Fuzzy Logic in Smart Meters to Support Operational Processes in Energy Management Systems

Abstract

Distribution network operators face the complex challenge of maintaining stable electricity access for diverse consumers while balancing economic constraints, user comfort, and the impact of stochastic events, particularly the increasing integration of renewable energy sources and electric vehicles. To address these challenges, this paper introduces a novel decision-making system for energy management within smart energy meters, leveraging a specifically designed fuzzy inference system. This fuzzy inference system autonomously interprets real-time energy consumption patterns and responds to control commands from distribution network operators, optimizing energy flow at the consumer level. Unlike generic energy management approaches, this study provides a detailed mathematical model of the proposed low-cost fuzzy inference system-based system, explicitly outlining its rule base and inference mechanisms. Simulation studies conducted under varying load conditions and renewable generation profiles demonstrate the system’s effectiveness in achieving a balanced response to grid demands and user needs, yielding a quantifiable reduction in peak demand during simulated stress scenarios. Furthermore, experimental validation on resource-constrained embedded platforms confirms the practical feasibility and real-time performance of the proposed system on low-cost smart energy meter hardware. The differential contribution of this work lies in its provision of a computationally efficient and readily implementable fuzzy logic-based solution tailored for the limitations of low-cost smart energy meters, offering a viable alternative to more complex artificial intelligence algorithms. The findings underscore the necessity and justification for optimizing algorithm code for resource-constrained smart energy meter deployments to facilitate widespread adoption of advanced energy management functionalities.

1. Introduction

Energy management in the electric power system (EPS) is an important issue and is considered from the perspective of transmission system operators (TSO) and distribution network operators (DSO). Commercial energy consumers (e.g., industry) and individual household energy consumers are also taken into account. Due to the progress of civilization, each group of electricity consumers requires uninterrupted access to energy. However, this access may be interrupted by a temporary lack of balance between demand and supply for electricity [1]. Such situations often occur, especially on days of high generation of energy from renewable energy sources (RES) or in autumn and winter when there is no generation, mainly from photovoltaic power plants. The human factor [2] can also be a source of problems for the integral operation of the EPS [3].

Energy storage technologies [4] are a key method for balancing electricity supply and demand in power grids. Research and operational data show promising outcomes for increased and rationally located energy storage. Treating electric vehicles as energy storage in Vehicle-to-Grid services is also reasonable. Electric vehicles can actively support modern grids by consuming excess renewable energy and supplying stored energy during low generation.

The DSO and TSO are two crucial players in the modern EPS (Figure 1). While DSOs are responsible for the distribution of electricity to local areas and individual consumers, TSOs ensure the transmission of electricity over long distances, connecting power generation sources to the distribution networks. TSOs enable the delivery of energy to both industrial and individual consumers, regardless of the energy source. This energy can come from conventional electricity suppliers, such as nuclear power plants or fossil fuel-based power plants (e.g., coal). DSOs also facilitate the integration of distributed generation, including small-scale RESs from prosumers. These green energy sources, such as photovoltaics and wind power, energy storage and active loads, are playing an increasingly important role in modern energy systems. The operation of the EPS requires a flexible and coordinated approach by DSOs and TSOs as well as energy consumers and producers to maintain the stability and reliability of the network. The EPS with smart-grid (SG) functionality are the answer to the current challenges related to electricity. The SG is a modernized electricity network that uses advanced digital technologies to enhance its efficiency, reliability, and sustainability. It goes beyond the traditional one-way flow of electricity from power plants to consumers, allowing a more dynamic and interactive grid that can respond to real-time changes in demand and supply.

The deployment of smart energy meters offers diverse possibilities across industrial, renewable energy, and prosumer self-consumption contexts (Figure 1). Within industrial facilities, smart energy meters may be strategically positioned at individual machinery and equipment to facilitate granular monitoring of energy consumption patterns, thereby enabling operational optimization, identification of inefficiencies, and predictive maintenance protocols. Integration along production lines allows for detailed energy accounting per unit of output or process stage, supporting cost allocation and the identification of energy-intensive bottlenecks. Furthermore, smart energy meters serve as integral data sources for building energy management systems (BEMS) [5], optimizing overall building energy utilization, and for the management of on-site energy storage systems, enhancing their efficacy in peak shaving and load balancing. In complex industrial settings, sub-metering via smart energy meters enables precise allocation of energy costs. In the domain of renewable energy systems, smart energy meters are critical for quantifying energy generation at solar and wind farms, providing essential data for billing and performance assessment. Their application extends to the management of energy storage systems integrated with renewable sources, optimizing energy dispatch and storage cycles. Hybrid energy systems benefit from smart energy meter deployment through the provision of disaggregated generation data. Moreover, smart energy meters are fundamental to electric vehicle charging infrastructure, enabling accurate energy dispensation tracking and load management. Their role is also paramount in smart grid operations, facilitating real-time monitoring of renewable energy integration and overall grid stability. For prosumers engaged in self-consumption, bidirectional smart energy meters are indispensable for accurately measuring both grid-supplied energy and surplus renewable energy fed back to the grid. When coupled with residential energy storage, smart energy meters optimize self-consumption strategies. They also provide essential data for home energy management systems (HEMS) [6], enabling intelligent control of domestic appliances. In community energy initiatives, smart energy meters ensure equitable energy sharing and billing, while within microgrid environments, they facilitate the metering of energy exchange. In conclusion, the strategic placement of smart energy meters provides the requisite granular, real-time data for enhanced energy management across a spectrum of applications, contributing to improved efficiency, cost management, and the operational stability of energy networks.

The difficulty in managing energy is also caused by events that are unpredictable and difficult to predict precisely. These events concern crisis situations that cause damage to the EPS infrastructure. Damage can result from the occurrence of violent atmospheric phenomena or intentional or accidental human actions.

A lack of energy in the modern EPS is currently a big problem. It may occur in a situation of increased demand for energy, in particular from heating, ventilation, air conditioning systems (HVAC) [7,8]. This situation is recurrent in summer and winter. The potential disruption to the comfort of users requiring the continuous operation of individual HVAC systems due to weather conditions is a factor of substantial consequence, especially in scenarios involving a lack of access to energy. In addition to the seasonality, the energy shortage may also occur in daily cycles related to the performance of periodic activities during the day. In the literature, this phenomenon is referred to as daily peak demand [9]. In households, increased energy demand most often occurs in the morning and afternoon.

One of the solutions that can support EPS balancing is the intentional or automatic shutdown of RES generation, including prosumer generation, or increasing the grid load level. It may be effective to regulate post-load level modifications in the industry as a result of using demand response [9]. Demand response is of particular importance in industries where there is a high demand for electricity, e.g., mining or metallurgy. Energy consumption can be optimized by machines themselves, for which dedicated algorithms are prepared [10]. Improving the energy balance can also be supported by using dedicated energy management algorithms in HEMS [6].

1.1. Energy Management Algorithms for Home Energy Management Systems

Each energy management algorithm has specific properties. By analyzing individual energy management algorithms, one common property can be found. Demand response is considered together with control decisions sent by the DSO. A comparison of the remaining properties is presented in

Table 1. Selected elements applicable to ensuring effective and reliable energy management using energy management algorithms in SGs.

Refs.	RES	Electric Vehicles	Frequency Regulation	Voltage Control	Energy Cost	HEMS	Weather and Environment
[11]	✓
[12,13]		✓
[14]	✓			✓
[15]			✓	✓
[16]					✓	✓
[17]	✓				✓	✓	✓
[18]	✓
[19]						✓	✓

.

In [11], a new approach is proposed for an economic dispatch optimization model for active distribution systems management that reduces power losses in unbalanced active distribution systems. The authors in [12] presented a method for estimating the maximum penetration levels of renewable-based distributed generation and electric vehicles in an electricity distribution system. The algorithm presented in [13] has similar properties considering RES and electric vehicles. This paper presents the application of demand side management techniques (peak clipping, valley filling and load shifting). The aim of peak shaving, valley filling, and flattening the load curve of the network during the optimal planning of an electric vehicle’s charging/discharging is devised. The increasing number of solar photovoltaic installations contributes to the problem of overvoltage. The problem was addressed in [14,15]. In [15], frequency regulation is also considered. In [16], the forecast engine based on demand response signal and energy consumption patterns is presented. In HEMS, smart home devices follow the forecasted price signal and energy consumption pattern for efficient energy management on a schedule. In [17], the reduction of electricity bill cost and CO2 emission was considered. Examples of energy management based on luminance and thermal comfort were given. The studies included solar and wind energy. Solar energy management using neural networks was the topic of [18]. The results were based on one day ahead solar power forecasting. The energy management algorithms presented in [19] distinguishes itself by the criterion of better protection of residential customers’ privacy. The amount of data transmitted between HEMS and DSO has been minimized. The presented energy management algorithms takes into account the impacts of weather and consumer behavior.

1.2. Home Energy Management System

As already mentioned, HEMS can play a significant role in balancing the EPS as an element of modern energy management algorithms. Figure 2 shows the HEMS as a hardware-software solution. The hardware solution includes: energy receiver, source of energy, and energy storage. Energy receiver includes classic electricity receivers and smart appliances (SA) [20,21].

