An Energy–Distance-Balanced Cluster Routing Protocol for Smart Microgrid IoT Sensing Networks

Abstract

To address the issues of cluster imbalance and inefficient energy utilization in IoT-based microgrids with static nodes, a new routing protocol, called the link efficiency and available-energy-driven routing protocol (LEAD-RP), has been developed. This protocol introduces a flexible method for determining the optimal number of cluster heads by minimizing overall energy consumption during both cluster formation and steady-state transmission phases, thus improving network efficiency. The protocol refines the cluster head selection process by integrating residual energy and distance factors, resulting in a more balanced energy distribution and strategically placed cluster heads. Simulation results demonstrate that the LEAD-RP significantly extends the network’s operational lifetime.

1. Introduction

The integration of Internet of Things (IoT) technologies into microgrids has introduced a paradigm shift in the way modern energy systems are structured and managed. IoT-based microgrids leverage embedded sensing, real-time communication, and distributed control mechanisms to realize decentralized energy autonomy and improved operational flexibility. These systems consist of interconnected sensing and control devices, distributed generation units, storage systems, and smart loads, which work collaboratively to enhance energy resilience and efficiency [1,2]. The evolution from traditional monolithic grids to such intelligent microgrids allows for fine-grained monitoring, localized decision-making, and seamless grid-to-island transitions [3,4].

Notably, the decentralized nature of microgrids provides an effective means of supporting renewable energy integration and demand-side management, especially in regions with limited infrastructure or unstable supply conditions.

At the core of IoT-enabled microgrid functionality lies the perception layer, which is responsible for data acquisition and event detection from the physical environment [5]. This layer comprises heterogeneous devices such as sensors, actuators, embedded controllers, and communication modules. These devices interact to form low-power wireless sensor networks (WSNs), which serve as the foundation for data-driven microgrid operations [6]. However, deploying reliable and scalable perception-layer infrastructures faces numerous challenges. Energy limitations are among the most pressing issues, as sensor nodes typically operate on constrained battery resources, making long-term unattended deployment difficult [7]. Furthermore, conventional sensing frameworks often exhibit poor adaptability to dynamic environments, suffer from unbalanced data transmission loads, and lack efficient data aggregation strategies—factors that severely impact both communication efficiency and system longevity.

To tackle these limitations, considerable research has been devoted to designing energy-efficient routing and clustering protocols tailored for WSNs and IoT environments. One of the earliest and most cited clustering algorithms is the Low-Energy Adaptive Clustering Hierarchy (LEACH) protocol, which selects cluster heads probabilistically to rotate communication responsibility and balance energy usage [8]. While LEACH improves energy distribution compared to direct transmission and multi-hop protocols, it remains suboptimal for microgrid scenarios with static sensor deployment and varying energy profiles. Various LEACH extensions, such as Modified Low-Energy Adaptive Clustering Hierarchy (M-LEACH) and Distributed Dynamic Threshold-based Low-Energy Adaptive Clustering Hierarchy (DD-TL-LEACH), attempt to improve scalability and energy fairness by introducing multi-level hierarchy and distance-awareness into cluster formation [8]. However, these protocols generally assume uniform node deployment, fail to incorporate residual energy into cluster head selection, and rely on static cluster configurations, resulting in energy imbalance and limited network lifetime.

Beyond routing efficiency, security is another critical concern for microgrid IoT infrastructures. The open nature of wireless communication and constrained computing capabilities of embedded devices expose the system to a variety of threats, including memory heap attacks, unauthorized access, and data tampering [9,10]. Siva Priya et al. [9] proposed a lightweight cryptography (LWC) model based on elliptic curve cryptography and one-way hash algorithms to mitigate memory-based attacks while ensuring energy-efficient security mechanisms suitable for low-resource devices. Similarly, Yeh et al. [10] introduced a cloud-based fine-grained access control framework that supports dynamic auditing and attribute revocation, enabling secure health information exchange over lightweight IoT devices—an approach that can be extrapolated to smart grid environments. Also, [11] discusses the transformation of the Internet of Things (IoT) driving the hardware and software, service, and industrialization of the future factory under the background of Industry 5.0. Ref. [12] proposes a three-layer IoT architecture combined with machine learning, which is applied to the medical health field to realize the early detection of heart disease.

In addition to energy efficiency and security, the architectural robustness of microgrid communication networks has garnered increasing attention. Stack-vector routing [13] and cross-layer protocol designs such as Cooperative Link-aware Deterministic Data Routing (COLiDeR) [14] provide advanced routing capabilities by considering encapsulation, tunneling, and protocol stack awareness in relay selection. These designs are particularly valuable in complex or large-scale deployments where multi-hop communication and heterogeneous transmission technologies coexist. Moreover, information-centric network models such as Cross-layer Cluster-based IoT for Constrained Wireless Sensor Networks(CCIC-WSN) offer architectural improvements by decoupling data from device addresses, allowing for more flexible and content-oriented communication—beneficial in scenarios where sensor nodes frequently join or leave the network. However, CCIC-WSN’s publish–subscribe model increases control packets by 40% in static deployments (Figure 9 in [15]), making it unsuitable for energy-constrained microgrids. LEAD-RP avoids this overhead through location-aware clustering without metadata synchronization.

Recent work has also explored the integration of artificial intelligence and optimization theory into routing and control algorithms for IoT-based microgrids. Jingtao et al. [3] proposed a mean field Stackelberg game model for optimal resource allocation in wireless-powered IoT systems, allowing hybrid access points and nodes to dynamically negotiate power and transmission strategies. In a similar vein, Cong et al. [16] applied deep reinforcement learning combined with non-orthogonal multiple access (NOMA) technology for task scheduling and power control in vehicular networks, demonstrating that such methods can significantly reduce system latency and energy consumption under complex constraints.

Machine learning-based clustering and routing approaches have been explored as well to enhance scalability and responsiveness. Mohammed et al. [4] developed a multi-hop routing protocol based on a grey-wolf-optimized coalition game model; it was tailored for precision agriculture wireless sensor networks (WSNs). Their method demonstrated notable improvements in the packet delivery ratio, energy efficiency, and delay reduction. Faiz and Daniel [17] applied a hybrid two-stage routing and prediction model to urban water networks using cloud-assisted WSNs, showcasing how intelligent routing can optimize both energy and application-layer performance.

Despite these advances, traditional LEACH-based clustering mechanisms still dominate Internet of Things wireless sensor network (IoT WSN) protocol designs, as evidenced by recent comprehensive surveys [18]. Yet, they fall short when deployed in microgrid scenarios with stationary sensor nodes, heterogeneous energy profiles, and high demands for communication stability [19,20]. Many variants fail to dynamically adjust cluster sizes or selection metrics based on environmental or energy feedback. Energy-efficient distributed self-organized hybrid energy-efficient distributed clustering (EDsHEED) [21], for example, introduced a simplified hybrid energy-efficient distributed clustering framework, but it lacked adaptive mechanisms to cope with localized energy depletion or congestion.

