy system on environment. The coupling of multiple renewable sources rejects large sizing problems as well as increasing the performance of the system and lower cost of power delivery [24, 26]. Also, HRES has the ability to reduce the sending and receiving losses on long distance areas. In recent days, HRES is accepted in most applications due to its technical as well as environmental advantages. Also, the better management systems will promising that HRES operations are done in better quality and lower cost way.

Various literary works are listed here. Elsisi et al. [27] have clarified a new IoT architecture for online gas-insulated switchgear (GIS) condition monitoring based on traditional observation systems. The presented IoT architecture was resultant from the Cyber-Physical System (CPS) concept on Industry 4.0. Though, cyber-attacks and classification of GIS isolation flaws signify the key challenges on execution of IoT topology for online monitoring and tracking of GIS status. Partial discharge pulse sequence features were taken out for every flaw to signify the inputs for the IoT architecture. Elsisi [28] have illustrated a novel robust control process for wind energy conversion system. The presented system may buffer deviations on generator speed due to wind speed penetration and load demand fluctuations on power grid. The novel system was built on the basis of novel simple frequency domain conditions as well as Whale Optimization Algorithm (WOA). This process was employed to design a robust proportional-integral-derivative (PID) controller depends on the WOA to improve the damping characteristics of wind energy conversion system. Elsisi [29] have provided a novel variable structure gain scheduling (VSGS) for frequency regulation. The VSGS may take benefit of the BFOA-fed PI controller that was reduction of settling time. Elsisi et al. [30] have studied an adaptive neuro-fuzzy inference system (ANFIS) from efficient control system for WECS. Though, ANFIS needs an appropriate data set for training and testing to tune their membership functions. In this sense, the study also proposes an efficient approach to make an enough data set. Exactly, an algorithm called mayfly optimization algorithm (MOA) was established to get optimal proportional integral derivative (PID) controller parameters. To prove the benefits of the proposed system, it was related with three dissimilar algorithms on literature. Many test scenarios were accomplished to authorize the efficacy and robustness of the proposed ANFIS-based system.

Objectives and Contribution:

An efficient hybrid strategy to obtain optimal solution of operational cost reduction, size reduction of HRES and optimal power flow control for off-grid system with hybrid technique.

The main innovation of the proposed work is the hybrid algorithm to get the general optimal solution is gathered as search space of these operators.

The proposed study is valuable to solve by two optimization issue. The hybrid approach is joint performance of GPC and BOA hence it is named GPC-BOA technique. The major purpose of proposed method is minimizing the operational cost as well as size of the HRES and improves the power flow of system. Here, the GPC method is employed for forecasting the load requirement of system. The BOA technique optimizes the off-grid system through the deliberation of forecasted load requirement.

The performance of the proposed system is performed on matrix laboratory/Simulink working platform.

The below explained sections are below: Section 2 clarifies the brief review of current investigation work. Section 3 describes that configuration of energy management optimal design of off-grid HRES. The proposed approach of Giza Pyramids Construction and Billiards-Inspired Optimization algorithm (GPC-BOA) described on section 4. Section 5 describes that result and discussions. Section 6 accomplishes the paper.

2 Recent research work: A brief review

In literature, numerous investigation tasks are obtainable depending on energy management for optimal design of off-grid HRES for residential electrification using various techniques. Some of the reviews are:

Kumar et al. [31] clarified the optimal control approach of Hybrid Renewable Energy System (HRES) that has parallel implementation of Lightning Search algorithm using Artificial Neural Network and Recurrent Neural Network (PLSANN). The implemented work was considered Photovoltaic (PV), Wind Turbine (WT), Fuel Cell (FC) and Battery. The DC link was utilized to interconnect the considered renewable sources. The PQ issues were assumed in the origin of wind / photovoltaic energy in a power grid. Through PLSANN/RNN approach, the converter was analyzed and the flow of energy was controlled. For the management of active power, LSA was utilized. For managing the reactive power RNN was utilized. A hybrid MDABSA approach was introduced by the Sureshkumar and Ponnusamy [32] for PFM under SG system. The hybrid MDABSA strategy was the hybrid wrapper of MDA and BSA. According to transmission power amid source as well as load side. The BSA was locating that online control signal. The major contribution of the introduced method was the control of flow of power. Aktaş and Kırçiçek [33] have suggested a strategy for PFM in hybrid system. The hybrid system was incorporated via offshore wind, marine current, battery, ultra capacitor and HRES. The introduced approach was determined the generated power amount as well as load demand by real time. The introduced strategy was assumed the nine different dynamic operations. In the HRES power generation, battery and ultra-capacitor were supported.

Collota et al. [34] have implemented fuzzy logic strategy with particle swarm optimization for effectual energy management. An industrial wireless sensor networks permits for utilizing energy storage devices for lossless power transmission, easy implementations and achieve better performance. The implementation of network elements was difficult work due to examine the needs. The energy usage of industrial wireless sensor networks has been reduced by using optimization methods. Based on storage device condition and ratio between maximum processing time and workload, the fuzzy controller techniques have been implemented with this approach. This approach has been used to find the resting period of sensors. The required output and criterions have been obtained by using particle swarm optimization algorithm. Nge et al. [35] have suggested the Lagrange multipliers for managing the energy of PV system. The contribution of the introduced approach was increase the return over a period when the battery stores the energy barrier. Based on the demand, the price signals were controlled by the introduced strategy. The SSA-CS approach was developed by Lingamuthu and Mariappan [36] for the control of power flow under HRES system. The sources of the MG system were taken as PV, WT, MT and battery using PHS. The objective of cost function was optimized by the introduced hybrid approach. Et-Taoussi el al. [37] has suggested a strategy for the management of power flow in the low voltage urban micro-grid. The control of power flow was analyzed under the day-ahead power flow, residential load consumption, power of PV, electricity tariffs. The stability and reliability of system were guaranteed by DES power references. The major purpose of the introduced method was cost reduction and CO2 emission.

Chang et al. [38] have illustrated a new secure management system for renewable microgrids taking into account the necessary policies to diagnose cyber-attacks that occur on communication networks, generally used at secondary control layer of microgrids (MG). The ability to extract high-level features based on the use of fast Fourier transform (FFT) and deep learning (DL) was considered a strong system against small mutations or novel attacks. Li et al. [39] have provided a new secure transactive power management structure for household AC/DC microgrids taking uncertainty concerns into account. The presented model was built with the advanced method of directed acyclic graphs to promise the privacy and security of the nodes. Hossain et al. [40] have explained energy management schemes in uncertain environments and scheduling system to diminish the working cost of grid-connected microgrid. Optimization issues were formulated as real-time programming methodswere solved by developing modified particle swarm optimization (MPSO) algorithms. He et al. [41] have exhibited a new distributed framework to solve the multi-objective issue that is composed of numerous conflicting objective functions. To overwhelmed the impact of inconsistent measurement units for every objective function. It will divide a multi-objective optimization issue into three sub-problems: the maximization, minimization, normalization. Mansouri et al. [42] have studied a three-goal optimization framework for microgrid energy management under the presence of smart homes and demand response (DR) program. The model was executed on distribution system of 83 buses through 11 microgrids. Uncertainties of power output and load demand of renewable energy resources (RES) were taken into account, and the objective function was modeled under the form of bio-objective and tri-objective models with the fuzzy max-min process.

