Enhancing Smart Home Efficiency with Heuristic-Based Energy Optimization

Abstract

In smart homes, heavy reliance on appliance automation has increased, along with the energy demand in developing urban areas, making efficient energy management an important factor. To address the scheduling of appliances under Demand-Side Management, this article explores the use of heuristic-based optimization techniques (HOTs) in smart homes (SHs) equipped with renewable and sustainable energy resources (RSERs) and energy storage systems (ESSs). The optimal model for minimization of the peak-to-average ratio (PAR), considering user comfort constraints, is validated by using different techniques, such as the Genetic Algorithm (GA), Binary Particle Swarm Optimization (BPSO), Wind-Driven Optimization (WDO), Bacterial Foraging Optimization (BFO) and the Genetic Modified Particle Swarm Optimization (GmPSO) algorithm, to minimize electricity costs, the PAR, carbon emissions and delay discomfort. This research investigates the energy optimization results of three real-world scenarios. The three scenarios demonstrate the benefits of gradually assembling RSERs and ESSs and integrating them into SHs employing HOTs. The simulation results show substantial outcomes, as in the scenario of Condition 1, GmPSO decreased carbon emissions from 300 kg to 69.23 kg, reducing emissions by 76.9%; bill prices were also cut from an unplanned value of 400.00 cents to 150 cents, a 62.5% reduction. The PAR was decreased from an unscheduled value of 4.5 to 2.2 with the GmPSO algorithm, which reduced the value by 51.1%. The scenario of Condition 2 showed that GmPSO reduced the PAR from 0.5 (unscheduled) to 0.2, a 60% reduction; the costs were reduced from 500.00 cents to 200.00 cents, a 60% reduction; and carbon emissions were reduced from 250.00 kg to 150 kg, a 60% reduction by GmPSO. In the scenario of Condition 3, where batteries and RSERs were integrated, the GmPSO algorithm reduced the carbon emission value to 158.3 kg from an unscheduled value of 208.3 kg, a reduction of 24%. The energy cost was decreased from an unplanned value of 500 cents to 300 cents with GmPSO, decreasing the overall cost by 40%. The GmPSO algorithm achieved a 57.1% reduction in the PAR value from an unscheduled value of 2.8 to 1.2.

1. Introduction

Global energy demand has risen in recent years, putting more emphasis on renewable and sustainable energy resources (RSERs). Smart homes (SHs) equipped with energy management systems are one viable solution for optimizing energy use. The world’s energy needs have grown during the last few decades. In the past, fossil fuels were used to generate most power. However, scientists have been creating innovative and real-time data-driven and machine learning-based methods of producing electricity to meet the growing need for power while emitting the fewest greenhouse gases possible, such as using renewable and sustainable energy resources [1]. Figure 1 depicts the statistics of electricity generation from various renewable energy sources from 2022 till 2030; RSERs are crucial to halting climate change, cutting greenhouse gas emissions and using fewer fossil fuels. Thus, combining energy storage systems (ESSs) with RSERs and adopting a machine learning (ML) method is a practical way to improve energy efficiency and lessen environmental effects and user discomfort [2].

Artificial intelligence (AI) and machine learning (ML)-based models can be used for energy prediction, anomaly detection and automated load scheduling in smart grids (SGs) and optimal household energy management schedulers (OHEMSs), for the purpose of energy management and saving [3]. These developments enable consumers and utility corporations to improve grid stability, optimize energy usage patterns and reduce peak loads. However, bill costs, carbon emissions and hybrid models of algorithms are not considered in these approaches. Moreover, there is a gap in providing comprehensive and user-centric energy management, because current OHEMS systems frequently ignore user comfort and preferences. Previously, the authors of this study investigated ML models, including supervised and unsupervised learning, to predict energy demand, detect inefficiencies and automate power scheduling. Their results showed that ML-driven systems can reduce energy waste, lower electricity costs and improve energy efficiency, while maintaining user comfort [4]. Their experiments demonstrated that this method is effective in reducing energy waste while maintaining optimal indoor conditions. By considering real-time pricing, user preferences, and renewable energy availability, the proposed system followed a multi-dimensional approach to optimize appliance scheduling and energy resource operation, improving both efficiency and sustainability [5]. The simulation results demonstrated the system’s effectiveness in significantly reducing energy costs, the PAR and carbon emissions, while maintaining optimal user comfort. However, ESSs and renewable energy and solar PV integration were not modeled in their work. Figure 2 illustrates the SH features managed by the OHEMS to achieve these objectives, considering their importance levels.

This study aims to develop a reliable and cost-effective OHEMS for efficient energy optimization in SHs. The proposed solution tackles rising energy demands, peak loads and inefficient usage, while maintaining user comfort [7]. The studies in [8,9] investigated the use of various ML techniques, such as the GA, BPSO, WDO, BFO and GmPSO, to create an intelligent energy management system for SHs. The GmPSO algorithm, in particular, excelled in optimizing appliance scheduling and energy consumption, leading to notable decreases in energy costs, carbon emissions and the PAR. This research contributes to the advancement of energy management, reveals important challenges and proposes heuristic-based optimization approaches, while providing practical implications for the implementation of green energy sources in SHs. The results not only open the door to new smart energy systems, but also offer valuable insights to academics and the industry. The objectives and novel contributions of this paper are as follows:

• To develop an optimized home energy management system for SHs to manage energy efficiently.
• To reduce the costs of energy consumption, the PAR and carbon emissions, while preserving users’ comfort.
• To efficiently integrate RSERs and ESSs into SHs employing energy management.
• For appliance scheduling and load shift control, to utilize advanced heuristic-based techniques, such as the GA, BPSO, WDO and GmPSO.
• To allow the system to respond quickly to RTP and consider user preferences for more intelligent usage of energy.
• To demonstrate the significance of GmPSO’s superiority over some prominent optimization techniques with respect to cost, carbon emissions and the reduction of the measured PAR.

The structure of this paper is as follows: In Section 2, we evaluate relevant literature to provide context for our research. Section 3 describes the procedures employed to perform our research. In Section 4, we look more closely at the evaluation criteria and simulations we used. Section 5 explains how combining RSERs with ESSs can result in more efficient energy management. Section 5 presents our results and compares various optimization strategies, followed by a discussion of the important discoveries and contributions of our proposed framework. Finally, Section 6 concludes the work by summarizing the key findings and making suggestions for future research.

This study thus provides a good contribution overall to the domain of SH energy management. Fusing cutting-edge techniques with real-world applications and critical perspectives, it tackles urgent issues in the field of energy optimization [10]. In addition to aiding advancements in SH technologies, the findings can inform utility companies, policymakers and technology developers. This study is an attempt to bridge the gap by addressing the pressing need for user-focused load management that is widely applicable in both residential and non-residential areas.

2. Literature Review

In smart homes, load and energy management has garnered a lot of attention due to the steady increase in linked devices and energy use in recent years [11]. In this paper, emphasis is placed on highlighting gaps in the literature, critically analyzing the important theoretical and experimental works on the issue, and demonstrating how the proposed study on optimization algorithms for load management in houses contributes to the body of knowledge already in existence. One of the important works in load management is the study in [12], which suggests a demand response framework for smart homes to reduce energy bill costs. However, the PAR, carbon emissions and comfort level are not taken into consideration. The authors emphasize how important it is to manage load and lower peak demand by utilizing price mechanisms and user preferences. They develop a load management system that optimizes appliance schedules to lower energy use, based on machine learning approaches [13]. Real-time pricing, appliance prioritization and consumer preferences are all considered in their approach. Although load control is the focus of these studies, user comfort and preferences are disregarded in favor of energy efficiency and peak load reduction. To bridge this gap, recent research by [14] proposes a load control algorithm that considers user comfort as well as energy efficiency. Using an RL framework, the authors adjust appliance schedules based on user preferences and comfort levels. Similarly, Ref. [15] provides a load management approach that enhances thermal comfort by accounting for user preferences and temperature fluctuations. These studies show that load management algorithms are increasingly taking user comfort into account, but further investigation and improvement are still required. The study in [16] builds on the body of current literature by developing ML approaches that bridge the load management gap by considering energy efficiency as well as customer comfort and preferences. Nevertheless, the overall energy bill cost, ESS and PV integration, comfort in terms of delay and PAR reduction are ignored. The authors of [17] provide an overview of the most recent developments in DR and HEMSs in the home market. There is also discussion of the significance of HEMSs for load restriction and relocation. They provide information on current optimization methods, such as heuristic algorithms, mathematical optimization and model predictive control. Additionally, the effects of timing consideration, device heterogeneity, computational limitations and uncertainty prediction on optimization algorithm design are covered. Nevertheless, there is no discussion of appliance waiting times or UC. The writers of [18] provide a succinct overview of the most recent developments in HEMSs. The difficulties of putting HEMSs into practice are discussed, along with new findings on DR, DSM, appliance scheduling and single- or multiple-objective optimizations. However, user comfort in SHs, ESS and PV integration and PAR reduction are ignored, and are not deduced from energy bill savings.

Table 1. Comparison between traditional grid and smart grid [19,20].

Infrastructure	Traditional Grid	Smart Grid
Electrical system	Centralized production. Energy flows from the utility to the customers in only one direction.	Decentralized production. The utility and its consumers exchange energy in both directions.
Absence of Power	Inadequate storage capacity and a centralized design lead to high power losses.	Significantly lowers the power losses caused by DGs at the distribution level; in other words, DGs eliminate communication system losses.
System of information	An outdated monitoring and metering system.	SCADA with an advanced metering and monitoring system (AMI).
System of communication	Technology that is wired.	Both wireless and wired technologies.
ESS	There are pump hydro-power plants for storage.	Makes it easier to integrate scattered ESSs.
RSERs	Comprises dispatchable RESs (hydro-power plants) in the main system.	Gives RSERs (such as solar, wind, tidal, geothermal and biomass energy) decentralized control.
Self-repair	Responds to prevent additional harm. The focus is on safeguarding assets after system malfunctions.	Automatically detects and responds to both current and potential situations. Prevention is the main focus.
Asset optimization	Inadequate integration of scarce operational data with technology and procedures for asset management. Time-based upkeep.	Grid technologies are closely linked with asset management procedures to efficiently manage costs and assets. Condition-based upkeep.
Engagement of consumers	Customers are not properly involved in DSM and DR activities.	Offers net metering, dynamic pricing and other incentive-based programs.
Quality of Power	Just concentrates on minimizing disruptions and failures.	Assures electrical quality so that delicate electronics equipment and devices run smoothly.

illustrates the comparison between smart grids and traditional grids. As evident from the table, smart grids offer numerous advantages over traditional grids.