SAs can adjust their power based on power grid regulations within manufacturer limits, potentially impacting user comfort (e.g., slower kettle boiling). Conversely, power can increase during energy surplus. Energy sources include conventional electricity suppliers (CES) and RES, with energy storage bridging SAs and these sources for consumption and storage.

1.3. Smart Energy Meters

The software solution of HEMS will involve the implementation of one of the energy management algorithms. The energy management algorithms will respond to demand response. The implementation of such an energy management algorithm can be embedded in a smart energy meter.

Table 2. Selected elements that apply to the operation of smart energy meter.

Refs.	Data Processing and IoT	AI and Energy Management Algorithms	Demand Side Management	Electric Vehicles	Energy Cost	RES	User Comfort	RTP
[22]	✓	✓	✓	✓
[23]	✓	✓	✓
[24]		✓					✓
[25]		✓	✓	✓	✓
[26]			✓	✓		✓
[27]	✓		✓
[28]		✓					✓
[29]	✓		✓					✓

summarizes the functionalities that are the subject of research.

In [22], the focus was on data collection and analytics. The results of the study proposed using artificial intelligence (AI) for electric load forecasting. The issues of electricity theft detection were also raised. Load monitoring, recurrent neural network and deep learning were the subject of research in [23]. AI in the context of energy decomposition and neurocomputing in smart home automation was considered in [24]. In [25], the functionalities for smart energy meters were defined for the electric vehicle charging operation system. The use of an advanced metering infrastructure (AMI) was proposed to reduce the cost of bills and enhance services. Demand side management was considered in the context of scheduling time horizon. The concept of intelligent building with RES was dedicated to [26]. The functionalities of smart energy meters in the context of big data and the Internet of Things (IoT) were considered in [27]. The researchers in [28] defined the functionalities of smart energy meters taking into account consumer privacy, model predictive control, mutual information and optimization methods. The functionality of Real-time pricing (RTP) was the subject of research on the functionalities of smart energy meters in [29]. In this case, service computing and demand side management were also considered.

Besides HEMS, other energy management systems that use smart energy meters also include BEMS [5], industrial energy management systems (IEMS) [30], smart grid energy management systems (SGEMS) [31], and renewable energy management systems (REMS) [32]. Smart energy meters are foundational components of various energy management systems within SGs. They provide the real-time data necessary for monitoring, control, and optimization of energy consumption and generation. In

Table 3. Key categories of energy management systems utilizing smart energy meters.

Type	Description	Key Smart Energy Meter Functionalities Utilized	Primary Goals
HEMS	Focus on managing energy consumption and generation within residential buildings.	Real-time energy consumption monitoring, providing data for home automation, enabling response to dynamic pricing signals, supporting integration of residential renewable energy (e.g., solar PV), facilitating demand response participation.	Reducing household energy bills, increasing energy efficiency, optimizing self-consumption of generated energy, enhancing user comfort, and contributing to grid stability.
BEMS	Manage energy use in commercial and institutional buildings (offices, hospitals, schools, etc.).	Detailed energy consumption monitoring across various building systems (HVAC, lighting, etc.), occupancy detection data, real-time reporting, fault detection, and providing data for automated control and optimization strategies.	Minimizing energy waste in buildings, reducing operational costs, improving building sustainability, ensuring occupant comfort, and complying with energy regulations.
IEMS	Focus on optimizing energy consumption in industrial facilities and manufacturing plants.	Real-time monitoring of energy usage in production processes, machinery, and other industrial equipment, identifying energy-intensive processes, providing data for process optimization, enabling demand-side management in industrial settings, and integrating with on-site generation.	Lowering energy costs in industrial operations, improving production efficiency, optimizing energy distribution within the facility, and enhancing sustainability.
SGEMS	Encompasses systems used by utilities and grid operators to manage energy flow, stability, and efficiency across the entire power grid.	Real-time data acquisition from numerous smart energy meters across the grid, load forecasting based on consumption patterns, voltage and frequency monitoring, enabling demand response programs, facilitating the integration of distributed renewable energy sources, and supporting grid automation and control.	Ensuring grid stability and reliability, optimizing energy distribution, managing peak demand, integrating renewable energy effectively, reducing transmission losses, and improving overall grid efficiency.
REMS	Focus on managing the generation, storage, and integration of renewable energy sources (solar, wind, etc.) into the grid or local energy systems. While not solely reliant on smart energy meters, they utilize data from them for demand-side management and grid interaction.	Monitoring renewable energy generation in real-time, forecasting generation output, managing energy storage systems, coordinating with smart grid operations based on demand data from smart energy meters, and optimizing the dispatch of renewable energy.	Maximizing the utilization of renewable energy, ensuring grid stability with variable generation sources, reducing reliance on fossil fuels, and optimizing energy storage operations.

, outlining key categories of energy management systems that utilize smart energy meters and their primary focus is presented.

Table 3 illustrates the diverse applications of smart energy meters within various energy management systems categories, highlighting their crucial role in enabling a more efficient, reliable, and sustainable energy future. The real-time data provided by smart energy meters is the foundation upon which these advanced energy management strategies are built.

In summary, smart energy meters provide the ability to monitor the flow of electricity in HEMSs. For example, they can determine when energy was supplied from RESs. The DSO can determine the energy consumption profile for each household. This functionality is available due to the logging of data on consumption of electric energy, voltage levels, current, and power factor. Two-way communication between CESs and HEMSs is possible due to the use of AMI. Smart energy meters from individual HEMSs will be part of a distributed control system [33].

1.4. The Application of Fuzzy Logic to Energy Management Algorithms

The fuzzy logic persists as a promising approach in numerous domains, notably in energy management. A case in point is a study [34] that leveraged fuzzy logic controllers and clustering to diagnose and forecast incipient faults and insulation status in power transformers, thereby optimizing asset management. Moreover, fuzzy logic has been instrumental in developing a risk assessment framework for enhancing the resilience of microgrids through lightning nowcasting [35]. Recent research [36] further underscores the potential of fuzzy logic in energy management, thus justifying ongoing research in this field. A fuzzy logic approach is proposed for energy management algorithms.

Table 4. Application examples of selected elements related to energy management algorithms in fuzzy logic.

Refs.	Voltage Control	RES	Energy Storage	RTP	User Comfort	Demand Side Management	Energy Cost	Electric Vehicles	Locating Faults in SGs	HEMS
[37]	✓
[38]	✓	✓
[39]	✓	✓
[40,41,42]			✓
[43]				✓	✓	✓				✓
[44]			✓	✓			✓
[45,46,47]								✓
[48,49]		✓
[50,51]									✓
[52]										✓

provides a comparison of various functionalities of using fuzzy logic in energy management algorithms with the proposed work.

Reference [37] provides a summary of some of the earlier work on the application of fuzzy logic in energy management algorithms, which deals with voltage control in SG networks. Reference [38] presents an approach to voltage regulation in low-voltage power distribution networks with high penetration of a photovoltaics. The results of the work describe a controller for a photovoltaics interfacing inverter based on intelligent adaptive neuro-fuzzy inference system. Paper [39] proposes an MROGI-FLL control with a fuzzy PID for grid-tied PV inverters, effectively mitigating harmonics and stabilizing the DC-link voltage with low computational cost. Simulations and experimental validation against existing techniques demonstrate its superior performance in harmonic reduction, DC-offset rejection, and frequency variation handling, adhering to IEEE-519 standards. Issues of energy storage systems management in micro grids based on fuzzy logic are presented in [40,41,42]. Dynamic RTP, user comfort, and load smoothing based on demand side management were the topics of the works presented in [43]. Fuzzy logic was used for dynamic pricing, reducing consumer energy consumption cost and energy storage in [44]. The issues of vehicle-to-grid and energy management in electric vehicles are presented in the works [45,46,47]. Fuzzy logic applied to energy management algorithms is presented in [49] for optimizing energy consumption. Additionally, [49] addresses RESs using a forecasting approach based on the Choquet integral and deep long short-term memory. Fuzzy logic was used for locating faults in SG [50]. The application of fuzzy logic in energy management algorithms in the context of optimizing the energy consumption of wind turbine is presented in [48]. The RES is also addressed in [49], which uses a forecasting approach based on the Choquet integral and deep long short-term memory. Fuzzy logic was used for locating faults in the SG [50] and for fault diagnosis based on intuitionistic fuzzy sets and incidence matrices in SG [51]. Energy management algorithms in the context of ventilation system control using fuzzy logic is presented in [52]. The proposed solution has the potential to be applied to a wide range of areas, including voltage control, RESs, energy storage, RTP, user comfort, demand side management, energy cost, electric vehicles, faults location in SGs, and HEMSs.

The reviewed literature confirms the established utility of fuzzy logic across diverse energy management applications, including fault diagnosis, microgrid resilience, voltage control, PV optimization, energy storage management, demand-side management, EV/V2G, general consumption optimization, RES forecasting, fault location, and control of specific energy systems. This demonstrates fuzzy logic’s adaptability for complex energy challenges. Building on this foundation, the present study proposes and evaluates a novel fuzzy logic approach for HEMS algorithms, specifically addressing the gap in practical implementation and validation on low-cost smart energy meter devices. This work aims to contribute a computationally feasible solution for real-time residential energy management, complementing the broader grid-level applications of fuzzy logic highlighted in the literature. The wide potential applicability of fuzzy logic in energy management underscores the significance of investigating its practical realization in smart homes.

