Multi-Objective Energy Management System in Smart Homes with Inverter-Based Air Conditioner Considering Costs, Peak-Average Ratio, and Battery Discharging Cycles of ESS and EV

Abstract

The smart home contributions in energy management systems can help the microgrid operator overcome technical problems and ensure economically viable operation by flattening the load profile. The purpose of this paper is to propose a smart home energy management system (SHEMS) that enables smart homes to monitor, store, and manage energy efficiently. SHEMS relies heavily on energy storage systems (ESSs) and electric vehicles (EVs), which enable smart homes to be more flexible and enhance the reliability and efficiency of renewable energy sources. It is vital to study the optimal operation of batteries in SHEMS; hence, a multi-objective optimization approach for SHEMS and demand response programs is proposed to simultaneously reduce the daily bills, the peak-to-average ratio, and the number of battery discharging cycles of ESSs and EVs. An inverter-based air conditioner, photovoltaic system, ESS, and EV, shiftable and non-shiftable equipment are considered in the suggested smart home. In addition, the amount of energy purchased and sold throughout the day is taken into account in the suggested mathematical formulation based on the real-time market pricing. The suggested multi-objective problem is solved by an improved gray wolf optimizer, and various weather conditions, including rainy, sunny, and cloudy days, are also analyzed. Additionally, simulations indicate that the proposed method achieves optimal results, with three objectives shown on the Pareto front of the optimal solutions.

1. Introduction

As the importance of decarbonization and sustainability grows, power systems are experiencing significant changes. Energy was distributed from producers to consumers in one direction before, but now the end consumer plays both the role of producer and consumer [1,2]. There are various challenges associated with this transition, and new operating standards need to be developed. The changes have also promoted the combination of renewable energy resources (RERs), which calls for the development of grid management methods to optimize energy sources. The novel approach to the energy management issue needs to account for the new operating patterns in smart grids, such as smart home energy management systems (SHEMS) [2,3].

By monitoring and managing production, storage, and consumption in smart homes, the SHEMS ensures secure, cost-effective operation. In smart grids, a SHEMS facilitates smart operations and management, like load shifting, which helps with demand response (DR) [4,5]. As smart grids and smart homes become more prevalent, SHEMS is becoming a more prominent concept. It is predicted that the number of SHEMS installed, based on Berg Insight, will increase by 43.8 percent per year in Europe and North America between 2022 and 2027 [2,6]. With SHEMS solutions, users inject and store power, thereby supporting distribution and transmission operators to maintain a balanced grid [7] and also reducing users’ energy costs [8]. The usage of air conditioner systems (ACSs) is associated with peak demand in smart homes. There is also a possibility of blackouts in warm regions due to extreme demand and high temperatures [9]; hence, it is extremely important to propose solutions to manage the energy demand in order to reduce the demand in peak periods to prevent blackouts and also reduce the electricity bills.

Several studies have been conducted on SHEMSs: Ref. [10] applies the binary gray wolf optimization to solve the optimal device-planning issue. An optimal energy management system to reduce energy prices is presented in Ref. [11], in order to measure and optimize energy by using the energy storage system (ESS) and plug-in hybrid EV (PHEV). In high-demand periods, ESSs and PHEVs discharge energy for home usage, and in low-demand periods, PHEVs and ESSs are charged. Linear programming was used to solve the optimization problem; however, RERs were not included [11]. Ref. [12] presented the problem of achieving a flat demand profile and reducing power prices by planning appliances as a non-convex mixed integer programming issue. In alternative methods, mixed-integer linear programming (MILP) schemes are used for optimizing energy prices and balancing technological limitations and user satisfaction [13]; however, by increasing the number of appliances in smart homes and considering RERs, ESSs, EVs, and ACSs, the number of variables in the optimization problem increases, and the MILP methods are not able to handle many variables to find the best solution. A multi-objective linear model based on time-of-use (TOU) tariffs and a stationary ESS was examined in Ref. [14]. By using the proposed method, residential energy costs could be mitigated, and peak load demand could be lowered as well. Ref. [15] employed an adaptive moth–flame optimization algorithm to reduce peak demand and power prices. In [16], the Harris Hawks optimization algorithm is used to improve energy prices and peak-to-average ratios (PARs), and to decrease wait times for consumers scheduling their controllable appliances. To further reduce demand and costs, controlling heating or cooling loads was not considered in that paper. In [17], a method for determining the operating techniques of SHEMS, such as a PV-battery hybrid system, is presented. The problem has been formulated as a multi-objective problem, and the weighting factor method is used to solve the problem with a binary particle swarm optimization algorithm. Ref. [18] examined a power-sharing method based on distributed energy transactions for peer-to-peer (P2P) power sharing between smart homes. This strategy proposed a non-cooperative game to resolve mutual power sharing between the first and second stages, and also, a swarm intelligence optimization algorithm is used to solve the optimization problem. Based on ToU tariffs, Ref. [19] conducted a comparative evaluation between various optimization algorithms. Even though comprehensive ACSs were taken into account, RERs were factored into the optimization method. A Non-Dominated Sorted Genetic Algorithm is examined in [20] that aims to decrease the price of energy and the level of dissatisfaction experienced by home users. Several Brazilian families of varying socioeconomic status were examined for the effectiveness of the suggested model. A MILP structure is presented in [21] for designing an optimum operation method for a SHEMS with an inverter-based heating, ventilation, and air conditioning (HVAC) system. It aims to determine the optimal configuration of home devices in conjunction with the optimal operation of the ACS for reducing daily costs and minimizing user dissatisfaction. In [22], an autonomous management structure is proposed for multi-HVAC systems for homes, according to the Autonomous Cycle of Data Analysis Tasks framework. By using the framework, the best operating mode for multi-HVAC systems is determined, i.e., which HVAC subsystems are to be deactivated, activated, or adjusted in a specific situation in real time. Ref. [23] developed a gray-box thermal method for predicting ACS energy usage based on outdoor and indoor temperatures. As a result of the anticipated energy usage, the air conditioning’s DR potential is investigated throughout DR hours for a summer day. In [24], an improved gray wolf optimizer is used to schedule appliances of a smart home in a smart grid in order to minimize the electricity bill, PAR, and emissions. The system includes the WT, PV, ESS, and trading energy with the grid; however, the EV, inverter-based ACS (IBACS), and the batteries’ discharging cycles are not considered [24]. In [25], the energy management system in smart homes is considered to optimize the electricity bill and PAR in order to schedule appliance usage and the operation of ESS. The smart home included PV, WT, and ESS, and the improved biogeography-based optimization algorithm was used to solve the optimization problem; however, the EV system, IBACS, and battery discharging cycles were not considered [25]. Mixed-integer linear programming is used to solve a single objective optimization problem in a smart home with PV and IBAC; however, the other objectives, such as PAR and battery discharging cycles, are not considered [26]. To provide a clear comparison,