In [21], the authors discuss the importance of energy planning and management in SCs. This study is a review of SC energy system optimization and planning. The SC energy system’s four components—generation, storage, transmission and end users—are thoroughly covered. However, in grid events, an ESS is included to accommodate residential load. However, there is no discussion of how to adjust the load and ESS or schedule appliances in response to the power market’s dynamic pricing. The writers of [22] provide information about the methods and practices that make it easier to integrate RESs and DGs into SGs, and the idea of SCs is thoroughly discussed. In [23], SG and SH inclinations are thoroughly examined by the authors. They look into the efficiency of several communication methods, such as Ethernet protocols, Wi-Fi, Z-Wave and Zig-Bee. Both the benefits and drawbacks of the present technologies and goods are highlighted by the writers. The usage of communication technology in SGs and SHs is also addressed, along with its advantages, drawbacks and prospects. The authors of [24] provide an illustration of an REMS. For the sake of demonstration, three SHs that are powered by a residential PV system, or RES, are examined. A comprehensive study of LF, present LF techniques in the electricity system, future trends and its importance for future SG deployment is given by Bektas et al. [25]. They go into great length into the two primary categories of LF mathematical modeling and computational models based on artificial intelligence, as well as their variants. By charging the ESS during off-peak hours and discharging it during peak hours, the LP foundation of the REMS lowers power expenses and the PAR. Although charging the ESS directly from the grid is not a cost-effective strategy, it is not believed that RESs should be incorporated into the residential sector. In order to rearrange shiftable appliances from peak to off-peak hours, the authors of [26] suggest an ILP-based HEMS with integrated RESs. To create the best operating patterns for appliances, the authors of [27] suggested a hybrid approach that combines the ANN and LSA. MATLAB/SIMULINK (R2019a) is used to model and construct four appliances, each having user-specified preferences. In [28], the authors exhibit a fully automated RL energy management system. By adding more intelligence to the EMS, the OLA algorithm solves the problems of energy management and appliance scheduling. The suggested method considerably lowers the PAR and expense, but UC is jeopardized. The writers of [29] address the issue of peak demand at specific hours. The idea of smart charging and clustering is presented to optimize the advantages in terms of UC and cost savings. Through the scheduling of the ESS and appliances, an efficient EMS based on the GA is built for the clusters. In [30], the author provides a distributed system that uses the greedy iterative approach for grid optimization and the REMS. The authors in [31] propose an energy management system that automatically manages SH power requirements based on utility constraints and user priorities. As illustrated in Figure 3, the system’s architecture facilitates two-way communication between the service provider and its clients. It is important to keep in mind that the energy service provider, acting as the program administrator, is often responsible for funding the necessary infrastructure and supporting technology.

Table 2. Comparison of home energy systems and SG energy management techniques.

Method	Domain	Targeted Goal	Results	Observations
LP [32]	REMSs	Lower the PAR and electricity expenses	During off-peak hours, the ESS is charged, and during peak hours, it is discharged.	With this approach, no RSERs are used.
ILP [33]	RSERs	Lower peak loads and electricity bills	Incorporating RSERs significantly reduces electricity costs and peak loads.	ESSs and UC are not factored into the optimization.
MILP [34]	Integration of RSERs, OHEMSs and grid systems	Minimize costs and the PAR	Achieves a reduction in electricity costs and the PAR.	Not feasible for small-scale residential users.
PSO-ANN and LSA-ANN [35]	Appliance scheduling and OHEMSs	Compare LSA-ANN with PSO-ANN to reduce energy costs	LSA-ANN outperforms PSO-ANN, significantly reducing electricity costs.	Does not address UC or PAR reductions.
PSO, K-WDO, and WDO [36]	Appliance scheduling	Optimize UC and lower energy costs	K-WDO delivers the best balance between UC and cost.	RESs are underutilized in this method.
RL [37]	Fully automated energy management systems	Optimize appliance operation times and lower the PAR	Reduces expenses and prevents the creation of new peaks.	Does not consider RSERs or UC in optimization.
GA	Renewable Energy Management Systems	Lower electricity costs and the PAR	Clusters appliances to prevent the formation of new peaks.	RSERs are ignored, and UC is compromised.
PSO and GA [38]	Appliance scheduling	Optimize appliance operation times to cut costs	GA-based scheduling uses less computing power and saves money.	Minimizing electricity costs involves trade-offs with UC.

illustrates the differences between traditional and heuristic algorithms. As evident from the table, heuristic optimization techniques such as the GA, BPSO, WDO, BFO and GmPSO are effective at optimizing electricity bills, the PAR and the carbon footprint in intelligent homes. These algorithms provide rapid and computationally efficient solutions for appliance scheduling and energy optimization. However, they are vulnerable to local optima and require parameter fine-tuning for peak performance. RL-based solutions, on the other hand, adaptively adjust energy scheduling in response to real-time demand and user preferences, providing greater flexibility at the expense of high computational power and extensive training data sets. LP and MILP give exact optimization results, and have been utilized to minimize energy expenses and peak demand, but are computationally costly when managing large-scale, non-linear smart home energy systems. However, hybrid strategies, such as the GmPSO algorithm proposed in this work, combine the benefits of heuristic algorithms like the GA and PSO with strong optimization methods, providing a more adaptive, balanced and scalable approach to optimizing energy consumption and reducing dependence on grid energy and fossil fuels, while taking into consideration user comfort and preferences.

3. Proposed Research Methodology

Due to increased usage of household electronic appliances, energy consumption has significantly increased, and the residential sector now consumes more than 40% of all electricity generated. Because fossil fuels now supply the bulk of the world’s electricity, efforts to limit greenhouse gas emissions must be measured against the rising demand for electricity. To this end, scientists have been studying innovative methods of energy production, such as methods that harness RSERs. The integration of RSERs with ESSs can be highly advantageous, according to studies. However, the large-scale integration of RSERs poses a potential risk to the stability of traditional power grids that are already under stress from excessive loads. To address this, scholars are working on distributed SG applications, making OHEMSs necessary to optimize the use of energy in home appliances. Thus, we are developing an OHEMS.

The main objectives of our research are two-fold:

• To enable the use of ESSs and RSERs in the residential sector.
• To develop appliance scheduling to control resource usage and energy consumption.

3.1. PV System Energy Generation Model

A rooftop PV system serves as the RSER for a smart prosumer’s house, which is integrated into the proposed OHEMS. Among other sources of renewable energy, such as wind, tidal, geothermal, biomass and biogas, solar energy is the most abundant and accessible. Essentially cost-free, as there is little operational and maintenance cost, it is the best possible solution for residential energy systems. The upper atmosphere of Earth receives about 174,000 TW of solar radiation. Roughly 30% of this energy is reflected back into space, with the remaining 70% absorbed by clouds, oceans and land masses. Most regions around the globe experience daily solar insolation levels between 150 and 300 watts/m², equivalent to 3.5 to 7.0 kWh/m² [39]. Given this widespread availability, the proposed OHEMS leverages the PV system to maximize its benefits.

This system is set up to accomplish multiple goals:

• Reduce household electricity bills.
• Abate carbon emissions to meet sustainable energy goals.
• Decrease the PAR for better energy distribution.

To calculate the output power of a PV system ${\mathrm{Y}}^{\mathrm{p}\mathrm{v}\left(\mathrm{t}\right)}$, expressed in kilowatts at a given time t, the following formula in Equation (1) can be used [40].

$${\mathrm{Y}}^{\mathrm{p}\mathrm{v}\left(\mathrm{t}\right)}={\mathrm{n}}^{\mathrm{p}\mathrm{v}}.{\mathrm{A}}^{\mathrm{p}\mathrm{v}}.\mathrm{I}\mathrm{r}\left(\mathrm{t}\right).\left(1-0.005\left({\mathrm{T}}^{\mathrm{ß}\left(\mathrm{t}\right)}-25\right)\right)\forall \mathrm{t}$$

(1)

• ${\mathrm{n}}^{\mathrm{p}\mathrm{v}}=$ the energy conversion efficiency of the PV system.
• ${\mathrm{A}}^{\mathrm{p}\mathrm{v}}=$ the state of the generator zone (m²).
• $\mathrm{I}\mathrm{r}\left(\mathrm{t}\right)=$ the solar radiation at time t (kW/m²).
• T^β(t) = the external temperature (°C) at time t.
• 25 degrees centigrade is the standard temperature.
• 0.005 = the factor used for temperature adjustment.

The Equation also considers changes in sunlight and temperature that affect how much output power it will provide. The solar irradiation Ir(t), which means the solar energy available at a certain time of year, varies by an hour. These distributions are often bicomodal, and can be expressed as mixtures of two unimodal distribution functions. The unimodal distribution functions can be modeled using the Weibull probability density function, expressed as in Equation (2):

$$\mathrm{f}\left(\mathrm{I}\mathrm{r}\left(\mathrm{t}\right)\right)=\mathsf{\zeta }\left({\displaystyle \frac{\mathsf{\alpha }1}{\mathsf{\beta }1}}\right){\left({\displaystyle \frac{\mathrm{I}\mathrm{r}\left(\mathrm{t}\right)}{\mathsf{\beta }1}}\right)}^{\mathsf{\alpha }1-1}{\mathrm{e}}^{-{\left({\displaystyle \frac{\mathrm{I}\mathrm{r}}{\mathsf{\beta }1}}\right)}^{\mathsf{\alpha }1}}+\left(1-\mathsf{\zeta }\right)\left({\displaystyle \frac{\mathsf{\alpha }2}{\mathsf{\beta }2}}\right){\left({\displaystyle \frac{\mathrm{I}\mathrm{r}\left(\mathrm{t}\right)}{\mathsf{\beta }2}}\right)}^{\mathsf{\alpha }2-1}{\mathrm{e}}^{-{\left({\displaystyle \frac{\mathrm{I}\mathrm{r}}{\mathsf{\beta }2}}\right)}^{\mathsf{\alpha }2}},0<\mathrm{I}\mathrm{r}\left(\mathrm{t}\right)<\infty$$

(2)

In this formula,

• ζ is a weighted component that shows each distribution’s contribution.
• α1 and α2 are distribution shape parameters.
• The scale parameters for the distributions are β1 and β2.