Mokhtara et al. [43] have illustrated a methodology for optimal design of diesel/PV/wind/battery hybrid renewable energy system (HRES) for the electrification of residential buildings in rural areas Barik and Das [44] have introduced to assess the optimal allocation of suitable integrated resources planning for eco friendly sustainable energy-based hybrid microgrids with distributed generation.

2.1 Background of research work

The literature review indicates that various optimization approaches have been utilized for efficient energy management under smart grid system. In recent days, research involving smart grids is maximum utilized in whole world as well as will turn into beautiful field of investigation, due to the entire advantages, which may be aimed for end-users with energy distributors. The smart grids may develop the grid energy efficiency to the advantage of end-users via scheduling and coordinating the small priority home devices; hence, its consumption of the power obtain benefit of the most suitable energy prices and/or energy sources in provided time. The effectiveness, reliability, and safety development of power distribution networks are consummate via the computing and communication technologies. However, to attempt the rising electricity demand, and proficient energy consumption, a novel approaches are required. Because, the existing approaches is not suitable for numerous homes to have the similar appliances with the power ratings (kW) and identical length of operation time (LOT). Moreover, the various analytic algorithms are accessible that may course enormous volume of data. These mentioned problems are motivated to do these research works.

3 Configuration of energy management for optimal design of off-grid HRES

The Fig. 1 portrays that general architecture of proposed system. The proposed off-grid system is connected with photovoltaic (PV), wind turbine (WT), Diesel Generator (DG), battery storage system (BSS), and power converter. The proposed method is the combination of GPC and BOA hence it is named GPC-BOA method.

Fig. 1

Overall architecture of GPC-BOA system.

The major purpose of GPC-BOA method is diminishing the cost of energy as well as size of HRES and control of power flow system. The PV system is associated through DC to DC converter that minimizes the ripple of the system and given the power to DC bus. The wind turbine is linked with AC to DC converter due to the energy generated from the WT is an AC. The direct ac supply is not secure for the energy management system so which is converted into DC form and then it’s given to the systems for doing the objective operations [37]. Also, Battery is connected with dc to dc converter. Battery is utilized for storing excess power of GPC-BOA system. The mathematical modelling of each component of GPC-BOA system is explained under beneath section.

The PV, WT, DG, powers are given to the load which is controlled by the proposed approach. In the proposed approach, the Multi Agent Systems (MAS) are considered for the smooth operations. The MAS is important for increasing demands in distributed energy systems which is a self-standing system and utilize the data to communicate with others as well as getting knowledge about the environment. Here, the MAS system includes load agent (home, colleges, etc.), generation agent (PV, WT, and DG), and storage agent (Battery), deign agent (GPC-BOA), and control agent.

3.1 Load agent (LA)

The main work of load agent is computing and controlling the loads at each hour’s as well assending the needed data’s to other agents. In this research work, the home is considered as the load.

3.2 Generation agent (GA)

The hybrid renewable energy resource comes under the generation agent. In this research work, PV, WT, and DG are considered as the generation agent. The main work of this agent is calculating the power generation conditions of the sources and sends the data about the availability of power to the control agent [37]. Based on the suggestions from the control agent, which joining, rejecting, and coupling or de-coupling the energy generating systems. The mathematical modelling of this agent is shown below,

3.2.1 Modelling of PV

The PV is employed for converting solar energy into corresponding electric energy. Based on weather condition, air temperature and the radiation of solar, the energy of PV is generated.

The PV array outcome may be expressed,

$\begin{matrix} p_{t}^{pv} = & p_{pv}^{r} \times r^{F} \times (\frac{g}{g_{STC}}) \\ \times (1 + β^{P} (t^{C} - t^{STC})) \end{matrix}$ (1) here solar cell output power is $p_{t}^{pv}$ , solar cell rated power is indicated as $p_{pv}^{r}$ , module de-rating factor is indicated as r^F, solar radiation is g, solar radiation under standard test conditions denoted g_STC, temperature coefficient denoted β^P, cell temperature is indicated t^C. The temperature of cell can be expressed as,

$\begin{matrix} t^{C} = & t^{A} + (t^{C, NOCT} - t^{A, NOCT}) (\frac{g^{t}}{g^{t, NOCT}}) \\ \times (1 - \frac{μ_{pv}^{mpp}}{0.9}) \end{matrix}$ (2) here ambient temperature is indicated t^A, ambient temperature at which normal operating cell temperature (NOCT) condition is t^A,NOCT, nominal operating photovoltaic cell temperature is t^C,NOCT, Solar radiation on PV array is specified as g^t, efficiency of photovoltaic array at MPP is specified as $μ_{pv}^{mpp}$ . The Fig. 2 shows equivalent circuit of PV system.

Fig. 2

Equivalent circuit of PV system.

3.2.2 Modelling of wind turbine

According to wind speed, the result of the WT is defined at four operational areas. Because of the low wind speed that means the speed is less than the cut in wind the output power of wind turbine similar with zero. Hence, the turbine does not rotate. When the speed of wind is amid the cut-in and nominal then the outcome is a function of wind speed. The rated output power is found as third region. While the wind speed is greater than cut out speed then it turned off, for the purpose of preventing from damage. The WT output power is used to evaluate the given expression,

Wind system generates the power depending on wind speed (WS). The result of the wind is defined as,

$P_{T}^{WT} = P_{ra} {\begin{matrix} 0, v < v_{cin} \\ P_{n} (v), v_{cin} ⩽ v < v_{N} \\ P_{ra}, v_{N} ⩽ v < v_{cout} \\ 0, v ⩾ v_{out} \end{matrix}$ (3)

$P^{WT} = η_{WT} P_{T}^{WT}$ (4) here rated power output of wind turbine specified as $P_{T}^{WT}$ , power output of wind turbine specified as P^WT, rated power of single WT is P_ra, wind speed at wind unit hub height, wind speed rated, cut in and cut out wind speed are indicated as v, v_N, v_cin, v_cout correspondingly.