Table 1. Comparison between the literature. √ means that the item is considered. × means that the item is not considered.

References	Technique	Objective Functions			RER	ESS	Smart EV	IBACS
		Cost	PAR	Batteries Discharging Cycles
[12]	Mixed-integer programming	√	√	×	√	×	×	×
[15]	Adaptive moth–flame optimization	√	√	×	×	×	×	×
[16]	Harris hawks optimization algorithm	√	√	×	×	×	×	×
[17]	Binary particle swarm optimization	√	√	×	√	√	×	×
[19]	Swarm intelligence algorithms	√	×	×	×	×	×	√
[23]	Genetic, particle swarm, and trust region algorithms	√	×	×	×	×	×	√
[25]	Improved biogeography-based optimization algorithm	√	√	×	√	√	×	×
[26]	Mixed-integer linear programming	√	×	×	√	√	×	√
This paper	Improved gray wolf optimizer	√	√	√	√	√	√	√

shows a comparison between the literature and this paper. As can be seen, and based on the knowledge of the authors, this paper is the first study that considers these three objective functions—cost, PAR, and battery discharging cycles— in a smart home, together with different technologies such as PV, ESS, smart EV, and IBAC systems.

Consumers can now take advantage of new technological developments in smart devices to manage the demand. By scheduling the optimal operation of home devices and electrical kitchenware, a SHEMS reduces consumers’ daily utility costs. A photovoltaic (PV) panel installation in the private area of the consumer can offer various benefits, such as local power generation, reduced electricity bills, energy independence, and environmental sustainability. PV power production is solely dependent on solar radiation, so using an ESS can help users generate power more efficiently. Consumers will be able to utilize various energy tariffs daily by optimizing the charging/discharging schedule for the ESS and EVs to decrease costs per day. Nevertheless, certain energy-consuming appliances, such as washing machines, spin dryers, electric vehicles (EVs), and ACSs, can be scheduled to minimize energy costs.

There are several operational points on the IBACS employed in this study, and it is controlled by an inverter. Since IBACS controls the indoor temperature, the optimum setting is selected in order to reduce both energy usage and the related energy costs while keeping the indoor temperature within the desired range. To optimize SHEMS and maximize the batteries’ lifespan, it is critical to understand the features that influence battery degradation, like the number of discharging cycles.

The purpose of this study is to solve a multi-objective optimization issue for SHEMS, aiming to minimize power bills per day, PAR, and battery discharging cycles of ESS and EV. A smart home is modeled using PV, ESS, EV, and appliances, including IBACS, non-shiftable, interruptible, and uninterruptible appliances. With an IBACS, the indoor temperature can be controlled per day. Buying and selling of power are determined based on the real-time market pricing model. The proposed SHEMS is considered within various weather statuses, such as sunny, cloudy, and rainy days. Also, an improved multi-objective gray wolf optimizer with Pareto front [24] has been applied to solve the suggested optimization problem.

Although multi-objective energy management has been examined in previous studies, this study offers several new findings, such as the following:

• This study examines a multi-objective model using three objective functions for optimizing the energy bill, PAR, and battery discharging cycles of the ESS and EV simultaneously;
• The shiftable appliances, IBACS, ESS, and EV, are scheduled simultaneously, and both ESS and EV trade energy with the main grid to buy and sell energy based on the real-time market pricing model;
• The proposed SHEMS considers various weather conditions, such as sunny, cloudy, and rainy days;
• An improved multi-objective gray wolf optimizer with a Pareto front is used to solve the proposed multi-objective problem.

The rest of the paper is organized as follows: The model of appliances, i.e., IBACS, ESS, EV, and their constraints, along with the suggested three objective functions—electricity bill, PAR, and battery discharging cycles of the ESS and EV—are described in Section 2. The smart home details and simulation results for different weather conditions are illustrated and explained in Section 3. The main conclusion is expressed in Section 4.