3.2. Energy Storage Model

The ESS stores some of the energy generated by the PV system and uses it later to maximize energy efficiency with minimal space consumption. The ESS only stores energy when its current charge level is below the maximum charge capacity. The energy stored in the ESS at a certain time t is given by an equation that accounts for the amount of energy charged and discharged, as well as the self-discharge rate of the system, ensuring that the energy available for consumption at a given point in time is correctly represented. It also considers energy losses that happen during all the charging and discharging processes; such losses have an effect on the overall performance of the ESS. This is known as the ESS turnaround efficiency, and allows the model to capture a realistic view of energy time management in the system through the constraints of energy storage described in Equation (3).

$$\mathrm{E}\mathrm{S}\left(\mathrm{t}\right)=\mathrm{E}\mathrm{S}\left(\mathrm{t}-1\right)+\mathrm{k}.{\mathrm{n}}^{\mathrm{E}\mathrm{S}\mathrm{S}}.\mathrm{E}{\mathrm{P}}^{\mathrm{Z}\mathrm{H}\left(\mathrm{t}\right)}-\mathrm{k}.{\displaystyle \frac{\mathrm{E}{\mathrm{P}}^{\mathrm{D}\mathrm{Z}\mathrm{H}\left(\mathrm{t}\right)}}{{\mathrm{n}}^{\mathrm{E}\mathrm{S}\mathrm{S}}}}\forall \mathrm{t}$$

(3)

In this model,

• Κ is the time slot duration (in hours).
• ${\mathrm{E}\mathrm{P}}^{\mathrm{Z}\mathrm{H}}$ is the power (kW) that the ESS receives from the RSER at a certain point in time.
• $\mathrm{E}{\mathrm{P}}^{\mathrm{D}\mathrm{Z}\mathrm{H}}$ is the power (kW) that the ESS delivers to meet the load demand at a given point in time.
• ${\mathrm{n}}^{\mathrm{E}\mathrm{S}\mathrm{S}}$ is the efficiency of the ESS, accounting for energy losses during charging and discharging.

One of the most significant controls for improving the ESS’s longevity and dependability is operation within the manufacturer’s suggested ranges for charge and discharge rates, as well as for stored energy levels. Following these recommendations helps to avoid the system being too full (which would damage the system) and too empty (which can degrade battery performance). Proper management ensures the long-term reliability and performance of the ESS, as expressed by the constraints in Equations (4) to (6).

$$\mathrm{E}{\mathrm{P}}^{\mathrm{Z}\mathrm{H}\left(\mathrm{t}\right)}\le \mathrm{E}{\mathrm{P}}_{\mathrm{U}\mathrm{B}}^{\mathrm{Z}\mathrm{H}}$$

(4)

$$\mathrm{E}\mathrm{P}{\left(\mathrm{t}\right)}^{\mathrm{D}\mathrm{Z}\mathrm{H}}\le \mathrm{E}{\mathrm{P}}_{\mathrm{L}\mathrm{B}}^{\mathrm{D}\mathrm{Z}\mathrm{H}}$$

(5)

$$\mathrm{E}\mathrm{S}\left(\mathrm{t}\right)\le {\mathrm{E}\mathrm{S}}_{\mathrm{U}\mathrm{B}}^{\mathrm{Z}\mathrm{H}}$$

(6)

In this context,

• $\mathrm{E}{\mathrm{P}}_{\mathrm{L}\mathrm{B}}^{\mathrm{D}\mathrm{Z}\mathrm{H}}$ represents the ESS discharge rate’s lower limit.
• $\mathrm{E}{\mathrm{P}}_{\mathrm{U}\mathrm{B}}^{\mathrm{Z}\mathrm{H}}$ shows the ESS charge rate’s maximum limit.
• ${\mathrm{E}}_{\mathrm{U}\mathrm{B}}^{\mathrm{Z}\mathrm{H}}$ specifies the ESS’s maximum permitted energy storage capacity.

3.3. Model of Energy Consumption

Household appliances are divided into two categories and utilized to realistically model the demand behavior of an intelligent user. Breaking down energy usage in this way allows the household to obtain context for their energy bill, or to look for opportunities for some simple optimization. This classification could additionally facilitate the deployment of optimized scheduling strategies and the steady combination of renewable power resources, which will improve energy efficiency, minimize costs and enable energy management of future SG systems.

• Shiftable Appliances (Set A): these appliances, represented as A = {a1, a2, a3, am}, can be scheduled to operate during low-price time slots to reduce energy costs.
• Non-Shiftable Appliances (Set B): represented as B = {b1, b2, b3, bn} these appliances operate at user-specified times, and are not influenced by dynamic pricing.

This smart integration of resources and scheduling ensures optimal energy usage for both prosumers and utilities, as shown in

Table 3. Classification of household appliances based on load shift ability.

Shiftable Loads	Non-Shiftable Loads
Washing machine	Personal computers
Air-conditioning	CCTV
Clothes dryer	Microwave oven
Dishwasher	Television

.

The system does this by tracking the allocated future consumption of shiftable appliances and, where possible, scheduling the consumption of the shiftable appliances alongside the already-fixed-in-place consumption of the non-shiftable appliances, as shown mathematically by Equations (7) and (8).

$${\mathrm{E}}^{\mathrm{a}}={\sum }_{\mathrm{t}=1}^{24}({\sum }_{\mathrm{A}=1}^{\mathrm{a}}{\mathrm{E}}_{\mathrm{t}}^{\mathrm{a}},\mathrm{a}∊\mathrm{A})=\left\{{\mathrm{E}}_{\mathrm{t}1}^{\mathrm{a}},\mathrm{a}∊\mathrm{A}+{\mathrm{E}}_{\mathrm{t}2}^{\mathrm{a}},\mathrm{a}∊\mathrm{A}+\cdots +{\mathrm{E}}_{\mathrm{t}24}^{\mathrm{a}},\mathrm{a}∊\mathrm{A}\right\}$$

(7)

$${\mathrm{E}}^{\mathrm{b}}={\sum }_{\mathrm{t}=1}^{24}({\sum }_{\mathrm{B}=1}^{\mathrm{b}}{\mathrm{E}}_{\mathrm{t}}^{\mathrm{b}},\mathrm{b}∊\mathrm{B}=\left\{{\mathrm{E}}_{\mathrm{t}1}^{\mathrm{b}},\mathrm{b}∊\mathrm{B}+{\mathrm{E}}_{\mathrm{t}2}^{\mathrm{b}},\mathrm{b}∊\mathrm{B}+\cdots +{\mathrm{E}}_{\mathrm{t}24}^{\mathrm{b}},\mathrm{b}∊\mathrm{B}\right\}$$

(8)

The energy usage of the smart prosumer’s appliances is represented as follows:

• ${\mathrm{E}}_{\mathrm{t}1}^{\mathrm{a}}$, a in A,…,${\mathrm{E}}_{\mathrm{t}24}^{\mathrm{a}}$, a in A indicates the energy consumption of shiftable appliances (A) over a 24 h period.
• ${\mathrm{E}}_{\mathrm{t}1}^{\mathrm{b}}$, b in B,${\mathrm{E}}_{\mathrm{t}2}^{\mathrm{b}},$ b belongs B,…, ${\mathrm{E}}_{\mathrm{t}24}^{\mathrm{b}}$,b in B represents the energy consumption of non-shiftable appliances (B) in each specific time slot t.

A formula that adds up the energy used by both shiftable and non-shiftable appliances during the day is used to determine the prosumer’s load’s total daily energy consumption, as expressed by Equation (9). This computation offers a thorough understanding of the energy requirements and permits efficient cost and energy efficiency optimization.

$${\mathrm{E}}^{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}={\sum }_{\mathrm{t}=1}^{24}({\sum }_{\mathrm{A}=1}^{\mathrm{a}}{\mathrm{E}}_{\mathrm{t}}^{\mathrm{a}},\mathrm{a}∊\mathrm{A}+{\sum }_{\mathrm{M}}^{\mathrm{n}}{\mathrm{E}}_{\mathrm{t}}^{\mathrm{b}},\mathrm{b}∊\mathrm{B})$$

(9)

3.4. PAR

The PAR is a metric that estimates the ratio between the highest load consumed within a specific timeslot t and the average of all loads used throughout the entire scheduling period (t = 1 to t = 24). The PAR is an important control variable for utilities because it reflects the energy consumption patterns of users. This can have significant impacts on the efficiency and cost of energy production, particularly on high-peak-demand power plants with resulting high PAR values. With a lower PAR, the utility and consumer are both able to maintain supply and demand operating limits, which removes stress from the power grid.

By minimizing the PAR, the energy consumption becomes more consistent, leading to a more efficient and stable energy system, given below in Equation (10).

$$\mathrm{P}\mathrm{A}\mathrm{R}={\displaystyle \frac{\frac{\max \left({\mathrm{E}}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}\left(\mathrm{t}\right)\right)}{1}}{\mathrm{T}\sum _{\mathrm{t}=1}^{\mathrm{T}}{\mathrm{E}}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}\left(\mathrm{t}\right)}}$$

(10)

For multiple users, denoted as M, the PAR can be computed by aggregating the energy consumption across all users and then applying the same formula. Specifically, the PAR for multiple users can be calculated with Equation (11):

$$\mathrm{P}\mathrm{A}\mathrm{R}={\displaystyle \frac{\max \left({\mathrm{E}}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}\left(\mathrm{t},\mathrm{m}\right)}\right)}{1}}/\mathrm{T}{\sum }_{\mathrm{n}=1}^{\mathrm{M}}{\mathrm{E}}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}\left(\mathrm{t},\mathrm{m}\right)}$$

(11)

where

• n in M represents each individual user.
• The peak load for each user is compared against their average load over the full scheduling period (24 h).