3.2.3 Model of Diesel generator

DG utilized under hybrid power system for achieving load requirement at time of lower availability of power from renewable sources as well as storage devices. The availability of utilized fuel with DG based on output power which can be expressed as,

$f_{CONS} = A . p_{dc} + B . p_{dg_R}$ (5) here the usage of power is denoted as f_CONS and p_{dg_R} represented as rated power. A, B is the constant values.

3.2.4 Modelling of Power Converter

The power converter is utilized to convert alternating current to direct current or direct current to alternating current. The efficiency of PC can be revealed as,

$μ_{cNV} = \frac{p_{OUT}}{p_{IN}}$ (6) where p_OUT and p_IN is the output and input powers. The HRES is incorporated with AC and DC components therefore converter is necessary in the system. The rating of the inverter can be expressed as,

${Con}^{R} = 3 L_{tot}^{indu} + L_{tot}^{non - indu}$ (7) here rating of inverter is specified as Con^R, total inductive load is specified as $L_{tot}^{indu}$ , total non-inductive load is specified as $L_{tot}^{non - indu}$ .

3.3 Storage agent (SA)

The main work of SA is monitoring the condition of power on storage devices as well as gathering the data from generation agent as well as load agent to make charging and discharging operations. The modeling of battery is explained in below section.

3.3.1 Modeling of battery

Here, the battery is considered as the storage agent. The implementation of battery is very simple process and it stores the amount of energy from the generating sources. It doing the charging operation at the time of power continuously supplied from generating sources. When it reaches the limited energy level, it starts to make the discharging operation. The equivalent circuit of battery portrays on Fig. 3.

Fig. 3

Equivalent circuit of Battery.

The charging and discharging functions of battery can be denoted,

$\begin{matrix} f_{B} (T + 1) = & f_{B} (T) \times (1 - a) \\ - (\frac{f_{1} (T)}{μ_{cNV}} - f_{G} (T)) \times μ_{bd} \end{matrix}$ (8)

$\begin{matrix} f_{B} (T + 1) = & f_{B} (T) \times (1 - a) \\ - (f_{G} (T) - \frac{f_{1} (T)}{μ_{cNV}}) \times μ_{bc} \end{matrix}$ (9)

here f₁ (T) is the energy demand as well as f_G (T) is the generated Energy, μ_bd is the discharging efficiency and μ_bc represents the charging efficiency, α is the self-discharging factor, here α is fixed at 0. The efficiency of converter is denoted as μ_cNV. The minimal and maximal storage ability of battery may be calculated with below equation,

${fB}_{MIN} ⩽ fB (T) ⩽ {fB}_{max}$ (10)

here

${fB}_{MIN} = (1 - dod) \times {fB}_{max}$ (11) here depth of discharge is denoted as dod.

3.4 Design agent (DA)

DA is utilized to optimize the hybrid renewable energy sources which choose the optimal size of HRES and change the size of HRES based on that value to provide an optimal result of energy management. In this paper, GPC-BOA is considered as the design agent; it helps to reduce the size of HRES and also helps to reduce the cost of energy (COE).

3.5 Control agent (CA)

CA performs the supervisory function which checks the data from the various agents with respect to their objective values. The main work of CA is monitoring all the equipment of HRES which uses the energy management condition to achieve the stability among demand and supply side for achieving the optimal result such that higher reliability, lower cost and minimum size [37]. In this research work, Demand supply Management (DSM) is introduced which is coupled with GPC-BOA technique for the objective functions. DSM was introduced to minimize the power utilization of loads and also minimize the maximum size of HRES. Here, two loads are considered for HRES optimization size. The processing stage of HRES size optimization is as follows,

•Initially, the PV and WT generate the energy and which is utilized for the charging purpose of battery.

•In second stage, the energy not utilized by the first load (if the battery is filly charged) is transmitted to the second load.

•If the PV and WT cannot gives the required amount of power to achieve the first load, the control agent needs for utilizing second load. Still it cannot give the needed load, the stored energy from the battery is utilized.

•If the power given by the HRES is not enough to achieve the needed load as well as the battery is filtered, DG is utilized to transmit the required amount of power. If the whole system cannot achieve the demand, the loss of power transmission is calculated.

3.6 Problem formulation

The Total Net Present Cost (TNPC) should be minimum for optimal energy transmission operations. To achieve this, the sizing of HRES is most important which can be derived as [37],

$\begin{matrix} F = & MIN * tnpc (p_{pv_R}, n_{wt_R}, \\ p_{dg_R}, {fB}_{max}, p_{cNV_R}) \end{matrix}$ (12)

$0 ⩽ lpsp ⩽ {lpsp}^{max}$ (13)

${rf}^{MIN} ⩽ rf ⩽ 1$ (14)

$\begin{matrix} 0 & ⩽ p_{{pv}_{R}}, n_{{wt}_{R}}, p_{{dg}_{R}}, eB max, p_{c_{{NV}_{R}}}, \\ ⩽ p_{{pv}_{R}}^{max}, n_{wt}^{max}, p_{{dg}_{R}}^{max}, {bs}^{max}, p_{cNV}^{max} \end{matrix}$ (15)

3.6.1 Total net present cost

TNPC is mostly utilized on HRES implementation process which may be calculated by using the following equation.

$tnpc (ψ) = (c_{CAP} + c_{o & m} + c_{REP} + c_{FUEL})$ (16) here, c_CAP is the cost of investment, c_o&m refers operation and preservation cost, the replacement as well as fuel cost can be denoted as, c_REP and c_FUEL

$\begin{matrix} . c_{CAP} (ψ) = & (p_{{pv}_{R} \cdot} c_{pv} + p_{{wt}_{R} \cdot} c_{wt} + p_{{dg}_{R} \cdot} c_{dg} \\ + {fB}_{max \cdot} c_{bs} + p_{{cNV}_{R} \cdot} c_{cNV}) \end{matrix}$ (17)

$c_{0 & m} (ψ) = 0.02 c_{a_{CAP}} . \sum_{K = 1}^{t} \frac{1}{{(1 + I)}^{K}}$ (18)

$\begin{matrix} c_{REP} (ψ) = ({eB}_{MAX} . c_{bs} . \sum_{K = 10}^{t} \frac{1}{{(1 + I)}^{K}} \\ + p_{cNV} . c_{cNV} . \sum_{K = 12}^{t} \frac{1}{{(1 + I)}^{K}} + p_{{dg}_{R}} . c_{dc} . \\ \sum_{K = A, 2 A, \dots, < t}^{t} \frac{1}{{(1 + I)}^{K}}) \end{matrix}$ (19)

$c_{FUEL} (ψ) = {FUEL}_{CONS} . c_{FUEL} . \sum_{K = 1}^{t} \frac{1}{{(1 + I)}^{K}}$ (20)

The cost of PV, WT, DG, battery and converter can be denoted as c_pv, c_wt, c_dg, c_bS, c_cNV. The consumption of fuel can be denoted as FUEL_CONS.