2. Problem Formulation

The SHEMS is considered in this paper for the optimal operation and scheduling problem in a smart home, which includes PV, ESSs, EVs, and an IBACS. Daily electricity bills, PAR, and battery discharge cycles of ESSs and EVs are the proposed three objective functions that are considered in this paper to be optimized simultaneously. The suggested problem has been solved in a multi-objective problem. Firstly, the PV, ESS, EV, IBACS, shiftable and non-shiftable appliances, and the constraints are considered, and eventually, the three main objective functions are described.

2.1. Load Classification

Based on the operation and energy consumption, household electrical appliances can also be categorized into three categories, including non-shiftable, interruptible, and uninterruptible [25], which are discussed below:

2.1.1. Non-Shiftable Appliances

Non-shiftable loads have a constant and unchanging operational pattern. A non-shiftable appliance’s overall energy consumption is determined in the following way:

$$P_{NSH}^{app}(t)={\sum }_{k_1\in NSH}{\mathit{PR}}_{k_1}\ast S_{k_1},$$

(1)

where $NSH$ represents a group of non-shiftable devices; $P_{NSH}^{app}(t)$ is the total energy consumption by non-shiftable loads during t; $k_1$, ${\mathit{PR}}_{k_1},$ and $S_{k_1}$ indicate the number, power rating, and off/on states of the non-shiftable appliances, respectively; $S_{k_1}$ is determined in the following way:

$$S_{k_1}=\left\{\begin{array}{c}1 if the appliance is ON\\ 0 if the appliance is OFF\end{array}\right..$$

(2)

2.1.2. Interruptible Appliances

The term interruptible appliance refers to devices that can alter their use time and be switched on and off while in use. In interruptible devices, the entire energy consumption would be as follows:

$$P_{INT}^{app}(t)={\sum }_{k_2\in INT}{\mathit{PR}}_{k_2}\ast S_{k_2},$$

(3)

where $INT$ is a group of interruptible devices; $P_{INT}^{app}(t)$ shows the entire energy consumption using interruptible devices during t; $k_2$, ${\mathit{PR}}_{k_2}$, and $S_{k_2}$ indicate the number, power rating, and off/on states of the interruptible appliances, respectively; $S_{k_2}$ is determined in the following way:

$$S_{k_2}=\left\{\begin{array}{c}1 if the appliance is ON\\ 0 if the appliance is OFF\end{array}\right..$$

(4)

2.1.3. Uninterruptible Appliances

The use of uninterrupted electrical appliances is continuous and cannot be interrupted after being turned on, but the time of their use can be changed. The entire power consumption of this type of load can be obtained by using (5):

$$P_{UINT}^{app}(t)={\sum }_{l\in UINT}{\mathit{PR}}_{k_3}(t)\ast S_{k_3},$$

(5)

where $UINT$ indicates a group of uninterruptible loads; $P_{UINT}^{app}(t)$ indicates the total energy consumption by uninterruptible loads at time t; $k_3$, ${\mathit{PR}}_{k_3},$ and $S_{k_3}$ indicate the number, power rating, and off/on states of the uninterruptible appliances, respectively; $S_{k_3}$ is determined in the following way by using (6):

$$S_{k_3}=\left\{\begin{array}{c}1 if the appliance is ON\\ 0 if the appliance is OFF\end{array}\right..$$

(6)

2.1.4. Inverter-Based Air Conditioner System

IBACSs are devices that can be interrupted and do not need to operate continuously. Depending on the mode of the appliance, the control system adjusts the temperature. The relation between indoor and outdoor temperature adjusted by IBACS is specified by (7). IBACS operation is modeled using (8) and (9). The energy consumption with the inverter-based IBACS, $P_{AC}(t)$, is exactly determined based on some discrete variables and the derated power. Therefore, $P_{AC}(t)$ during each time is determined through a group of binary decision variables, ${\partial }^{(i)}(t)$, in which just 1 binary variable equals one during a specific time. Since the prosumer specifies the desirable temperature range, each operational condition that exceeds it is applied to the objective function. Limitations (10) are used to model the violation of the desirable temperature, in which $D^{+}(t)$ and $D^{-}(t)$ show positive variables [26].

$${\theta }^{In}(t)=\alpha {\theta }^{In}(t-1)+\beta {\theta }^{out}(t)+\gamma P_{AC}(t),$$

(7)

$$P_{AC}(t)=\left[0.2{\partial }^{\left(1\right)}\left(t\right)+0.4{\partial }^{\left(2\right)}\left(t\right)+0.6{\partial }^{\left(3\right)}\left(t\right)+0.8{\partial }^{\left(4\right)}\left(t\right)+{\partial }^{\left(5\right)}\left(t\right)\right]P_{AC}^{max},$$

(8)

$$\sum _{i=1}^5{\partial }^{(i)}\le 1,$$

(9)

$$\left\{\begin{array}{c}{D}^{+}(t) \ge {\theta }^{In}(t)-{\theta }^{max}(t)\\ D^{-}(t) \ge {\theta }^{min}(t)-{\theta }^{In}(t)\end{array}\right.,$$

(10)

where ${\theta }^{In}(t)$ and ${\theta }^{out}(t)$ show the indoor and outdoor temperatures, respectively. $\alpha$, $\beta$, and $\gamma$ are the constant parameters. $P_{AC}^{max}$ is the maximum power of IBACS. ${\theta }^{min}(t)$ and ${\theta }^{max}(t)$ show the minimum and maximum desirable indoor temperatures, respectively.

