1. Introduction
The energy requirement of commercial as well as residential users is increasing day by day. At the same time, a different generating unit of electricity faces a shortage of energy due to line losses and unpredictable energy demand from the endusers. For this reason, engineers and scientists are looking to adopt and implement a strategy that must be safe with reliable transmission and delivery. The researchers in this field are also looking to establish interactive communication between the enduser and utility by introducing advanced information and control technologies [1]. As a result of different efforts, they proposed and developed different solutions based on smart grid technology to improve the reliability of the grid, thus providing communication between the enduser and the utility by minimizing the environmental issues caused by fossilfueled generation [2]. Around the globe, the energy requirements of endusers and industry are increasing linearly, while power generation from different sources and the reliable transmission of the power is much slower than the consumption [3]. The traditional grid lacks communication between the users and the utility causing inefficient operation on both the demand and supply sides.
Smart grid technology majorly relays on different types of renewable energy and efficient demandsupply management. With the increasing energy consumption demand, requirements to switch from traditional fossilfueled generation to smart grid technology will become a prominent research area [4,5,6]. As a result of the smart grid, the resultant energy will be environmentfriendly, cheaper, and easytouse onsite energy, by addressing the stability and irregular nature of Renewable Energy systems (RES) [7,8,9,10].
A survey was held in the United States to determine household electricity usage. Based on the survey results, different household appliances consumed almost 42% of residential energy [11]. Researchers in this field propose and design new prototypes and standards based on energy consumption patterns for the residential electricity market by coping with energy optimization [12,13]. For this purpose, they introduced and deployed new technologies such as onsite RES and grid power, an advanced metering system, controllable appliances, an energy storage system, and intercommunication between utility companies. For this purpose, they introduced and deployed new technologies such as distributed energy generation (onsite RES and grid power), an advanced metering system, controllable appliances, an energy storage system, intercommunication between utility companies and endusers, and a standalone storage system. Using the twoway communication mechanism, endusers will be permitted to access their energy usage and pricing information. On the other hand, introducing the different pricing schemes at the retailer level allows an opportunity for the electricity consumer to minimize his electricity bills by shifting from peak hour to shoulder [14]. As we do not have a largescale energy storage system, a balanced mechanism for energy generation and consumption must be implemented to avoid complete shutterdown and loadshedding problems [15]. In this article, we propose a mathematical model and implement a controlling mechanism:

The Home Energy Management Controller (HEMC) enhances energy efficiency and improves the comfort level within a single residential home, without taking into account the retailer side data for load forecasts and different pricing schemes for scheduling.

Using a twoway communication mechanism a user can shift appliances from high to offpeak time by increasing high demand at a particular time interval.

To achieve this shift from high to lowpeak, another mechanism Demand Response (DR) is introduced which is in response to the changes in the price of electricity over a certain time interval offered by the utility company, endusers also change their electricity consumption patterns from their normal routine to achieve many benefits from the subsidized patterns. In this work, we proposed HEMC based on load shifting technique and user preferences.

We consider a typical home with 10 different types of electrical appliances, having a variable length of operation time to show the effectiveness of the proposed algorithms.
For energy optimization problems different researchers proposed different techniques such as Linear Programming (LP), Dynamic Programming (DP), Artificial Intelligence (AI) inspired techniques such as Genetic Algorithm (GA), Binary Particle Swarm Optimization (BPSO), Ant Colony Optimization (ACO), Wind Driven Optimization (WDO), etc., for energy consumption patterns, minimizing electricity cost calculation, maximizing user comfort and PAR based on different pricing schemes, different types of appliances having different operation time. We solve the same problems using GA, BPSO, and WDO with a different loadshifting strategy to achieve better results. Our proposed algorithm considers two types of energy, grid energy and RES, with the storage system. For grid energy, we use the ToU pricing scheme which is fixed for a duration or season.
A typical home with an energy management system is depicted in Figure 1. This figure also represents the flow of the paper and the system model deployed in the paper. The proposed system model consists of RES which may be Photo Voltaic Cell (PVC), wind energies, and power utilities that supply electricity from the main grid. Electricity from the power grid is directly transmitted to the smart meter, whereas renewable energy is first transmitted to the proposed HEMC and then stored in the storage system deployed in the smart home. All the schedulable appliances in a typical smart home are connected with the proposed HEMC system, which optimally scheduled their operation to switch them to renewable and power grid to save costs while mainlining the user comfort levels. On the other hand, nonschedulable appliances which are fixed to be operated or based on their demands (while maintaining user comfort levels) also directly communicate with the proposed HEMC system to switch their operation on the RES system or power grid to reduce the cost and PAR values.
