Research on Distributed Smart Home Energy Management Strategies Based on Non-Intrusive Load Monitoring (NILM)

Abstract

Home energy optimization management improves energy utilization efficiency and reduces electricity costs through intelligent load control, strategic utilization of time-of-use pricing, and optimized integration of energy storage and distributed energy systems. Simultaneously, it enhances energy autonomy, lowers carbon emissions, and promotes sustainable low-carbon lifestyles. By coordinating demand response programs with flexible load scheduling strategies, this approach effectively reduces peak loads and improves grid stability, thereby advancing smart grid development. This paper investigates the optimized scheduling problem in smart home energy management systems, focusing on achieving integrated optimization of multiple factors, including load balancing, cost control, carbon emission reduction, user comfort, and demand response. Considering the diverse load characteristics of residential energy systems, we propose a novel optimization framework incorporating dynamic pricing mechanisms and intelligent scheduling algorithms, which is rigorously validated through simulation experiments. Results demonstrate that the proposed scheduling strategy successfully balances economic efficiency, load management, and environmental sustainability while maintaining acceptable user comfort levels—providing a comprehensive solution for intelligent home energy management systems.

1. Introduction

As global energy shortages and environmental pollution issues become increasingly severe, the efficient use of energy has become a focal point of societal concern. Smart home energy management (SHEM), as a critical component of smart energy systems, aims to utilize advanced technological means to achieve optimized scheduling of residential energy resources, improve energy utilization efficiency, reduce user electricity costs, and promote renewable energy integration. In recent years, with advancements in the Internet of Things (IoT), artificial intelligence (AI), and big data analytics, SHEM has emerged as a prominent research frontier [1].

SHEM employs intelligent scheduling technologies to optimize the control of household electrical devices, energy storage systems, renewable energy generation units (e.g., photovoltaics and wind turbines), and distributed energy systems, thereby improving energy efficiency, lowering electricity expenses, and enhancing energy autonomy. Its core mechanism involves rational allocation and dynamic adjustment of residential energy flows through time-of-use pricing, demand response programs, and intelligent control strategies [2]. This optimization framework not only reduces user energy expenditures and improves comfort but also facilitates renewable energy adoption, minimizes carbon emissions, and fosters sustainable low-carbon lifestyles. Furthermore, it supports power grid stability by flattening demand peaks and adapting to grid requirements, advancing the development of smart grids and integrated energy systems.

In recent years, global researchers have extensively explored smart home energy management strategies, focusing primarily on optimization algorithm-based scheduling, artificial intelligence/machine learning applications, and demand response mechanisms. Numerous studies leverage mixed-integer linear programming (MILP) [3], heuristic algorithms (e.g., genetic algorithms [4], particle swarm optimization [5], and ant colony algorithms [6]), and hybrid optimization methods [7,8] to optimize household energy distribution and maximize renewable energy utilization. These algorithms provide optimal solutions for complex scheduling problems, effectively reducing energy waste and enhancing grid efficiency. Researchers have further proposed enhanced heuristic approaches [9] and game-theoretic models [10] to improve the economic efficiency of residential energy use. Notably, intelligent scheduling strategies aligned with peak/off-peak pricing guide users to shift high-energy activities to low-cost periods, significantly reducing overall electricity expenditures.

Artificial intelligence techniques enable precise energy management solutions through deep learning and historical data analysis, enhancing system adaptability in dynamic environments. With advancements in reinforcement learning, these methods are increasingly integrated into home energy management. For instance, Wei et al. [11] applied deep reinforcement learning to optimize energy allocation, while Ye et al. [12] developed a long short-term memory (LSTM)-based load forecasting model to improve scheduling accuracy. Ma et al. [13] proposed a Markov decision process (MDP)-driven strategy accounting for user behavior uncertainty and price fluctuations, achieving intelligent device scheduling. Research on distributed renewable energy integration has also investigated coordinated scheduling of photovoltaics, energy storage, and electric vehicles in SHEM systems to maximize renewable utilization [3].

Scholars have examined user participation mechanisms in electricity markets, including real-time pricing (RTP) and incentive-based demand-side management strategies. Navesi et al. [14] analyzed demand response strategies under RTP to enhance smart distribution network reliability, demonstrating how dynamic pricing guides consumption pattern adjustments for grid stability and economic efficiency. Hu et al. [15] designed a reinforcement learning-driven incentive model addressing demand-side coupling factors (e.g., inter-load correlations) to optimize management efficiency. Dey et al. [16] developed a microgrid-focused incentive scheme integrating carbon emissions, renewable penetration, and economic constraints, evaluating various strategies’ operational impacts. These studies confirm that tailored pricing and incentive mechanisms effectively reshape household consumption patterns, optimizing grid load distribution and energy efficiency.

Amid global efforts toward climate change mitigation, “carbon neutrality” and “peak carbon” have become central objectives in energy transitions. As a vital element of smart energy ecosystems, SHEM plays a pivotal role in carbon reduction and efficiency enhancement. By integrating distributed energy resources (e.g., photovoltaics, energy storage, and EVs) via intelligent scheduling algorithms, SHEM reduces fossil fuel dependence and enables low-carbon smart energy consumption. Ikram A. I. et al. [17] proposed a load scheduling strategy balancing user demand and price fluctuations to minimize peak consumption. Akram A. et al. [18] combined machine learning with SHEM to predict consumption patterns and optimize scheduling for cost and emission reduction. Youssef H. et al. [19] employed an enhanced Northern Goshawk Optimizer (NGO) to jointly optimize comfort, energy costs, and renewable utilization, while Youssef H. et al. [20] developed a modified bald eagle search (BES) algorithm for dynamic pricing-constrained energy scheduling.

In summary, significant progress has been made in smart home energy management research, with optimization algorithms, AI, and demand response strategies forming core research pillars. However, as residential energy demands diversify, achieving multi-objective coordination among load balancing, cost control, carbon reduction, user comfort, and demand response remains challenging. Developing advanced scheduling strategies is essential for improving energy efficiency, user experience, grid stability, and renewable energy integration.

MILP has become a cornerstone of residential energy scheduling due to its ability to handle discrete variables (e.g., device on/off states) and continuous variables (e.g., power allocation). With advantages in global optimality, rigorous constraint modeling, and transparent decision logic, MILP outperforms deep learning’s opacity and heuristic algorithms’ approximations, providing verifiable solutions for small-to-medium-scale problems. The branch and bound (B&B) method systematically identifies global optima by decomposing solution spaces and iteratively narrowing feasible regions. However, B&B suffers from exponential complexity, slow bound convergence, and high computational costs. In contrast, genetic algorithms (GA) enhance MILP-solving efficiency through dynamic feasible solution generation and global search optimization. This paper proposes a hybrid genetic branch and bound algorithm that embeds GA within B&B to rapidly generate integer-feasible solutions, update bounds, and accelerate pruning. This approach addresses the co-optimization of load balancing, cost control, carbon emissions, user comfort, and demand response in household energy management. For the convenience, we have listed all abbreviations used in the paper in

Table 1. All abbreviations used in the paper.