2.1.5. Total Required Power for Home Appliances

Lastly, the entire power needed for home devices would be as follows:

$$P^{app}\left(t\right)=P_{NSH}^{app}(t)+P_{INT}^{app}(t)+P_{UINT}^{app}(t)+P_{AC}(t),$$

(11)

In which, $P^{app}\left(t\right)$ shows the total energy needed for home devices.

2.2. Rooftop PV System

Energy resources with low carbon and renewable potential play an increasingly crucial role in meeting the growing global energy demand and minimizing greenhouse gas effects [27,28]. Various smart buildings in subtropical areas with long summer heating durations have adopted this technology due to its benefits and economic feasibility. The uncertainties of PV generation are caused by weather conditions, modeling inaccuracies, and losses; hence, to analyze the performance of the PV system, the Gaussian distribution is used [29]. As the purpose is to solve a multi-objective optimization problem in this paper, it is assumed that the PV power production is limited and can be described using (12) based on day-ahead anticipated PV production.

$$0\le P_{PV}\left(t\right)\le P_{PV}^{max},$$

(12)

where $P_{PV}\left(t\right)$ shows the PV energy production by the PV system during $t$. $P_{PV}^{max}$ defines the maximum generated power by the PV at time $t$.

2.3. ESS

Limitations (13) and (14) restrict the charge and discharge energy of the ESS based on the converter’s capacity ($P_{ESS}^{ch/disch-max}$), and the binary variable $u_{ESS}$ ensures that no charge or discharge takes place simultaneously. Limitation (15) shows the battery energy balance, in which ${SoC}_{ESS}(t)$ shows the battery state of charge, and ${\eta }_{ESS}$ shows the charge and discharge performance. Limitation (16) limits the battery state of charge (${SoC}_{ESS}(t)$), and Limitations (17) and (18) show the charging ($R_{ESS}^{ch}(t)$) and discharging ($R_{ESS}^{disch}(t)$) rates of the battery. Limitation (19) shows the overall number of battery cycles ($N_{ESS}^{cycle}$) [2,30,31].

$$0\le P_{ESS}^{ch}\left(t\right)=P_{ESS}^{ch-grid}\left(t\right)+P_{ESS}^{ch-PV}(t)\le u_{ESS}{P}_{ESS}^{ch/disch-max},$$

(13)

$$0\le P_{ESS}^{disch}\left(t\right)=P_{ESS}^{sold}\left(t\right)+P_{ESS}^{app}\left(t\right)\le (1-u_{ESS})P_{ESS}^{ch/disch-max},$$

(14)

$${SoC}_{ESS}\left(t\right)={SoC}_{ESS}\left(t-1\right)({\eta }_{ESS}{P}_{ESS}^{ch}\left(t\right)-{\displaystyle \frac{1}{{\eta }_{ESS}}}{P}_{ESS}^{disch}\left(t\right)),$$

(15)

$${SoC}_{ESS}^{min}\le {SoC}_{ESS}\left(t\right)\le {SoC}_{ESS}^{max},$$

(16)

$$R_{ESS}^{ch}\left(t\right)={\displaystyle \frac{{\eta }_{ESS}{P}_{ESS}^{ch}\left(t\right)}{E_{BESS}^{max}}},$$

(17)

$$R_{ESS}^{disch}\left(t\right)={\displaystyle \frac{\frac{1}{{\eta }_{ESS}}{P}_{ESS}^{disch}\left(t\right)}{{SoC}_{ESS}^{max}}},$$

(18)

$$N_{ESS}^{cycle}=\sum _t{R}_{ESS}^{disch}\left(t\right).$$

(19)

2.4. EV

Due to the optimum charging and discharging plan of the EV’s battery, users are able to use their EV’s total energy within peak load durations and plug in their vehicles within off-peak times, minimizing energy costs and pressure on smart homes and main grids. The market prices affect EVs’ charging and discharging schedules.

If EVs participate in the SHEMS, they provide power for household loads and sell extra power to the main grid, as well as store PV and grid power. So, we have

$$P_{EV}^{disch}\left(t\right)=\left[\left(P_{EV}^{sold}\left(t\right)+P_{EV}^{app}\left(t\right)\right).\left(1-u_{EV}\left(t\right)\right)\right].(U_{EV}^{Home}),$$

(20)

$$P_{EV}^{ch}\left(t\right)=[\left(P_{PV}^{ch-EV}\left(t\right)+P_{grid}^{ch-EV}\left(t\right)\right).u_{EV}\left(t\right)].(U_{EV}^{Home}(t)),$$

(21)

where $P_{EV}^{disch}\left(t\right)$, and $P_{EV}^{ch}\left(t\right)$ indicate the discharge and charge power volume of $EV$ at hour $t$, respectively. $P_{EV}^{app}\left(t\right)$ indicates the power amount used to feed the home loads at hour $t$. $P_{EV}^{sold}\left(t\right)$ shows the discharge power volume that is sold to the grid at hour $t$. $P_{PV}^{ch-EV}\left(t\right)$ and $P_{grid}^{ch-EV}\left(t\right)$ indicate the power quantity stored in $EV$ from PV and upstream at the hour $t$, respectively. As EVs are just recharged or discharged, $u_{EV}\left(t\right)$ shows a binary variable showing $EV$’s status during $t$. $U_{EV}^{Home}(t)$ is a binary variable showing $EV$’s parked status during $t$.