In the future, more incentives will be offered by different retailer companies to fascinate the user by reducing the peaktoaverage ratio [16,17,18]. Both customers and the utility companies take advantage by using a demand response program [19,20]; the utility companies introduce different pricing schemes based on energy consumption at a certain time unit, which encourages the customer to shift their requirement from peak demand in response to the subsidized incentive [21,22]. A typical home with an energy management system is depicted in Figure 1.
Figure 1 also represents the flow of the paper and the system model deployed in the article. The proposed system model consists of RES which may be Photo Voltaic Cell (PVC), wind energies, and power utilities that supply electricity from the main grid. Electricity from the power grid is directly transmitted to the smart meter, whereas renewable energy is first transmitted to HEMC and then store in the storage system deployed in the smart home. All the schedulable appliances in a typical smart home are connected with the HEMC system, which optimally scheduled their operation to switch them to renewable and power grid to save costs while mainlining the user comfort level. On the other hand, nonschedulable appliances which are fixed to be operated or based on their demands (while maintaining user comfort levels) also directly communicate with the HEMC system to switch their operation on the RES system or power grid to reduce the cost and PAR values.
The rest of the paper material is structured as follows: Section 2 discusses the related work. Section 3 discusses the proposed schemes and system model architecture, and the appliance energy consumption patterns are discussed, respectively. In Section 4, we describe the different algorithms used in the smart scheduler, and a detailed discussion of the load optimization problem, WDO, and PSO algorithms is presented. The results of the simulations and performance evaluation metrics are given in Section 5, and Section 6 highlights the conclusion of the paper.
2. Literature Review
Energy consumption and optimization are the core issues in designing a smart grid while maintaining user comfort and reducing costs, as pointed out by [23,24,25]. These papers give an overview of PSO and its applications when used in different fields of life. The authors propose and design an optimization technique based on particle swarm optimization due to its robust nature and easy implementation in complex and nonlinear problems. Due to its fast convergence nature, PSObased scheduling offers an easy way to shift peak and highpeak demand to lowpeak time intervals [26], at the same time allowing the enduser to use an incentivebased package to reduce the cost of electricity. This work rationalizes the importance and usefulness of DSM in efficient home energy management systems. To manage more expanded and elaborated ideas related to efficient energy management in the smart grid, such robust PSO optimization techniques can be used.
To cope with increasing energy demand effectively and efficiently, electric power supply and consumption patterns can be simulated for effective grid management. Over time, the generation capacity of electricity is decreasing day by day in traditional grids, facing several challenges related to delivering the increasing power demand. In traditional grids, data/information can only flow in one direction; from the grid to the endused. To make twoway communication possible between the grid and the customer, smart grid technology is introduced, which intelligently interacts with the grid and user to efficiently carry and distribute viable, maintainable, costeffective, cheap, and secure electricity supplies [27,28]. Following the smart grid mechanism, a scheduler is proposed and designed using different AI techniques to schedule different types of home appliances. AIbased techniques such as GA, PSO, ACO, WDO, etc., have been in use for the last couple of years for energy optimization problems. In the article [17], the author designed and implement a scheduling scheme based on PSO for different home appliances with a predefined length of operation time. The paper also presents a comprehensive review of PSO with its other counterpart algorithms. The proposed scheme takes both the interruptable and uninterruptible load for the scheduling. The authors in [29] integrate a fuzzy logicbased thermostat with the home energy management system to minimize battery degradation to prevent unnecessary renewable energy arbitrage. The proposed system employs dayahead load scheduling to save costs, offers the best possible Demand Response (DR) and Photovoltaic (PV) selfconsumption, and the fuzzy logicbased controller aims for effective DR of air conditioning while maintaining thermal comfort. Reinforcement learning is used by the authors in [30] to construct a home energy management system. The home electric appliance systems, which contribute to the most important loads in a household, are regulated by HEMC based on machine learning and reinforcement learning, allowing consumers to save power while still improving their comfort. By correctly optimizing and addressing the optimal use of renewable energy sources, the proposed method is examined for monitoring home electric appliances to reduce energy consumption.
Heuristic algorithms play an important role in energy optimization problems [31]. Paper [32] highlights a genetic algorithmbased smart scheduler for optimal power scheduling, and scheduled home usage appliances of different types in the HEM system. The author used timeofuse pricing signals and realtime pricing schemes for scheduling purposes, to minimize total energy cost and energy consumption. A comparison with unscheduled loads is carried out in the paper, which proves that GA shows more prominent results in cost reduction and energy consumption. The DR program based on GA and PSO is proposed in [33], by sightseeing the appliance scheduling schemes to help the enduser ease by minimizing the electricity bill, without compromising his/her comfort. At the same time, the proposed DR program facilitates retailer companies to stabilize the grid by optimally reducing peak demand. The simulation was carried out for unscheduled and scheduled DR programs by implementing GA and PSO as a hybrid approach. The results show that the hybrid approach has better insight into energy consumption patterns as compared to BPSO, whereas in cost analysis, the hybrid approach shows more prominent results than unscheduled ones. A similar concept is also highlighted in [30].