3.5. Model of Energy Pricing

To determine the energy cost for a given day, a variety of power tariffs are available, including PP, ToUP, DAP, CPP and RTP. Because RTP complicates communication, most appliance scheduling systems assume DAP or ToUP electricity rates. In addition, ToUP divides the pricing horizon in half and establishes a fixed price for every block. We employ RTP in this situation, where the hourly electricity price fluctuates and stays the same for a particular hour. Equations are used to calculate the daily power bills for the moveable appliances ${\mathrm{E}}_{\mathrm{P}}^{\mathrm{X}}$ and the immovable devices ${\mathrm{E}}_{\mathrm{P}}^{\mathrm{Y}}$, as given by Equations (12) to (17).

$${\mathrm{E}}_{\mathrm{P}}^{\mathrm{X}}={\sum }_{\mathrm{t}=1}^{24}({\sum }_{\mathrm{M}=1}^{\mathrm{m}}{\mathrm{E}}_{\mathrm{m}}^{\mathrm{x}}\mathrm{m}∊\mathrm{M}\left(\mathrm{t}\right)\times {\mathrm{X}}^{\mathrm{X}\mathrm{M}}∊\mathrm{M}\left(\mathrm{t}\right)\times {\mathrm{P}}^{\mathrm{R}\mathrm{T}\mathrm{P}}\left(\mathrm{t}\right))$$

(12)

$${\mathrm{E}}_{\mathrm{p}}^{\mathrm{y}}={\sum }_{\mathrm{t}=1}^{24}\left({\sum }_{\mathrm{N}=1}^{\mathrm{n}}({\mathrm{E}}_{\mathrm{n}}^{\mathrm{y}}∊\mathrm{N}\left(\mathrm{t}\right)\times {\mathrm{P}}^{\mathrm{R}\mathrm{T}\mathrm{P}\left(\mathrm{t}\right)})\right)$$

(13)

$$\begin{array}{l}{\mathrm{E}}_{\mathrm{p}}^{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}={\mathrm{E}}_{\mathrm{P}}^{\mathrm{X}}+{\mathrm{E}}_{\mathrm{p}}^{\mathrm{y}}={\sum }_{\mathrm{t}=1}^{24}({\sum }_{\mathrm{M}=1}^{\mathrm{m}}({\mathrm{E}}_{\mathrm{M}}^{\mathrm{X}}∊\mathrm{M}(\mathrm{t})\times {\mathrm{X}}_{\mathrm{m}}^{\mathrm{X}}∊\mathrm{M}(\mathrm{t})\times {\sum }_{\mathrm{N}=1}^{\mathrm{n}}\begin{array}{c}({\mathrm{E}}_{\mathrm{n}}^{\mathrm{y}}∊N\left(\mathrm{t}\right)\times {\mathrm{X}}_{\mathrm{n}}^{\mathrm{y}}∊N\left(\mathrm{t}\right)\times \\ \end{array}{\mathrm{P}}^{\mathrm{R}\mathrm{T}\mathrm{P}\left(\mathrm{t}\right)}))\\ \hspace{1em}\hspace{1em}+{\sum }_{\mathrm{N}=1}^{\mathrm{n}}({\mathrm{E}}_{\mathrm{n}}^{\mathrm{y}}∊\mathrm{N}\left(\mathrm{t}\right)\times {\mathrm{X}}_{\mathrm{n}}^{\mathrm{y}}∊\mathrm{N}\left(\mathrm{t}\right)\times {\mathrm{P}}^{\mathrm{R}\mathrm{T}\mathrm{P}\left(\mathrm{t}\right)}))\end{array}$$

(14)

$${\mathrm{X}}_{\mathrm{m}}^{\mathrm{x}}\in \mathrm{M}(\mathrm{t})=\left\{\begin{array}{c}1\mathrm{i}\mathrm{f}\mathrm{s}\mathrm{h}\mathrm{i}\mathrm{f}\mathrm{t}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{a}\mathrm{p}\mathrm{p}\mathrm{l}\mathrm{i}\mathrm{o}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}\mathrm{i}\mathrm{s}\mathrm{o}\mathrm{n}\\ 0\mathrm{i}\mathrm{f}\mathrm{s}\mathrm{h}\mathrm{i}\mathrm{f}\mathrm{t}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{a}\mathrm{p}\mathrm{p}\mathrm{l}\mathrm{i}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}\mathrm{i}\mathrm{s}\mathrm{o}\mathrm{f}\mathrm{f}\end{array}\right.$$

(15)

$${\mathrm{X}}_{\mathrm{n}}^{\mathrm{y}}\in \mathrm{N}(\mathrm{t})=\left\{\begin{array}{c}1\mathrm{i}\mathrm{f}\mathrm{n}\mathrm{o}\mathrm{n}-\mathrm{s}\mathrm{h}\mathrm{i}\mathrm{f}\mathrm{t}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{a}\mathrm{p}\mathrm{p}\mathrm{l}\mathrm{i}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}\mathrm{i}\mathrm{s}\mathrm{o}\mathrm{n}\\ 0\mathrm{i}\mathrm{f}\mathrm{n}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{h}\mathrm{i}\mathrm{f}\mathrm{t}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{a}\mathrm{p}\mathrm{p}\mathrm{l}\mathrm{i}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}\mathrm{i}\mathrm{s}\mathrm{o}\mathrm{f}\mathrm{f}\end{array}\right.$$

(16)

Here, ${\mathrm{X}}_{\mathrm{m}}^{\mathrm{x}}$ in M (t) displays the ON/OFF state of a shiftable appliance M, and ${\mathrm{X}}_{\mathrm{n}}^{\mathrm{y}}$, belonging to N (t), shows the ON/OFF state of a non-shiftable appliance N. Additionally, for a given time slot T, ${\mathrm{P}}^{\mathrm{R}\mathrm{T}\mathrm{P}}\left(\mathrm{T}\right)$ is RTP. After accounting for the RSER and ESS, the electricity bill EP (t) for any time slot t is determined as follows:

$${\mathrm{E}}_{\mathrm{p}}\left(\mathrm{t}\right)=\left({\mathrm{E}}^{\mathrm{x}}\left(\mathrm{t}\right)+{\mathrm{E}}^{\mathrm{y}}\left(\mathrm{t}\right)-\mathrm{E}\mathrm{R}\left(\mathsf{\tau }\right)\right)\times {\mathrm{P}}^{\mathrm{R}\mathrm{T}\mathrm{P}}\left(\mathrm{t}\right))$$

(17)

The time slot with the highest bill between T = 8 and T = 10 is denoted by τ.

3.6. Scheduling of Appliances

Through better appliance scheduling and less reliance on costly backup generators, this project aims to reduce electricity expenditures and the peak-to-average ratio (PAR). To maintain balanced power consumption, appliances are controlled by an OHEMS using binary choices and limitations (Equations (18)–(21)):

$$\mathrm{m}\mathrm{i}\mathrm{n}\left(\right({\mathrm{E}}^{\mathrm{x}}\left(\mathrm{t}\right)+{\mathrm{E}}^{\mathrm{y}}\left(\mathrm{t}\right)-{\mathrm{E}}^{\mathrm{p}\mathrm{v}}\left(\mathrm{t}\right)-\mathrm{E}\mathrm{R}\left(\mathsf{\tau }\right))\times {\mathrm{P}}^{\mathrm{R}\mathrm{T}\mathrm{P}}(\mathrm{t})$$

(18)

subject to

$${\mathrm{E}}^{\mathrm{T}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}\left(\mathrm{t}\right)\le {\mathrm{E}}_{\mathrm{g}\mathrm{r}\mathrm{i}\mathrm{d}}\left(\mathrm{t}\right)+{\mathrm{E}}^{\mathrm{p}\mathrm{v}}\left(\mathrm{t}\right)+\mathrm{E}\mathrm{R}\left(\mathsf{\tau }\right),\forall 1\le \mathrm{t}\le 24$$

(19)

$${\mathrm{E}}^{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}\left(\mathrm{t}\right)\mathrm{E} \underset{\mathit{unsch}}{\min }\left(t\right)$$

(20)

$${\mathsf{\tau }}_0\le {\mathsf{\tau }}_{\mathrm{s}\mathrm{c}\mathrm{h}}\le {\mathsf{\tau }}_{\max }$$

(21)

The maximum permitted load withdrawal is determined by Egrid(t), and effective energy management is ensured by scheduling parameters (τ₀, τ_sch and τ_max).

3.7. Proposed System Architecture

The OHEMS optimizes energy utilization to reduce electricity bills and the PAR, while Demand-Side Management (DSM) and DR are implemented in smart networks to increase stability. Using the OHEMS to dynamically schedule appliances based on market rates, smart prosumers effectively manage their energy by combining grid electricity, an ESS and an RSER. A PV system, a DC/AC inverter, an ESS, an SM, an SS, an MC and a variety of appliances are the main elements of the suggested system architecture, as illustrated in Figure 4.

Solid lines in the diagram denote energy flow, whereas dotted lines show information flow. For smooth data sharing, Advanced Metering Infrastructure (AMI) incorporates Information and Communication Technology (ICT) into the grid. By processing pricing signals and DR directives and monitoring energy consumption, the Smart Meter (SM) serves as a link between utilities and smart homes. Through the use of an inverter, RSERs like solar photovoltaic systems lessen dependency on fossil fuels by transforming sunlight into usable AC electricity.

• The ESS acts as a sink, as well as acting as a source. Therefore, it constitutes an efficient approach in integrating RSERs with distribution and residential networks.
• Scattered between the SM and MC scenario is an SS, which involves heuristic-based programming. The MC implements the per-appliance ideal/best energy usage patterns that the SS develops.
• The MC, which is the main module of the OHEMS, saves energy and optimizes usage by managing the ESS and home appliances’ actions in agreement with the timings generated by the SS.

4. Optimization Algorithms

In appliance scheduling, evolutionary algorithms like the GA, BPSO, WDO, BFO and GmPSO are introduced here. These algorithms perform better than more conventional techniques like DP, ILP, LP and MILP. By avoiding local optima and improving scheduling efficiency, these sophisticated algorithms offer powerful optimization possibilities.

4.1. Genetic Algorithm

Natural genetic processors serve as the inspiration for the heuristic optimization method known as the GA. In order to avoid premature convergence, it employs crossover (with a 90% chance) and mutation to generate new solutions, while using binary-coded chromosomes to describe appliance states. The finest solutions are chosen for the generation following examination, guaranteeing ongoing progress. Table 6 provides specifics about the algorithm’s parameters.