3.6.2 Loss of power supply probability (LPSP)

LPSP is mainly utilized for calculating system reliability. Basically, the total power shortage proportion in excess of total power requirements is called as LPSP. LPSP means that the rate of disappointment of load which is expressed as,

$lpsp (%) = \frac{\sum_{T = 1}^{t} e_{1} (T) - p_{pv} (T) - p_{wt} (T) - p_{dg} (T) - (eB (T) - {eB}_{MIN})}{\sum_{T = 1}^{t} p_{LOAD} (T)}$ (21) where The power of PV, WT, DG, load and battery may be denoted as, p_pv, p_wt, p_dg, eB_MIN, and p_LOAD

3.6.3 Renewable Fraction (RF)

RF is utilized for fixing lower energy value at whole load supplied using HRES. The following equation helps to calculate the RF value,

$rf (%) = 1 - \frac{\sum p_{dg}}{\sum p_{pv} + p_{wt} + p_{dg}}$ (22)

3.6.4 Cost of energy (COE)

The annualized cost of system is separated by served cost is known as the COE of system which can be expressed as,

$coe (ψ / KWh) = \frac{c_{ANUALIZED}}{e_{SERVED}}$ (23)

$c_{ANNUALIZED} (ψ) = tnpc . crf$ (24)

$crf = \frac{| I {(I + 1)}^{t} |}{| {(I + 1)}^{t} - 1 |}$ (25) here The total annualized cost is c_ANUALIZED and the annual served cost is e_SERVED Also the processing time of the system is denotes as t and Real Interest rate can be denoted as I

3.6.5 Fuel consumption with CO₂ emission

In long distance areas, fuel usage is lower due to higher transmission cost. According to the fuel usage, the CO₂ emission is calculated which is as follows,

$\begin{matrix} FUEL CONSUMPTION (l / YEAR) \\ = \sum_{T = 1}^{7806} {FUEL}_{CONS} (T) \end{matrix}$ (26)

${co}_{2} (kg / YEAR) = ef . FUELCONSUMPTION$ (27)

4 Proposed approach of Giza Pyramids Construction and Billiards-Inspired Optimization Algorithm (GPC-BOA)

To reduce the cost of energy as well as size of HRES, GPC-BOA is implemented in this approach. In this research work, GPC-BOA is considered as the design agent. The integration of Giza Pyramids construction and Billiards-inspired Optimization algorithm helps to achieve the optimal result of energy management operations.

4.1 Processing steps of Giza Pyramids Construction

In GPC, initially the stone blocks are dispersed on all sides of the pyramid construction point. So, the workers want to move the stone blocks into the construction point. The starting positions of every block are analyzed first. Ramp is utilized to pass the stone blocks into the construction point [45]. The transmission time of stone from dispersed place to construction place is depends on the strength and availability of workers. At first all the workers try to identify the best position to moving the stone and start to push the stone after finding the correct position. If one worker cannot move the stone block, new worker is placed on that place instead of previous worker. This process is continuing until the stone reaches the destination point. The force utilized by the workers for the movement of stone can be expressed as,

$F_{K} = η_{K} MGCos θ$ (28)

The acceleration of stone block may be computed with below equation,

$A = - G (Sin θ + η_{K} Cos θ)$ (29) where M Represents mass of stone, G denotes gravity of earth, θ specifies angle, and η_K is Kinetic friction coefficient. The motion of stone block can be calculated using the following expression,

$M = \frac{V_{0}^{2}}{2 G (Sin θ + η_{K} Cos θ)}$ (30) where G specifies gravity of earth, θ specifies angle and velocity of stone is denoted as V₀. When a workers giving force to the stone block, it starts to move towards the pyramid construction point with starting velocity. After some time, the motion of stone will be stop due to the friction. Further, the workers gives new force to the stone, so which again starts to move with starting velocity. During this process, the moving positions of workers are varied. The calculation of new position may be done through the aid of following equation,

$\vec{P} = ({\vec{P}}_{I} + M) \times X {\vec{Σ}}_{I}$ (31)

$X = \frac{V_{0}^{2}}{2 GSin θ}$ (32) where the current position is denoted as ${\vec{P}}_{I}$ and motion of stone is denoted as M as well as movement of workers is denoted as X. The step-by-step method of GPC denotes below,

Step 1. Initiation

Initially generate the input power and input voltage of the system, cost function, and maximal iteration of system. Also, initialize the population of stone blocks and workers.

$P = {p_{pv}, p_{wt}, p_{dg}}$ (33)

$S = {S_{1}, S_{2}, S_{3} \dots S_{N}}$ (34)

$W = {W_{1}, W_{2}, W_{3} \dots W_{N}}$ (35)

where the generated power from PV, WT, and DG can be denoted as p_pv, p_wt, p_dg. S specifies number of stone blocks and W specifies number of workers.

Step 2. Random Generation

The input parameters are randomly created after the method of initiation. In this research, the power and voltages are randomly created with below matrix Z:

$Z = [\begin{matrix} P^{11} (t) & P^{12} (t) & \dots & P^{1 m} (t) \\ P^{21} (t) & P^{22} (t) & ⋮ & P^{2 m} (t) \\ P^{n 1} (t) & P^{n 2} (t) & \dots & P^{nm} (t) \end{matrix}]$ (36) where P (t) represent the power and voltages of the system.

Step 3. Fitness Function

The equation for fitness function may be denoted,

$F = MIN \sum_{I = 1}^{N} C_{I}$ (37)

$C_{I} = {c_{pv}, c_{wt}, c_{dg}, c_{bs}, c_{cNV}}$ (38) where The cost of PV, WT, DG, battery and converter can be denoted as c_pv, c_wt, c_dg, c_bS, c_cNV.

Step 4. Calculation

The motion of stone block and motion of workers can be computed using the following equations,

$M = \frac{V_{0}^{2}}{2 G (Sin θ + η_{K} Cos θ)}$ (39)

$X = \frac{V_{0}^{2}}{2 GSin θ}$ (40) where, M indicates the motion of stone block and X indicates motion of workers.

Step 5. New Position Estimation

Based on the motion of stone block as well as motion of workers, the new position can be evaluated which is expressed as,

$\vec{P} = ({\vec{P}}_{I} + M) \times X {\vec{Σ}}_{I}$ (41) where the current position is denoted as ${\vec{P}}_{I}$ and motion of stone is denoted as M as well as movement of workers is denoted as X.