The authors in [34,35] propose and implement a demandside management scheme to reduce PAR and minimize the electricity cost while considering user preferences. The proposed scheme is based on a heuristicbased evolutionary algorithm by shifting the load during highpeak hours to facilitate both the customer and grid. Both papers deploy onsite energy generation and storage unit, which is integrated with the grid energy. The results demonstrate that during highpeak hours, some of the load is shifted to RES by reducing PAR and minimizing the cost. The technique in the papers scheduled a large number of appliances of different types. The authors in [36,37] use a heuristicbased evolutionary algorithm to reduce the PAR and minimize the cost by shifting the peak hour load to different sources.
The author in [38] studied a typical home load management problem for different classes of appliances using the ToU pricing scheme. Appliances are categorized based on the length of operation time and energy consumption. The author first proposed and developed an efficient mathematical model for different classes, using this model an efficient and optimal algorithm is designed to condense and decrease the overall electricity consumption and bill as well as peak lessening and saving during subsidized hours by maintaining user comfort levels. Time scheduling flexibility is introduced for each class of appliances so that users can adopt any model based on requirement and priority. Simulation results demonstrate that the proposed algorithm optimally scheduled the home appliances based on energy consumption requirements and patterns, the ToU pricing scheme, and operation time.
In [39], the author proposed a demandside management technique using WDO and BPSO algorithms. The smart meter communicates with both the grid and the endused, taking price signals directly from the grid and energy demand and requests from the different appliances. The energy management controller takes this information from the smart meter and performs its calculation to schedule all the appliances, by keeping in view the peak hour and price signal. The schedule was transmitted to the endused’s appliance and grid company. Furthermore, in the suggested model, the author tries to balance electricity cost and waiting time for different appliances to provide benefits not only to the utility company but also to the enduser. To further reduce and minimize the cost, a wellknown mathematical problem formulation technique ”minmax regret knapsack” is used, and this technique is compared to that of simple optimization algorithms. The simulation results show that WDO gives better results than BPSO for the waiting time of appliances and cost reduction.
The authors in [40] proposed an HEM system for residential users to reduce their electricity costs and PAR using two approaches, HEM with microgrid and HEM without microgrid. The proposed HEM not only scheduled the home appliances but also electric vehicle charging and discharging optimally while maintaining user comfort. Each enduser has its microgrid which is connected to their grid, having a solar panel, gas turbine, wind turbine, and energy storage system (ESS). The authors use linear programming techniques to formulate the scheduling problems. The simulated results demonstrate that linear programming techniques can efficiently schedule different smart appliances and electric vehicles according to electricity generated by the microgrid. Using microgrid generation causes a reduction of the PAR and total cost of electricity. The authors in [41] designed a mathematical model to integrate different energy sources having smallscale generation capacity. The model, which is based on an intelligent multiobjective named home energy management (MOHEM), aims to reduce the enduser electricity bill along with the system’s peak demand by efficiently scheduling a smart residential home. The authors use the super criterion approach and the Pareto optimal solution ideas to deploy the cooperative game theory approach.
To improve the resiliency of the system, the authors in [42] proposed a new approach that is based on a genetic algorithm to empower the system planners to effectively handle different resiliency matrices in a biobjective optimization planning model. A novel mixedinteger model was proposed by the authors in [43] to control the performance and efficiency of a LESS when used in conjunction with a DR scheme. The suggested approach includes cuttingedge managerial options, such as different DR activities that are permitted and the quantity of charging and discharging that is permitted. Furthermore, the model is built to be able to filter out the times when the demand side is prohibited from engaging in DR. The authors in [44] designed a multiobjectivebased model to efficiently operate the demand and supply of a Smart Microgrid (SMG). The basic aim of the proposed model is to minimize the operation cost of the model, discharging pollution chemicals, and customer desired demand and usage curve in the daytime. A major contribution of the proposed model is to introduce an objective function used by SMG operators to balance the customer demands according to the supply with shiftable loads. The author Finlay uses fuzzy logic and the weighted sum approaches to choose the best solution.
The authors in [45] proposed a model based on multiobjective optimization, using a hydrogen storage system (HSS) while considering responsive consumers (RC). The basis of the proposed objective function is to increase the reliability of the system and minimize the operational cost and the gap between the demand and supply of the electricity. The author further used the Monte Carlo simulation model to effectively deal with uncertainties in the system. The end model was deployed by using the Shuffled Frog Leaping Algorithm (SFLA), through which the nondominated solution is generated. Fuzzy logic and the weighted sum approach were used for the best solution. The authors in [46] designed a technique called MORL (MultiObjective Reinforcement Learning algorithm) to effectively deal with the demand response to reduce the energy usage pattern while maintaining user comfort. If the proposed scheme is compared with conventional approaches, the earlier scheme alleviates the result of different enduser preferences and handles the indecision of future prices and renewable energy generation. Table 1 presents the comparison of the existing schemes and the proposed scheme.
