Numéro 
Sci. Tech. Energ. Transition
Volume 79, 2024
Emerging Advances in Hybrid Renewable Energy Systems and Integration



Numéro d'article  29  
Nombre de pages  15  
DOI  https://doi.org/10.2516/stet/2024025  
Publié en ligne  7 mai 2024 
Regular Article
Efficient economic energy scheduling in smart cities using distributed energy resources
^{1}
Department of Computer Science, COMSATS University Islamabad, Islamabad 44500, Pakistan
^{2}
Department of Engineering, University of Palermo, 90133 Palermo, PA, Italy
^{3}
Faculty of Computing, Engineering and the Built Environment, Ulster University, BT37 0QB Newtownabbey, UK
^{4}
Information & Computer Science Department King Fahd University of Petroleum and Minerals (KFUPM), Dhahran 31261, Saudi Arabia
^{5}
Faculty of Computing and Information Technology, Sohar University, Sohar 311, Oman
^{6}
National University of Sciences and Technology (NUST), Islamabad 44500, Pakistan
^{*} Corresponding author: hasan.alikhattak@acm.org
Received:
1
February
2024
Accepted:
3
April
2024
Machine learning provides a powerful mechanism to enhance the capabilities of the next generation of smart cities. Whether healthcare monitoring, building automation, energy management, or traffic management, use cases of capability enhancement using machine learning have been significant in recent years. This paper proposes a modeling approach for scheduling energy consumption within smart homes based on a nondominated sorting genetic algorithm (NSGA). Distributed energy management plays a significant role in reducing energy consumption and carbon emissions as compared to centralized energy generation. Multiple energy consumers can schedule energyconsuming household tasks using home energy management systems in coordination to reduce economic costs and greenhouse gas emissions. In this work, such a home energy management system is used to collect energy price data from the electricity company via an embedded deviceenabled smart meter and schedule energy consumption tasks based on this data. We schedule daily power consumption tasks using a multiobjective optimization method that considers environmental and economic sustainability. Two conflicting objectives are minimizing daily energy costs and reducing carbon dioxide emissions. Based on electricity tariffs, CO_{2} intensity, and the window of time during which electricity is consumed, energy consumption tasks involving distributed energy resources (DERs) and electricity consumption are scheduled. The proposed model is implemented in a model smart building consisting of 30 homes under 3 pricing schemes. The energy demand is spread out across a 24hour period for points A2–A4 under CPPPDC, which produces a more flattened curve than point A1. There are competing goals between electricity costs and carbon footprints at points B2–B4 under the CPPPDC, where electricity demand is set between 20:00 and 0:00. Power grids’ peak energy demand is comparatively low when scheduling under CPPPDC for points A5 and B5. Reducing carbon emissions, CPPPDC reduces the maximum demand for electricity from the grid and the overall demand above the predetermined level. The maximum power demand from the grid is minimized for points A5 and B5, reducing up to 22% compared to A2. The proposed method minimizes both energy costs as well as CO_{2} emissions. A Pareto curve illustrates the tradeoff between cost and CO_{2} emissions.
Key words: Micro grid / Demand response / Multiobjective optimization / Home energy management / Distributed energy resources / Nondominated sorting genetic algorithm
© The Author(s), published by EDP Sciences, 2024
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
1 Introduction
Power networks are considered the most comprehensive and complex energy systems ever made, and it is crucial to balance energy demand and supply continuously throughout the system to maintain a stable power supply [1, 2]. Due to increased electricity demand in recent years, conventional energy sources do not meet the increasing energy requirements [3]. Integration of renewable energy sources (RESs) alongside energy management systems (EMSs) and modern technology into the conventional grid may lower the excessive energy demand [4]. When connected with the loads, various RESs like photovoltaic (PV) and wind energy (WE) units make an MG. Additionally, this MG is converted into a smart microgrid (SMG) when incorporated with intelligent schemes [5] and mitigates various complex issues encountered in conventional electrical networks [6]. MGs are a satisfactory solution to meet consumers’ everincreasing energy demands. MGs offered an emerging power system and shifted the traditional centralized power system towards a more localized and distributed generation system, particularly in urban areas. SMG enables twoway communication between utilities and endusers.
Developing effective demand response (DR) can be challenging, including integrating RESs, monitoring, intelligent sensors, and advanced control [7, 8]. DSM is a modern technology used for planning, directing, and coordinating utilities’ actions and behaviors [9, 10]. Using DSM combined with incentives, electricity rates, and punishments, energy consumption can be significantly increased. The power supply operation of a specific load is manually interrupted in a traditional power system during peak times. However, utilities offer DSM in order to reduce grid load during peak hours and avoid peaktoaverage ratio (PAR) by encouraging endusers to shift their loads during onpeak hours. As a result of rescheduling the load, monetary advantages are gained at the end of the day, but enduser satisfaction may compromised [11, 12].
In other words, it is impossible to achieve electricity cost savings and user satisfaction simultaneously. Therefore, the constraints include everyday energy consumption, price signals, PAR, and enduser satisfaction. This has led to the development of smart EMS that can control a wide range of loads and respond to price changes [13–15]. The EMS is an essential technology for controlling future electricity distribution networks because it may move residential power usage away from peak consumption periods and minimize the amount of local generation that enters the distribution system. Due to this, they may also be able to deliver considerable cost reductions to household power consumers. Increased data interoperability, improved forecasting, and more excellent optimization of energy management systems are necessary to realize the full potential of the smart grid [16].
In the past few years, the use of RESs has been vital in minimizing global warnings. However, production is highly dependent on environmental conditions. This required an integrated and intelligent MG system to provide continuous power to the endusers [5]. Due to technological advancements, SMGs are monitored and controlled through intelligent and automated control schemes. These SMGs are small in size and offer integrated distribution networks. However, connecting the various loads, batteries, PVs, and WE to the system is vital for successfully implementing the SMGs. During this process, there exist fluctuations in power generation and usage due to the dynamic nature of the RESs. Thereby, the concept of optimal allocation of power in the home energy management system (HEMS) has a significant impact on the system. In this regard, several optimizationbased and artificial intelligencebased approaches have been studied in the literature. These techniques have been designed to optimize the generation cost, pollution, and CO_{2} emissions subject to load balance and system constraints during scheduling time. The effective utilization and optimization of the SMGs’ components enhance system performance and provide a costeffective distributed power generation system. The contributions of this work are highlighted below:

Considering the variations in power generation and consumption from RESs, it is essential to allocate power optimally in HEMS. This study aims to optimize generation cost, carbon emission, and pollution using an optimizationbased approach while considering the load balance and system constraints.

This work implemented the NSGA, which effectively evaluates the Pareto front and offers a range of solutions that indicate tradeoffs between contrasting objectives.

An economically distributed electrical power system is developed by the efficient use and optimization of SMG components, which also improves system reliability.
The paper is organized as follows: After a thorough introduction and forming the basis for our paper, Section 2 presents a detailed literature review of the state of the art. Section 3 discusses the proposed system model, and we show our problem statement based on the literature in Section 4. Section 5 presents experimental analysis and proposed optimization methodology. After discussing the results in Section 6, we present our conclusion and future directions in Section 7.
2 Related works
Over the past few decades, researchers worldwide have researched DR management and load scheduling in SMG. For instance, a few examples are included: in [17], a multiobjective model is used for scheduling MG status; in [18], authors worked on reducing energy consumption and waiting time of the power supply. Similarly, in [19], authors worked on improving the quality of the energy supply by using ant colony optimization approaches. The authors of [20] proposed an Adaptive Fuzzy Campus Placement Optimization Algorithm to solve both the singleobjective and multiobjective optimization problems. The authors have defined an algorithm evaluated on 25 benchmark functions and then compared it with existing methods. Through results, we see that minimizing real and reactive power losses and voltage deviation, with consideration of improving voltage profiles, can be easily achieved. The nondominated sorting genetic algorithm (NSGA) is used in [21] to address energy consumption cost and consumer satisfaction issues. The MG environment’s economic index and voltage stability problems are studied in [22] using a multiobjective optimization planning approach. In [23], load fluctuations and user satisfaction issues are addressed by using gametheoretical approaches. In addition, reference [24] used a genetic algorithm to solve demand and energy consumption issues, reference [25] worked on balancing energy demand and power supply in MG, and reference [26] proposed a multiobjective grasshopper optimization method to solve the load forecasting problem in MG.
Multiple smart homes with IoT are considered with their MGs to provide energy. MGs include distributed energy resources (DERs) such as boilers, CHP generators, as well as electrical and thermal storage systems. The DERs in a building are shared by all the homes. Authors [27] explore the integration of DERs within MGs to address energy challenges, employing a novel approach using the random forest (RF) machine learning algorithm. The experimental study considers historical data to optimize and improve DERsbased microgrid configuration, considering conflicting objectives like seasonal battery sizing and degradation, minimum generation cost, and, at the same time, reduced battery charging cost. Results are compared across various seasons with metaheuristics and artificial intelligence methods, including particle swarm optimization and artificial neural networks.
Energy scheduling in MG can be optimized through the use of an enhanced adaptive bat algorithm (EABA) [28]. The EABA implements a system for information exchange and provides an adaptive weight to the speed of each bat in the previous generation. Furthermore, different search techniques are used to increase search performance in the early and late stages of the search. EABA’s performance is proven by scheduling the generation of distributed generators in a gridoff MG, which includes three wind power plants, two solar power plants, and a combined heat and power plant. In [29], an optimum power flow (OPF) issue is defined and addressed using the bird swarm algorithm (BSA), to reduce costs and reduce carbon emissions. The suggested solution is evaluated using an IEEE 30bus testing system to determine the best settings while maintaining the specified limitations for active and reactive power, voltage stability, and line capacity in mind. In [30], the grey wolf optimizer (GWO), a robust swarmbased optimization algorithm inspired by the grey wolf lifestyle, is adapted to address the power scheduling problem in a smart home (PSPSH) as a multiobjective optimization problem that reduces the effect of constraints in obtaining optimal/nearoptimal solutions under a set of constraints and a dynamic pricing scheme(s) produced by a power supplier company. In [31], an optimum hybrid energy system model utilizing existing PV and WE resources with battery storage to meet the electrical demands of rural communities in India. A firefly algorithmbased technique determines the best hybrid system configuration based on the lowest COE while meeting a set of reliability criteria indicated by the loss of load probability (LOLP) reliability index.