Step 6. Finding the Availability of Substituting Workers

If one worker cannot push the stone, another one person is substituted on which place instead of that worker. The availability of substituting workers can be evaluated using the following expression,

$ς_{K} = {\begin{matrix} φ_{K}, if RAND [0, 1] ⩽ 0.5 \\ ϑ_{K}, else \end{matrix}$ (42) where ϑ_K Represents the primary solution and φ_K Represents the generated solution.

Step 7. Position Updation

Update the position of the workers as well as stone blocks in all iteration.

Step 8. Termination

If the process reaches the objective condition, it will be terminated otherwise it continuing from step 3.

4.2 Processing steps of Billiards-Inspired Optimization Algorithm (BOA)

BOA is type of meta-heuristic algorithm depends on billiards games. The long stick utilized for playing billiards game is known as cue. The purpose of this stick is to restrict the billiards balls [46]. All the players consist of the number of balls. The position of all the balls assumed as the variables. Initially, all the balls are randomly distributed on the billiards table, from which the best ball is choose as pockets. Then all balls are splitted into two groups namely cue and normal balls. After that, all the cue balls beat their aiming balls and goes near the pocket. The kinematic as well as collision law is generated during the time of cue ball beating the normal balls. The GPC-BOA algorithm shows a Fig. 4(a). Figure 4(b) shows the Flow process of the proposed work.

Fig. 4(a)

Flowchart of GPC-BOA algorithm.

Fig. 4(b)

Flow process of the proposed work.

The kinetic energy as well as speed of the balls can be expressed as,

$2 M_{1} V_{1. ∐}^{2} + \frac{1}{2} M_{2} V_{2. ∐}^{2} + \frac{1}{2} M_{1} V_{1. ⊥}^{2} + \frac{1}{2} M_{2} V_{2. ⊥}^{2} = 2 M_{1} V_{1. ∐}^{' 2} + \frac{1}{2} M_{2} V_{2. ∐}^{' 2} + \frac{1}{2} M_{1} V_{1. ⊥}^{' 2} + \frac{1}{2} M_{2} V_{2. ⊥}^{' 2}$ (43) where V₁ and V₂ is the velocity of balls 1 and 2 before impact. $V_{1}^{'}$ and $V_{2}^{'}$ is the velocity of balls 1 and 2 after impact. M₁ and M₂ represent the mass of the balls. The step by step method of BOA is below,

Step 1. Initiation

Initially generate the input power and input voltage of the system, cost function, equivalent generation limits and maximal iteration of system. Also initialize the number of balls and position of balls using the following expression,

$\begin{matrix} b_{N, M}^{0} = & {VAR}_{M}^{MIN} + {RAND}_{[0, 1]} \\ ({VAR}_{M}^{MAX} - {VAR}_{M}^{MIN}) \end{matrix}$ (44)

N = 1, 2, … 2n, M = 1, 2, … m

here, ${VAR}_{M}^{MAX}$ and ${VAR}_{M}^{MIN}$ represent the minimum and maximum permitable value. N and M specifies number of balls and position.

Step 2. Random Generation

The input parameters are randomly generate on range of [0, 1] which can be expressed as,

$S = [\begin{matrix} X_{11}^{a} X_{12}^{b} X_{13}^{c} \dots \dots X_{mn}^{z} \\ X_{21}^{a} X_{22}^{b} X_{23}^{c} \dots \dots X_{mn}^{z} \\ X_{31}^{a} X_{32}^{b} X_{33}^{c} \dots \dots X_{mn}^{z} \end{matrix}]$ (45)

Step 3. Fitness Function

The calculation of fitness function determined from objective function that may be denoted as,

${OBJ}_{F} = MIN {Cost}$ (46)

Step 4. Pockets Estimation

Calculate the number of pockets and position of each pocket. The pockets collect the balls when the players move the balls into the pockets. The pocket helps to find the winner of the game with less evaluation cost.

Step 5. Grouping Balls

Then finding the pockets, the balls ordered in one by one and after that are splitted into two similar groups’ namely normal balls and cue balls. The grouping of normal balls can be expressed as,

$N = 1, 2, \dots n$ (47)

The grouping of cue balls can be expressed as,

$C = c + 1, \dots \dots \dots, 2 c$ (48)

Step 6. Assigning pockets to balls

The pockets are choose for each ball using the following expression,

$p_{K} = \frac{E^{- α F_{k}}}{\sum_{K} E^{- α F_{k}}}$ (49)

$K = 1, 2, \dots \dots M$ (50) where α represents the selection pressure as well as F represents the objective function. K is the number of pockets.

Step 7. Updation

After the collision, the new position of balls are updated using below expression,

$\begin{matrix} b_{N, M}^{NEW} \\ = {RAND}_{[- er . er]} (1 - pr) (b_{N, M}^{OLD} - p_{K, M}^{N}) + p_{K, M}^{N} \end{matrix}$ (51)

$pr = \frac{ITER}{{ITER}_{MAX}}$ (52) where the new positions as well as old position values of balls are denoted as $b_{N, M}^{NEW}$ and $b_{N, M}^{OLD}$ . The precision rate is denoted as pr. RAND_[-er.er] represented asthe random values and er represent the Error Rate. The recent iteration and maximum iteration is denoted as ITER and ITER_MAX.

Step 8. Termination

When the winner of game is selected, the process reaches the termination point otherwise the process is continuing from step3.

5 Results and discussion

In this segment the simulation result of proposed approach is defined. For diminishing energy cost as well as size of HRES, GPC-BOA is implemented in this work. The proposed approach is executed through MATLAB Simulink platform. The efficiency of the proposed approach is examined with comparison of existing methods as genetic algorithm (GA), particle swarm optimization (PSO), and wing fly suit algorithm (WFSA) [47]. In the below section described the analysis of case studies. Figure 5 portrays that analysis of predicted electricity demand of proposed system. Here, the predicted electricity demand is 0 at starting stage then it increased to 2GJ/h at 7 h. It reaches maximal value of 12GJ/h at 18 h and then starts to decrease. Figure 6 portrays that cost performance of proposed technique with existing methods (a) GA (b) PSO (c) WFSA. In Fig. 6 (a), the cost of GA is 50$MWh at starting stage but the cost of proposed method is 30$MWh at starting stage. The cost of GA arrives maximal value of 300$MWh at 5 hour. In Fig. 6(b), the cost of PSO is 50$MWh at starting stage but the cost of proposed method is 30$MWh at starting stage. The cost of PSO reaches maximal value of 300$MWh at 5hour. In Fig. 6(c), the cost of WFSA is 40$MWh at starting stage but the cost of proposed method is 30$MWh at starting stage. The cost of WFSA arrives maximal value of 290$MWh at 5hour but the cost of proposed method arrives maximal value of 270$MWh at 5hour. The cost of proposed method is lower than existing GA, PSO and WFSA systems.