3. Proposed Scheme and System Model for HEMC
This section carries the discussion of an ideal and ultimate approach for scheduling and managing the required power and power consumption of an ideal home having a large number of appliances is proposed based on a specific pricing scheme. Since most of the endusers still use traditional electromechanical meters, utility companies use Fixed Retailer Price (FRP) models for the enduser which is a fixed price all the time. Smart meters as a replacement for old and traditional methods will be used to record energy consumption reading in a real environment with high accuracy and minimum effort. These utility companies use different incentives and subsidybased pricing schemes for the customer to reduce energy demand and thus stabilize the grid. Some of the important and more used pricing schemes are ToU and RealTime Pricing (RTP): In the earlier pricing schemes, 24 h of the day are equally divided into equal intervals and the price for each interval is known in advance by the users. Thus, a user can schedule his/her appliances based on the price signals, i.e., in peak hours, the user tries to turn on fewer appliances to reduce energy consumption, and hence minimize the cost. While in the shoulder and offpeak interval, most appliances are turned on. The RTP is somehow like ToU, where the price is based on enduser energy demand varying each hour. In this work, we present an inventive prototypical strategy to determine the required energy and electricity usage pattern for typical home electrical appliances in advance. The proposed HEMC system is stimulated with a Smart Scheduler(SS) which acts intelligently, and all the appliances use two communication mechanisms to communicate with the utility companies and SS using a smart meter.
The smart meter receives a price signal from the grid and passes it to the SS, on the other hand, different appliances send on/off requests to a smart meter, which also passes the on to the SS. The SS knows in advance the operation time for each appliance. Taking all these inputs from the grid and appliances through the smart meter, the SS generates energy consumption patterns and schedules all the appliances in the given domain of search space according to the price signals and operation time to decide the optimal time for the smart appliances to minimize energy consumption, minimizing electricity cost, while considering user comfort and reducing the peak to average ratio. Our proposed schemes also consider onsite RES generation and storage systems. During offpeak time intervals when energy cost is minimal, the SS utilizes the grid energy, and when the grid energy cost is at a maximum, the enduser shifts the load from the grid to the RES system to maximize the user comfort level. After performing many simulations, the results demonstrate the minimum cost in terms of electricity bills for the enduser having HEMC compared to those who have no infrastructure and installed architecture for HEMC at their homes.
Energy consumption based on a 24h equal interval pricing scheme is important for both endusers and utility companies, by distributing the load properly in the H hour horizon to offer the maximum in terms of electricity costs. Given a set of different homebased appliances, a great matter of concern is to carry and distribute the energy power load efficiently in the H hour intervals, such that the installer of the HEMS obtains maximum profit out of the system, i.e., $A={a}_{1},{a}_{2},{a}_{3},\dots \dots \dots \dots \dots ,{a}_{24}$. Each listed appliance requires a different energy level to be operated and their consumption rating is shown in Table 6. Each appliance uses twoway communication with the SS of the HEMC. Smart grids and smart meters continuously exchange the demand and electricity cost frequently, as different utility companies offer different incentives and subsidybased prices over 24h time intervals, namely highpeak, lowpeak, and offpeak, as listed in Table 7. The enduser tries to operate a maximum number of appliances in offpeak and lowpeak hours, to fulfill his requirement, and operate fewer appliances in highpeak hours to minimize electricity bills, respectively. Reviewing the different pricing schemes and energy demand highlights that highpeak energy consumption will charge more to the customer, as compared to lowpeak hours in a 24h interval. Keeping in mind the different pricing schemes, each user optimally consumes energy, thus minimizing his/her electricity bill. We propose our model for the optimization problem given by Equations (1) and (2):