4.2. BPSO

By monitoring particle position, velocity, personal best and global best, BPSO, an optimization method inspired by nature, determines the optimal solution. In order to achieve the best outcome, it iteratively updates velocities using Equation (22), after initializing a population. The particles modify their velocities according to Equation (22) in each iteration.

$${\sum }_{\mathrm{t}=1}^{24}{\sum }_{\mathrm{j}=1}^{`1}{\mathrm{v}}_{\mathrm{j}}^{\mathrm{t}+1}={\sum }_{\mathrm{t}=1}^{24}{\sum }_{\mathrm{j}=1}^1\left({\mathrm{w}\mathrm{V}}_{\mathrm{q}}^{\mathrm{t}}\left(\mathrm{q}\right)+\mathrm{z}1\mathrm{t}1\left({\mathrm{X}}_{\mathrm{f}\mathrm{b}\mathrm{e}\mathrm{s}\mathrm{t},\mathrm{j}}\left(\mathrm{q}\right)\right)-{\mathrm{x}}_{\mathrm{j}}^{\mathrm{t}}\left(\mathrm{q}\right)\right)+\mathrm{z}2\mathrm{t}2\left({\mathrm{X}}_{\mathrm{d}\mathrm{b}\mathrm{e}\mathrm{s}\mathrm{t}},\mathrm{j}\left(\mathrm{q}\right)-{\mathrm{x}}_{\mathrm{j}}^{\mathrm{t}}\left(\mathrm{q}\right)\right)$$

(22)

The velocity of the particle (appliance) in the next time slot is represented by v(t+1); w is the factor of inertia, v(t) is the current velocity, X(t) is the current particle position; ${\mathrm{X}}_{\mathrm{d}\mathrm{b}\mathrm{e}\mathrm{s}\mathrm{t}}$ is the global best position, and ${\mathrm{X}}_{\mathrm{f}\mathrm{b}\mathrm{e}\mathrm{s}\mathrm{t}}$ is the local best position; and using Equation (23), t1 and t2, respectively, represent the local pull Z1 and the global pull Z2. Using the sigmoid function (from the following equation) allows us to map the particle speeds between 0 and 1.

$$\mathrm{s}\mathrm{i}\mathrm{g}\left({{\mathrm{V}}^{\mathrm{t}}}_{\mathrm{j}}^{+1}\left(\mathrm{q}\right)\right)=1/1+\mathrm{e}\mathrm{x}\mathrm{p}(-{{\mathrm{V}}^{\mathrm{t}}}_{\mathrm{j}}^{+1}\left(\mathrm{q}\right))$$

(23)

A binary-coded population is produced by comparing the random values allocated to each particle in the population using the sigmoid function.

$${{\mathrm{x}}^{\mathrm{t}}}_{\mathrm{j}}^{+1}=\left\{\begin{array}{c}1\mathrm{s}\mathrm{i}\mathrm{g}\left({{\mathrm{V}}^{\mathrm{t}}}_{\mathrm{j}}^{+1}\left(\mathrm{q}\right)\right)<{\mathrm{t}}_{\mathrm{j}\mathrm{q}}\\ 0\mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{w}\mathrm{i}\mathrm{s}\mathrm{e}\end{array}\right.,$$

(24)

4.3. WDO

Using the four main forces of gravity, friction, pressure gradient and Coriolis, Wind-Driven Optimization (WDO) simulates the motion of air parcels to identify the best solutions. Equations (25)–(30) define these forces, which direct the optimization process.

$${\mathrm{H}}_{\mathrm{k}\mathrm{l}}=-∆\mathsf{\rho }\mathsf{\delta }\mathrm{v}$$

(25)

$${\mathrm{H}}_{\mathrm{M}}=-2\mathrm{\Omega }\times \mathsf{\mu }$$

(26)

$${\mathrm{H}}_{\mathrm{N}}=\mathsf{\rho }\mathsf{\delta }\mathrm{v}\times \mathrm{g}$$

(27)

$${\mathrm{H}}_{\mathrm{O}}=-\mathsf{\rho }\mathsf{\delta }\mathsf{\mu }$$

(28)

Here, Ω indicates earth rotation, µ is the wind velocity vector, ${\mathrm{H}}_{\mathrm{N}}$ is the vertical force exerted on the Earth’s surface, g is the acceleration due to gravity, ${\mathrm{H}}_{\mathrm{O}}$ is the friction force and α is the friction coefficient. Where ρ is the air density, δv is the finite air volume and Hm is the Coriolis force. Each cycle updates the position and velocity of the air packets.

$${\mathrm{V}}_{\mathrm{n}\mathrm{e}\mathrm{w}}=(\left(1-\mathsf{\alpha }\right){\mathrm{V}}_{\mathrm{o}\mathrm{l}\mathrm{d}}-\mathrm{z}{\mathrm{x}}_{\mathrm{o}\mathrm{l}\mathrm{d}}+\left[\left|{\displaystyle \frac{\mathrm{P}\mathrm{m}\mathrm{a}\mathrm{x}}{\mathrm{P}\mathrm{o}\mathrm{l}\mathrm{d}}}\right|\mathrm{S}\mathrm{L}\left(\mathrm{X}\mathrm{m}\mathrm{a}\mathrm{x}-\mathrm{X}\mathrm{o}\mathrm{l}\mathrm{d}\right)\right]-{\displaystyle \frac{\mathrm{H}{\mathrm{V}}_{\mathrm{o}\mathrm{l}\mathrm{d}}}{{\mathrm{P}}_{\mathrm{o}\mathrm{l}\mathrm{d}}}}$$

(29)

$${\mathrm{x}}_{\mathrm{n}\mathrm{e}\mathrm{w}}={\mathrm{x}}_{\mathrm{o}\mathrm{l}\mathrm{d}}+\left({\mathrm{V}}_{\mathrm{n}\mathrm{e}\mathrm{w}}\times ∆\mathrm{t}\right)$$

(30)

In order to enhance appliance scheduling, WDO continuously compares fitness values and changes air parcel velocities, while taking opposing, gravitational and Coriolis forces into account.

4.4. BFO

Inspired by the foraging habits of Escherichia coli bacteria, Bacterial Foraging Optimization (BFO) maximizes solutions by means of swimming, chemotaxis, reproduction and elimination–dispersion. It refines the results by updating the placement of the bacteria within the solution matrix after assessing appliance statuses.

$${\mathsf{\theta }}^i\left(\mathrm{q}+i,\mathrm{M},\mathrm{t}\right)={\mathsf{\theta }}^i\left(\mathrm{q},\mathrm{M},\mathrm{t}\right)+\mathrm{L}\left(i\right)∆\left(i\right)\backslash \sqrt{{∆}^t\left(i\right)∆\left(\mathrm{q}\right)}$$

(31)

With the i-th bacterium at stage (q, M, t) traveling in a random direction ∆ within the range [−1, 1] with a step size L(i), the air pressure for each particle is computed.

$${\mathrm{Q}}_{\mathrm{C}\mathrm{C}}(\mathsf{\theta },\mathrm{S}\left(i,\mathrm{k},\mathrm{t}\right)={\sum }_{\mathrm{q}=1}^{\mathrm{n}}{\mathrm{Q}}_{\mathrm{t}\mathrm{t}}\left({\mathsf{\theta }}^q,\mathsf{\theta }\left(\mathrm{q},h,\mathrm{t}\right)\right)={\sum }_{\mathrm{j}}^{\mathrm{n}}[-i_{\mathrm{a}\mathrm{t}\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}}\mathrm{e}\mathrm{x}\mathrm{p}(-X_{\mathrm{a}\mathrm{t}\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{t}}{\sum }_{\mathrm{b}=1}^{\mathrm{a}}{\left({\mathsf{\theta }}_{\mathrm{b}}-{\mathsf{\theta }}_{\mathrm{b}}^{\mathrm{j}}\right)}^2)]+{\sum }_{\mathrm{q}=1}^{\mathrm{n}}[-{\mathrm{C}}_{\mathrm{r}\mathrm{e}\mathrm{p}\mathrm{e}\mathrm{l}\mathrm{l}\mathrm{e}\mathrm{n}\mathrm{t}}\mathrm{e}\mathrm{x}\mathrm{p}(-{\mathrm{X}}_{\mathrm{r}\mathrm{e}\mathrm{p}\mathrm{e}\mathrm{l}\mathrm{l}\mathrm{e}\mathrm{n}\mathrm{t}}{\sum }_{\mathrm{b}}^{\mathrm{a}}{\left({\mathsf{\theta }}_{\mathrm{b}}-{\mathsf{\theta }}_{\mathrm{b}}^{\mathrm{j}}\right)}^2)]$$

(32)

The objective function is as follows: Qcc (θ, S (q, h, t)), where θ = (θ1, θ1,…, θa) is an a-dimensional search space, a is the number of appliances and n is the total number of germs. There is a variety of coefficients (e.g., i_attractant, X_attractant, C_repellant, X_repellant).

4.5. Our Proposed GmPSO

We propose a GmPSO algorithm, which uses the product characteristics of the GA and BPSO algorithms to minimize the PAR, power bill cost and carbon emissions simultaneously. The selected two algorithms are employed as a hybrid, because BPSO can effectively reduce the electricity cost, while the GA can better reduce the PAR. In the first step of GmPSO, PSO techniques are used, and then mutation and crossover of the GA phase are employed to find the current global best position of PSO, named $P_{\left\{pgbest\right\}}^{\left\{t-1\right\}}$.Performing crossover and mutation at the right time for velocity updating of PSO produces better results than applying them to a random population. The proposed and benchmark algorithm are evaluated in terms of time complexity and convergence rate in simulations. Our proposed method/algorithm achieves better results compared to others in terms of the fitness functions and convergence rate in the desired scenarios. The computational cost of both the proposed and existing algorithms is evaluated based on two key factors, execution time and convergence rate: (a) execution time refers to how long an algorithm takes to achieve the desired objectives while managing energy, and (b) the convergence rate indicates how quickly an algorithm reaches a particular iteration to find the global optimal solution. An algorithm is considered computationally efficient if it has a shorter execution time and converges faster. The execution time is measured in seconds, while the convergence rate is determined by the number of iterations. The computational costs of the algorithms are detailed in

Table 4. Computation cost evaluation of the proposed and existing techniques.

Algorithms	Iterations	Time Complexity (s)	Convergence Rate
GA	200	150	110
BFO	200	180	130
WDO	200	170	95
BPSO	200	160	120
GmPSO	200	130	85

. The flowchart in Figure 5 represents the GmPSO process for optimizing smart home energy management by minimizing cost, the PAR and carbon emissions. It begins with initializing the RTP signals, temperature, appliance operation patterns and energy resources (RSERs) of the ESS, along with setting GA and PSO parameters. The algorithm iterates through evaluating the fitness function, updating velocity and position, and assigning the personal best pgbest solution. The hybrid approach integrates GA operations like crossover and mutation to enhance global search, while objective calculations determine the cost, PAR and emissions based on user comfort and billing. The system assesses whether the current fitness is superior, and updates the best solution accordingly. The process repeats until convergence is reached, ensuring a balanced trade-off between cost-effectiveness, energy efficiency and carbon emissions in smart home energy management.