$$U_{EV}^{Home}\left(t\right)=\left\{\begin{array}{c}1 if EV is inside the home\\ 0 if EV is outside the home\end{array}\right.,$$

(22)

If the EVs are at home, we have

$$u_{EV}\left(t\right)=\left\{\begin{array}{cc}1\hfill & \hfill if EV is in charging mode\\ 0\hfill & \hfill if EV is in discharging mode\end{array}\right.,$$

(23)

On the other hand, EVs do not charge or discharge when they are outside the home. ${SoC}_{EV}^{Level}(t)$ shows the energy level of EV during t, where $\forall t 1\le t\le T$, so

$${SoC}_{EV}\left(t\right)={SoC}_{EV}\left(t-1\right)({\eta }_{EV}{P}_{EV}^{ch}\left(t\right)-{\displaystyle \frac{1}{{\eta }_{EV}}}{P}_{EV}^{disch}\left(t\right)),$$

(24)

where ${\eta }_{EV}$ defines the charging/discharging efficiency of the $EV$. ${SoC}_{EV}(t)$ shows the state of charge of the EV. $EV$ should follow the following restrictions.

• $P_{EV}^{disch}$ and $P_{EV}^{ch}$ indicate the discharge and charge rates of $EV$. It is possible to accumulate or consume just a particular amount of power during a given $∆t$;
• ${SoC}_{EV}^{min}$ and ${SoC}_{EV}^{max}$ show the minimum and maximum ranges of EV. EV’s power levels must meet ${SoC}_{EV}^{min}$ and ${SoC}_{EV}^{max}$ ranges.

According to the prior restrictions, with $\forall t 1\le t\le T$,

$$0\le P_{EV}^{disch}\left(t\right)=P_{EV}^{sold}\left(t\right)+P_{EV}^{app}\left(t\right)\le P_{EV}^{ch/disch-max},$$

(25)

$$0\le P_{EV}^{ch}\left(t\right)=P_{EV}^{ch-grid}\left(t\right)+P_{EV}^{ch-PV}(t)\le P_{EV}^{ch/disch-max},$$

(26)

$${SoC}_{EV}^{min}\le So{C}_{EV}(t)\le {SoC}_{EV}^{max}.$$

(27)

Since the system is taken into account daily, both ESS and EV should be restored to their original levels on the following day, so the following constraints are applied:

$$\left\{\begin{array}{c}{SoC}_{ESS}\left(T\right)={SOC}_{ESS}^{min}\\ {SoC}_{EV}\left(T\right)={SOC}_{EV}^{min}\end{array}\right..$$

(28)

Since EVs must fully charge prior to departure, the following constraint is applied:

$$So{C}_{EV}\left(t_{depat}\right)={SOC}_{EV}^{max},$$

(29)

where $t_{depat}$ shows the time the EV leaves the parking. EV consumes power when pulling out of a parking lot and traveling, so it is assumed that upon returning, 60 percent of the energy is consumed and 40 percent is still available; hence, we have

$${SoC}_{EV}\left(t_{arriv}\right)=0.4\ast {SOC}_{EV}^{max},$$

(30)

where $t_{arriv}$ shows the time of returning the EV to the parking slot.

Equation (32) shows the overall number of battery cycles ($N_{EV}^{cycle}$) [2].

$$R_{EV}^{disch}\left(t\right)={\displaystyle \frac{\frac{1}{{\eta }_{EV}}{P}_{EV}^{disch}\left(t\right)}{{SoC}_{EV}^{max}}}; \forall t,$$

(31)

$$N_{EV}^{cycle}=\sum _t{R}_{EV}^{disch}\left(t\right).$$

(32)

2.5. Power Balance Limitations

Equation (33) shows the active power balance. In which, $P_{G2H}\left(t\right)$ shows the power bought from the upstream; $P_{H2G}\left(t\right)$ indicates the sold power to the upstream grid.

$$P_{PV}\left(t\right)+P_{G2H}\left(t\right)+P_{ESS}^{disch}\left(t\right)+P_{EV}^{disch}\left(t\right)=P^{app}\left(t\right)+P_{H2G}\left(t\right)+P_{ESS}^{ch}\left(t\right)+P_{EV}^{ch}(t).$$

(33)

2.6. Objective Functions

The following describes the suggested three objective functions: electricity bill, PAR, and the number of battery discharging cycles of ESS and EV.

2.6.1. First Objective Function: Total Cost

The suggested first objective function includes the cost of demand energy from the upstream grid minus the achieved revenue from energy sales to the upstream. When the demand for energy in a smart home (required energy for appliances, ESS charging, and EV charging) is less than the energy produced by PV, the excess energy from PV is lost. Hence, to avoid the loss of energy from the PV, the lost energy is added to this objective function by a penalty factor. Therefore, the first suggested objective function is defined as shown below:

$$\begin{array}{ll}O{F}_1=\min cost& =\mathrm{m}\mathrm{i}\mathrm{n}({\displaystyle \sum _{t=1}^T}(\left(P^{app}\left(t\right)+P_{ESS}^{ch-grid}\left(t\right)+P_{EV}^{ch-grid}\left(t\right)-P_{PV}^{app}\left(t\right)-P_{ESS}^{app}\left(t\right)-P_{EV}^{app}\left(t\right)\right)\\ & \times {Price}_{bought}\left(t\right)-{[P}_{ESS}^{sold}\left(t\right)+P_{EV}^{sold}\left(t\right)]\times {Price}_{sold}(t))+L\ast {\displaystyle \sum _{t=1}^{24}}{P}_{PV}^{Lose}\left(t\right))\end{array}$$