Abbreviations	Meanings
SHEM	Smart home energy management
NILM	Non-intrusive load monitoring
AI	Artificial intelligence
IoT	Internet of Things
MILP	Mixed-integer linear programming
GA	Genetic algorithm
DR	Demand response
$TOU$	Time-of-use pricing
$SOC$	State of charge
$PV$	Photovoltaic
RTP	Real-time pricing
EV	Electric vehicle
B&B	Branch and bound
LP	Linear programming
MDP	Markov decision process
LSTM	Long short-term memory
HVAC	Heating, ventilation, and air conditioning
CNY	Chinese yuan

.

2. Smart Home Energy Management

2.1. Home Energy Management

Home energy management refers to the coordinated control and optimization of residential energy devices through advanced scheduling technologies, aiming to maximize efficiency, minimize costs, and promote renewable energy utilization. With the advancement of distributed energy systems, smart grids, and IoT infrastructure, SHEM has evolved into a critical component of modern intelligent households.

As illustrated in Figure 1, a typical SHEM system comprises smart meters, energy management controllers, renewable energy generation units (e.g., photovoltaic panels and wind turbines), energy storage systems (e.g., batteries), and smart appliances. By integrating real-time data collection and intelligent scheduling algorithms, SHEM dynamically monitors energy consumption, forecasts load demands, and generates optimal energy allocation plans based on grid pricing signals, user preferences, and environmental conditions. For instance, during periods of low electricity prices or high renewable energy availability, SHEM prioritizes local power generation and stored energy usage. Conversely, it suppresses high-power device operation during peak pricing intervals to reduce energy expenditures.

The core objectives of home energy management include load balancing, cost optimization, carbon reduction, and user comfort preservation. Load balancing involves rational scheduling of appliances and storage systems to avoid grid stress caused by excessive peak demand. Cost optimization focuses on strategic energy procurement and usage to minimize household expenses. Carbon reduction is achieved by increasing renewable energy penetration and decreasing fossil fuel reliance, while user comfort ensures that energy-saving measures do not compromise basic living standards—such as maintaining thermal comfort, adequate lighting, and habitual appliance usage patterns.

2.2. Household Load Model

In home energy management, rigid loads refer to appliances that must operate and cannot be easily adjusted or reduced, such as lighting, refrigerators, and medical devices. These loads have low scheduling flexibility and typically form the household’s baseline electricity demand. Their operating times are nearly fixed since they are essential for users. The modeling of rigid loads usually considers factors such as time dimensions, power characteristics, and uncertainty. For loads with relatively stable power demand and operating times, such as refrigerators and lighting, a common mathematical expression is

$$P_{\mathit{rigid}} \left(t\right)= P_{rated}\left(t\right)$$

(1)

where P_rigid (t) represents the power of the rigid load at time t and $P_{rated}\left(t\right)$ is the rated power of the load at time t.

Flexible loads can be scheduled and adjusted within a certain range based on grid demand or economic incentives. Unlike rigid loads, flexible loads can be shifted in time or have their operational power reduced according to scheduling strategies to optimize overall energy use. Based on load scheduling, flexible loads can be classified into three categories: power-adjustable loads, time-adjustable loads, and power-time adjustable loads.

• Power-adjustable load: These loads have adjustable power output through step control, such as air conditioners, water heaters, and lighting. The energy consumption of these devices can be controlled by adjusting their power levels. The model is expressed as

P_adjustable (t) = P_i

(2)

where P_adjustable (t) is the power-adjustable load at time t, P_i is the power value for the i-th power level, and t represents a specific moment.

• Time-adjustable load: These loads, such as washing machines and dishwashers, can have their operating times adjusted. Once started, they must complete their entire work cycle without interruption. The model is

$$P_{adjustable}\left(t\right)=\left\{\begin{array}{c}{P}_{rated}\left(t\right), t\in (\left(n-1\right)\ast T_{cycle},n\ast T_{cycle})\\ 0\end{array}\right\},$$

(3)

where $P_{rated}\left(t\right)$ is the rated power of the load at time t and $T_{cycle}$ is the operating cycle of the equipment.

• Power-time adjustable load: Power-time loads are time-variable and interruptible loads, such as electric vehicles and other new energy transportation tools. Due to their flexible adjustability, they are a primary target for demand-side response scheduling. In a sense, they can be considered a form of energy storage without the discharge process. Power-time loads can be modeled using a power-time function, where both the power and time of operation are adjustable and can be interrupted within a certain time period. Charging an electric vehicle or a battery is a common example, where the charging power can be adjusted or interrupted during a time period, and the charging process is considered a variable time window. The model can be expressed as follows:

$$P_{flexible}\left(t\right)=\left\{\begin{array}{c}{P}_{rated}\left(t\right), t\in (T_{start},T_{end})\\ 0\end{array}\right\},$$

(4)

where $P_{flexible}\left(t\right)$ is the power-time adjustable load at time t, $P_{rated}\left(t\right)$ is the rated power of the load, $T_{cycle}$ is the operating cycle of the equipment, and $T_{start}$ and $T_{end}$ are the start time and end time, respectively.

Batteries, as the most common power-time adjustable load, can be modeled as [21]

$$\begin{array}{l}SOC\left(t\right)=C_{net}\left(t\right)/C_{bat}\\ SOC\left(t+1\right)=SOC\left(t\right)+P_{ch}\left(t\right)\cdot \Delta t\cdot {\eta }_{ch}/C_{bat}\\ SOC\left(t+1\right)=SOC\left(t\right)-P_{disch}\left(t\right)\cdot \Delta t/\left(C_{bat}\cdot {\eta }_{disch}\right)\\ 0\le P_{ch}\left(t\right)\le P_{ch,max}\\ 0\le P_{disch}\left(t\right)\le P_{disch,max}\\ SO{C}_{min}\le SOC\left(t\right)\le SO{C}_{max}\\ P_{ch}\left(t\right)\cdot P_{disch}\left(t\right)=0\end{array}$$

(5)

where $SOC\left(t\right)$ represents the state of charge of the battery at time $t$; $C_{net}\left(t\right)$ and $C_{bat}$ represent the remaining energy and rated capacity of the battery at time $t$; $P_{\mathit{ch}}$ and $P_{\mathit{disch}}$ represent the charging and discharging power, respectively; ${\eta }_{\mathit{ch}}$ and ${\eta }_{\mathit{disch}}$ are the charging and discharging efficiencies; $P_{ch,max}$ and $P_{disch,max}$ are the maximum charging and discharging powers, respectively; and ${SOC}_{max}$ is the maximum state of charge.