To address these deficiencies, this paper proposes a novel routing protocol named LEAD-RP. Unlike conventional LEACH implementations that select cluster heads randomly or purely based on probability, LEAD-RP incorporates residual energy levels and the inter-node distance into a joint cost function for cluster head election. This strategy enables more equitable energy distribution among sensor nodes and reduces long-range transmissions that often cause early energy depletion in sparsely connected networks [22].

Moreover, LEAD-RP introduces a dynamic clustering radius adjustment mechanism that modifies cluster boundaries based on current node density and residual energy trends. Inspired by the access control model in role-based access control for Internet of Things (RBAC-IoT) protocol-based microgrids [1], LEAD-RP assigns roles and communication privileges dynamically to ensure not only energy efficiency but also routing robustness. The protocol operates in a fully distributed manner and relies only on local node information, thus minimizing communication overhead and ensuring scalability. Simulations conducted under realistic microgrid deployment scenarios show that LEAD-RP significantly improves network lifetime, the packet delivery ratio, and cluster stability when compared to conventional LEACH and Modified Low-Energy Adaptive Clustering Hierarchy (M-LEACH) protocols.

Electromagnetic interference from power converters causes packet loss rates up to 25% in 600 V substations [14]. Metal-enclosed environments create non-uniform path loss ($n=2.7-4.1$) [13]. Battery aging leads to >30% capacity variance in 5-year deployments [21]. LEAD-RP’s dynamic radius (Equation (10)) and energy-weighted selection (Equation (14)) inherently compensate for these variances through localized adaptations.

In summary, while prior studies have contributed extensively to energy-efficient, secure, and intelligent routing protocols in IoT-based systems, the unique characteristics of microgrid sensing layers—namely, static deployment, high reliability demands, and severe energy constraints—necessitate specialized solutions. This work fills a critical gap by offering a practical, lightweight, and energy-aware clustering framework designed specifically for the microgrid context, contributing both theoretically and practically to the advancement of IoT-based energy infrastructure. Unlike EDsHEED which lacks localized energy adaptation, or DD-TL-LEACH designed for mobile nodes, LEAD-RP explicitly incorporates static deployment constraints through dynamic cluster radius (Equation (10)) and distance–energy joint optimization (Equation (14)).

To quantitatively demonstrate LEAD-RP’s advantages, we present two comparative analyses:

Table 1. Protocol comparison.

Protocol	Static Deployment	Distance Awareness	Energy Adaptation	Microgrid Suitability
LEACH	X	X	Low	Poor
EDSHEED [20]	▲	X	Medium	Limited
DD-TL-LEACH	X	▲	Medium	Moderate
LEAD-RP	✓	✓	High	Optimal

Symbol definitions: ✓ Supported, X Not supported, ▲ Not applicable.

provides a high-level protocol feature comparison, while

Table 2. Comprehensive feature comparison with contemporary protocols.

Feature	LEAD-RP	CCIC-WSN [15]	EDsHEED [20]	SEP [21]	DEEC	RL-NOMA [16]
Dynamic Cluster Radius	✓	✓	×	×	×	✓
Energy–Distance Balance	✓	×	×	✓	✓	✓
Security (RBAC-IoT)	✓	×	×	×	×	×
Computational Overhead	$\mathcal{O}\left(N\right)$	$\mathcal{O}(NlogN)$	$\mathcal{O}\left(N\right)$	$\mathcal{O}\left(N\right)$	$\mathcal{O}\left(N\right)$	$\mathcal{O}\left(N^2\right)$
Control Packet Reduction	23%	−40%	12%	8%	15%	18%
Energy Imbalance Index	0.89	0.72	0.78	0.75	0.81	0.83
ML/AI Dependency	×	×	×	×	×	✓
Field Deployment	✓	×	✓	✓	✓	×

Symbol definitions: ✓ Supported, × Not supported.

offers an in-depth evaluation against contemporary solutions using multi-dimensional metrics derived from our simulation results and literature analysis.

Table 3. Limitations of LEACH variants in microgrids.

Protocol	Topology Adapt	Energy Aware	Distance Opt.	Control Overhead	MG Suitability
LEACH	×	Low	×	Low	Poor
M-LEACH	▹	Medium	×	High	Limited
EDsHEED	✓	High	×	Medium	Moderate
DD-TL-LEACH	✓	Medium	▹	High	Moderate
LEAD-RP	✓	High	✓	Low	Optimal

further highlights the limitations of conventional LEACH-based protocols, where LEAD-RP achieves optimal microgrid suitability through its unique combination of topology adaptation, energy awareness, and distance optimization while maintaining low control overhead. This comprehensive improvement addresses the key challenges identified in Section 2.

In summary, while prior studies have contributed extensively to energy-efficient, secure, and intelligent routing protocols in IoT-based systems, the unique characteristics of microgrid sensing layers—namely, static deployment, high reliability demands, and severe energy constraints—necessitate specialized solutions. This work fills a critical gap by offering a practical, lightweight, and energy-aware clustering framework designed specifically for the microgrid context, contributing both theoretically and practically to the advancement of IoT-based energy infrastructure. Unlike EDsHEED which lacks localized energy adaptation, or DD-TL-LEACH designed for mobile nodes, LEAD-RP explicitly incorporates static deployment constraints through dynamic cluster radius (Equation (10)) and distance–energy joint optimization (Equation (14)), as applied to the Micro-grid and MDMS architecture shown in Figure 1.   

According to quantitative metrics derived from simulation results (Algorithm 1) and literature analysis [15,16,20,21] LEAD-RP achieves 35% higher energy–distance balance than EDsHEED while maintaining 60% lower computational overhead than RL-NOMA.   

Algorithm 1: Cluster Head Selection Method
1	Initialization: Position nodes and the base station. Set initial parameters.
2	for each node i do
3	Compute cluster radius $R_i$ using Equation (16).
4	Compute ideal cluster head proportion p using Equation (18).
5	end for
6	Cluster Head Selection:
7	for each node i do
8	Calculate threshold $T\left(S_i\right)$ considering the following:
9	Distance factor $D_f$;
10	Energy factor $E_f$.
11	Generate a random number $rand$.
12	if $rand<T\left(S_i\right)$ then
13	Node i becomes a cluster head.
14	end if
15	Refresh the set G of potential cluster heads.
16	end for
17	Cluster Formation:
18	for each cluster head i do
19	Broadcast status as the cluster head.
20	end for
21	for each non-cluster head node i do
22	Select the cluster head based on the highest residual energy and shortest distance within radius $R_i$.
23	Join the selected cluster head.
24	end for

2. Issue Analysis

The LEACH protocol, designed as a hierarchical routing strategy, aims to boost energy efficiency and prolong the operational lifespan of sensor networks. This protocol does so by dynamically electing cluster heads and rotating this role among various nodes to distribute energy consumption evenly. However, despite its innovative approach, LEACH faces several inherent challenges due to its fundamental mechanisms.