1.5. Research Issues, Limitations, and Gaps

Smart energy meters are devices that, for a given energy management algorithm application area (e.g., in HEMS), will take into account additional factors (energy cost, weather, and environment). Energy management algorithm components or application areas are also considered (RES, electric vehicles). Power grid management elements such as frequency regulation and voltage control can also be included in smart energy meters. Smart energy meters offer sufficient computing power to perform the tasks resulting from the implementation of AI or energy management algorithms. In [53], the use of smart energy meters or water flow meters was proposed for performing calculations resulting from the implemented hardware solution algorithms based on the Raspberry Pi or Arduino platform.

Due to the functions that smart energy meters perform, it was decided to focus on this type of device included in the SG. The aim of this work was to use fuzzy logic in smart energy meters. The effect of such action is to estimate and map the power values that can be achieved, e.g., in the HEMS. In this case, it will be about determining the potential for increasing or decreasing the power of SAs in the HEMS, for example, in critical situations. After receiving data on the possible potential for modifying the load of the SG network, the DSO will be able to use it in analytical models. To this end, load and generation data assuming a perfect forecasting of one hour ahead [54] or elastic energy management algorithms (EEM) [55] are used in the SG.

The gap between similar research and the present study lies primarily in two key areas. Firstly, while the reviewed literature demonstrates the broad applicability and effectiveness of fuzzy logic across various energy management domains such as voltage control, renewable energy sources, energy storage, real-time pricing, and electric vehicles, there is a noticeable lack of specific focus on the development and evaluation of fuzzy logic-based energy management algorithms explicitly designed for implementation within Home Energy Management Systems. Secondly, the existing body of work, while validating the potential of fuzzy logic in energy management, does not adequately address the practical challenges and considerations associated with deploying these sophisticated algorithms on the resource-constrained, low-cost embedded devices that are commonly found in contemporary smart energy meters deployed in residential environments. Consequently, the present study aims to bridge this gap by specifically proposing and evaluating a novel fuzzy logic approach for energy management algorithms tailored for HEMS, with a particular emphasis on its feasibility and performance when implemented on the computational platforms typical of low-cost smart energy meters at the residential level, an aspect that has not been sufficiently explored in the reviewed literature.

As a justification for conducting the research, it can be stated that fuzzy logic in smart energy meters is crucial due to data uncertainty and variable conditions. It enables adaptation to weather forecasts, optimization of consumption, integration of renewable energy sources, and personalization of services, thereby enhancing energy management efficiency. A solution designed to meet all the criteria outlined in Table 1, Table 2, and Table 4 has been proposed based on these criteria. Regarding the integration of RES, fuzzy logic facilitates the management of their intermittent and variable generation. Smart energy meters employing fuzzy algorithms can assess the availability and stability of local RES based on fuzzy rules incorporating weather forecasts and real-time production data, enabling informed decisions on local consumption, energy storage dispatch, or grid injection, thus fostering smoother RES integration. In the context of electric vehicles, fuzzy logic enables intelligent charging management. Smart energy meters can dynamically adjust charging rates based on user preferences, grid load, energy prices, and local RES availability, utilizing fuzzy rules to optimize charging schedules for both user benefit and grid stability. For frequency regulation, fuzzy logic embedded in smart energy meters allows for localized responses to frequency deviations. Through fuzzy assessment of the deviation magnitude and available local resources (e.g., energy storage, flexible loads), meters can enact rapid, short-term adjustments in power consumption or injection, supporting centralized frequency control mechanisms. Similarly, voltage control can be enhanced through fuzzy logic-equipped smart energy meters that monitor local voltage levels and employ fuzzy rules to manage local reactive power resources (e.g., RES inverters, local storage), contributing to a more distributed and resilient voltage regulation strategy. Energy cost optimization is another key application. Smart energy meters analyzing RTP signals, price forecasts, local RES generation, and user preferences via fuzzy logic can autonomously manage energy-intensive appliances, electric vehicle charging, and energy storage utilization during periods of lower tariffs, thereby minimizing user expenses. Integration with HEMS benefits from fuzzy logic by enabling more intelligent and autonomous energy management within households. HEMS leveraging smart energy meter data and internal sensors can employ fuzzy rules to optimize energy consumption across various appliances, considering user comfort, RES availability, and pricing signals. Processing weather and environmental data for enhanced energy management is facilitated by fuzzy logic’s ability to handle imprecise linguistic variables (e.g., “moderate cloud cover”, “high temperature”). Fuzzy predictive models within smart energy meters can utilize this information to improve forecasting of RES generation and energy demand, leading to better local resource management. In the realm of Data Processing and IoT, fuzzy logic enables localized pre-processing of the vast data streams generated by smart energy meters and connected devices. Fuzzy algorithms can identify significant patterns, anomalies, or optimization opportunities, reducing the volume of data transmitted to central systems and enabling faster local responses. As a component of AI and energy management algorithms, fuzzy logic can complement more complex AI techniques. It can serve to interpret the outputs of neural networks or to create decision-making layers that translate abstract AI results into actionable commands for smart energy meters, fostering more comprehensive intelligent energy management solutions. Demand side management strategies are naturally supported by fuzzy logic. Smart energy meters can employ fuzzy rules to react autonomously to grid signals (e.g., high load conditions) by controlling local loads (e.g., delaying appliance operation, adjusting EV charging), considering user priorities and grid conditions to reduce peak demand. The responsiveness to RTP is significantly enhanced by fuzzy logic, allowing smart energy meters to autonomously adjust energy consumption and local resource operation based on fuzzy evaluations of cost-effectiveness at any given moment, yielding savings for users and optimizing grid load. Energy storage management within smart energy meters benefits from fuzzy logic by enabling intelligent control of charging and discharging cycles based on factors such as RES availability, tariffs, demand forecasts, and user needs, maximizing economic benefits and supporting grid stability. Finally, in locating faults in SGs, fuzzy logic can be applied to the local analysis of voltage and current patterns detected by smart energy meters. Fuzzy algorithms can identify unusual behaviors that, with a certain degree of likelihood, indicate a fault in the vicinity of the meter, potentially accelerating fault localization and repair processes.

1.6. Contributions

The main contributions of this paper, addressing the identified gaps in the existing literature, can be listed as follows:

• A novel decision-making system for energy management in smart energy meters with a FIS tailored for HEMS. This contribution specifically targets the under-explored area of implementing fuzzy logic-based energy management within residential smart energy meters, moving beyond broader applications in grid-level control and optimization.
• A detailed mathematical description of the low-cost decision-making system, explicitly considering resource constraints. Unlike prior work that may not have focused on the practical limitations of embedded devices, this paper provides a comprehensive mathematical formulation of the proposed FIS-based system, designed with the computational capabilities of low-cost smart energy meter hardware in mind.
• Comprehensive simulation studies and experimental verification carried out on both a PC and representative low-cost resource-constrained devices. To directly address the lack of validation on target hardware, this study includes rigorous simulations and real-world experiments conducted not only on a standard PC but also on embedded platforms representative of the resource limitations of smart energy meters intended for residential deployment.
• Empirical confirmation of the justification for the need to optimize algorithms for practical deployment in smart energy meters. Through the simulation and experimental results obtained on low-cost devices, this paper provides concrete evidence supporting the critical necessity of algorithm optimization to ensure the feasibility and real-time performance of advanced energy management functionalities within commercially viable smart energy meters.

1.7. Paper Organisation

The remainder of this paper is organized as follows. Section 1 provides a literature review of energy management algorithms, home energy management systems, smart energy meters, and the use of fuzzy logic in energy management algorithms. Section 2 presents fundamental assumptions for home energy management system facilities. This section also provides a description of the implementation of the Fuzzy Inference System Model in Smart Energy Meters. Section 3 provides the results of the simulation tests carried out in the Matlab environment. The results of the experimental verification on a PC and low-cost resource-constrained devices are also presented in this section. Finally, conclusions are listed in Section 5.

2. Mathematical Modeling

Devices with SA functionality offer the possibility of adjusting the power level at which they work ($P_{\mathrm{SA}}$). The range of allowable modifications is specified by the manufacturer of a given SA. In this case, technical requirements are taken into account that will ensure the functionality of the given SA at the expense of reduced user comfort. This means, for example, reducing the power of, for example, a kettle, which will cause it take longer to boil the water. In a situation of excess energy, it is also possible to increase the power of the kettle.

The solution presented in the article applies to households, where all the actions of the algorithm would be carried out in a smart electricity meter [56]. With the additional computing power of such a device, it would be possible to implement additional functionalities related to energy supply and demand management.

The implementation of such actions would be triggered from the DSO’s point of view in the event of an overload or underload of the power grid infrastructure due to an excess or shortage of electrical energy or an imbalance of power supply and demand in the SG, for example, in the event of overproduction of electricity from renewable energy sources.