4.6. Price Forecasting Technique

In order to estimate energy prices in smart homes and help with cost management and appliance scheduling optimization, this study investigates Support Vector Regression (SVR) and auto-regressive models (AR1, AR2 and AR3). The study discusses their advantages, while pointing out their drawbacks in terms of offering real-time price information for efficient energy management.

$${\mathrm{Z}}_{\mathrm{t}}={\mathrm{ß}}_0+{\mathrm{ß}}_1{{\mathrm{Z}}_{\mathrm{t}}}_{-1}+{\mathrm{ß}}_2{{\mathrm{Z}}_{\mathrm{t}}}_{-2}+{\mathrm{ß}}_3{{\mathrm{Z}}_{\mathrm{t}}}_{-3}+\mathrm{u}$$

(33)

$${\mathrm{Z}}_{\mathrm{t}}={\mathrm{ß}}_0+{\mathrm{ß}}_1{{\mathrm{Z}}_{\mathrm{t}}}_{-1}+{\mathrm{ß}}_2{{\mathrm{Z}}_{\mathrm{t}}}_{-2}+{\mathrm{ß}}_3{\mathrm{Z}}_{3\mathrm{t}-3}+\sum _{\mathrm{m}=1}^{12}{\mathrm{ᾳ}}_{\mathrm{k}}{{\mathrm{M}}_{\mathrm{k}}}_{,\mathrm{t}}+{\mathrm{u}}_{\mathrm{t}}$$

(34)

$${\mathrm{Z}}_{\mathrm{t}}={\mathrm{ß}}_0+{\mathrm{ß}}_1{{\mathrm{Z}}_{\mathrm{t}}}_{-1}+{\mathrm{ß}}_2{{\mathrm{Z}}_{\mathrm{t}}}_{-2}+{\mathrm{ß}}_3{{\mathrm{Z}}_{\mathrm{t}}}_{-3}+{\mathrm{Ύ}}_{\mathrm{m}}{{\mathrm{B}}_{\mathrm{m}}}_{,\mathrm{t}}+\sum _{\mathrm{m}=1}^{12}{\mathrm{ᾳ}}_{\mathrm{m}}{{\mathrm{Ỹ}}_{\mathrm{m}}}_{,\mathrm{t}}+{\mathrm{u}}_{\mathrm{t}}$$

(35)

SVR is another important technique. This machine learning method is good for prediction, because it can handle non-linear correlations in the data, a necessary feature for forecasting dynamic and variable energy prices. Given SVR’s strong generalization to complicated scenarios, it further enables the energy management system to effectively respond to real-time pricing signals and enhances energy usage optimization.

$${{\mathrm{Z}}_{\mathrm{t}}}_{,\mathrm{Q}\mathrm{C}\mathrm{R}}=\mathrm{Q}\mathrm{C}\mathrm{R}\left({{\mathrm{Z}}_{\mathrm{t}}}_{-1},{{\mathrm{Z}}_{\mathrm{t}}}_{-2},{{\mathrm{Z}}_{\mathrm{t}}}_{-3}\right)$$

(36)

In addition, the framework is augmented with the implementation of ANFIS. ANFIS is primarily used for load and energy optimization; however, due to its predictive ability, it is also employed for price forecasting. This hybrid approach leverages the strengths of fuzzy logic and neural networks, which are expected to improve decision making under the scenario of energy price volatility.

The main objective of the proposed price forecasting method is to support energy efficiency and SH cost reduction. By applying these innovative techniques, this study demonstrates how machine learning can enhance the efficacy and sustainability of energy management systems. Figure 6 shows a flowchart illustrating the of operations of the proposed ANFIS feedback algorithm.

5. Results and Discussion

In this section, we introduce the results and analysis associated with the proposed Smart Home Machine Learning Techniques system. Specifically, the system determines the coupling of RESs and an ESS, and analyzes the effectiveness and robustness of the GmPSO algorithm for achieving this goal. To adapt Smart Home Machine Learning Techniques, simulations were carried out in MATLAB, treating six passive sectors as appliances and the ESS as the source.

The suggested GmPSO algorithm was created and tested using MATLAB R2019a. Rather than using common MATLAB toolboxes, the simulation was run using a proprietary framework written in MATLAB. The implementation involved writing scripts for initializing parameters, executing optimization iterations and analyzing the performance of the scheduling policy. The simulations used the parameters given in

Table 5. Algorithm parameters.

Algorithms	Parameters	Values
GA	Max. iterations	200
	Size of population	500
	Zn → Crossover rate	0.1
	Mn → Mutation rate	0.8
	N → Number of elites	10
BPSO	Number of reruns	200
	Size of swarm	500
	Vmax → Maximum velocity	4
	Vmin → Minimum velocity	−4
	Xf → Inertia weight upper bound	1
	XD → Inertia weight lower bound	0.6
	Z1 → Cognitive component	4
	Z2 → Social component	3
WDO	Number of reruns	200
	Quantity of individuals	500
	DimMin → Minimum dimension boundary	−6
	Vmin → Minimum velocity	7
	Vmax → Maximum velocity	−0.4
	SL → Local search factor	0.2
	N → Number of dimensions	3
	G → Gravitational constant	10
	ᾳ → Air resistance coefficient	0.3
BFO	Maximum generation	200
	Se → Total bacteria in population	24
	Sr → Reproducing bacteria	7
	SL(i) → Swim length for bacterium i	5
	Ss → Number of steps	30
	Sn → Number of nutrients	2
	L(i) → Step size of bacterium i	0.01
	Ped → Elimination and dispersal probability	0.5
	θ → Chemotaxis step size	0.3

for each algorithm. The initial inertia weight $wi$ for BPSO was set to 1.0, which gradually decreased to a final value of 0.4. The mutation rate $pm$ in the GA was set to 0.1 to maintain population diversity and prevent premature convergence. The crossover probability $pc$ in the GA was set to 0.9, enabling a more thorough exploration of the search space. The swarm size $Hswarm$ was set to 500 particles during the optimization phase, and the algorithm was run for 200 iterations $nitra$ to ensure convergence. Velocity constraints were set with a maximum velocity $vmax$ of 4, and a minimum velocity $vmin$ of −4. To ensure reproducibility, simulations for all instances were run using random seed values as constants, allowing the results to be replicated.

The algorithm’s computational complexity, computational cost and convergence rate are given in Table 4, which provides a comparative evaluation of the computational cost of various optimization techniques, highlighting their efficiency in terms of iterations, time complexity and convergence rate. Among the listed algorithms, the GA, BFO and WDO exhibit higher time complexity and slower convergence rates, indicating their computational inefficiency in large-scale optimization problems. BPSO demonstrates a moderate improvement, reducing time complexity slightly while enhancing convergence. However, the superiority of GmPSO is evident, as it achieves the lowest time complexity (130 s) and the fastest convergence rate (85), making it the most efficient technique. This efficiency stems from GmPSO’s enhanced exploration–exploitation balance, enabling faster convergence without being trapped in local optima, thus outperforming traditional heuristic methods in SH energy management and other complex optimization tasks. In addition, using high-quality exogenous grid signal-type RTPs, forecasted temperature and solar irradiance data, which were fed from the EMS, were used for energy pricing and compensation of the user’s load.

5.1. Condition 1: Without PV and ESS Appliance Scheduling

In Condition 1, energy optimization is achieved with a scheduling algorithm alone, without the consideration of the PV and ESS. The solution aims to reduce the energy cost, PAR and carbon emissions by optimizing appliance utilizations. The data set contains various household appliances that are classified as shiftable (appliances are scheduled to run during low-cost hours) and non-shiftable appliances (appliances run at certain fixed time). In order to achieve this goal, some optimization methods, such as the GA, BPSO, WDO, BFO and GmPSO, are used.

5.2. Condition 2: Integration of PV Systems

In Condition 2, PV systems, as a renewable energy source, are integrated into the energy management system. Solar energy is the primary household energy source that powers appliances and reduces dependency on grid electricity and fossil fuels. The condition-based scheduling algorithms designed in Condition 2 are used to maximize the consumption of solar energy and to schedule appliances. The integration is then assessed based on several metrics (energy costs, PAR, carbon emissions).

5.3. Condition 3: Integration of PV and ESS

The third condition combines the PV system and the ESS together to use more energy and ensure energy efficiency. The PV system generates renewable energy during sunlight hours, while the ESS stores this surplus energy for periods of high demand or when there is a lack of sunlight. This enables dynamic load balancing between the grid, the PV system and the ESS, optimizing energy usage while reducing reliance on grid energy.

The primary determinants of photovoltaic system power generation are sun irradiation and ambient temperature. Each scheduling window is calculated using 90% of the total RE. Furthermore, 30% of the 90% of the total RE is used to charge the ESS throughout each time period. An example of sun radiation during a 24 h period is depicted in Figure 7a. The Figure’s y-axis shows the sun radiance in W/m², while the x-axis shows the time in hours. The sun radiation graph indicates that it reaches its highest value of 1200 W/m² at noon or between 11 AM and 3 PM. Sunlight intensity progressively drops throughout the day, and by midnight, it is almost completely gone. This is a normal pattern for solar radiation throughout the day, with peak levels at midday and a decrease in the early morning and late afternoon. Figure 7b illustrates the charging behavior of a battery over a 24 h period. The x-axis displays the time in hours, while the y-axis displays the battery storage level in Ah. Figure 7b shows that the battery starts charging at a relatively slow rate, gradually increasing its storage level until around 11 AM. From 11 AM to 19 PM, the charging rate appears to accelerate, with the battery storage level increasing rapidly. After 19 PM, the charging rate slows down again, and the battery’s storage level stabilizes at around 275 Ah. This pattern suggests that the battery may have reached its maximum capacity, or is being charged at a reduced rate to prevent overheating or damage. Figure 7c shows the predicted ambient temperature during a 24 h period. The temperature rises steadily from its starting point of about 20 °C to a peak of about 30 °C between the hours of 1400 and 1600. Following this, the temperature gradually drops until it reaches about 20 °C by the end of the day. With warmer temperatures during the midday and cooler temperatures at night, this pattern represents the normal daily temperature cycle. Figure 7d shows the amount of RE generated and used during a 24 h period. Time is shown on the x-axis in hours, and RE generation is represented on the y-axis in WH. The estimated generation of RE is depicted by the red line, which peaks at midday and progressively decreases towards dusk. The 90% of the predicted RE is shown by the black line, which shows how much RE is still usable once losses are taken into consideration. After the BSS is charged, the blue line displays the amount of RE that is left over and can be stored for later use or put to other uses. According to the graph, the BSS efficiently absorbs excess RE at times of peak generation, guaranteeing that a sizable amount of the energy produced is accessible for use or storage. Figure 7e displays the RTP for power over a 24 h period. Time is plotted on the x-axis in hours, while electricity costs are plotted on the y-axis in Cents/kWh.

The hourly electricity prices of different load control techniques in a microgrid are compared in Figure 8a. Although the peak costs of all strategies range from 12 to 15 h, optimization-based methods such as the GA, PSO and WDO show notable decreases in peak costs when compared to uncontrolled scheduling. A key component in reducing peak prices and balancing the total electricity cost profile is the battery storage system. These results demonstrate how well optimization-based scheduling strategies work to control electricity prices in microgrids that have battery storage and renewable energy sources. The Figure 8b compares hourly electricity prices for various load management schemes. It demonstrates that electricity costs peak between hours 7 and 10, with the “Unsch cost/hour” scenario (red line) being the most expensive. When RES is included, as shown in the “Unsch + RES cost/hour” scenario (blue line), costs decrease, but there are still occasional peaks. Introducing a BSS, as shown in the "Unsch + RES + BSS cost/hour" scenario (magenta line), further smoothes out the cost profile, lowering the peak and increasing overall cost control. This demonstrates how using renewable energy and battery storage can substantially reduce electricity prices, especially during peak demand periods.