• Temperature-controlled adjustable load: These are loads whose operation is influenced by temperature constraints, with their operating status depending on indoor and outdoor temperatures, set temperature values, and the thermal properties of the building. The indoor temperature setting is determined based on user demand within a given time period. When required, the indoor temperature should remain within the upper and lower bounds of the specified value. The mathematical model for air conditioners and water heaters is typically represented by a discrete thermal dynamic model as shown:

$$T_{in}\left(t+1\right)=e^{-\mathsf{\Delta }t/R{C}_{room}}{T}_{\mathrm{i}\mathrm{n}}(t)+R\cdot (e^{-\mathsf{\Delta }t/R{C}_{room}}-1)\cdot P_{\mathrm{A}\mathrm{C}}+(1-e^{-\mathsf{\Delta }t/R{C}_{room}})\cdot T_{\mathrm{o}\mathrm{u}\mathrm{t}}(t),$$

(6)

where $T_{\mathit{in}}\left(t\right)$ is the indoor temperature at time $t,$ $R$ is the room thermal resistance $\left(°\mathrm{C}/\mathrm{k}\mathrm{W}\right)$, $C_{room}$ is the room thermal capacity $\left(\mathrm{k}\mathrm{W}\mathrm{h}/°\mathrm{C}\right),$ $P_{\mathit{rated}}\left(t\right)$ is the rated power of the air conditioner or water heater, and $T_{\mathit{out}}\left(t\right)$ is the outdoor temperature at time $t$.

2.3. DR Incentives

DR is a load management strategy in power systems that encourages users to adjust their electricity consumption behavior during high load periods or when electricity prices are high in order to improve the stability and economy of the power system. To attract users to participate in demand response, economic incentives are usually designed to provide subsidies to users. Economic incentives mainly encourage users to adjust their consumption behavior through price signals or direct compensation.

• Time-of-Use Pricing

The time-of-use (TOU) pricing mechanism encourages users to consume electricity when prices are lower and reduce consumption when prices are higher, based on fluctuations in the electricity market. Different electricity rates are set according to the load conditions at different times of the day, typically categorized into peak, mid-peak, and off-peak periods. During extreme peak load periods, temporary price increases incentivize users to reduce electricity consumption.

• DR Compensation

DR compensation is an economic reward provided by grid operators or power supply companies to users participating in DR programs. It encourages users to adjust their electricity consumption behavior during peak periods to enhance grid stability and improve energy utilization efficiency. DR compensation can be implemented through load reduction rewards and load shift compensation. Users receive compensation based on the amount of load they reduce during DR events, incentivizing electricity consumption during off-peak periods and providing corresponding subsidies.

In home energy management, to encourage users to adjust consumption during off-peak hours, a dynamic incentive subsidy mechanism is employed, adjusting the incentive based on real-time electricity prices. Specifically, when the electricity price is below 0.3 CNY/kWh (off-peak period), the subsidy is issued at twice the base rate; when the price is above 0.6 CNY/kWh (peak period), no subsidy is issued; during the intermediate periods, the base subsidy is issued. 1 CNY ≈ 0.14 USD. The total incentive(t) subsidy for period t is calculated as

$$incentive\left(t\right)=\left\{\begin{array}{l}m\left(t\right)\times incentive\_rate\times 2, Low valley period\\ m\left(t\right)\times incentive\_rate, Off peak period\\ 0,\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}Peak hours\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\end{array}\right.$$

(7)

where m(t) represents the adjustment amount or response scale for period t and $incentive\_rate$ is the base incentive rate. The total incentive subsidy is the sum of the incentives for all periods.

$$T={\sum }_{t=1}^N incentive(t).$$

(8)

2.4. User Comfort

In home energy management, user comfort refers to the level of electricity consumption adjustment that users can tolerate when accepting optimized scheduling or DR without significantly affecting their quality of life and satisfaction. Comfort is a subjective metric that typically involves factors such as temperature, appliance usage habits, tolerance for delays, and lifestyle impacts. Proper comfort modeling ensures user satisfaction while achieving energy-saving optimization. User comfort generally falls into two categories: time comfort and temperature comfort.

• Time Comfort

Time comfort refers to the extent to which the operating time of home appliances aligns with the user’s expectations. For example, a user may prefer the washing machine to operate between 8:00 and 10:00 p.m., but if the system schedules it at 7:00 or 11:00 p.m., the user may be dissatisfied. Similarly, an electric vehicle owner may expect the vehicle to be fully charged between 12:00 a.m. and 6:00 a.m. If the system schedules charging between 6:00 and 8:00 a.m., it could disrupt the user’s travel plans. To quantify time comfort, the user’s expected time window is defined, and a time deviation metric is introduced

$$\begin{gathered} U_{\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{e}}^i\left(t\right)=1-{\displaystyle \frac{|T_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{t}}-T_{\mathrm{o}\mathrm{p}\mathrm{t}}|}{T_{\mathrm{m}\mathrm{a}\mathrm{x}}-T_{\mathrm{m}\mathrm{i}\mathrm{n}}}}, \\ {U}_{time}\left(t\right)={\displaystyle \frac{\sum _{i=0}^M{U}_{time}^i\left(t\right)}{M}}, \end{gathered}$$

(9)

where M is the number of devices, $T_{start}$ is the actual start time of the device, and $T_{opt}$ is the user’s preferred start time. $[T_{min},T_{max}]$ is the acceptable time window.

• Temperature Comfort

Temperature comfort refers to the user’s satisfaction with indoor temperatures, which are typically regulated by HVAC systems (e.g., air conditioners and heaters). Key influencing factors include the target temperature and acceptable temperature fluctuations. A comfortable temperature range is defined, within which the user feels comfortable. If the indoor temperature deviates beyond this range, comfort decreases.

The temperature comfort function is given by

$$\begin{gathered} U_{\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{m}\mathrm{a}\mathrm{l}}^i\left(t\right)=\left\{\begin{array}{ll}1,& T_{\mathrm{m}\mathrm{i}\mathrm{n}}\le T_{\mathit{indoor}}\le T_{\mathrm{m}\mathrm{a}\mathrm{x}}\\ 1-{\displaystyle \frac{|T_{\mathit{indoor}}-T_{opt\_temp}|}{T_{\mathrm{m}\mathrm{a}\mathrm{x}}-T_{\mathrm{m}\mathrm{i}\mathrm{n}}}},& \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{w}\mathrm{i}\mathrm{s}\mathrm{e}\end{array}\right., \\ {U}_{\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{m}\mathrm{a}\mathrm{l}}\left(t\right)={\displaystyle \frac{\sum _{i=0}^M{U}_{\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{m}\mathrm{a}\mathrm{l}}^i\left(t\right)}{M}}, \end{gathered}$$

(10)

where $T_{\mathit{indoor}}$ is the indoor temperature at time $t,$ $T_{\mathit{opt}\_\mathit{temp}}$ is the user’s preferred temperature (e.g., $26 °\mathrm{C}$), and the acceptable range is the range of temperatures the user finds comfortable (e.g., $22–28 °\mathrm{C}$). If the temperature exceeds this range, comfort decreases progressively.