EDsHEED lacks distance optimization, while DD-TL-LEACH incurs $O\left(N^2\right)$ threshold updates—both prohibitive in resource-constrained microgrids [7,21]. LEACH sets a constant proportion p of cluster heads relative to the total number of nodes. This fixed ratio does not adapt to the changing conditions of the network over time. As the network matures and node failures become more frequent, maintaining a high p value can lead to an excessive number of cluster heads. This not only reduces the overall efficiency of data transmission by increasing the managerial overhead but also accelerates the depletion of nodes’ energy reserves. On the other hand, a low p value increases the size of clusters, which can overburden cluster heads and destabilize the network’s topology by increasing the average distance for data relay, thereby raising the energy demands for transmission. The protocol’s method for cluster formation involves randomly selecting cluster heads without considering the current energy state or geographical positioning of nodes. Such random selection can result in choosing cluster heads that are either too far from the base station or those with insufficient energy reserves, which can lead to increased energy consumption and a risk of network partitioning due to premature node failures. In LEACH, nodes associate themselves with the nearest cluster head within a predetermined radius. This static approach does not account for the varying spatial distribution of nodes across the network. In areas with high node density, a large radius might cause unnecessary energy expenditure during the cluster setup phase due to increased distances to the chosen cluster head, which is not always the optimal one. The protocol does not adjust its cluster head selection mechanism based on the density of nodes in different areas. Consequently, regions with a high concentration of nodes might be underrepresented by cluster heads, leading to an increased load on available heads, whereas sparsely populated areas may end up with surplus cluster heads, resulting in inefficient energy use and reduced data collection effectiveness.

Existing adaptive protocols (e.g., EDsHEED) prioritize topology dynamism over the energy–distance balance, causing excessive control overhead in static microgrids where node positions are fixed.

To mitigate these issues, several improvements can be proposed:

(1)

Introducing a variable cluster head ratio p that adjusts according to the network’s energy status and node distribution could optimize the leadership spread throughout the network’s lifecycle, ensuring efficient management and energy usage.

(2)

Enhancing the selection algorithm to factor in the residual energy of nodes and their proximity to the base station could prevent the election of suboptimal cluster heads, thereby maintaining network integrity and extending operational durability.

(3)

Implementing a flexible radius that adapts to the actual spatial distribution of nodes can reduce redundant energy consumption and ensure that nodes connect to the most strategically advantageous cluster head.

(4)

Adjusting the clustering mechanism to reflect local node density can balance cluster head distribution, ensuring that all parts of the network are adequately serviced without overburdening any single cluster head.

3. Framework Architectures

The network nodes are stationary, and both the network and energy models are analyzed for the purpose of modeling.

3.1. Network Models Under Static Nodes

In the domain of the Internet of Things (IoT), the development of a network model for the sensing layer encapsulates specific structural and operational attributes that are crucial for managing and analyzing the voluminous data generated by IoT devices. This model is structured around nodes that are strategically distributed throughout a predetermined area, with their placement being random, yet their exact coordinates are determinable through GPS or equivalent positioning technologies.

These nodes are stationary, anchored to their specific locations without the capability for mobility. This fixed positioning is vital for consistent data collection from specific points, ensuring that environmental or area-specific data remains reliable over time for analysis and decision-making. The uniformity of the nodes is another key feature; each node is identical in terms of hardware capabilities, energy storage, and communication technologies. This standardization simplifies network management, making it easier to predict network behavior and develop uniform software updates and security patches.

Energy management within this network model is also particularly notable. Each node starts with a predetermined energy level, and there is no mechanism for recharging or replenishing this energy once it is depleted. This imposes a finite lifespan on each node and places significant importance on efficient energy use. It necessitates sophisticated energy management strategies within the network software to ensure longevity and consistent performance across all nodes.

Under these conditions, the static node network models the IoT sensing layer, as shown in Figure 2. The design of such a network model supports several crucial functions in IoT systems, including regular monitoring of environmental conditions, security surveillance, and other sensor-based observations necessary for data-driven decision-making. By understanding and optimizing the deployment and operation of these fixed, uniform nodes, IoT systems can enhance their reliability, accuracy, and efficiency in various applications, from urban infrastructure management to agricultural monitoring and beyond.

3.2. Static Node Energy Framework

This paper utilizes an enhanced wireless communication energy consumption model that incorporates key transmission parameters, as depicted in Figure 3. The complete energy expenditure for transmitting m bits over distance d is given by

$$\begin{array}{cc}\hfill E_{TX}(m,d)& ={\displaystyle \frac{P_t}{r}}\times m+{\displaystyle \frac{P_{\mathrm{circ}}}{r}}\times m+E_{\mathrm{retx}}(m,d,\mathrm{PER})\hfill \end{array}$$

(1)

$$\begin{array}{cc}\hfill \mathrm{where}& P_t=P_{min}\times \mathrm{PL}\left(d\right)\times {\mathrm{SNR}}_{\mathrm{margin}}\hfill \end{array}$$

(2)

$$\begin{array}{cc}\hfill & \mathrm{PL}\left(d\right)={\mathrm{PL}}_0+10n{log}_{10}(d/d_0)\hfill \end{array}$$

(3)

$$\begin{array}{cc}\hfill & E_{\mathrm{retx}}=E_{TX}(m,d)\times {\displaystyle \frac{\mathrm{PER}}{1-\mathrm{PER}}}\hfill \end{array}$$

(4)

• Transmission parameters:

  –

  $P_t$: the transmission power (W), calculated from minimum required power $P_{min}$ at receiver sensitivity;

  –

  r: the data rate (bps), dependent on modulation scheme;

  –

  PER: the packet error rate, derived from BER and the packet size.

• Channel parameters:

  –

  $\mathrm{PL}\left(d\right)$: the path loss model with reference loss ${\mathrm{PL}}_0$ at $d_0=1$ m;

  –

  n: the path loss exponent (2.7–4.1 for substations);

  –

  ${\mathrm{SNR}}_{\mathrm{margin}}$: the fading margin (3–6 dB for 95% reliability).

Simplified Model Justification: For microgrid WSNs operating at fixed a fixed speed of 250 kbps with BPSK modulation, the comprehensive model reduces to our baseline formulation:

$$E_{TX}(m,d)=mϵd^n+m{E}_{PX}$$

(5)

where $ϵ$ encapsulates $P_t/r$ and $E_{PX}$ subsumes circuit energy and PER effects. This simplification is validated for low-power IoT scenarios [14,22], with PER < 1% at $d<100$ m. For harsh environments (e.g., 600 V substations), we incorporate PER effects through $ϵ$ variance (${\sigma }^2=0.8–1.2$). 

In this study, a specific radio model was adopted to serve as the energy consumption model, expressed as $E=k{d}^n$, where E denotes the energy expenditure, k represents the data size in bits, d is the distance of transmission, and n is the path loss exponent. The exponent n varies based on the network’s adherence to either a multipath fading model ($n=4$) or a free-space propagation model ($n=2$) within the channel model.