In [32], optimization of a component sizing of a gridconnected solar PVfuel cellbased hybrid energy system to supply the electrical load demands of a small shopping complex was performed using three metaheuristic algorithms, namely artificial bee colony, particle swarm optimization, and a hybrid of both. The trial findings from three algorithms were evaluated regarding the system’s costeffectiveness. In [33], presents TGMFO (Timeconstrained GeneticMoth Flame Optimization), a hybrid version of two bioinspired heuristic algorithms, GA and mothflame optimization (MFO), for an EMS in smart homes and buildings. Their performance in energy cost reduction, PAR minimization, and enduser discomfort minimization is examined and reviewed.
A hybrid version of two bioinspired algorithms is proposed in [34] firefly algorithm (FA) and lion algorithm (LA) for energy scheduling to reduce the cost of energy and the waiting time of consumers or endusers in a smart home environment by categorizing all appliances into shiftable and nonshiftable appliances, and performing DSM. In [28], for optimum energy scheduling in an MG system, an EABA is suggested. EABA implements a system for information exchange and provides an adaptive weight to the speed of each bat in the previous generation.
Furthermore, different search techniques are used to increase search performance in the early and late stages of the search. EABA’s performance is proven by scheduling the generation of distributed generators in a gridoff MG, which includes three wind power plants, two solar power plants, and a combined heat and power plant. In [35], an OPF issue is defined and addressed using the bird’s swarm algorithm (BSA) to reduce costs and carbon emissions. The suggested solution is evaluated using an IEEE 30bus testing system to determine the best settings while maintaining the limitations for active and reactive power, voltage stability, and line capacity.
In [36], the polar bear optimization (PBO) [37] strategy was used for handling the scheduling problem of demandresponsive appliances in a HEMS to reduce power consumption costs and PAR. Case studies demonstrate the approach’s usefulness for a home customer using various base loads and uninterruptible deferrable and interruptible appliances in a realtime energy price program. In [38], an energy management approach for gridconnected net zero energy buildings (NZEB) that assists in achieving a netzero energy balance was presented, resulting in cost savings for the consumer’s net energy consumption and a lower carbon footprint. A singleobjective DE optimization method is used for energy management to prune the demand for electrical energy via household appliance scheduling. In [39], the artificial ecosystem optimizer (AEO) method, inspired by energy flocking amongst living creatures in the ecosystem, is utilized for DSM as an optimization problem with restrictions on appliance start and stop times. The approach is tested on two distinct pricing schemes while considering two operating time intervals (OTI) to give the best scheduling pattern for smart homes. In [40], an artificial immune system (AIS) to solve demand response and schedule optimization. OptaiNet is a specific AIS that is used to solve a power system optimization problem for a domestic environment with various appliances connected to the network. At the same time, the OptaiNet algorithm is adapted to include complex constraints in the optimization problem and to work with many variables in this domestic environment.
In [22], the authors worked on optimal allocation and coordination by considering wind, solar, and batteries under renewable curtailment and battery degradation levels. The multiobjective optimization problem aims to maximize economic cost and voltage stability and minimize power losses during the power supply. Furthermore, the dynamic of wind and solar is handled using stochastic approaches. The proposed scheme is implemented on the IEEE 33bus network. The simulation results demonstrated the effectiveness in maximizing the economic cost and voltage stability while the power losses were successfully reduced. In [41], authors worked on energy scheduling in the smart home environment. The twoobjective optimization problem minimizes the operation cost of consumer comfort and emissions. This work is implemented on a 69bus network and a 14node gas network.
Furthermore, consumer demand, price, and RESs are considered uncertain entities. The simulation demonstrated the effectiveness of the scheme regardless of the operating seasons. In [18], authors worked on load scheduling in smart homes using a multiobjective optimization approach. In this work, flexible loads of AC appliances are considered. Moreover, four types of loads consisting of interruptible and deferrable loads with a combination of flexible AC loads are simulated. The simulation results demonstrated the scheme’s effectiveness for optimal scheduling of different dynamic loads. In [42], authors worked on modeling power scheduling and multitype consumers. In this work, consumers are categorized into different groups, and energy costs and consumption levels are allocated to each group. Furthermore, the dynamic of energy and consumption is considered. The multiobjective optimization problem is used to minimize energy consumption and cost. The simulation results demonstrated that consumer satisfaction level is increased for all types of consumers.
By carefully reviewing the literature mentioned above, the following challenges and gaps have been identified and tried to address in this work. These challenges are listed below:

Handling multiobjective optimization: The challenge of achieving balanced conflicting objectives such as cost minimization, consumer satisfaction, and carbon reduction are challenging to solve [17].

Integrating renewable energy sources: Maintaining a balance between wind and solar curtailment and battery degradation while integrating renewable energy sources into microgrids [22].

Uncertainty management: To ensure robust scheduling and optimization, uncertainty in factors such as consumer demand, energy prices, and renewable energy sources must be addressed [41].

Dynamic pricing schemes: The development of strategies for optimizing energy scheduling under dynamic pricing schemes that consider varying costs and incentives during the energy scheduling process [30].

Modeling consumer behavior: Integrating dynamic consumer behavior models to predict and manage energy consumption optimally [42].
3 Proposed system model
This paper considers an IoTenabled smart building with multiple smart homes and its own local MG as an energy provider. All the households, smart meters, and DERs are IoTenabled. The MGs are comprised of DERs such as boilers and CHP generators with electrical and thermal storage systems. These DERs are shared among all homes in a building. Smart meters are electronic devices communicating between utilities and local communities through a communication link. Utility companies produce massive amounts of data, such as pricing signals, and transmit them to smart meters through a communication link. The smart meter can send this data to HEMS. The HEMS can gather data such as the appliance’s energy usage patterns, appliance’s on/off times, electricity generation data from DERs, and electricity price data from smart meters. HEMS then communicates with IoTenabled smart appliances and performs the energy management process. Furthermore, the generated data can be stored in the data center and used on demand. All of the devices, as mentioned earlier, are IoTenabled and connected via a communication link. The graphical representation of the proposed system model is shown in Figure 1. This work considers one CHP generator, boiler, electrical storage, and thermal storage unit. The output of CHP is 1.2 in terms of heattopower ratio. For electricity storage (ES), the charging and discharging efficiencies are assumed to be 95%.
Fig. 1 The concept of IoTenabled smart building EMS. 
The time is split into equal timeslots and there are 48 time intervals, each of half an hour. The appliances and their parameter are provided in Table 1. The operational constraints of this household must be fulfilled and must start their operations between between their request and end time. Based on the requirements, the system needs to determine the energy plan, start time of appliances, storage plans, and electricity bought from the grid. The objective is to find the optimum schedule for energy consumption and DER operations which minimizes electricity cost and CO_{2} emissions (Table 2). The details for carbon emission from CHP and boiler operations are considered to be constant (provided in Table 3). The carbon footprints of the system are estimated during the use phase, based on a functional unit of 1 kWh of electrical and thermal output for the CHP and boiler, respectively. The efficiencies for boiler and CHP are assumed to be 85% and 40%, respectively. CO_{2} details in Table 3 represent the total heat and electricity emissions generated by CHP based on power output. CHP has a heattopower ratio of 1.2 and produces 0.1821gCO_{2} kWh of electricity. The fuel cell for CHP is assumed to have a capacity of 10 kW with 40% electrical efficiency.
Appliances technical specifications including the rating power and time duration.
Technical parameters of DERs.
CO_{2} footprint for the CHP and the boiler.
Cost comparison with unscheduled scheme.
4 Problem formulation
A multiobjective optimization model of the energy consumption management problem is formulated as mixed integer linear programming that combines both economical and environmental sustainability in a multiobjective framework. The scheduling of everyday electrical appliances is based on their operating time slots, everyday electricity cost, and carbon emissions profile. The goal of this project is to lower everyday electricity costs, reduce carbon emissions, and cut offpeak power consumption. Energy costs and carbon emissions are reduced within the scope of relevant constraints, such as equipment sizing, energy demand, and thermal & electrical storage constraints.
Mathematical model of imposing constraints are:
4.1 Equipment sizing constraint
The output of each unit should remain within its designed size.
4.2 Thermal/electrical storage constraints
In a time t, the amount of energy stored is the amount of electricity stored at t − 1, plus/minus the amount of electricity charged/discharged. Here η^{E} is represented as a loss of electricity during the charging/discharging process. For instance, during the charging process, η^{E} δx_{ t } will be required for charging at any period δ. While in discharging, δy_{ t }/η^{E} of electricity is needed so that the customer can receive δy_{ t }.(5)
Here we assume that storing electricity is not allowed. Therefore, each storage unit must return to its original condition at the end of the day.(6)
Equations (7) and (8) describe the rate of charge/discharge of electricity that is assumed to remain within the designed capacity of charging/discharging limits of the storage device.(7) (8)
In a time t, the amount of heat stored is the amount of heat stored at t − 1, plus/minus the amount of heat charged/discharged. As in the case of electrical storage, η^{TH} is represented as heat loss during the charging/discharging process. At the end of each day, the stored heat must return to its original state. No heat can accumulate over the course of one day.(9) (10)
Based on the defined thermal storage capacity, the rate of charge and discharge of heat cannot exceed the design limit.(11) (12)
4.3 Mixed energy sources
Here, the energy demand is met by mixed energy sources such as energy generated from CHP generators, electrical storage devices, and the grid. Additionally, surplus energy is sent back to an electrical storage device. In equation (13), y_{ t } represents surplus energy with a minus sign. The minus sign indicates that energy is being sent to the storage device.(13)
In order to satisfy heat demand, the CHP generator, boiler, heat obtained from thermal storage, and heat sent to thermal storage need to be used in combination. This is exactly similar to energy demand. As shown in equation (14), Surplus heat is represented as m_{ t }, and the minus sign indicates that heat is being sent to the thermal storage device.(14)
4.4 Appliance operational time constraint
All appliances must start/finish their operation within the starting/ending time. L_{ jit } indicates the binary variable where appliance i in a house j turns ON at time t. Each appliance must start/finish its working operation within the starting/ending time minus the appliance operational time.(15)
4.5 Extra charges constraint
The normal electricity price applies if, at any time, the internal grid load is below the agreed threshold value. Excess amounts are, however, accounted for and charged at a higher rate in equation (18). Moreover, the objective function has to be minimized, which implies that the β_{ t } value has to be minimized as well.(16)
4.6 Objective function
Primarily, our objective is to reduce the overall cost of every day’s electricity. This includes the cost of purchasing electricity from the grid, the cost of electrical and thermal storage, and the cost of operating, and maintaining the CHP generator. It is mentioned that capital costs are not taken into account.(17)
Whenever the electricity demand exceeds the agreed threshold, extra charges are taken into account in the original cost. If the demand falls below the threshold, there is no additional cost and the price reflects the realtime electricity price. Equation (18) is applied when extra electricity charges are included.(18)
Equation (19) includes the penalty value in the objective function for the maximum daily power demand.(19)
Our second objective is to reduce the total CO_{2} emissions from three main sources such as emissions from traditional grid, CHP generators, and boiler plants.(20)
We formulate the aforementioned two objectives as follows in a multiobjective problem:(21)
In the above equation, x represents decision variables and space V identifies feasible solutions.
5 Proposed optimization method
In this work, an enhanced fast NSGA algorithm is used to solve the multiobjective optimization problem. The proposed method was previously presented by [43] and further elaborated in our work for the understudy problem. The algorithm works through the estimation of special crowding distance, an improved binary tournament selection, an adaptive crossover scheme, and offspring generation. It is a wellknown multiobjective optimization algorithm that is employed to find optimal decisions in complex decisionmaking problems. The workflow of the algorithm is listed below:

Initialization: As an initial step, the NSGAII generates a random population of possible solutions.

Evaluation: The fitness of each solution is determined by evaluating it on multiple objective functions.

Nondominated sorting: This step relies on the notion of nondominance, which implies that if a solution is not dominated by anyone else, it is regarded as better. This sorting creates multiple fronts in which the first front contains solutions that are not dominated.

Crowding distance assignment: In the objective space, by using crowding distance, solutions are further ranked according to the density of solutions surrounding them.

Selection: This step involves selecting new individuals for the next generation using a combination of nondominated sorting and crowding distance.

Genetic operations: By applying genetic operators, such as crossover and mutation, offspring solutions are created.

Termination: The algorithm iterates through genetic operation until the termination criterion is met. The algorithm reaches a maximum number of generations or successfully finds a satisfactory solution.
Next, we describe these steps along with the algorithms (see Algorithms 1, 2, and 3).
Initialization:
1: set: N
1: for i in (0, pop_{size}) do
2: choose: Randomly choose X_{1} and X_{2}
3: if Rank(X_{1}) < Rank(X_{2}) then
4: choose X_{1}
5: else if Rank(X_{1}) > Rank(X_{2}) then
6: choose X_{2}
7: end if
8: if Rank(X_{1}) = Rank(X_{2}) then
9: if SCD(X_{1}) > SCD(X_{2}) then
10: choose X_{1}
11: else
12: choose X_{2}
13: end if
14: end if
15: end for
1: Q1 = SBX + Polynomial mutation
2: Q2 = BLX − α + Polynomial mutation
3: P11 = Improved binary tournament selectiond (P1 ∪ Q1)
4: P22 = Improved binary tournament selectiond (P2 ∪ Q2)
5: Calculate PSP1 according to P11
6: Calculate PSP2 according to P22
7: if PSP1 > PSP2 then
8: Q1 = SBX + Polynomial mutation
9: else
10: Q2 = BLX – α + Polynomial mutation
11: else if
1: Input: Given Population
2: Output: The best solution
1: Init P
2: Evaluate Population P
3: while Generation < maxGeneration do state Determine the fitness of P1, P2
4: Sort fast nondominated solutions
5: Determine SCD of the individuals
6: Apply improved binary tournamentbased selection(P1, P2)
7: Q1 = SBX + Polynomial mutation
8: Q2 = BLX − α + Polynomial mutation
9: P11 = Improved binary tournament selection (P1 ∪ Q1)
10: P22 = Improved binary tournament selection (P2 ∪ Q2)
11: Calculate PSP1 according to P11
12: Calculate PSP2 according to P22
13: if PSP1 > PSP2 then state choose Q1
14: else state choose Q2
15: end if
16: P1 = Improved Selection (P1 ∪ Q1)
17: P2 = Improved Selection (P2 ∪ Q2)
18: Return P1, P2
19: end while
5.1 Special crowding distance
The NSGA uses the crowd distance which calculates the density of the individuals after the sorting process. Then, it selects the individual by considering the degree of the estimated crowding distance. The crowding degree demonstrates the size of the surrounding area. For example, if the degree of the crowding distance is small, it shows that the surrounding individuals are denser. The algorithm first determines the rank of individuals in ascending order of values. The crowding degree is set to 1 for the first and last individuals. Next, determining the degree of the crowding distance for other individuals takes the form as follows:(22)where and represent maximum fitness value and minimum fitness value in the kth rank respectively. Moreover, and show the adjacent fitness value of the kth rank representing the ith individual.
In general, the proposed method works as follows. First, all individuals are sorted based on the proposed sorting method. Next, the degree of the crowding distance is determined for each individual, and a special crowding distance is obtained. The individuals are given their rank based on their special crowding distance. Next, the matching of individuals is performed by taking into account those with a higher crowded degree. The special crowding distance is estimated by the following formulas:
In this case, first, we calculate the crowding decision space (CD_{ i,a }) and the object space (CD_{ i,b }) of the kth individual. Then, the special crowding distance for the kth individual is calculated as follows:(23)where CD_{avg,a } and CD_{avg,b } show the average degree for crowding distance of the decision space and object space respectively.
5.2 Improved binary tournament selection
Tournamentbased selection selects a certain individual from the population, the best are used in offspring. The process repeats itself until it selects the original population size of individuals. For example, if we have N individuals in a population, there will be N number of tournaments from the population at once and obtain the best individual from the given population. In this work, the selection strategy is based on a binary tournament selection strategy which uses a degree of the crowding distance and rank of individuals as quality factors. The overall procedure is presented in Algorithm 1.
5.3 Adaptive crossover strategy
5.3.1 SBX crossover
The proposed scheme follows the SBX crossover operator used for the singlepoint binary for solving multiobjective optimization problems. The working of the SBX crossover operator is as follows. Let’s suppose, there are two ndimensional parent individuals mathematically defined as:(24)
Moreover, and represent new individuals obtained by the crossing process. Then, to generate the next generation of individuals, the SBX function is defined as follows:(25)where β is obtained dynamically and randomly with the help of the following equation.
(26)where η_{ c } shows a custom parameter. The nature of the offspring depends on the value of η_{ c } e.g. the larger value generates offspring closer to the parent. Moreover, μ shows a random number in the range (0 and 1).
5.3.2 BLXα crossover
The second crossover operator used in this work is BLXα which is a blend operator. Let’s suppose the parent individuals as in 24, then the BLX crossover is obtained as:(27)where β = (1 + 2α)U(0, 1) − α. α = 0.5 and U = (0, 1) are used.