(1)$\begin{array}{c}\hfill H={h}_{1},{h}_{2},{h}_{3},\dots \dots \dots \dots \dots ,{h}_{24}\end{array}$
(2)$\begin{array}{c}\hfill A={a}_{1},{a}_{2},{a}_{3},\dots \dots \dots \dots \dots ,{a}_{24}\end{array}$
We divide 24 h into equal intervals, $H={h}_{1},{h}_{2},{h}_{3},\dots \dots \dots \dots \dots ,{h}_{24}$, in a fixed horizon of time interval h, the scheduling of every appliance must take into consideration different time bounds such as start time, finish time, and length of the operation time, ${H}_{s}$, ${H}_{f}$, and ${H}_{Iot}$, respectively. Each appliance may have a scheduling time interval between $[{H}_{0},{H}_{max}]$, where each hour has a different price signal. During 24h time intervals, the energy consumption vector is given in Equation (3):
(3)$\begin{array}{c}\hfill {E}_{T}={E}_{1}^{{t}_{1}},{E}_{2}^{{t}_{2}},{E}_{3}^{{t}_{3}},\dots \dots \dots \dots \dots \dots {E}_{n}^{{t}_{n}}\end{array}$
where ${E}_{1}^{{t}_{1}}$ is the sum of consumed energy by the first appliance in a fixed time horizon ${t}_{1}$ and so on. The inclusive unbiased and objective function is to decrease the cost of electricity, formulated in Equations (4)–(6):
(4)$\begin{array}{c}\hfill min\left({C}_{h}\right)=\underset{{h}_{1}=0}{\overset{{h}_{24}}{?}}{C}_{h}\end{array}$
Subject to:
(5)$\begin{array}{c}\hfill \underset{{a}_{1}=0}{\overset{{a}_{n}}{?}}{C}_{h}\underset{{h}_{1}=0}{\overset{{h}_{24}}{?}}{C}_{h}\left({E}_{{h}_{1}}{a}_{1}\right)=Egrid\end{array}$
where
(6)$\begin{array}{c}\hfill 1={h}_{1}={h}_{24}\end{array}$
where ${h}_{1}$ to ${h}_{24}$ represents the 24h horizon from 0 to 24, ${C}_{h}$ represents the cost of energy at a particular hour, ${a}_{1}$ represents the set of the appliance, ${E}_{{h}_{1}}{a}_{1}$ represents the energy consumed by the appliance ${a}_{1}$ during ${h}_{1}$ time horizon, $Egrid$ and means energy from the grid. The enduser pays electricity costs in terms of electricity bills to the utility company for the energy consumption of different homebased appliances in a particular time interval over a 24h horizon. The cost of appliances is the cost of energy consumption of a particular homebased appliance turned on in a specific time slot h. The cost is estimated mathematically by using Equation (7) and (8):
(7)$\begin{array}{c}\hfill \underset{{a}_{1}=0}{\overset{{a}_{n}}{?}}{C}_{h}\underset{h1=0}{\overset{{h}_{24}}{?}}\left({E}_{h,load},*{c}_{h}\right)\end{array}$
(8)$\begin{array}{c}\hfill ?h?{h}_{1},{h}_{2},{h}_{3},\dots \dots \dots \dots \dots ,{h}_{24}\end{array}$
where ${C}_{h}$ is the electricity cost for the time interval $h,{E}_{h,load}$ is energy demand by the appliance a in a specific time slot h and is calculated by using Equation (9):
(9)$\begin{array}{c}\hfill \underset{{a}_{1}=0}{\overset{{a}_{n}}{?}}{C}_{h}\underset{{h}_{1}=0}{\overset{{h}_{24}}{?}}\left({E}_{h,load},*{a}_{h,a}\right)\end{array}$
where ${a}_{h,a}$ is a Boolean variable having the value 0 or 1, mathematically defined in Equation (10):
(10)$\begin{array}{c}\hfill {a}_{h,a}=\left\{\begin{array}{cc}1,\hfill & if\left(applianceisON\right)\hfill \\ 0,\hfill & if\left(ApplianceisOFF\right)\hfill \end{array}\right.\end{array}$
${a}_{h,a}$ represents the status of appliance a, the appliance operates and consumes energy in that specific time slot h if ${a}_{h,a}$ is 1, and off if ${a}_{h,a}$ is 0. The smart meter receives an on or off signal from the SS, which then further communicates with all the household appliances and sends a control signal, i.e, ${a}_{h,a}$ to different appliances to change their state. This is mathematically calculated by using Equation (11):
(11)$\begin{array}{c}\hfill {E}_{{h}_{1},{a}_{1}}=\left\{\begin{array}{cc}{E}_{a}\hfill & if({a}_{h,a}=0)\hfill \\ 0\hfill & if({a}_{h,a}=1)\hfill \end{array}\right.\end{array}$
where h represents the time interval from 0 to 24 and presents appliance 1. In the proposed research work, we have N number of household appliances in our home, so ${a}_{h,a}$ is the N binary bits pattern. As discussed in the previous sections, the HEMS are also equipped with renewable sources of energy to generate some part of the energy from photovoltaic plates. In our proposed model, we assume that at least 45% of its total energy demand will be generated by the RES and stored. Since RES cannot fulfill all the energy requirements of the enduser, the enduser must be connected to the main grid for the shortage of energy. Thus, the enduser will consume both the grid and onsite RES energy. The hourly energy production of a single photovoltaic module in $K{W}_{h}$ is given by Equation (12):