Energy consumption in a given household would be mapped using the advocated Fuzzy Inference System (FIS) [57] model based on the criteria defined by DSO. The FIS model provides for the criterion of the SG status and the costs resulting from the need to modify household energy consumption. A modification in such a case could consist in activating the charging of an electric vehicle or using the energy already stored in the battery of such a vehicle [58].

In the further part of the article, simulation studies will be devoted to the issue of obtaining an estimation of the possibilities at a given moment of time (t). The research will concern the increase or decrease of the load level in a given part of the SG. In particular, the considerations will concern households where user activities, e.g., cooking, is carried out using SA devices.

Fuzzy Inference System Model for Smart Energy Meters

The theory of fuzzy sets [59] for the cost of modifying the level of energy consumption was defined as $\tilde{A}$ in the universe of discourse X in the set of ordered pairs (1)

$$\tilde{A}=\left\{\left(x,{\mu }_{\tilde{A}}\left(x\right)\right):x\in X\right\},$$

(1)

where: x—element/value, ${\mu }_{\tilde{A}}\left(x\right)$—membership function ${\mu }_{\tilde{A}}\left(x\right)\in \left[0,1\right]$, X—Universe of Discourse for $\tilde{A}$.

$\tilde{A}$ indicates that the cost of modifying the energy consumption level is represented as a fuzzy set, which allows for the modeling of uncertainty and imprecision. A linguistic term is a verbal expression that represents a concept or value. Representation for fuzzy set $\tilde{A}$ for a linguistic term on a three-point scale designating the cost of modifying the level of energy consumption (low (L), normal (N), high (H)) was defined using:

$$\tilde{A}=\{\left(x_{\tilde{A}}^{\mathrm{L}},{\mu }_{\tilde{A}}^{\mathrm{L}}\left(x_{\tilde{A}}^{\mathrm{L}}\right)\right),\left(x_{\tilde{A}}^{\mathrm{A}},{\mu }_{\tilde{A}}^{\mathrm{A}}\left(x_{\tilde{A}}^{\mathrm{A}}\right)\right),\left(x_{\tilde{A}}^{\mathrm{H}},{\mu }_{\tilde{A}}^{\mathrm{H}}\left(x_{\tilde{A}}^{\mathrm{H}}\right)\right)\}$$

(2)

Similarly, the representation for the fuzzy set $\tilde{B}$ for the linguistic term of the five-point scale of the SG status (critical low (CL), L, N, H, critical high (CH)) was determined using (3).

$$\begin{array}{c}\tilde{B}=\{\left(x_{\tilde{B}}^{\mathrm{CL}},{\mu }_{\tilde{B}}^{\mathrm{CL}}\left(x_{\tilde{B}}^{\mathrm{CL}}\right)\right),\left(x_{\tilde{B}}^{\mathrm{L}},{\mu }_{\tilde{B}}^{\mathrm{L}}\left(x_{\tilde{B}}^{\mathrm{L}}\right)\right),\hfill \\ \left(x_{\tilde{B}}^{\mathrm{N}},{\mu }_{\tilde{B}}^{\mathrm{N}}\left(x_{\tilde{B}}^{\mathrm{N}}\right)\right),\left(x_{\tilde{B}}^{\mathrm{H}},{\mu }_{\tilde{B}}^{\mathrm{H}}\left(x_{\tilde{B}}^{\mathrm{H}}\right)\right),\\ \hfill \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\left(x_{\tilde{B}}^{\mathrm{CH}},{\mu }_{\tilde{B}}^{\mathrm{CH}}\left(x_{\tilde{B}}^{\mathrm{CH}}\right)\right)\}\end{array}$$

(3)

Following the processing of data by a fuzzy system, the output is obtained in the form of a fuzzy set, which represents possible output values along with their degrees of membership. To obtain a specific, numerical output value, it is necessary to perform a defuzzification process, which involves converting this fuzzy set into a single number. Given an output fuzzy set $\tilde{Y}={\mu }_{\tilde{Y}}\left(v\right)$ defined in the universe V of the variable v, the defuzzified output $\tilde{Y}$ is given by:

$$\begin{array}{c}\tilde{Y}=\{\left(v_{\tilde{Y}}^{\mathrm{DL}},{\mu }_{\tilde{Y}}^{\mathrm{DL}}\left(v_{\tilde{Y}}^{\mathrm{DL}}\right)\right),\left(v_{\tilde{Y}}^{\mathrm{D}},{\mu }_{\tilde{Y}}^{\mathrm{D}}\left(v_{\tilde{Y}}^{\mathrm{D}}\right)\right),\hfill \\ \left(v_{\tilde{Y}}^{\mathrm{DNC}},{\mu }_{\tilde{Y}}^{\mathrm{DNC}}\left(v_{\tilde{Y}}^{\mathrm{DNC}}\right)\right),\left(v_{\tilde{Y}}^{\mathrm{I}},{\mu }_{\tilde{Y}}^{\mathrm{I}}\left(v_{\tilde{Y}}^{\mathrm{I}}\right)\right),\\ \hfill \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\left(v_{\tilde{Y}}^{\mathrm{IH}},{\mu }_{\tilde{Y}}^{\mathrm{IH}}\left(v_{\tilde{Y}}^{\mathrm{IH}}\right)\right)\}\end{array}$$

(4)

The process that produces a crisp output from a fuzzy set $\tilde{Y}$ is known as defuzzification. The method of defuzzification adopted here is the center of areas. In the course of the research, the methods for defuzzifying the output fuzzy set of a type-1 Mamdani fuzzy inference system were selected. The output scale for the energy level modification action was a five-point scale, with decrease low (DL), decrease (D), do not change (DNC), increase (I), increase high (IH).

In the proposed FIS model, it was assumed that the value range of the cost of modifying the level of energy consumption $x_{\tilde{A}}$, provided by the DSO, must be based on the following assumption:

$$x_{\tilde{A}}\in \langle x_{{\tilde{A}}_{min}};x_{{\tilde{A}}_{max}}\rangle \iff x_{{\tilde{A}}_{min}}\le x_{\tilde{A}}\le x_{{\tilde{A}}_{max}}$$

(5)

Using (5) it is possible to enter a numerical range in a specific currency for the cost of modifying the level of energy consumption. In addition, the expected cost value $x_{{\tilde{A}}_{nom}}$ was specified, which is to correspond to the linguistic term scale: A. The value of $x_{{\tilde{A}}_{nom}}$ is given by:

$$x_{{\tilde{A}}_{min}}\le x_{{\tilde{A}}_{nom}}\le x_{{\tilde{A}}_{max}}$$

(6)

The assumptions for the range of SG status values $x_{\tilde{A}}$ were written in a similar way. The $x_{\tilde{A}}$ range is defined with:

$$x_{\tilde{B}}\in \langle x_{{\tilde{B}}_{min}};x_{{\tilde{B}}_{max}}\rangle \iff x_{{\tilde{B}}_{min}}\le x_{\tilde{B}}\le x_{{\tilde{B}}_{max}}$$

(7)

The expected $x_{{\tilde{B}}_{nom}}$ numerical value of the SG status has been entered:

$$x_{{\tilde{B}}_{min}}\le x_{{\tilde{B}}_{nom}}\le x_{{\tilde{B}}_{max}}$$

(8)

The definition for the output of the FIS model of the assumptions of the range of numerical values $v_{\tilde{Y}}$ describing the prediction of the energy consumption level is described by:

$$v_{\tilde{Y}}\in \langle v_{{\tilde{Y}}_{min}};v_{{\tilde{Y}}_{max}}\rangle \iff v_{{\tilde{Y}}_{min}}\le v_{\tilde{Y}}\le v_{{\tilde{Y}}_{max}}$$

(9)

The expected (nominal) value of energy consumption is denoted by $v_{{\tilde{Y}}_{nom}}$. For $v_{{\tilde{Y}}_{nom}}$ must be met:

$$v_{{\tilde{Y}}_{min}}\le v_{{\tilde{Y}}_{nom}}\le v_{{\tilde{Y}}_{max}}$$

(10)

In order to ensure proper functioning of the FIS model, it is also necessary to specify the membership functions $\mu \left(x\right)$ and their types for each fuzzy sets. For defined fuzzy sets: $\tilde{A}$ (2), $\tilde{B}$ (3) and $\tilde{Y}$ (4) three kinds of membership functions $\mu \left(x\right)$ are selected: triangular $\mu (x;a,b,c)$, S-shaped $\mu (x;a,b)$ and Z-shaped $\mu (x;a,b)$.

Triangular membership function returns fuzzy membership values computed for each input value in x for three parameters: a, b and c. This type is the membership function and is the most widely accepted and used membership function in FIS model. S-shaped membership function and Z-shaped membership function returns fuzzy membership values computed using the spline-based S-shaped and Z-shaped membership function. Both functions have two input parameters: a and b. While mapping the level of consumed energy, two types of additionally selected types of membership functions are assigned the task of providing the values of extreme power levels in crisis situations of the status SG (CL, CH). In

Table 5. Membership Functions and Fuzzy Sets for energy management systems.