The Figure 8c depicts how power costs fluctuate during the day for various load management strategies, with a focus on optimization techniques and the usage of renewable energy in conjunction with battery storage. The red line, which represents the “Unsch + RES + BSS cost/hour” scenario, serves as the baseline, with costs being relatively high throughout the day. However, when optimization algorithms such as GA (black), PSO (blue), WDO (magenta), and GmPSO (green) are implemented, electricity prices fall significantly, particularly during peak hours. Among these, the GmPSO approach consistently produces the lowest expenses over a 24-hour period. These findings show that optimization strategies, when combined with renewable energy and battery storage, can significantly reduce electricity expenditures, especially during peak demand periods.

The load management options in a microgrid are compared in Figure 8d with respect to their total electricity costs. The most notable cost savings are found with scheduling that incorporates battery storage systems and renewable energy sources; however, there is a minor cost decrease with uncontrolled scheduling as well. According to these results, microgrid systems’ overall electricity costs can be decreased through the use of efficient load control techniques.

Figure 8e shows how different load control techniques in a microgrid compare in terms of hourly energy consumption. All strategies have peak loads that range from 12 to 15 h, although optimization-based approaches, such as the GA, PSO, WDO, BFO and GmPSO, show better peak load control than uncontrolled scheduling. In order to reduce peak loads and even out the total energy consumption profile, the battery storage system is essential. The efficiency of optimization-based scheduling strategies in controlling energy consumption in microgrids with battery storage and renewable energy sources is demonstrated by these results. Figure 8f compares the hourly energy usage of several microgrid load control strategies. Even when the overall energy usage for all strategies remains constant, optimization-based techniques like the GA, PSO and WDO demonstrate superior peak load management compared to uncontrolled scheduling. In order to level out the total energy consumption profile and reduce peak loads, the battery storage system is essential. These results demonstrate how well optimization-based scheduling strategies work to control energy consumption in microgrids with battery storage and renewable energy sources. Figure 8g compares the hourly CO₂ emissions to those of strategies without an RES and ESS, measured in KGs. The x-axis indicates the hour of the day, and the y-axis depicts CO₂ emissions in KGs. The graph contains many bars representing various optimization techniques, as specified by the legend: unscheduled load, WDO, BFO, BPSO and GmPSO. The visualization clearly demonstrates that unscheduled load (light-blue bars) leads to the highest CO₂ emissions throughout all hours, suggesting the need for optimization to reduce emissions. WDO (brown bars), BFO (yellow bars), BPSO (red bars) and GmPSO (green bars) have lower emissions than the unplanned load. GmPSO (green bars) has the lowest CO₂ emissions compared to other optimization approaches, suggesting superior efficacy in lowering carbon production. The general trend is that utilizing optimization algorithms for load scheduling can significantly cut carbon emissions, with GmPSO being the most efficient. This comparison emphasizes the role of efficient energy management in reducing effects on the environment, especially in the absence of renewable energy sources. Figure 8h compares hourly CO₂ emissions under Condition 2, unscheduled + RES, measured in KGs. The x-axis indicates the hour of the day, while the y-axis displays CO₂ emissions in KGs. The legend depicts various optimization strategies, including unscheduled load with an RES, WDO, BFO, BPSO and GmPSO. Unscheduled + RES (light-blue bars) has the greatest CO₂ emissions across all hours, indicating that without adequate scheduling, emissions remain extremely high, even with RES integration. Optimization approaches (WDO, BFO, BPSO and GmPSO) lower emissions when compared to unscheduled loads. GmPSO (green bars) has the lowest CO₂ emissions, making it the most efficient algorithm for reducing emissions when an RES is included. The overall trend demonstrates that using optimization approaches helps to cut emissions at all hours, stressing the necessity of intelligent load scheduling in improving energy efficiency. Figure 8i compares the hourly CO₂ emissions for Condition 3—Unscheduled + RES + ESS—in KGs. The x-axis indicates the hour of the day, while the y-axis shows CO₂ emissions (in KGs). The legend distinguishes between several instances, including unscheduled load with RES + ESS and optimization approaches (WDO, BFO, BPSO and GmPSO). Unscheduled + RES + ESS (light-blue bars) has the greatest CO₂ emissions throughout all hours, indicating that even with optimization, emissions remain high. The optimization approaches (WDO, BFO, BPSO and GmPSO) considerably decrease CO₂ emissions compared to the unplanned scenario. GmPSO (green bars) has the lowest CO₂ emissions, indicating its success in reducing emissions through optimal energy management. A consistent pattern is seen over all hours, where each optimization technique gradually reduces emissions, with GmPSO performing the best, followed by BPSO, BFO and WDO. Figure 9a compares the load distribution across the BSS, RES and utility grid for different microgrid configurations. As the microgrid complexity increases from “Utility” to “Utility + RES + BSS”, the load on the RES and BSS increases, but the load on the utility grid decreases significantly. This implies that battery storage systems and renewable energy sources effectively reduce reliance on the utility grid, leading to a more cost-effective and environmentally friendly microgrid.

The PAR for several microgrid load management techniques is contrasted in Figure 9b. The y-axis shows the PAR value, while the x-axis depicts the various strategies. The findings demonstrate that adding a BSS and RES to the microgrid, particularly when scheduling is employed, considerably lowers the PAR value. This suggests that with the right load control technology, peak loads can be successfully reduced, resulting in more reliable and effective grid operations. The PAR for several microgrid load management techniques is contrasted in Figure 9c. The y-axis shows the PAR value, while the x-axis depicts the various strategies. The findings demonstrate that adding a BSS and renewable energy sources (RESs) considerably lowers the microgrid’s PAR value, particularly when optimization-based scheduling strategies like the GA, PSO and WDO are used. This suggests that with the right load control technology, peak loads can be successfully reduced, resulting in more reliable and effective grid operation. The PAR for several microgrid load management techniques is contrasted in Figure 9d. The y-axis shows the PAR value, while the x-axis depicts the various strategies. The findings demonstrate that adding a BSS and RES considerably lowers the microgrid’s PAR value, particularly when optimization-based scheduling strategies like the GA, PSO, WDO and GmPSO are used. This suggests that with the right load control technology, peak loads can be successfully reduced, resulting in more reliable and effective grid operations. Figure 10a illustrates how much electricity costs overall for various load control techniques in a microgrid. The various strategies are shown on the x-axis, while the total cost in cents is shown on the y-axis. The findings demonstrate that, in comparison to uncontrolled scheduling using renewable energy sources and battery storage systems (Unsch + RES + BSSGA), optimization-based scheduling strategies such as PSO, WDO, BFO and GmPSO significantly lower total costs. This suggests that in microgrid systems, optimal load management techniques can efficiently control energy usage and lower electricity prices. Figure 10b illustrates how much electricity costs overall for various load control techniques in a microgrid. The various strategies are shown on the x-axis, while the total cost in cents is shown on the y-axis. The findings demonstrate that, in comparison to uncontrolled scheduling using renewable energy sources and battery storage systems (Unsch + RES + BSSGA), optimization-based scheduling strategies such as PSO, WDO and GmPSO significantly lower total costs. This suggests that in microgrid systems, optimal load management techniques can efficiently control energy usage and lower electricity prices. Figure 10c compares the electricity prices of several optimization methods used in a smart home energy management system. The UNSCH (unscheduled load) has the greatest electricity cost, showing inefficiency until optimized. As optimization procedures are implemented, the cost gradually falls. The GA cuts prices marginally, followed by BPSO and WDO, which also enhance cost-effectiveness. BFO achieves even lower prices, while GmPSO provides the greatest cost decrease, indicating its efficiency in reducing electricity costs. Uncontrolled scheduling (Unsch), uncontrolled scheduling with renewable energy sources (Unsch + RES) and uncontrolled scheduling with renewable energy sources and a battery storage system (Unsch + RES + BSS) are the three different load management strategies in a microgrid that are compared in Figure 10d. Each technique’s hourly energy consumption is displayed. The findings demonstrate that adding battery storage devices and renewable energy sources considerably lowers peak energy use and balances the load profile overall. This suggests that microgrid systems can increase grid stability and energy efficiency by including battery storage and renewable energy sources.

Table 6 contrasts how well the various optimization algorithms perform in lowering energy expenses in cents under specific circumstances. Without any optimization, the baseline cost of 400 cents is shown by the “Unscheduled” row. The cost attained by a particular algorithm is displayed in each succeeding row, together with the percentage decrease and the cost difference from the unscheduled cost. With the lowest cost of 150 cents, GmPSO produces the greatest decrease of 62.5% among the algorithms. The cost is also significantly reduced to 250 cents from unscheduled 400 cents in the case of the WDO algorithm, which achieves a percentage reduction of 37.5%. The BFO algorithm decreases the price from 400 cents to 200 cents, and achieves a reduction of 50%. The GA decreases the price from 400 cents to 350 cents, and achieves a reduction of 12.5%. Similarly, BPSO decreases the price from 400 cents to 300 cents, and achieves a percentage reduction of 25%. For a given situation,

Table 7. Carbon emission comparison for Condition 1.

Algorithm	Carbon Emissions (Kg)	Difference (Kg)	Reduction (%)
Unscheduled	300	-	-
WDO	270	30	10%
BPSO	83.08	216.92	72%
GA	96.92	203.08	67.6%
BFO	240	60	20%
GmPSO	69.23	230.77	76.9%

examines how well various algorithms reduce carbon emissions (measured in kg). With a unscheduled carbon emission of 300 kg, the “unscheduled” row depicts the situation in which no optimization is performed. The emissions produced by a certain algorithm are shown in each succeeding row, together with the percentage decrease in carbon emissions and the difference compared to the carbon emissions of the unscheduled scenario. With carbon emissions down to 69.23 kg from the unscheduled value of 300 kg, the GmPSO achieves a percentage reduction of 76.9% in carbon emissions; as such, GmPSO exhibits the largest reduction in carbon emissions among the algorithms. Additionally, BFO reduces carbon emissions by 20%, followed by BPSO and the GA, which reduce emissions by 72% and 67.6%, respectively. WDO has the lowest decrease of all the optimized methods, at 10%. This suggests that the best algorithm for reducing carbon emissions in this situation is GmPSO. The PAR values for several algorithms and an unscheduled scenario under Condition 1 are compared in

Table 8. PAR for Condition 1.