(34)

where ${Price}_{bought}\left(t\right)$ and ${Price}_{sold}(t)$ are the prices of bought and sold energy, respectively; L is the penalty factor; $P_{PV}^{Lose}$ shows the wasted energy of PV, and it is achieved as follows:

$$P_{PV}^{Lose}\left(t\right)=P_{PV}\left(t\right)-[P_{PV}^{app}\left(t\right)+P_{ESS}^{ch-PV}\left(t\right)+P_{EV}^{ch-PV}\left(t\right)].$$

(35)

2.6.2. Second Objective Function: PAR

For a 24 h period, the ratio between peak power demand and the average of the entire power demand can be shown by PAR. As a measure of the energy behavior of the system, PAR influences the performance of the main grid. The power supply company keeps the PAR of the users low, and therefore,

$$O{F}_2=PAR={\displaystyle \frac{\mathrm{m}\mathrm{a}\mathrm{x}(P_D\left(t\right))}{\frac{1}{T}\sum _{t=1}^T{P}_D\left(t\right)}},$$

(36)

where (35) determines $P_D(t)$ as follows:

$$P_D\left(t\right)=P^{app}\left(t\right)+P_{ESS}^{ch-grid}\left(t\right)+P_{EV}^{ch-grid}\left(t\right)-P_{PV}^{app}\left(t\right)-P_{ESS}^{app}\left(t\right)-P_{EV}^{app}\left(t\right).$$

(37)

2.6.3. Third Objective Function: Number of Battery Discharging Cycles of ESS and EV

As ESSs and EVs have an increasingly important role in SHEMS, they make smart homes more flexible and improve RERs’ production performance and reliability. It is therefore imperative to conduct investigations to determine whether they can be optimized in SHEMS. The degradation of batteries, which pertains to the state-of-health, can be influenced by optimizing their operational patterns. Thus, the number of charging/discharging cycles of batteries of ESSs and EVs is considered as an objective function to be minimized simultaneously with the other objective functions in the proposed SHEMS, so we have the following:

$$O{F}_3=N_{ESS}^{cycle}+N_{EV}^{cycle}.$$

(38)

3. Proposed System and Results

A smart home is shown in Figure 1, which includes different kinds of loads such as non-shiftable, interruptible, uninterruptible loads, an IBACS, a PV system, an ESS, and an EV. It is possible to store main grid power during low-cost periods with ESS and EV, in order to provide power for home appliances during high-cost periods. In addition, ESS and EV are used to make better use of PV systems. PV power is stored and reused by an ESS and EV when required. In addition, the system is capable of selling power to upstream grids and neighboring smart buildings.

In the following section, the system details are first described, and then the simulation results for four scenarios are evaluated for a day with 24 time slots. The suggested SHEMS is considered under three scenarios for different weather conditions, including a sunny day, a cloudy day, and a rainy day, as well as a scenario with varying battery efficiencies.

Table 2. Specification of loads.

Non-Shiftable Loads
Device	Microwave Oven	Refrigerator	Personal Computers	Lights	Television	Security Cameras
Power Rating (kW)	1.7	0.9	0.3	0.3	0.2	0.12
Start time	16:00	2:00	7:00	18:00	16:00	00:00
Daily Usage (h)	4	22	18	6	8	24
Continuous Shiftable Loads
Device	Cloth Dryer	Dish Washer	Washing Machine	Iron	Vacuum Cleaner	Cooker Oven	Rice Cooker
Power Rating (kW)	2.3	1.9	1.5	1.3	1.2	0.9	0.8
Used Time Slot	8–22	10–23	17–21	9–20	10–18	9–20	14–22
Daily Usage (h)	2	3	2	1	1	3	2
	Continuous					Interruptible Load
Device	Bread Machine	Electric Kettle	Juicer	Coffee Machine	Music Center	Water Heater
Power Rating (kW)	0.6	0.5	0.5	0.4	0.2	2.3
Used Time Slot	6–10	10–19	6–23	6–10	17–23	7–22
Daily Usage (h)	1	2	2	1	4	8

presents the details of various types of loads. The technical parameters of the ESS and EV are presented in

Table 3. Technical parameters of ESS.

Parameters	${\mathit{S}\mathit{o}\mathit{c}}^{\mathit{m}\mathit{i}\mathit{n}}$ (kWh)	${\mathit{S}\mathit{o}\mathit{C}}^{\mathit{m}\mathit{a}\mathit{x}}$ (kWh)	${\mathit{S}\mathit{o}\mathit{C}}^{\mathit{I}\mathit{n}\mathit{i}\mathit{t}\mathit{i}\mathit{a}\mathit{l}}$ (kWh)	${\mathit{P}}^{\mathit{c}\mathit{h}/\mathit{d}\mathit{i}\mathit{s}\mathit{c}\mathit{h},\mathit{m}\mathit{a}\mathit{x}}$ (kW)	$\mathit{\eta }$ (%)
ESS	1	5	1	0.9	100
EV	2	10	2	2.2	100

.

Table 4. Technical parameters of IBACS.