2.5. Carbon Emissions and Carbon Consumption

Carbon emissions generally refer to the total amount of carbon dioxide (CO₂) and other greenhouse gases produced from energy consumption (e.g., electricity, natural gas, oil, etc.). For households, the primary sources include household electricity use, heating, and cooking with gas, which result in both direct and indirect emissions. Carbon consumption refers to the amount of carbon emissions “consumed” during energy usage, i.e., the cost of energy consumption expressed in terms of carbon emissions. It can be understood as the carbon quota “used” by a household over a given period due to its energy consumption. Changes in carbon pricing can affect users’ willingness to adjust their electricity consumption behavior. The tiered carbon trading mechanism establishes multiple emission tiers, where carbon pricing increases progressively with emission levels, penalizing excess emissions through incremental cost escalation.

Assuming the household’s electricity consumption in period $t$ is $E\left(t\right)$ (in kWh), with a corresponding carbon emission factor $\alpha \left(t\right)$ (in ${\mathrm{k}\mathrm{g}\mathrm{C}\mathrm{O}}_2/\mathrm{k}\mathrm{W}\mathrm{h}$) [22], the carbon emissions (or carbon consumption) for that period can be expressed as

$$C\left(t\right)=\alpha \left(t\right)\cdot E\left(t\right).$$

(11)

For tiered carbon trading, α(t) may vary over time, reflecting the proportion of different energy sources (e.g., thermal power, wind, or solar) in the grid during different time periods. The total carbon consumption $C_{total}$ for the entire period (such as a day or month) is

$$C_{total}={\sum }_t C(t).$$

(12)

2.6. Load Balancing

In home energy management, load balancing refers to the process of maintaining a stable household power demand over a specified time period, avoiding significant fluctuations or peak loads. A stable load curve helps not only in reducing electricity costs but also in alleviating grid pressure, improving energy efficiency, and promoting the effective integration of renewable energy sources. Typically, load balancing is expressed in terms of the net load curve flatness. The net load is the remaining electricity demand after subtracting the electricity generated by the household’s distributed energy systems (e.g., solar PV). The flatness of the net load curve can be quantified in various ways, with common methods including the peak-to-valley difference, standard deviation, and maximum adjacent difference. This paper comprehensively considers system load fluctuations (e.g., standard deviation or dispersion), the magnitude range of loads, and the matching degree between control variables and load fluctuations to quantify the flatness of the net load curve. The calculation is as follows:

1.

Let $S_i$ represent the system load at the $i$-th moment and ${\mu }_S={\displaystyle \frac{1}{N}}\sum _{i=1}^N S_i$ represent the average system load over $N$ time periods. The system load dispersion can be defined as the standard deviation of the system load.

$$h_{\mathrm{s}\mathrm{f}\mathrm{s}\mathrm{y}\mathrm{s}}=-\sqrt{{\sum }_{i=1}^N (S_i-{\mu }_S{)}^2}$$

(13)

2.

The baseline flatness calculation is calculated as

$$h_{\mathrm{s}\mathrm{f}\mathrm{b}\mathrm{a}\mathrm{s}\mathrm{e}}={\displaystyle \frac{h_{\mathrm{s}\mathrm{f}\mathrm{s}\mathrm{y}\mathrm{s}}}{max\left(S_i\right)-min\left(S_i\right)}}.$$

(14)

3.

Let $X_i$ represent the flexible load in the $i$-th period. The correlation or matching degree between the control variable $X$ and system load fluctuations can be calculated as

$$h_{\mathrm{s}\mathrm{f}\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}={\displaystyle \frac{\sum _{i=1}^N \left[(X_i-{\mu }_X)(S_i-{\mu }_S)\right]}{\sqrt{\sum _{i=1}^N (S_i-{\mu }_S{)}^2}}}.$$

(15)

4.

Finally, the flatness index can be calculated as

$$h=\left|{\displaystyle \frac{h_{\mathrm{s}\mathrm{f}\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}}{h_{\mathrm{s}\mathrm{f}\mathrm{b}\mathrm{a}\mathrm{s}\mathrm{e}}}}\right|.$$

(16)

3. SHEM Based on Mixed-Integer Linear Programming

3.1. Objective Function

For the optimization scheduling problem of household or small commercial building loads, this paper aims to comprehensively consider electricity costs, user comfort, carbon emission costs, and dynamic incentive subsidies to develop a reasonable electricity optimization strategy. The model, based on photovoltaic generation, electricity price information, external temperature, rigid loads, and flexible loads, optimizes the usage schedule of various electrical appliances to reduce electricity costs, enhance load balance, and improve user satisfaction. Based on the linear weighting method, the home energy management optimization objective is as follows:

$$\begin{gathered} \min f= \alpha ·Z-\beta ·U-\gamma ·H-\delta ·T+\epsilon ·C_{total}, \\ Z={\sum }_{t=1}^N{P}_{\mathrm{e}\mathrm{l}\mathrm{e}}\left(t\right)\cdot \left(m\right(t)-0.8P_{\mathrm{p}\mathrm{h}\mathrm{o}}(t\left)\right), \\ U={\sum }_{t=1}^{N}U\left(t\right)=U_{\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{m}\mathrm{a}\mathrm{l}}+U_{\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{e}}, \\ H={\sum }_{t=1}^{N}H\left(t\right)=h=\alpha \times {\displaystyle \frac{h_{\mathrm{s}\mathrm{f}\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}}{h_{\mathrm{s}\mathrm{f}\mathrm{b}\mathrm{a}\mathrm{s}\mathrm{e}}}}, \\ T={\sum }_{t=1}^N incentive(t), \\ {C}_{total}={\sum }_{t=1}^N \alpha (t)\cdot E(t), \end{gathered}$$

(17)

where $\alpha ,\beta ,\gamma ,\delta ,\epsilon$ are the weight coefficients; N is the total number of time intervals in the cycle; $Z$ is the electricity cost of the load, excluding photovoltaic output; $P_{\mathit{ele}}\left(t\right)$ is the electricity price at time $t$; and $P_{\mathit{pho}}\left(t\right)$ is the photovoltaic power generation, with a degradation coefficient of 0.8 to account for generation quality losses. The lower the load electricity cost, the smaller the objective function. $U_{\mathit{thermal}}$ and $U_{\mathit{time}}$ represent temperature and time comfort, respectively. The higher the total comfort level, the smaller the objective function. $H$ represents the quantified flatness of the net load curve, which is used to measure load balance. The higher the flatness, the smaller the objective function. $T$ is the total incentive subsidy from demand response. The higher the subsidy, the smaller the objective function. $C_{total}$ is the total carbon emission cost. The smaller the carbon emission cost, the smaller the objective function.