Fuzzy Sets	Linguistic Term	Membership Function
		Type	$\mathsf{\mu }\left(\mathit{x}\right)$
$\tilde{A}$	L	Triangular	${\mu }_{\tilde{A}}^L\left(x_{\tilde{A}}^L;a_{\tilde{A}}^{\mathrm{L}},b_{\tilde{A}}^{\mathrm{L}},c_{\tilde{A}}^{\mathrm{L}}\right)$
	A	Triangular	${\mu }_{\tilde{A}}^A\left(x_{\tilde{A}}^A;a_{\tilde{A}}^{\mathrm{A}},b_{\tilde{A}}^{\mathrm{A}},c_{\tilde{A}}^{\mathrm{A}}\right)$
	H	Triangular	${\mu }_{\tilde{A}}^H\left(x_{\tilde{A}}^H;a_{\tilde{A}}^{\mathrm{H}},b_{\tilde{A}}^{\mathrm{H}},c_{\tilde{A}}^{\mathrm{H}}\right)$
$\tilde{B}$	CL	Z-shaped	${\mu }_{\tilde{B}}^{CL}\left(x_{\tilde{B}}^{CL};a_{\tilde{B}}^{\mathrm{CL}},b_{\tilde{B}}^{\mathrm{CL}}\right)$
	L	Triangular	${\mu }_{\tilde{B}}^L\left(x_{\tilde{B}}^L;a_{\tilde{B}}^{\mathrm{L}},b_{\tilde{B}}^{\mathrm{L}},c_{\tilde{B}}^{\mathrm{L}}\right)$
	N	Triangular	${\mu }_{\tilde{B}}^N\left(x_{\tilde{B}}^N;a_{\tilde{B}}^{\mathrm{N}},b_{\tilde{B}}^{\mathrm{N}},c_{\tilde{B}}^{\mathrm{N}}\right)$
	H	Triangular	${\mu }_{\tilde{B}}^H\left(x_{\tilde{B}}^H;a_{\tilde{B}}^{\mathrm{H}},b_{\tilde{B}}^{\mathrm{H}},c_{\tilde{B}}^{\mathrm{H}}\right)$
	CH	S-shaped	${\mu }_{\tilde{B}}^{CH}\left(x_{\tilde{B}}^{CH};a_{\tilde{B}}^{\mathrm{CH}},b_{\tilde{B}}^{\mathrm{CH}}\right)$
$\tilde{Y}$	DL	Z-shaped	${\mu }_{\tilde{Y}}^{DL}\left(v_{\tilde{Y}}^{DL};a_{\tilde{Y}}^{\mathrm{DL}},b_{\tilde{Y}}^{\mathrm{DL}}\right)$
	D	Triangular	${\mu }_{\tilde{Y}}^D\left(v_{\tilde{Y}}^D;a_{\tilde{Y}}^{\mathrm{D}},b_{\tilde{Y}}^{\mathrm{D}},c_{\tilde{Y}}^{\mathrm{D}}\right)$
	DNC	Triangular	$\begin{array}{c}{\mu }_{\tilde{Y}}^{DNC}\left(v^{DNC};a_{\tilde{Y}}^{\mathrm{DNC}},b_{\tilde{Y}}^{\mathrm{DNC}},c_{\tilde{Y}}^{\mathrm{DNC}}\right)\hfill \end{array}$
	I	Triangular	${\mu }_{\tilde{Y}}^I\left(v_{\tilde{B}}^I;a_{\tilde{Y}}^{\mathrm{I}},b_{\tilde{Y}}^{\mathrm{I}},c_{\tilde{Y}}^{\mathrm{I}}\right)$
	IH	S-shaped	${\mu }_{\tilde{Y}}^{IH}\left(v_{\tilde{B}}^{IH};a_{\tilde{Y}}^{\mathrm{IH}},b_{\tilde{Y}}^{\mathrm{IH}}\right)$

, the determination of individual membership function properties for the corresponding linguistic term for fuzzy sets $\tilde{A}$ (2), $\tilde{B}$ (3) and $\tilde{Y}$ (4) is summarized.

The selection of individual input values (a, b and c) for each membership function $\mu \left(x\right)$ has been customized. The values of individual parameters depend on the data range x and the expected value where full membership of a given set is achieved. In this way, the following values are considered: $x_{{\tilde{A}}_{\min }}$, $x_{{\tilde{A}}_{\mathrm{nom}}}$ and $x_{{\tilde{A}}_{\max }}$ (5)–(6) for fuzzy sets $\tilde{A}$ (2), $x_{{\tilde{B}}_{\min }}$, $x_{{\tilde{B}}_{\mathrm{nom}}}$ and $x_{{\tilde{B}}_{\max }}$ (7)–(8) for fuzzy sets $\tilde{B}$ (3) and $v_{{\tilde{Y}}_{\min }}$, $v_{{\tilde{Y}}_{\mathrm{nom}}}$ and $v_{{\tilde{Y}}_{\max }}$ (9)–(10) for fuzzy sets $\tilde{Y}$ (4).

To precisely define the degree to which the cost of modifying the energy consumption level is low, normal, or high, we utilize fuzzy sets. Each of these fuzzy sets (representing low, normal, and high costs) is defined by three specific numerical values: $a_{\tilde{A}}$, $b_{\tilde{A}}$, and $c_{\tilde{A}}$. These values determine the shape of the fuzzy set and are calculated using a defined method. The individual parameter values $a_{\tilde{A}}$, $b_{\tilde{A}}$ and $c_{\tilde{A}}$ for the linguistic term of the three-level scale determine the cost of modifying the level of energy consumption (L, N, H) for $\tilde{A}$ using (11)–(13).

$$\begin{array}{cc}\hfill a_{\tilde{A}}& =\left\{\begin{array}{cc}{x}_{{\tilde{A}}_{min}}-{\zeta }_{\tilde{A}}\hfill & \mathrm{if}{a}_{\tilde{A}}=a_{\tilde{A}}^{\mathrm{L}}\hfill \\ x_{{\tilde{A}}_{nom}}-{\zeta }_{\tilde{A}}\hfill & \mathrm{if}{a}_{\tilde{A}}=a_{\tilde{A}}^{\mathrm{A}}\hfill \\ x_{{\tilde{A}}_{max}}-{\zeta }_{\tilde{A}}\hfill & \mathrm{if}{a}_{\tilde{A}}=a_{\tilde{A}}^{\mathrm{H}}\hfill \end{array}\right.\hfill \end{array}$$

(11)

$$\begin{array}{cc}\hfill b_{\tilde{A}}& =\left\{\begin{array}{cc}{x}_{{\tilde{A}}_{min}}\hfill & \mathrm{if}{a}_{\tilde{A}}=a_{\tilde{A}}^{\mathrm{L}}\hfill \\ x_{{\tilde{A}}_{nom}}\hfill & \mathrm{if}{a}_{\tilde{A}}=a_{\tilde{A}}^{\mathrm{A}}\hfill \\ x_{{\tilde{A}}_{max}}\hfill & \mathrm{if}{a}_{\tilde{A}}=a_{\tilde{A}}^{\mathrm{H}}\hfill \end{array}\right.\hfill \end{array}$$

(12)

$$\begin{array}{cc}\hfill c_{\tilde{A}}& =\left\{\begin{array}{cc}{x}_{{\tilde{A}}_{min}}+{\zeta }_{\tilde{A}}\hfill & \mathrm{if}{a}_{\tilde{A}}=a_{\tilde{A}}^{\mathrm{L}}\hfill \\ x_{{\tilde{A}}_{nom}}+{\zeta }_{\tilde{A}}\hfill & \mathrm{if}{a}_{\tilde{A}}=a_{\tilde{A}}^{\mathrm{A}}\hfill \\ x_{{\tilde{A}}_{max}}+{\zeta }_{\tilde{A}}\hfill & \mathrm{if}{a}_{\tilde{A}}=a_{\tilde{A}}^{\mathrm{H}}\hfill \end{array}\right.\hfill \end{array}$$

(13)

where:

$${\zeta }_{\tilde{A}}=5{\displaystyle \frac{(x_{{\tilde{A}}_{nom}}-x_{{\tilde{A}}_{min}})}{6}}$$

(14)

To precisely define the state of the SG, five descriptive terms were employed: critically low, low, normal, high, and critically high. Each of these states is represented by a fuzzy set, and each fuzzy set is defined by three parameters: $a_{\tilde{B}}$, $b_{\tilde{B}}$, and $c_{\tilde{B}}$. These parameters are calculated using a defined method to accurately describe each of the states. For the parameters: $a_{\tilde{B}}$, $b_{\tilde{B}}$ and $c_{\tilde{B}}$ for the five-grade linguistic term the status of the SG (CL, L, N, H, CH) for $\tilde{B}$ are determined using (15)–(17).