Fig. 5

Analysis of predicted electricity demand of GPC-BOA system.

Fig. 6

Cost performance of proposed technique with existing methods (a) GA (b) PSO (c) WFSA.

Figure 7 portrays that cost comparison of GPC-BOA with existing systems. The maximum cost of existing techniques as GA, PSO, and WFSA is 320$MWh, 290$MWh, and 300$MWh at 5hour. But the maximum cost of proposed system is 270$MWh at the time of 5hour. The cost of GPC-BOA is lower than existing methods. The performance of GPC-BOA system is analyzed depending on weather condition under the four cases like spring, summer, autumn and winter which is explained below.

Fig. 7

Cost comparison of GPC-BOA with existing systems.

Case 1. Analysis of electrical energy on spring

This section explains the performance of electrical energy of proposed system on spring season. Figure 8 shows the power consumption of proposed method. The maximum consumption of power through compression chiller (CoC), light, non-schedulable residential electrical appliances (nsch), dish washer (dw), washing machine (wm), vacuum cleaner (vc), and car is 0.3GJ/h, 1GJ/h, 2GJ/h, 2GJ/h, 2.5GJ/h, 3GJ/h and 12GJ/h. Figure 9 portrays power performance of proposed method (a) SOFC-GT, dch,e, ch,e (b) De,t, eES. In Fig. 9(a), the solid oxide fuel cell-gas turbine power (SOFC-GT), charging (ch,e) and discharging (dch,e) power of proposed system reaches the maximum value of 4GJ/h at 17 h, 12.2GJ/h at 20 h, and 4.8GJ/h at 16 h. In Fig. 9(b), the demand power and electricity stored in energy storage system (eES) reaches the maximum value of 25GJ at 7hour and 34GJ at the time of 8 h.

Fig. 8

Power consumption of proposed method for case 1.

Fig. 9

Power analysis of GPC-BOA system (a) SOFC-GT, dch,e, ch,e (b) De,t, eES for case 1.

Figure 10 shows power analysis of GPC-BOA system (a) SOFC-GT, dch,e, ch,e (b) De,t, eES. In Fig. 10(a), the SOFC-GT, charging (ch,e) and discharging (dch,e) power of proposed system reaches the maximum value of 3.5GJ/h at 21 h, 5.5GJ/h at 21 h, and 3.5GJ/h at 3 h. In Fig. 10(b), the demand power and electricity stored in energy storage system (eES) reaches the maximum value of 12GJ at 4hour and 22GJ at the time of 7 h.

Fig. 10

Electricity power and energy for case 1.

Case 2. Analysis of electrical energy on summer

This section explains the analysis of electrical energy of GPC-BOA system on summer season. Figure 11 shows power consumption of proposed system. The maximum consumption of power through compression chiller (CoC), light, non-schedulable residential electrical appliances (nsch), dish washer (dw), washing machine (wm), vacuum cleaner (vc), and car is 0.3GJ/h, 1.6GJ/h, 2GJ/h, 1.8GJ/h, 3GJ/h, 3.6GJ/h and 12.2GJ/h. Figure 12 portrays power analysis of proposed method (a) SOFC-GT, dch,e, ch,e (b) De,t, eES. In Fig. 12(a), the SOFC-GT, charging (ch,e) and discharging (dch,e) power of proposed system reaches the maximum value of 3.5GJ/h at 7 h, 4.9GJ/h at 7 h, and 3.5GJ/h at 5 h. In Fig. 12(b), the demand power and electricity stored in energy storage system (eES) reaches the maximum value of 10GJ at 8hour and 20GJ at the time of 6 h.

Fig. 11

Power consumption of proposed method for case 2.

Fig. 12

Power performance of proposed method (a) SOFC-GT, dch,e, ch,e (b) De,t, eES for case 2.

Figure 13 shows the power performance of GPC-BOA system (a) SOFC-GT, dch,e, ch,e (b) De,t, eES. In Fig. 13(a), the SOFC-GT, charging (ch,e) and discharging (dch,e) power of proposed system reaches the maximum value of 4.4GJ/h at 18 h, 12.4GJ/h at 18 h, and 4.6GJ/h at 2 h. In Fig. 13(b), the demand power and electricity stored in energy storage system (eES) reaches the maximum value of 25GJ at 6hour and 35GJ at the time of 8 h.

Fig. 13

Electrical power and energy for case 2.

Case 3. Analysis of Electrical Energy on Autumn

This section explains that performance of electrical energy of proposed system on summer season. Figure 14 portrays that power consumption of proposed method. The maximum consumption of power through compression chiller (CoC), light, non-schedulable residential electrical appliances (nsch), dish washer (dw), washing machine (wm), vacuum cleaner (vc), and car is 0.1GJ/h at 5 h, 1GJ/h at 21 h, 2GJ/h at 7 h, 1.4GJ/h 18 h, 3GJ/h, 1.6GJ/h at 18 h and 10.8GJ/h at 18 h. Figure 15 portrays power analysis of proposed method (a) SOFC-GT, dch,e, ch,e (b) De,t, eES. In Fig. 15(a), the SOFC-GT, charging (ch,e) and discharging (dch,e) power of proposed system reaches the maximum value of 2GJ/h at 7 h, 12GJ/h at 18 h, and 4GJ/h at 4 h. In Fig. 15(b) the demand power and electricity stored in energy storage system (eES) reaches the maximum value of 25GJ at 6hour and 35GJ at the time of 8 h.

Fig. 14

Power consumption of proposed method for case 3.

Fig. 15

Power performance of GPC-BOA system (a) SOFC-GT, dch,e, ch,e (b) De,t, eES for case 3.

Figure 16 shows the power performance of GPC-BOA system (a) SOFC-GT, dch,e, ch,e (b) De,t, eES. In Fig. 16(a), the SOFC-GT, charging (ch,e) and discharging (dch,e) power of proposed system reaches the maximum value of 2GJ/h at 7 h, 12GJ/h at 18 h, and 4GJ/h at 4 h. In Fig. 16(b), the demand power and electricity stored in energy storage system (eES) reaches the maximum value of 25GJ at 6hour and 35GJ at the time of 8 h.

Fig. 16

Electrical power and energy for case 3.