${\mathit{P}}_{\mathit{A}\mathit{C}}^{\mathit{m}\mathit{a}\mathit{x}}$ (kW)	$\mathit{\alpha }$	$\mathit{\beta }$	$\mathit{\gamma }$ (°C/kWh)	${\mathit{\theta }}^{\mathit{m}\mathit{i}\mathit{n}}$ (°C)	${\mathit{\theta }}^{\mathit{m}\mathit{a}\mathit{x}}$ (°C)	${\mathit{\theta }}^{\mathit{i}\mathit{n}\mathit{i}\mathit{t}\mathit{i}\mathit{a}\mathit{l}}$ (°C)
2.5	1	0.9	5.5	20	26	23

shows the technical parameters of IBACS.

Figure 2 illustrates the purchased and sold prices of energy over 24 h. The energy generation power of the PV system for various types of days, including sunny, cloudy, and rainy days, is displayed in Figure 3. The outdoor temperature for various kinds of days, such as sunny, cloudy, and rainy days, is depicted in Figure 4.

To solve the proposed multi-objective optimization problem, an improved multi-objective gray wolf optimizer with Pareto front [24] is applied, whose performance in solving the optimization problem is confirmed in [24], in comparison to other well-known optimization algorithms like the gray wolf optimizer, and another improvement in the gray wolf optimizer [32]. Another reason to select a metaheuristic optimization algorithm is that the second objective function—PAR—is non-linear. The evaluations are carried out in the MATLAB Software Package 2024a, and the program runs on Intel(R) Core(TM) i5-1335U 1.30 GHz with 32 GB RAM, running Windows 11 Pro.

3.1. Scenario 1: SHEMS During a Sunny Day

In this scenario, the suggested SHEMS is considered during a sunny day to optimize the proposed three objective functions simultaneously. Figure 5 shows the Pareto front of optimal solutions, which is achieved by solving the proposed optimization problem for Scenario 1. The solution with the closest average to the entire set of results is selected in Figure 5 as the optimal solution, which has a total cost, PAR, and number of discharging cycles of 907.6633 (Cents), 2.2717, and 1.5492 (the number of discharging cycles of ESS and EV are 0.7057 and 0.8435), respectively. The operational details of ESS, EV, IBACS, the entire demand power, bought energy, and sold energy are shown in Figure 6. The appliance scheduling for the selected solution is presented in

Table 5. Shiftable load scheduling results of the proposed SHEMS during a sunny day for the selected solution specified in Figure 5.

Shiftable Loads	Cloth Dryer	Dish Washer	Washing Machine	Iron	Vacuum Cleaner
Used time (h)	21, 22	14–16	20, 21	13	18
Shiftable Loads	Cooker Oven	Rice Cooker	Bread Machine	Electric Kettle
Used time (h)	18–20	15, 16	7	13, 14
Shiftable Loads	Juicer	Coffee Machine	Music Center	Water Heater
Used time (h)	13, 14	10	20–23	14, 16–22

. The charging/discharging rates and the energy level of the ESS and EV are shown in Figure 6a and Figure 6b, respectively. Figure 6c shows the demand power of an IBACS. As can be seen during the high temperature from 10 to 20 h, it is working at maximum, and at other times, the demand power is reduced. The indoor and outdoor temperature is shown in Figure 6d. As can be seen during 14 to 17 h, the indoor temperature is not at the desired temperature due to the power of the IBACS. Figure 6e shows the total demanded power for the smart home, the bought and sold energy to the upstream, and also the amount of provided energy by each resource.

3.2. Scenario 2: SHEMS During a Cloudy Day

In scenario 2, the suggested SHEMS is considered during a cloudy day. Figure 7 shows the Pareto front of optimal solutions, which is achieved by solving the proposed optimization problem for Scenario 2. The solution with the closest average to the entire set of results is shown in Figure 7 as the optimal solution, which has a total cost, PAR, and number of discharging cycles of 1058.9759 (Cents), 2.0859, and 1.7746 (the number of discharging cycles of ESS and EV are 0.7413 and 1.0334), respectively. The operational details of ESS, EV, and IBACS, the entire demand power, bought energy, and sold energy are shown in Figure 8. The appliance scheduling for the selected solution is presented in

Table 6. Shiftable load scheduling results of the proposed SHEMS during a cloudy day for the selected solution specified in Figure 7.

Shiftable Loads	Cloth Dryer	Dish Washer	Washing Machine	Iron	Vacuum Cleaner
Used time (h)	14, 15	21–23	19, 20	13	17
Shiftable Loads	Cooker Oven	Rice Cooker	Bread Machine	Electric Kettle
Used time (h)	15–17	16, 17	6	13, 14
Shiftable Loads	Juicer	Coffee Machine	Music Center	Water Heater
Used time (h)	16, 17	6	17–20	11, 14, 15, 18–22

. The charging/discharging rates and the energy level of the ESS and EV are shown in Figure 8a and Figure 8b, respectively. Figure 8c shows the demand power of an IBACS. As can be seen during the high temperature from 11 to 18 h, it is working at maximum, and at other times, the demand power is reduced. The indoor and outdoor temperature is shown in Figure 8d; as can be seen, the indoor temperature is within the desired temperature range. Figure 8e shows the total demanded power for the smart home, the bought and sold energy to the upstream, and the amount of energy provided by each resource.