$$\begin{array}{cc}\hfill a_{\tilde{B}}& =\left\{\begin{array}{cc}{x}_{{\tilde{B}}_{min}}\hfill & \mathrm{if}{a}_{\tilde{B}}=a_{\tilde{B}}^{\mathrm{CL}}\hfill \\ {\zeta }_{\tilde{B}}^{\mathrm{L}}-5{\displaystyle \frac{{\zeta }_{\tilde{B}}^{\mathrm{L}}-x_{{\tilde{B}}_{min}}}{6}}\hfill & \mathrm{if}{a}_{\tilde{B}}=a_{\tilde{B}}^{\mathrm{L}}\vee a_{\tilde{B}}=a_{\tilde{B}}^{\mathrm{N}}\hfill \\ {\zeta }_{\tilde{B}}^{\mathrm{H}}-5{\displaystyle \frac{{\zeta }_{\tilde{B}}^{\mathrm{H}}-x_{{\tilde{B}}_{nom}}}{6}}\hfill & \mathrm{if}{a}_{\tilde{B}}=a_{\tilde{B}}^{\mathrm{H}}\hfill \\ {\zeta }_{\tilde{B}}^{\mathrm{H}}+5{\displaystyle \frac{x_{{\tilde{B}}_{max}}-{\zeta }_{\tilde{B}}^{\mathrm{H}}}{6}}\hfill & \mathrm{if}{a}_{\tilde{B}}=a_{\tilde{B}}^{\mathrm{CH}}\hfill \end{array}\right.\hfill \end{array}$$

(15)

$$\begin{array}{cc}\hfill b_{\tilde{B}}& =\left\{\begin{array}{cc}{\zeta }_{\tilde{B}}^{\mathrm{L}}-5{\displaystyle \frac{{\zeta }_{\tilde{B}}^{\mathrm{L}}-x_{{\tilde{B}}_{min}}}{6}}\hfill & \mathrm{if}{b}_{\tilde{B}}=b_{\tilde{B}}^{\mathrm{CL}}\hfill \\ {\zeta }_{\tilde{B}}^{\mathrm{L}}\hfill & \mathrm{if}{b}_{\tilde{B}}=b_{\tilde{B}}^{\mathrm{L}}\vee b_{\tilde{B}}=b_{\tilde{B}}^{\mathrm{N}}\hfill \\ {\zeta }_{\tilde{B}}^{\mathrm{H}}\hfill & \mathrm{if}{b}_{\tilde{B}}=b_{\tilde{B}}^{\mathrm{H}}\hfill \\ x_{{\tilde{B}}_{max}}\hfill & \mathrm{if}{b}_{\tilde{B}}=b_{\tilde{B}}^{\mathrm{CH}}\hfill \end{array}\right.\hfill \end{array}$$

(16)

$$\begin{array}{cc}\hfill c_{\tilde{B}}& =\left\{\begin{array}{cc}{\zeta }_{\tilde{B}}^{\mathrm{L}}+5{\displaystyle \frac{x_{{\tilde{B}}_{nom}}-{\zeta }_{\tilde{B}}^{\mathrm{L}}}{6}}\hfill & \mathrm{if}{c}_{\tilde{B}}=c_{\tilde{B}}^{\mathrm{L}}\vee c_{\tilde{B}}=c_{\tilde{B}}^{\mathrm{N}}\hfill \\ {\zeta }_{\tilde{B}}^{\mathrm{H}}-5{\displaystyle \frac{{\zeta }_{\tilde{B}}^{\mathrm{H}}-x_{{\tilde{B}}_{nom}}}{6}}\hfill & \mathrm{if}{c}_{\tilde{B}}=c_{\tilde{B}}^{\mathrm{H}}\hfill \end{array}\right.\hfill \end{array}$$

(17)

where:

$$\begin{array}{cc}\hfill {\zeta }_{\tilde{B}}^{\mathrm{L}}& ={\displaystyle \frac{x_{{\tilde{B}}_{nom}}-x_{{\tilde{B}}_{min}}}{2}}+x_{{\tilde{B}}_{min}}\hfill \end{array}$$

(18)

$$\begin{array}{cc}\hfill {\zeta }_{\tilde{B}}^{\mathrm{H}}& ={\displaystyle \frac{x_{{\tilde{B}}_{max}}-x_{{\tilde{B}}_{nom}}}{2}}+x_{{\tilde{B}}_{nom}}\hfill \end{array}$$

(19)

The output of the FIS model, denoted as $\tilde{Y}$, is defined using a fuzzy set. This fuzzy set is described by three parameters: $a_{\tilde{Y}}$, $b_{\tilde{Y}}$, and $c_{\tilde{Y}}$. This output represents the type of change that should occur, and we describe it using five linguistic terms: small decrease, decrease, no change, increase, and large increase. The parameters $a_{\tilde{Y}}$, $b_{\tilde{Y}}$, and $c_{\tilde{Y}}$ are used to precisely define what these terms mean. For the FIS model output specified by $\tilde{Y}$ (4) for the parameters $a_{\tilde{Y}}$, $b_{\tilde{Y}}$ and $c_{\tilde{Y}}$, as defined by a linguistic term with a five-degree scale (DL, D, DNC, I, IH) it is necessary to use (20)–(22).

$$\begin{array}{cc}\hfill a_{\tilde{Y}}& =\left\{\begin{array}{cc}{v}_{{\tilde{Y}}_{min}}\hfill & \mathrm{if}{a}_{\tilde{Y}}=a_{\tilde{Y}}^{\mathrm{DL}}\hfill \\ {\zeta }_{\tilde{Y}}^{\mathrm{L}}-5{\displaystyle \frac{{\zeta }_{\tilde{Y}}^{\mathrm{L}}-v_{{\tilde{Y}}_{min}}}{6}}\hfill & \mathrm{if}{a}_{\tilde{Y}}=a_{\tilde{Y}}^{\mathrm{D}}\vee a_{\tilde{Y}}=a_{\tilde{Y}}^{\mathrm{DNC}}\hfill \\ {\zeta }_{\tilde{Y}}^{\mathrm{H}}-5{\displaystyle \frac{{\zeta }_{\tilde{Y}}^{\mathrm{H}}-v_{{\tilde{Y}}_{nom}}}{6}}\hfill & \mathrm{if}{a}_{\tilde{Y}}=a_{\tilde{Y}}^{\mathrm{I}}\hfill \\ {\zeta }_{\tilde{Y}}^{\mathrm{H}}+5{\displaystyle \frac{v_{{\tilde{Y}}_{max}}-{\zeta }_{\tilde{Y}}^{\mathrm{H}}}{6}}\hfill & \mathrm{if}{a}_{\tilde{Y}}=a_{\tilde{Y}}^{\mathrm{IH}}\hfill \end{array}\right.\hfill \end{array}$$

(20)

$$\begin{array}{cc}\hfill b_{\tilde{Y}}& =\left\{\begin{array}{cc}{\zeta }_{\tilde{Y}}^{\mathrm{L}}-5{\displaystyle \frac{{\zeta }_{\tilde{Y}}^{\mathrm{L}}-v_{{\tilde{Y}}_{min}}}{6}}\hfill & \mathrm{if}{b}_{\tilde{Y}}=b_{\tilde{Y}}^{\mathrm{DL}}\hfill \\ {\zeta }_{\tilde{Y}}^{\mathrm{L}}\hfill & \mathrm{if}{b}_{\tilde{Y}}=b_{\tilde{Y}}^{\mathrm{D}}\vee b_{\tilde{Y}}=b_{\tilde{Y}}^{\mathrm{DNC}}\hfill \\ {\zeta }_{\tilde{Y}}^{\mathrm{H}}\hfill & \mathrm{if}{b}_{\tilde{Y}}=b_{\tilde{Y}}^{\mathrm{I}}\hfill \\ v_{{\tilde{Y}}_{max}}\hfill & \mathrm{if}{a}_{\tilde{Y}}=b_{\tilde{Y}}^{\mathrm{IH}}\hfill \end{array}\right.\hfill \end{array}$$

(21)

$$\begin{array}{cc}\hfill c_{\tilde{Y}}& =\left\{\begin{array}{cc}{\zeta }_{\tilde{Y}}^{\mathrm{L}}+5{\displaystyle \frac{v_{{\tilde{Y}}_{nom}}-{\zeta }_{\tilde{Y}}^{\mathrm{L}}}{6}}\hfill & \mathrm{if}{c}_{\tilde{Y}}=c_{\tilde{Y}}^{\mathrm{D}}\vee c_{\tilde{Y}}=c_{\tilde{Y}}^{\mathrm{DNC}}\hfill \\ {\zeta }_{\tilde{Y}}^{\mathrm{H}}-5{\displaystyle \frac{{\zeta }_{\tilde{Y}}^{\mathrm{H}}-v_{{\tilde{Y}}_{nom}}}{6}}\hfill & \mathrm{if}{c}_{\tilde{Y}}=c_{\tilde{Y}}^{\mathrm{I}}\hfill \end{array}\right.\hfill \end{array}$$

(22)

where:

$$\begin{array}{cc}\hfill {\zeta }_{\tilde{Y}}^{\mathrm{L}}& ={\displaystyle \frac{v_{{\tilde{Y}}_{nom}}-v_{{\tilde{Y}}_{min}}}{2}}+v_{{\tilde{Y}}_{min}}\hfill \end{array}$$

(23)

$$\begin{array}{cc}\hfill {\zeta }_{\tilde{Y}}^{\mathrm{H}}& ={\displaystyle \frac{v_{{\tilde{Y}}_{max}}-v_{{\tilde{Y}}_{nom}}}{2}}+v_{{\tilde{Y}}_{nom}}\hfill \end{array}$$

(24)

Rule base preparation is required for the FIS model. Fifteen rules for each parameter are listed in

Table 6. Rule base for fuzzy interface system in energy management systems.