3.2. Calculation of Efficacy Coefficients

Considering that the five optimization objectives above have different units of measurement, this paper designs a comprehensive evaluation index based on the efficacy coefficient method to balance the impacts of economic efficiency, comfort, and flatness (load balancing) on scheduling results. The core idea of the efficacy coefficient method is to normalize each optimization objective into an efficacy coefficient within the range [0, 1], where 1 represents the best performance and 0 the worst. The geometric mean of all efficacy coefficients serves as the total efficacy coefficient.

(1)

For the economic optimization objective Z, T, $C_{total}$, the calculation method for its efficacy coefficient is

$$G_i={\displaystyle \frac{\max F_{i }-F_{i }}{\max F_{i }-\min F_i}}$$

(18)

where $F_i$ represents any of the three economic objectives, i.e., electricity cost (Z), incentive subsidy (T), or carbon emission cost ($C_{total}$). Max $F_{i }$ and min $F_{i }$ denote the maximum and minimum values of these objectives across all scheduling schemes.

(2)

For the comfort optimization objective $U$, which consists of time comfort and temperature comfort, the efficiency coefficient calculation method is

$$\begin{gathered} U_{\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{e}}^i={\displaystyle \frac{\sum _{t=1}^N{U}_{\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{e}}^i\left(t\right)}{N}}, \\ {U}_{\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{m}\mathrm{a}\mathrm{l}}^i={\displaystyle \frac{\sum _{t=1}^N{U}_{\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{m}\mathrm{a}\mathrm{l}}^i\left(t\right)}{N}}, \\ {K}_{time}^i=1-{\displaystyle \frac{e^{U_{\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{e}}^i}-1}{e-1}}, \\ {K}_{\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{m}\mathrm{a}\mathrm{l}}^i=1-{\displaystyle \frac{e^{U_{\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{m}\mathrm{a}\mathrm{l}}^i}-1}{e-1}}, \\ U=\sqrt[M]{{\prod }_{i=1}^M{K_{time}^i\times K}_{\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{m}\mathrm{a}\mathrm{l}}^i}. \end{gathered}$$

(19)

(3)

The calculation method for the efficiency coefficient of the flatness optimization objective H is

$$H=1-e^{-h}$$

(20)

Based on the calculation process of the five optimization objectives mentioned above, using the power coefficient calculation method, the optimization objective for household energy management is transformed into

$$\max f=\sqrt[5]{G_1·G_2·G_3·U·H}$$

(21)

3.3. Mixed-Integer Linear Programming

Mixed-integer linear programming (MILP) is a mathematical programming method that involves both continuous and integer variables in optimization problems. It is widely used in logistics scheduling, supply chain management, production planning, and other fields. The standard form of MILP is as follows:

$$\begin{array}{c}min{\mathbf{c}}^T\mathbf{x}+{\mathbf{d}}^T\mathbf{y}\\ \mathrm{s}.\mathrm{t}.A\mathbf{x}+D\mathbf{y}\le \mathbf{b}\\ \mathbf{x}\in {\mathbb{Z}}_{+}^n,\mathbf{y}\in {\mathbb{R}}_{+}^m\end{array}$$

(22)

where x is the integer variable and y is the continuous variable, and both the objective function and constraints are linear. ${\mathbf{c}}^T$ is cost vector associated with the integer variables x. ${\mathbf{d}}^T$ is cost vector associated with the continuous variables y. ${\mathbb{Z}}_{+}^{\mathit{n}}$ represents non-negative integers (0, 1, 2,⋯). ${\mathbb{R}}_{+}^m$ denotes non-negative real numbers (x ≥ 0).

Due to the presence of integer variables, MILP problems are typically NP-hard, and branch and bound methods are commonly used to solve these types of problems. The branch and bound method is an exact algorithm for solving MILP problems, and its core idea is to systematically decompose the problem space, progressively narrowing the feasible solution space to eventually find the global optimum. The algorithm combines two key operations: “branching” and “bounding”:

• Branching: The original problem is decomposed into several subproblems (subnodes); each subproblem reduces the solution space by adding additional constraints (e.g., fixing the integer values of variables).
• Bounding: By solving the relaxed version of the subproblem (e.g., linear programming relaxation), upper and lower bounds are calculated. These bounds are used to prune branches that cannot contain the optimal solution, thereby reducing the computational effort.

The detailed implementation process of the branch and bound method is as follows:

Step 1: Initialization

• Create the root node corresponding to the original MILP problem.
• Set the global upper bound (UB) and the lower bound (LB).

Step 2: Relaxation Solution

• Perform linear programming relaxation on the current node (ignoring integer constraints) to solve the relaxed problem:

$$\min {\mathbf{c}}^T\mathbf{x}+{\mathbf{d}}^T\mathbf{y} \mathrm{s}.\mathrm{t}.A\mathbf{x}+D\mathbf{y}\le \mathbf{b},\mathbf{x}\in {\mathbb{R}}_{+}^n,\mathbf{y}\in {\mathbb{R}}_{+}^m$$

(23)

• If the relaxed problem has no feasible solution, prune this branch; otherwise, obtain the relaxed solution $x_{LP}$ and its objective value ${f(x}_{LP})$.

Step 3: Pruning Conditions

• Optimality Pruning: If the relaxed solution satisfies the integer constraints, update the global upper bound as min (${f(x}_{LP})$,UB) and record this solution.
• Bounding Pruning: If ${f(x}_{LP})$ ≥ UB, it means that this branch cannot produce a better solution, so prune this branch. Otherwise, update LB = max (${LB, f(x}_{LP})$).

Step 4: Branching Operation

If there are non-integer integer variables $x_i$ in the relaxed solution, select this variable for branching. Create two subproblems:

• Subproblem 1: $x_i\le \lfloor x_i^{\mathrm{*}}\rfloor$
• Subproblem 2: $x_i\ge \lceil x_i^{\mathrm{*}}\rceil$

Then, add these subproblems to the queue of nodes to be processed.

Step 5: Node Selection Strategy

• Use depth-first search (DFS) to select the next node to process from the queue. DFS is a tree/graph traversal or search strategy that prioritizes exploring along one branch as deeply as possible until a leaf node is reached or no further progress is possible. In branch and bound, DFS processes the most recently generated subnodes first, quickly delving deeper into the tree, potentially finding feasible solutions early, which can update the global upper bound and trigger pruning, thus reducing the exploration of subsequent invalid branches.

Step 6: Termination Condition

The algorithm terminates when one of the following conditions is met:

• All branches have been pruned or processed.
• The difference between the global UB and LB is smaller than the preset threshold ϵ = 10⁻⁴.