Case 4. Analysis of Electrical Energy on Winter

This section explains that performance of electrical energy of GPC-BOA system on winter season. Figure 17 shows the power consumption of proposed method. The maximum consumption of power through lift, non-schedulable residential electrical appliances (nsch), dish washer (dw), washing machine (wm), vacuum cleaner (vc), and car is 0.8GJ/h at 7 h, 1.8GJ/h at 7 h, 1.2GJ/h at 18 h, 2.4GJ/h 18 h, 3GJ/h at 18 h, 12GJ/h at 18 h. Figure 18 shows the power analysis of proposed method (a) SOFC-GT, dch,e, ch,e (b) De,t, eES. In Fig. 18(a), the SOFC-GT, charging (ch,e) and discharging (dch,e) power of proposed system reaches the maximum value of 3.4GJ/h at 17 h, 12.2GJ/h at 18 h, and 3.7GJ/h at 1 h. In Fig. 18(b), the demand power and electricity stored in energy storage system (eES) reaches the maximum value of 24GJ at 6hour and 35GJ at the time of 8 h.

Fig. 17

Power consumption of proposed method for case 4.

Fig. 18

Power performance of GPC-BOA system (a) SOFC-GT, dch,e, ch,e (b) De,t, eES for case 4.

Figure 19 shows the power performance of GPC-BOA system (a) SOFC-GT, dch,e, ch,e (b) De,t, eES. In Fig. 19a), the SOFC-GT, charging (ch,e) and discharging (dch,e) power of proposed system reaches the maximum value of 4GJ/h at 20 h, 4.8GJ/h at 18 h, and 3.6GJ/h at 1 h. In Fig. 19(b), the demand power and electricity stored in energy storage system (eES) reaches the maximum value of 10GJ at 6hour and 22.5GJ at the time of 7 h.

Fig. 19

Electrical power and energy for case 4.

Table 1 describes that output power of PV, WT, MT, and battery using GPC-BOA strategy. The maximal power of PV is 5KW with the minimal power refers 0. The maximal power of WT implies 5 kW and minimal power implies 2KW. The maximal power of battery implies 1 kW and minimal power implies 0. Table 2 illustrates the cost performance of GPC-BOA and existing process. Here, the cost of proposed method reaches the maximum cost of 45$. But the cost of existing WFSA, PSO, and GA methods are 53$, 55$, and 57$. The cost of proposed method is lower to existing methods.

Table 1

The output power of PV, WT, DG, and battery using proposed approach

Time (h)	PV (KW)	WT(KW)	MT(KW)	Battery (KW)
1	0	2	19	0
2	0	3	17	1
3	0	3	17	1
4	1	2	16	1
5	1	1	2	3
6	2	2	25	4
7	3	3	27	2
8	4	3	29	1
9	4	4	30	3
10	5	5	32	1

Table 2

Cost analysis of GPC-BOA and existing techniques

Technique	Cost ($)
GA	57$
PSO	55$
WFSA	53$
Proposed technique	45$

6 Conclusion

In this manuscript proposed a hybrid approach for off-grid connected system. The proposed approach is efficiently diminish the system cost, size of HRES and improve power flow of the system as well as satisfies the load requirement system. The simulation outcome analyzed under four cases like spring, summer, autumn, and winter season. The proposed approach used for generate the evaluation of the sources, storage and approachable load offers. The cost analysis point of view, proposed system efficiently reduce that cost compared to existing system and provide less solution time. The cost of the proposed system achieves the minimum cost of 45$.Based on this work, control problems for the whole system, to recover the security of the whole system may be further investigated on future.

References

Sami

, Intelligent energy management for off-grid renewable hybrid system using multi-agent approach, IEEE Access 8 (2019), 8681–8696. Available: 10.1109/access.2019.2963584.

Jafari

, Malekjamshidi

, Zhu

and Khooban

, A novel predictive fuzzy logic-based energy management system for grid-connected and off-grid operation of residential smart microgrids, IEEE Journal of Emerging and Selected Topics in Power Electronics 8(2) (2020), 1391–1404.

Imran

et al. Heuristic-based programable controller for efficient energy management under renewable energy sources and energy storage system in smart grid, IEEE Access 8 (2020), 139587–139608.

Housseini

, Okou

and Beguenane

, Robust nonlinear controller design for on-grid/off-grid wind energy battery-storage system, IEEE Transactions on Smart Grid 9(6) (2018), 5588–5598.

Jafari

, Malekjamshidi

, Lu

and Zhu

, Development of a fuzzy-logic-based energy management system for a multiport multioperation mode residential smart microgrid, IEEE Transactions on Power Electronics 34(4) (2019), 3283–3301.

Nizami

, Hossain

and Fernandez

, Multiagent-based transactive energy management systems for residential buildings with distributed energy resources, IEEE Transactions on Industrial Informatics 16(3) (2020), 1836–1847.

Javaid

, Hafeez

, Iqbal

, Alrajeh

, Alabed

and Guizani

, Energy efficient integration of renewable energy sources in the smart grid for demand side management, IEEE Access 6 (2018), 77077–77096.

Hamdi

, Driouch

and Ajib

, Energy management in hybrid energy large-scale MIMO systems, IEEE Transactions on Vehicular Technology 66(11) (2017), 10183–10193.

Rajesh

, Shajin

F.H.

, Mouli Chandra

, Kommula

B.N.

Diminishing energy consumption cost and optimal energy management of photovoltaic aided electric vehicle (PV-EV) by GFO-VITG approach, Energy Sources, Part A: Recovery, Utilization, and Environmental Effects (2021), 1–9.

10.

Shajin

F.H.

, Rajesh

and Raja

M.R.

, An efficient VLSI architecture for fast motion estimation exploiting zero motion prejudgment technique and a new quadrant-based search algorithm in HEVC, Circuits, Systems, and Signal Processing 41(3) (2022), 1751–1774.

11.

Rajesh

, Shajin

F.H.

, Cherukupalli

An efficient hybrid tunicate swarm algorithm and radial basis function searching technique for maximum power point tracking in wind energy conversion system, Journal of Engineering, Design and Technology (2021).

12.

Shajin

F.H.

, Rajesh

and Thilaha

, Bald eagle search optimization algorithm for cluster head selection with prolong lifetime in wireless sensor network, Journal of Soft Computing and Engineering Applications 1(1) (2020), 7.

13.

Pearson

, Wagner

, Delorit

and Schuldt

, Meeting temporary facility energy demand with climate-optimized off-grid energy systems, IEEE Open Access Journal of Power and Energy 7 (2020), 203–211.

14.

Rahbar

, Chai

and Zhang

, Energy cooperation optimization in microgrids with renewable energy integration, IEEE Transactions on Smart Grid 9(2) (2018), 1482–1493.

15.

Alfaverh

, Denai

and Sun

, Demand response strategy based on reinforcement learning and fuzzy reasoning for home energy management, IEEE Access 8 (2020), 39310–39321.

16.