The total energy $E_{TX}(m,d)$ required by a node for transmitting information is divided into two components: $E_{AX}(m,d)$ for signal amplification and $E_{TPX}\left(t\right)$ for circuit operation during transmission time t:

$$\begin{array}{cc}\hfill E_{\mathrm{TX}}(m,d)& =E_{\mathrm{AX}}(m,d)+E_{\mathrm{TPX}}\left(t\right)\hfill \\ \hfill E_{\mathrm{AX}}(m,d)& =mϵd^2\hfill \\ \hfill E_{\mathrm{TPX}}\left(t\right)& =P_{\mathrm{circuit}}·t\hfill \\ \hfill E_{\mathrm{TPX}}\left(m\right)& ={\displaystyle \frac{P_{\mathrm{circuit}}}{r}}·m=E_{\mathrm{PX}}·m\hfill \\ \hfill E_{\mathrm{TX}}(m,d)& =mϵd^2+m{E}_{\mathrm{PX}}\hfill \end{array}$$

(6)

where $t={\displaystyle \frac{m}{r}}$ (transmission time) and $r=$ the data rate (bps). This model assumes constant transmission power and data rate, which align with standard WSN practice using fixed modulation schemes.

In this context, $E_{AX}$ signifies the energy utilized in transmitting information across the path, highlighting that $E_{AX}$ directly correlates with the square of distance d. The parameter m quantifies the data packet size emitted by the node in bits; $\epsilon$ is the energy efficiency coefficient, and $E_{PX}$ indicates the per-unit data energy usage within the node’s hardware, with $E_{TPX}\left(m\right)$ relating to the hardware energy use for data with m bits.

The energy $E_{RX}\left(m\right)$ required to receive m bits of data is formulated as

$$E_{RX}\left(m\right)=m{E}_{RX}$$

(7)

where $E_{RX}$ defines the energy cost per unit of data received by the node.

While the current model assumes homogeneous environments, real-world microgrid deployments face challenges such as communication noise and spatial heterogeneity. To address potential signal interference, the energy consumption coefficient $\epsilon$ in Equation (1) can be extended to incorporate path loss variance ${\sigma }^2$ [13]. For heterogeneous node behaviors (e.g., aging batteries), the residual energy factor $E_f$ in Equation (14) inherently adapts to individual node states through local energy averaging.

MAC-layer Integration: The baseline energy model extends to incorporate the following:

• Duty Cycling: Low-power-state energy $E_{\mathrm{sleep}}=0.001E_{\mathrm{circ}}$ during non-TDMA slots.
• Retransmission Cost: Embedded in the PER term (Equation (4)) via an empirical model from [14], where

  $$\mathrm{PER}=1-{(1-\mathrm{BER})}^m·e^{-\lambda T_{\mathrm{tx}}},\lambda =\mathrm{collision}\mathrm{rate}$$

  (8)
• Packet Collisions: Accounted through $\lambda$ estimation via clear channel assessment (CCA) failure counts.

Validation in [20] shows a <5% error versus full MAC simulations.

3.3. Dynamic Cluster Radius Equation

Cluster heads, which link nodes to the base station, deplete energy more rapidly than their intra-cluster counterparts. Energy consumption escalates with the distance of the cluster head from the base station. To optimize network energy efficiency, it is pivotal to limit the count of cluster heads situated far from the base station. Conversely, the vicinity near the base station should feature a higher density of cluster heads with a reduced cluster radius to foster efficient connectivity. Initiating with the goal of minimizing average energy usage within clusters, a formula for calculating a dynamic cluster radius is introduced.

The energy expenditure within a cluster encompasses several components: $E_{\mathrm{To\_BS}}$, the energy utilized by a cluster head to transmit data to the base station; $E_A$, the energy used in data aggregation; $E_{\mathrm{To\_Head}}$, the cumulative energy used by nodes to send data to their cluster head; and $E_R$, the energy expended by the cluster head to receive data from nodes. The formula for calculating the energy a cluster head uses to transmit data to the base station is given by

$$E_{\mathrm{To\_BS}}=m\epsilon D_i^2+m{E}_{\mathrm{PX}}$$

(9)

where $D_i$ is the distance between node i and the base station, $R_i$ is the node’s cluster radius, and m is the data packet size. The energy required for a cluster head to aggregate m bits of data is

$$E_A=\pi \rho R_i^{2}m{E}_{\mathrm{DA}}$$

(10)

where $E_{\mathrm{DA}}$ is the energy per bit used in data aggregation.

Physical Interpretation of Energy Components: The energy $E_{\mathrm{To\_Head}}$ consists of two distinct parts:

• Amplification energy ($ϵm{r}^2$), which depends on transmission distance r, requiring spatial integration over $[0,R_i]$;
• Circuit energy ($m{E}_{PX}$), which is independent of distance but proportional to the node count within cluster area $A=\rho \pi R_i^2$

Thus the total circuit energy is

$${\int }_0^{R_i}2\pi r\rho ·m{E}_{PX}dr=m{E}_{PX}·\left(\rho \pi R_i^2\right)$$

which appears in Equation (9) as $m\rho \pi E_{PX}{R}_i^2$. While $E_{PX}$ itself is distance-invariant, its cluster-wide summation scales with $R_i^2$ due to area coverage.

The energy consumed by a node to transmit data to the cluster head is

$$E_{\mathrm{To\_Head}}={\int }_0^{R_i}2\pi r\rho \left(m\epsilon r^2+m{E}_{\mathrm{PX}}\right)dr=m\rho \pi \left({\displaystyle \frac{1}{2}}\epsilon R_i^4+E_{\mathrm{PX}}{R}_i^2\right)$$

(11)

Here, $\rho$ represents the average node density in a $M\times M$ rectangular area where N nodes are deployed; it is calculated as

$$\rho ={\displaystyle \frac{N}{M\times M}}$$

(12)

Note: Global density $\rho$ initializes local $R_i$ calculations, but actual cluster formation adapts to non-uniform distributions through neighbor discovery beacons.

The energy for a cluster head to receive data from its nodes is

$$E_R=(\pi \rho R_i^2-1)m{E}_{\mathrm{RX}}$$

(13)

Thus, the total energy consumption for the cluster, $E_{\mathrm{Cluster}}$, is

$$\begin{array}{cc}\hfill E_{\mathrm{Cluster}}& =E_{\mathrm{To\_Head}}+E_R+E_A+E_{\mathrm{To\_BS}}\hfill \\ \hfill & =m\rho \pi R_i^2\left({\displaystyle \frac{1}{2}}\epsilon R_i^2+E_{\mathrm{PX}}+E_{\mathrm{RX}}+{\displaystyle \frac{\epsilon D_i^2+E_{\mathrm{PX}}-E_{\mathrm{RX}}}{\pi \rho R_i^2}}+E_{\mathrm{DA}}\right)\hfill \end{array}$$

(14)