3.4. Hybrid Genetic Branch-and-Bound Algorithm

GA is an optimization algorithm based on natural selection and Darwin’s theory of evolution. It simulates the process of biological evolution, iteratively optimizes, and seeks the optimal solution. The algorithm first randomly generates an initial population, with each individual representing a potential solution. In each generation, individuals’ strengths and weaknesses are evaluated according to the fitness function, and individuals with higher fitness are selected for inheritance based on the principle of “survival of the fittest”. Subsequently, new individuals are generated through crossover and mutation operations, allowing the population to continuously evolve. After multiple iterations, the algorithm ultimately converges to the optimal or approximate optimal solution.

This paper uses a hybrid genetic branch and bound algorithm to embed genetic algorithms in the branching process to quickly generate integer feasible solutions, update upper bounds, and accelerate pruning. The detailed implementation process of the hybrid genetic branch and bound algorithm is as follows:

Step 1: Initialization

• Encode the integer variables of MILP into gene sequences.
• Randomly generate O individuals (O = 50), calculate the fitness value of each individual, and record the optimal solution $x_{ga}$.
• Let the global upper bound be the initial optimal solution UB = ${ f(x}_{ga})$ and the lower bound LB = $-\propto$.
• Add the original MILP problem as the root node to the active node queue, and prioritize the queue by LP relaxation value.

Step 2: Relaxation Solution

• Perform linear programming relaxation on the current node (ignoring integer constraints) to solve the relaxed problem.

$$\min {\mathbf{c}}^T\mathbf{x}+{\mathbf{d}}^T\mathbf{y} \mathrm{s}.\mathrm{t}.A\mathbf{x}+D\mathbf{y}\le \mathbf{b},\mathbf{x}\in {\mathbb{R}}_{+}^n,\mathbf{y}\in {\mathbb{R}}_{+}^m$$

(24)

• If the relaxed problem has no feasible solution, prune this branch; otherwise, obtain the relaxed solution $x_{LP}$ and its objective value ${f(x}_{LP})$.

Step 3: Pruning Conditions

• Optimality Pruning: If the relaxed solution satisfies the integer constraints, update the global upper bound as min (${f(x}_{LP})$,UB), and record this solution.
• Bounding Pruning: If ${f(x}_{LP})$ ≥ UB, it means that this branch cannot produce a better solution, so prune this branch. Otherwise, update LB = max (${LB, f(x}_{LP})$).

Step 4: Branching Operation

If there are non-integer integer variables $x_i$ in the relaxed solution, select this variable for branching. Create two subproblems:

• Subproblem 1: $x_i\le \lfloor x_i^{\mathrm{*}}\rfloor$
• Subproblem 2: $x_i\ge \lceil x_i^{\mathrm{*}}\rceil$

Then, add these subproblems to the queue of nodes to be processed.

Step 5: Dynamic Feasible Solution Generation via Genetic Algorithm

• Trigger Conditions:
  • Process K = 50 branch and bound nodes;
  • No update to the global UB for T = 10 consecutive iterations;
  • LP relaxation solution is close to integrality (e.g., fractional variables have values near 0 or 1).
• Genetic Operations:
  • Crossover: Combine the current best solution x_i with the rounded integer solution $x_{LP}$ to round($x_{LP}$) to generate offspring.
  • Mutation: Apply random perturbations (e.g., flipping binary variables or adjusting integer values) to offspring while ensuring constraint satisfaction.
  • Selection: Retain the top p = 20 individuals with the highest fitness (i.e., lowest objective value f(x)).
• Update Upper Bound:

If the new population’s best solution $x_{ga\_new}$ satisfies ${f(x}_{ga})<UB$, then update $UB={f(x}_{ga\_new})$ and set $x_i^{\mathrm{*}}=x_{ga\_new}$.

• Dynamic Pruning:

Remove all nodes from the active queue where the LP relaxation value $f_{LP}>UB$.

Step 6: Termination Condition

The algorithm terminates when one of the following conditions is met:

• All branches have been pruned or processed.
• The difference between the global UB and LB is smaller than the preset threshold ϵ = 10⁻⁴.

3.5. Constraints

SHEM typically includes various constraints, which can be divided into power balance constraints and load operation constraints.

3.5.1. Balance Constraints

In each scheduling period, power balance must be maintained, i.e.,

$$P_{load}\left(t\right)-P_{pho}\left(t\right)-P_{disch}\left(t\right)=P_{grid}\left(t\right)$$

(25)

where $P_{load}\left(t\right)$ is the total household load power (kW) at time t,$P_{pho}\left(t\right)$ is the photovoltaic output power (kW) at time t, $P_{disch}\left(t\right)$ is the discharging power of the energy storage device (kW) at time t, and $P_{grid}\left(t\right)$ is the total interaction power between the household and the grid at time t, which includes both rigid and flexible loads (kW).

3.5.2. Load Operation Constraints

For power-adjustable loads: These loads, such as smart lighting, air conditioning, and water heaters, can adjust their power output within certain limits. The operating power must be within the rated power range of the device and must avoid instantaneous overload to ensure grid stability and equipment safety.

For time-adjustable loads: These loads can adjust their operation time, but their power output remains largely fixed, such as washing machines, dishwashers, and dryers. Constraints for time-adjustable loads include:

• Operating Time Range: The device must start within the allowed operating time window, for example, prioritizing operation during off-peak hours with lower electricity rates.
• Optimal Comfort Time Window: The load should operate primarily within the user’s desired time window, such as having the dishwasher automatically run after dinner.

For power-duration adjustable loads: These loads can adjust both their power output and operation duration, such as electric vehicle charging and energy storage devices. Constraints for these loads include:

• Minimum/Maximum Power Limits:

$$P_{ch,min}⩽P_{ch}\left(t\right)⩽P_{ch,max} {P_{disch,min}⩽P_{ch}\left(t\right)⩽P}_{disch,max},$$

(26)

where $P_{ch}\left(t\right)$ and $P_{\mathit{disch}}\left(t\right)$ are the charging and discharging power at time $t$ and $P_{ch,min},{ P}_{ch,max},{ P}_{disch,min},{ P}_{\mathit{disch}, \mathit{max}}$ are the respective minimum and maximum power limits.

• Minimum/Maximum Capacity Limits:

$${SOC}_{min}⩽SOC\left(t\right)⩽{SOC}_{max},$$

(27)

where $SOC\left(t\right)$ is the state of charge of the storage device at time $t$ and $SO{C}_{min}$ and $SO{C}_{max}$ are the minimum and maximum allowable charge levels.

• Load Distribution Balance: These loads should operate primarily during periods with low electricity rates and low grid load to flatten the peak demand and fill the valley periods.