5.3.3 Adaptive crossover
It is noted that the SBXbased crossover method showed better performance in terms of distribution and convergence of PF in singlemodal multiobjective optimization problems. However, it also experienced that the SBXbased crossover method showed poor performance in terms of distribution and convergence of PF in multimodal multiobjective optimization problems. In contrast, the BLXα based crossover method showed good performance on solving lowdimensional multiobjective optimization problems. However, this method demonstrated poor performance in PS distribution and convergence. To address this issue, we proposed an adaptive crossover scheme for solving multiobjective optimization problems. We present a combination of crossover schemes by integrating SBXbased crossover for solving high dimensions and BLXα for getting the Pareto solution set in solving multiobjective optimization problems. The proposed adaptive scheme creates offspring with a higher degree of crowding distance in the population. Furthermore, it also has the ability to balance the convergence of the decision space and object space. The overall scheme is depicted in Algorithm 2.
The proposed scheme integrates an adaptive crossover method for generating new offspring and an improved selection method for selecting the best individuals in the offspring in order to solve multiobjective optimization problems. The overall working of the method is shown in Algorithm 3.
6 Result and discussions
This section discusses the simulation and results of our applied scheme. DERs operation and appliances are scheduled for 24 h, from 8 am to 8 am on the next day. The model is implemented in Matlab 2021a on a laptop with Intel Core i54300 CPU, 2.50 GHz processor, and 4GB of RAM.
Three pricing schemes are applied for the simulation of cost and carbon emission minimization schemes. Figure 2 shows the Pareto optimal solutions to demonstrate the tradeoff between cost and carbon emissions. The points on these curves are marked with letters As, Bs, and Cs. Points As and Cs are the points where only a single objective is considered, for instance, point As only minimizes cost, and point Cs considers only CO_{2} emissions. Both these become a single objective, whereas, Bs are the points of our interest showing a tradeoff between cost and CO_{2} emissions. These five curves represent different pricing schemes such as RTP, CPPDC, and CPPPDC as discussed in Section 6.1.
Fig. 2 Pareto fronts for cost and carbon emission. 
6.1 Electricity demand schedule
Figure 2 shows that all Cs (C1–C5) are very similar, which means that electricity balances for this point are the same. For this reason, only one figure (Fig. 3) is given for all generic Cs. This is a single objective optimization, their demand is scheduled only for minimizing the carbon emissions. However, it is also noteworthy that cost is different when the single objective cost is minimized. For point Cs (CO_{2} minimization), it is observed that our algorithm has scheduled CHP operation at its maximum capacity during most of the time periods due to low CO_{2} intensity, whereas the remaining demand is covered by buying electricity from the conventional power grid. It is also noticed that there are two peaks, one in the early morning at 08:00 and the other in the evening at 16:30 due to operations of inflexible appliances. When CO_{2} intensity is low, electricity demand is fulfilled by scheduling the energy bought from the grid as provided in Figure 4. The ES is charged at 22:00 and 22:30 and discharged at 8:00 and 8:30.
Fig. 3 Energy balance for point Cs. 
Fig. 4 Representation of carbon emission over 24 h period. 
Figure 5 shows energy balances for cost and tradeoff schemes under realtime pricing schemes. For point A1 (cost minimization), the only objective is to minimize the total cost based on a realtime pricing scheme, so electricity demand is scheduled solely on the pricing signal without considering CO_{2} footprints. Figure 5a shows that most of the demand is scheduled in the early morning hours between 4:00 and 7:00 when energy prices are low (see Fig. 6). In the case of point B1 (tradeoff between cost and CO_{2}), the peak energy demand hours are between 3:00 and 6:00 in the morning. ES charging and discharging are also scheduled accordingly as provided in Figure 5b, and ES works more frequently at both these points as compared to point Cs. CHP is also operating at its full capacity during most of the hours not only in the daytime but also at night.
Fig. 5 Energy balances under RTP for A1 and B1. 
Fig. 6 Realtime pricing signal between 12:00 midnight and the following midnight. 
Figure 7 shows electricity demand for A2–A4 and B2–B4 under CPPPDC with three thresholds considered in this work. The total energy demand is distributed over 24 h for points A2–A4, which resulted in a more flattened curve than point A1 (except the time when inflexible households are operating). Threshold values in peak demand avoid the creation of peak by operating CHP at full capacity during most of the hours, thus avoiding peak demand penalty. For B2–B4, the energy demand is scheduled between 20:00 and 0:00 as compared to B1. This shows conflicting objectives between electricity prices and carbon footprints. The demand curves are more or less similar, except from 9:00 to 16:30. Furthermore, the peak power demand from the grid has also been curtailed. Figure 8 shows the results of scheduling under CPPPDC for points A5 and B5. It can be observed from the figures that maximum energy demand from power grids is relatively low as compared to Figures 5 and 7. For A5, electricity is only bought from the grid during periods when there are low prices. For B5, the demand is scheduled at the periods according to the tradeoff between the carbon emissions profile and electricity prices. ES is charged at times of low prices and discharged at times of high prices of electricity from the grid. It is also observed that ES is less frequently used due to low heat demand in summer. There is a limited electricity output from CHP, ES usage is also low. The ES is only used if there is a significant difference in prices, and not used if maintenance cost and the cost of charging discharging energy loss surpasses the price difference.