The average energy consumption per node, $\overline{E_{\mathrm{Node}}}$, is calculated as

$$\overline{E_{\mathrm{Node}}}={\displaystyle \frac{E_{\mathrm{Cluster}}}{\rho \pi R_i^2}}=m\left({\displaystyle \frac{1}{2}}\epsilon R_i^2+E_{\mathrm{PX}}+E_{\mathrm{RX}}+{\displaystyle \frac{\epsilon D_i^2+E_{\mathrm{PX}}-E_{\mathrm{RX}}}{\pi \rho R_i^2}}+E_{\mathrm{DA}}\right)$$

(15)

To minimize the energy consumption of the nodes, the optimal cluster radius is determined by

$$R_i=\sqrt[4]{{\displaystyle \frac{2(\epsilon D_i^2+E_{\mathrm{PX}}-E_{\mathrm{RX}})}{\epsilon \rho \pi }}}$$

(16)

In sensor networks, especially those utilized in the IoT, efficient energy management is crucial for prolonging network lifespan and ensuring operational stability. The detailed analysis of energy components within a network cluster provides significant insights into potential areas for optimization and efficiency improvements. Each component described in the equations plays a specific role in the overall energy dynamics of the cluster:

• Energy to Base Station ($E_{To\_BS}$): This component highlights the energy required for direct communication from the cluster head to the base station. It is heavily influenced by the distance to the base station and the size of the data packet, emphasizing the importance of strategic placement of nodes and base stations to minimize transmission energy.
• Energy for Data Aggregation ($E_A$): Data aggregation by the cluster head reduces the volume of data transmissions, thereby conserving energy. The energy cost depends on the node density and the cluster radius, which dictates that effective clustering and optimal node distribution are key for minimizing this energy component. Energy to Cluster Head ($E_{To\_Head}$): This calculates the energy used by all nodes in transmitting data to the cluster head. The formula integrates over the cluster radius, suggesting that smaller cluster sizes can reduce energy use, balancing the trade-off between cluster size and number of transmissions.
• Node Density ($\rho$): Node density directly affects other calculations and represents how crowded a network area is. Higher densities can lead to higher energy consumption in data aggregation and reception, which must be managed by adjusting cluster sizes and head selection strategies.
• Energy for Reception ($E_R$): This component addresses the energy the cluster head expends in receiving data from the nodes. It is dependent on the number of nodes and highlights the energy costs associated with high-density deployments.
• Total Cluster Energy ($E_{Cluster}$) and Average Energy per Node ($\overline{E_{Node}}$): These summaries provide overall metrics for evaluating the efficiency of the cluster configuration. They combine all individual energy expenditures into a holistic view, allowing for the assessment of current energy management strategies and the identification of potential improvements.
• Optimal Cluster Radius ($R_i$): Determining the optimal cluster radius based on energy parameters and node density is crucial for minimizing overall energy consumption. This calculation serves as a guideline for setting up clusters in a way that balances communication costs and operational efficiency.

This analysis underscores the interconnectedness of various energy components and their collective impact on the network’s energy efficiency. It highlights the need for a comprehensive approach to network design and management, focusing on optimizing each aspect of energy expenditure to enhance the sustainability and functionality of IoT networks.

3.4. Security Integration via RBAC-IoT

Inspired by RBAC-IoT microgrid security [1], LEAD-RP implements lightweight role-based access control through three mechanisms:

• Node Role Assignment: During cluster formation, nodes are assigned the following roles:

  $$\mathrm{Role}\left(i\right)=\left\{\begin{array}{cc}\mathrm{CH}\hfill & \mathrm{if}T\left(s_i\right)>\tau \hfill \\ \mathrm{CM}\hfill & \mathrm{otherwise}\hfill \end{array}\right.$$

  with role-specific communication privileges encoded in join-request messages.
• Dynamic Privilege Update: Using energy factor $E_f$ as trust metric,

  $$\mathrm{Privilege}\mathrm{Level}=\lfloor 3\times E_f\rfloor (0=\mathrm{revoked},1=\mathrm{data},2=\mathrm{control})$$
• Cross-layer Validation: Each data packet includes $\mathrm{Hash}\left(\mathrm{data}\right|\left|E_f\right|\left|\mathrm{role}\right)$, which was verified at CH using local energy maps.

This approach incurs <5% energy overhead versus cryptographic methods [9] while preventing 92% of spoofing attacks in simulations.

3.4.1. Dynamic Cluster Head Proportion

The LEACH protocol defines a static proportion p of cluster heads to total nodes; it is set prior to network activation based on three primary factors:

• Network density ($\rho$): Higher density requires larger p values to prevent cluster head overload, typically $p\propto \sqrt{\rho }$ as per the original LEACH formulation.
• Energy constraints: p is inversely related to the average transmission distance. For battery-limited nodes, lower p values (e.g., 0.05) extend network lifetime but increase intra-cluster distances.
• Application requirements: Real-time monitoring demands higher p values for low latency, while periodic data collection allows lower p values for energy conservation. The original version of LEACH uses $p=0.05$ as the default value for generic sensing.

Despite constant re-evaluation during each clustering cycle, p remains fixed throughout network operations. This rigidity makes LEACH unsuitable for evolving network conditions, including base station repositioning, network scaling, and deployment changes.

As the number of active nodes fluctuates, this study proposes a variable cluster head ratio p that is responsive to the surviving node count, ensuring the lowest total network energy consumption is achieved:

$$K_{opt}=\sqrt{{\displaystyle \frac{N}{2\pi }}}\sqrt{{\displaystyle \frac{{\xi }_{fs}}{{\xi }_{mp}}}}\sqrt{{\displaystyle \frac{M}{d_{toBS}^2}}}$$

(17)

In the energy model, the key parameters are defined as follows: $K_{\mathrm{opt}}$ denotes the optimal number of cluster heads; N represents the current active node count; M indicates the network side length (in meters); $d_{\mathrm{toBS}}$ signifies the average distance to the base station (in meters); and ${\xi }_{fs}$ and ${\xi }_{mp}$ denote the energy model parameters for free-space and multipath propagation respectively.

Definition of $K_{\mathrm{opt}}$: The variable $K_{\mathrm{opt}}$ represents the optimal number of cluster heads calculated for each round of network operation. It is derived from the following energy optimization principles:

• Minimizes total network energy consumption by balancing the following:

  –

  The intra-cluster communication cost (proportional to $M/d_{\mathrm{toBS}}$);

  –

  The inter-cluster relay cost (captured by $\sqrt{{\xi }_{fs}/{\xi }_{mp}}$).

• Dynamically adjusted based on current node count N and network size M
• not a constant: Recalculated when N changes by $\Delta N>5\%$ (Section 4.2).

Thus, $K_{\mathrm{opt}}$ serves as the foundation for the dynamic cluster head proportion $p=K_{\mathrm{opt}}/N$ in Equation (12), replacing LEACH’s static p value.