For temperature-controlled adjustable loads: These loads are subject to temperature constraints, such as air conditioners and water heaters, whose operation is controlled by temperature. Constraints for temperature-controlled loads include:

• Temperature range for adjustment: For air conditioning, the cooling temperature cannot fall below a set lower limit, and in heating mode, it cannot exceed a set upper limit. For water heaters, the minimum water temperature must meet household needs.
• Optimal temperature comfort range: The temperature should ideally be maintained within the user’s most comfortable range, such as keeping air conditioning between 24–26 °C and water heaters between 45–55 °C, balancing both comfort and energy efficiency.
• Dynamic adjustment mechanism: The system adjusts the operation strategy based on environmental temperature, load status, and electricity prices. For example, the air conditioning temperature setpoint can be raised during peak times to reduce energy consumption.

4. Example Analysis

4.1. Parameter Settings

In this study, the distributed power source is primarily photovoltaic (PV) generation. The charging and discharging efficiencies of the battery, denoted as ${\eta }_{\mathit{ch}}$ and ${\eta }_{\mathit{disch},}$, are 0.9 and 0.8, respectively. The maximum charging and discharging power, $P_{\mathit{ch},\mathit{max}}$ and $P_{\mathit{disch},\mathit{max},}$ are 2 kW and 1.8 kW, respectively. The minimum and maximum state of charge (SOC), $SO{C}_{min}$ and $SO{C}_{max}$, are 0.2 and 1, respectively. The real-time electricity prices, rigid load, and photovoltaic output in each period are shown in Figure 2. The flexible load parameters are provided in

Table 2. Flexible load parameters.

Appliance Name	Power (kW)	Operating Window	Required Operating Duration (h)	Minimum Continuous Operating Duration (h)
Washing Machine	0.5	12:00–22:00	1	1
Kettle	1.5	18:00–07:00	0.5	0.5
Vacuum Cleaner	1.0	08:00–12:00	1	1
Dishwasher	0.5	19:00–02:00	1	1
Disinfection Cabinet	0.3	19:00–07:00	0.5	0.5
Tumble Dryer	1.5	19:00–07:00	1	1
Electric Car	3.0	18:00–06:00	3	1
Computer	0.15	19:00–24:00	1.5	1
Air Conditioner	2.0	All day	-	-
Water Heater	2.5	07:00–00:00	-	-

.

Table 3. Symbol definitions.

Symbols	Meanings
Prigid (t)	Power of the rigid load at time t
Prated(t)	Rated power of the load at time t
Padjustable (t)	Power-adjustable load
Pflexible (t)	Power-time adjustable load
SOC (t)	State of charge of the battery at time t
$U_{\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{e}}^i\left(t\right)$	Time comfort of device i at time t
$U_{\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{m}\mathrm{a}\mathrm{l}}^i\left(t\right)$	Temperature comfort of device i at time t
$\alpha \left(t\right)$	Carbon emission factor
$Z$	Electricity cost of the load excluding photovoltaic output
$P_{\mathit{ele}}\left(t\right)$	Electricity price at time t
$P_{\mathit{pho}}\left(t\right)$	Photovoltaic power generation
$H$	Quantified flatness of the net load curve
$T$	Total incentive subsidy from demand response
$C_{total}$	Total carbon emission cost for one period
$C\left(t\right)$	Carbon emissions (or carbon consumption) at period t
$C_{room}$	Room thermal capacity $\left(\mathrm{k}\mathrm{W}\mathrm{h}/°\mathrm{C}\right)$
$x_{LP}$	Relaxed solution
UB	Upper bound
LB	Lower bound
DR	Demand response
${\eta }_{\mathit{ch}}$	Charging efficiencies
${\eta }_{\mathit{disch}}$	Discharging efficiencies

lists the symbol definitions.

4.2. Simulation and Result Analysis

The load optimization scheduling results in the home energy management system are shown in Figure 3. Figure 3a presents the optimized scheduling results for the washing machine, kettle, computer, and electric vehicle. In the case setup, the operating time window for the washing machine includes the low, peak, and off-peak pricing periods. After optimization, the model selects the low-price period from 23:00 to 24:00 for the washing machine operation. Similarly, the operating windows for the kettle and computer also include these three periods. After optimization, the kettle is scheduled to operate from 21:00 to 21:30, and the computer from 21:00 to 22:30, both during the off-peak pricing period. The energy storage device, the electric vehicle, is scheduled for charging from 01:00 to 04:00, following the low-price strategy, effectively reducing electricity costs.

Figure 3b shows the optimized scheduling results for the dishwasher, sterilizer, dryer, and vacuum cleaner. In the case study, the dishwasher’s operational time range includes three periods: off-peak, peak, and mid-peak hours. After optimization, the model schedules the dishwasher to run during the mid-peak period from 20:00 to 21:00. Similarly, the sterilizer and dryer are scheduled to operate during the off-peak periods from 21:00 to 21:30 and 22:00 to 23:00, respectively. The vacuum cleaner is scheduled to run during the off-peak period from 09:00 to 10:00.

Figure 3c presents the optimized scheduling results for temperature-controlled loads, such as air conditioners and water heaters. As seen in the figure, the water heater’s operating time spans multiple periods but is always within mid-peak or off-peak times. The use of the water heater is closely linked with other household appliance usage, such as the 20:00–21:30 period, which overlaps with the dishwasher’s operating time. The 22:00–23:30 period also includes part of the washing machine’s operation and is a peak time for household members taking showers. Additionally, 07:30–08:00 is the peak time for morning washing, leading to a significant increase in hot water demand. The air conditioner maintains a temperature of around 26°C, ensuring maximum comfort for the user. The case study results show that this temperature-controlled load optimization strategy efficiently schedules the air conditioner and water heater, ensuring comfort while avoiding unnecessary energy waste and reducing overall electricity costs by optimizing based on real-time electricity prices.

Figure 4 illustrates the model’s control of battery charging and discharging, showing the comparison between time-of-use electricity prices and the SOC of the battery. The purpose of using the battery is to store energy during low-price periods and release it during high-price periods to reduce electricity costs. From the figure, it is clear that during the off-peak period (23:00–06:30), the battery charges from 23:30 to 01:30. Between 01:30 and 06:30, the SOC reaches its maximum value. During the mid-peak period (06:30–09:30), the battery neither charges nor discharges. During the peak period (10:00–14:30), the battery first discharges, reaching the minimum SOC value of 0.2 at 13:00, and then charges again, reaching 0.4. During other mid-peak periods (15:00–17:30 and 21:00–22:30), the battery continuously charges. During the evening peak (18:00–20:30), the battery discharges to reduce the load.