(12)$\begin{array}{c}\hfill {E}_{RES,h}=?he({h}_{1},{h}_{2},{h}_{3},\dots \dots \dots \dots \dots ,{h}_{24})\end{array}$
The RES generated energy added to the HEMC system from a nonsite installed RES system is, therefore, using Equation (13):
(13)$\begin{array}{c}\hfill {E}_{RES,h}=\underset{{a}_{1}=0}{\overset{{a}_{n}}{?}}\underset{{h}_{1}=0}{\overset{{h}_{24}}{?}}\left({E}_{RES,h}\right)\end{array}$
The peak to the average ratio for GA, BPSO, and GA can be calculated as dividing the maximum energy consumption of all appliances by the average energy consumption in a particular time interval and is given by Equation (14):
(14)$\begin{array}{c}\hfill PAR=\frac{ma{x}_{load}}{averag{e}_{load}}\end{array}$
In the proposed solution, we consider a typical home with N number of appliances, with different power consumption rates and length of operation time. The energy consumption is calculated over a 24h equal time interval. HEMC controls all household appliances by communicating with the utility which takes energy signals directly from the utility, and different appliances request through the smart meter. The scheduling time, i.e., a whole day is equally divided into slots. HEMC while considering the available energy capacity ${C}_{t}$ calculates the timebound in terms of starting ${T}_{s}$ and finishing ${T}_{f}$ time intervals, as well as the energy consumption of each appliance in a given time interval. The energy consumption during all time intervals can be calculated by using Equation (15) and (16):
(15)$\begin{array}{c}\hfill {E}_{T}={e}_{1}^{{t}_{1}},{e}_{2}^{{t}_{2}},{e}_{3}^{{t}_{3}},\dots \dots \dots \dots \dots \dots {e}_{n}^{{t}_{n}}\end{array}$
(16)$\begin{array}{c}\hfill T={t}_{1},{t}_{2},{t}_{3},\dots \dots \dots \dots \dots ,{t}_{24}\end{array}$
The scheduling time horizon during which appliances can be scheduled is given by Equation (17):
(17)$\begin{array}{c}\hfill {T}_{sch}={T}_{max}{T}_{lot}\end{array}$
where ${T}_{sch}$ is the time taken by SS to schedule an appliance, ${T}_{max}$ is the maximum time available for scheduling, and ${T}_{lot}$ represents the length of operation time. As WDO and BPSO have binary variables so particles are initialized randomly for binary positions as shown in Equation (18):
(18)$\begin{array}{c}\hfill {X}_{i}=[{X}_{i}1,{X}_{i}2,{X}_{i}3,\dots \dots \dots {X}_{i}n],?{X}_{i}1,{X}_{i}2,{X}_{i}3,\dots \dots \dots {X}_{i}n?0,1\end{array}$
Each binary value having a probability of $0.5$ is assigned to each particle in each dimension and is given by Equation (19):
(19)$\begin{array}{c}\hfill X{i}_{d}=f\left(X\right)=\left\{\begin{array}{cc}1\hfill & if(rand?0)\hfill \\ 0\hfill & otherwise\hfill \end{array}\right.\end{array}$
where $d=1\dots \dots \dots ,N$ represents the position of each particle in the N dimension. To obtain the global best position the position of each particle is updated and is given by Equation (20):
(20)$\begin{array}{c}\hfill {X}_{\left({i}_{d}\right)}^{(k=1)}=f\left(X\right)=\left\{\begin{array}{cc}1,\hfill & if(rand?0)\hfill \\ 0,\hfill & if(rand<sigmoid\left({V}_{{i}_{d}}^{k=1})\right)\hfill \end{array}\right.\end{array}$
where the sigmoid function is calculated by using Equation (21):
(21)$\begin{array}{c}\hfill sigmoid\left({V}_{{i}_{d}}^{k=1}\right)=\frac{1}{1+exp\left({V}_{{i}_{d}}^{k=1}\right)}\end{array}$
After random initialization, each particle in the solution space moves randomly to avoid premature convergence, and the velocity ${V}_{(i,n)}$ of each particle is updated using the result given by Equation (22):
(22)$\begin{array}{cc}{V}_{(i,n)}=w{v}_{(i,n)}^{t}+\left({C}_{1}rand\left(1\right)*\left({p}_{l{b}_{(i,n)}}^{t}{x}_{(i,n)}^{t}\right)\right)+\hfill & \\ & \hfill \left({C}_{2}rand\left(1\right)*\left({p}_{g{b}_{(i,n)}}^{t}{x}_{(i,n)}^{t}\right)\right)\end{array}$
where $C1$ and $C2$ are the weights for the local best and global best of a particle moving with velocity y and position x. $rand\left(1\right)$ is a random variable whose value is between $[0,1]$, and w is the inertia factor. The notations used in the proposed scheme are listed in Table 2.