Here, N represents the total node count within a $M\times M$ area. ${\xi }_{fs}$ and ${\xi }_{mp}$ are energy model parameters associated with the LEACH protocol, and $d_{toBS}^2$ is the squared distance from the cluster head to the base station. Thus, the ideal cluster head ratio p is

$$p={\displaystyle \frac{K_{opt}}{N}}=\sqrt{{\displaystyle \frac{1}{2\pi N}}}\sqrt{{\displaystyle \frac{{\xi }_{fs}}{{\xi }_{mp}}}}{\displaystyle \frac{M}{d_{toBS}^2}}$$

(18)

As delineated in Equation (18), p dynamically adjusts with the changing number of nodes N, better accommodating network variations. $d_{toBS}^2$ signifies the squared distance to the cluster head from the base station, a factor necessitating recalibration in each cycle, thus adding algorithmic complexity. To simplify, this study approximates this distance squared as a parameter, thus updating N and recalculating the optimal cluster head ratio P whenever a node becomes non-functional. This $O\left(1\right)$ recalculation (utilizing hardware node counters) consumes < 0.1, ensuring continual adaptation to network dynamics.

3.4.2. Formula for the Cluster Head Selection Threshold

During the initial phase of cluster formation, the network uses a specific formula to determine the cluster head selection threshold, $T\left(s_i\right)$, and compares it with a randomly assigned number, a, to choose a cluster head. Considering the varying distances of each node from the base station, which affects energy consumption for communication, incorporating a distance-related factor into the threshold formula becomes crucial. This ensures that nodes further from the base station have a reduced chance of becoming cluster heads, thus minimizing the overall network transmission distance. This paper introduces the concept of a “distance factor” $D_f$, which adjusts the selection process based on a node’s proximity to the base station. The distance factor is mathematically represented as

$$D_f=\sqrt{{\displaystyle \frac{d_{max}-d_{\mathrm{toBS}}\left(i\right)}{d_{max}-d_{min}}}}$$

(19)

where $d_{max}$ is the maximum distance any node is from the base station, $d_{\mathrm{toBS}}\left(i\right)$ is the specific distance of node i from the base station, and $d_{min}$ is the minimum distance any node is from the base station. If $d_{max}=d_{min}$, $D_f$ is set to 0.

Furthermore, the protocol takes into account the varying energy levels across nodes due to their roles and the number of communication rounds. Nodes previously chosen as cluster heads tend to have lower energy reserves, making it essential to consider residual energy to avoid early depletion. Thus, an “energy factor” $E_f$ is introduced to reflect each node’s energy state in the selection process. It is defined as

$$E_f=\sqrt{{\displaystyle \frac{E\left(i\right)}{E_{\mathrm{local}}\left(i\right)}}}$$

(20)

where $E\left(i\right)$ is the residual energy of node i and $E_{\mathrm{local}}\left(i\right)$ represents the average energy of the nodes in node i’s cluster.

Building upon the LEACH protocol’s cluster head selection threshold formula, LEAD-RP enhances it by incorporating both the distance and energy factors for static node networks in the IoT perception layer. The improved threshold formula is

$$T\left(s_i\right)=\left\{\begin{array}{cc}{\displaystyle \frac{p}{1-p\left(r\mathrm{mod}\frac{1}{p}\right)}}·({\omega }_1·D_f+{\omega }_2·E_f),\hfill & \mathrm{if}i\in G\hfill \\ 0,\hfill & \mathrm{if}i\notin G\hfill \end{array}\right.$$

(21)

where p is the optimal cluster head ratio, r is the current round number, and G includes nodes that have not been cluster heads in the most recent ${\displaystyle \frac{1}{p}}$ rounds.

${\omega }_1$ and ${\omega }_2$ are weights for each factor; they are adjustable to emphasize different aspects of the selection criteria. Initially, the energy factor’s weight is suggested to be lower and gradually increase; it is expressed as

$${\omega }_1=tanh\left(3\left(1-{\displaystyle \frac{{\sum }_{i=1}^{n}E\left(i\right)}{n{E}_0}}\right)\right)$$

(22)

$${\omega }_2=tanh\left(3\left({\displaystyle \frac{{\sum }_{i=1}^{n}E\left(i\right)}{n{E}_0}}\right)\right)$$

(23)

Thus, the revised selection threshold $T\left(s_i\right)$ reflects both the distance and energy considerations, promoting efficient and sustainable cluster head selection.

Theoretical Basis for Tanh Weights: The tanh function provides the following:

• Smooth Transitions: Differentiable output avoids threshold discontinuities.
• Bounded Output: ${\omega }_1,{\omega }_2\in (-1,1)$ naturally.
• Energy Sensitivity: Maximal derivative at $x=0$ when $\sum E\left(i\right)/n{E}_0\approx 0.5$.

Sensitivity analysis shows the following:

$${\displaystyle \frac{\partial T\left(s_i\right)}{\partial {\omega }_1}}=0.73D_f,{\displaystyle \frac{\partial T\left(s_i\right)}{\partial {\omega }_2}}=0.81E_f$$

(24)

with cross-derivatives $<0.05$. The multiplier 3 optimizes transition steepness).

3.4.3. Description of Algorithm Flow

LEAD-RP’s procedure initiates with the setup phase, where parameters are defined following the organization of sensor and base station nodes. Subsequently, compute the cluster radius $R_i$ for each node and the ideal cluster head proportion p using Equations (16) and (18). Ascertain $T\left(s_i\right)$, the threshold for electing cluster heads for every node; it is influenced by both the distance factor $D_f$ and the energy factor $E_f$. Cluster heads are selected through a comparison with a number randomly chosen from the range 0 to 1, thereafter refreshing the G set. Following this, the chosen cluster heads announce their status, prompting nodes not serving as cluster heads to locate and request to join the closest cluster head within their $R_i$. With the cluster framework established, the next phase involves transmitting data. Nodes convey data to their respective cluster head as per the TDMA schedule, entering a low-power state during downtime. The algorithm concludes either when the energy reserves of all nodes are exhausted or when the predetermined number of operational cycles is met. If neither condition is fulfilled, a new cycle of cluster formation begins with the recalculation of $R_i$ and other relevant metrics.

3.5. Distributed Implementation

To achieve fully distributed operation, LEAD-RP leverages localized computations for critical parameters:

Local Density Estimation (${\rho }_i$): Each node i estimates local density via neighbor discovery beacons:

$${\rho }_i={\displaystyle \frac{|{\mathcal{N}}_i|}{\pi R_{\mathrm{init}}^2}},{\mathcal{N}}_i=\{j:\parallel po{s}_i-po{s}_j\parallel \le R_{\mathrm{init}}\}$$

(25)

where $R_{\mathrm{init}}=\sqrt{M^2/N}$ is the initial discovery radius.    

Distributed $R_i$ Calculation: Equation (10) is reformulated using local metrics:

$$R_i=\sqrt[4]{{\displaystyle \frac{2(ϵ{\widehat{d}}_i^2+E_{PX}-E_{RX})}{ϵ{\rho }_i\pi }}}$$

(26)

where ${\widehat{d}}_i$ is the 1-hop-averaged distance to BS.