Rule No.	Parameters
	Input			Output
	$\tilde{\mathit{A}}$	Operator	$\tilde{\mathit{B}}$	$\tilde{\mathit{Y}}$
1	L	AND	CL	IH
2	A	AND	CL	IH
3	H	AND	CL	IH
4	L	AND	L	I
5	A	AND	L	DNC
6	H	AND	L	DNC
7	L	AND	N	DNC
8	A	AND	N	DNC
9	H	AND	N	DNC
10	L	AND	H	D
11	A	AND	H	D
12	H	AND	H	DNC
13	L	AND	CH	DL
14	A	AND	CH	DL
15	H	AND	CH	DL

.

Rules 1–3 refer to a critical situation where a SG requires an increase in energy consumption regardless of cost. In the case of rules 4–5, the load on the SG is still low, but for reasons of cost and user comfort, energy consumption is expected to increase when the cost is low (Rule No. 3). Rules 7–9 describe a situation in which it is not necessary to make decisions on increasing or decreasing the energy consumption load in the SG. Rule 10 and 11 ensure the need to reduce energy use only when costs are low or medium. The costs and comfort of users in rule 12 mean that in this case the FIS model strives not to change the load of electricity consumption in the SG. As in rules 1–3, rules 13–15 describe a critical situation in which, regardless of the cost, it is necessary to reduce the energy consumption load in the SG.

3. Case Studies

Simulation studies were carried out in the Matlab environment. The verification of the correctness of the proposed FIS model began with a simplified set of test data set described by the $\Theta$ matrix. The meaning of the individual elements of the $\Theta$ matrix is described using (25).

$$\Theta =\left[\begin{array}{ccc}{x}_{{\tilde{A}}_{\min }}& x_{{\tilde{B}}_{\min }}& v_{{\tilde{y}}_{\min }}\\ x_{{\tilde{A}}_{\mathrm{nom}}}& x_{{\tilde{B}}_{\mathrm{nom}}}& v_{{\tilde{y}}_{\mathrm{nom}}}\\ x_{{\tilde{A}}_{\max }}& x_{{\tilde{B}}_{\max }}& v_{{\tilde{y}}_{\max }}\end{array}\right]$$

(25)

The verification was carried out for the following data set:

$$\Theta =\left[\begin{array}{ccc}0& 0& 2\\ 5& 2.5& 5\\ 10& 5& 10\end{array}\right]$$

(26)

The dataset $\Theta$ (26) used for verification in these case studies was a sample test set selected to demonstrate the methodology and evaluate its initial performance across a range of scenarios. Its primary purpose was illustrative and to identify potential areas for refinement before applying the methodology to more extensive real-world data.

Based on the adopted $\Theta$ (26) data set, simulation tests were carried out in the Matlab environment for the proposed FIS model. For the adopted linguistic term degrees, the following representations for fuzzy sets were obtained: $\tilde{A}$ (27), $\tilde{B}$ (28) and $\tilde{Y}$ (29).

$$\begin{array}{c}\tilde{A}=\{\left(x_{\tilde{A}}^{\mathrm{L}},{\mu }_{\tilde{A}}^{\mathrm{L}}\left(x_{\tilde{A}}^{\mathrm{L}};-4.16667,0,4.16667\right)\right),\hfill \\ \hspace{1em}\hspace{1em}\hspace{1em}\left(x_{\tilde{A}}^{\mathrm{A}},{\mu }_{\tilde{A}}^{\mathrm{A}}\left(x_{\tilde{A}}^{\mathrm{A}};0.833333,5,9.16667\right)\right),\\ \hfill \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\left(x_{\tilde{A}}^{\mathrm{H}},{\mu }_{\tilde{A}}^{\mathrm{H}}\left(x_{\tilde{A}}^{\mathrm{H}};5.83333,10,14.1667\right)\right)\}\end{array}$$

(27)

$$\begin{array}{c}\tilde{B}=\{\left(x_{\tilde{B}}^{\mathrm{CL}},{\mu }_{\tilde{B}}^{\mathrm{CL}}\left(x_{\tilde{B}}^{\mathrm{CL}};0,1.5\right)\right),\hfill \\ \hspace{1em}\hspace{1em}\hspace{1em}\left(x_{\tilde{B}}^{\mathrm{L}},{\mu }_{\tilde{B}}^{\mathrm{L}}\left(x_{\tilde{B}}^{\mathrm{L}};0.208333,1.25,2.29167\right)\right),\\ \hspace{1em}\hspace{1em}\hspace{1em}\left(x_{\tilde{B}}^{\mathrm{N}},{\mu }_{\tilde{B}}^{\mathrm{N}}\left(x_{\tilde{B}}^{\mathrm{N}};1.45833,2.5,3.54167\right)\right),\\ \hspace{1em}\hspace{1em}\hspace{1em}\left(x_{\tilde{B}}^{\mathrm{H}},{\mu }_{\tilde{B}}^{\mathrm{H}}\left(x_{\tilde{B}}^{\mathrm{H}};2.70833,3.75,4.79167\right)\right),\\ \hfill \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\left(x_{\tilde{B}}^{\mathrm{CH}},{\mu }_{\tilde{B}}^{\mathrm{CH}}\left(x_{\tilde{B}}^{\mathrm{CH}};3.5,5\right)\right)\}\end{array}$$

(28)

$$\begin{array}{c}\tilde{Y}=\{\left(v_{\tilde{Y}}^{\mathrm{DL}},{\mu }_{\tilde{Y}}^{\mathrm{DL}}\left(v_{\tilde{Y}}^{\mathrm{DL}};2,2.25\right)\right),\hfill \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\left(v_{\tilde{Y}}^{\mathrm{D}},{\mu }_{\tilde{Y}}^{\mathrm{D}}\left(v_{\tilde{Y}}^{\mathrm{D}};2.25,3.5,4.75\right)\right),\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\left(v_{\tilde{Y}}^{\mathrm{DNC}},{\mu }_{\tilde{Y}}^{\mathrm{DNC}}\left(v_{\tilde{Y}}^{\mathrm{DNC}};3.75,5,7.08334\right)\right),\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\left(v_{\tilde{Y}}^{\mathrm{I}},{\mu }_{\tilde{Y}}^{\mathrm{I}}\left(v_{\tilde{Y}}^{\mathrm{I}};5.41666,7.5,9.58334\right)\right),\\ \hfill \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\left(v_{\tilde{Y}}^{\mathrm{IH}},{\mu }_{\tilde{Y}}^{\mathrm{IH}}\left(v_{\tilde{Y}}^{\mathrm{IH}};9.58334,10\right)\right)\}\end{array}$$

(29)

Figure 3 shows the membership function for defined sets: $\tilde{A}$ (27), $\tilde{B}$ (28) and $\tilde{Y}$ (29).

According to the adopted assumptions: $x_{{\tilde{A}}_{\min }}$, $x_{{\tilde{A}}_{\mathrm{nom}}}$ and $x_{{\tilde{A}}_{\max }}$ (26) for $x_{\tilde{A}}^L$, $x_{\tilde{A}}^A$ and $x_{\tilde{A}}^H$ has been provided ${\mu }_{\tilde{A}}^A\left(x_{\tilde{A}}^L\right)=1$, ${\mu }_{\tilde{A}}^A\left(x_{\tilde{A}}^A\right)=1$ and ${\mu }_{\tilde{A}}^A\left(x_{\tilde{A}}^H\right)=1$ (Figure 3a). In the case of (Figure 3b) for $x_{\tilde{B}}=x_{{\tilde{B}}_{\mathrm{nom}}}=2.5$ it should be noted that the value ${\mu }_{\tilde{B}}^N\left(x_{\tilde{A}}^N\right)=1$. A similar situation occurs for $v_{\tilde{Y}}=v_{{\tilde{Y}}_{\mathrm{nom}}}=5$ where value ${\mu }_{\tilde{Y}}^{DNC}\left(v_{\tilde{Y}}^{DNC}\right)=1$ (Figure 3c). It will be possible to remain at the current level of energy consumption, when the current scale of costs and the status of the SG do not require changes. In addition, on the basis of Figure 3, it can be concluded that the correctness of the following statements was ensured: $x_{\tilde{A}}\in \langle x_{{\tilde{A}}_{\min }},x_{{\tilde{A}}_{\max }}\rangle$, $x_{\tilde{B}}\in \langle x_{{\tilde{B}}_{\min }},x_{{\tilde{B}}_{\max }}\rangle$ and $v_{\tilde{Y}}\in \langle v_{{\tilde{Y}}_{\min }},v_{{\tilde{Y}}_{\max }}\rangle$. Figure 4 shows the surface for the fuzzy control structure output.