3.3. Scenario 3: SHEMS During a Rainy Day

In this scenario, the suggested SHEMS is considered on a rainy day. Figure 9 shows the Pareto front of optimal solutions, which is achieved by solving the proposed optimization problem for Scenario 3. The solution with the closest average to the entire set of results is shown in Figure 9 as the optimal solution, which has a total cost, PAR, and number of discharging cycles of 1073.543 (Cents), 2.19094, and 1.67023 (the number of discharging cycles of ESS and EV are 0.8011 and 0.8691), respectively. The operational details of ESS, EV, IBACS, the entire demand power, bought energy, and sold energy are shown in Figure 10. The appliance scheduling for the selected solution is presented in

Table 7. Shiftable load scheduling results of the proposed SHEMS during a rainy day for the selected solution specified in Figure 9.

Shiftable Loads	Cloth Dryer	Dish Washer	Washing Machine	Iron	Vacuum Cleaner
Used time (h)	20, 21	21–23	17, 18	18	14
Shiftable Loads	Cooker Oven	Rice Cooker	Bread Machine	Electric Kettle
Used time (h)	15–17	16, 17	8	18, 19
Shiftable Loads	Juicer	Coffee Machine	Music Center	Water Heater
Used time (h)	6, 7	7	17–20	10, 12, 17–22

. The charging/discharging rates and the energy level of the ESS and EV are shown in Figure 10a and Figure 10b, respectively. Figure 10c shows the demand power of an IBACS. As can be seen during the high temperature from 12 to 14 h, it is working at maximum, and at other times, the demand power is reduced. The indoor and outdoor temperature is shown in Figure 10d; as can be seen, the indoor temperature is within the desired temperature range. Figure 10e shows the total demanded power for the smart home, the bought and sold energy to the upstream, and the amount of energy provided by each resource.

3.4. Scenario 4: Different Efficiencies for ESS and EV

In this scenario, the different efficiencies of ESS and EV (0.9 and 0.8) are considered for the suggested SHEMS on a cloudy day. Figure 11a,b show the Pareto front of possible solutions achieved by solving the proposed optimization problem for the diverse efficiencies of ESS and EV, equal to 0.9 and 0.8, respectively. For efficiencies equal to 0.9, the selected solution in Figure 11a has a total cost, PAR, and number of discharging cycles of 1043.127 (Cents), 2.3172, and 1.4780, respectively. For efficiencies equal to 0.9, the selected solution in Figure 11b has a total cost, PAR, and number of discharging cycles of 1082.053 (Cents), 2.2573, and 1.5145, respectively. As can be seen, by reducing the efficiencies from 0.9 to 0.8, the total cost increases by 3.73% from 1043.127 to 1082.053, and the battery discharging cycles of ESS and EV increase by 2.47% from 1.4780 to 1.5145, but the PAR decreases by 2.59% from 2.3172 to 2.2573. The charging/discharging rates, as well as the energy levels, of the ESS for the selected solution in Figure 11, with efficiencies of 0.9 and 0.8, are shown in Figure 12a and Figure 13a, respectively. Figure 12b and Figure 13b show the charging/discharging rate and energy level of the EV for the selected solution in Figure 11, with efficiencies of 0.9 and 0.8, respectively.

4. Conclusions

An enhanced SHEMS that considers three objective functions simultaneously—electricity bills, PAR, and the number of battery discharging cycles of ESS and EV—was suggested in this study. A rooftop PV system, EV, ESS, different kinds of appliances including non-shiftable, interruptible, and uninterruptible loads, and an IBACS are considered in this paper in order to determine the operation of each of them. The suggested scheme is considered under three scenarios under diverse weather conditions, such as sunny, cloudy, and rainy days, as well as scenarios with varying battery efficiencies. In addition, the real-time market pricing model is used to facilitate the active participation of the smart home in energy trading with the upstream grid. Moreover, the suggested multi-objective optimization optimizes the operation of the system and also considers three objective functions —electricity bills, PAR, and the number of battery discharging cycles of ESS and EV—which ensures that objectives are not sacrificed to achieve an appropriate solution. IBACSs using inverters are modeled as interruptible loads, and their primary function is to maintain indoor temperatures within a set level. The IBACS contributes significantly to the cost per day, and the energy usage is proportional to the outside temperature. By incorporating the ESS and EV batteries, the SHEMS can be made more flexible, and the total price can be reduced. Additionally, Pareto front outcomes showed that, despite reducing power prices through an increase in the number of charging/discharging cycles, it would result in a deterioration of batteries. Charging and discharging batteries at deeper rates increasingly accelerates the degradation of battery capacity. For SHEMS to operate efficiently, it is necessary to consider how ESS and EV batteries can be made more durable while saving costs as well. For the selected solutions, by decreasing the efficiencies of batteries from 1 to 0.9 on a cloudy day, the total cost and number of discharging cycles reduce by 1.497% and 16.714%, respectively; however, the PAR increases by 11.089%. Additionally, by decreasing the efficiencies of batteries from 1 to 0.8 on a cloudy day, the total cost and PAR increase by 2.179% and 8.217%, respectively; however, the number of discharging cycles reduces by 14.657%.

For future plans, the exact cost of battery degradation and the depth of discharge will be considered in a smart home model to take into account the depth of discharge effects and estimate the battery’s lifespan. Furthermore, other cost functions, such as emissions, will be considered in a stochastic model with a low sampling time, such as 5 or 15 min, to increase the accuracy of the results. Additionally, as the computational burden increases, edge computing can be applied to mitigate it.