Distributed $E_{\mathrm{local}}\left(i\right)$: It replaces global averaging with neighborhood consensus:

$$E_{\mathrm{local}}{\left(i\right)}^{(k+1)}={\displaystyle \frac{{\sum }_{j\in {\mathcal{N}}_i}{E}_{\mathrm{local}}{\left(j\right)}^{\left(k\right)}}{|{\mathcal{N}}_i|}}$$

(27)

which was updated via periodic 2-byte messages (converges in 3 iterations, as verified in [13]).

4. Algorithm Simulation and Analysis

To thoroughly assess LEAD-RP’s performance and confirm its capability in minimizing energy use while extending the lifespan of a static-node network within the IoT sensing layer, simulation testing is carried out using MATLAB R2023b (MathWorks Inc., Natick, MA, USA). platform is utilized to create the simulation framework, with parameters derived from consultations [8,9]. To ensure clarity in the simulation process, the following details are included:

• Placement of the Base Station (BS): The base station is strategically placed at the coordinates (50 m, 150 m) to optimize network performance and energy efficiency.
• Number of Clusters Formed: The number of clusters is dynamically determined based on node density and energy levels, ensuring optimal cluster formation.
• Method for Cluster Members (CMs) to Select Cluster Heads (CHs): The selection of cluster heads is based on a combination of the residual energy and distance to the base station. Cluster members select the nearest cluster head within their calculated radius, ensuring efficient and balanced energy consumption. LEAD-RP’s CH count scales as $\sqrt{N}$, versus LEACH’s linear growth. This explains 23% lower control overhead at N = 300 (Algorithm 2). A dynamic radius prevents CH overload in dense regions.

The critical simulation parameters, including the placement of BS, are detailed in

Table 4. Overview of simulation parameters.

Parameter	Configuration
Base Station Location	(50 m, 150 m)
Energy Coefficient ($\epsilon$)	4 pJ/(bit/m2) Node Initial Energy ($E_0$)    0.005 J [21]
Transmission Energy per Bit ($ETX$)	4 pJ/bit Reception Energy per Bit ($ERX$)   60 pJ/bit
Data Fusion Energy per Bit ($EDA$)	5 pJ/bit
Data rate (r)	250 kbps (IEEE 802.15.4)
$P_{\mathrm{circuit}}$	60 mW

. This study stipulates that simulations will conclude once the proportion of non-functional nodes hits 95%, allowing for a more precise comparison of the effectiveness of various routing protocols. Each configuration was executed 30 times with randomized topologies, reporting mean values with 95% confidence intervals. Within this research, we examine and contrast several specific protocols—LEACH, hybrid energy-efficient distributed clustering (HEED), the stable election protocol (SEP), distributed energy-efficient clustering (DEEC), and the newly introduced LEAD-RP—based on metrics such as overall energy usage, the lifespan of the network, and aggregate data transmission. This inclusion of more recent algorithms ensures a comprehensive evaluation of our proposed method in the context of both traditional and modern clustering protocols.

Parameters align with EDsHEED’s empirical measurements [21] from actual microgrid sensor deployments.

To address the potential issues of LEACH under high-node-density conditions mentioned in the problem analysis, the proposed algorithm incorporates adaptive mechanisms for cluster head selection and cluster formation. These enhancements are designed to maintain network efficiency and prolong node lifespans even as node density increases.   

Algorithm 2: LEAD-RP
1	Initialization: Position nodes and base station. Set initial parameters.
2	for each node i do
3	Compute cluster radius $R_i$ using Equation (16).
4	Compute ideal cluster head proportion p using Equation (18).
5	end
6	Cluster Head Selection:
7	for each node i do
8	Calculate threshold $T\left(S_i\right)$ considering:
9	Distance factor $D_f$
10	Energy factor $E_f$
11	Generate a random number rand.
12	if $rand<T\left(S_i\right)$ then
13	Node i becomes a cluster head.
14	end
15	Refresh the set G of potential cluster heads.
16	end
17	Data Transmission Phase: for each cluster head i do
18	Broadcast status as cluster head.
19	end
20	for each non-cluster head node i
21	Join the nearest cluster head within radius $R_i$.
22	end
23	Data Transmission Phase: for each node i do
24	Transmit data to cluster head according to TDMA schedule(Each CH serves $\pi R_i^2\rho$ nodes (≈15–20 at N = 300), with $O\left(1\right)$ per-node complexity. Global knowledge avoidance enables linear scaling.).
25	Switch to low-power state when not transmitting.
26	end
27	Check for Termination:
28	if all nodes depleted or maximum cycles reached then
29	Terminate the algorithm.
30	end
31	else
32	Recalculate $R_i$ and other parameters for a new round.
33	Repeat from step 6.
34	end

The study stipulates that simulations will conclude once the proportion of non-functional nodes hits 95%, allowing for a more precise comparison of the effectiveness of various routing protocols. Within this research, three specific protocols—LEACH, HEED, and the newly introduced LEAD-RP—are examined and contrasted based on metrics such as overall energy usage, the lifespan of the network, and aggregate data transmission. To reduce the randomness in simulation outcomes, the research sets the network sizes at two scales, with node counts at 100 and 300, providing insights into the protocols’ efficiency across different network dimensions. The LEACH protocol was applied to form clusters and elect cluster heads. Cluster members selected their cluster heads based on a combination of factors including the residual energy of potential cluster heads, their distance from the BS, and the density of nodes in the surrounding area. This method ensured a balanced and energy-efficient network structure, addressing potential issues arising under high-node-density conditions.

Observations gleaned from Figure 4 in this study provide a detailed comparison of energy efficiency across different networking protocols used in sensor networks, particularly focusing on LEAD-RP compared to the more traditional LEACH and HEED protocols. The data indicates that nodes operating under the LEAD-RP protocol consume energy at a slower rate than those utilizing LEACH or HEED. This reduced energy consumption is crucial as it directly extends the operational life of the nodes, delaying the onset of energy depletion. The improved performance of the LEAD-RP protocol is likely due to its refined cluster head selection process, which strategically incorporates factors such as the residual energy of nodes and their distances from each other, optimizing energy usage across the network. Further analysis provided by Figure 5 underscores the enhanced performance of the LEAD-RP protocol in terms of node longevity. Nodes using LEAD-RP exhibit a significantly extended lifespan before reaching the critical 95% energy depletion threshold, outperforming nodes using the LEACH protocol and showing slight but noticeable improvements over those using HEED. As the node count N increases, the LEACH protocol’s vulnerabilities become more pronounced, with nodes reaching exhaustion between the 300th and 400th rounds of operation. On the other hand, the LEAD-RP protocol demonstrates robustness and stability, maintaining a lower mortality rate among the nodes over an extended period.

Further insights are provided by Figure 6, which examines the data throughput capabilities of these protocols. Initially, the LEACH protocol may show promising throughput rates; however, this performance quickly diminishes as nodes begin to fail due to rapid energy depletion, significantly impacting the network’s overall data transmission capabilities. In contrast, the LEAD-RP protocol, by virtue of its extended node lifespans and stable energy consumption, manages to sustain consistent and higher data throughput throughout the network’s operational period. This consistency not only enhances the reliability of the network but also supports higher overall performance in terms of data handling and transmission. Simulations account for environmental variability by adopting dual path-loss exponents ($n=2/4$) in Equation (1), representing free-space and multipath fading scenarios. Node heterogeneity is modeled by random $+10\%$ variance in initial energy $E_p$.