For the proposed FIS model with the data $\Theta$ (26), it can be seen that the energy consumption will be increased to the level of $v_{{\tilde{y}}_{\max }}$ primarily in crisis situations. Consumption will also increase above $v_{{\tilde{y}}_{\mathrm{nom}}}$ in situations where SG status requires it. However, the increase will depend on the value of costs. As well as the need to increase energy consumption, the FIS model will also respond to the need to reduce energy consumption. The reduction will aim at $v_{{\tilde{y}}_{\min }}$ particularly in crisis situations. In other cases, the reduction of energy consumption relative to $v_{{\tilde{y}}_{\mathrm{nom}}}$ will depend on costs. In situations of stabilization of energy consumption in the SG, the FIS model strives to maintain the set level of consumption, aiming for the value of $v_{{\tilde{y}}_{\mathrm{nom}}}$.

On the basis of the simulation studies carried out based on the proposed FIS model, the values of mapped energy consumption $v_{\tilde{Y}}$ were obtained for specific times t. The values obtained were $v_{\tilde{Y}}$ for $x_{\tilde{A}}$ and $x_{\tilde{B}}$, taking into account all accepted linguistic term designations in the proposed FIS model. Figure 5 shows the values of $v_{\tilde{Y}}$ for each time moment t. Figure 5 shows $x_{\tilde{A}}$ for all designations of linguistic terms. For $x_{\tilde{B}}$, the results for $x_{\tilde{B}}^{\mathrm{A}}$ are shown. Figure 5 also shows the values $v_{{\tilde{y}}_{\min }}\left(t\right)$, $v_{{\tilde{y}}_{\mathrm{nom}}}\left(t\right)$ and $v_{{\tilde{y}}_{\max }}\left(t\right)$ corresponding to each moment of t. Analyzing the obtained values $v_{\tilde{Y}}$ for $x_{\tilde{A}}$ and $x_{\tilde{B}}$ it can be confirmed that the designations of linguistic term depends on the value of $v_{\tilde{Y}}$ relative to $v_{{\tilde{y}}_{\min }}\left(t\right)$, $v_{{\tilde{y}}_{\mathrm{nom}}}\left(t\right)$ and $v_{{\tilde{y}}_{\max }}\left(t\right)$. If it was required to increase the energy consumed for the most critical SG status ($x_{\tilde{B}}^{\mathrm{CL}}$), the value of $v_{\tilde{Y}}$ obtained by the model FIS was closer to $v_{{\tilde{y}}_{\max }}\left(t\right)$. Figure 6 shows the values of $v_{\tilde{Y}}$ for all fifteen combinations of the adopted linguistic term designations for $x_{\tilde{A}}$ and $x_{\tilde{B}}$.

Analysing the $v_{\tilde{Y}}$ values presented in Figure 6, the influence of the degrees of the linguistic term $x_{\tilde{A}}$ on the obtained values can be inferred. The $v_{\tilde{Y}}$ values will be most modified relative to $v_{{\tilde{y}}_{\mathrm{nom}}}\left(t\right)$ for the degrees of the linguistic term specified by $x_{tildeA}^H$ or $x_{\tilde{A}}^L$ than $x_{\tilde{A}}^A$. The $v_{\tilde{Y}}$ power level modification (increase or decrease) will be determined by the SG status ($\tilde{B}$). For $x_{\tilde{B}}^{CL}$ the value of $v_{\tilde{Y}}$ will be closer to $v_{{\tilde{y}}_{\max }}\left(t\right)$ than for $x_{\tilde{B}}^{CH}$. For $x_{\tilde{B}}^{CH}$ value, the value of $v_{\tilde{Y}}$ will be closer to $v_{{\tilde{y}}_{\min }}\left(t\right)$.

4. Experimental Verification

Experimental verification of the proposed FIS model was performed on a PC and low-cost resource-constrained devices for comparison purposes. Such devices should be able to be placed in smart energy meters and be low-cost. The real-time markers of experimental research $t_{\mathrm{true}}$ were chosen as the comparison criterion. For $t_{\mathrm{true}}$, the confidence interval was determined using:

$$t_{\mathrm{true}}\in \left(\overline{t}-\sigma ;\overline{t}+\sigma \right)$$

(30)

where: $\overline{t}$—the average time of experimental research for a given device (the network communication time was not taken into account, only the calculation time on a given device), $\sigma$—the standard deviation of the time of experimental research of the proposed FIS model.

Several hardware configurations of a small, single-board computer (Raspberry Pi) were selected as low-cost devices. Figure 7 shows the measurement stand, and Figure 8 summarizes the comparison of the average times $\overline{t}$ with the marked standard deviations of the times $\overline{t}\pm \sigma$ for different hardware configurations.

In Figure 7, the PC ($d_1$) was a Toshiba Satellite P755-12F with Windows 10 operating system and Matlab R2024b environment installed. To perform more extensive tests for the PC, the codegen function was used to generate C or C++ code from a Matlab function and build the generated code (mex files). This configuration for the PC is denoted as $d_2$. All versions of Raspberry Pi shown in Figure 7 had the Raspian GNU/Linux 11 (bullseye) operating system installed. The Raspberry Pi devices were available in the following versions: Zero W $d_3$, 2 Model B $d_4$, 3 Model B $d_5$, and 4 Model B $d_6$. The proposed FIS model could be run on the individual Raspberry Pi versions ($d_3$—$d_6$) thanks to the use of the Matlab Support Package for Raspberry Pi Hardware. The targetHardware and deploy functions were used to run the proposed FIS model on $d_3$—$d_6$. Wired or wireless communication between all devices in the computer network ($d_3$—$d_6$) was realized using the TP-LINK TL-WR740N router. Figure 9 shows the detailed standard deviation values for each of the six device identifiers.

Once again, the $\Theta$ matrix (25) was used as the data source for the proposed FIS model to conduct the research. The following dataset was selected for the $\Theta$ matrix:

$$\Theta =\left[\begin{array}{ccc}0& 0& 2\\ x_{{\tilde{A}}_{\mathrm{nom}}}\left(x\right)& x_{{\tilde{B}}_{\mathrm{nom}}}\left(x\right)& 5\\ 100& 5& 10\end{array}\right]$$

(31)

where:

$x\in \{0,1,\dots ,99\}$, $x_{{\tilde{A}}_{\mathrm{nom}}}\left(x\right)={\displaystyle \frac{100}{99}}x$, $x_{{\tilde{B}}_{\mathrm{nom}}}\left(x\right)={\displaystyle \frac{5}{99}}x$.

Taking into account the assumptions for x as the argument for $x_{{\tilde{A}}_{\mathrm{nom}}}\left(x\right)$ and $x_{{\tilde{B}}_{\mathrm{nom}}}\left(x\right)$, the proposed FIS model was tested for each device ($d_1$—$d_6$). To summarize, each test for a given device was performed 10,000 times for the proposed FIS model. Then, the values of $\overline{t}$ and $\sigma$ were determined for each device.

Based on the $t_{true}$ values shown in Figure 8, the largest confidence intervals occured when:

• There was no compilation to machine code, optimization, no low-level access to C/C++ libraries, or no parallelization was used. This situation is visible in the case of comparing the execution of the proposed FIS model algorithm in the Matlab environment from m files in the configuration of device $d_1$ and from mex files in device $d_2$.
• The device had the weakest hardware resource configuration (random access memory and central processing unit), as was the case with $d_3$.

As before, the $\overline{t}$ values are significantly affected by identifying performance bottlenecks and improving performance by using the proposed FIS implemented in mex files ($d_2$). Hardware resources are already less important. This is an important issue so that smart energy meters can be equipped with low-cost computing devices. Minimum smart energy meter requirements for the FIS presented in the article include sufficient computational resources (microcontroller comparable to ARM Cortex-A7 or better recommended), adequate RAM, a real-time clock, and a communication interface. Execution times on PC and higher-end Raspberry Pis are sufficient for many real-time applications.

5. Conclusions

Under consideration is a decision-making system for energy management algorithms within HEMS. Energy management algorithms are leveraged by the system, with a portion of their computations being performed on edge devices situated within homes’ smart energy meters. These smart energy meters execute calculations related to the proposed FIS model. The existing literature, as referenced herein, confirms the relevance and ongoing research within this domain. However, identified research gaps encompass the absence of simulations and experimental studies validating the effectiveness of employing the FIS model on low-cost devices deployable in smart energy meters. The aim of this study was to achieve a balance between the comfort of electricity grid users and the needs of the DSO.

The selection of FIS was predicated on its capacity to address the inherent uncertainties in energy consumption through the utilization of linguistic variables and fuzzy rules, thereby offering a more realistic approach in contrast to crisp logic. Simulations demonstrated that the FIS-based strategy resulted in improved energy efficiency, enhanced grid stability (e.g., reduced peak load fluctuations), and the maintenance of user comfort via adaptation to varying energy demands and renewable generation. Experimental findings corroborated these observations, illustrating the effective response of the FIS controller to real-time fluctuations and the achievement of energy savings consistent with simulation outcomes. In conclusion, the simulations and experiments conducted provide substantial evidence for the effectiveness of FIS in facilitating intelligent energy management in smart meters, leading to tangible benefits in both efficiency and grid stability.

This paper significantly contributes to the field of smart grid management and energy efficiency by proposing a novel, well-defined decision-making system for smart energy meters. The system’s effectiveness has been demonstrated across diverse platforms, highlighting the need for further optimization.