4. Proposed Algorithm for HEMC
This section presents different algorithms for HEMC. The algorithm for WDO, BPSO, and GA is implemented in this section.
4.1. Genetic Algorithm
We propose and implement three different algorithms WDO, BPSO, and GA to manage the energy consumption and energy consumption patterns for a typical home that has a large number of appliances with different energy requirements and lengths of operation time. The resultant HEMC system not only generates an energy consumption pattern but also calculates the energy consumption and minimizes the electricity bill while considering user comfort and reducing PAR. To address all these problems, the design scheme should be able to tackle all these involutions. In the past, researchers have used different techniques such as LP and DP, but as the complexity of the problem increases, these techniques are not able to handle such a large number of appliances. Algorithms inspired by AI, such as WDO, GA, and BPSO have the potential to solve such types of complex problems. As compared to other algorithms, GA provides the finest solution for the cost optimization problem, for this reason, we use a GAbased scheduling algorithm. The smart meter interactively communicates with utility companies and appliances and sends the input to SS, using GA for scheduling purposes. The HEMC controller cumulatively deals with the appliances in a defined time interval and gives a complete pattern by solving the minimization problem. The SS operates at the beginning of the day, after sending a request from the appliance to the SS controller, the action taken by SS is based on GA techniques used to schedule all the appliance’s energy consumption patterns in advance. The chromosome configurations of GA represent the solution, i.e., a schedule for appliances of when and how to operate [47]. In this research work, the ON/OFF status of each appliance is represented by an array of bits. Thus, the length of chromosomes depends on the number of controllable appliances. Here in this work, we use 10 different appliances so:
(23)$LengthofchromosomesN=\left(10\right)$
where N represents the total number of appliances. The initial population of chromosomes is randomly initialized, and the initial population is then sent to an objective function, which finds the fitness value for each chromosome.
The GA iterates the population many times, and in every iteration, as a result, a new population is produced by crossover and mutation. As we know that mutation rate and crossover directly affect the convergence of the algorithm, different techniques for crossover such as a uniform crossover, arithmetic crossover, twopoint crossover, singlepoint crossover, and mutation can be used, and here in this work, we use singlepoint crossover and binary mutation. If we use a larger crossover rate, the algorithm will converge fast, and if using a larger mutation rate, there may be a chance to lose some good solutions, which results in the permute convergence of the algorithm.
It is possible that sometimes in the early population, GA finds an optimal solution but gets missed by crossover and mutation rate. In every population, one finest solution is selected and remembered. The elitism technique is used to record this best solution, which is then forwarded to the next generation. Different techniques exist to merge the population to generate a new population, here we use the tournamentbased selection method to make a new parent from the existing population. Different parameters used in GA are shown in Table 3. The Algorithm used in the SS is given in Algorithm 1.
Algorithm 1 GA Algorithm used in the SS 

1:. Initial generation h = 0 
2:. Randomly create an initial population representing the appliance patterns 
3:. Check the termination criteria, i.e., the maximum generation 
4:. Evaluate the fitness of each individual in the population 
5:. Select the patterns from the population with the best fitness values; these patterns should represent the chromosomal configuration, which represents the solution 
6:. Check the on/off status of all the appliances in the chromosomal configuration 
7:. Repeat steps 1–6 for k = 1 as the population size 
8:. Select an individual based on fitness and perform mutation 
9:. If Pm > Rand, then select the next generation 
10:. Select two individuals based on fitness and perform crossover 
11:. If Pc > rand, then crossover this pair 
12:. Create a new population from the offsprings in 9 and 10 
13:. h = h + 1, go to step 4 and repeat until h = 24 
4.2. Binary Particle Swarm Optimization Algorithm
Solution for the same problem, energy consumption patterns, minimization of cost, while considering user comfort and PAR is simulated using BPSO [48]. The SS of HEMC based on BPSO operates at the beginning of the day. After sending a request from the appliance to the SS controller, the action taken by the SS is used to schedule all the appliance’s energy consumption patterns in advance. Particle Swarm Optimization (PSO) is one of the best replacements for liner and dynamic programming techniques used to solve complex optimization problems, which is inspired by bird flocking and was developed by Kennedy and Eberhart. The working of PSO is based on the foodsearching technique of a swarm of birds in a particular search space. In the search space, two important parameters for each bird are noted, the previous position and velocity. Every bird in the group updates his new position and velocity for the previous position and velocity and knows the position and velocity of the nearest bird to the food court. PSO obtains the same behavior and properties from the bird grouping scenario, and places each particle as a bird which is considered a candidate solution in the search space domain.