To further verify the effectiveness of the model proposed in this paper for demand response, Figure 5 shows the dynamic incentive subsidy in relation to electricity price fluctuations. From the figure, it can be seen that during the off-peak price period, the subsidy is higher, encouraging users to use electricity at night; during the mid-peak price period, the subsidy decreases to avoid further increasing the grid load; during the peak price period, the subsidy is zero, guiding users to shift their electricity usage.

Figure 6 shows the variation of different types of loads in the household energy system under the dynamic pricing mechanism. As can be seen from the results, flexible loads are mostly intelligently scheduled to operate during off-peak or mid-peak hours, reducing overall electricity costs and improving energy efficiency. The scheduling optimization of these loads fully takes advantage of electricity price fluctuations, running them during periods of lower prices to alleviate the grid load during peak hours. In contrast, rigid loads generally have higher electricity demand during morning and evening peak periods. This is because the usage of these devices is often constrained by users’ daily routines and habits, making it difficult to adjust their operation time flexibly.

Overall, the intelligent scheduling of flexible loads can effectively reduce household energy costs and ease the burden on the grid to some extent, while rigid loads are more driven by user demand and are still concentrated during peak hours. This study enhances the intelligence of household energy management by reasonably configuring flexible load scheduling strategies, combined with the collaborative optimization of energy storage systems and distributed energy sources (e.g., photovoltaic generation), achieving a balance between economic and reliability goals.

To validate the effectiveness of the proposed model in reducing household electricity costs, optimizing load curve flatness, reducing carbon emissions, and ensuring user comfort, Table 3 presents the simulation results before and after optimization using the linear weighting method and the efficacy coefficient method for constructing the objective function. This further evaluates the model’s applicability and optimization performance.

From the comparative data in

Table 4. Comparison before and after optimization.

Metrics	Methods of Efficacy Coefficients		Linear Weighting Method
	Before Optimization	After Optimization	Before Optimization	After Optimization
Flexible load electricity fee	3.94	2.776	3.94	2.481
Flatness of load curve	1.23	1.84	1.23	1.46
Carbon consumption	1.418	0.994	1.418	0.883
User comfort	1	0.95	1	0.61

, it is evident that for the objective functions constructed using both methods, the proposed scheduling approach achieves significant improvements in reducing electricity costs, optimizing load balance, and decreasing carbon emissions. Specifically, after optimization with the efficacy coefficient method, in terms of economic efficiency, the flexible load electricity cost decreased from 3.94 to 2.776, a reduction of approximately 29.6%, demonstrating that the scheduling method effectively reduces users’ electricity expenses. Regarding load balance, the load curve flatness increased from 1.23 to 1.84, an improvement of approximately 49.6%, indicating that the optimized load curve is smoother, achieving better peak shaving and valley filling effects, thereby alleviating grid pressure and enhancing energy utilization efficiency. In terms of carbon emissions, carbon consumption costs dropped from 1.418 to 0.994, a decrease of about 29.9%, demonstrating that the optimization approach effectively reduces carbon emissions and enhances the environmental friendliness of household energy use. In terms of user comfort, there was a slight decline after optimization, from 1 to 0.95, but it remained at a relatively high level, indicating that the optimization method balances electricity cost reduction and load balancing while maintaining a good user experience, preventing excessive disruption to users’ daily electricity usage.

By comparing the simulation results before and after optimization using the linear weighting method and the efficacy coefficient method for constructing the objective function, it is found that the efficacy coefficient method better balances the impact of differences in dimensional scales among different optimization objectives. Although optimization with the efficacy coefficient method resulted in an 11.89% increase in flexible load electricity costs and a 12.5% increase in carbon consumption, the load curve flatness and user comfort improved by 26.02% and 55.73%, respectively.

In summary, the proposed scheduling method performs excellently in economic efficiency, load balance, and carbon emission reduction while also considering user comfort, proving its effectiveness and practical value in household energy management.

To verify the effectiveness of the proposed algorithm in multi-objective balancing, this study compares multiple indicators under different scenarios and algorithms.

• Scenario 1: Only electricity cost is considered, while user comfort is not taken into account.
• Scenario 2: A comprehensive consideration of electricity cost, user comfort, load curve flatness, and carbon consumption.

Table 5. Comparison results of different metrics under various scenarios and algorithms.

Metrics	Scenario 1			Scenario 2
	GA	MILP	MILP +GA	GA	MILP	MILP +GA
Flexible load electricity fee	1.904	1.316	1.422	3.446	2.912	2.776
Flatness of load curve	1.049	1.274	1.315	1.54	1.71	1.84
Carbon consumption	0.669	0.571	0.476	1.214	1.133	0.994
User comfort	0.149	0.207	0.243	0.78	0.87	0.95
Time (s)	3346.8	139.74	3547.6	3538.1	141.54	3661.3

presents the comparison results of different metrics under various scenarios and algorithms. It can be observed that in Scenario 1, where only electricity cost is considered without accounting for user comfort, all three algorithms effectively reduce electricity costs; however, user comfort also decreases significantly.

Comparing the optimization results of the three algorithms in Scenario 1 and Scenario 2, it is evident that the MILP algorithm achieves better optimization than the GA algorithm but is still inferior to the proposed MILP + GA algorithm. However, the MILP algorithm has a significant advantage in solving time compared to the proposed MILP + GA algorithm. The proposed MILP + GA algorithm achieves a trade-off between performance and computation time, making it better suited for real-world applications.

5. Conclusions

This paper investigates the optimization scheduling problem in smart home energy management, focusing on how to achieve coordinated optimization across multiple factors such as load balancing, cost control, carbon emissions, user comfort, and demand-side response. For various load characteristics in home energy systems, this paper proposes an optimization method based on dynamic electricity pricing and intelligent scheduling strategies, and its effectiveness is verified through simulation. The simulation results show that the proposed method can effectively reduce household electricity costs, optimize load curve flatness, and reduce carbon emissions. Economically, the cost of flexible loads decreases by approximately 29.6%, indicating that the optimized scheduling strategy makes full use of off-peak electricity prices, effectively reducing electricity expenses. In terms of load balancing, the load curve flatness improves by about 49.6%, which helps to reduce peak loads and fill valleys, thus alleviating grid stress and improving energy efficiency. Regarding carbon emissions, carbon consumption costs decrease by 29.9%, suggesting that the optimization method contributes to reducing the carbon footprint of the household energy system and promotes green and low-carbon development. Furthermore, user comfort remains at a relatively high level, with a slight decrease of 5% in the comfort index, indicating that the optimization strategy maintains a good balance between improving economy and environmental performance while ensuring user experience. Overall, the proposed optimization scheduling strategy achieves a good balance between economic efficiency, load balancing, and carbon emissions optimization while also ensuring user comfort. This provides an effective solution for smart home energy management. Future research will further integrate artificial intelligence and deep learning technologies to enhance the intelligence of scheduling models and explore more flexible demand-side response strategies to meet increasingly complex home energy management needs.