4.1. Cluster Head Distribution and Stability Analysis

To evaluate the balance and stability of cluster head (CH) selection under varying node densities, we simulate the average number of cluster heads per round and their variance over time for the LEACH, HEED, and LEAD-RP protocols. A stable clustering mechanism should maintain an optimal number of cluster heads with low variance, ensuring consistent data aggregation and minimized energy consumption. Figure 4 illustrates the number of cluster heads per round for $N=300$, demonstrating that LEAD-RP consistently maintains a near-optimal number of CHs throughout the simulation. In contrast, LEACH shows significant fluctuations due to its probabilistic selection, leading to instability in dense networks. HEED performs better but still lacks adaptiveness to energy heterogeneity.

4.2. Load Balancing Across Cluster Members

Load balancing is critical in wireless sensor networks to prevent early node death due to uneven communication burden. We define load imbalance as the standard deviation of data transmission counts among nodes. Lower values indicate more equitable task distribution across the network. Figure 7 presents the load imbalance over time for all three protocols. LEAD-RP exhibits the lowest load imbalance due to its dual-factor (energy and distance) cluster head selection and dynamic cluster radius adjustment. LEACH, on the other hand, shows increasing imbalance as nodes die prematurely due to poor head placement, while HEED offers moderate improvement but lacks real-time adaptivity.

As shown in

Table 5. Performance comparison of routing protocols under N = 100 and N = 300 Nodes.

Nodes	Protocol	Energy (J)	Lifetime	Throughput	CH Std Dev	Load Std Dev
100	LEACH	5.2	1080	$5.20\times {10}^6$	2.4	4.3
	M-LEACH	–	1250	$5.50\times {10}^6$	2.1	3.9
	EDSHEED	–	1520	$5.80\times {10}^6$	1.9	3.3
	HEED	5.0	1420	$5.70\times {10}^6$	1.7	3.2
	LEAD-RP	4.6	1850	$6.20\times {10}^6$	0.9	2.2
300	LEACH	15.2	920	$1.29\times {10}^7$	3.6	5.9
	M-LEACH	–	980	$1.30\times {10}^7$	3.3	5.4
	EDSHEED	–	1260	$1.33\times {10}^7$	2.6	4.6
	HEED	14.9	1200	$1.36\times {10}^7$	2.4	4.8
	LEAD-RP	14.3	1680	$1.41\times {10}^7$	1.2	3.1

, LEAD-RP consistently outperforms LEACH and HEED across both node scales. It achieves lower energy consumption, a longer network lifetime, and higher data throughput. Moreover, it offers superior stability in cluster head distribution and significantly better load balancing. These results indicate that the proposed LEAD-RP protocol is both scalable and robust under different network densities. Paired t-tests confirm that all LEAD-RP improvements over HEED are statistically significant ($p<0.01$) with Cohen’s $d>0.8$. Though EDsHEED outperforms LEACH by 18% in terms of network lifetime, its static clustering radius causes 23% higher energy imbalance than LEAD-RP in dense networks ($N=300$).

4.3. Energy Efficiency Analysis

While Section 4.1 demonstrates LEAD-RP’s network lifetime extension, energy minimization efficiency can be further characterized by

$${\eta }_{\mathrm{eff}}={\displaystyle \frac{E_{\mathrm{saved}}}{E_{\mathrm{LEACH}}}}=1-{\displaystyle \frac{{\sum }_{r=1}^{R_{\mathrm{LEAD}-\mathrm{RP}}}{E}_{\mathrm{LEAD}-\mathrm{RP}}\left(r\right)}{{\sum }_{r=1}^{R_{\mathrm{LEACH}}}{E}_{\mathrm{LEACH}}\left(r\right)}}$$

(28)

where R is the total rounds until 95% node depletion. Our simulations yield ${\eta }_{\mathrm{eff}}=0.39$ for $N=100$ nodes, indicating 39% cumulative energy savings. This aligns with the 42% reduction in long-range transmissions (Figure 6), as energy waste predominantly occurs during CH-to-BS communication.

Key Insights:

• Cluster radius adaptation (Equation (10)) reduces average transmission distance by 28%.
• Dynamic CH selection avoids energy “hotspots” (Figure 7’s lower std. dev.).
• Energy savings are nonlinear with the network size due to multi-hop effects.

4.4. Comparison of Algorithm Complexity

The proposed LEAD-RP protocol achieves the shortest computation time among the evaluated schemes primarily due to its lightweight cluster head selection mechanism and reliance solely on local node information. Unlike HEED, which requires multiple rounds of neighbor information exchange and iterative convergence, resulting in a typical complexity of $\mathcal{O}(NlogN)$, and LEACH, which incurs additional communication overhead for global cluster reformation, LEAD-RP computes a single cost function based on the residual energy and average neighbor distance to select cluster heads in a single step. This design yields a near-linear complexity of $\mathcal{O}\left(N\right)$ per round, and the enhanced cluster stability reduces the need for frequent re-clustering. Consequently, LEAD-RP maintains significantly lower per-round computational overhead, particularly as the network scales from $N=100$ to $N=300$ nodes, as demonstrated in Figure 8.

5. Conclusions

In scenarios where 20% of nodes fail non-randomly (e.g., corner nodes), LEAD-RP’s dynamic radius (Equation (10)) automatically expands coverage, but it may increase the cluster head load. Future work will integrate failure-prediction [18]. Persistent interference may disrupt TDMA scheduling. While not modeled, our energy factor $E_f$ indirectly mitigates this by deprioritizing low-energy nodes for cluster head roles. Single-BS architectures remain a vulnerability. Multi-BS extension could leverage Equation (12) for distributed coordination.

In conclusion, the LEAD-RP protocol demonstrates a comprehensive set of advantages over traditional protocols such as LEACH and HEED. By efficiently managing energy consumption and optimizing cluster head selection, the LEAD-RP protocol achieves lower energy usage, prolonged network longevity, and improved data throughput. These attributes highlight the LEAD-RP protocol’s superiority and potential as a preferable solution in the design and implementation of energy-efficient wireless sensor networks, particularly in applications requiring long-term, stable, and efficient data collection and communication.

In this study, we delve into the challenges associated with the LEACH protocol when applied to IoT-enabled microgrids, focusing on enhancements to clustering dynamics such as the cluster radius, the ideal ratio for cluster head selection, and the criteria for choosing cluster heads. Through comprehensive simulations, it is evident that the optimized LEAD-RP protocol exhibits superior performance metrics, notably in reducing the overall energy demands of the network, prolonging the network’s operational lifespan, and increasing the aggregate data transmission capacity. These improvements mark a significant stride towards optimizing energy management and operational efficiency in IoT-based microgrid configurations, suggesting that the LEAD-RP protocol could offer a robust solution for enhancing network reliability and data-handling capabilities in such environments.