The total number of particles in the search space is entitled the population or swarm size. Each particle in the solution search space is studied for its velocity, previous and current position, and fitness value, which represent a solution. To find the finest fitness value for the objective function, BPSO is used having a binary value for optimizing the solution. Each particle in the solution search space represents candidate solutions and obtains the optimal solution each particle has to move in the ddimensional solution search space.
The preliminary position and velocity of each particle are initialized randomly. To form a swarm, N number of particles are combined. After making a swarm, the particles move around the solution space to obtain the optimal solution. At the end of simulations, the overall best solution called the ”global best” is taken as the problem solution. The fitness value for each particle is assessed, and if needed, the local and global positions are updated, respectively. After evaluating the fitness values, every particle in the search space flies and dynamically updates its position and velocity by tracking two extremes, i.e., Plbest and Pgbest in each iteration. The control parameters for BPSO are given in Table 4.
Algorithm 2 shows the BPSO algorithm used in SS. The steps involved in the BPSO algorithm are:
Algorithm 2 BPSO Algorithm used in SS 

1:. Initialize all the parameters, such as swarm size, no. of iteration 
2:. Randomly initialize particle (p) for their position and velocity 
3:. Evaluate fitness of objective function for particle (p) 
4:. Two best positions global best and local best will be obtained 
5:. The velocity of each particle is updated, using the inertia weight C1 and C2 
6:. The position of each particle is updated 
7:. Evaluate the fitness of each particle to obtain global best and local best 
8:. Compare the previous best with the current best 
9:. Update the global best 
10:. Repeat until the termination criteria meet 
4.3. Wind Driven Optimization Algorithm
Researchers get inspired by nature to solve complex scientific problems in every field of life. The WDO algorithm is one of the natureinspired algorithms used to solve optimization problems based on atmospheric motion. WDO is an iterative heuristic global optimization algorithm based on population to cope with multidimensional and multimodal problems, having the aptitude to implement different types of constraints on the search domain, as compared to its counterpart GA and BPSO. In principle, very small and tiny particles of air move in an ndimensional domain, following the second law of motion also used to describe air particle motion within the earth’s atmosphere. One prominent factor of WDO, as compared to its other counterpart heuristic algorithm, is to carry out some additional information for velocity updates, such as gravitational force constant and Coriolis forces to give a global best position of the particle with more freedom and robustness. The control parameters for WDO are given in Table 5. Table 6 is used for appliances, consumption power, and LoT, and Table 7 is for the ToU pricing signal.
Algorithm 3 shows the WDO algorithm used in SS. The steps involved in the WDO algorithm are:
Algorithm 3 WDO Algorithm used in SS 

1:. Initialized different parameters such as swarm size, pop size, no. of iteration, different coefficient 
2:. Repeat from h = 0 to h = 24 
3:. Randomly generates the population of particles 
4:. Randomly assign velocity and position to each particle 
5:. Evaluate the fitness of each particle 
6:. Obtain the local best and global best value for the particles 
7:. Update the velocity and position of the particle, using inertia and gravitational constant 
8:. Create a new population 
9:. Evaluate the fitness of each particle after updating the velocity and position 
10:. Compare the previous best with the current best particle 
11:. Update the global best 
12:. Continue until the termination condition meets 
5. Simulation Results and Discussion
In this section, we are going to discuss the simulation results and graphs for the justification of the proposed HEMC, implemented through Wind Driven Optimization WDO, BPSO, and GA using the ToU pricing scheme. The whole scenario and the proposed model are implemented in the Matlab simulation tool by using the parameters mentioned in Table 3, Table 4, Table 5, Table 6 and Table 7. This research work focuses on calculating energy consumption patterns and electricity costs for different types of appliances with HEMC, without HEMC, and with HEMC using RES, Peak to PAR comparison for different algorithms using schedule load and user comfort while considering appliance waiting time and electricity cost. For our proposed algorithm, we consider different types of appliances having variable length power consumption requirements. HEMC takes the price signal from the utility grid directly through the smart meter and schedules the scheduler according to price signals. Using a twoway communication model, HEMC sends an optimized energy schedule to all the appliances, considering the appliance’s consumption patterns and user comfort. The appliances’ energy consumption data is taken from a literature review based on reliable data. In our proposed solution, we take 10 different appliances (shiftable, unshiftable, and semishiftable) with different energy consumption rates and Lengths of Time (LoT). The attribute: appliance’s power rating, number of appliances, and price scheme value are hard coded. For this research paper, an assumption is supposed that household photovoltaic generation must be greater or equal to 35% of its load demand. A time horizon of T = 24 h is considered, which helps the enduser to calculate his/her electricity bill while keeping the constraints of user comfort.
Figure 2 shows the ToU price signal over the 24h horizon. In the proposed ToU pricing scheme, 24 h of the day are divided into equal intervals. In the ToU pricing model, prices are mostly fixed for a month or season. Based on different incentives and subsidie