Fig. 7 Energy balances under CPPPDC (Threshold = 60 kW, 40 kW, and 20 kW). 
Fig. 8 Energy balances under CPPDC. 
In terms of total and maximum electricity demand, CPPPDC minimizes the total demand over the agreed threshold, whereas CPPPDC minimizes maximum power demand from the grid. Peak power demand and total power demand from the grid exceeding the agreed demand threshold are provided in Table 4. CPPPDC price minimizes the maximum power demand from the grid and total demand over the agreed threshold for most of the points. It has reduced the maximum as well as total power demand from the grid, and hence carbon emissions. The total electricity demand from the grid increases when carbon emission constraints become tight (B3–B4). When the CHP is operating at its maximum capacity, the remaining power requirements are covered by the grid. 60 kW threshold is good for all cases; however, the penalty is charged even if the threshold is set at 60 kW and even if CHP is operating at full capacity. This is due to some inflexible tasks which must operate at their fixed time. For points A5 and B5, the maximum power demand from the grid is minimized. The maximum power demand is reduced up to 22% as compared to A2. The maximum carbon emissions are similar to the results of CPPPDC with thresholds. Table 4 provides the total demands under the RTP and CPPDC price scheme. The total power demand above the agreed thresholds of the other two pricing schemes is higher than the individual power demands of the CPPPDC pricing schemes (see Tab. 4).
6.2 Heat demand schedule
Heat balances for points A1–B1 and A2–B2 are provided in Figure 9 under RTP and PDC with 60 kW threshold, respectively. Under the RTP scheme, the CHP generator operates less frequently when only cost is considered. The reason for this is low heat demand in summer and CHP can’t produce more electricity unless the heat produced as a result is consumed or stored in thermal storage. Thermal storage balances the CHP output but is limited by its capacity. During the time interval when electricity demand is high but heat demand is low, the generated heat is stored in thermal storage and released at the time of heat demand. So, thermal storage stores heat in the daytime and discharges at night. The thermal storage charges eight times both, in the case of costminimizing and tradeoff schemes but at different time intervals. However, CHP operates at full capacity when CO_{2} emissions are taken into consideration. Since the heat requirements are provided rather than the power demand, So the heat balances for points As and Bs are similar in the case of CPPPDC and CPPDC pricing schemes. So, only the balances for heat are provided for A2 and B2.
Fig. 9 Heat balances. 
7 Conclusion
This paper proposes a nondominated sorting genetic algorithm approach for optimally scheduling the energy consumption profile of multiple smart homes in an MG environment. We consider two objective optimization problems, such as the minimization of economic costs and environmental impacts. In this work, an IoTenabled smart building is considered with 30 smart homes with its own local MG as an energy provider. All the households, smart meters, and DERs are IoTenabled. The MGs are comprised of DERs, such as a boiler and a CHP generator with thermal and electrical storage. These DERs are shared among all homes in a building. Results show that the proposed scheme efficiently schedules electrical appliances and optimizes the operation of DERs in such a way that minimizes both consumers’ electrical bills by avoiding peak hour schedules and CO_{2} emissions by utilizing local DERs as a source of energy.
With the proliferation of objectives and decision variables, the complexity of multiobjective optimization problems grows exponentially, making them computationally challenging. The curse of dimensionality is one of the limitations of solving multiobjective optimization problems. Additionally, due to the curse of dimensionality, it becomes increasingly difficult to identify the entire Pareto front, which represents the tradeoffs between objectives. Further, finding solutions that satisfy all objectives simultaneously is difficult since it requires making tradeoffs between conflicting objectives. In the future, we aim to extend the approach by incorporating the communication bandwidth of IoTenabled devices, which also influences the optimization outcomes. In addition, we will focus on the scalability and applicability of the proposed method in the realworld application.
Funding
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Authors contribution statement
Awais Manzoor: Conceptualization, Methodology, Software, Writing – Original Draft, Formal Analysis, Writing – Reviews and Editing. Waseem Akram: Methodology, Writing – Original Draft, Investigation. Malik Ali Judge: Software, Formal Analysis, Writing – Original Draft. Hasan Ali Khattak: Conceptualization, Formal Analysis, Writing – Reviews and Editing.
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All Tables
Appliances technical specifications including the rating power and time duration.
All Figures
Fig. 1 The concept of IoTenabled smart building EMS. 

In the text 
Fig. 2 Pareto fronts for cost and carbon emission. 

In the text 
Fig. 3 Energy balance for point Cs. 

In the text 
Fig. 4 Representation of carbon emission over 24 h period. 

In the text 
Fig. 5 Energy balances under RTP for A1 and B1. 

In the text 
Fig. 6 Realtime pricing signal between 12:00 midnight and the following midnight. 

In the text 
Fig. 7 Energy balances under CPPPDC (Threshold = 60 kW, 40 kW, and 20 kW). 

In the text 
Fig. 8 Energy balances under CPPDC. 

In the text 
Fig. 9 Heat balances. 

In the text 
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