Algorithm	PAR	Difference	Reduction (%)
Unscheduled	4.5	-	-
BPSO	3.2	1.3	28.8%
WDO	3	1.5	33.33%
BFO	2.8	1.7	37.77%
GA	3.5	1	22.2%
GmPSO	2.2	2.3	51.1%

. The highest PAR value, 4.5, is seen in the unscheduled scenario. GmPSO achieves the biggest reduction of 51.1%, followed by the GA (22.2%), WDO (33.55%) and BPSO (28.8%), while all the other algorithms show little reduction in PAR. BFO displays a 37.7% decrease. This suggests that, in comparison to the unscheduled scenario, the algorithms, in particular, GmPSO and the GA, are more successful in lowering the PAR.

Table 6. Cost comparison of scenario 1.

Algorithm	Cost (Cents)	Difference (Cents)	Reduction (%)
Unscheduled	400.00	-	-
WDO	250	150	37.5%
BPSO	300	100	25%
GA	350	50	12.5%
BFO	200	200	50%
GmPSO	150	250	62.5%

Table 6. Cost comparison of scenario 1.

Algorithm	Cost (Cents)	Difference (Cents)	Reduction (%)
Unscheduled	400.00	-	-
WDO	250	150	37.5%
BPSO	300	100	25%
GA	350	50	12.5%
BFO	200	200	50%
GmPSO	150	250	62.5%

A comparison of the costs in cents for the different algorithms under Condition 2 is shown in

Table 9. Cost reduction for Condition 2.

Algorithm	Cost (Cents)	Difference (Cents)	Reduction (%)
Unscheduled	500	-	-
BFO	300	200	40%
WDO	50	150	30%
BPSO	400	100	20%
GA	450	50	10%
GmPSO	200	300	60%

. At a cost of 500 cents, the unscheduled scenario acts as a baseline. The expenses of all the other algorithms are lower than those of the unscheduled scenario. Interestingly, GmPSO reduces costs the most, by 60%, followed by the GA (10%) and WDO (30%). Additionally, there are notable 40% and 20% decreases for BFO and BPSO, respectively. These findings imply that, under the given circumstances, the GmPSO algorithm is particularly successful in minimizing costs.

Table 10. PAR for Condition 2.

Algorithm	PAR	Difference	Reduction (%)
Unscheduled	0.5	-	-
GA	0.45	0.05	10%
WDO	0.3	0.2	40%
BPSO	0.46	0.04	8%
GmPSO	0.2	0.3	60%

compares the PAR for different algorithms under Condition 2, to determine how well they lessen energy usage imbalances. The baseline is the unscheduled value of PAR, which is 0.5. With a noteworthy 10% reduction, the GA lowers the PAR to 0.45 from unscheduled value of 0.5, with a 10% reduction, WDO reduces it by 40%, and BPSO further reduces it by 8%. With a phenomenal 60% decrease and a PAR brough down to 0.2 from an unscheduled value of 0.5, the GmPSO approach is the most successful. These findings demonstrate how GmPSO is better than other methods at maximizing energy distribution.

Under Condition 2, the carbon emissions in KGs from several methods are compared in

Table 11. Carbon emissions for Condition 2.

Algorithm	Carbon Emissions (Kg)	Difference (Kg)	Reduction (%)
Unscheduled	250.00	-	-
BFO	187.5	62.5	25%
WDO	208.3	41.7	16.68%
BPSO	158.3	91.7	36.68%
GA	166.7	83.3	33.32%
GmPSO	150.00	150	60%

. As a baseline, the unscheduled scenario emits 250 kg of carbon dioxide. In comparison to the unscheduled scenario, all other algorithms show a decrease in carbon emissions. Notably, the GA (33.32%), BFO (25%), WDO (16.68%) and GmPSO (60%) obtain the largest reductions. BPSO reduces carbon emissions to 36.68%. These findings imply that, under the given circumstances, the algorithms, particularly GmPSO, are quite successful at reducing carbon emissions. A comparison of the costs in cents for the different algorithms under Condition 3 is shown in

Table 12. Cost reduction for Condition 3.

Algorithm	Cost (Cents)	Difference (Cents)	Decrease (%)
Unscheduled	500	-	-
GA	400	100	20%
BFO	330	170	34%
WDO	350	150	30%
BPSO	380	120	24%
GmPSO	300	200	40%

. At 500 cents, the unscheduled scenario acts as a baseline. The expenses of all the other algorithms are lower than those of the unscheduled scenario. Notably, the GA reduces costs the most (20%), followed by WDO (30%), BPSO (24%) and GmPSO (40%). At 34%, BFO also exhibits a decline. These findings imply that, under the given circumstances, the GmPSO algorithm is particularly efficient at minimizing costs.

The PAR values for several algorithms and an unscheduled scenario under Condition 3 are compared in

Table 13. PAR reduction for Condition 3.

Algorithm	PAR	Difference	Reduction (%)
Unscheduled	2.8	-	-
GA	2.5	0.3	10.7%
BFO	1.8	1	35.7%
BPSO	2.2	0.6	21.42%
GmPSO	1.2	1.6	57.1%

. The highest PAR value, 2.8, is found in the unscheduled scenario. The GmPSO algorithm shows the highest reduction in PAR, which is 57.1%, and BPSO shows a 21.42% reduction in PAR, while BFO reduces the PAR to 35.7%, and the GA reduces the PAR value to 10.7%. The carbon emissions, in KGs, from several algorithms and the unscheduled scenario under Condition 3 are compared in

Table 14. Carbon emissions for Condition 3.

Algorithm	Carbon Emissions (Kg)	Difference (Kg)	Reduction (%)
Unscheduled	208.3	-	-
WDO	187.5	20.8	9.9%
BPSO	166.7	41.6	19.9%
BFO	179.8	28.5	13.6%
GA	170.8	37.5	18%
GmPSO	158.3	50	24%

. At 208.3 kg, the unscheduled scenario has the highest carbon emissions. In comparison to the unscheduled scenario, all the other algorithms show a decrease in carbon emissions. Remarkably, GmPSO attains the greatest reduction of 24%, with the GA (18%), WDO (9.9%) and BPSO (19.9%) following behind. BFO shows a reduction in carbon emissions of 13.6%. These findings imply that, under the given circumstances, the algorithm GmPSO is successful in reducing carbon emissions. Although this work focuses on the optimization of energy management for a single smart home, the GmPSO algorithm’s scalability to larger environments, such as smart neighborhoods, office buildings, or smart cities, remains an unanswered question. GmPSO’s decentralized nature makes it an acceptable alternative for scalability; yet, several concerns arise, such as its higher computing complexity, increased communication cost and heterogeneity in load demand variation. Future research should look into multi-agent energy management systems and cloud-based optimization methodologies to enable effective real-time scheduling in large applications. Furthermore, the integration of distributed renewable energy sources (PV + Wind) on a larger scale will demand additional changes to the current optimization model to maintain system stability and cost-effectiveness.

6. Conclusions and Future Work

This study explores heuristic-based algorithms to manage energy consumption in SHs. With the growing popularity of smart appliances, the study highlights that these possible novel energy management approaches are needed to nearly eliminate customer discomfort, as well as to significantly reduces peak energy demand. The study finds that achieving this goal forces us to integrate ESSs and RSERs, and the OHEMS system developed in this study investigates the contributions of these integrations to the PAR and energy costs, showing significant improvements. The simulations still confirm that the use of heuristic advance techniques, such as WDO, GA, BPSO and BFO, and our hybrid of the GA and PSO, GmPSO, lead to better energy efficiency performance in SHs. This research analyzes the best energy optimization cases under three conditions: scenario 1 emphasizes the scheduling of household appliances with the help of heuristic algorithms, without considering RSERs, and providing significant savings in terms of energy bill costs, carbon emissions and the PAR. Using solar energy, scenario 2 incorporates a PV system to raise energy efficiency, and GmPSO shows excellent reductions in cost, the PAR and emissions. Finally, scenario 3 is a configuration that consists of a PV system and an ESS, which can supply the remainder of the solar energy that may have been generated during peak demand even if solar energy is scarce, thus allowing solar energy to be stored for later use, and adjusting the load distribution, reducing the amount of energy purchased from the grid, reducing costs and enhancing the reliability of the grid. These conditions showcase the advantages of combining renewable energy and storage with heuristic-based algorithms progressively. The simulation results demonstrate significant improvements. Under scenario 1, GmPSO lowered carbon emissions from 4.40 kg to 0.70 kg, bringing them down to 84.09%; GmPSO also cut prices from an unplanned value of 871.00 to 93.73, resulting in an 89.23% reduction percentage. The GmPSO method reduced the PAR by 68.03%, from an unplanned value of 1.55 to 0.4955. In scenario 2, GmPSO reduced the PAR from an unscheduled value of 0.4078 to 0.0140, resulting in a 96.57% reduction; further, GmPSO reduced the costs from 250.00 cents to 8.00 cents, achieving a 96.80% reduction; and finally, GmPSO reduced the carbon emissions from 4797.4734 kg to 5.9413kg, resulting in a 99.88% reduction. The GmPSO algorithm generated an ideal carbon emission value of 5999.15 kg from an unplanned value of 7581.58 kg when batteries and renewable energy sources were combined in scenario 3, resulting in a reduction percentage of 20.85%. GmPSO also achieved a 19.89% cost reduction, bringing energy expenses down from an unplanned value of 378.27 to 303.00. GmPSO obtained a reduction percentage of 90.12% and decreased the PAR value from an unplanned value of 1.519 to 0.150. These results highlight how heuristic-based optimization algorithms, such as GmPSO, can provide SH energy management that is sustainable.

This study offers significant insights for stakeholders, including energy companies, regulators and SH device manufacturers, by enhancing energy efficiency and advancing SH energy management through RSER and ESS integration. Future work will focus on implementing advanced ML algorithms to improve the accuracy of price, load and user behavior predictions, while adapting to dynamic user preferences. Additionally, real-world deployment of the proposed OHEMS will be conducted to evaluate its practical effectiveness across diverse populations and climate conditions. Our proposed system can be adopted in energy management systems beyond a single SH. While the proposed approach effectively optimizes energy consumption in an SH, its applicability to larger settings, such as smart cities and commercial buildings, presents additional challenges. These include increased computational complexity, communication overhead and the need for seamless integration with diverse energy sources and user behaviors. Future work should explore scalable architectures, distributed optimization techniques and edge computing solutions to enhance the system’s adaptability for large-scale deployment, while maintaining efficiency and responsiveness.