Kim

, Lee

and Choi

, Joint demand response and energy trading for electric vehicles in off-grid system, IEEE Access 8 (2020), 130576–130587.

17.

Jahid

, Islam

, Hossain

, Monju

and Hossain

, Toward energy efficiency aware renewable energy management in green cellular networks with joint coordination, IEEE Access 7 (2019), 75782–75797.

18.

Hossain

, Jahid

, Islam

and Rahman

, Solar PV and biomass resources-based sustainable energy supply for off-grid cellular base stations, IEEE Access 8 (2020), 53817–53840.

19.

Pippia

, Sijs

and De

, Schutter, A single-level rule-based model predictive control approach for energy management of grid-connected microgrids, IEEE Transactions on Control Systems Technology 28(6) (2020), 2364–2376.

20.

Kotra

and Mishra

, A supervisory power management system for a hybrid microgrid with HESS, IEEE Transactions on Industrial Electronics 64(5) (2017), 3640–3649.

21.

, Wang

, Yin

, Yuan

and Leng

, Application conditions of bounded rationality and a microgrid energy management control strategy combining real-time power price and demand-side response, IEEE Access 8 (2020), 227327–227339.

22.

Marzband

, Azarinejadian

, Savaghebi

and Guerrero

, An optimal energy management system for islanded microgrids based on multiperiod artificial bee colony combined with markov chain, IEEE Systems Journal 11(3) (2017), 1712–1722.

23.

Luo

X.J.

and Fong

K.F.

, Development of integrateddemand and supply side management strategy of multi-energy system for residential building application, Applied Energy 242 (2019), 570–587.

24.

Dabbaghjamanesh

, Kavousi-Fard

and Dong

, A novel distributed cloud-fog based framework for energy management of networked microgrids, IEEE Transactions on Power Systems 35(4) (2020), 2847–2862.

25.

Nasir

, Anees

, Khan

, Xu

and Guerrero

, Integration and decentralized control of standalone solar home systems for off community applications, IEEE Transactions on Industry Applications 55(6) (2019), 7240–7250.

26.

Erdinc

and Uzunoglu

, Optimum design of hybrid renewable energy systems: Overview of different approaches, Renewable and Sustainable Energy Reviews 16(3) (2012), 1412–1425.

27.

Elsisi

, Tran

, Mahmoud

, Mansour

, Lehtonen

and Darwish

, Towards secured online monitoring for digitalized GIS against cyber-attacks based on IoT and machine learning, IEEE Access 9 (2021), 5–7. Available: 10.1109/access.2021.3083499 [Accessed 6 July 2021].

28.

Elsisi

, New design of robust PID controller based on meta-heuristic algorithms for wind energy conversion system, Wind Energy 23(2) (2020), 391–403.

29.

Elsisi

, New variable structure control based on different meta-heuristics algorithms for frequency regulation considering nonlinearities effects, International Transactions on Electrical Energy Systems 30(7) (2020).

30.

Elsisi

, Tran

, Mahmoud

, Lehtonen

and Darwish

, Robust design of ANFIS-based blade pitch controller for wind energy conversion systems against wind speed fluctuations, IEEE Access 9 (2021), 37894–37904.

31.

Kumar

, Mishra

, Ranjan

LVRT enhancement in grid connected DFIG based wind turbine using PSO optionized DVR, Distributed Generation & Alternative Energy Journal (2021).

32.

Sureshkumar

and Ponnusamy

, Power flow management in micro grid through renewable energy sources using a hybrid modified dragonfly algorithm with bat search algorithm, Energy 181 (2019), 1166–1178.

33.

Aktas

and Kırçiçek

, A novel optimal energy management strategy for offshore wind/marine current/battery/ultracapacitor hybrid renewable energy system, Energy 199 (2020), 117425.

34.

Collotta

, Pau

and Maniscalco

, A fuzzy logic approach by using particle swarm optimization for effective energy management in IWSNs, IEEE Transactions on Industrial Electronics 64(12) (2017), 9496–9506.

35.

Nge

, Ranaweera

, Midtgård

and Norum

, A real-timeenergy management system for smart grid integrated photovoltaicgeneration with battery storage, Renewable Energy 130(2019), 774–785.

36.

Lingamuthu

and Mariappan

, Power flow control of grid connected hybrid renewable energy system using hybrid controller with pumped storage, International Journal of Hydrogen Energy 44(7) (2019), 3790–3802.

37.

Et-Taoussi

, Ouadi

and Chakir

, Hybrid optimal management of active and reactive power flow in a smart microgrid with photovoltaic generation, Microsystem Technologies 25(11) (2019), 4077–4090.

38.

Chang

, Ma

, Chen

, Gao

and Dehghani

, A deep learning based securedenergy management framework within a smart island, Sustainable Cities and Society 70 (2021), 102938.

39.

, Hou

and Ghoreyshipour

, A secured transactive energy management framework for home AC/DC microgrids, Sustainable Cities and Society (2021), 103165.

40.

Hossain

, Chakrabortty

, Ryan

and Pota

, Energy management of community energy storage in grid-connected microgrid under uncertain real-time prices, Sustainable Cities and Society 66 (2021), 102658.

41.

, Liang

and Wang

, Distributed neurodynamic algorithm for multi-objective problem optimization and its applications to isolated micro-grid energy management, Sustainable Cities and Society 70 (2021), 102866.

42.

Mansouri

, Ahmarinejad

, Nematbakhsh

, Javadi

, Jordehi

and Catalão

, Energy management in microgrids including smart homes: A multi-objective approach, Sustainable Cities and Society 69 (2021), 102852.

43.

Mokhtara

, Negrou

, Settou

and Samy

M.M.

, Design optimization of off-grid Hybrid Renewable Energy Systems considering the effects of building energy performance and climate change: Case study of Algeria, Energy 219 (2021), 119605.

44.

Barik

A.K.

and Das

D.C.

, Integrated resource planning in sustainable energy-based distributed microgrids, Sustainable Energy Technologies and Assessments 48 (2021), 101622.

45.

Mokhtara

, Negrou

, Bouferrouk

, Yao

, Settou

and Ramadan

, Integrated supply–demand energy management for optimal design of off-grid hybrid renewable energy systems for residential electrification in arid climates, Energy Conversion and Management 221 (2020), 113192.

46.

Harifi

, Mohammadzadeh

, Khalilian

and Ebrahimnejad

, Giza pyramids construction: An ancient-inspired metaheuristic algorithm for optimization, Evolutionary Intelligence 14(4) (2020), 1743–1761.

47.

Kaveh

, Khanzadi

and Rastegar

, Moghaddam, Billiards-inspired optimization algorithm; a new meta-heuristic method, Structures 27 (2020), 1722–1739.